DISTRIBUTION OF PERMEABILITY PATTERNS -UPPER SAN ANDRES FORMATION OUTCROP, GUADALUPE MOUNTAINS, NEW MEXICO APPROVED: Supervisor: ~ Charles Kerans DISTRIBUTION OF PERMEABILITY PATTERNS -UPPER SAN ANDRES FORMATION OUTCROP, GUADALUPE MOUNTAINS, NEW MEXICO by MALCOLM ALEXANDER FERRIS, B. S. THESIS Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of MASTER OF ARTS THE UNIVERSITY OF TEXAS AT AUSTIN May,1993 ACKNOWLEDGMENTS WORD ... This thesis was written on Macintosh computers using MicrosoftWord software (5.0). My greatest thanks go to the members of my advising committee: Dr. J. M. Sharp, Dr. L.W. Lake, and Dr. C. Kerans, whose combined support has helped make this thesis possible. I also wish to thank the members of the Reservoir Characterization Research Lab who contributed their time to the collection of data: M. Barton, A. Czebiniack, M. Holtz, H.S. Nance, Dr. R. Senger, and R. Single. Additional credit and thanks to (Dr., in progress) B. Fitchen for editing the geologic interpretations. And thanks again to all for staying with me. The most profound appreciation for the opportunity to pursue this degree goes to my parents, J. Burkam and Eileen, without whose support nothing would have been possible. Love you always. Word again to everyone who shared the years with me: John2, Keg, Leo, Bob, Becky, Dave, Rob2, Carla, Rich, Edna, Tim, and all professors and staff members of the UT-DoGS and BEG with whom I have relied upon for technical support. And the last word to the little people: Dub, W.K., Whamo, Dorie, Tesnus, Otto, Dwim, Dante, Idaho, Carl, and Milt. v DISTRIBUTION OF PERMEABILITY PATTERNS -UPPER SAN ANDRES FORMATION OUTCROP, GUADALUPE MOUNTAINS, NEW MEXICO. Abstract: Permeability patterns in the subsurface are primary controls on fluid flow. Predictable patterns of permeability can be applied to secondary oil recovery or modeling of solute transport. Conventional field data from well tests are insufficient for accurate modeling of the subsurface environment. The use of analog models from outcrop data with emphasis on analog textures and facies can provide needed insights. Permeability was measured on a 2613 ft. long and 20 -25 ft. thick outcrop of a single mudstone-bounded carbonate parasequence in a transgressive shelf margin. The four genetic facies were: 1) a mud-dominated deep-water flooded shelf; 2) a coarsening upward, mud-supported ooid and peloid wackestone/packstone shallow shelf; 3) an ooid and peloid grain-supported bar crest; and 4) an ooid and peloid grain-supported, coarsening-upward bar flank. Data were collected in the field with a mini-permeameter and on core plugs from the outcrop. Sampling was performed at 769 locations along 31 vertical transects and in two small-scale grid patterns. Separation distances varied from 325 ft. between the widest spaced vertical transects, down to 1 in. separation within the smallest scale grid. Horizontal variogram analysis for range values indicate a scale dependency based on the sample separation and related variogram step distance, h. Horizontal variogram ranges were 253 ft. (77.8 m) and 748 ft. (230 m) for h of 100 ft. (30.7 m); 22 ft. (6.7 m) for h of 10 ft. (3.1 m); 4 ft. (1.3 m), for h of 1 ft. (0.3 m); and 8 in. (0.2 m) for h of 1 in. (0.03 m). These all exhibited a proportionately high nugget-to-sill ratio of poorly developed spherical variogram models. Development of vertical variograms indicate vertical variability within the parasequence. In populations which represented increasingly less of the whole parasequence thickness, an h of 1 ft. provided vertical ranges of 13 ft., 10.2 ft. and 4 ft. (a nested set), and 2.1 ft. In the 1 in. grid, an h of 1 in. provided a vertical variogram of range 4.2 in. Nugget-to-sill ratios were all moderate with exhibited poorly developed spherical variogram models. A preliminary model based upon the data in a single parasequence can be applied as a grainstone sequence with randomly distributed permeabilities that is bounded above and below by a confining mud dominated layer which may or may not be continuous. Vl TABLE OF CONTENTS ACKNOWLEDGEMENTS .............................................................. v ABSTRACT ................................................. ............................... vi TABLE OF CONTENTS ................................................................. vii LIST OF FIGURES ....................................................................... x LIST OF TABLES ......................................................................... xiv INTRODUCTION ......................................................................... 1 1.1 Project Outline ............................................................... 2 1.2 Overview ..... .................................................. .............. 3 1.2.1 Theory ............................................ .. .............. 3 1.2. 2 The mechanical field pe1meameter ............................. 5 1.2. 3 Sta tis tical analysis ................................................ 7 1.3 Previous Stu dies ............................................................ 8 1.3. 1 Pe1meability distributions in carbonate rock f 01mations ..................................................... 8 1.3. 2 Pe1meability distributions for other lithologies .......... .. ... 10 GEOLOGY ................................................................................. 11 2.1 Study Site Selection ......................................................... 11 2.2 Regional Structural and Stratigraphic Framework ....................... 14 2.3 Local Geology ............................................................... 16 2.4 Geologic Descriptions Of Study Area ..................................... 20 2.5 Outcrop Weathering ......................................................... 28 2.6 Concepts of Permeability and Porosity for the Carbonate Rocks in this Study ............................................. 32 Vil GEOSTATISTICS ......................................................................... 37 3.1 Definition of Permeability as a Regionalized Variable .................. 37 3.2 General Statistical Analysis ................................................ 38 3.2.1 Sample statistics .............................. .................... 38 3.2.2 Nmmal and lognormal distributions ........................... 40 3.2.3 Moment and stationarity ......................................... 41 3.2.4 The vaiiogram .................................................... 42 3.2.4.1 General theory ........................................ 42 3.2.4.2 The power-law variogram ........................... 48 METHODS OF PERMEABILITY MEASUREMENT ................................ 51 4.1 MFP Sample Point Preparation ............................................ 51 4.2 Core Plug Permeability Measurements .................... .. ............. 58 4.3 Permeability Sampling Patterns ............................................ 58 DATA AND RESULTS ................................................................... 66 5.1 Permeability and Porosity Data ............................................ 67 5.1.1 MFP data ........ .................................................. 67 5.1.2 Core plug data .................................................... 67 5.2 Statistical Analyses of Sample Data ....................................... 70 5.2.1 GRID A ..... ........................:............................. 70 5.2.2 GRID B ........................................................... 77 5.2.3 GRID C ........................................................... 83 5.2.4 GRID D ........................................................... 90 5.3 Distributions of Data in the Genetic Facies ............................... 96 5.4 Compaiison of Sample Pe1meability Data Sets .......................... 101 viii 5.5 Power-law Variograms ..................................................... 105 DISCUSSION AND CONCLUSIONS ................................................. 113 6.1 Discussion .................................................................... 113 6.1.1 Two-dimensional visualization of the sample data ........... 113 6.1.2 Lognormal distributions in the sample data ................... 115 6.1.3 V ariogram parameters and scale dependency ................. 117 6.2 Conclusions .................................................................. 120 6.3 Recommendations ........................................................... 121 REFERENCES ............................................................................ 124 APPENDICES ............................................................................. 131 Appendix A: MFP Measured Permeability Data .............................. 132 G1id A.............................................................. 132 Glid B... ........................................................... 143 Glid C .............................................................. 147 Glid D .............................................................. 154 Appendix B: Core Plug Permeability and Porosity Data .................... 157 Appendix C: Pe1meability Calculation Program and Input Instructions ....................................................... 159 Appendix D: FORTRAN Code of Variogram Computation Routine ...... 174 Appendix E: V ariogram Output Data .......................................... 180 VITA ......................................................................................... 186 IX LIST OF FIGURES Figure 1. Site location map of Guadalupe Mountains and west Texas ............ 4 Figure 2. Mechanical field permeameter (MFP) device ............................. 6 Figure 3. Classification and nomenclature of carbonate rocks used in this study (from Choquette and Pray, 1970) ........................... 12 Figure 4. Regional structural geology, Guadalupe Mountains ..................... 15 Figure 5. Sequence stratigraphic model of San Andres Formation outcrop in the Guadalupe Mountains (from Kerans and others, 1990).................................................................... 17 Figure 6. Photograph of lmSA I uSA sequence boundary .......................... 18 Figure 7. Fourth-order sequences of uSA F01mation, Alge1ita Escarpment, Guadalupe Mountains (from Kerans and others, 1990) ......................................................... 19 Figure 8. Aerial photograph of Lawyer Canyon, Guadalupe Mountains ......... 21 Figure 9. Model of shallowing-upward cycle in carbonate deposition (after James, 1979) .................................................. 22 Figure 10. Measured sections used to define parasequence geology of Lawyer Canyon (from Kerans and others, 1990) ................ 23,24 Figure 11. Thin section photornicrographs of facies #1 -#4 as identified for parasequence 1, uSAl, Lawyer Canyon ...................... 26,27 Figure 12. Macroscopic fractures on outcrop in Lawyer Canyon ................... 30 Figure 13. Core recovery well location map, Lawyer Canyon ...................... 31 Figure 14. Thin section photomicrographs of calcite in-filled fractures from core plug samples, Lawyer Canyon ......................... 33,34 x Figure 15. Variogram diagrams for spherical, spherical with nugget, and all nugget (white noise) models .............................. .. .... 45 Figure 16. Additional variogram diagrams for nested and whole effects ........... 47 Figure 17. Scanning electron microscope photornicrographs of variously prepared smfaces on carbonate rock samples ..................... 53,54 Figure 18. Marking created on outcrop by hammer and chisel surface preparation method............ ....................................... 55 Figure 19. Sample pattern within a prepared "patch" on outcrop .................... 57 Figure 20. GRID A transects and permeability measurement locations ............. 60,61 Figure 21. GRID B transects and permeability measurement locations ............. 62 Figure 22. GRID C transects and permeability measurement locations ............. 64 Figure 23. GRID D transects and permeability measurement locations ............. 65 Figure 24. Location map of core plug sampling in parasequence 1, uSAl, Lawyer Canyon ...................................................... 69 Figure 25. Combined frequency histogram and probability plots for sample data, GRID A ................................................ 72 Figure 26. Combined frequency histogram and probability plots for sample data, GRID A, MFP data only ............................. 74 Figure 27. Combined frequency histogram and probability plots for sample data, GRID A, non-transformed data ............. ........ 75 Figure 28. Horizontal vruiogram, GRID A, log-tramsformed data ................. 76 Figure 29. Vertical variogram GRID A, log-transformed data ....................... 78 Figure 30. Contour map of GRID B posted data ...................................... 79 X1 Figure 31. Combined frequency histogram and probability plots for sample data, GRID B ................................................ 81 Figure 32. Horizontal vaiiogram, GRID B, log-tramsformed data ................. 82 Figure 33. Vertical variogram GRID B, log-transformed data ....................... 84 Figure 34. Contour map of GRID C posted data ...................................... 85 Figure 35. Combined frequency histogram and probability plots for sample data, GRID C ................................................ 86 Figure 36. Horizontal vaiiogram, GRID C, log-tramsformed data ................. 88 Figure 37. Vertical variogram GRID C, log-transformed data ....................... 89 Figure 38. Contour map of GRID D posted data ...................................... 91 Figure 39. Combined frequency histogram and probability plots for sample data, GRID D ................................................ 92 Figure 40. Horizontal vaiiogram, GRID D, log-tramsformed data ................. 94 Figure 41. Vertical variogram GRID D, log-transformed data ....................... 95 Figure 42. Combined frequency histogram and probability plots for sample data, facies #1 ............................................... 97 Figure 43. Combined frequency histogram and probability plots for sample data, facies #2 ............................................... 99 Figure 44. Combined frequency histogram and probability plots for sample data, facies #3 ............................................... 100 Figure 45. Combined frequency histogram and probability plots for sample data, facies #4 ............................................... 102 Figure 46. All GRID sample data for hmizontal variograms posted on logrithmic axes ....................................................... 108 XU Figure 47. All GRID sample data based on significant calculations of semivariance for horizontal variograms posted on logrithmic axes ....................................................... 109 Figure 48. A, B, and C GRID sample data for horizontal variograms posted on logrithmic axes ........................................... 110 Figure 49. A and C GRID sample data for horizontal variograms posted on logrithmic axes.................................................... 112 X.111 LIST OF TABLES Table 1. Statistics of GRID and facies defined samples, non- transformed and !or-transformed ................................... 104 Table 2. One-factor ANOV A comparisons for GRID samples .................... 106 Table 3. Variogram results for GRID samples ...................................... 119 J... ---7 I , . .. . I ~ xiv CHAPTER 1 INTRODUCTION Characterization of permeability variation is a fundamental science of the petroleum engineer and the hydrogeologist in order to understand the movements of fluids in the subsurface. In most subsurface environments, the accurate description of permeability distributions is limited by the inaccessibility of the subsurface environment for the required detail of sampling. For this reason, the use of geologically analogous outcrop sampling has been suggested to dete1mine whether the permeability values measw·ed on outcrop exhibit a characterizable pattern that can be applied to fluid flow models. The concepts of statistical evaluation of analogous geologic settings are being widely developed in the field of hydrocarbon reservoir engineering, but the same principles are applicable in hydrogeology for the modeling of environmental contamination, though this later use is less well developed. This study differs from previous published work in outcrop modeling in that the data are concentrated within genetically-related bed sets bounded by flooding surfaces. This geologic description fits the definition of a single parasequence within cyclically stacked carbonate deposits (Van Wagoner and others, 1988). Selection of the study site was based on attributes of a proven geologic analog between the outcrop and the subsurface of a known productive oil-field, and for an extensive exposure of outcrop accessible for sampling. Throughout this study, the scale of sample collection has been a most important consideration. To address the unknown scales at which permeability variation within the outcrop may exist, this study was implemented through a series 1 of sampling schemes at various scales. The main consideration for determining the largest scale of permeability sampling used in the investigation was that the results could be used to enhance oil field production and recovery efficiency. This required that the scale of the sampling was comparable with intra-and inter-well spacing of oil fields (i.e., tens to thousands of feet or meters). 1.1 PROJECT OUTLINE To present the data and findings of this study this thesis is organized as follows: 1) introduce the project through the discussion of its goals and references to previous studies (Chapter 1), 2) provide the general geologic setting of the pore textures obse1ved in the rock fabrics of the study site (Chapter 2), 3) present the theoretical statistics as applied to the data set (Chapter 3), 4) elucidate the methods of data sample collection with reference to the geology of the study area (Chapter 4), 5) analyze the results of the study using geostatistical tools and geologic observations of the stratigraphic and petrologic relationships (Chapter 5), and 6) discussion of results (Chapter 6). 1.2 OVERVIEW 1.2.1 THEORY As a study of spatial variations in permeability within a depositional unit, this project required an extensive sampling program that would create data sets of spatially-distributed permeability values for statistical interpretation. Because the investigation targeted the ability to detennine reservoir-scale heterogeneities, the study site needed to be large enough for outcrop exposures to match the size of typical hydrocarbon reservoirs. In order to apply the results of this study's to actual systems, it was necessary that the study site be proximal to oil fields producing from the same or an otherwise similar formation. Outcrops of the San Andres Limestone on the Algerita Escarpment of the Guadalupe Mountains in Otero County of southwestern New Mexico (Fig. 1) were studied previously by Hinrichs and others (1986) and Kittridge ( 1988), and the choice of that location for another study was most logical. This study follows geostatistic techniques first developed by Krige (1943) for estimation of economic ore reserves. These principles were furthered in the fields of geostatistics and stochastic modeling by Matheron (1963), David (1977), and Journel and Huijbregts (1978). More recently, advances have been made that go beyond the early applications of geostatistic theory in ore reserve estimation. These advances have been mainly in the applications of stochastic principles and conditional simulation models to petroleum reservoir and ground water systems (Amhed and de Marsily, 1987; Behrens and Hewett, 1990; Dagan, 1985; Delhomme, 1978 and 1979; Fogg, 1986; Gelhar, 1986; Sudicky and others, 1986; and Weber, 1982). O SO mi I •. , 11 I1 ,·,I 1oilfields. 0 40 SOkm Figure 1. Site map of west Texas Permian Basins and oil fields of the San Andres formation. Adapted from Kerans and others, 1991. 1.2.2 THE MECHANICAL FIELD PERMEAMETER Measurement of permeability values in the field was made possible with a mechanical field permeameter (hereafter referred to as MFP, photo shown in Fig. 2). The particular instrument used in this study was developed within the University of Texas at Austin, Petroleum Engineering Department by D. Goggin, from a prototype design published by Eijpe and Weber (1971), founded on principles of permeability measurement described by Dykstra and Parsons (1950), and extended by Chandler and others ( 1989b) and Goggin ( 1988). Pe1meability values were calculated through a mass-balance application of Darcy's Law (Goggin, 1988; reprinted in Appendix E), using a flow rotameter and pressure gage recordings to estimate the rate at which a known gas was injected at the rock surface. Previous applications of the MFP on outcrop of the San Andres fo1mation by Kituidge (1988) and on outcrop of the Page Sandstone, northern Arizona, by Chandler ( 1986) and by Goggin ( 1988) have proven the accuracy and viability of the MFP in outcrop permeability descriptions. A more precise electronic field mini-permeameter was developed by the Department of Geological Sciences (Fu and others, 1992) after the data collection of this study was completed. In addition to the MFP derived permeability values, core plug samples were collected from the outcrop. Core plugs were collected on outcrop in selected locations to provide petrographic data through thin section, porosity, and permeability analyses. The spatial distribution of the core plugs sampling was intended to both expand and validate MFP derived permeability data. Figure 2. Mechanical Field Perm ea meter (MFP) used for field collection of permeability data. MFP components: A -High pressure nitrogen gas source. B -Three (3) rotarneter stands to hold interchangeable flow tubes. C -Test quality pressure gage and back-up units. D ­Flexible tubing with silicon probe-tip and on/off valve. 1.2.3 STA TISTICAL ANALYSIS Data were analyzed through the comparison of variances between permeability values based on their spatial relationships. This was accomplished through a FORTRAN demonstration program published by David (1977) that computed semivariance as a function of a vector, h. Values of the semivariance, y(h), were calculated for horizontal and vertical search directions. Represented graphically as experimental variogram plots, )'(h) versus distance, these were interpreted for the statistical parameters of range (horizontal or vertical distances defined by the vector, h) and characteristic variance, or sill value. Range, sill, and other characteristics of the permeability distribution were interpreted from the experimental variograms. These results were compared for direction and relative distance (i.e., the distance value of vector h) between permeability values in catagorized, scale-based sample sets of the permeabil.ity data. Comparison of the experimental variogram parameters between the sample sets provided insight as to the statistical nature of the disuibution was identifiable from the and estimations for permeability values at distances from known values provided were predictable as a function of the observed statistical parameters. These characteristics of permeability disuibutions are useful for representing permeability structure of carbonate units in fluid flow simulations. 1.3 PREVIOUS STUDIES 1.3.l PERMEABILITY DISTRIBUTIONS IN CARBONATE ROCK FORMATIONS Previous studies have been conducted by Hinrichs and others (1986) and Kittridge (1988) to determine the distribution of permeability measured on the San Andres formation outcrop on the Algerita escarpment of the Guadalupe Mountains. These investigators used permeability and porosity data, supplemented by petrographic data from thin section descriptions, to compare the observed textural characteristics of the rock with the measured pe1meability. Pe1meability values were the principal variable for analyses. Other information was interpreted to reinforce correlation between the permeability of the rock and textural characteristics. These preliminary studies addressed two basic questions. The first question concerned the validity of the assumption that discrete zones of high or low flow exist within a geologic unit. The second question was how these findings might be incorporated into reservoir models that would predict permeability distribution patterns in the subsurface based upon limited information. In both of the early studies, the range of distances and the patterns of sampling were designed to incorporate multiple and varied textures for the identification of permeability correlations within the formation. These were intended to provide accurate parameters for reservoir models. The accuracy of these models depends on the initial assumptions used in the data collection that produces the parameters. Hinrichs and others (1986) used core plug sample data taken from eight individual porous beds at sample separation distances of 100, 10, and 1 ft or less. The permeability and porosity values were then compared to subsurface data available from the San Andres formation in Wasson field, located to the Northeast in Texas (see Fig. 1). Statistical data of the permeability values were compared for individual bed and for the different lateral sampling distances. Visual representation of the permeability patterns was obtained by contouring the data between individual beds, showing tortuous and discontinuous zones of high permeability within a background of relatively lower permeability. Kittridge (1988) sampled within a discrete area of the San Andres formation that extended across the boundary of the middle and upper sequences of the fo1mation (sequences as interpreted by Sarg and Lehmann, 1986, and Kerans and others, 1991, and discussed below in Chapter II, Geology). His sampling consisted of closely spaced points within evenly spaced grids and vertical transects of variable separation distances. Kittridge tried to evaluate outcrop distri bu ti on patterns and the comparability of outcrop and subsurface data given analogous geologic characteristics. The raw data collected for the study were confounded by an error in the preparation of the weathered surface through his use of a mechanical grinder. Computer contouring showed the permeability heterogeneities to extend down to scales as small as one-half inch, and results of semivariance analysis detected statistical correlation at ranges that were dependent of the distances between sample points. The statistical work presented in these previous studies on the San Andres formation were able to show two general conclusions. First, the distribution patterns of permeability values were heterogeneous within packages of genetic facies. Second, there exist isolated high permeability zones within an overall low permeability rock matrix. However, these preliminary studies were inconclusive in defining tractable statistical relationships to indicate a predictable trend in the permeability expectations based upon semivariance between known permeability values. 1.3.2 PERMEABILITY DISTRIBUTIONS FOR OTHER LITHOLOGIES The application of geostatistical analysis should be restricted to geologic sections similar to those where the study was conducted. However, the methodology incorporated in geostatistical analysis is not restricted to any particular rock type, or particular variable (e.g., permeability). Other researchers have investigated reservoirs and aquifers for permeability patterns in sandstones (Chandler and others, 1989; Fu and others, 1992; Goggin, 1988; Goggin and others, 1988a; and Weber, 1982), unconsolidated deposits (Sudicky and others, 1985, and Beard and Weyl, 1973), and welded ash flow tuffs (Fuller, 1990, Fuller and Sharp, in press; and Sharp and others, in press). The emphases of these studies revolve about the ability of data to determine patterns of permeabilities for use in modeling applications. Of the above, some have used analogous outcrop data to set the model controls (e.g. Chandler, 1986; Chandler and others, 1989; Goggin, 1988; and Weber, 1982), while others have relied upon dense sampling strategies using cores and well tests for their permeability data base (Sudicky and others, 1985) or the inference of geologic process controls such as fracturing and surf ace weathering on permeability and porosity development (Fu and others, 1992; Fuller, 1990; Fuller and Sharp, 1992; and Sharp and others, in press). CHAPTER 2 GEOLOGY The geologic descriptions that follow are compiled from King (1942 and 1948), Skinner (1946), Hayes (1964), Todd and Silver (1969), Sarg and Lehmann (1986), and Kerans and others ( 1991). Terminology for the facies textures follows that developed for application to carbonate rock systems by Choquette and Pray (1970; Fig. 3). Stratigraphic placement and description of the San Andres formation rely upon the work of Sarg and Lehmann (1986), augmented by Kerans and others (1991) for descriptions in the more immediate area of the Algerita Escarpment. Terminology used in the description of sequence-stratigraphic relationships follows Van Wagoner and others (1988) for carbonate depositional systems and specific application of terms to the local facies geology follows the interpretations of Kerans and others (1991) in their mapping of the Alge1ita Escarpment. 2.1 STUDY SITE SELECTION The selection of the San Andres Formation for an outcrop reservoir analog study was based upon the history of the formation as a prolific oil producer in west Texas (Galloway and others, 1983), the accessibility of extensive outcrop exposure on the Algerita Escarpment of the Guadalupe Mountains in southwestern New Mexico, and the proximity of the outcrop to two producing San Andres Formation reservoirs (in Texas, the Seminole Field in Gaines Co., and the Wasson Field in Yoakum/Gaines Co.).The positive results reported by Hinrichs and others (1986) and 11 BASIC POROSITY TYPES I FABRIC SEL.ECTIVE I I NOT FABRIC SEL.ECTIVE I R INTERPARTICLE BP FRACTURE FR ~ INTRAPARTICLE WP -~ CE CHAllllEL• CH INTERCRYSTAL BC MOLOIC 110 w&• VU& Ift I I~:J ~ - FENESTRAL FE u CAVERN• CV SHELTER SH ~ ml. GROWTH· *co,...rn appha to "*1·11ztd or lor91r port1 of GFFRAMEWORK cr.3nntJ or YUQ shapes . I FABRIC SEL.ECTIVE OR NOT I B§BRECCIA ~BORING ~BURROW ~SHRINKAGE BR BO BU SK MODIF'YING TERMS GENETIC MODIFIERS SIZE• MODIFIERS I PROCESS I IDIRECTION OR STAGE I CL.ASSES .. mm' 256­ l1r91 11119 SOLUTIOll I ENLARGEO I MEGAPORE 32­ IMll .... , CEMENTATION c REDUCED 4­ lartt 11111 .. INT£RNAL SEDIMENT i FILLED I MESOPORE 'lz­ 1111011 11111 l/11­ MICROPORE llC PRIMARY p ITIME OF FORMATION I UM IOlt IQ!ilft --~ly''"' ' ......... '"'VUG pre -depositionol Pp smell~ ..."° fft iCrointet,.,ticte .... dtpositioftol Pd .,. t99'110r·....-.... WMllef ft'tOtl CO'\lt'rR tile. SECONDARY s t MH'Wrft ,,.., .. ...,... port dtonwtflt of • l"'tle "9N • IN '"91 ift ILH Of 0 pore HlitfftOIOtt. t09llllllic St 1MS09tftttic Siii F0t tvbulor porn .,.. owero99 croa• Mctioft. Far ltlogtntlic St ,..., porn UM wid"' oM ..,.. "'°"· ABUNDANCE MODIFIERS Gttlttic lllOdil1111 ort combifttd os follows : perettt porosity (15'4) !PROCESS! • IDIRECTIONI • ITIMEI or EXAMPLES: tolutioll -t•lorgtd u rotil of porosity typn (1 :2) cement -rtdvctd prnoary crP or stdimtnt • lilltd ..,,.tit if St ratio Hd perc•I (1:2) 05'41 Figure 3. Classification and nomenclature of pore types and pore systems in carbonate rocks as used in this study (from Choquette and Pray, 1970). Kittridge (1988) further justified locating the study site in the San Andres outcrop of the Algerita Escarpment. In particular, Kittridge's (1988) comparison of the San Andres Fo1mation outcrop at Lawyer Canyon to the subsurface unit at Wasson Field obviated the choice for the same general study area. San Andres reservoirs are within shallow-water platform top and upper slope carbonates with laterally extensive facies distributions and generally low (30%) recovery efficiencies (Galloway and others, 1983). Well spacing in the Wasson and Seminole fields is one well per 10-or 20-acres, in standard 5-spot or 9-spot pattern, providing inter-well distances of 660 to 1320 feet. To be able to characterize lateral variability of permeabilities at such distances, the outcrop selected needed to be undisrupted laterally for at least 2,000 feet. The Lawyer Canyon area easily satisfies this requirement, because lateral exposw·es of continuous outcrop are double the inter­well distances of the oil-fields. Finalizing the decision of site selection was the criterion that this study would characterize a single cycle of genetically related beds. In the previous investigations of Himichs and others (1986) and Kitttidge (1988), the goals were to sample at a large scale and thereby include many different rock textures. For this study, the area was confined to a single cycle of genetically related and flood-bounded bed sets, the single parasequence of Van Wagoner and others (1988). This limits the number of different facies involved in the analyses of permeability distributions and allows a significant number of measurements to be collected at various lateral separation distances within each depositional facies of the parasequence. 2.2 REGIONAL STRUCTURAL AND STRATIGRAPHIC FRAMEWORK Early structural descriptions of the Guadalupe Mountains were provided by King (1942, 1948) and Hayes (1964). They identified the mountains as the· desiccated remnants of a Tertiary age uplift that tilts gently to the northeast (Fig. 4). The uplift is bounded by north-northwest striking normal faults to the west (the Algerita Escarpment in the north section of the mountains) and to the east by a monoclinal fold superimposed over late Paleozoic thrust faults (the Huapache monocline). To the southeast, the boundary is represented by the intersecting northeast striking reef front composed of the resistant Capitan Limestone. West of the Guadalupe uplift, Big Dog and Little Dog Canyons form a graben area that separates the Brokeoff Mountains, a collapsed plateau, from the Guadalupe Mountain uplift (King, 1948). The north­northeast striking line of normal faults continues south of the Guadalupe Mountains where it forms the western boundary of the Delaware Mountains. The San Andres Formation was originally named by Lee (1909) for outcrops in the San Andres Mountains of south-central New Mexico. The San Andres is acknowledged to be part of a wide spread Permian (Leonardian/Guadalupian) aged platform composed of stacked upward-coarsening carbonate cycles rimming the margins of the Delaware and Midland Basins in southeastern New Mexico and west Texas (King, 1942 and 1948). In the area of the Algerita Escarpment, the San Andres rests between unconformable contacts at the top of the Y eso and at the bottom of the Grayburg (Sarg and Lehmann, 1986, and Kerans and others, 1991). In this area, the San Andres Formation is predominantly dolomitic, the principle diagenetic alteration Figure 4. Guadalupe Mountains and location of Lawyer Canyon on the Algerita Escarpment, Otero Co., New Mexico. Shown are the major structural features in relation to the study site (after King, 1942). dated to have occurred in late Guadalupian time, with infiltration of hypersaline waters percolating down from overlying tidal flats (Leary, 1984; Todd and Silver, 1969). 2.3 LOCAL GEOLOGY Development of a sequence-stratigraphic model for the San Andres in the region of the Guadalupe Mountains was first presented by Sarg and Lehmann (1986) and recently refined by Kerans and others (1991; Figs. 5-7). This model divides the San Andres into two major third-order sequences, the combined lower and middle lithologic units (lmSA) and an upper unit (uSA). The lower-middle San Andres third­order sequence (lmSA) is composed of a lower open marine transgressive bank unit overlain by a middle prograding restricted ramp system. The sequence boundary between lmSA and uSA is a conformable boundary that is well exposed in Lawyer Canyon. The upper third-order sequence (uSA) is further divided into four fourth­order sequences (uSAl-4) by Kerans and others (1991) based on interpretations of detailed stratigraphic maps completed along the Algerita Escarpment. Each fourth­order sequence is a progradational, generally offlapping package of parasequence sets composed of ramp crest, restricted outer ramp, and inner ramp facies tracts. Fourth-order sequence boundaries are identified from karst surfaces or tidal flat complexes located in the top parasequence of the previous sequence. The top of GRA'f8URG FORMATION -SI ­ EXPLANATION .. B boPOri•• Clir•c• ~ ~ r ~ LJ ....... _.._ .\I' IOOO jooj Ooi4-polood pac:UIOoe/.,.._ 00 -,__ ....­ ~0oll1&""""­~Clll•IJ ..,.,._ !·~~· i"'IOld-1....-pocl•­1~· :-· :-] "°"'"'"""Gii-id ........_ ~ ..,....~............. - fi l.:.!.:..:J poclalOlll/;nlntlone I SB SoQ..c,.,. lloOO ~ ,__ I 2 HST H19~11011d 1r11em1 trDct ~ ... TS T irona1rn1J.,. '""'"' troct IOO TST : : --...,. ' 0 0 SI 'fESO FORMATION Figure 5. Simplified geologic cross-section of San Andres formation based on compiled information from outcrop data along the Algerita Escarpment (top). Sequence stratigraphic interpretation of major (third order) sequences (from Kerans and others, 1990). Figure 6. Sequence boundary (lmSA/uSA) exposure at Lawyer Canyon, Algerita Escarpment. View is from north-side of canyon looking south at transec-ts A 17 and A 18. . ­ - North South . ~e So" ~v ~q; "'li ,e' e' · ~e, J~ ,,, ~c, ,,~ "''1;~*" "''1;~*" ~' o~ -~" · be, vo-s ';\o c;o"' e, e" e, · 0 I 0 I I 2 2 I I 4 3 ' 4 I I 6 5 mi I 8km Sequence boundary Maximum flooding sur1aco D D llIIIIIll FACIES TRACT Open manne ramp ~Restricted outer ramp Open to restricted outer -Ramp crest ramp Distal outer ramp to E] Inner ramp . basin - Figure 7. Fomth-order sequences of San Andres formation outcrop, Algerira Escarpment, Guadalupe Mountains. From Keraris and others (1991). ..... \0 uSAl is a karsted bar-top surface exhibiting characteristics of subaerial exposure and subsequent onlap of uSA2 burrowed mud facies. Exposure of uSA2 is predominant 1.5 miles (approximately 2 kilometers) down-dip from Lawyer Canyon. At the top of uSA2, the sequence boundary of uSA2/3 is demarked by a karst surface. Between the uSA3 and uSA4 the sequence boundary is interpreted from a tidal flat complex at the top of uSA3. The top of uSA4 is set at a variably developed karst surface that is also the upper sequence boundary between the San Andres and Grayburg formations. 2.4 GEOLOGIC DESCRIPTIONS OF STUDY AREA Exposure of uSA 1 in the Lawyer Canyon area (Fig. 8) varies from 140-190 ft thick and it is composed of nine identified parasequences, of which the basal parasequence is the study area for this investigation. Here, the third-order sequence boundary (lmSNuSAl-SB) exists at the base of a thick, light-white colored mudstone bed that overlies darker, fusulinid-rich packstones. This mudstone is interpreted as the flooded surface in the basal parasequence of uSA 1, representing a minor downward shift in relative sea-level (30 -50 feet) and a lateral shift of several miles in facies tracts (Kerans and others, 1991). As the general case among the parasequences of uSA 1, the basal parasequence is a shallowing-upward cycle (after James, 1979; Fig. 9) composed of dolomitic, upward-coarsening mudstone to grainstone beds. A cross-section of sixteen (16) measured sections (Fig. 10), provided by C. Kerans, shows this basal parasequence to be composed of four genetically related deep-to-shallow water facies: (1) deeper­water, flooded shelf mudstone; (2) shallow shelf mud-supported, ooid and peloid Figure 8. Aerial photograph of Lawyer Canyon taken from over Dog Canyon facing east­northeast. Arrows point to lmSNuSA sequence boundary at approximated lateral boundaries of the study area. Facies Model: Upward Shallowing Lawyer Canyon Carbonate Cycle Section A 17 (modified from James, 1979) (courtesy of C. Kerans) ·­ .. -------.. -....... .. -........ -"' ­ i1II111!li•~ti-~~i :t)/t'::>:: LAGOO.N\:'''' ::::::::::::=SlifeliF:t: :: .. .... ----..... -.. --.. .......... -.. .. .. ---.... .. . .......... ~:}:{({{{:}}~({{:}~:}~: ..•..•..•..•...••• ... :.•·..•.•.••..•.•.•.,•.•.•.•...•., . •..•.•..•, ...•.:•..,•.•..•.•..•., . •..•.,. .•••..•..•..•.•:.•.•. ..,..... •,.,•.•...•.•.•...., .•' •..•.•....•.••...•., •.• ----.... .. --.... .. .. -.. -... .. -.. .. .. .. ... --.. .. :~=~~==~1:(i1~r-o::=~'!: ' soAiitt>N~·i @ Dasyclad :I Burrows b Mollusc ~ Stromatol~es * Crinoid ,_,,,.,... Mud-cracks @ Ooid ~ Wavy-parallel laminations Figure 9. Generic model for shallowing-upward carbonate deposition with comparison to a measured section used in this study. A) Lithoclast-rich lime conglomerate or sand (this facies not present in uSAl basal parasequence). B) Fossiliferous limestone (present as mud-dominated flooded shelf in uSAl basal parasequence). C) Stromatolitic, mud­cracked cryptalgal limestone or dolomite (present but with few mud-cracks evident in uSAl basal parasequence). D) Well laminated dolomite or limestone, flat-pebble breccia (present in uSAl basal parasequence as tabular or troughed-cross bedded dolomite, no breccia). E) Shale or calcrete, this unit often missing (not present in uSAI basal para­sequence). Figure 10. Symbols. DEPOSITIONAL TEXTURE Grains tone Packs tone Wackestone Muds tone SEDIMENTARY STRUCTURES I~I Trough cross stratification ~Planar-tabular cross stratification E₯] Wavy-parallel current lamination r:.--:1 Vuggy porosity ~Evaporite psuedomorphs ~ GRAIN TYPES D­ Mud D• Peloids ~. Ooids 1~ 0ol Fusulinids ~ Pelmatozoa GENETIC FACIES 1 Flooded shelf 2 Shallow shelf 3 Bar crest 4 Bar flank, shallow shelf 900 1000 1100 1200 1}00 1400 1500 1600 1700 1800 ft. 20 ft. A20 A21 A22 A24 10 ------------------ -------­ 0 1800 1900 2000 2100 2200 2300 2400 , ... 2500 2600 2700 ft . Figure 10. Original sixteen (16) measured geologic sections mapped in parasequence 1, Upper San Andres formation, in Lawyer Canyon study site, as mapped by Kerans and Nance (1989, unpublished). Depositional texture, grain types and sedimentary structures shown with interpretations of genetic facies lateral continuity (see explanation on opposite page). 100 200 JOO 400 500 600 700 800 900 ft . AJ6 A17 A18 A19 ft. N .i:-. wackestone/packstone; (3) ooid and peloid grainstone bar crest deposits; and (4) shallow shelf, bar flank coarsening upward ooid and peloid wackestone to grains tone. Facies #1 is a low-energy, flooded shelf, sheet-like deposit that thickens southward. This facies is the marker bed that is continuous throughout the study area. Within the study area, the bed thickens from approximately five (5) feet in the north (sections A3 to Al3) to 13 feet in the south (section A24). Internally, the facies is characteristically massive and lacking in preserved laminations. This may be indicative of bioturbation or diagenetic alteration of the carbonate mudstone fabric that resulted in a recrystallization of lime mud to dolomite microspar (5 to 10 ΅m diameter; Fig. l lA). The exposed rock fabric is repeatedly interrupted by fractures at microscopic and larger scales, of which many at the smaller scales are filled by calcite and dolomite cements. Facies #2 is a laterally discontinuous, low-energy draped shallow shelf deposit that overlies the mudstone bed (facies #1). Facies #2 coarsens gradationally upward from mudstone to wackestone. Thicknesses vary from 2 ft (section A 1) to 5 ft (section A9) and the facies is assumed to pinch out between sections All and Al3. Facies #2 contains wavy, parallel laminations interspersed with more massive intervals that show signs of bioturbation. Dolomite microspar replacement of carbonate mud and peloids overprints the original texture. Intercrystalline porosity is observed in thin section (Fig. l lB) as the dominant pore type. As in facies #1, calcite cement infilled fractures are also present in facies #2. Facies #3 consists of a high-energy, shallow shelf ooid-rich grainstone and has been interpreted as a bar crest deposit. This facies caps the lower mud-rich facies Figure 11. Thin sections from Lawyer Canyon core plug samples (uSAl first parasequence) showing the variable textures found within each of the four identified generic fades. All scales are 1.3 mm= 100 ΅(magnification 40x). (A -top left) Flooded shelf fades (#1), mudstone texture: carbonate mudstone replaced dolomite microspars (>30 ΅ diameter), fractures and vugs have been infilled by later calcite cement. Core plug location: A9 -2 ft. from base of parasequence; ~ =9.50; k =13.51 md. (B -top right) Shallow shelf fades (#2), mudstone/wackestone texture: remnant peloids (arrows) in mudstone replaced by dolomite microspars, fractures have been infilled by later calcite cement. Core plug location: A9 -7 ft. from base of parasequence; ~ =8.50; k = 0.71 md. (C -bottom left) Bar crest fades (#3), grainstone texture: grains replaced by dolomite microspars, later dissolution and cementation (dolomite/calcite) has disrupted the grain fabric and filled intergranular pore spaces. Core plug location: AS -13 ft. from base of parasequence; ~ =15.60; k =13.67 md. (D -bottom right) Bar flank fades (#4), grainstone texture: micritic-dolomite crystalization has replaced the grain-dominant fabric with relatively large crystals, later dissolution and compaction has disrupted the original intergranular porosity. Core plug location: A18 -15 ft. from base of parasequence; ~ =19.60; k =333.0 md. 27 #2 in the northern end of the study area and is observed to pinch-out to the south (between sections A 19 and A20) after varying thicknesses of 6 ft (section A3) to 15 ft (section A 15). Trough cross stratification and planar-tabular stratification patterns are observed within facies #3, indicating reworking of the sediments by wave and tidal currents. The fabric is largely replaced by dolomitic microspar (less than 30 microns; Fig. 11 C). Interparticle porosity is retained in thin section, though later dissolution and cementation by calcite and dolomite disrupts the grain-dominated fabric and infills some interparticle and fracture pore space. Facies #4 is a shallow water, moderate energy shallow shelf facies, composed of packstone and wackes tone textures. It is transitional between facies #2 and #3 and is interpreted as a bar-flank deposit. Thicknesses range from 9 feet (section A22) to a near pinch-out of 1 feet at the southern-most transect of the study area (section A24). The transition from mud-to grain-dominated texture is gradational through this facies. Facies #4 is typified by an upward increase in grain size. The southern (basinward) deposits show intermittently preserved wavy to parallel lamination. Replacement of the mud and grain fabric by dolomite microspar (10 to 30 ΅m diameter) caused an increase in intercrystalline porosity in the mud-supported fabric but did not significantly change the interparticle porosity (Fig. 110). 2.5 OUTCROP WEATHERING Alteration of the rock matrix with the weathering of the outcrop was an important concern in the set-up of the outcrop-reservoir analog study. Differences in porosity and permeability values for Lawyer Canyon outcrop and proximal subsurface reservoir samples were observed by Hinrichs and others (1986), Kittridge (1988) and Kerans and others (1991). These differences correlated with the presence of anhydrite and gypsum in the subsurface which are missing from the outcrop. Weathering of the sulfates from the outcrop increased porosity and permeability measurements of those rocks, but the overall change in values was assumed to represent a relative shift in values and not a change in the relative distribution of values in the rock matrix. Surface weathering of the outcrop was assumed to be moderate, although examination of outcrop hand-samples revealed a dark-colored weathering rind between from 1/32-to 1/8-inch in thickness. Kittridge (1988) recognized the significance of removing this rind to expose the unaltered rock matrix for measuring permeability with the MFP device, however, the method he employed was later determined to be destructive and inappropriate for the study. For this study, the method of removing the weathered rind from the rock surface was dete1mined prior to sampling and is presented in Chapter 4, Section 3 (Permeability Sampling Patterns). As explained in that section, the technique was chosen for the completeness of rind removal and relative lack of damage to the newly exposed rock fabric. The most distinctive feature of the Lawyer Canyon study area is the pervasive fracturing on the outcrop. Fractures were observed to occur along bedding contacts as well as numerous other planes unassociated with depositional structure. Fractures range from the microscopic to the macroscopic scale (Fig. 12). Cored wells drilled through the San Andres formation in a location 1,000 feet behind the Escarpment front (Kerans and others, 1991; Fig. 13) provided evidence of similar fracturing extending into the raised plateau. This fracturing of the formation was not a shared VJ feature in the subsurface rocks of the compared reservoirs (Kittridge, 1988; Hinrichs and others, 1986; and Kerans and others, 1991). The fracturing of the outcrop was attributed to the Tertiary faulting and uplift. Another influence on outcrop permeability and porosity was a surficial calcareous tufa, observed as a white precipitate deposited on the rock surface and within fractures. Leaching of the rock matrix by dissolution of carbonate minerals and the precipitation of calcite on the rock surface has a dual effect on the rock permeability. Initial dissolution of the solids opened the pores and/or fractures in the rock, while subsequent precipitation of tufa reduces the pore connectivity on the rock surface. Thin sections from selected core plugs confirmed the presence of calcite infilled fractures in the near surface of the rock (Fig. 14 A and B). In conclusion, the effect of weathering on the distribution of permeabilities beneath the weathered rind was assumed minimal. On the basis of on these assumptions, the relative distribution of permeability and porosity on outcrop was comparable with the subsurface data. The MFP device precluded sampling the permeability of macroscopic fractures; smaller fractures were usually associated with gas-leakage around the probe-tip. These were easily observable indicators of the presence of fractures and such samples were avoided in the data collection. 2.6 CONCEPTS OF PERMEABILITY AND POROSITY FOR THE CARBONATE ROCKS IN THIS STUDY In order to characterize permeability, it is important to define permeability as a quantitative variable based on the pertinent physical aspects of the specific rock type Figure 14. Thin section photomicrographs of calcite infilling fractures and interparticle pore spaces in rock matrix at the surface of the outcrop. Scales are 1.3 mm = 100΅ (magnification 40x) (A -top) Calcite infilled fracture in dolomitized wackestone, flooded shelf fades. Core plug location: A23 ­6 ft. above base of the parasequence; = 5.60, k =0.13 md. (B -bottom) Calcite infilled pore space in dolomitized grainstone, bar flank fades. Core plug location: A9 -9 ft. above base of the parasequence; magnificaion 40x, 1.3 mm = 100΅; =7.80, k =5.27 md. targeted for measurement. This requires a description of the rock's physical texture and the formulation of a conceptual model that describes the permeability within the rock in question. Permeability is a measure of the ease with which a porous medium transmits a fluid. Aside from fluid properties and fluid-rock interaction, the differences in pore connectivity are critical in determining relative permeability. The physical differences are important for the identification of a volume that is representative of a permeability value. Ideally, the representative volume of a porous medium is that which encapsulates the average ratio of pore to solid spaces in the material. Therefore, the ideal scale of a sample to characterize the medium should be the scale for which the void space and solid connections are equally represented. A model of pore-texture relationships in rocks (Meinzer, 1942, his figure XA­1) illustrates the variability of geometries possible for various lithologies. As a composite of capillary tubes and variable pore textures, Meinzer's model also illustrates the variability of size-scales encountered in determining the ability of a porous medium to transmit a fluid (i.e., permeability). Pore spaces have been shown to extend from small-scale micropores within individual grains to large-scale fractures in crystalline rocks and karstic solution cavities in carbonate rocks. In carbonate rocks, the size of the connecting pores spaces in the rock matrix covers a wide spectrum of sizes from the microscopic to the macroscopic (Choquette and Pray, 1970; see also Fig. 3 above). Assumptions stated above consider only those porous connections in the rock fabric that were measurable by the MFP. Consequently, the smallest intraparticle micropores and most larger-scale (micro-to macroscopic) fractures were excluded since these were not directly measurable by the MFP. To correct for this limitation, core plug porosity and permeability data were incorporated in this study, though most fracture permeability remained outside of the measurement capability of the core plugs. However, as stated above, fracture permeability was not germane to the scope of the project, especially so since the fractures were assumed to result from outcrop weathering. Variability of pore sizes within core plug samples collected from the outcrop was illustrated in thin section photomicrographs (see also Fig. 11 A-0 above). It was from the examination of pore space configurations, at the microscopic scale, that facies classifications were defined for use in this study (Kerans and others, 1991). The petrographic analysis separated the permeability data into subsets of related rock type for further statistical analysis. CHAPTER 3 GEOSTATISTICS The purpose of this section is to state the nomenclature and methods for the statistical analyses upon which the conclusions are based. This study applies statistical theory to the geologically-defined permeability data to investigate the influences of textures and depositional environment on permeability values. The nomenclature used in this study has been compiled from the works of David (1977), Davis (1973), Hewett and Behrens (1990), Isaaks and Srivastava ( 1989), Journel and Huijbregts (1978), and Mandelbrot (1984). 3.1 DEFINITION OF PERMEABILITY AS A REGIONALIZED VARIABLE Basic to geostatistical theory is the concept of the regionalized variable (Journel and Huijbregts, 1978). This term for the theoretical behavior of a measurable natural phenomenon is defined as the value of a measurement that is found to vary systematically over space and yet exhibits a randomness that is superficially unpredictable. Permeability values measured from the outcrop satisfy this definition since they are associated with a measurement point location and, in a heterogeneous and anisotropic rock, are observed to vary in a seemingly unpredictable fashion between locations. An initial assumption is made that each measurement of permeability represents an occurrence of the value z(x) for the location x. For a particular location 37 on a rock the permeability value is an unknown until measured. This is because naturally occurring rocks are heterogeneous to some degree, the location at which a permeability value occurs is variable and for any one location the permeability can be assumed to vary within some upper and lower limits. For this study, it was possible to determine that the vaiiance observed in permeability would be constrained (i.e., the range of values would be noncontinuous) by the nature of the rock matrix and by the limits of detection for the measuring apparatus. From the above conditions, the collected permeability data are definable as a set of random variables, Z(xi). By definition { Krige (1943); Matheron (1960); David (1977); and Joumel and Huijbregts (1978)}, the random variable Z(xi) represents a set of random occurrences for the permeability variable z(x), which are known to vary within a continuous or a noncontinuous range as the coordinate location xi varies within the study area. In these terms, each permeability measurement, z(xi), is a true realization of the expected value for the random variable Z(xi) at a location xi. 3.2 GENERAL STATISTICAL AN AL YSIS The primary statistics of a sample are the arithmetic mean (x), variance ( cr2) and standai·d deviation (cr). These numerical representations of distribution within the sample are used to describe the data and compare one sample (or presumed subsets of a single sample) to another. The assumption of a Gaussian distribution for the sample data is fundamental to the development of the geostatistical theory. 3.2.l SArvtPLE STATISTICS The arithmetic mean x of a sample is the sum of measured values L z(xi) divided by the number n of measurements in the sample or: L z(xi) (1) x= n The sample variance (s2) of a sample is the sum of the squared differences from the mean and represents a measure of the distribution of values about the mean: s2 =_1 :E(z(xi) -:x)2 (2) n-1 The sample standard deviation (s) provides another description of the data distribution and is simply the positive square root of the variance (s2), or: (3) s={;,-=-vn'.l L (Z(Xj) -X)' Equations 1 through 3 are parameters that characterize the sample to which they are applied. A frequency histogram allows for visual display of a sample's statistical analysis. This simple graphic provides an observation of the distributions in the sample. The mean (x) of the sample provides a numerical mark from which the variance (s2) and standard deviation (s) measure the distribution of the data about that mean. The symmetry of the histogram is described by the coefficient of skewness, which is calculated as: (4) L (z(xi) -xf Y= n(s3) Skewness is the second-order moment of the variance and the symmetry of the sample distribution is indicated by the sign of the coefficient. A positive Ymeans that the sample possesses a long tail of values to the right (above the mean) and a negative Yindicates a sample in which there is a long tail of values to the left (below the mean). Another statistical measurement of the shape of the distribution is provided by the coefficient of variation, Cy, defined as the ratio of the sample standard deviation to the mean: s Cv=­(5) x This is commonly applied to sample data sets in which the data values and the yare positive. A coefficient of variation greater than one indicates erratically high values within the sample. 3.2.2 NORMAL AND LOGNORMAL DISTRIBUTIONS A common distribution about the mean is the no1mal distribution. A normally distributed data set is commonly referred to as bell-shaped. Variance and standard deviation both indicate the spread of values about the mean. For many geologic and natural phenomena the data are found normally distributed when the data is transformed to log10 values. This is referred to as a lognormal distribution. In this case, we utilize the geometric mean (Y), where: Y=~TIZ(X)j, (6) in which Tiz(x)i are the products of the n measurements of the occurrence z(xi) (permeability). For this study, it is required that the data exhibit a no1mal distribution with a minimal amount of skewness. Other distributions of data are not valid for the assumptions of the geostatistical theories that follow and, while not discussed here, these are explained in detail for geologic applications in the works of David (1977), Davis (1973), Isaaks and Srivastava (1989), and Joumel and Huijbregts (1978). The above sequence of parameters leads toward the formulation of a mathematical expression for the expected measured values of permeability within a geologically-related sample area. The expression of expected occmTences depends upon the assumptions of the spatial behavior of the regionalized variable. This "spatial behavior" is the vectoral relationship of the function m(x) between the data points in the defined study area. In geostatistics, this spatial behavior is defined as the moment (the variance between values separated by a vector of length increment h) and the stationarity (the variance in Euclidean space) of the permeability. 3.2.3 MOMENT AND STATIONARITY The moment of the variable takes on two definitions. The theory of the first­order moment states that the expectation of a random vaiiable, E {Z(x)}, is the function m(x), or: E{Z(x)} = m(x). (7) The second-order moment is developed from the assumption for the random variable that stated that the disuibution of values is finite and within finite limits of variance. This is often called the "a p1io1i" vruiance of z(x) which is expressed as: Var{Z(x)} =E{[Z(x) -m(x)f}. (8) For two points, x1 and x2, the assumption of variance applies as a function of the random variable, where: C(x1, x2) =E{ [Z(x1) -m(x1)] [Z(x2) -m(x2)]}. (9) Equation 8 solves for covariance as calculated between the points x1 and x2. Finally, given the increment between the two points, the variance between the points is the semivariogram function y(x 1, x2), expressed as: (10) The introduction of a vector dimension h, representing the separation between x1 and x2. leads to the theory of stationarity in the random variable Z(x). Stationarity assumes that the mean and variance are true functions and are the same throughout the field of interest. This assumption is the groundwork for the "intrinsic hypothesis", which has the following properties (Journel and Huijbregts, 1978): 1) the mathematical expectation is, E{Z(x)} =m(x), for all x; 2) and, the vector h increment [Z(x) -Z(x+h)] is finite and variable for the set of all x and x +h. where h represents the direction and distance of separation between data points. Given the intrinsic hypothesis, the set of data pairs separated by the vector h are different realizations z(x) and z(x+h) of the set Z(xi)· In a purely homogeneous medium, the expected relationship between individual realizations of the random variable is constant regardless of the vector h. By comparison, in a heterogeneous medium, the relationship between two points is dependent solely on the vector h. The variogram function between the points x and x+h is: 2y(x. x+h) =E { [Z(x) -Z(x+h)]2}. (11) This last equation is the equation from which a variogram is created. 3.2.4 THE VARIOGRAM 3.2.4.1 General theory As explained above, the variance (or the standard deviation) of a sample describes the distribution of the regionalized variable. To find the variation from point to point in the 2-D realization of the data set it is necessary to use a different statistical tool, the vruiogram function, 2y{x, x+h}. By computing the squares of differences between the known data points z(xi) and Z(xi+h), it is possible to create subsets of the data related by h, the multiples of h, and the radial dimension ascribed to the vector h. The semivariance 'Y(h) is one-half the sum of the squared differences of the set of realizations z(xD for the vector quantity h, or: 1 n~) ., (12) y(h) = -h-~ { z(xi) -z(xi+h)} -. 2n( ) I=l By plotting the semivariance y(h) against the average separation distance of the data pairs that fit the description of the subset, it is possible to visualize the data set in the form of a graph. In addition to the distance component of the vector h, there are additional prerequisites for inclusion to the subsets of data for the computation of the variogram function. These requirements are the direction and window which serve to constrain the data within the subset such that the resultant values of semivariance describe defined vectoral quantities as are desired by the application to the geological context. The direction is the compass direction or rotational orientation to which the length quantity of h is to be defined for the subset. The window is the latitude or margin of spatial distortion to either side of the directional vector of length h at which the data pairs can be located for inclusion into the subset. Variations of the direction and window allow for the isolation of anisotropic trends in the distribution of the realizations z(~). The graph of the semivariance y(h) versus separation distance h is the standru·d means of presenting and interpreting the variogram function 2y(x, h). This graph has various expected shapes and associated terminology for the characteristics of these shapes. The primary of these is the spherical variogram (Fig. 15a). In theory of these shapes. The primary of these is the spherical variogram (Fig. 15a). In theory a regionalized random variable is given expectations E { Z(xi)} which are related by the function of the second order moment m(xi) to have values approaching the set of realizations z(xi) as the separation distance decreases (i.e., E { Z(xi+h)} z(xi) as h-+ 0). Conversely, as the separation distance h increases, the expectation for the regionalized random variable E{Z(xi+h)} becomes less correlatable to the realization z(xi). Finally, at some separation distance the correlation of the values will be undeterministically random (as white noise). The separation distance and the nondeterministic randomness of the variogram function 2y(x,h) are characteristic for the sample of realizations z(xi). These characteristic parameters are termed the range and sill of the variogram function 2y(x,h) for the vector h. In the graphic presentation of the spherical variogram, the sill and range are interpreted at the inflection of semiva1iance, ideally, this increases from near y(h) = 0 to a plateau of characteristic variance. The sill, or C(i)• is the characteristic variance limit at which yh) is (ideally) unchanging or (more practically) non-deterministic and characterized by a scatter of yh) values below and or above the sill C(i)· The range is the separation distance at which the relationship between z(xi) and Z(xi+h) becomes random, which is the zone of influence for the expectations of the regionalized random variable E{Z(xi)} based upon the vector h. The nugget effect is a perturbation of the spherical variogram (Fig. 15b) which is named from the observed disruption in the continuity of the rate at which y(h) increases at small separation distances. This is created by the sampling of a regional variable that exists as nuggets (e.g., gold) or as concentrated veinlets within the parent material. The immediate occurrence of a characteristic variance (C(o)) at the A) Spherical variogram model oli 20/i Average Distance B) Nugget effect on spherical variogram O+.o.............,....,...,.............................,....,...,........­ 0/i . 20 Ii Average Distance C) Pure nugget effect oli 20/i Average Distance Figure 15. Models of the standard variogram configurations. A) Spherical model, covariance approaches zero as /i--0. B) Nugget effect in a spherical variogram, immediate variance between values at the smallest distances. C) Pure nugget, all values vary about a characteristic sill. smallest intervals (h-+ 0) is the measure of the low-scale variability as expressed by the regionalized variable. An extreme condition of the nugget affected variogram is one in which the variogram is described as "all nugget". Such a variogram (e.g., Fig. 15c) indicates unfiltered randomness, or a white-noise signal, in the regionalized variable at the separation distances tested for in the data set. In this case, the observed phenomenon is either effected by another unaccounted for variable, hence the appellation of white­noise, or it otherwise falls outside of the definition for a regionalized variable. Another explanation may lie in the separation distance h used in the calculation of semivariance. For should the continuity exist at smaller separation distances than tested for in the sample collection, then the range will not be perceived in the computation of the variogram function 2y(x,h). Pe1mutations of the above variogram types are the developments of nested sets and that of the "hole effect" or saddles at distances beyond the range (Fogg, 1986). The concept of a nested set (Fig. 16a) incorporates the theory that a characteristic correlation (C(i» may exist for the regionalized random variable Z(xj) at more than one range. Given the assumption that the length h will detect such layered correlation, the variogram function 2y(x,h) will increase as h increases until the lowest order of characteristic variance is reached, at which the sill C(l) and range(l) are interpreted; then the values of y(h) will again be seen to increase as h increases until the next order of characteristic variance is reached at Cc2) and range(2). The nugget value is effectively the characteristic variance of 2y(x,h) at h =0 (i.e., Cco» and constitutes a first order nested set. Development of a saddle in the values of )'(h) after the interpreted range (Fig. A) Nested sets of variograms: first sill at 0.3 and range at 3. length units; 1.o second sill at 0.6 and range at 12. length units 0.6 ........... ........................:;;···,..·'"1'""----­ 0 .5 Y(ft) 0.3 3.0 12.0 0.-.........--.-.-.......................................................................... Oft 20ft Average Distance B) Development of a saddle or a "hole effect" in a variogram 1.0 Y 0.5 (ft } 20ft Average Distance Figure 16. Variations of variogram models considered in this study. A) Nested variogram sets indicating multiple correlation ranges (3.0 and 12.0) with characteristic variances for each range. B) Saddle or "hole effect' of increased covariance after an initial sill has been reached (Fogg, 1983). 16b) is seen as the lowering of variance at the multiples of h after the characteristic variance has been reached. The ideal saddle is one in which y(h) is seen to decrease and increase back to the original sill value and does not increase to a new plateau that may be interpreted as a nested variogram characteristic. The saddle or hole effect is an indication of recurrent correlation distances based on the characteristic length h. 3.2.4.2 The power-law variogram For a more advanced analysis of the permeability distributions, an intrinsic test function of the Euclidean geometries is suggested by Mandelbrot (1983) for self-similar regionalized variables. The form of the intrinsic test function is given as: hs(P) =y(D)po (13) where hs(P), the intrinsic test function is the fractal measure of S when S is the set of very small discs (in two-dimensions) or balls (in three-dimensions) which approximate an area (two-dimensions) or a volume (three-dimensions), h(p) is a function of the radii p of the shapes in the set of S. And the expression y(D)pD is the D-dimensional function for the standard shape of radius p, such that y(D) is the function of the contents of the shape with radius p (and related to, but not to be confused with, the use of y(h) in semi variance). The D-dimension is the Hausdorff­Besicovitch dimension (Mandelbrot, 1983) of Sand, if S is self-similar, then the similar dimension is equal to D. In this form and applied to a 2-dimensional shape defined by a self-similar regionalized variable, the intrinsic test function is a power­law relationship of the characteristic length p and the fractal dimension D. From the above function for a test of the fractal dimension D, the application to the variogram was suggested by Hewett and Behrens (1990) for variograms that exhibit a characteristic increase in sill and range which corresponded to an increase in the separation distance h. For that case, the power-law variogram model was developed by the superposition of variograms of different h. The mathematical expression for the power-law relationship for the variogram was proposed by Hewett and Behrens ( 1990) to be: y(h) =Yoh2H (14) where: y(h) is the mean-square vruiation of the regionalized variable as a function of h; yis the characteristic variance scale at a reference-unit of the separation distance h; 0 and H is the fractal codimension equal to the difference between the Euclidean dimension E in which the disuibution is described and the fractal dimension of the disuibution D, or simply stated E-0 (Hewett and Behrens, 1990). In log-transform, the power-law vruiogram function becomes the equation of a straight line: log("f(h)) = log(y0) + 2H log(h). (15) This power-law relationship provides 2H as the slope of the best-fit line through the superpositioned points of the combined variograms, log(y0) as the value of the characteristic variance value at the reference h=l (log10(1)=0), and log(Y(h)) as the function of the set of mean-square variation in the realizations z(xi) and z(xi+h) that tends to 0 with h. The relationship follows the theory of power-law relationships forwarded by Hewett and Behrens (1990) for identification of fractal relationships in reservoir heterogeneities and the above discourse on the intrinsic test function of Mandelbrot (1984) in studies of the fractal dimension of natural systems. The relationship between the intrinsic test function and the power-law variogram function rests in the dimensional quality of the fractal dimension D and the fractal codimension H (defined by D), the characteristic length properties of both p and h, and the functions hs(p) and y(h) which define sets of shapes in the Euclidean dimension based upon the characteristic lengths p and h, respectively. For the fractal codimension H the values have been found to generally vary between 0.7 and 0.9 for measurements of topographic features such as coastlines (Hewett and Behrens, 1990). CHAPTER 4 METHODS OF PERMEABILITY MEASUREMENT Permeability data were collected with the Mechanical Field Permeameter (MFP) and augmented by permeabilities estimated from core plug measured pe1meability. Permeabilities were calculated from steady-state flow and pressure values as recorded from flow tubes and dial gages, respectively, on the device. The particular MFP apparatus used in this study was constructed and calibrated by D. Goggin, for The University of Texas at Austin Petroleum Engineering Dept., through adaptation of published designs for air flow permeameters (Dykstra and Parsons, 1950; Eijpe and Weber, 1971). 4.1 MFP SAMPLE POINT PREPARATION The reason for using a mobile permeameter such as the Mechanical Field Permeameter was to create a "robust" sample of spatially disuibuted permeability realizations z(xj). A robust sample was one for which data were well founded upon the principles required for analysis. Application of the term "robust" in this context was defined as: 1) in definition, the measured variable (i.e., permeability) is conformed to by the measurement method, 2) the value of the variable was statistically representative of the location, and 3) creation of a sample that was sufficient for analytical review based on the statistical theory. As stated above, sampling with the MFP device required preparation of the 51 rock surface. The study by Ki midge ( 1988) was complicated by the practice of preparing the outcrop surface with a mechanical grinder. The impact of rock fines generation by the destruction of the outcrop surface was considered by Kittridge to be most significant for samples where the rock is in the lower range of permeability. This lower range of permeability, as defined by Kittridge, coincided with the lower range of detection for the mini-field permeameter. Therefore, another surface preparation method was required. Several swface preparation methods were tested: the mechanical grinder, a water saw, and a hammer and chisel. Prepared samples were viewed by scanning electron microscope (S.E.M.) for pore throat disruption effects of three possible surface preparation techniques. This analysis indicated that the surface exposed by breaking the rock (Fig. 17a) was less disrupted than the surfaces created by either the saw-cut method (Fig. l 7b) or the mechanical grinding of the smface (Fig. 17c). Figure 18 shows the typical markings on the outcrop after preparation with the hammer and chisel. Noticeable in the photograph are the outlines of powdered rock around the sample point. This exemplifies the problems encountered when applying laboratory results in the field. Obviously the hammer and chisel did not create a perfectly clean sample smface at the edge of the sample point. Therefore, sampling was conducted with the MFP nozzle-tip positioned inside of the chisel marks for each measurement. The inability to obtain data on an evenly spaced small scale grid was an unfortunate side effect of the smface preparation method on the outcrop using a hammer and chisel. With the mechanical grinder Kittridge (1988) was able to expose a continuous area of the outcrop for sampling down to one-half of an inch in an Figure 17. Scanning electron micrographs of rock surfaces subjected to three means of removing the weathered rind to expose the pristine rock matrix. (A -top) Broken rock surface exposing undisturbed dolomite crystals at lower left (arrow). (B -middle) Cut with a water saw, the end of a core plug retains curvaceous grain surface and pore throat with few white rock fines in view (arrow). (C -bottom) Mechanically ground rock surface is heavily littered with fine white rock particles, especially in the low areas of the pore throats, also flat ground surfaces are partially smeared (arrow) in the direction of grinder rotation. evenly spaced grid. Sampling in an evenly spaced grid has obvious advantages for equitable statistical analysis of the permeability in the vertical and horizontal, as well as at intervening angles if sufficient data is obtained. Because this was not feasible, the smallest scale of outcrop data collection was limited to straight-line sampling at one inch intervals along transects which connected further spaced sample points. Another significant problem in the field sampling program was the difficulty of maintaining a proper seal between the rock surface and the MFP's nozzle-tip. Fractures, large vuggy pore spaces, irregularities from large or cemented clumps of grains, and the chisel markings all combined in the difficulty of chipping away the weathered rind and exposing a large and flat unweathered surf ace. Initially, MFP measurements were pe1formed once or twice at each sample point within a newly chipped area. However, it was known that small scale heterogeneities did not guarantee a spatially representative realization of permeability z(xi) for a single sample point; therefore, a new sampling scheme was suggested which reflected the representative permeability at the sample location. This new sampling design was suggested coincidentally by D. Goggin and G. Fogg (personal communications, 1989) so as to make the most use of statistical interpretation of an average value for the sample point. Through the improved data collection method, multiple measurements were made in a single prepared "patch" (Fig. 19). Ideally, this "patch" was a chiseled-off square of one and one-quarter inch sides, and measurements were made in a five spot pattern to provide maximum separation distances inside the sample location. For the purpose of this study, the assumption was made that averaged values of the permeabilities measured in each "patch" were more accurately representative of i-------1.25"------4 disturbed edge of I 0 -·--·--··)> 0 I sample-I ;/ I patch I G) I~ \._I I L--~~~~I Figure 19. Typical MFP sampling of a hammer and chisel prepared "patch" showing the order and relative positions of the individual measurement sites. permeability values at a sample location. 4.2 CORE PLUG PERMEABILITY MEASUREMENTS The collected core plugs were sent for contracted analysis as part of the related projects conducted by the Bureau of Economic Geology Reservoir Characterization Research Laboratory. After collection from the outcrop with a portable drill, each plug sample was trimmed at both ends. The whole cylinders were sent for analysis while the trimmed ends were used to make thin section slides by the Core Research Center (CRC) division of the BEG. The data of permeability and porosity values were received for only those core plug samples which conformed to the requirements of length and regularity of shape as required for the Hassler sleeve method. This meant that not all of the collected core plugs were measured for permeability and porosity values. However, all of the sampled locations were available for microscopic review in thin section. 4.3 PERMEABILITY SAMPLING PATTERNS The permeability and porosity data were collected in four distinctly scaled grids with each smaller scale grid existing within the larger scale grid(s). The largest scale grid is herein referred to as GRID A. This incorporates the measured geologic sections provided by Kerans and others (1991) and covers nearly one-half mile of the first parasequence in outcrop on the Algerita Escarpment. Because the initial permeability measurements in GRID A indicated a region of high permeability values at the center of the grid, a second scale of investigation (GRID B) was prepared as vertical transects intended to follow the trend of the high permeability values. The third and the fourth grids (GRIDs C and D) followed in turn as the investigation delved into increasingly smaller scale. For individual referencing, all of the sample points have been assigned "x"­and "y"-coordinates based upon a combination of aerial photographs (for large distances) and real ground measurements (for small distances). In this manner, the sample points have been assigned a distance from an arbitrarily positioned "zero" coordinate to the north of the study site and measured vertically from the base of the first parasequence. GRID A was the most laterally extensive in area and included all of the genetic facies described in Chapter 2 (Geology). The sample pattern of GRID A included the sixteen measured geologic sections described above and was augmented by infilling vertical transects (Fig. 20) in the northern section of the study area. The average separation distance between transects on the no1th-side of the canyon (transects Al ­A 16) was less than that of the south-side of the canyon (transects A 17 -A23). This was the unfortunate result of the loss of exposed outcrop in the south by talus from the overlying parasequences. However, the few vertical transects on the south-side of the canyon allowed for a laterally extensive view of the permeability values. GRID B (Fig. 21) was located between the transects A15 and A16 of GRID A. This was the direct result of the preliminary permeability measurements in the study site which at the time had included the u·ansects referred here as B1, B2, B3, B4, B5, B 12, B 13, and B 14. The addition of six (6) more closely spaced u·ansects in between B5 and B 12 were intended to detail a high permeability zone where the N s Algerita Escarpment northward of Lawyer Canyon Re-entrant area of Lawyer Canyon ...;.;~~. .................................................................................................................. ............................................................................ ....................................................................~~=~::-;-•.•:;:;~~~···•·••.•.•.• .•• •.o.••.••••.•.••.o•.•.•.o.•.• •.••.• •.o.•n .•.••.-.o.o.•.•.•.•.•.o.•.o.o.••.•.o.•.•.•.•.•.o.•.o•.•.•.•.•.o.•.o.-.•.•.•.•.•.•.o.•.•.•.•.•.•.•.• 30 A 25 . ] 20 ai' u @ ..... 5 1 • 1 0 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 Horizontal distance, feet • combined core plug and MFP samples o core plug samples • MFP samples Figure 20a. First of two figures that show the san1ple point locations used in the GRIDA data set. Shown are the relative positions of the points and transects san1plcd with the MFP and/or core plugs. Perspective is facing east from Big Dog Canyon toward the Algerita Escarpment. Also shown are the identified genetic facies #1 through #4 (see Fig. 10). ~ N S L.C. re-entrant Algerita Escarpment southward of Lawyer Canyon . ;::::~j···.,-· ·--··· .........·.········i~:::::.·· ·~-:~:;~·.... .,. ....... ................... ............. . .. ....,. . ... .,. .... . ...... .. ......... ... ....... .............. ... ,.,.,. . ..... .......... . . ......,,.,. ... . . ..... ,. ··· · ······ · ·· · ·· · · ····· · · · · .....·· · ··. ·· · ··· · · · · .. ...... . ... .. . .. ....... .... -....-.. ..... .... ...........,...,. ..... ·· · .·· ··· · · .-.-.-..-.·.·····.·:$:~~:.· · A22 A23 :::::· ::::>:­ .. .... Alr·2......o A·. ·.·2. ·.·.. ·. ~·1 ' I =g 0 0 0 0 0 0 0 0 1 0 0 0 0 . IB 0 0 . 1 0 • 0 30 25 20 -<:i ;)' a 0.. 15 ~· Ill ::i (') ,Ill 10 if .... 5 111111111111111111111111111"'I'11111"'I"1111111p1""'11p11 "'"'I"' 111111p1111111111111111111"'"11111111111 "'I'""' 11q1111111 ul 0 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 Horizontal distance, feet • combined core plug and MFP samples O core plug samples • MFP samples Figure 20b. Second of two figures that show the san1ple point locations used in the GRIDA data set. Shown are the relative positions of the points and the transects sampled with MFP and core plugs on the south side of Lawyer Canyon. Also shown are the boundaries of the genetic facies #l through #4 (see Fig. 10). ...... °' GRID B Sample Locations N s Transects: Bl B2 B3 B4 B14 30 Top of para­sequence 1 • • • :!:'!I •• • • • Facies# 3 : : : : ~11l~I~: •••• ~=i::i::. •• (bar crest) • • • ; •• ~1~~1 • • • ;::$]P• • • Facies # 1 • • • •• (flooded shelf) I I I I I I 950 1000 1050 Horizontal distance, feet C: MFP sample positions) Figure 21. Sample point locations of GRIDB data set. The vertical and horizontal distances correlate with the coordinates used in GRIDA. The fades boundary positions have been extrapolated from the geologic sections of Kerans and others (1990). N °' outcrop was well exposed and accessible. The average separation distance of the transects in GRID B actually existed in two lengths: the original eight (8) transects at thirty-five (35) ft. intervals, and the additional six (6) transects at five (5) ft. intervals. Included within the sampled boundaries of GRID B were rocks of the facies #1 and #3, though it should be noted that facies #1 was available in only a few of the transects and in poor quality for sampling of the permeability. GRID C (Fig. 22) was planned as a regular one-foot square grid overlapping transects B 10 and B 11 of GRID B. Similar to GRID B, this grid pattern was designed to identify the small scale continuity of a high permeability zone that was observed to continue through GRID B from GRID A. The positions of the sample points were of too small a scale to be corrected for in the aerial photographs used to locate positions in GRIDs A and B, therefore the horizontal coordinate positions of GRID C are relative to themselves and not to the coordinates of GRID A. The position of GRID C was in an area of broad exposure on the outcrop which allowed for the construction of a regularly spaced grid, but the location was also one were the entire vertical section of facies #1 was covered. Therefore, the permeability data set of GRID C includes only permeability values taken from the outcrop in the facies #3. GRID D (Fig. 23) followed the progression to smaller scales to a separation distance of one inch between measurements. Even more so than in GRID C, the small scale (one inch) separation between sample points precluded the use of aerial photographs to correlate positions in the coordinate system as in GRIDs A and B. The surface preparation of sample points in GRID D was too destructive for an equally spaced small scale grid. Since the entire sampling area of GRID D was within that of GRID C, then it follows that the permeability values are representative of facies #3. GRID C Sample Locations N s 1 5 j • ..... Q) • • • • • • .. • • • • • ~ Q) u 10 i:: ro ..... V) ·­ "O -ro u ·-..... 5 ~ Q) :11~11::::::· > • • • • • • • Area of • • • • • GRIDD O-+-......---..-----.------.........,....-......--.--.---.---.---.---.--.----.--.-------.---.---. ~ 0 5 10 15 20 25 Horizontal distance, feet t MFPs;~~i~S) Figure 22. Sample point locations of GRIDC data set. The vertical and horizontal distances do not correlate with the coordinates used in GRIDA. The position of the grids within the bar crest grain-dominated genetic fades #3 (as seen in Figure 20). ~ GRID D Sam,12le Locations N s Horizontal distance, inches 0 10 20 30 40 50 0 I· I I I I I I I I I I I I I I I I I ~ i ••••••• •·•••••••••••••••••••••••••••••••••••••· ••• Q) ~ • • • • ...s::: u s:: 1O.J • • • • ·­ Q) u s:: ~ ..... ;aV,) ••••••••••••••••••+ •• 20.J • • • • -; u ·-..... • •• • •$.... Q) •• • • • > • • • I (.MFr..~~~·~i~..~-~~~~~~S) 30 Figure 23. Sample point locations of GRID D data set. The vertical and horizontal distances do not correlate with the coordinates used in GRID A. The entire grid is located completely within the grain-dominated bar-crest fades #3. 0\ Va CHAPTER 5 DAT A AND RESULTS Permeability data collected from the outcrop were analyzed using various methods in order to illustrate, support, and further define the results of statistical correlation based on the previously identified samples of grids and facies. Contour maps of the digitally posted data were created for each of the grid samples to illustrate whether identifiable continuities existed within the samples. Histograms and probability plots provided graphic evidence that the permeability data were lognormally distributed. The coefficients of variation (Cv) were calculated for each sample data set and compared to determine whether the sample data sets were representative of the same sample. Semivariance values (y(h)) were calculated for both vertical and horizontal search directions with step (lag) distances conforming to the scales in the various samples. Experimental variograms of semivaiiance (y(h)) vs. average separation distance were interpreted for range and sill estimates of covariance within the permeability data. Horizontal variograms were overlaid on logarithmic axes to solve for 2H, the fractal codimension, in the power-law equation (see Eqn. 13). The value of the fractal codimension was anticipated to determine the validity of a hypothesis concerning the scale dependent correlation of permeability distribution. 66 5.1 PERMEABILITY AND POROSITY DATA The permeability data analyzed in this study are representative of two measurement techniques, the MFP surface permeability method and the Hassler­sleeve method for core plugs. Previous studies by Goggin ( 1988) and Kittridge ( 1988) demonstrated the accuracy of the MFP derived permeability data when compared with the more conventional Hassler-sleeve permeability data from core plugs. Because the two methods are comparable, incorporating the permeability data derived from the core plugs augments the data derived from the MFP, most significantly for the low permeability range (less than 1 md). 5.1.1 MFP DATA Appendix A contains all of the MFP permeability measurements which were used in this study. MFP measurements which recorded no observable gas flow (below detection limit, or bdl) were included. The bell measurements were assumed to be non-zero, low-permeability measurements (less than 1 md). However, the assignment of definitive values for those measurements would have been statistically unsound, hence the bdl measurements were dropped from the samples for the statistical analyses. As stated above, this limitation of the MFP device was anticipated and partially compensated by the inclusion of core plug permeability data. 5.1.2 CORE PLUG DATA Core plug sampling extended over a wide area compared to the MFP sampling. This wide spread sampling provided porosity and textural data for the various rock fabrics, as well as providing additional permeability data. Core-plug permeability measurements were most valuable where MFP data was not collected or where permeability values were below detection range for the MFP (i.e., in the mudstone of the flooded shelf and shallow shelf facies) in order to provide more robust data. Figure 24 shows the locations of the core plugs in vertical transects where they were collected. By themselves, the core plug permeability data are too widely dispersed to be analyzed through va.riograms for the goals of this investigation. Core plug collection destroyed the rock surface and sampling was unreproducible for a precise position. In this respect, the collection of core plug permeability values was not conducive to the generation of a robust sample of data, but combined with the MFP permeability data made the entire sample of pe1meability data more robust. Appendix B contains the permeability and porosity data from core plugs in the first parasequence. In the core plug collection, there were cases where more than one core plug was collected from the same coordinate location on the outcrop. The data in Appendix B shows the low variability among these dual samples. The low variance was an advantage of the core plug data collection which was not shared by the MFP data collection. The advantage of the core-plug pe1meabilities low variance at closely spaced sample points allowed the assumption to be made that the core-plug values were less influenced by small scale heterogeneities, and therefore more representative of the average permeability for a sample point. Core plug sample locations 25 ~ 20-I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...... 1 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (!.) ~ 0 0 0 0 0 0 0 0 0 0 0 0 c:: .9 ...... C<:l > (!.) ti3 10 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 500 1000 1500 2000 2500 3000 Horizontal Distance, feet Figure 24. Location of core plugs in the first parasequence study site, Lawyer Canyon. Distances conform to those of GRID A locations, as shown in Figure 20. 0\ '° 5.2 STATISTICAL ANALYSES OF SAMPLE DATA The variogram function 2y(x,h) is based on the premise that the regionalized variable (i.e., permeability) displays a normal or lognormal distribution about the mean of the sample. In the previous studies of permeability distributions on the San Andres formation outcrop of the Guadalupe Mountains (Kittridge, 1988; and Hinrichs and others, 1986), permeabilities were found to approximate a lognormal distribution. The data for this study was also found to exhibit lognormal distributions. In the following section, the data for each of the previously identified sample sets (GRIDs A -D and genetic facies #1 -#4) were each analyzed for the parameters of a lognormal distribution and then presented with results from the interpretations of experimental variograms. The experimental variograms presented in this section were calculated for horizontal (0°) and vertical (90°) search directions, with step increments (h) based on the (ideal) average distance between transects (GRIDs A, B, and D) or the spacing in a regular grid pattern (GRID C). Additional experimental variograms were created for other step increments for analysis and comparison of the sample data. 5.2.1 GRID A The largest sampled grid in area and in number of measurements, GRID A is the only sample set to include data from all four of the identified genetic facies. A contour map of the log-transformed GRID A permeability values was created (Plate 1) for a contour interval of 0.25 log units. The most notable relationship between rock fabric and permeability is the bottom-to-top correlation of increasing permeability with the coarsening of the grain fabric (see measured sections presented above in Fig. 21). This illustrates permeability variation between facies #1 (generally low permeabilities) and the overlying facies (generally higher permeabilities). No other obvious facies and permeability relationships have been deduced from the contour map of GRID A. Also from the contour map of GRID A data, permeability heterogeneities are interpreted for vertical and horizontal directions. Permeability varies over two orders of magnitude between sample points one foot apart along the individual vertical transects of the GRID A sample data. Transects Al, A3, AIO, and Al6 are noted for such vertical permeability variability between consecutive one-foot spaced sample points. These fluctuations suggest that vertical heterogeneities exist on, at least, the one foot scale. Horizontally continuous permeability relationships are only obse1ved in the relationship of the average low values of facies #1 and the average high values in the overlying facies (#2 -#4). The relatively wide horizontal separation distances (35 feet to 350 feet) between vertical transects provide neither proof of dramatic changes in permeabilities nor proof for horizontal continuity of permeabilities across the transects. In the most densely sampled area, the northern half of GRID A (transects Al -Al5), the complexity values suggests that horizontal pe1meability heterogeneities exist at smaller scales than that of the GRID A sampled pattern. Statistics for the GRID A log-transformed data (Fig. 25) indicate a deviation from lognormality in the low permeabilities range. In a frequency histogram, the tail of low permeabilities below 1 md is characterized by the negative coefficient of skewness (-0.739). In the same low permeability range, the plot of log-transformed GRID A data on probability paper produces an observable deviation from the ideal Frequency Histogram and Probability Plot Sample: GRID A data 99.99 5.TAIISIICAL PARAMETERS: non-tranformed log10 transformed 99.9 n 320 320 99.8 mean 37.716 1.04 standard dev. 86.702 0.767 • 99 variance 7517.205 0.588 - ~ - 0.01 1.0 10.0 100.0 1000.0 Permeability (md) Figure 25. Frequency histogram and probability plot graphs for GRID A san1ple data. Data shown to exhibit lognormal distribution with exeption in the low permeability range (i.e., <1.0 md), corresponding to bdl range for MFP. The negative and relatively high coefficient of skewness corresponds to this observed deviation from lognormality. straight-line pattern for lognormal distribution. The offset between the straight-line relationships <0.1 and >1.0 md on this probability plot indicates a possible bimodal distribution for the data sample. However, mean and standard deviation values of the log-transformed data (1.04 or 10.959 md and 0.588 or 3.87 md, respectively) conform to a lognormally distributed sample (i.e., the standard deviation was less than the mean). Removal of the core-plug derived permeabilities from the sample data results in a better fit to a lognormal distribution. For the restricted sample data, the deviation from lognormality in the low permeability range ( <1 md) is not present in the probability plot (Fig. 26), and the mean (1.137 or 13.713 md) is greater than the standard deviation (0.767 or md). The most significant change in the data statistics is the change in the coefficient of skewness from negative to positive and closer to zero. Alternatively, statistics for the non-transformed GRID A data do not confo1m to the model for a normal distribution. The data statistics for mean (37.716 md), standard deviation (86.702 md), va1iance (7517.205), and skewness (6.023) are not indicative of a normal disuibution. In frequency histogram and cumulative probability plot (Fig. 27) presentation the non-no1mal disttibution is plainly observed. Horizontal semiva1iance calculations made on the GRID A data (Fig. 28) provides the most significant variogram interpretations for h = 100 feet. This experimental horizontal variogram is interpreted as two sets of nested spherical variograms. Interpretation for a nested variogram model indicates an initial nugget value (C) and 0.497 (C(2>), for ranges of 253.5 feet (r(l>) and 748.3 feet (r(2)). Beyond the second range value (r(2)). the calculated Frequency Histogram and Probability Plot MFP Sampled Locations Only S,TATISTICAL PARAMETERS: non-tranformed log10 transformed 1.0 10.0 100.0 1000.0 Permeability (md) Figure 26. Frequency histogram and probability plot graphs of a restricted sample populaation of the log-transfonned GRID A data, only the MFP penneabilities. Removal of the core plug penneability data produced a slight down-tum in the low­penneability end of the cumulative probability plot, an increase in the mean, and a shift to positive value for the coefficient of skewness. 99.99 99.9 99.8 99 98 95 - 90 ~ - 80 ~ u s:: 70 Q) ::s 60 i 50 .... i:i.. 40 Q) 30 ....> .... t'3 20 -::s s 10 ::s u 5 2 1 0.5 0.2 0.1 0.05 0.01 n 489 mean standard dev. variance Coef. of var. skewness kurtosis 60 50 ~ 40 u s:: Q) 30 ::s O' Q) • .... 20 i:i.. 10 0 489 Frequency Histogram and Probability Plot Sample: GRID A data • non-transformed SIADSIKAL fARAMEllB.Si non-tranformed log10 transformed n 236 236 mean 83.5 1.526 standard dev. 166.8 0.552 variance 27,824.2 0.304 Coef. of var. 1.998 0.362 skewness 4.07 0.377 kurtosis 17.43 0.17 • • •• • • • • 200 175 150 >. u 125 c Cl) :::3 100 O" Cl) ... 75 50 25 f..t. 99.99 99.9 99.8 • 99 • • • • 95 - 90 ~ - 80 >. u c 70 Cl) :3 60 O" Cl) 50 ... f..t. 40 Cl) 30 > ~ - ~ 20 - :3 10 8 :3 u 5 2 1 0.5 0.2 0.1 0.05 0.01 200 300 400 500 600 700 800 Permeability (md) Figure 27. Frequency histogram and probability plot graphs of nontransformed GRID A data. The data do not exhibit a normal distribution in either the shape of the histogram nor the curve of the cumulative frequencies plotted on probability axes. 1. 0.8 0. YrliJ 0.4 direction: 0° Horizontal Variogram: GRID A window: 0° lag distance: Ii= 100 ft. • • cr2 = 0.566 '"' 0.497 ·.·.-.......... ····· ···" ····· ...... ······ .,.,....."...........-........._,______________,....11................................ ,,.....-. . . : /" : . . 0.305 ... ...::1("---~ .I ,,,.,:; , ' ~­ 0.2 0.2 ; , 253.5 : 748.3 0. 0 500 1000 1500 2000 Average Lag Distance, in feet Figure 28. Horizontal variogram of GRID A data, Ii= 100 feet. The variogram has been interpreted for nested variograms with an initial nugget. Nugget (C\0) =0.2; range(r0 i) =253.5 ft.; sill (C0 i> =0.305; range(r(2)) =748.3 ft.; sill (C(2)) =0.497; sample population variance (cr2 = 0.566). Legend • n;::: 30, statistically significant c n < 30, not statistically significant semivariance values are scattered about both the estimated sill (C(2)) and the data statistic of variance ( cr2 = 0.588). The experimental vertical variogram for h = 1 foot (Fig. 29) provides a distinct linear relationship for semivariance and average separation distances. This is followed by a precipitous drop in semivariance values beyond the average separation distance of 13 feet. This drop in semivariance coincides with a decrease in the number of data pairs used in calculating semivariance; from a peak of 268 at 1 foot, to 57 at 13 feet, 41 at 14 feet, and 30 or less for average distances of 15 feet and greater. The initial linear relationship exhibits a possible nugget value (0.162) based on a well fit line (R2 = 0.986). Beyond the average separation distance of 13 feet, calculated semivariance values decrease in a nearly linear fashion, hence, neither sill nor range values were estimated. 5.2.2 GRID B The contoured posting of the GRID B sample permeability data (Fig. 30) exhibit similar distribution characteristics as GRID A. The pattern of the contour lines is complex in the areas of densest sampling (transects B5 -B 12), indicating heterogeneous permeability distributions at the smallest scale of the grid. Also as noted in the GRID A sample data, permeability values generally increased in value from the bottom to the top of the vertical transects. In contrast to the contour map of GRID A sample data, continuous high permeability streaks are observed in GRID B. In GRID A, the high permeability occurs as isolated zones against a background of average low permeability, whereas transects B2 -B5 and B9 -B12 are connected by tongues of high permeabilities. 1. 0.8 0.6 YrnJ 0.4 02 · direction: 90° Vertical Variogram: GRID A window: 0° lag distance: fi = 1 ft. / •./ /.,/'• . -~ . 80 u s::: 70 Q) = 60 O" Q) 1-o so ~ 40 30 ~ .... -~ ~ 20 = e 10 = u 5 2 1 0 .5 0.2 0.1 0.05 0 .01 direction: 0° Horizontal Variogram: GRID B window: 0° Jag distance: Ii= 10 ft. 1. c 0.8 c c c 0 so 100 150 200 250 Average Lag Distance (feet) Figure 32. Horizontal variogram of GRID Bdata, Ii= 10 feet. This variogram was interpreted for a single nugget effected variogram. Nugget (C(o) =0.32; range(r0 i> =22.2 ft.; sill(C0 i) =0.57; sample population variance (cr2) = 0.558 . r Legend • n ~ 30, statistically significant \... c n < 30, not statistically significant~ 83 As in the above horizontal variogram, the initial slope and sill of the experimental vertical variogam is a poor match to the spherical variogram model (Fig. 33). The initial y(h) value is high (0.313) and is followed by a slope of three y(h) values. After this initial short range (4 feet) and sill (0.44), another four points form a second slope from which second values for range and sill are estimated (10 feet and 0.71, respectively). This variation of the spherical variogram model indicates a correlation of permeability values in the GRID B sample data at two scales with individual characteristic variances. 5.2.3 GRID C Located within the densest sampled area of GRID B, GRID C represents an attempt to determine the continuity of the high permeability zones at a smaller scale. Separation distances of the data in GRID C are an equal one foot distance in the vertical and the horizontal, except for a central patch of one-half and one-third foot separations. The contoured pattern (Fig. 34) exhibits both horizontal and vertical heterogeneities. A near continuous horizontal streak of high permeabilities is extends across the upper middle section of GRID C, and correlates the nearly continuous high permeability streak observed in GRID B. The probability plot of GRID C data (Fig. 35) indicates the most definitively lognormal distribution of all the other sample data, although there is a slight deviation at the high permeability values. The frequency histogram also indicates a lognormal distribution because of the very symmetrical bell shape to the histogram, this correlates with the sample's low coefficient of skewness (0.377). Mean and standard deviation values of the log-transformed sample data (33.60 md and 3.565 md, direction: 90° Vertical Variogram: GRID B window: 0° lag distance: fi = 1 ft. 1. • c c• c c 0.8 c 0. 0.4 0.2 0.71 c :~-~~-~;--7r-~-~-~--------~ --.cr'2 =0.558 /~ I c ;-! f E 0.2 c i I I I E 4.0 I 10.2 o.r.....~~~~~~..-~~~....,.;.~~~~~~~~~~~~~~~~ 0 5 10 15 20 25 Average Lag Distance (feet) Figure 33. Vertical variogram of GRID B data, Fi= 1 foot. Nested sets of two variograms with an initial nugget effect are interpreted for this example. Nugget (C<0J) =0.2; range(r1n) =4.0 ft.; sill (C11 ,) =0.44; range(r\2>) =10.2 ft.; sill(C(2)) =0.71; population variance (cr2) =0.558 . / Legend • n ~ 30, statistically significant \.. c n < 30, not statistically significant,, 0 5 10 15 20 O) = 0.165, range tJ = 2.1 ft., sill(!)= 0.34; sample population variance (cr'.!) = 0.321 . Legend • n ~ 30, statistically significant c n < 30 , not statistically significant 5.2.4 GRID D As stated above, GRID D is located at the center of GRID C, entirely in the wackestone/packstone fabric of the transition zone between the mud-dominated facies #1 and the grain-dominated facies #3 (see Fig. 22, p. 64). Due to the site preparation method and the small-scale of the investigation, the data are not composed of averaged MFP measurements for each location, but rather the direct representation of a single measurement. In that respect, the site is unique among the scale-based sample data sets. The combination of the singular MFP measurements and the location of the giid, resulted in a relatively high number of points for which no data are available due to the detection limit of the MFP device. Unrecovered data are noted for 15 of the 196 sampled locations (7 .65% ). The lack of these assumed low permeability data is perceived as a sampling bias which affects the sample statistics in the manner of elevating the mean and decreasing the variance. The GRID D sample data are contoured on Figure 38, they exhibit a dominant matrix of low average permeability smTounding localized zones of high and low permeabilities. The heterogeneity of permeabilities in the vertical and horizontal transact lines are not conducive to the contoming algorithm, this was observed in the high and low permeabilities which followed the grid pattern as viewed against the background averaged permeability as drawn by the CPS-1 program. Frequency histogram and probability plot presentations of the log transformed sample data (Fig. 39) indicates that the distribution is weighted to the low end of the permeability range. The histogram shape is nearly flat for the 0.6 md to 100 md range, exhibiting two modes and a short tail of high values. The cumulative frequencies plotted on a probability graph vary slightly from a straight-line. These 5 10 15 20 25 30 35 40 45 25 25 20 20 15 15 10 10 5 5 0 5 10 15 20 25 30 35 40 45 50 0 < 0.0or1.0 md El < 0.7S or 5.623 md 11111 < 1.5or31.62md II < 2.25 or 177.8 md II < 3.0or1000.0 md EJ < 0.25or1 .778 md El< l .OorlO.O md II < 1.75 or 56.234 md II < 2.5 or 316.2 md II < 3.0 or 1000.0 md EJ<0.5or3.162md mJ < 1.25or17.78 md II < 2.0or100.0 md II < 2.7S or 562.3 md horizontal heterogeneities are observed and are especially noticable about the sample points. The complexity of the heterogeneities created difficulties in the ability of the computer software to contour the data, this resulted in uncontoured areas, unconnected contours, and other contouring mistakes in the figure. ...... "° Frequency Histogram and Probability Plot Sample: GRID D data n mean standard dev. variance Coef. of var. skewness kurtosis 30 20 0 1000.0 99.99 99.9 99.8 99 98 95 90 80 ­ ~ 70 ­60 50 40 30 20 10 5 2 1 0.5 0.2 0.1 0.05 0.01 Figure 39. Frequency histogram and probabiilty plot graphs of GRID D data. The data exhibit a lognom1al distribution with a slight deviation in the low pem1eability range (i.e., <1.0 md). This is seen as the presence of two modes in the histogram and the sinoidal curve of the cumulative frequncies in the probability scale graph. observations of non-characteristic logn01mality are not significant to the assessment of a Gaussian distribution for the sample data. Statistics of the sample data confirms a lognormal distribution, while the statistics of the non-transformed data were not representative of a normal distribution. For the log-transformed data, the geometric mean (12.089 md) is greater than the standard deviation (5.598 md), and the skew is very low and positive (0.051). These indicate that the log-transformed data are well-behaved about the mean. In contrast, statistics of the non-transformed data follow a similar non-Gaussian model as observed in the other non-transformed sample data sets. Experimental horizontal and vertical variograms (Fig. 40 and Fig. 41, respectively) of the sample data were analyzed for the step interval (h) of 1inch. The experimental horizontal variogram (psi =0°) displays the characteristics of a well developed spherical model, with a relatively low nugget (0.256) based on a range of 7 inches and a sill (0.378) which is significantly less than the sample variance (0.559). The experimental ve11ical vaiiogram is relatively poorly developed, exhibiting a slope based on the initial two semivariance values which is followed by an increasingly scattered sill. The overall shape of the vertical variogram differs from an all-nugget variogram model by the initial semivariance value calculated for a lag increment of 1 inch. The nugget indicated by the vertical variogram is 0.35, only slightly lower than the sample variance value of 0.559, which itself is very close to the estimated sill value (0.54). direction: 0° Horizontal Variogram: GRID D window: 0° lag distance: Ii= 1 inch 1.0 0.8 0.6 a Yr!iJ D Cl 0.4 a a Cl Cl Cl Cl a aa ···· c· ··· D D cr2 = 0.304 0.2 I I 9.0 O.O-+-,...-.--.-.,.....,.-.-.........,.-+--.-...-.--.-..........-.-.........-.-...--.,.........,.....,........-.-.,.....,.-.-.........,........................-.-..........~ 0 5 10 15 20 25 30 35 40 Average Lag Distance (inches) Figure 40. Horizontal variogram of GRID D data, Ii= 1 inch. A singe nugget affected variogram is interpreted for this example. The variance is highly vaiable at the intermediate distances indicative of undeveloped nested sets or "hole effects" in the statistics. Nugget (C .... ns .... ::s e ::s u Figure 43. Frequency histogram and probability plot graphs for facies #2 data. The data exhibit attributes of a lognonnal distribution in cumulative frequency plot, but the low coefficient of skewness and low relief over short range in histo­ gram were difficult lo interpret due lo the small size of the sample population (29). Frequency Histogram and Probability Plot Sample: Facies #3 data STATISTICAL PARAMETERS: non-tranformed log10 transformed n 617 617 mean 85.85 1.460 standard dev. 174.6 0.629 variance 30,465.9 0.396 Coef. of var. 2.034 0.431 skewness 4.003 0.245 kurtosis 18.313 -0.245 1.0 10.0 100.0 Permeability (md) 1000.0 99.99 99.9 99.8 99 98 95 90 ~ - 80 70 60 50 40 30 20 10 5 2 1 0.5 0.2 0.1 0.05 0.01 Figure 44. Frequency hstogram and probability plot graphs for Facies #3 data. The data exhibits lognormal distribution in both the shape of the histogram and the close fit of the cumulative frequency to a straight-line. The shallow shelf, mud suppo1ted wackestone facies (#4) of the southern end of the parasequence is poorly fit to the lognormal model of distribution. The sample data for the facies include some or all of the core plug data of transects A19, A20, A22, A23, and A24. In the probability plot and frequency histogram (Fig. 45), a deviation from the lognormal distribution is observed in the below detection limit (bdl) range of the MFP device. This deviation is also observed in the relatively high negative value of the coefficient of skewness (-0.431). The statistics of the log­transformed sample data supports the graphical observations, since the mean (10.955 md) is greater than the standard deviation (5.689 md). 5.4 COMPARISON OF SAMPLE PERMEABILITY DATA SETS Determination of whether the four scale-based data sets and the facies-defined data sets were representative of a single total population of permeability data was necessary in order to fulfill the above mentioned assumptions for the behavior of permeability as a regionalized variable. These assumptions were that the ­permeabilities measured in the parasequence, uSAl, were randomized occmTences of a natural phenomenon and were sample statistics of a total population which was characterizable as a function (m [x]) with a single mean value and a Gaussian distribution (i.e., lognormal). The method for comparing the sample data sets and determining whether these were representative of a single population was the calculation of the coefficients of variation (Cv) and an ANO VA (one-sided test) comparisons for each sample data set. Frequency Histogram and Probability Plot Sample: Fades #4 data 99.99 SIAilHI~ALfARAMEUR~i n mean standard dev. variance Coef. of var. skewness ~ u s:: non-tranformed 32 36.67 72.06 5, 192.54 1.965 3.748 log10 transformed 32 1.04 0.755 0.571 0.726 -0.431 • Q) 4 ::s C" Cl) ~ ~ 2 0 0.1 1.0 10.0 100.0 Permeability (md) 99.9 99.8 99 98 95 - 90 ~ - 80 ~ u 70 = Cl) ::s 60 8' 50 ~ ~ 40 Cl) 30 .....> ~ Clj 20 -::s 10 e ::s u 5 2 1 0.5 0.2 0.1 0.05 0.01 The coefficients of variation compared the sample statistics as the ratio of the mean to the variance for each sample data set (fable 1). This method of characterizing the shapes of the distributions provides a simple comparison between the sample data sets. For all sample data sets, both scale-based and facies defined, the coefficient of variation values calculated for statistics of the log-transformed data falls within a closer range than the CV values of the non-transformed data. The Cv values for statistics of log-transformed data are closely related and describable in two groups with one outlier. GRIDs A, D, and facies #4 (values between 0.517 and 0.565) comprise one group, and GRIDs B, C, and facies #2 and #3 (values between 0.199 and 0.391) comprise another group. The CV calculated for the facies #1 statistics is the greatest outlier of the sample data sets, possibly indicative of the high ratio of core plug permeability data associated with that sample data. Though slightly dissimilar, these CV values do not disprove the hypothesis that the above data sets represent related samples of a larger population. Determination of the relationship between the samples of the GRIDs permeability data in the terms of whether the sample data represent a larger population, in this case the population of permeability data for the entire parasequence, was deemed necessary in order to substantiate further discussion in which the variogram parameters of the samples were to be grouped and analyzed. The means for this comparison is through the statistical method of analysis of variance (ANOVA). The null hypothesis (H0 ) tested was whether the comparison of the sample means are significant at a 5% level, and this test was conducted through a one-way (regressive) analysis for a 5% level of significance. The ANOV A test was analyzed TABLE la STATISTICS OF UNTRANSFORMED DATA Number in Sample Mean (md) Geometric Mean (md) Standard Deviation (md) Variance Coefficient of Variation Minimum Maximum Coefficient of Skewness GRIDA 320 37.716 10.959 86.702 7.517.2 199.311 O.Dl 827.0 6.023 GRIDB 221 109.8 27.14 214.2 45.873.8 417.794 1.215 1388.5 3.301 GRIDC 236 83.5 33.60 166.8 27.824.2 333.224 1.284 1066.55 4.07 GRIDD 176 42.4 12.089 74.0 5.476.1 129.153 0.786 460.31 3.24 FACIES #1 91 5.652 2.31 8.112 65.802 11.642 0.01 46.285 3.285 FACIES#2 29 14.166 7.874 15.181 230.453 16.268 1.047 52.891 1.218 FACJES #3 617 85.851 28.872 174.545 30.465.928 354.87 1.215 1,388.461 4.003 FACIES #4 32 36.672 10.955 72.059 5.192.54 141.594 0.15 382.613 3.748 TABLE lb STATISTICS OF LOG-TRANSFORMED DATA Number in Samo le Mean (md) Geometric Mean (md) Standard Deviation (md) Variance Coefficient of Variation Minimum Maximum Coefficient of Skewness GRIDA 320 1.04 - 0.767 0.588 0.565 -2.0 2.917 -0.739 GRIDB 221 1.434 - 0.748 0.560 0.391 0.084 3.143 0.279 GRIDC 236 1.526 - 0.552 0.304 0.199 0.109 3.028 0.377 GRIDD 176 1.082 - 0.748 0.559 0.517 -0.105 2.663 0.051 FACIES #1 91 0.364 - 0.751 0.564 1.55 -2.0 1.665 -1 .255 FACIES#2 29 0.896 - 0.499 0.249 0.278 0.02 1.723 0.074 FACIES#3 617 1.46 - 0.629 0.396 0.271 0.084 3.143 0.245 FACIES #4 32 1.04 - 0.755 0.571 0.549 -0.824 2.583 -0.431 .... ~ for the least significant difference (LSD) given the proven significance of the F-test, as prosclibed by Fisher (1935) and referenced by Snedecor (1980). This type of the ANOV A test is commonly referred to as the protected least significant difference method (PLSD). Since the lognormality of sample data was of interest, the compaiisons were conducted on the pe1meability data in the log-transform state. Results from the ANOV A test (Table 2) substantiate the continued analysis of the sample GRIDs with nearly a 5% level of confidence. The F-test results are found to be significant for comparisons between samples and within samples. Comparisons of the samples are found to be significant to the 5% level for all sample GRIDs except for that between GRIDs B and D. These sample grids are found to have a difference between means which is less than the to.os value for four samples at 173 degrees of freedom. This result indicates that there is greater than a 5% probability of error in the assumption that sample GRIDs B and D shared the same population mean. Continued analysis of the sample GRIDs is not precluded by this result, however, the following power-law variogram results are strengthened by the exclusion of both the B and D sample GRIDs. 5.5 POWER-LAW VARIOGRAMS The power-law variograms were created from the combined horizontal vaiiograms of all four sample data sets plotted on a log-n·ansformed axis of average distance. Originally, the scales of each sampled grid were established, in part, to represent the pattern of permeability distribution for different orders of magnitude. The GRID A sample data represented the permeability distribution in hundreds of TABLE2 ONE FACTOR ANOVA COMPARISONS (Calculations and table configuration modified from Statview 512+ vl.0, 1986) ANOVATABLE source: df: sumorsquares: Mean s1quare s : Ft-es : t p Between Subjects 173 224.192 1.296 6.846 0.0001 Within subjects 522 98.817 0.189 treatments 3 74.984 24.995 544.289 0.0001 residual 519 23.833 0.046 Total 695 323.009 Note: first 174 measurements from sorted (ascending) sample GRID data incorporated in comparisons. I:x2 Pooled Mean Squares (SJ,) = dfw Standard Error of the Difference Between Two Means (So)= ( ~) STATISTICS OF SELECTED SAMPLE GRID DATA e ec e t d S C M St d d D . f S dard E S I ampe: oun: ean: an ar ev1a aon: tan rror: GRIDA 174 0.492 0.581 0.044 GRIDB 174 1.072 0.509 0.039 GRIDC 174 1.404 0.548 0.042 GRIDD 174 1.064 0.733 0.056 (-f2s2 ) Standard Error = 'J =-:;­ COMPARISON OF SAMPLE GRID DATA Protected Least Scheffe s· ·fi o-a comoarason: Mean I ere nee: um1 1cant I erence: F-test: GRID A vs. GRID B • 0.581 0.045* 212.916* GRID A vs. GRID C • 0.913 0.045* 525.902* GRID A vs. GRID D • 0.573 0.045* 207.333* GRID B vs. GRID C • 0.332 0.045* 69.571* GRID B vs. GRID D 7.663E-3 0.045 0.037 GRID C vs. GRID D 0.34 0.045* 72.82* * S1gmficant at the 5% level of confidence. Protected Least Significant Difference =(Si)) * (to.05 ). for total n = 696 and total df = 695. Sheffe's F-test: the comparison L (= A.1\o(x. fi + A.2\:J(x. ); + ... + A..'<>(x, ). ) is significant at the 5% level if ILi I sL >--./(a -l)Fo.os , where: a is the number of san1ples and sL is the mean squares of the samples which are being compared. feet, the GRID B sample data represented the distribution in tens of feet, GRID C data represented distribution in individual feet, and the GRID D data represented distribution in inches (approximately tenths of feet). Combinations of experimental horizontal variograms were made for step increments representing each scale of sample data and analyzed for possible correlation. The four horizontal variograms presented above were posted on log-axes and the powerlog parameters were estimated using fitted lines through the data. Calculations of the slope, y-intercept and the coefficient of correlation for the fitted line were compared for various configurations of the ~h) values. Comparisons of the parameters for selected data sets were intended to find the most statistically significant results which could be applied to the powerlog equation (Eqn. 13) and provide a value for the fractal codimension (H). The combined )'(h) values of all four sample grids (Fig. 46) were determined to represent an uncorrelated scatter by fitted lines calculated for the data. The slope of the best fit line was low (0.067) and a low coefficient of correlation (R2 =0.228) confirmed the unacceptability of the statistical relationship for these ~h) values. Removal of selected semivariance data resulted in increasingly better fit lines and steeper positive slopes. The )'(h) values based on less than 30 data pairs from the data were removed and the remaining data (Fig. 47) produced a fitted line with a slightly higher coefficient of correlation (0.288) and a similar slope (0.068). For the data collected at separation intervals 1 foot and greater (i.e., GRIDs A, B and C; Fig. 48), the fitted lines were better correlated (R2 =0.617) and were defined by a higher positive slope (m =0.143). Similarly, the removal of another variogram set stated above as poorly matching the spherical model (i.e., the GRID B sample data) 1. YrnJ o GRID c horlzonllll v1riogram. ~ • I root A GRID D horlzonllll Vlri0(!1"m. ~ • I Inch 0.1~---....-_...................r-----....-,,....,....,......-r-~-.--.-...........................~~.........,_.,,......,..,~~....--.-....................----.-_,........................ 0.01 0.1 10 100 1,000 10,000 Average Distance (feet) Figure 46. Variogram postings from GRIDs A, B, C, and D sample data calculations for semivariance [~h)]. plotted on log-axes. Best fit line through variogram data: y =-0.515 + 6.65e-2x (R2 = 0.228). 1. YrliJ o <30 pairs of data in calculation of '}'(h) 0.1 +----.---........................-T--.-.....-_.............__..--...-.-..................--.--.-......................._-.....-.,.._.................---.----............. 0.01 0.1 10 100 1,000 10,000 Average Distance (feet) - '° 0.1-t----..--.......................,,--._..._......,.....,....,..........,..,...._____........,..............,...,...._......-..._,,........,,.......,..,..-.--,_..,,............................--.........................._......, 0.01 0.1 10 100 1,000 10,000 Average Distance (feet) produced powerlog variograms (Fig. 49) with a steeper slope (m = 0.155) and highest R2 value (0.824). Parameters of the powerlog variogram which displayed the most statistical confidence were analyzed for the fit the powerlaw theoretical model. The slope of superimposed experimental variograms on log-transformed axes described the fractal codimension (2H) in Eqn. 14 [log(y(h)) =log("{o) + 2H(log(h))]. The fitted line through the log-transforms of the horizontal variograms for GRIDs A and C, with y(h) values based on greater than 30 data pairs (R2 =0.824), provided a slope of 0.155 which coITesponds to the fractal codimension (2H) parameter of Eqn. 14. This value transfo1ms to a (horizontal) fractal codimension (H) of 0.0775, which falls an order of magnitude below the stated range of 0.7 -0.9 for typical fractal codimension values of natural phenomena, as suggested by both Hewett and Berhens (1990) and Mandelbrot (1983). Average Distance (feet) N CHAPTER6 DISCUSSION AND CONCLUSIONS Permeability data collected from the outcrop of the first parasequence in the upper San Andres formation's first third-order sequence (uSAl), at Lawyer Canyon on the Algerita Escarpment in the Guadalupe Mountains of New Mexico, were analyzed for identifiable patterns of distribution. The purpose for this type of study was to statistically ·characterize permeability patterns as an aid in understanding the expectations of permeability occurrences in analogous subsurface environments. The parameters of statistical characterizations covered in these analyses were those of the spatial covariance based on the value and the relative location of permeability measurements. Spatial covariance relationships were analyzed from variograms and determined to exhibit scale-dependent attributes. As a test for the existence of fractal sets in the data, the variograms were analyzed for adherence to power-law theory. 6.1 DISCUSSION 6.1.1 Two-DIMENSIONAL VISUALIZATION OF THE SAMPLE DATA The sample populations of scale-based permeability data (GRIDs A, B, C, and D) were initially analyzed as the posting and contouring of the data in sample populations. Contouring of the data was intended to show whether the permeability values exhibited continuity between data points at the separation distances of the 113 transects in the grid. The contoured postings exhibited a tortuous pattern of localized high permeabilities in a background of low average permeabilities. Horizontal heterogeneities were observed at each scale of the grids, and vertical heterogeneities were observed at the one foot scale in all transects and grid patterns. In the vertical transects (GRIDs A and B) and the regular spaced pattern of GRID C, vertical and horizontal variation of values was noted to range across two orders of magnitude between measurements taken one foot apart. At the inch scale of GRID D, the vertical and horizontal variations of values was also noted to range over two orders of magnitude. These variations were similar to those noted in the previous studies of Kittridge (1988) and Hinrichs and others (1986). At the largest scale, GRID A (see Plate #1) was divided horizontally into two regions, one of low permeabilities (<10 md) which was overlain by a region of higher permeabilities (10 -100 md). This pattern coincided with the area of facies #1 (mud-dominated fabric) which underlaid the other three identified facies (mud­supported grain to grain-dominated fabrics). Since the model for a shallowing­upward depositional parasequence predicted a bed of mud-dominated fabric at the base of each cycle, the assumption of low flow boundaries controlling fluid movement was validated in the observed contouring of the sample data. Some horizontally and vertically continuous high permeability (> 100 md) streaks were noted in the larger scaled (GRIDs A and B) contour postings. In GRID A, two high permeability zones were observed between transects A18-A20. The pattern of GRID B data was more akin to irregular tongues of high permeabilities which extended both horizontally and vertically. These large scale continuities (376 to 35 feet horizontally, and 5 feet vertically) were based on few data points and were disrupted irregularly. The contour patterns of GRIDs B, C, and D indicated that continuity at the large scale was not carried through to the smaller scales. The location of the smaller-scale sample populations inside the area of the larger-scale sample populations provided the opportunity for visual comparisons of permeability pattern continuities. The primary target for these comparisons were the zones of high permeability first identified in the sampling of the parasequence, in patticular at the center of the study area. This was observed between the sample populations as the horizontal scale of sampling decreased, the zones of high permeability that were identified at the larger scales were disrupted in the contoured patterns of data for the smaller-scale patterns. 6.1.2 LOGNORMAL DISTRIBUTIONS IN THE SAMPLE DATA The statistical theory of the regionalized variable requires that the natural phenomenon exhibit a Gaussian distribution (normal or lognormal). In view of the heterogeneity observed in the contour patterns, this step of data analysis was a most serious consideration. To prove normality in the populations, the sample populations of permeability data were analyzed through statistical and graphical methods. Analyzed in the above results were the relationships for normal and log­transformed values of mean-to-standard deviation comparisons, coefficients of variation (mean divided by variance), and coefficients of skewness. Also, graphical presentations were constructed to view the distribution of each sample population. The sample data statistics and observed distributions were compared to the theoretical expectations for Gaussian distributions. From this analysis, the permeability data collected for this study were found to be lognormally or nearly lognormally distributed for each of the sample populations. The description of GRID A permeability data indicated some deviation from lognormality for the low-end of the pe1meabifity range ( <10 md). This was seen in the frequency histogram and probability plot graphics and in the statistics of the sample data. The data in that range was comprised of mostly core plug measurements, stated above as measurements representative of a larger sample of the rock matrix than that of the MFP device and providing data for permeabilities as low as 0.01 md. The MFP's detection limit was stated as <1 md (Goggin, 1988), but the nature of the rock which exhibited low permeabilities (i.e., mud-dominated) was heavily fractured and rarely provided a smooth and expansive prepared surface for accurate MFP-sampling. Therefore, a sampling bias was determined as the cause for the data distribution abnormalities which were observed in the low range of permeability data. The sampling bias was the result of the inclusion of core plug permeability measurements with the MFP data. The core plugs were collected preferentially within the parasequence where low permeabilities (<10 md) were anticipated. Sampling bias resulted since the core plug data were fewer numerically than the MFP data, yet these values were concentrated in the low end of the total range of permeabilities. The deviation noted in the probability plot was, therefore, the rise in relative cumulative percentages represented by core plug permeabilities in the range where the population of MFP permeabilities were undeITepresented due to the detection limit of the apparatus. Since the facies #1 and #4 sample data were the only other sample population which included core plug measurements, the presence of similar deviations from lognormality follows the above discussion for GRID A. Again, the distributions of the sample data deviated in the range of core plug permeabilities. This deviation reflected the bias of collecting core plugs preferentially in the areas where low permeability values were anticipated, and these areas were predominantly those of the mud-dominated facies #1 and #4. The deviation from lognormality observed in the probability plot for facies #4 data was less pronounced than that for facies #1 or for GRID A. This due in part to the fact that core plug pe1meabilities comprised 8 of the 9 transects of that sample data, and in part to the relatively few data points from which the sample population was derived. Both facies #1 and GRID A sample data included significantly less core-plug than MFP data, so that the numerical superiority of the MFP data over the core plug data effectively smoothed-out any potential deviation from a lognormal distribution. 6.1.3 VARIOGRAM PARAMETERS AND SCALE DEPENDENCY Confirmation of lognormal distributions in the sample data sets validated the further statistical analyses of permeability as a regionalized variable. These further analyses included the estimation of variogram parameters from the semivariance calculations. The variogram parameters of sill, range, and nugget are the results needed to "Krige" permeability values between known permeability values for characterization models of analogous reservoirs. The dete1mination that both the permeability sample data were representative of a regionalized variable, and were describable as a Gaussian distribution, were crucial to the theory of the variogram. The semivariance calculations for the GRIDs A, B, C, and D indicated the best development of nugget effected spherical variogram models for the lag increments of 100, 10, 1 feet, and 1 inch, respectively. These values of lag increments represented the orders of magnitude which were of interest to the study, the characterization of permeability patterns and distributions for intra-well distances ( <2,000 feet). The parameters interpreted from the experimental variograms were presented above for each sample GRID and facies sample data set. Each experimental variogram was interpreted for sill, range, and nugget values based on a spherical variogram model. These parameters (Table 3) were compared for each scale of the lag interval (h) used in the calculation of semivariance (y(h)). The sill and range values represented the characteristic variance in which pe1meability values could be expected. These variogram parameters provided insight to the existence of a scale­dependent relationship between permeability and distance. At each of the sampling scales represented by the GRID data, sill and ranges were interpreted from nugget­effected spherical variograms which possessed moderately well developed initial slopes based on 3 to 8 semivariance values. The initial semivariance, or nugget values, for these variograms were also closely related, varying by only 0.1 for GRIDs A, C, and D, and by 0.2 for GRID B. These similarities and the scale­dependency for the values of the variogram parameters indicated the possible TABLE3 VARIOGRAM RESULTS FOR GRID SAMPLES Sample Horizontal (0 =0°) Vertical (0 =90°) GRID A nugget (Cm)) 0.2 0.16 range (rm) 253.5 feet 13.0 feet sill (Cn)) 0.305 0.95 range (rm) 748.3 feet N.A. sill (Cm) 0.497 N.A. GRIDB nugget (Ccm) 0.32 0.2 range (rn)) 22.2 feet 4.0 feet sill (Cm) 0.57 0.44 range (rm) N.A. 10.2 feet sill (Cm) N.A. 0.71 GRIDC nugget (Crm) 0.16 0.165 range (rm) 2.1 feet 2.1 feet sill (Cm) 0.22 0.34 GRIDD nugget (Ccm) 0.26 0.35 range (rm) 9.0 inches 2.0 inches sill (Cm) 0.42 0.57 existence of fractal relationships for permeability based on the separation distance between known values. Application of the power-law theory to estimate the fractal codimension was introduced to extend the usefulness of information gained in the experimental variograms. Results from variograins representing different horizontal separation distances indicated that variogram parameters were interpretable for scales from one foot to one hundred feet. In particular, the sample GRIDs A and C were compared on logarithmic axes and were found to be described by a best fit line with a slope of O. l 5454x. This was applied to the power-law equation (13) as the value for 2 H, resulting in a fractal codimension (H =0.07727) an order of magnitude lower than the range proposed by Hewett and Berhens (1990) for natural phenomena. 6.2 CONCLUSIONS Based upon the statistical analyses of the variograms and power-law variograms this investigation has determined certain aspects of the permeability distribution and anisotropy for a single shallowing upward carbonate parasequence .. · 1) The pattern of permeability observed on the outcrop was characterizable as vertically and horizontally heterogeneous high (>100 md) and low (<10 md) zones distributed within a matrix of average (moderately low, <100 md) permeability values. 2) The observed heterogeneity of the permeability patterns were found to exist at all linear scales covered in this study, from inches to hundreds of feet. 3) The analysis of horizontal and vertical search direction variograms supported the visual observations of the existence of continuous heterogeneity across the range of scales. 4) The distribution of permeability within genetically defined depositional facies was found to reflect the range and mean permeabilities based on the fabric textures of the facies. 5) The application of power-law theory to the variogram data based on linear scale samples produced a result for the fractal codimension which was an order of magnitude below the range proposed by other researchers (Mandelbrot, 1983, and Hewett and Berhens, 1990) for natural phenomena. 6.3 RECOMMENDATIONS From these conclusions, the recommendations for further study are a based upon the success of this study and an urge to promote interest in the determination of the fundamental controls on permeability. This study shows that it is reasonable to accept the conclusions of anisotropy and the scale dependence of the permeability distributions, at least, for this particular shallowing-upward parasequence in the upper San Andres formation outcrop of the Guadalupe Mountains. These conclusions should be tested in other parasequences of this outcrop. This will provide both additional evidence of the distributional characteristics in shallowing­upward parasequences and a comparison of the effects of the different depositional histories for the other parasequences. For other investigations into the disuibution of permeabilities on outcrop, it is suggested that the sampling pattern follow the guidelines adhered to in the start of this study. Most importantly, the sampling pattern should be specifically targeted to a well defined geologic interval (i.e., one which is as homogeneous in depositional environment as possible). Sampling should be equally spaced both horizontally and vertically for all scales of the investigation to reduce variogram range bias which may have contributed to the development of the nested variogram sets in the GRID A data. The heightened degree of heterogeneity at the small (inch spaced) scale of investigation in this study is an indication that more information is required for determination of the controls of permeabilities at dimensions of less than a square foot. Heterogeneities within the generally high permeable bar crest facies indicate that values do vary widely within the space of an inch, creating low permeability baffles and high pe1meability conduits. Small scale continuity and prevalence of the occurrence within a formation can be most significant in determining the capacity of a reservoir to retain trapped fluids. Small scale heterogeneities are the most difficult area of study for the characterization of permeability. The problem is one of diminishing returns on the quantity of work needed to collect the measurements. Preparation and measurement of the permeability data are equally time consuming for large and small scaled sample sets. The small scale investigation is tied to a very localized site of specific geologic conditions, while the large scale investigation produces analyses which may be applied to a more general condition or sets of conditions. Also, the small scale investigation is perhaps most influenced by the "noise" of anisotropy in all three (3) dimensions than a broad profile of large scaled data. In closing, the suggestions for further study are summed as the following. 1) Apply similar sampling and analyses of this study to other parasequences of shallowing-upward carbonate deposition. 2) Retain a rigorous adherence to equal spacing between sample points at all scales of the investigation, while the scale of the investigation is controlled by outcrop and geologic changes in texture and structure. 3) Investigate the small scale patterns of permeability more completely for all rock fabrics in the study site, especially for three-dimensional anisotropy effects on permeability distributions. REFERENCES Amhed, S. and de Marsily, G., 1987, Comparison of geostatistical methods for estimating transmissivity using data on transmissivity and specific capacity: Water Resources Research, v. 23, no. 9 (Sept.), p. 171-1737. Bear, J., 1972, Dynamics of fluids in porous media: Dover Publications, Inc., New York, 764 p. Reprint, 1988: originally published: New York: American Elsevier Pub. Co., 1972. Beard, D. C. and Weyl, P. K., 1973, Influence of texture on porosity and permeability of unconsolidated sand: Am. Assoc. of Petrol. Geol. Bulletin, v. 57 'p. 349-369. Bodner, D. P., 1985, Heat variation caused by groundwater flow in growth faults of the south Texas Gulf Coast basin: University of Texas at Austin, Masters thesis, December, 188 p., 1 plate. Boyd, D. W., 1958, Permian Sedimentary Facies, Central Guadalupe Mountains, New Mexico: Bulletin 49, State Bureau of Mines and Mineral Resources, New Mexico Institute of Mining and Technology, Socorro, New Mexico, 100 p., 2 plates. Brown, S. R., 1987, A note on the description of surface roughness using fractal dimension: Geophysical Research Letters, v. 14, no. 11, p. 1095-1098. Chandler, M. A., 1986, Depositional Controls on Permeability in an Eolian Sandstone Sequence, Page Sandstone, N01thern Arizona: The University of Texas at Austin, M.A. thesis (December), 131 p. Chandler, M. A., Goggin, D. J. and Lake, L. W. 1989b, Field measurement of permeability using a rninipermeameter: Journ. of Sed. Petrology, Research Methods. Chandler, M. A., Kocurek, G., Goggin, D.J. and Lake, L.W., 1989a, Effects of stratigraphic heterogeneity on permeability in eolian sandstone sequence, Page Sandstone, northern Arizona: Amer. Assoc. of Petrol. Geol. Bulletin, v. 73 , no. 5 (May), p. 658-668. Choquette, P. W. and Pray, L. C., 1970, Geologic nomenclature and classification of . porosity in sedimentary carbonates: Am. Assoc. of Petroleum Geologists Bulletin, v.54, no. 2 (February), p. 207-250. Dagan, G. 1985, Stochastic modeling of groundwater flow by unconditional and conditional probabilities: The inverse problem: Water Resources Research, v. 21, no. 1 (January), p. 65-72. Dagan, G., 1986, Statistical theory of groundwater flow and transport: pore to laboratory, laboratory to formation, and formation to regional scale: Water Resources Research, v. 22, no. 9 (August), p. 120S-134S. Dake, L. P., 1978, Fundamentals of Reservoir Engineering: (Developments in Petroleum Science, 8): Elsevier Science Publishing Co. Inc., Amsterdam., 432 p. David, M., 1977, Geostatistical Ore Reserve Estimation: Elsevier Scientific Publishing c;o., New York. Davis, J.C., 1986, Statistical and Data Analysis in Geology: John Wiley and Sons, New York, 2nd ed., 646 p. Delhomme, J. P., 1978, Kriging in the hydrosciences: Advances in Water Resources, v. 1 no. 5, p. 251-266. Delhomme, J. P., 1979, Spatial variability and uncertainty in groundwater flow parameters: A geostatistical approach: Water Resources Research, v. 15 no. 2 (April), p. 269-180. Dykstra, H., and Parsons, R. L., 1950, The prediction of oil recovery by water flood: in Secondary recovery in the USA, 2nd ed.; Am. Petroleum Inst., p. 160-174. Eijpe, R. and Weber, K. J., 1971, Mini-permeameters for consolidated rock and unconsolidated sand: Am. Assoc. Petroleum Geologists Bulletin, v. 55, no. 2, p. 307-309. Feinerman, E., Dagan, G. and Bresler, E., 1986, Statistical inference of spatial random functions: Water Resources Research, v. 22, no. 6 (June), p. 935­ 942. Fogg, G. E., 1986, Stochastic Analysis of Aquifer Interconnections, with a Test Case in the Wilcox Group, East Texas: Ph.D. dissertation, Univ. of Texas at Austin, Texas. Fu, L., Milliken, K. L., and Sharp, J. M., Jr., 1992, Permeability variations in liesegang-banded Breathitt Sandstone (Pennsylvanian) -diagenetic controls: Geol. Soc. America Abs. with Programs (Ann. Mtg.), v. 24, p. 254. Fuller, Carla Mathern, 1990, Fracture and permeability analysis of the Santana Tuff, Trans-Pecos Texas: M.A. Thesis, Dept. of Geological Sciences, Univ. of Texas at Austin. Fuller, C. M. and Sharp, J. M., 1992, Permeability and fracture patterns in extrusive volcanic rocks: Implications from the welded Santana Tuff, Trans-Pecos Texas: Geological Society of America Bulletin, v. 104 (November), p. 1485­1496. Gelhar, L. W., 1986, Stochastic subsurface hydrology from theory to applications: Water Resources Research, v. 22, no. 9 (August), p. 135S-145S. Goggin, D. J., 1988, Geologically-sensible modeling of the spatial distribution of pe1meability in eolian deposits: Page Sandstone (Jurassic), n011hern Arizona: Ph.D. dissertation, University of Texas at Austin, Texas, 417 p. Goggin, D. J., Chandler, M. A., Kocurek, G.A. and Lake, L.W., 1988(a), Patterns of permeability in eolian deposits: Page Sandstone (Jurassic), northern Arizona: SPE Formation Evaluation (June), p. 297-306. Goggin, D. J., Thrasher, R. and Lake, L. W., 1988(b), A theoretical and experimental analysis of mini-permeameter response Including Gas-Slippage and High-Velocity Flow Effects: In-Situ, v. 12, nos. 1 &2, p. 79-116. Hewett, T. A. and Behrens, R. A., 1990, Conditional Simulation of Reservoir Heterogeneity With Fractals: SPE Formation Evaluation (September), p. 217­ 225. Hild, G. P., 1986, The Relationship of San Andres Facies to the Distribution of Porosity and Permeability -Garza Field, Garza County, Texas: Permian Basin/Soc. Econ. Paleon. and Mineralogists, Publication 86-26, p. 17-20. James, Noel P., 1979, Shallowing upward sequences in carbonates: in Facies Models, ed. Roger G. Walker, Geological Assoc. of Canada, p. Journel, A. G. and Huijbregts, C., 1978, Mining Geostatistics: Academic Press, London. Kerans, C., Lucia, F. J., Senger, R. K., Fogg, G. E., Nance, H. S., Kasap, E., and Hovorka, S. D., 1991, Characterization of reservoir heterogeneity in carbonate-ramp systems, San Andres/Grayburg, Permian Basin: Reservoir Characterization Research Laboratory, Final Report, Bureau of Economic Geology, University of Texas at Austin, Texas, 245 p., 2 plates. King, P., 1942, Pennian of west Texas and southeastern New Mexico: A.A.P.G. Publication, p 229. Kittridge, M. G., 1988, Analysis of Aerial Permeability Variations, San Andres Formation (Guadalupian): Algerita Escarpment, Otero County, New Mexico: M.S. Thesis, Dept. of Petroleum Engineering, U. of Texas at Austin, 361 p. Kittridge, M. G., Lake, L. W., Lucia, F. J., and Fogg, G. E., 1990, Outcrop/Subsurface Comparisons of Heterogeneity in the San Andres Formation: SPE Formation Evaluation (September), p. 233-240. Mandelbrot, B. B., 1983, The Fractal Geometry of Nature: W.H. Freeman & Co., New York City Matheron, G. and de Marsily, G., 1980, Is transport in porous media always diffusive? A Counterexample: Water Resources Research, v. 16, no. 5 (October), p. 901-917. Matheron, G., 1963, Principles of Geostatistics: Economic Geology, v. 58, p. 1246­1266. Meinzer, 0. E., 1942, Hydrology: Physics of the Earth -IX, Dover Publications, Inc., New York. Press, Wm. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, Wm. T., 1986, Numerical Recipes: the art of scientific computing: Cambridge University Press, Cambridge. Radian Corporation, 1989, CPS-1 user's guide. Sarg, J. F. and Lehmann, P. J., 1986, Facies and Stratigraphy of Lower-Upper San Andres Shelf Crest and Outer Shelf and Lower Grayburg Inner Shelf: Proc., San Andres/Grayburg Formations, Guadalupe Mountains, New Mexico and Texas: Soc. Economic Paleontologists and Mineralogists, Permian Basin Section Pub. No. 86-25, p. 9-36. Scheidegger,, 1974, The Physics of Flow Through Porous Media: Univ of Toronto Press, 3rd edition, 353 p. Sharp, J. M., Jr., Fuller, C. M., and Smyth, R., 1993, Permeability-porosity variations and fracture patterns in tuffs: in Hydrogeology of Hard Rocks, Proceedings of the 241h Congress, International Association of Hydrologists, Oslo, June 1993, in~- Snedecor, G.W. and Cochran, W.G., 1980, Statistical Methods, The Iowa State University Press, Ames, Iowa, 7th edition, 507 p. Sudicky, E. A., Gillham, R. W. and Frind, E. 0 ., 1985, Experimental investigation of solute transport in stratified porous media 1. The nonreactive case: Water Resources Research, v. 21, no. 7 (July), p. 1035-1041. Sudicky, E.A., 1986, A natural gradient experiment on solute transport in a sand aquifer: spatial variability of the hydraulic conductivity and its role in the dispersion process: Water Resources Research, v. 22, no. 13 (December), p. 2069-2083. Van Wagoner, J.C., Posamentier, H.W., Mitchum, R.M., Vail, P.R., Sarg, J.F., Loutit, T.S., and Hardenbol, J., 1988, An overview of the fundamentals of sequence stratigraphy and key definitions: in Sea-Level Changes -An Integrated Approach, SEPM Special Publication, No. 42, pp. 40-45. Weber, K. J., 1982, Influence of common sedimentary structures on fluid flow in reservoir models: Journal of Petroleum Technology, v. 34, no. 3 (March), p. 665-672. Weber, K. J., 1986, How Heterogeneity Affects Oil Recovery: in Reservoir Characterization; Lake, L. W. and Carroll, H. B., Jr. (eds.): April 29 -May 1, 1985, Dallas, Texas, U.S. Acad. Press, Orlando, FL., p.487-544. APPENDICES APPENDIX A MFP MEASURED PERMEABILITY DATA GRID A DATA Coordinates (feet) Tube Pe=nt Pressure Permeability Coordinates (feet) Tube Percent Pressure Permeability X Y nwnber of flow (psi) (md) X Y nwnber of flow (psi) (md) 20 18 s 10 12.5 20.39082 25 13 4 17 13 80.96838 20 18 5 12 12.5 26.00821 25 13 5 30 12.4 69.88026 20 18 5 11 12.5 23.18361 25 13 5 95 12.2 182.39359 20 19 4 11 12.45 48.20317 25 13 5 60 12.4 116.55519 20 19 5 40 12.3 85.75803 25 13 5 60 12.4 116.55519 20 19 5 12 12.5 26.00821 25 14 7 26 12.7 2.99331 20 19 5 17 12.5 40.61234 25 14 4 45 12.3 216.26797 20 20 4 11 12.5 48.05441 25 14 4 40 12.3 198.42722 20 20 5 75 12.3 141.92081 25 14 4 14 12.4 59.89384 20 20 5 20 12.5 49.63115 25 14 4 10 12.4 38.60483 20 20 5 17 12.5 40.61234 25 14 4 12 12.3 49.49736 20 21 4 1 13 3.16213 25 15 7 20 12.5 2.18698 20 21 s 15 12.4 34.90329 25 15 7 12 12.8 1.11387 20 21 7 65 12.2 11.88119 25 15 7 34 12.7 4 .43144 20 21 7 22 12.7 2.42937 25 16 4 28 12.1 149.79184 20 22 4 0 13.3 0 25 16 5 85 12.3 158.61641 20 22 7 70 12.6 12.1958 25 16 5 30 12.3 70.36008 20 22 7 80 12.3 14.83)43 25 16 5 50 12.4 99.20332 20 22 7 85 12.3 15.67978 25 16 5 40 12.4 85 .19501 20 22 7 70 12.6 12.1958 25 17 4 0 13 0 25 4 4 0 13.35 0 25 17 5 35 12.4 77.45811 25 4 7 0 12.8 0 25 17 5 85 12.3 158.61641 25 5 4 13.05 3.15259 25 17 5 30 12.4 69.88026 25 5 4 26 12. I 138.56409 25 18 4 12.6 3.24111 25 5 7 64 12.6 11.46423 75 4 13.3 3.10591 25 5 5 16 12.5 37.6321 8 75 5 7 12.8 13.52416 25 5 5 17 12.5 40.61234 75 7 0 13.l 0 25 6 4 I 13 3.16213 75 7 12 13.1 1.08933 25 6 7 50 12.6 8.38048 75 5 15 12.7 34.23092 25 6 7 24 12.7 2.71002 75 12 4 10 12.55 42.14788 25 7 4 13.1 3. 14311 75 12 5 5 12.8 9.32142 25 7 7 16 12.8 1.61614 75 12 7 50 12.4 8.47898 25 7 5 65 12.3 125.04013 75 12 5 6 12.9 11.33893 25 7 7 16 12.8 1.61614 75 12 5 30 12.6 68.94514 25 8 4 10 12.85 41.41633 75 12 5 15 12.8 34.01368 25 8 4 I 12.7 3.22091 75 12 5 25 12.7 58.6216 25 8 5 9 12.6 18.05258 75 13 4 0 13.2 0 25 8 5 50 12.4 99.20332 75 13 7 0 13.2 0 25 9 4 10 13 41.06246 75 13 5 6 12.9 11.33893 25 9 5 60 12.3 117.37685 75 13 5 14 12.8 31.16 25 9 5 35 12.4 77.45 811 75 13 5 9 12.9 17.73627 25 9 5 85 12.4 157.53995 75 14 4 23 12.1 121.99863 25 9 5 20 12.4 49.97361 75 14 4 25 12.2 132.04112 25 10 4 28 12.l 149.79184 75 14 5 14 12.7 31.35711 25 10 5 11 126 23.04125 75 14 5 60 12.5 115.74745 25 10 5 35 12.4 77.45811 75 14 5 95 12.5 178.43701 25 10 5 16 12.6 37.38681 75 15 4 0 13 0 25 10 5 16 12.5 37.63218 75 15 5 16 12.6 37.38681 25 11 4 32 12.1 173.53099 75 15 5 25 12.4 59.83427 25 11 5 9 12.6 18.05258 75 15 7 50 13 8.19211 25 11 5 2S 12.4 59.83427 75 15 7 42 13 6.14964 25 11 5 16 12.5 37.63218 75 16 4 0 13.2 0 25 11 5 17 12.4 40.88382 75 16 5 6 12.9 11.33893 25 12 4 14 12.5 65.62891 75 16 7 28 13 3.21279 25 12 5 12 12.6 25.84533 75 16 7 32 13 3.91961 25 12 5 10 12.4 20.51441 75 17 4 0 13.3 0 25 12 5 12 12.5 26.00821 75 17 5 20 12.5 49.63115 25 12 5 2S 12.6 59.01941 75 17 5 30 12.5 69.40867 25 12 5 10 12.4 20.51441 75 17 5 80 12.5 149.18785 25 12 5 14 12.4 31.95506 75 18 4 5 12.7 19.42876 25 13 4 52 12 273.16299 75 18 5 12 12.7 25.68499 Coordinates (fret) Tube Percent Pressure Permeability Coordinates (feet) Tube Percent Pressure Permeability X Y nwnbcr of flow (psi) (md) X Y nwnber of flow (psi) (md) 75 18 5 15 12.8 34.01368 132 17 7 32 13 3.91961 75 18 5 17 12.6 40.34498 132 17 5 6 12.9 11.33893 76.5 14 5 30 12.6 68.94514 132 17 5 6 12.8 1 J.40575 76.5 14 5 7 12.8 13.52416 132 18 4 0 13.3 0 76.5 14 5 50 12.6 97.87176 132 18 4 40 12.4 196.94371 132 5 4 0 13.6 0 132 18 4 35 12.5 169.4614 132 5 7 0 13.1 0 132 18 5 10 12.8 20.03105 132 5 7 0 13.1 0 185 5 4 20 12. l 105.4657 132 6 4 13.35 3.09678 185 5 5 11 12.2 23.62414 132 6 7 45 12.9 6.9501 185 5 5 17 12.l 41.72412 132 6 5 10 12.4 20.51441 185 6 4 0.5 12.5 1.47126 132 6 7 18 13 1.84431 185 6 7 65 11.8 12.19581 132 6 7 75 12.9 13.12992 185 6 7 53 12.3 9.32195 132 7 4 13.3 3.10591 185 12 4 0.5 13.05 1.42185 132 7 5 14 11.9 33.04047 185 12 7 33 12.4 4.29896 132 7 5 10 12.8 20.03105 185 12 5 15 11.5 37.12889 132 7 5 4 12.8 7.27828 185 12 6 40 12.3 14.94192 132 7 7 50 12.5 8.42936 185 12 6 19 12.4 4.23537 132 7 7 75 12.8 13.20905 185 13 4 5.5 12.4 21.98209 132 8 4 1 13.35 3.09678 185 13 6 14 12.4 2.62084 132 8 4 JO 13 41.06246 185 13 7 22 12.4 2.48681 132 8 5 17 12.6 40.34498 185 13 7 80 12.2 14.93193 132 8 12 12.6 25.84533 185 13 6 42 I 1.7 16.62049 132 8 5 30 12.6 68.94514 185 13 6 42 12.I 16.18019 132 10 4 0 13.4 0 185 14 4 6.5 12.6 26.10039 132 10 7 0 13.3 0 185 14 5 20 11.4 53.70881 132 10 7 32 13 3.91961 185 14 5 6 12.3 11.75538 132 10 7 10 13.2 0.84638 185 14 5 10 12.2 20.76732 132 10 7 24 13 2.65149 240 2 4 0 14 0 132 II 4 0 13.2 0 240 2 7 17 12.4 1.80132 132 II 7 10 13.2 0.84638 240 2 7 19 12.5 2.05273 132 II 5 70 12.5 131.08252 240 4 0 14.I 0 132 12 4 0 13.55 0 240 7 21 12.3 2.36467 132 12 7 12 13.l 1.08933 240 7 70 12.2 12.49695 132 12 7 24 13.l 2.63259 240 9 4 0 13.85 0 132 12 7 24 13.l 2.63259 240 9 6 17 12.3 3.60786 132 13 4 0.5 13.6 1.37635 240 9 6 24 12.2 6.58049 132 13 4 0.5 13.55 1.38033 240 10 4 10.5 12.45 45.29262 132 13 7 70 12.9 11.98163 240 10 6 17 12.3 3.60786 132 13 5 8 12.2 16.24823 240 10 7 15 12.5 1.52449 132 13 4 35 12.4 170.65923 240 11 4 0.5 12.95 1.43053 132 13 4 30 12.5 142.61304 240 II 6 34 12.2 11.74968 132 13 4 24 12.5 112.24384 240 11 5 25 11.3 64.82305 132 13 4 35 12.5 169.4614 240 12 4 14 12.2 66.98052 132 14 4 0 12.85 0 240 12 5 40 12 87.50269 132 14 5 9 12.2 18.49709 240 12 5 13 12.1 29.62923 132 14 7 75 12.3 13.62312 240 13 4 8.5 12.35 35.61609 132 14 7 65 12.9 11.37599 240 13 5 18 12. I 44.81544 132 14 7 50 13 8.19211 240 13 5 18 12.I 44.81544 132 14 7 34 13 4.34639 240 14 4 13.5 12.15 64.17744 132 14 7 46 13 7.16433 240 14 5 18 12.l 44.81544 132 15 4 10 12.7 41.77805 240 14 5 10 12.2 20.76732 132 15 7 75 12.8 13.20905 240 15 4 35.5 12.I 195.33777 132 15 5 10 12.7 20.14918 240 15 5 20 12. I 51.03306 132 15 5 14 12.7 31.35711 240 15 5 16 12.1 38.65316 132 16 4 0 13.3 0 240 16 4 0 12.6 0 132 16 7 12 13.1 1.08933 240 16 5 16 12.1 38.65316 132 16 7 15 13.J 1.45495 240 16 5 6 12.3 11.75538 132 16 7 32 13 3.91961 240 17 4 0 12.7 0 132 17 4 0 13.2 0 240 17 5 10 12.2 20.76732 132 17 7 32 13 3.91961 240 17 8 12.2 16.24823 Coordinates (feet) Tube Percent Pressure Permeability Coordinates (feet) Tube Percent Pressure Permeability X Y number of flow (psi) (md) X Y number of flow (psi) (md) 240 19 4 0.5 12.4 1.48071 350 10 7 12 12.3 1.15752 240 19 5 8 12.2 16.24823 350 JO 7 34 12.3 4.55119 240 19 5 6 12.3 11.75538 350 11 4 0 12.9 0 240 20 4 0.5 12.9 1.43492 350 11 7 40 12.2 5.94665 240 20 5 50 J2 101.98283 350 11 7 50 12.3 8.52938 240 20 5 13 12.J 29.62923 350 12 4 0 12.4 0 240 21 4 0.5 12.6 1.46197 350 12 6 56 12.J 23.4479 240 21 5 35 12 79.58904 350 12 6 14 12.2 2.66277 240 21 5 45 12 94.72251 350 13 4 20 12 106.21929 240 22 4 6.5 12.5 26.25987 350 13 5 25 12. J 61.10664 240 22 5 9 12.2 18.49709 350 13 5 22 12. J 55.04947 240 22 7 42 J 1.9 6.59605 350 14 4 31 11.65 172.97401 240 22 5 20 12.2 50.67445 350 14 5 10 12.2 20.76732 295 4 J2.l 3.34694 350 J4 5 13 12.2 29.43386 295 5 12 12.2 26.51251 350 15 4 32 11.65 179.26221 295 5 25 12.1 61.10664 350 15 5 12 12.2 26.5J 251 295 9 4 0 12.9 0 350 J5 5 16 12.2 38.39179 295 9 7 0 12.2 0 350 16 4 0 13 0 295 9 7 14 12.5 1.39497 350 16 5 6 12.3 11.75538 295 9 7 16 12.4 1.66853 350 16 5 7 12.3 13.93721 295 12 4 0 12.8 0 350 17 4 26 11.75 142.2851 295 12 7 30 12.3 3.66556 350 17 5 12 12.2 26.51251 295 12 7 36 12.3 4.9998 350 17 5 52 12.l 104.82548 295 19 4 0 12.95 0 350 18 4 0 12.9 0 295 19 7 18 J2.4 1.93505 350 18 7 J6 12.3 1.68219 295 19 6 24 12.2 6.58049 350 J8 6 30 12.2 9.60JJ 295 20 4 0 12.6 0 350 J9 4 0 12.9 0 295 20 7 J2 J2.5 1.13962 350 19 6 12 12.4 1.997 295 20 7 22 J2.4 2.4868J 350 19 5 J9 J2.J 47.9204 295 21 4 10.5 12.1 46.28325 350 20 4 12 12.05 55.48689 295 21 4 0 12.5 0 350 20 4 14 12.05 67 .68066 295 21 7 45 J2.3 7.20781 350 20 5 6 J2.3 11.75538 295 21 7 32 12.3 4.10632 350 20 5 5 12.3 9.60868 295 22 4 0 12.45 0 350 2J 4 1 12.3 3.3036 295 22 7 34 J2.3 4.55JJ9 350 2J 7 25 12.2 2.9588J 295 22 7 34 J2.4 4.52053 350 2J 7 40 12.2 5.94665 295 23 4 0 J2.9 0 400 5 4 0 13.3 0 295 23 6 48 J2.2 J9.2J 783 400 5 7 26 J2.3 3.08J25 295 23 5 20 J2.2 50.67445 400 5 7 J4 J2.3 l.4J 74) 295 24 4 8.5 12.35 35 .6J609 400 6 4 1 12. J 3.34694 295 24 5 JO 12.3 20.6399 400 6 7 38 J2.2 5.48856 295 24 5 JO J2.3 20.6399 400 6 7 30 J2.2 3.69J23 295 25 4 0.5 J2.6 l.46J97 400 7 4 9 J2.05 38.652J6 295 25 5 JS J2.2 44.50697 400 7 7 20 12.2 2.24227 295 25 5 6 12.4 Jl.6833 400 7 7 J2 12.2 1.1667 350 5 4 0 J2.7 0 400 8 4 1 J2.15 3.33597 350 5 5 6 12.3 11.75538 400 8 7 90 12.l 16.75062 350 5 7 20 J2.3 2.22352 400 7 16 12.2 1.69608 350 6 4 J2.8 3.20J02 400 J3 4 19 12.6 95.55928 350 6 7 12 12.4 1.1485 400 13 4 53 11.7 284.06229 350 6 7 14 12.3 1.41741 400 13 6 40 12.2 15.03679 350 7 4 0 12.7 0 400 13 6 60 12. J 25.48675 350 7 7 16 12.2 1.69608 400 14 4 13 12.05 61.56932 350 7 7 14 12.4 1.4061 400 14 6 18 12.3 3.93538 350 8 4 1 12.65 3.23097 400 14 6 18 12.3 3.93538 350 8 7 50 12.2 8.58055 400 15 4 0 13 0 350 8 7 20 12.3 2.22352 400 15 7 18 12.3 1.95108 350 9 4 0 12.8 0 400 15 7 20 12.2 2.24227 350 9 7 30 12.3 3.66556 400 16 4 0 12.6 0 350 9 7 80 12.2 14.93193 400 16 7 30 12.2 3.69123 350 10 4 0 12.7 0 400 16 7 56 12.2 10.18542 Coordinates (feet) Tube Percent Pressure Permeability Coordinates (feet) Tube Percent Pressure Permeability X Y number of flow (psi) (md) X Y number of flow (psi) (md) 400 17 4 0 12.7 0 455 17 4 II 12.45 48.20317 400 17 6 65 12.2 27.0576 455 17 4 50 12.l 263.18417 400 17 6 48 12.2 19.21783 455 17 5 20 11.4 53.70881 400 18 4 0 12.8 0 455 17 5 20 12.4 49.97361 400 18 6 16 12.3 3.28289 455 18 4 17 12.l 86.03898 400 18 6 16 12.3 3.28289 455 18 5 10 12.3 20.6399 400 19 4 9 12.1 38.53181 455 18 5 10 12.3 20.6399 400 19 5 20 12.1 51.03306 455 19 4 0 12.7 0 400 19 5 12 12.2 26.51251 455 19 5 6 12.4 11.6833 400 20 5 18 12.I 44.81544 455 19 6 37 11.7 13.82954 400 20 5 20 12.I 51.03306 495 4 4 0 13.6 0 444 15 4 I 12.85 3.19119 495 4 7 24 12.6 2.73016 447 20 4 19 12.65 95.23891 495 4 7 20 12.4 2.2051 447 20 6 20 12.4 4.56562 495 5 4 0 13.35 0 447 20 6 40 12.3 14.94192 495 5 5 20 11.5 53.30783 447 21 4 23 12.05 122.44761 495 6 20 12.4 4.56562 447 21 6 18 12.4 3.90731 495 6 4 0 13.75 0 447 21 6 80 12.3 32.67113 495 6 6 38 12.3 13.84536 455 3 4 I 13 3.16213 495 6 6 26 12.2 7.57605 455 3 7 34 12.2 4.58233 495 6 6 56 12 23.61542 455 3 7 38 12.2 5.48856 495 6 6 80 12.2 32.89445 455 4 4 0 13.l 0 495 7 4 17.5 13.5 81.3607 455 4 7 30 12.2 3.69123 495 7 6 58 12.l 24.46537 455 4 7 20 12.3 2.22352 495 7 7 26 12.I 3.12742 455 5 4 18 12 93.08128 495 8 4 0 13.7 0 455 5 7 40 12.2 5.94665 495 8 7 60 12.4 11.12121 455 5 75 12.2 13.70983 495 8 7 38 12.4 5.41579 455 6 4 12.8 3.20102 495 9 4 0 13.6 0 455 6 7 24 12. 3 2.7926 495 9 7 30 12.4 3.6403 455 6 7 24 12.3 2.7926 495 9 7 14 12.6 1.38402 455 7 4 I 12.95 3.17174 495 10 4 I 13.35 3.09678 455 7 7 20 12.3 2.22352 495 10 4 0 13.9 0 455 7 7 65 12. 2 I 1.88119 495 JO 7 40 12.4 5.86836 455 8 4 0 13 0 495 IO 7 70 12.3 12.41992 455 8 7 34 12.4 4.52053 495 II 4 0 13.8 0 455 8 24 12.3 2.7926 495 II 7 32 12.3 4.10632 455 9 4 II 12.1 49.2764 495 II 7 23 12.5 2.60864 455 9 7 15 12.3 1.54924 495 12 4 0.5 13.3 1.40071 455 9 7 54 12.4 9.52817 495 12 7 14 12.5 1.39497 455 IO 4 7 12.I 29.21009 495 12 6 28 11.7 8.87637 455 10 7 73 12.1 13.30767 495 12 6 30 12.4 9.47847 455 IO 7 25 12. 3 2.93661 495 13 4 28.5 12.8 145.33603 455 11 4 I 12.95 3.17174 495 13 5 50 11.2 108.06399 455 11 6 56 12.2 23.28307 495 13 5 60 12.2 118.21263 455 II 6 52 12.4 20.9793 495 14 4 0 13.6 0 455 12 4 0.5 12.45 1.47597 495 14 5 JO 12.J 20.89675 455 12 6 40 12.4 14.84851 495 14 7 22 12.2 2.52672 455 12 5 13 12.4 29.05254 495 15 4 27 12.5 140.01833 455 13 4 27 12 145.22768 495 15 5 19 11.6 49.66793 455 13 5 35 12.4 77.45811 495 15 5 75 12.2 142.89215 455 13 5 75 12 144.89281 495 16 4 0 13.6 0 455 14 4 22 12.I 116.49016 495 16 6 12 12.6 1.96349 455 14 4 0 12.3 0 495 16 6 36 12.2 12.83757 455 14 5 40 12.1 86.91157 495 17 4 0 13.6 0 455 14 5 55 12.l 110.15192 495 17 7 22 12.4 2.48681 455 15 5 10 12.3 20.6399 495 17 7 60 12.5 11.04943 455 15 5 95 12 185.11929 532 5 7 34 12.5 4.49037 455 16 4 0.5 12.7 1.45281 532 5 7 42 12.5 6.34309 455 16 5 10 12. 3 20.6399 532 6 7 46 12.5 7.37968 455 16 5 12 12.3 26.34174 532 6 7 75 12.4 13.53775 455 17 4 44 12.1 238.84694 532 7 5 8 12.5 15.95287 Coordinates (feet) Tube Percent Pressure Permeability Coordinates (feet) Tube Percent Pressure Permeability X Y nwnber of flo w (psi ) (md) X Y nwnber of flow (psi) (md) 532 7 5 16 12.4 37.8814 585 15 6 14 12.7 2.5605 532 8 4 0.5 13.7 1.36845 585 16 4 0.5 J3.75 1.36455 532 8 7 10 12.5 0.89017 585 16 6 30 12.6 9.35963 532 8 7 10 12.6 0.8836J 585 J6 6 50 12.6 19.72215 532 9 4 19 12.7 94.921 585 J7 4 JO 13.1 40.83073 532 9 4 0.5 13.4 1.39247 585 J7 6 48 12.6 18.70176 532 9 7 70 12.5 12.26937 585 J7 6 12 12.8 1.93108 532 9 7 40 12.5 5.83014 585 18 4 0 13.6 0 532 10 4 0.5 13.4 1.39247 585 18 4 0.5 13.5 1.38435 532 10 7 26 12.6 3.01477 585 J8 6 57 12.6 23.14093 532 10 7 20 12.6 2. J6916 585 18 6 14 12.7 2.5605 532 11 4 0 13.5 0 585 19 4 0 J3.8 0 532 11 7 18 12.5 1.9193 585 J9 6 JO 12.8 1.33909 532 11 7 24 12.6 2.73016 585 19 6 14 12.8 2.54104 532 12 4 0 13.5 0 585 20 4 13.4 3.08771 532 12 7 20 12.6 2. J69J6 585 20 5 45 11.4 98.82943 532 12 7 70 12.5 12.26937 585 20 7 20 12.8 2.13441 532 12 7 16 J2.6 1.6419 585 21 4 0 13.7 0 532 12 7 24 J2.5 2.75064 585 2J 7 17 12.8 1.7444 532 13 4 0 13.6 0 585 21 7 65 12.7 11.51486 532 13 7 20 12.6 2.J6916 585 22 4 0 13.8 0 532 13 7 70 12.5 12.26937 585 22 7 80 12.6 14.55478 532 14 4 22 13.1 108.63085 585 22 7 10 12.9 0.86455 532 14 4 14.5 13.55 64.10949 585 23 4 0 13.6 0 532 14 7 75 12.5 13.45369 585 23 7 38 12.7 5.31086 532 14 5 15 12.5 34.67563 585 24 4 0 13.5 0 532 15 4 0 13.7 0 585 24 7 26 12.8 2.97219 532 15 5 6 12.6 11.54243 585 24 7 36 12.8 4.8381 532 15 7 22 12.6 2.4482 640 2 4 0 13.7 0 585 4 4 20 13 99.17632 640 2 6 20 12.8 4.44357 585 4 7 28 12.6 3.30176 640 2 6 J8 12.8 3.79944 585 5 4 13. 55 3.0609 640 3 4 9 12.2 38.29402 585 5 7 16 12.6 1.6419 640 3 6 J8 12.8 3.79944 585 5 7 12 12.6 1.1309 640 3 6 J6 12.8 3.16469 585 6 4 0 J3. 8 0 640 4 4 0 13 0 585 6 7 18 12.6 1.9038 640 4 6 30 12.7 9.30158 585 6 7 75 J2.5 13.45369 640 4 6 17 12.8 3.4808 585 7 7 14 12.6 1.38402 640 5 4 10 12.45 42.39913 585 7 7 11 12.8 .0.99153 640 5 4 0 13.45 0 585 8 4 0 13.35 0 640 5 6 22 12.7 5.4J 319 585 8 7 II J2.8 0.99153 640 6 18 12.8 3.79944 585 9 4 0.5 13.2 1.40908 640 6 4 0 13.3 0 585 9 7 26 12.6 3.01477 640 6 6 18 12.8 3.79944 585 10 4 0 13.6 0 640 6 6 18 12.8 3.79944 585 10 7 12 12.7 1.12231 640 7 4 0 13.I 0 585 10 7 14 12.7 1.37325 640 7 6 30 12.7 9.30158 585 II 4 0 13.6 0 640 7 6 14 12.8 2.54104 585 II 7 40 12.7 5.75547 640 8 4 8 12.45 33.10484 585 11 7 22 12.7 2.42937 640 8 6 60 12.6 24.6209 585 12 4 15 J3.2 68.35593 640 8 6 90 12.6 34.31661 585 12 4 10 J3.I 40.83073 640 9 4 0 13.2 0 585 12 6 90 12.5 34.54901 640 9 6 60 12.6 24.6209 585 12 5 18 11.7 46.09963 640 9 6 63 12.6 25.63717 585 12 5 12 12.7 25.68499 640 10 4 10 12.6 42.02369 585 13 4 0 13.7 0 640 10 5 20 12.6 49.29386 585 13 7 14 12.7 1.37325 640 10 5 14 12.7 31.35711 585 14 4 0 13.5 0 640 11 4 23 12.25 120.67171 585 14 7 80 12.6 14.55478 640 11 5 35 12.5 76.94772 585 15 4 19 12.9 93.67313 640 11 5 J9 12.6 46.30301 585 15 4 8 13.25 31.60037 640 J2 4 6 12.8 23.612 585 15 7 75 12.6 J3.3709 640 12 6 J6 12.9 3.14216 Coordinates (fret) Tube Percent Pressure Permeability Coordinates (feet) Tube Percent Pressure Permeability X Y number of flow (psi) (mdJ X Y number of flow (psi) (md) 640 12 6 17 12.8 3.4808 695 14 4 16 12.4 78.11102 640 13 4 0 13.35 0 695 14 5 8 12.8 15.67056 640 13 6 30 12.8 9.2444 695 14 5 12 12.7 25.68499 640 13 6 20 12.7 4.47337 695 15 4 10 12.55 42.14788 640 14 4 0 13.2 0 695 15 5 25 12.3 60.25157 640 14 6 22 12.8 5.37798 695 15 5 16 12.5 37.63218 640 14 6 28 12.8 8.26106 695 16 4 12.9 3.18143 640 15 4 0.5 12.9 1.43492 695 16 6 77 12.4 31.24226 640 15 6 26 12.8 7.28814 695 16 6 20 12.7 4.47337 640 15 6 28 12.9 8.2102 705 7 16 12.6 1.6419 640 16 4 0 13.5 0 705 7 20 12.6 2.16916 640 17 4 0 13.4 0 705 6 7 18 12.5 1.9193 640 17 6 56 12.7 22.49738 705 6 7 50 12.4 8.47898 640 17 6 15 12.9 2.83051 705 7 7 28 12.5 3.3249 640 18 4 0 13.4 0 705 7 7 75 12.3 13.62312 640 18 6 10 12.9 1.3266 705 8 7 70 12.4 12.34406 640 18 6 28 12.9 8.21(12 705 9 7 80 12.4 14.74043 640 21 4 0.5 12.5 1.47126 705 9 7 22 12.5 2.46734 640 22 4 0 12.85 0 705 10 5 13 12.3 29.24166 640 23 4 12.65 3.23097 705 10 18 12.2 44.50697 695 I 4 0 13.4 0 705 11 45 12.7 90.39119 695 7 10 12.9 0.86455 705 11 5 20 12.8 48.63429 695 I 7 II 12.9 0.98426 705 12 6 28 13.I 8.11073 695 2 4 0 13.4 0 705 12 6 45 13 16.7457 695 2 7 52 12.8 8.79103 705 13 5 14 12.9 30.96591 695 2 7 2(l 13 2.10077 705 13 5 35 12.8 75.4661 1 695 3 4 0 13.4 0 705 14 5 17 12.9 39.56662 695 7 34 12.9 4.3743 705 14 5 10 13 19.79992 695 3 7 32 12.9 3.94506 705 15 5 5 13 9.21245 695 4 4 0.5 12.75 1.44829 705 15 5 9 13 17.63389 695 4 7 42 12.9 6.18717 705 16 5 20 12.9 48.31179 695 4 6 24 12.8 6.32671 705 16 5 16 12.9 36.67286 695 5 4 I 12.9 3.18143 705 17 5 14 12.9 30.96591 695 5 6 30 12.8 9.2444 705 17 5 6 13.2 11.14425 695 5 6 16 13 3.11999 705 18 5 35 12.8 75.46611 695 6 4 12.75 3.21093 705 18 5 20 12.9 48.31179 695 6 6 42 12.8 15.4734 705 19 5 10 13 19.79992 695 6 6 28 13 8.16009 705 19 5 10 13 19.79992 695 7 4 I 12.8 3.20102 705 20 6 22 13.2 5.24238 695 7 6 46 12.8 17.45696 705 20 6 26 13.I 7.15385 695 7 6 22 12.9 5.3433 705 21 6 24 13.I 6.20837 695 8 4 12.3 3.3036 705 21 6 32 13 10.1526 695 8 6 24 12.8 6.32671 705 22 6 18 13.2 3.69811 695 8 6 22 12.9 5.3433 705 22 6 29 13 8.64511 695 9 4 52 122.3 46.52975 705 23 6 16 13.2 3.07667 695 9 5 10 12.7 20.14918 705 23 6 16 13.2 3.07667 695 9 5 22 12.6 53.16828 705 24 6 14 13.3 2.44825 695 10 4 12 12.5 53.88377 705 24 6 52 12.9 20.28252 695 10 4 17 12.3 84.84309 705 25 6 38 13 13.26472 695 10 5 40 12.3 85.75803 705 25 6 18 13.3 3.67373 695 10 5 20 12.6 49.29386 747 9 4 1 12.5 3.26161 695 11 4 6 12.8 23.612 747 9 7 12 12.3 1.15752 695 II 5 6 12.9 11.33893 747 9 7 85 12.2 15.78327 695 II 5 14 12.7 31.35711 747 10 4 6 12.5 24.04461 695 12 4 I 12.9 3.18143 747 10 4 13 12.05 61.56932 695 12 5 6 12.9 11.33893 747 10 5 18 11.3 47.47121 695 12 14 12.7 31.35711 747 10 5 25 12.l 61.10664 695 13 4 16 12.6 77.05556 747 II 4 4 12.2 15.65755 695 13 5 40 12.4 85.19501 747 II 5 18 12.2 44.50697 695 13 5 45 12.3 92.81168 747 11 5 13 12.2 29.43386 695 14 4 6 13.2 23.(16425 747 12 4 0 12.6 0 Coordinates (feet) Tube Percent Pressure Permeability Coordinates (feet) Tube Percent Pressure Permeability X Y number of flow (psi) (md) X Y number of flow (psi) (md) 747 12 6 14 12.4 2.62084 820 13 3 30 12.3 415.65112 747 12 6 20 12.3 4.59736 820 13 3 75 I 1.5 1178.25732 747 13 4 0 12.6 0 820 14 4 89 11.3 468.57709 747 13 6 13 12.4 2.30698 820 14 3 12.I 126.32437 747 13 6 16 12.3 3.28289 820 14 3 26 12.4 397.89029 747 14 4 0 12.6 0 820 14 3 20 12.6 281.4758 747 14 6 16 12.4 3.25848 820 14 5 70 12.6 130.20815 747 14 6 18 12.4 3.90731 820 14 3 25 12.4 348.16125 747 17 4 15.5 12 77.20576 820 15 4 II 11.6 50.91467 747 17 6 40 12.2 15.03679 820 15 5 18 12.8 42.75167 747 17 6 30 12.3 9.53931 820 15 5 20 12.8 48.63429 747 18 4 I 12.3 3.3036 820 16 3 26 12.3 400.80194 747 18 6 65 12.2 27.0576 820 16 5 95 12.6 177.15273 747 18 6 30 12.3 9.53931 820 16 3 50 12.3 709.49554 747 19 4 15 12 74.09592 820 17 3 68 10.85 1221.91064 747 19 5 55 12.l 110.15192 820 17 3 60 12 872.118% 747 19 18 12.2 44.50697 820 17 5 19 12 48.25895 747 20 4 28 12.35 147.09598 820 18 3 26.5 12.4 404.95871 747 20 6 24 12.3 6.53651 820 18 3 30 I 1.3 495.48572 747 20 6 30 12.3 9.53931 820 18 3 30 12.3 415.65112 795 I 4 0 14.2 0 820 19 4 I 12.l 3.34694 795 6 4 0.5 11.9 1.53027 820 19 4 9.5 12. I 40.91207 795 7 4 0.5 11.6 1.56203 820 19 7 50 13 8.19211 795 8 4 0.5 12.4 1.48071 820 19 7 80 13 14.19993 795 9 4 12.7 3.22091 820 20 3 51.5 10.9 902.52008 795 9 4 11 12.J 49.2764 820 20 3 10 12.7 142.41273 795 10 4 18 12.05 92.75114 820 20 3 20 12.5 283.34833 795 II 4 14 12.1 67.44541 820 21 3 52 10.9 910.99133 795 II 4 29.5 I 1.55 165.0934 820 21 3 20 12.5 283.34833 795 12 4 0.5 12.4 1.48071 820 21 3 5 12.7 65.09188 795 13 4 I 1.5 12.1 52.28471 820 22 4 15 12.I 73.57364 795 13 4 11 12.1 49.2764 820 22 5 20 12.8 48.63429 795 14 4 20 12.1 105.4657 820 22 14 12.8 31.16 795 15 4 11 11.7 50.57642 820 23 4 0.5 12.7 1.45281 795 16 4 35 I 1.7 197.93155 820 23 7 26 13.I 2.9108 795 17 4 0 12.6 0 855 3 4 0 13.3 0 795 17 4 0.5 12.5 J.47126 855 3 7 20 13.3 2.05229 795 18 4 22 12.J 116.49016 855 7 42 13 6.14964 795 19 4 9 12.I 38.53181 855 4 4 0 13.3 0 795 20 4 19.5 11.8 104.40034 855 4 7 22 13.I 2.3570i 795 21 4 0 12.5 0 855 4 7 32 13.J 3.89455 795 21 4 8 12.15 33.72299 855 5 4 0 13.3 0 795 22 4 0.5 12.4 1.48071 855 5 7 22 13.I 2.35701 795 23 4 0 12.9 0 855 5 7 20 13.2 2.0682 795 24 4 10 I 1.7 44.41413 855 9 4 0 13.25 0 795 25 4 0 12.6 0 855 9 5 5 13 9.21245 820 4 0 12.05 0 855 9 5 10 12.9 19.91464 820 6 14 13.3 2.44825 855 10 4 0 13.25 0 820 6 20 13 4.38534 855 10 5 5 13 9.21245 820 8 4 0 12.7 0 855 10 8 12.9 15.57919 820 8 6 26 13 7.19794 855 11 4 1 13.2 3.12438 820 8 6 20 13 4.38534 855 11 5 20 12.8 48.63429 820 9 4 6 12.3 24.34412 855 11 5 8 13 15.48914 820 9 4 0 12.9 0 855 12 4 0 13.2 0 820 9 6 18 13 3.74799 855 12 7 23 13.2 2.47646 820 9 6 46 12.9 17.34512 855 13 3 32 11.3 526.02893 820 12 3 79.5 10.65 1496.94092 855 13 3 10 12.6 143.19189 820 12 2 29 11.85 1385.48145 855 13 3 15 12.5 211.86848 820 12 3 80 11.4 1282.96033 855 14 3 26 11.25 434.36099 820 13 3 68 11.2 1185.70605 855 14 3 50 12.2 714.75079 820 13 47 II.I 802.26135 855 14 3 20 12.5 283.34833 Coordinates (feet) Tube Pe=nt Pressure Penneability Coordinates (feet) Tube Percent Pressure Penneability X Y nwnber of flow (psi) (md) X Y nwnber of flow (psi) (md) 855 15 3 38 II.I 630.61163 890 14 5 30 12.7 68.48952 855 15 3 40 12.3 548.12238 890 15 4 37 11.4 215.80817 855 15 3 25 12.5 345.75021 890 15 4 25.5 11.4 143.2951 855 17 4 8 12.2 33.6179 890 15 5 50 12.6 97 .87176 855 17 5 20 12.8 48.63429 890 15 7 20 13 2.10077 855 17 5 10 12.9 19.91464 890 16 3 40 12 617.96869 855 18 4 21 12.I 110.97361 890 16 3 41 12 636.01526 855 18 4 19 12.I 98.90776 890 16 3 35 12.2 484.52576 855 18 4 21 11.9 112.5854 890 16 3 35 12.3 481.09653 855 18 5 70 12.7 129.35123 890 17 4 12 12.I 55.30344 855 18 5 8 13 15.48914 890 17 5 8 12.8 15.67056 855 20 4 9 12.7 37.15991 890 17 5 50 12.6 97.87176 855 20 5 13 15.48914 890 18 4 16 12.I 79.7632 855 20 3 20 12.5 283.34833 890 18 5 60 12.6 114.95346 855 20 3 20 12.6 281.4758 890 18 5 5 12.8 9.32142 855 21 80 11.4 1414.&4241 890 19 4 II 12.I 49.2764 855 21 2 27.5 10.7 1425.61816 890 19 5 12 12.8 25.52709 855 21 2 16 II 752.91541 890 19 5 35 12.6 76.44574 855 21 3 5 12.9 64.29708 890 20 4 28.5 11.5 159.76903 855 21 5 16 12 38.91882 890 20 3 15 12.5 211.86848 855 21 5 13 12.9 28.1508 890 20 3 10 12.5 143.98293 855 22 4 0 13 0 890 21 4 34 11.35 196.50688 855 22 5 13 15.48914 890 21 3 15 12.4 213.32048 855 22 5 12 12.9 25.37159 890 21 3 5 12.6 65.49924 855 23 4 0 13 0 890 22 4 0 12.3 0 855 23 7 26 13.2 2.89096 890 22 7 46 12.9 7.20612 855 23 7 22 13.1 2.35701 890 22 7 75 12.9 13.12992 855 24 5 25 12 61.5447 995 I 4 0 12.2 0 855 24 3 20 12.5 283.34833 995 I 7 20 13.5 2.24548 890 4 I 12.7 3.22091 995 I 7 12 13.7 1.15222 890 7 54 . 12.8 9.29978 995 2 4 0 12.9 0 890 7 80 12.7 14.46407 995 2 7 26 13.5 3.15578 890 4 0 12.8 0 995 2 7 80 13.5 15.49109 890 2 7 16 12.9 1.60358 995 3 4 0 13 0 890 2 7 26 12.9 2.95141 995 3 7 30 13.5 3.77737 890 3 4 0 13 0 995 3 7 18 13.5 1.96997 890 3 7 38 12.9 5.24356 995 4 4 0 12.I 0 890 3 7 15 13 1.46608 995 4 7 18 13.6 1.95479 890 4 4 0 12.75 0 995 4 7 25 13.5 3.00208 890 4 7 31 12.9 3.73192 995 5 4 0 12.75 0 890 4 7 46 12.8 7.24854 995 5 5 4 13.5 7.82933 890 5 4 0 12.45 0 995 5 5 6 13.5 12.30156 890 5 7 24 13 2.65149 995 6 4 0 12.5 0 890 5 7 34 12.9 4.3743 995 6 7 18 13.5 1.96997 890 6 4 9 12.6 37.37971 995 6 7 20 13.6 2.22801 890 6 7 46 12.8 7.24854 995 7 4 0 12.95 0 890 6 7 38 12.9 5.24356 995 7 7 70 13.5 13.00378 890 7 4 0 12.9 0 995 7 7 26 13.6 3.13412 890 7 7 II 13.2 0.96312 995 8 4 0 12.8 0 890 7 7 15 13 1.46608 995 8 7 12 13.7 1.15222 890 8 4 80 12.I 395.46112 995 8 7 14 13.7 1.40985 890 8 5 40 11.8 88.71529 995 9 4 0 12.65 0 890 8 5 55 12.6 106.37453 995 9 7 95 13.1 18.43862 890 II 4 0 13.2 0 995 9 7 34 13.6 4.6756 890 II 5 6 12.8 11.40575 995 11 3 40 12.6 590.78021 890 II 5 4 12.9 7.23514 995 12 4 0 13.3 0 890 12 3 56 10.7 997.33179 995 13 4 39 12.85 204.72464 890 12 3 25 12.4 348.16125 995 13 5 20 12.6 55.77725 890 12 7 48 12.9 7.72059 995 13 3 20 13 309.77655 890 14 4 18 .5 11.4 100.67909 995 14 4 38 12.I 210.64638 890 14 5 16 12.7 37.14521 995 14 5 18 12.5 49.32502 Coordinates (feet) Tube Percent Pressure Penneability Coordinates (feet) Tube Percent Pressure Penneability X Y number of flow (psi) (md) X Y number of flow (psi) (md) 995 14 5 55 13.2 115.56769 1072 3 5 6 13 12.67433 995 15 4 43 12.8 222.3629 1072 4 5 7 13 15.04043 995 15 5 30 13.3 74.40796 1072 4 7 16 13.1 1.75207 995 15 3 25 13 377.6506 1072 5 7 49 13 8.90524 995 15 3 45 12.7 688.60876 1072 5 7 24 13.l 2.93336 995 16 2 35 10.15 1973.60095 1072 6 7 60 13 12.03466 995 16 3 40 12.7 602.02814 1072 6 5 16 12.3 43.13987 995 16 2 35 10.3 2002.02441 1072 7 4 32 12.7 170.9274 995 16 2 35 10 2057.24487 1072 7 4 12 13 53.60254 995 17 3 52 11.45 868.91846 1072 11 5 80 12.9 163.87489 995 17 3 55 11.45 918.65424 1072 11 5 10 13 22.3156 995 17 3 25 12.7 385.68903 1072 13 7 60 13 12.03466 995 17 3 70 11.5 1228.73474 1072 13 5 14 13 34.70987 995 18 3 15 12.85 228 .36462 1072 14 5 13 13 31.56111 995 18 5 45 12.l 106.59996 1072 14 7 24 13 2.95526 995 18 3 30 12.2 474.23239 1072 15 7 14 13 1.48718 995 18 3 20 12.9 311.86816 1072 15 7 24 13.1 2.93336 995 19 4 0 13.25 0 1072 16 7 24 13 2.95526 995 19 5 50 12.9 95.94406 1072 16 7 60 13 12.03466 995 19 7 75 13.5 14.24274 1072 17 5 25 12.8 65 .88681 995 19 7 16 13.6 1.68538 1072 17 5 12 13 28.4429 995 20 4 0 13.6 0 1352 2 7 20 12.9 2.35635 995 20 7 20 13.5 2.24548 1352 2 7 24 13 2.95526 995 20 5 50 12.2 113.98105 1352 2 7 26 13 3.2692 995 20 5 8 13 17.43933 1352 3 7 20 12.9 2.35635 995 21 4 20 12.1 105.4657 1352 3 7 22 13 2.64444 995 21 5 30 13 75.91518 1352 4 7 38 12.8 5.91249 995 21 10 13 22.3156 1352 4 7 54 12.9 10.38716 995 22 4 30 12.l 161.35692 1352 5 7 26 12.8 3.31711 995 22 5 50 13 107.80484 1352 5 7 28 12.9 3.61128 995 22 5 45 13 100.20515 1352 6 7 30 13 3.90541 995 23 3 28 11.6 452.98135 1352 6 7 70 12.8 13.56162 995 23 3 20 12.9 311.86816 1352 7 5 10 12.9 22.45181 995 23 3 10 12.9 158.85789 1352 7 5 12 12.8 28.80966 995 23 4 30 12.7 158.89728 1352 8 5 14 12.8 35.1678 995 23 4 65 12.5 323.25208 1352 7 42 12.9 6.93711 1030 4 43 12.05 235.75957 1352 8 7 44 12.9 7.50973 1030 8 4 16 12.8 78.06532 1352 9 5 18 12.8 48.31111 1030 8 5 30 12.9 76.4345 1352 9 5 25 12.8 65.88681 1030 8 5 30 12.9 76.4345 1352 10 5 40 12.7 94.48206 1030 9 4 17 12.15 85.736 1352 10 5 60 12.7 129.29102 1030 9 5 80 13 162.77887 1352 11 4 80 12.5 393.78891 1030 9 5 80 12.7 166.11916 1352 11 4 50 12.6 259.87387 1030 10 4 53 12.1 274.87778 1352 15 4 18 12.8 90.46283 1030 JO 5 75 12.8 154.92863 1352 15 4 18 12.8 90.46283 1030 JO 5 60 12.8 128.3727 1352 15 5 25 12.8 65.88681 1030 11 4 15 12.8 70.14718 1352 15 5 30 12.8 76.96252 1030 II 7 16 13.1 1.75207 1352 16 4 35 12.6 190.42363 1030 11 7 26 13.1 3.24581 1352 16 4 20 12.7 103.88091 1030 12 4 23 12.9 118.34447 1352 16 5 27 12.8 70.28721 1030 12 4 50 12.7 257.86774 1352 16 5 40 12.8 93.85275 1030 13 7 26 13 3.2692 1428 2 7 26 13.l 3.24581 1030 13 7 24 13.l 2.93336 1428 2 7 24 13 2.95526 1030 14 3 27 11.8 430.99127 1428 3 7 24 13. J 2.93336 1030 17 4 6 12.5 24.04461 1428 3 7 26 13 3.2692 1030 23 4 2 12.4 7.15697 1428 4 7 30 13 3.90541 1072 7 14 13 1.48718 1428 4 7 24 13 2.95526 1072 1 7 20 13 2.33712 1428 5 7 25 13 3.11186 1072 2 7 22 13 2.64444 1428 5 7 24 13 2.95526 1072 2 7 16 13.J 1.75207 1428 6 7 50 13 9.19641 1072 3 7 95 12.9 18.68715 1428 6 7 80 13 15.98151 Coordinates !feet) Tube Percent Pressure Permeability X Y nwnber of flow (psi) (mdJ 1428 6 7 85 12.9 16.99404 1428 7 7 34 13 4.86141 1428 7 7 32 13 4.38104 1428 8 7 26 13 3.2692 1428 8 7 22 13 2.64444 1428 9 5 15 12.9 38.1546 1428 9 5 6 13 12.67433 1428 10 4 60 12.5 301.53488 1428 10 4 55 12.6 279.3038 1428 II 5 19 12.8 51.65022 1428 II 5 10 13 22.3156 1428 12 7 32 13 4.38104 1428 12 7 30 13 3.90541 1428 13 5 14 12.9 34.93704 1428 13 5 16 12.9 41.4055 1428 14 5 25 12.9 65.42874 1428 14 5 40 12.8 93.85275 1428 15 4 80 12.5 393.78891 1428 15 3 70 11.9 1189.32947 1428 15 3 45 12. l 721.51263 1428 16 4 10 12.9 42.38251 1428 16 3 50 12.1 814.75427 1428 16 3 50 12.2 808.34149 1428 17 4 10 12.9 42.38251 1428 17 5 20 12.8 54.99789 1428 17 5 40 12.8 93.85275 1428 18 4 50 12.6 259.87387 1428 18 4 45 12.5 241.75627 1428 19 4 10 12.8 42.63029 1428 19 5 16 12.8 41.68337 1428 19 5 45 12.5 103.64897 1428 20 5 16 12.7 41.96557 1428 20 5 10 12.9 22.45181 1428 20 5 80 12.5 168.4399 1428 20.5 7 38 12.9 5.87335 1990 5 6 14 13 2.78856 1990 5 6 14 13 2. 78856 1990 6 6 24 12.8 7.09632 1990 6 6 38 12.9 15.01815 1990 7 6 22 13 5.94576 1990 7 6 19 13 4.54531 1990 8 6 30 12.9 10.32311 1990 8 6 30 12.9 10.32311 1990 9 6 14 13 2.78856 1990 9 6 30 13 10.25767 1990 10 6 14 13 2.78856 1990 10 6 16 13 3.48168 1990 II 6 12 13 2.11169 1990 11 6 18 13 4.18793 1990 12 6 30 13 10.25767 1990 12 6 80 12.9 35.44609 1990 13 6 20 13 4.90526 1990 13 6 50 12.9 21.78988 1990 14 6 30 13 10.25767 1990 14 6 16 13 3.48168 1990 15 6 18 13 4.18793 1990 15 6 38 13 14.92442 1998 2 6 12 13 2.11169 1998 2 6 26 13 8.07499 1998 3 6 14 13 2.78856 1998 3 6 14 13.l 2.7671 Coordinates (feet) Tube Percent Pressure Permeability X Y nwnber of flow (psi) (md) 1998 4 6 18 13 4.18793 1998 4 6 16 13 3.48168 1998 5 6 75 12.8 33.43349 1998 5 6 14 13 2.78856 MFP MEASURED PERMEABILITY DATA GRID B DATA Coordinates (feet) Tube Percent Pressure Permeability Coordinates (feet) Tube Percent Pressure Permeability X Y number of flow (psi) (md) X Y number of flow (psi) (md) 925 4 0 12.2 0 930 7 7 60 12.8 10.84064 925 7 16 13 1.59121 930 7 7 20 12.9 2.11745 925 7 16 13 1.59121 930 8 7 20 13.1 2.08435 925 4 4 0 13 0 930 8 7 80 12.8 14.3747 925 4 7 28 12.9 3.23452 930 9 5 25 12.l 61.10664 925 4 7 32 12.8 3.9709 930 9 7 26 12.9 2.95141 925 5 4 0 12.6 0 930 10 5 20 12.1 51.03306 925 5 7 26 13 2.93094 930 10 5 16 12.7 37.14521 925 5 7 70 12.8 12.05196 930 II 5 10 12.8 20.03105 925 6 4 0 12.25 0 930 11 5 12 12.8 25.52709 925 6 7 20 12.9 2.11745 930 12 5 20 12.7 48.96161 925 6 7 24 12.9 2.67069 930 12 5 25 12.7 58.6216 925 7 4 6 111.55 5.6123 930 14 7 24 12.9 2.67069 925 7 7 85 12.8 15.18568 930 14 5 50 11.9 102.70292 925 7 7 50 12.8 8.2849 930 14 3 25 12.4 348.16125 925 8 4 11.7 3.43793 930 15 5 18 12.6 43.31935 925 7 60 12.9 10. 77315 930 15 7 24 12.7 2.71002 925 8 7 22 12.9 2.39261 930 15 7 40 12.9 5.68306 925 9 4 0 12.2 0 930 16 7 20 13.l 2.08435 925 9 7 20 13 2.10077 930 16 5 40 12.l 86 .91157 925 9 7 18 13 1.84431 930 17 14 12.7 31.35711 925 10 4 0 II 0 930 17 5 95 12.5 178.43701 925 10 7 42 12.9 6.18717 930 18 5 25 12.6 59.01941 925 10 7 65 12.8 11.4449 930 18 5 18 12.7 43.03344 925 II 4 9 12.05 38.65216 930 19 7 20 12.9 2.11745 925 II 5 30 12.6 68.94514 930 19 7 34 12.9 4.3743 925 II 5 9 12.7 17.94558 935 8 7 36 12.8 4.8381 925 12 4 9 12.05 38.65216 935 8 7 26 13.l 2.9108 925 12 5 8 12.8 15.67056 935 9 7 40 12.8 5.71899 925 12 5 14 12.7 31.35711 935 9 7 40 12.8 5.71899 925 13 4 0 12. 4 0 935 IO 5 45 12.5 91.58425 925 13 5 10 12.8 20.03105 935 IO 40 12.6 84.09503 925 13 7 30 12.9 3.51983 935 II 5 4 12.8 7.27828 925 13 7 30 13 3.49684 935 II 7 50 12.9 8.23817 925 14 4 0 12.1 0 935 12 7 14 13.1 1.3319 925 14 5 6 12.9 11.33893 935 12 7 26 12.9 2.95141 925 14 5 9 12.8 17.84016 935 13 7 34 12.8 4.40265 925 15 4 0 12.05 0 935 13 7 24 12.9 2.67069 925 15 5 7 12.9 13.44519 935 13 75 12.6 139.11258 925 15 5 9 12.8 17.84(116 935 14 19 12.7 45 .99385 925 16 4 38 11.3 224.21811 935 14 25 12.8 58.23 925 16 3 15 12.5 211.86848 935 15 12 12.8 25 .52709 925 16 3 15 12.4 213.32048 935 15 5 6 12.9 11.33893 925 17 3 27 I I.I 455 .57227 935 16 5 45 12.7 90.39119 925 17 3 45 12.l 636.65942 935 16 60 12.6 114.95346 925 17 3 40 12.2 552.17194 935 16 5 16 12.7 37.14521 925 18 4 0 12.25 0 935 17 5 18 12.7 43.03344 925 18 7 18 13 1.84431 935 17 5 50 12.6 97.87176 925 18 7 36 12.9 4.80723 935 18 3 50 12.l 720.09772 925 19 4 0 12.7 0 935 18 3 40 12.3 548.12238 925 19 7 50 12.9 8.23817 935 19 3 20 12.5 283.34833 925 19 7 46 12.9 7.20612 935 19 15 12.5 211.86848 925 20 4 0 12.35 0 935 20 5 16 12. I 38.65316 925 20 7 48 12.9 7.72059 935 20 5 16 12.7 37.14521 925 20 7 26 13 2.93094 940 7 7 32 12.8 3.9709 925 21 4 14 .5 12.45 68.82347 940 7 7 20 12.7 2.15164 925 21 5 10 12.8 20.03105 940 8 7 26 12.7 2.99331 925 21 5 25 12.7 58.6216 940 9 7 42 12.7 6.26394 925 22 4 0 12.9 0 940 9 7 75 12.8 13.20905 925 22 5 8 12.8 15.67056 940 10 5 J(l 12.4 20.51441 925 22 7 32 12.4 4.07837 940 10 5 20 12.8 48.63429 Coordinates (fret) Tube Percent Pressure Permeability Coordinates (feet) Tube Percent Pressure Permeability X Y number of flo w (psi) (md) X Y number of flow (psi) (md) 940 11 5 7 12.4 13.85207 950 13 7 30 13 3.49684 940 II 5 12 12.7 25.68499 950 13 7 50 12.9 8.23817 940 12 5 10 12.9 19.91464 950 14 7 42 12.9 6.18717 940 12 7 38 12.7 5.31086 950 14 7 80 12.9 14.28668 940 13 7 50 13 8.19211 950 15 7 16 13.1 1.57904 940 13 5 12 12.4 26.17366 950 15 7 24 13.1 2.63259 940 14 7 50 12.8 8.2849 950 16 5 45 12.8 89.80678 940 14 5 18 12. I 44.81544 950 16 5 95 12.7 175.88554 940 15 5 55 12.6 106.37453 950 17 5 80 12.7 147.22572 940 15 5 8 12.9 15.57919 950 17 5 9 13 17.63389 940 16 3 15 12.5 211.86848 950 17 7 24 12.9 2.67069 940 16 3 25 12.5 345.75021 950 18 5 10 12.9 19.91464 940 16 3 40 12.4 544.13092 950 18 5 20 12.9 48.31179 940 17 3 45 12.3 627.13043 950 19 5 10 12.9 19.91464 940 17 3 35 12.3 481.09653 950 19 5 12 12.9 25.37159 940 18 5 30 12.7 68.48952 950 20 5 12 12.9 25.37159 940 18 5 40 12.6 84.09503 950 20 16 12.9 36.67286 940 19 5 95 12.6 177.15273 955 6 7 30 12.6 3.59097 940 19 3 20 11.9 295.2366 955 6 7 14 13 1.34199 940 19 3 15 12.6 210.44266 955 7 7 90 13 15.79988 945 7 14 12.9 1.35224 955 7 7 20 13 2.10077 945 8 7 15 12.9 1.47738 955 3 15 12.4 213.32048 945 9 5 18 12.7 43.03344 955 8 3 10 12.8 141.64447 945 9 7 32 12.8 3.9709 955 9 5 16 12.3 38.13457 945 10 7 28 12.9 3.23452 955 9 5 6 13 11.27309 945 10 7 22 12.9 2.39261 955 9 7 26 13 2.93094 945 II 5 10 12.2 20.76732 955 10 7 50 13 8.19211 945 II 5 9 12.8 17.84016 955 10 7 70 13 11.91233 945 12 5 10 12.8 20.03105 955 II 5 65 12.7 121.646% 945 12 5 14 12.8 31.16 955 II 5 16 12.7 37.14521 945 13 15 12.7 34.23092 955 12 5 8 13 15.48914 945 15 5 6 12.7 11.47357 955 12 3 15 11.8 222.58832 945 15 5 18 12.7 43.03344 955 13 5 6 13 11.27309 945 16 7 14 13 1.34199 955 13 5 20 12.9 48.31179 945 16 7 90 12.7 16.10237 955 14 3 50 12.4 704.32928 945 16 5 9 12.4 18.27146 955 14 3 10 12.8 141.64447 945 17 7 14 13 1.34199 955 14 3 15 12.7 209.04298 945 17 7 18 12.9 1.85882 955 15 5 10 13 19.79992 945 18 3 40 12.4 544.13092 955 15 3 20 12.7 279.63232 945 18 3 35 12.6 471.12378 955 15 3 25 12.6 343.37546 945 19 7 85 12.5 15.47758 955 16 3 75 11.8 1151.01819 945 19 7 50 12.9 8.23817 955 16 3 70 11.9 1051.84558 945 20 7 22 13 2.37467 955 17 3 25 12.6 343.37546 945 20 7 35 13 4.56117 955 17 5 20 13 47.99402 945 21 7 60 12.9 10.77315 955 18 7 18 13.2 1.81598 945 21 5 23 12.4 55.87463 955 18 7 40 13.l 5.6128 945 22 5 70 12.8 128.51094 955 19 5 9 12.6 18.05258 945 22 5 18 12.9 42.47397 955 20 7 15 13.2 1.444 945 23 7 60 13 10.70666 955 20 7 17 13.2 1.69108 945 23 7 40 13 5.64767 955 21 7 50 13.1 8.14672 950 7 7 12 13.2 1.08141 960 2 4 0 12. I 0 950 7 7 60 13 10.70666 960 3 4 0 12.l 0 950 7 7 20 13 2.10077 960 3 7 32 13.2 4.32297 950 9 5 50 12.8 96.57752 960 3 7 28 13.2 3.5366 950 9 5 50 12.9 95 .94406 960 4 4 0 13 0 950 10 3 15 12.7 209.04298 960 6 4 0 12.6 0 950 10 3 20 12.6 281.4758 960 6 7 60 13.1 11.95741 950 11 5 12 12.9 25.37159 960 6 7 40 13.2 6.24604 950 II 5 15 12.9 33.79973 960 7 4 10 11.65 44.55736 950 12 5 6 12.9 11.33893 960 7 5 14 13 34.70987 950 12 7 32 12.7 3.99714 960 7 5 8 13.2 17.23059 Coordinates (feet) Tube Percent Pressure Permeability Coordinates (feet) Tube Percent Pressure Permeability x y nwnber of flow (psi) (md) x y nwnber of flow (psi) (md) 960 8 4 13 11.55 63.75771 960 8 5 11 13.1 25.20485 960 8 5 20 13 54.2414 960 9 4 1 12.l 3.34694 960 9 5 8 13.2 17.23059 960 9 5 18 13 47.66008 960 10 4 0 12.7 0 960 10 7 12 13.3 1.18658 960 10 7 95 13.2 18.31713 960 11 4 18 11.5 96.55164 960 11 5 16 13 41.13183 960 11 5 12 13 28.4429 960 11 5 14 13.1 34.48618 960 12 4 16.5 11.6 85.95828 960 12 5 18 13 47.66008 960 12 5 20 13 54.2414 960 13 4 0 12.5 0 960 13 7 30 13.3 3.82743 960 13 7 50 13. l 9.14275 960 14 4 0 12.5 0 960 14 7 16 13.3 1.72475 960 14 7 95 13.l 18.43862 960 15 4 8 12. l 33.82893 960 15 5 10 13. l 22.18136 960 15 5 6 13.2 12.52197 960 16 4 56 11.3 306.54303 960 16 5 50 13 107.80484 960 16 5 14 13.1 34.48618 960 17 4 55 11.5 297.15814 960 17 3 70 12.2 1161.54382 960 17 3 60 12.3 963.70856 960 17 3 50 12.5 789.79401 960 18 4 0 12.65 0 960 18 5 4 13.3 7.92311 960 18 7 24 13.4 2.86969 960 19 4 0 13 0 960 19 7 34 13.3 4.76642 960 19 7 48 13.3 8.46383 960 20 4 0 12.05 0 960 20 7 60 13.3 11.80636 960 20 5 12 13.2 28.0871 960 21 4 0 12.8 0 960 21 5 8 13.2 17.23059 960 21 5 5 13.3 10.16177 960 21 7 56 13.3 10.69076 MFP MEASURED PERMEABILITY DATA GRID C DATA Coordinates (feet) Tube Percent Pressure Permeability Coordinates (feet) Tube Percent Pressure Permeability X Y nwnber of flow (psi) (md) X Y nwnber of flow (psi) (md) 4 I 4 25 13.80 118.37946 3 7 6 18 14.7 3.66136 I 3 6 78 14.3 30.82139 3 7 6 31 14.4 9.7296 3 6 27 14.5 7.68589 3 8 6 46 14.5 17.24739 3 6 13 14.7 2.10768 3 8 5 30 14.l 68 .96229 4 6 36 14.4 12.35153 3 9 4 50 13.9 230.37314 4 6 10 14.8 1.214 3 9 4 14 14.2 59.03829 5 6 30 14.7 9.06123 3 10 7 42 14.6 6.12338 5 6 36 14.5 12.28386 3 10 7 17 15 1.60933 6 6 19 14.4 4.05371 3 10 5 12 14 26.10426 6 6 31 14.3 9.78411 3 10 7 18 15 1.72762 7 5 18 14.2 43.01988 3 11 5 15 13.55 35.67588 7 5 14 14.2 31.44975 3 11 5 15 13.9 34.92345 7 5 18 14.2 43.01988 3 11 5 19.5 14.6 46.26831 8 6 32 14.6 10.13708 3 11 5 30 14.15 68.75516 8 6 29 14.6 8.61896 3 12 4 66 12.9 309.77936 8 5 12 14.4 25.51987 3 12 4 70 12.9 326.49924 II 7 33 14.6 4.08552 3 12 4 46 13 230.24782 11 7 65 14 I J.68507 3 12 4 82 12.8 384.09769 11 7 53 14.15 9.16992 3 12 4 61 12.5 297.84933 2 3 6 36 14.4 12.35153 4 4 35 13.8 170.74991 2 3 6 12 14.7 L80795 4 2 6 52 14.3 20.35943 2 3 6 14 14.7 2.41166 4 2 6 14 14.7 2.41166 2 5 6 15 14.7 2.71937 4 2 6 30 14.5 9.16131 2 5 6 25 14.3 6.79418 4 3 6 47 14.4 17.83014 2 5 6 29 14.6 8.61896 4 3 6 41 14.4 14.95921 2 4 63 13.8 279.09311 4 3 6 14 14.7 2.41166 2 7 6 14 14.7 2.41166 4 4 6 0 14.7 0 2 7 13 14.2 28.61105 4 4 6 0 14.7 0 2 9 5 75 14.I 139.03484 4 5 5 43 14.2 87 .81989 2 9 5 28 14.5 63.36814 4 5 6 17 14.3 3.42992 2 9 6 28 14.5 8.17498 4 5 6 40 14.4 14.4849 2 9 6 90 14.3 33.82864 4 6 6 40 14.3 14.56501 2 10 5 5 14.5 9.26 854 4 6 5 55 14 106.86218 2 10 5 29 13.4 69.92488 4 6 5 II 14.2 23.04357 2 10 5 84 13.15 163.26059 4 7 5 25 14.I 58.92549 2 10 5 17.5 14.l 41.81478 4 7 5 37 14.l 79.66366 2 II 5 18 13.3 45.52971 4 5 9 14.4 17.89009 2 II 5 32 13.3 75 .65646 4 8 6 37 14.5 12.81172 2 II 5 14 13.9 31.99793 4 9 4 14 14.I 59.38125 2 II 5 5 14.6 9.21926 4 9 4 13 14.2 53.82322 2 13 7 73 13.5 13.40982 4 10 7 0 15.2 0 2 13 5 9 14 18.28347 4 10 7 20 14.5 2.03747 2 13 5 14 13.9 31.99793 4 10 7 21 14.3 2.20814 2 13 5 12 14.3 25.66291 4 10 7 18 14.6 1.77654 2 13 7 53 14 9.24588 4 10 7 19 14.6 1.89932 3 2 6 56 14 22.71001 4 10 7 20 14.6 2.02289 3 2 6 22 14.6 5.25686 4 11 7 40 14 5.8058 3 2 6 18 14.7 3.66136 4 11 5 22 13.6 54.77392 3 3 6 18 14.7 3.66136 4 11 5 4 14.6 7.18725 3 3 6 21 14.8 4.73496 4 11 7 49 14.6 7.95941 3 3 6 14 14.7 2.41166 4 11 7 34 14.8 4.25104 3 3 6 35 14.5 11.75793 4 12 5 22 14.3 52.40255 3 3 6 52 14.4 20.2358 4 12 5 33 13.9 74.4088 3 4 5 43 14.l 88.3517 4 12 4 55 12.9 265.93839 3 4 6 39 14.4 13.949 4 12 4 99 13.8 431.10098 3 5 5 17 14.3 39.86481 5 6 27 14 7.90945 3 5 6 27 14.6 7.64297 5 5 17 14 40.59379 3 5 6 53 14.4 20.71476 5 I 6 0 14.8 0 3 6 5 12 14.2 25.80797 5 I 6 20 14.4 4.38018 3 6 5 94 13.9 175.40359 5 2 6 20 14.7 4.30255 3 7 5 18 14.I 43.28392 5 2 6 22 14.6 5.25686 Coordinates (ff.1HG/ 760. PATMl=RAWPR(IDATA) PRPSI=PATM1*14.696 c 400 NITER=NITER+l ALPHA=ACONST BETA=BCONST IF(PERM0.LT.TOL) GO TO 410 ALPHA=ACONST*PERM0**AEXP BETA=BCONST*PERM0**BEXP 410 CONTINUE CALL PPHI(PATM0,PPHI0) CALL PPHI(PATMl,PPHil) DMPHI=PPHI1-PPHI0 CALL ZFACT(PRPSI,T,PCN2,TCN2,Z) CALL GASVIS(PRPSI,T,PCN2,TCN2,Z,GV) c XDATA(IDATA)=l.E-7*(ALPHA*(l.+BETA/ PATMl)*PERM0*PERM0* + DMPHI)/(ARAD*GV) IF(XDATA(IDATA) .GE.TOL) GO TO 420 YDATA(IDATA)=l. IF(XDATA(IDATA) .GE .l. E-10) RETURN PERMA(IDATA)•FRMASS/ (ARAD*GEOM*DMPHI) RETURN c 420 CONTINUE YDATA(IDATA)=SEVAL(NCPTS,XDATA(IDATA),REYGA2,GRATIO,B,C,D) GFACT·YDATA(IDATA)*GEOM PERMl=FRMASS/(ARAO*GFACT*DMPHI) PERMA(IDATA)=PERMl PRATIO=ABS((PERM1-PERM0)/ PERM1) IF(PRATIO.LE.PERMTOL) RETURN C WRITE(3,3000) NITER,PERMl,PERMTOL IF(NITER .GE .MAXIT) RETURN PERM0=PERM1 GO TO 400 END c c ...................................•..........•..................................•......... SUBROUTINE SPLINE (N, X, Y, B, C, D) c ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• INTEGER N REAL X(N), Y(N), B(N), C(N), D(N) ( +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C THE COEFFICIENTS B(I) , C(I), AND O(I), I=l,2, . .. ,N ARE CQt.f>UTED FOR A CUBIC INTERPOLATING C SPLINE S(X) • Y(I) + B(I)*(X-X(I)) + C(I)*(X-X(I))**2 + O(I)*(X-X(I))**3 C FOR X(I) .LE. X .LE. X(I+l) C INPUT ... N =THE NUMBER OF DATA POINTS OR KNOTS (N .GE .2) C X = THE ABSCISSAS OF THE KNOTS IN STRICTLY INCREASING ORDER C Y = THE ORDINATES OF THE KNOTS C OUTPUT .. B, C, D •ARRAYS OF SPLINE COEFFICIENTS AS DEFINED ABOVE . C USING P TO DENOTE DIFFERENTIATION , C Y(I) = S(X(I)) C B(I) = SP(X(I)) C C(I) = SPP(X(I))/ 2 C D(I) SPPP(X(I))/6 (DERIVATIVE FROM THE RIGHT) C THE ACCQt.f>ANYING FUNCTION SUBPROGRAM SEVAL CAN BE USED TO EVALUATE THE SPLINE. c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ INTEGER NMl, IB, I REAL T c NMl = N-1 IF ( N .LT. 2) RETURN IF ( N .LT. 3) GO TO 550 c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C SET UP TRIDIAGONAL SYSTEM B = DIAGONAL, D= OFFDIAGONAL, C = RIGHT HAND SIDE . c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ D(l) = X(2) -X(l) C(2) = (Y(2) -Y(l))/ D(l) DO 500 I = 2, NMl D(I) = X(I+l) -X(I) B(I) = 2.*(D(I-1) + D(I)) C(I+l) = (Y(I+l) -Y(I))/ D(I) C(I) = C(I+l) -C(I) 500 CONTINUE c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C END CONDITIONS . THIRD DERIVATIVES AT X(l) AND X(N) OBTAINED FROM DIVIDED DIFFERENCES . c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ B(l) = -0(1) B(N) = -D(N-1) C(l) 0. C(N) 0. IF ( N .EQ. 3) GO TO 510 C(l) C(3)/(X(4)-X(2)) -C(2)/(X(3)-X(l)) C(N) C(N-1)/(X(N)-X(N-2)) -C(N-2)/(X(N-l)-X(N-3)) C(l) = C(l)*D(l)**2/ (X(4)-X(l)) C(N) -C(N)*D(N-1)**2/ (X(N)-X(N-3)) s c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C FORWARD ELIMINATION ( +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 510 DO 520 I = 2, N T • D(I-1)/B(I-l) B(I) -B(I) -T*D(I-1) C(I) -C(I) -T*C(I-1) 520 CONTINUE ( +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C BACK SUBSTITUTION c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C(N) • C(N)/B(N) DO S30 IB = 1, NMl I • N-IB C(I) • (C(I) -D(I)*C(I+l))/B(I) 530 CONTINUE ( +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C C(I) IS NOW THE SIGMA(!) OF THE TEXT COMPUTE POLYNOMIAL COEFFICIENTS ( +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 167 B(N) = (Y(N) -Y(NMl))/D(NMl) + D(NMl)*(C(NMl) + 2.*C(N)) DO 540 I = 1, NMl B(I) (Y(I+l) -Y(I))/D(I) -D(I)*(C(I+l) + 2.*C(I)) D(I) = (C(I+l) -C(I))/D(I) C(I) = 3.*C(I) 540 CONTINUE C(N) • 3.*C(N) D(N) • D(N-1) RETURN c 550 B(l) • (Y(2)-Y(l))/(X(2)-X(l)) C(l) • 0. D(l) -0. B(2) -B(l) C(2) • 0. D(2) -0. c RETURN END c c ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• FUNCTION SEVAL(N, U, X, Y, B, C, D) c ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c THIS SUBROUTINE EVALUATES THE CUBIC SPLINE FUNCTION c SEVAL = Y(I) + B(I)*(U-X(I)) + C(I)*(U-X(I))**2 + D(I)*(U-X(I))**3 c WHERE X(I) . LT. U .LT. X(I+l), USING HORNER~S RULE c IF U . LT. X(l) THEN I 1 IS USED. c IF U .GE. X(N) THEN I = N IS USED. c INPUT .. c N = THE NUMBER OF DATA POINTS c U = THE ABSCISSA AT WHICH THE SPLINE IS TO BE EVALUATED c X,Y =THE ARRAYS OF DATA ABSCISSAS AND ORDINATES c B,C,D = ARRAYS OF SPLINE COEFFICIENTS COMPUTED BY SPLINE c IF U IS NOT IN THE SAME INTERVAL AS THE PREVIOUS CALL, THEN. A BINARY SEARCH IS c PERFORMED TO DETERMINE THE PROPER INTERVAL. c ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• INTEGER N, I, J, K REAL DX, U, X(N), Y(N), B(N), C(N), D(N) c DATA I/l/ IF ( I .GE. N) I = 1 IF ( U . LT. X(I)) GO TO 600 IF ( U .LE. X(I+l) ) GO TO 620 c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C BINARY SEARCH c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 600 I 1 J = N+l 610 K = (I+J)/2 IF ( U .LT. X(K) ) J = K IF ( U .GE. X(K) ) I = K IF ( J .GT. I+l) GO TO 610 c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C EVALUATE SPLINE ( +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 620 DX = U -X(I) SEVAL • Y(I) + DX*(B(I) + DX*(C(I) + DX*D(I))) c RETURN END c ( ........................................................•...............•................•. SUBROUTINE PPHI(PRESS,FPPHI) c ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• C PPHI EVALUATES THE PSEUDO-POTENTIAL FUNCTION INTEGRAL C USING THE AUTOMATIC QUADRATURE ROUTINE QUANC8. c ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• EXTERNAL FUN c COMMON/DATA4/ACONST,AEXP,BCONST,BEXP,ALPHA,BETA,STEMP c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C COMPUTE THE PSEUDO-POTENTIAL FUNCTION INTEGRAL, (FPPHI) FROM THE REFERENCE POTENTIAL (ALIM) C TO THE ' PRESS' POTENTIAL (BLIM) IN UNITS OF (GM-ATM/ CM3-CP). ( +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ PREF-0 .5 PHIREF=PREF•PREF/2 .+BETA•PREF ALIM=PHIREF BLIM=PRESS•PRESS/2.+BETA•PRESS c IF(BETA.LT.0 . 2) GO TO 700 c AERR=l.E-6 RERR=l . E-6 c CALL QUANC8(FUN,ALIM,BLIM,AERR,RERR,FPPHl,ERR,NIT,FLAG) IF(FLAG.NE.0.0) WRITE(6,6700) ALIM,BLIM,PRESS,NIT,FLAG RETURN c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C THIS SECTION WAS ADDED TO SPEED-UP THE PPHI CALCULATION FOR PRACTICAL CASES WHERE BETA IS C SMALL AND THE MEASURED DIFFERENTIAL PRESSURE IS SMALL . THE SPEED-UP MAY BE REMOVED BY C DELETING THE IF-STATEMENT ABOVE . c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 700 CONTINUE PCN2=493 . TCN2=227 . GMW=28 .013 R=82.06 PRPSl=l4 .696 T=STEMP TKELV=5 .*(T-32.)/9.+273. CALL ZFACT(PRPSl,T,PCN2,TCN2,Z) CALL GASVIS(PRPSl,T,PCN2,TCN2,Z,GV) c FPPHl=(BLIM-ALIM)*GMW/ (R•TKELV*Gv•z) RETURN c 6700 FORMAT(2X,'WARNING --PHI CALCULATION MAY BE UNRELIABLE & //5X,'ALIM =' ,G10.3,10X, 'BLIM =' ,G10.3, & /5X, 'PRESS=' ,G10.3,/ 5X,'NIT =' ,15, & /5X, 'FLAG =' ,G10.3) c END c ( .................•...........................................•....................•.••••... REAL FUNCTION FUN(X) c ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• C FUN(X) EVALUATES THE INTEGRAND OF THE PSEUDO-POTENTIAL INTEGRAL AND IS CALLED BY QUANC8 C SET THE CRITICAL PROPERTIES FOR NITROGEN C PC IN UNITS OF PSIA C TC IN UNITS OF DEGREES RANKINE C G.fN IN UNITS OF LBM/ LB-MOLE C R UNIVERSAL GAS CONSTANT (CM••3 ATM I GM-MOLE DEG-K) c NOTE: 1 ATM E 14.696 PSIA E 760. ""1HG ( ...................•....•..••.•...•.............•................•..••..............•...... CQl.t.10N/CALIB/PLM(l0,10),RINTM(l0,10),RSLPM(10,10),RMETER(10) CCJl.t.10N/CNTRL1/NSETS,ITYPE,IDIM,IKREL CCJl.t.10N/ CNTRL2/ISYSPL,ILEAK,IHVC,IMODE CCJl.t.10N/ CNTRL3/IHVPLT,IDSPL CCJl.t.10N/CURVE/GRATI0(50) , REYGA2(50),B(50),C(50),D(50),NCPTS CCJl.t.10N/DATA1/IMETER(5000),RAWPR(5000),RAWFR(5000),IDATA,NDATA CCJl.t.10N/DATA2/PINV(5000),PERMA(5000),XDATA(5000),YDATA(5000) CCJl.t.10N/ DATA3/ARAD,GEOM,AREA,Bpt.f.1HG,CORED,COREL CCJl.t.10N/ DATA4/ACONST,AEXP,BCONST,BEXP,ALPHA,BETA,STEMP CCJl.t.10N/ DATA5/ XZEROP,YZEROP,ZZEROP,DELXP,DELYP,DELZP CCJl.t.10N/ DATA6/XPOSN(5000),YPOSN(5000),ZPOSN(5000) CCJl.t.10N/ GFACT/HSGEOM(50),BD(50),BGF(50),CGF(50),DGF(50),NHSG CCJl.t.10N/TITLE/ ILABEL(5) CQl.t.10N/ PFUN2/FRMASS,PATM0,PATM1,PRPSI CQl.t.10N/ INPUT/TUBE(5000),F(5000),P(5000) PCN2=493 . TCN2=227 . GMW-28.013 R=82 .06 ( +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C --COMPUTE THE PRESSURE ASSOCIATED WITH A GIVEN X-POTENTIAL c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ PRATM=-BETA+SQRT(BETA*BETA+2.*X) PRPSI=14 .696*PRATM T· STEMP TKELV=5.*(T-32.)/9.+273 . c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C --COMPUTE THE Z-FACTOR AND VISCOSITY OF THE GAS FOR THE SPECIFIED TEMPERATURE AND PRESSURE . c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ CALL ZFACT(PRPSI,T,PCN2,TCN2,Z) CALL GASVIS(PRPSI,T,PCN2,TCN2,Z,GV) c FUN=GMN/ (R*TKELV*GV*Z) c RETURN END c ( ••••••..•.•.••••.•..••.............................•...•••••••••..•.•...................... SUBROUTINE QUANC8(FUN,A , B,ABSE , RELE,RESULT,ERREST,NOFUN,FLAG) c ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c ESTIMATE THE INTEGRAL OF FUN(X) FROM A TO B TO A USER PROVIDED TOLERANCE . AN AUTOMATIC c ADAPTIVE ROUTINE BASED ON THE 8-PANEL NEWTON-COTES RULE . c INPUT . . c FUN THE NAME OF THE INTEGRAND FUNCTION SUBPROGRAM FUN(X) . c A THE LOWER LIMIT OF INTEGRATION . c B THE UPPER LIMIT OF INTEGRATION.(B MAY BE LESS THAN A.) c RELE A RELATIVE ERROR TOLERANCE . (SHOULD BE NON-NEGATIVE) c ABSE AN ABSOLUTE ERROR TOLERANCE . (SHOULD BE NON-NEGATIVE) c OUTPUT .. c RESULT AN APPROXIMATION TO THE INTEGRAL HOPEFULLY SATISFYING THE LEAST STRINGENT OF THE c TWO ERROR TOLERANCES . c ERR EST AN ESTIMATE OF THE MAGNITUDE OF THE ACTUAL ERROR . c NOFUN THE NUMBER OF FUNCTION VALUES USED IN CALCULATION OF RESULT . c FLAG A RELIABILITY INDICATOR . IF FLAG IS ZERO, THEN RESULT PROBABLY SATISFIES THE c ERROR TOLERANCE . IF FLAG IS XXX .YYY, THEN XXX =THE NU"'BER OF INTERVALS WHICH c HAVE NOT CONVERGED ANO 0. YYY =THE FRACTION OF THE INTERVAL LEFT TO DO WHEN THE c LIMIT ON NOFUN WAS APPROACHED ........................................................................................... c REAL FUN, A, B, ABSE, RELE, RESULT, ERREST, FLAG REAL W0,Wl,W2,W3,W4,AREA,X0,F0,STONE,STEP,COR11,TEMP REAL QPREV,QNON,QDIFF,QLEFT,ESTERR,TOLERR REAL QRIGHT(31),F(16),X(16),FSAVE(8,30),XSAVE(8,30) INTEGER LEVMIN,LEVMAX,LEVOUT,NOMAX,NOFIN , LEV,NIM,I,J INTEGER NOFUN c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C ••• STAGE 1 ••• GENERAL INITIALIZATION SET CONSTANTS . c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ LEVMIN 1 LEVMAX = 30 LEVOUT = 6 NOMAX = 5000 NOFIN • NOMAX -8*(LEVMAX-LEVOUT+2**(LEVOUT+l)) c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C TROUBLE WHEN NOFUN REACHES NOFIN c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ W0 -3956.0 I 14175.0 Wl • 23552.0 I 14175.0 W2 --3712.0 I 14175 .0 W3 ~ 41984 .0 I 14175 .0 W4 -18160.0 I 14175 .0 ( +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C INITIALIZE RUNNING SUMS TO ZERO . c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ FLAG • 0.0 RESULT = 0.0 CORll 0.0 E ERREST 0.0 z AREA • 0.0 NOFUN • 0 IF (A .EQ. B) RETURN ( +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C ••• STAGE 2 ••• INITIALIZATION FOR FIRST INTERVAL ( +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ LEV • 0 NIM • 1 X0 = A X(16) = B QPREV = 0.0 F0 • FUN(X0) STONE • (B -A) I 16.0 X(8) (X0 + X(16)) I 2.0 X(4) (X0 + X(8)) I 2.0 X(12) (X(8) + X(16)) I 2.0 E X(2) (X0 + X(4)) I 2.0 X(6) (X(4) + X(8)) I 2.0 X(10) = (X(8) + X(12)) I 2.0 X(l4) (X(12) + X(16)) I 2.0 [)() 800 J = 2, 16, 2 F(J) = FUN(X(J)) 800 CONTINUE NOFUN = 9 c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C •••STAGE 3 •••CALCULATION REQUIRES QPREV,X0,X2,X4, . . . ,X16,F0,F2,F4, . .. ,F16. C CALCULATES Xl,X3, ...XlS, Fl,F3, ... F1S,QLEFT,QRIGHT,QNOW,QOIFF,AREA. ( +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 810 X(l) = (X0 + X(2)) I 2.0 F(l) = FUN(X(l)) [)() 820 J = 3, 15, 2 X(J) = (X(J-1) + X(J+l)) I 2.0 F(J) = FUN(X(J)) 820 CONTINUE NOFUN = NOFUN + 8 STEP = (X(16) -X0) I 16.0 QLEFT (W0*(F0 + F(8)) + Wl*(F(l)+F(7)) + W2*(F(2)+F(6)) 1 + W3*(F(3)+F(5)) + W4*F(4)) * STEP QRIGHT(LEV+l)=(W0*(F(8)+F(16))+Wl*(F(9)+F(1S))+W2*(F(10)+F(l4)) 1 + W3*(F(ll)+F(13)) + W4*F(12)) * STEP QNOW = QLEFT + QRIGHT(LEV+l) QDIFF = QNOW -QPREV AREA = AREA + QDIFF c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C *** STAGE 4 ••• INTERVAL CONVERGENCE TEST c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ESTERR = ABS(QOIFF) I 1023.0 TOLERR = AMAXl(ABSE,RELE*ABS(AREA)) * (STEP/ STONE) IF (LEV .LT . LEVMIN) GO TO 830 IF (LEV .GE . LEVMAX) GO TO 870 IF (NOFUN .GT. NOFIN) GO TO 860 IF (ESTERR .LE. TOLERR) GO TO 880 c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C ••• STAGE S *** NO CONVERGENCE LOCATE NEXT INTERVAL. c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 830 NIM • 2*NIM LEV • LEV+l ( +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C STORE RIGHT HAND ELEMENTS FOR FUTURE USE . c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ DO 840 I • 1, 8 FSAVE(I,LEV) • F(I+8) XSAVE(I,LEV) = X(I+8) 840 CONTINUE c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C ASSEMBLE LEFT HAND ELEMENTS FOR IMMEDIATE USE. c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ QPREV = QLEFT DO 850 I = 1, 8 J • -I F(2*J+18) F(J+9) X(2*J+18) = X(J+9) 850 CONTINUE GO TO 810 ( +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C ••• STAGE 6 ••• NUMBER OF FUNCTION VALUES IS ABOUT TO EXCEED LIMIT . c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 860 NOFIN ~ 2*NOFIN LEVMAX • LEVOUT FLAG • FLAG + (B -X0) I (B -A) GO TO 880 ( +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C CURRENT LEVEL IS LEVMAX . ( +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 870 FLAG = FLAG + 1.0 c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ c ••• STAGE 7 ••• INTERVAL CONVERGED ADD CONTRIBUTIONS INTO RUNNING s~s. c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 880 RESULT RESULT + QNOW ERREST = ERREST + ESTERR CORll = CORll + QDIFF I 1023.0 c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C LOCATE NEXT INTERVAL . c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 890 IF (NIM .EQ. 2*(NIM/ 2)) GO TO 900 NIM = NIM/2 LEV = LEV-1 GO TO 890 900 NIM • NIM + 1 IF (LEV .LE. 0) GO TO 920 c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C ASSEMBLE ELEMENTS REQUIRED FOR THE NEXT INTERVAL. c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ QPREV = QRIGHT(LEV) X0 = X(lG) F0 = F(16) DO 910 I = 1, 8 F(2*I) FSAVE(I,LEV) X(2*I) = XSAVE(I,LEV) 910 CONTINUE GO TO 810 c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C ••• STAGE 8 ••• FINALIZE AND RETURN c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 920 RESULT • RESULT + CORll c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C MAKE SURE ERREST NOT LESS THAN ROUNDOFF LEVEL . c +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ IF (ERREST .EQ. 0.0) RETURN 930 TEMP = ABS(RESULT) + ERREST IF (TEMP .NE . ABS(RESULT)) RETURN ERREST = 2.0*ERREST GO TO 930 END c c ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• SUBROUTINE ZFACT(P,TF,PC,TC,ZF) c ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• C ZFACT CQl.f>UTES THE GAS DEVIATION FACTOR FOR A PURE COMPONENT WITH A GIVEN PC AND TC FOR A C USER-SPECIFIED PRESSURE AND TE~ERATURE USING THE HALL-YARBOROUGH METHOD (1973) AS C DEVELOPED FROM THE STARLING-CARNAHAN EQUATION OF STATE . c ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• EPS=l. E-10 TOL=l. E-6 TRANKaTF+460. T=TC/TRANK PR=P/ PC IF(ABS(PR) .LT .EPS) GO TO 1030 Y=0 . 5 c 1000 F=-0.06125*PR*T*EXP(-l.2*(1. -T)*(l.-T)) & +(Y+Y*Y+Y*Y*Y-Y*Y*Y*Y)/(l.-Y)**3 & -(14.7*T-9. 76*T*T+4.58*T*T*T)*Y*Y & +(90.7*T-242. 2*T*T+42.4*T*T*T)*Y**(2.18+2.82*T) FPRIME=3 . *(Y+Y*Y+Y*Y*Y-Y*Y*Y*Y)*(l . -Y)**(-4) & +(l.+2.*Y+3.*Y*Y-4.*Y*Y*Y)/(l.-Y)**3 & -2.*Y*(l4.7*T-9. 76*T*T+4.58*T*T*T) & +(2.18+2.82*T)*(90.7*T-242. 2*T*T+42.4*T*T*T)*Y**(l.18+2.82*T) c YNEW=Y-F/ FPRIME YFRAC=AB5(1 . -YNEW/ Y) IF(YFRAC.LT.TOL) GO TO 1010 IF((AB5(YNEW-l.0).LT.EPS).OR.ABS(YNEW).LT.EPS) GO TO 1020 Y=YNEW GO TO 1000 c 1010 ZF-0.06125*PR*T*EXP(-l.2*(1. -T)*(l.-T))/ YNEW RETURN c 1020 WRITE(ITTY,*) YNEW,' CONVERGENCE PROBLEM IN ZFACT ROUTINE' STOP c 1030 ZF=l.0 c RETURN END c ( ........................................................................................... SUBROUTINE GASVIS(P,T,PC,TC,ZFACT,GV) ( ........................................................................................... c GASVIS COMPUTES THE GAS VISCOSITY FOR A MIXTURE OF HYDROCARBON GASES GIVEN THE CRITICAL c PROPERTIES OF THE GAS, PRESSURE , TEMPERATURE AND GAS GRAVITY USING THE CARR, KOBAYASHI c AND BURROWS (1954) CORRELATION . c IF THE !FORM OPTION IS SET TO ZERO , A PURE COMPONENT VISCOSITY IS COMPUTED USING A c CORRECTION FACTOR IF A NON -HYDROCARBON IS USED (!TYPE= 0) . THE USER-INPUT PC AND TC c ARE USED TO GAS COMPUTE REDUCED PROPERTIES DIRECTLY . c IF THE !FORM OPTION IS SET TO ONE, THE PSEUDOCRITICAL PRESSURE AND TEMPERATURE IS ESTIMATED c FROM THE TH().IAS, HANKINSON ANDPHILLIPS (1970) CORRELATIONS . THE REDUCED PROPERTIES ARE c THEN COMPUTED IN THE USUAL MANNER . c IF THE !FORM OPTION IS SET TO TWO , THE LEE, GONZALES AND EAKIN CORRELATION IS USED . c UNITS : c T INPUT TEMPERATURE IN DEGREES F c TC INPUT/ COMPUTED CRITICAL TEMPERATURE IN DEGREES R c TK SYSTEM TEMPERATURE IN DEGREES K c TS SYSTEM TEMPERATURE IN DEGREES R c p INPUT PRESSURE IN PSIA c PC INPUT / COMPUTED CRITICAL PRESSURE IN PSIA c GGRAV GAS GRAVITY = MW(GAS) I MN(AIR) c GMW MOLECULAR WEIGHT OF GAS c GVC GAS VISCOSITY CORRECTION FACTOR FOR PURE NON-HYDROCARBON GASES AT 1 ATM c GVl COMPUTED GAS VISCOSITY AT 1 ATM c GV --OUTPUT GAS VISCOSITY AT SPECIFIED T AND P IN CP c RG --COMPUTED GAS DENSITY IN GM/ CC c ZFACT --GAS DEVIATION FACTOR OR Z-FACTOR c ................................•.............•............................................ DATA GMW/28.013/ DATA GVC/0.0086/ DATA A0/-2.46211820/, Al/2.97054714/, A2/-0.286264054/, A3/8.05420522E-03/, & A4/2.80860949/ , A5/-3.49803305/, A6/0.36037302/, A7/-0.0104432413/ , & A8/-0.793385684/, A9/l. 39643306/, Al0/-0.149144925/, All/0.00441015512/, & A12/0.0839387178/, A13/-0. 186408848/, Al4/0.0203367881/, A15/-0.000609579263/ c DATA B0/l.11231913E-02/, Bl/l.67726604E-05/, B2/2.11360496E-09/, B3/-1.0948505E-04/, & B4/-6.40316395E-08/, B5/-8.99374533E-ll/, B6/4. 57735189E-07/, B7/2.1290339E-10/, & B8/3.97732249E-13/ c IFORM=0 GGRAV=GMW/ 28 .97 TS=T+460 IF(IFORM.GT.0) GO TO 1200 ( PR=P/PC TR=TS/TC ( 1100 GVl•GVC+B0+Bl-T+B2*T*T+B3*GMW+B4*T*GMW+BS*T*T*G.Nl+B6*GMitl*GMW+B7*T*GMW*GMitl+B8*T*T*GMW ( ARG0=A0+Al*PR+A2*PR*PR+A3*PR*PR*PR ARG1=A4+AS*PR+A6*PR*PR+A7*PR*PR*PR ARG2aA8+A9*PR+A10*PR*PR+All*PR*PR*PR ARG3=A12+A13*PR+A14*PR*PR+Al5*PR*PR*PR ARG=ARG0+ARG1-TR+ARG2*TR*TR+ARG3*TR*TR*TR VRATIO=EXP(ARG)/TR GVaGVl*VRATIO RETURN ( 1200 IF(IFORM.GT . 1) GOTO 1300 ( PPC=709 .604-58 . 718*GGRAV TPC=170.491+307 . 344*GGRAV GO TO 1100 ( 1300 X=3 . 5+986/TS+0 .01*GMW Y=2.4-0.2*X TK=S .*(T-32.)/9.+273 . RG=(P*GMW/ 14.69)/(82.057477*ZFACT*TK) CONST=(9.4+0.02*GMW)*TS**l .5/ (209+19*GMitl+TS) GV=l.E-4*CONST*EXP(X*RG**Y) ( RETURN END APPENDIX D FORTRAN CODE OF VARIOGRAM COMPUTATION ROUTINE (Adapted from David, 1977). Program VGCODE4 175 PROGRAM VGCODE4 c ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c PROGRAM VGCODE4 c VERSION AUTHOR: MALCOLM A. FERRIS (ADAPTED FROM DAVIS, 1977) c DATE: 11/8/90 c c PURPOSE: TO CREATE A 2-D VARIOGRAM FROM DATA. TAKEN FROM c DAVID (1977), THIS PROGRAM SEARCHES THE DATA SET FOR c PAIRS BASED UPON THE DIRECTION AND WINDOW PARAMETERS . c VARIABLES: TITLE(80) -PRIMARY TITLE OF DATA SET c X(2000) -INPUT COORDINATE (HORIZONTAL) c Y(2000) -INPUT COORDINATE (VERTICAL) c Z(2000) -COMPUTATIONAL VALUE OF DATA c ZL(2000) -LOG10 TRANSFORMED DATA VALUES c PHI(10) -SEARCH DIRECTION OF PROGRAM RUN c PSI(10) -WINDOW ANGLE OF PROGRAM RUN c !LOG -INDICATOR FOR COMPUTATION OF LOG VALUES c NDIR -NUMBER OF SEARCH DIRECTIONS TO RUN c STEP -STEP INTERVAL USED TO GROUP DATA SEPARATION c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• CQt.t.lON /DATAl/ X(2000),Y(2000),Z(2000),ZL(2000) COMMON /DATA2/ STEP(10),PHI(10),PSI(10) COMMON /DATA3/ NDIR,NUM,J,ID,L COMMON /VARGR/ PAIRS(400),DIST(400),Sl(400),S2(400) CHARACTER*80 TITLE,TEMPLATE INTEGER N2,ID,ND,ILOG c READ(lS, '(A)') TITLE WRITE(3,1000) TITLE READ(lS,*) NDIR , ILOG DO 100 ND=l,NDIR READ(lS,•) STEP(ND),PHI(ND),PSI(ND) 100 CONTINUE READ(lS, '(A) ' ) TEMPLATE READ(15,TEMPLATE,END=110) (X(N),Y(N),Z(N),N=l,2000) 110 NUM = N -1 DO 120 N2=1,NUM IF(ILOG.EQ.1) THEN IF(Z(N2).LE.0.0) THEN ZL(N2)=-1. 301 ELSE ZL(N2) = LOG10(Z(N2)) ENDIF ENDIF IF(ILOG.EQ.2) THEN IF(Z(N2).LE.0.0) THEN ZL(N2)=-2 .9957 ELSE ZL(N2) = LOG(Z(N2)) ENDIF ENDIF IF(ILOG.EQ.0) THEN ZL(N2) = Z(N2) ENDIF 120 CONTINUE c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c c DESCRIPTION OF INPUT CARDS c •••••••••••••••••••••••••• c c COL FORMAT NAME DESCRIPTION c ••••••••••••• .............. c c CARD ONE c •••••••• c 1-80 A80 TITLE TITLE OF RUN c c CARD TWO c •••••••• c • INTEGER NDIR NUMBER OF SEARCH DIRECTIONS IN RUN c (10 MAXIMUM) c • INTEGER !LOG TRANSFORM INDICATOR c 1 DATA TO BE TRANFORMED TO LOG10 c 2 DATA TO BE TRANFORMED TO LOG-N c 0 DATA NOT TO BE TRANFORMED c c CARD THREE PARAMETERS OF VARIOGRAM SEARCH ROUTINE c •••••••••• ONE CARD REQUIRED PER "NDIR" . c • REAL PHI(!) SEARCH DIRECTION OF VARIOGRAM RUN c HORIZONTAL-RIGHT = 0° c COUNTER-CLOCKWISE INCREASING ANGLES c • REAL PSI(!) SEARCH WINDOW ANGLE OF PROGRAM c c CARD FOUR c ••••••••• c • A80 TEMPLATE FORMAT OF INPUT DATA ex, Y, "VARIABLE") c c DATA CARDS X,Y COORDINATES AND VARIABLE VALUES MUST BR IN THE c FORMAT SUPPLIE ABOVE c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• NUM=NZ-1 WRITE(*,*) X(l),Y(l),Z(l),ZL(l) WRITE(*,*) X(NUM),Y(NUM),Z(NUM),ZL(NUM) WRITE(3,1300) NUM c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• C HAVING WRITTEN TO SCREEN THE FIRST AND LAST DATA AND LOG-TRANS­( FORMS, THE OUTPUT FILES ARE HEADED WITH THE STATISTICAL C PARAMETERS FROM THE SUBROUTINE 'MOMENT'. c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• DO 130 ID=l,NDIR WRITE(3, '(A)') ' POPULATION STATISTICS FROM NUMERICAL ' & 'RECIPES I CALL MOMENT(Z,NUM,AVE,ADEV,SDEV,VAR,SKEW,CURT) WRITE(3, '(A)') ' POPULATION STATISTICS ON UNALTERED DATA WRITE(3,3100) AVE,ADEV,SDEV,VAR,SKEW,CURT IF (ILOG.GT.0) THEN CALL MOMENT(ZL,NUM,AVE,ADEV,SDEV,VAR,SKEW,CURT) WRITE(3, '(A)') ' POPULATION STATISTICS ON ALTERED DATA ' IF(ILOG.EQ.0) WRITE(3,1100) IF(ILOG.EQ.1) WRITE(3,1101) IF(ILOG.EQ.2) WRITE(3,1102) WRITE(3,3100) AVE,ADEV,SDEV,VAR,SKEW,CURT ENDIF c•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• C SUBROUTINE 'DATASET' SEARCHES THE INPUT DATA FOR PAIRS BASED C UPON THE 'PHI(I)' AND 'PSI(!)' [DIRECTION AND WINDOW] PARAMETERS. c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• CALL DATASET CALL OUTPUT 130 CONTINUE c •• FORMAT STATEMENTS •• 1000 FORMAT(16X, 'STARTING PROGRAM VGCODE4 -RUN TITLED:',/,A80, & l,22X, 'EQUAL DISTANCE SEARCH ROUTINE') 1100 FORMAT(2X, 'DATA UNCONVERTED FROM INPUT') 1101 FORMAT(2X, 'DATA CONVERTED TO LOG BASE 10') 1102 FORMAT(2X, 'DATA CONVERTED TO NATURAL LOG') 1300 FORMAT(2X,IS,2X, 'DATA SETS READ FROM FILE INPUT') 3100 FORMAT(2X, 'AVERAGE',F9.3, ', ADEV',F9.3, ', SDEV',F9.3, & ', VARIANCE',F9.3,/,SX'SKEW',F9.3, ', CURTOSIS' ,F9.3) STOP END c SUBROUTINE MOMENT(DATA,N,AVE,ADEV,SDEV,VAR,SKEW,CURT) c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• C THIS SUBROUTINE IS TRANSLATED DIRECTLY FROM "NUMERICAL RECIPES", C PRESS AND OTHERS, 1986. c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• DIMENSION DATA(N) IF(N.LE.l)PAUSE 'N must be at least 2' S=0. DO 11 J=l,N S=S+DATA(J) 11 CONTINUE AVE=S/N ADEV=0. VAR=0. SKEW=0. CURT=0. DO 12 J=l,N S=DATA(J)-AVE ADEV=ADEV+ABS(S) P=S*S VAR=VAR+P P=P*S SKEW=SKEW+P P=P*S CURT=CURT+P 12 CONTINUE ADEV=ADEV/N VAR=VAR/(N-1) SDEV=SQRT(VAR) IF(VAR.NE.0.)THEN SKEW=SKEW/(N*SDEV**3) CURT=CURT/(N*VAR**2)-3. ELSE PAUSE 'no skew or kurtosis when zero variance' ENDIF RETURN END c SUBROUTINE DATASET C******************************************************************* C THIS FORM OF THE PROGRAM SEARCHES FOR [CCl.EQ.Tl], THE SEARCH C WINDOW PARAMETERS, THE AVERAGE DISTANCES ARE ASSUMED EQUAL STEP C INCREMENTS OF THE SEPARATION/LAG DISTANCE. C******************************************************************* COMMON /DATAl/ X(2000),Y(2000),Z(2000),ZL(2000) COMMON /DATA2/ STEP(10),PHI(10),PSI(10) CQt.t.10N /DATA3/ NDIR,NUM,J,ID,L COMMON /VARGR/ PAIRS(400),DIST(400),Sl(400),S2(400) INTEGER IK,IP,ICOUNT REAL SUM,D2,DELTZ,Dl c APSI=3.141592*PSI(ID)/180. Tl=COS(APSI) APHI=3.141592*PHI(ID)/180. CA=COS(APHI) SA=SIN(APHI) C******************************************************************* C DIRECTION (PHI) IS SET FOR SINE AND COSINE WINDOW (PSI) IS SET C TO Tl AS THE COSINE VALUE OF THE ANGLE. C******************************************************************* DO 210 IP=l,40 PAIRS(IP)=0. DIST(IP)=0. Sl(IP)=0. S2(IP)=0. 210 CONTINUE C******************************************************************* C PAIRS(IP) THE COUNTER-ARRAY OF DISTANCES WHERE PAIRS EXIST C DIST(IP) THE SUMS OF THE DISTANCES SEPARATED BY THE MULTIPLE C OF THE CLASS SIZE (MULTIPLE VALUE IS IP C Sl(IP) VARIANCE -THE SUMS OF THE DIFERENCES IN VARIABLES C S2(IP) ST. DEV. -THE SUMS OF THE SQUARED DIFERENCES IN VALUES (**************************•········································ D1=0. ]=40 DELTZ=0. IK=0 L=0 WRITE(3,998) NUM ICOUNT=0 DO 240 Ll=l,NUM I2=Ll+l IF(I2.GT.NUM) GO TO 260 DO 250 L2=I2,NUM ICOUNT=ICOUNT+l D2=((X(Ll)-X(L2))*(X(Ll)-X(L2)))+ & ((Y(Ll)-Y(L2))*(Y(Ll)-Y(L2))) IF(D2.LT.0.00000001) GO TO 250 Dl=SQRT(D2) CC=((X(Ll)-X(L2))*CA/Dl)+((Y(Ll)-Y(L2))*SA/Dl) CCl=ABS(CC) IK=l+(Dl/STEP(ID)) c IF(IK.GT.41) GO TO 250 c IF(CCl.EQ.Tl)THEN IF(L.LT.IK) L=IK IF(J.GT.IK) J=IK DELTZ=ZL(Ll)-ZL(L2) PAIRS(IK)=PAIRS(IK)+l. Sl(IK)=Sl(IK)+DELTZ S2(IK)=S2(IK)+DELTZ*DELTZ DIST(IK)=DIST(IK)+Dl DELTZ=0. D1=0. IK=0 ENDIF 250 CONTINUE 240 CONTINUE 260 CONTINUE 998 FORMAT(lX, 'NUM CARRIED FROM MAIN PROGRAM. CHECK NUM =',I6) RETURN END c SUBROUTINE OUTPUT c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• C WRITES TO FILE 3 AND FILE 13 (VGCODE4.0UT AND GRAPH.DAT) C OUTPUT IS FORMATED FOR STANDARD DISPLAY OF THE STATISTICS FOR C THE SAMPLE SET AND THE GRAPH-READY DATA (NUMBER OF PAIRS, C AVERAGE DISTANCE IN THE SET AND VALUE OF SEMIVARIANCE). c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• COMMON /DATAl/ X(2000),Y(2000),Z(2000),ZL(2000) COMMON /DATA2/ STEP(10),PHI(10),PSI(10) COMMON /DATA3/ NDIR,NUM,J,ID,L CQt.t.lON /VARGR/ PAIRS(400),DIST(400),S1(400),S2(400) REAL BINF,BSUP,Ml,M2,DISMOY INTEGER I WRITE(3,3000) ID,PHI(ID),PSI(ID),STEP(ID) WRITE(3,3200) DO 300 I=J,L IF(I.GT.40) GO TO 300 IF(PAIRS(I).LE.0) GO TO 300 Ml=Sl(I)/PAIRS(I) M2=0.S*S2(I)/PAIRS(I)DISMOY=DIST(I)/PAIRS(I) BINF=(STEP(ID)*I)-STEP(ID)BSUP=STEP(ID)*I WRITE(3,3300) BINF,BSUP,PAIRS(I),Ml,M2,DISMOY WRITE(13,3400) PAIRS(I),DISMOY,M2 300 CONTINUE c c •• FORMAT STATEMENTS •• 3000 FORMAT(2X, 'RUN NUMBER',I3, ', DIRECTION',FS.1, ', ' & 'WINDOW',FS.1, ', STEP',FS.1) 3200 FORMAT(6X, 'DISTANCE',4X, '# PAIRS',SX, 'DRIFT',?X, 'GAMMA',SX, & 'AVER DIST') 3300 FORMAT(1X,F6.1,' -',F6.1,F7.0,2X,2E12.3,Fl2.2) 3400 FORMAT(1X,2F12.2,E12.4) RETURN END APPENDIX E VARIOGRAM OUTPUT DATA STARTING PROGRAM VGCODE4 -RUN TITLED: GRID A/ final variogram runs/ BEG:VGCODE4/ MAF -6/25/91 320 DATA SETS READ FROM FILE INPUT RUN NUMBER 1, DIRECTION 0. 0 , WINOOW 0.0 , STEPlOO.O DISTANCE # PAIRS DRIFT GAMMA AVER DIST 0.0 -100.0 155. 0.842E-01 0.238E+OO 57.34 100 . 0 -200.0 198. -0.433E-01 0.283E+OO 137. 92 200.0 -300.0 227. 0.488E-01 0.305E+OO 253.54 300.0 -400.0 181. 0.916E-01 0.298E+OO 355.05 400.0 -500.0 125. 0.545E-01 0. 396E+OO 436.31 500 .0 -600.0 115. 0.792E-01 0.460E+OO 540.72 600.0 -700.0 162. 0.109E+OO 0.488E+OO 651.68 700.0 -800.0 84. 0.438E-01 0.497E+OO 748.29 800.0 -900.0 66. -0. 372E+OO 0.437E+OO 867.59 900.0 -1000.0 98. 0.474E-01 0.476E+OO 952.97 1000.0 -1100. 0 98. 0.361E-01 0.682E+OO 1047 .46 1100. 0 -1200. 0 38. -0.259E+ OO 0.439E+OO 1162 .34 1200.0 -1300. 0 84. 0.255E+ OO 0.655E+OO 1256.98 1300.0 -1400.0 70. -0 .696E-01 0.477E+OO 1346.34 1400. 0 -1500.0 73. 0.154E+OO 0.481E+OO 1449.78 1500.0 -1600. 0 52. 0.225E+ OO 0.638E+OO 1565.85 1600. 0 -1700. 0 62. 0.275E+OO 0.669E+OO 1654 .33 1700.0 -1800.0 41. 0.552E+ OO 0.839E+OO 1744.10 1800.0 -1900.0 36. 0.272E+OO 0.451E+OO 1855.97 1900.0 -2000.0 66. 0.706E+OO 0.780E+OO 1954.30 RUN NUMBER 2, DIRECTIO!J 0. 0, WINOOW 0. 0, STEP 50.0 DISTANCE # PAIRS DRIFT GAMMA AVER DIST - 50.0 ~ ') 0 .15 9E+OO 0 . 25 8E+ OO 37.23 0.0 -'~ · 50.0 -100.0 123. 0.648E-01 0.233E+ OO 62.57 100.0 -150.0 126. -0 .458E-01 0.315E+OO 119. 36 150.0 -200.0 72. -0 .388E-01 0.227E+OO 170. 40 200.0 -250.0 98. 0.180E-01 0.270E+OO 220.69 250.0 -300.0 129. 0. 722E-01 0.332E+OO 278.48 300.0 -350.0 89. 0.478E-01 0.246E+ OO 331.70 350.0 -400.0 92 . 0 .134E+OO 0 . 34 8E+O O 377.64 400.0 -450.0 74. 0.160E+OO 0.400E+OO 414.90 450.0 -500.0 51. -0.980E-01 0. 391E+ OO 467.38 500.0 -550.0 59. 0 .130E+OO 0.506E+OO 515.27 550.0 -600.0 56. 0.259E-bl 0.412E+OO 567. 53 600.0 -650.0 72. 0.192E+OO 0.422E+ OO 624.52 650.0 -700.0 90. 0.424E-01 0.541E+OO 673.41 700.0 -750.0 50. 0.572E-01 0.306E+OO 724. 44 750.0 -800.0 34. 0.242E-01 0.777E+ OO 783.35 800.0 -850.0 23. -0.205E+OO 0.346E+OO 831. 91 850.0 -900.0 43. -0.462E+OO 0.486E+OO 886.67 900.0 -950.0 40. -0.630E-01 0.358E+ OO 927.05 950.0 -1000.0 58. 0.124E+OO 0.557E+OO 970.84 1000 .0 -1050 .0 57. 0.508E-01 0.674E+OO 1026 .11 RUN NUMBER 3' DIRECTION 0 . 0 , WINOOW 0 . 0, STEP 45. 0 DIST!o.NCE # P.Z\IRS DRIFT GAMMA AVER DIST 0.0 -45.0 31. 0.145E+OO 0. 262E+OO 36.92 45.0 -90.0 110. O.lOOE+OO 0.225E+OO 58.40 90.0 -135.0 105. -0.768E-01 0.271E+OO 108.32 135. 0 -180.0 79. -0.679E-01 0.320E+OO 153.25 180.0 -225.0 94. 0.498E-01 0.234E+OO 203.64 225. 0 -270.0 67. 0.548E-01 0.335E+ OO 249.96 270.0 -315 . 0 100. 0 . 477E-01 0.323E+OO 286.61 315.0 -360.0 95. 0.486E-01 0.307E+OO 336.25 360 .0 -405.0 113. 0.205E+OO 0.389E+ OO 386.62 405.0 -450.0 41. 0.238E-01 0.227E+OO 426.45 450.0 -495.0 44. 0.290E-01 0.335E+OO 462.51 495.0 -540.0 59. 0. 557E-01 0.566E+OO 510.29 540.0 -585.0 63. -0. 711E-02 0.393E+OO 564.47 585.0 -630.0 45. -0 .384E-01 0.272E+OO 615.57 630.0 -675.0 77. 0.229E+OO 0.505E+OO 655 . 16 675.0 -720 .0 51. -0 .777E-02 0.576E+OO 691. 29 72 0 . 0 -765 . 0 39. 0.128E+OO 0.358E+OO 727.95 765 . 0 -810.0 34. 0.242E-01 0 . 777E+OO 783.35 810.0 -855.0 23. -0 . 205E+OO 0.346E+OO 831. 91 855 . 0 -900 .0 43. -0 . 462E+OO 0.486E+OO 886.67 900.0 -945.0 40. -0.630E-01 0.358E+OO 927.05 945 . 0 -990.0 51. 0 . 754E-01 0.606E+OO 967.28 990.0 -1035.0 48. -0 . 878E-01 0.533E+OO 1014.74 RUN NUMBER 4, DIRECTION 90.0, WINOOW 0.0, STEP 1. 0 DISTANCE # PAIRS DRIFT GAMMA AVER DIST 0.0 -1.0 6. 0.865E-01 0.263E+OO 0.50 1.0 -2.0 268 . -0.410E-01 0.236E+OO 1. 01 2 . 0 -3.0 238. -0.lOlE+OO 0.319E+OO 2.01 3.0 -4.0 213. -0.158E+OO 0. 342E+OO 3.02 4.0 -5.0 187. -0. 221E+OO 0.367E+OO 4.01 5.0 -6 . 0 170 . -0.356E+OO 0.454E+OO 5.01 6.0 -7.0 153. -0 .433E+OO 0. 485E+OO 6.02 7. (I -8.0 134. -0.465E+OO 0.541E+OO 7.01 8.0 -9.0 122. -0 .594E+OO 0.659E+OO 8.02 9. (I -10.0 105. -0.550E+OO 0.646E+OO 9.02 10.0 -11.0 93 . -0 .623E+OO 0. 771E+OO 10.03 11. 0 -12.0 82. -0.756E+ OO 0. 796E+OO 11. 03 u.o -13.0 69. -0.838E+ OO 0. 868E+OO 12.04 13. 0 -14.0 57. -0 .788E+OO 0.956E+ OO 13 . 04 14.0 -15. 0 41. -0.701E+OO 0.742E+OO 14.05 15.0 -16.0 30. -0.652E+OO 0.588E+OO 15.05 16.0 -17.0 20. -0 .591E+OO 0.552E+OO 16.08 17.0 -18.0 13. -0.405E+OO 0. 270E+OO 17.08 18.0 -19.0 9. -0 .487E+OO 0.363E+OO 18 .11 19.0 -20.0 5. -0. 248E+OO 0.225E+ OO 19.00 20.0 -21.0 4. -0 .346E+OO 0.228E+OO 20. 00 21. 0 -22.0 2. -0 .141E+OO 0.127E+OO 21.00 22.0 -23.0 1. 0.416E+ OO 0.864E-01 22.00 STARTHJG PROGPAM VGCODE4 -RUN TITLED: GRID B/ final variogram runs/ BEG:VGCODE4/ MAF -6/25/91 221 DA.TA SETS READ FROM FILE INPUT RUH NUMBER 1, DIRECTIO!J 0 . 0, WINOOW 0 . 0, STEP 35.0 DISTANCE # PA.IRS D!UFT GAMMA AVER DIST 0.0 -35.0 339. -0. lllE+OO 0.453E+OO 14.47 35.0 -70.0 227. -0 .771E-01 0 .490E+OO 45.26 70.0 -105.0 186. 0.370E-01 0.476E+OO 80.19 105. 0 -14 0 .0 132. 0 .44 9E+ OO 0.672E+OO 113 . 90 140.0 -175.0 131. 0 .171E+OO 0.299E+OO 151. 37 175. 0 -210.0 38. 0.294E-01 0.305E+OO 175. 00 210. 0 -245.0 24. -0.215E+ OO 0 . 64 0E+OO 210.00 245.0 -28 0 . 0 9. -0 . 132E+OO 0 . 372E+OO 245.00 ') RUN NUMBER DIHECTION 0 . 0 , WINOOW 0 . 0, STEP 10.0 DISTANCE ~, # PAIRS DRIFT GAMMA AVER DIST 0.0 -10.0 86. -0.426E-01 0.378E+OO 5.00 10.0 -20.0 136. -0.923E-01 0.455E+OO 12.24 20 . 0 -30. 0 89. -0.136E+ OO 0.571E+OO 22.13 30 . 0 -40.0 121. -0.lllE+OO 0.409E+O O 33.84 40.0 -50.0 45. -0 . 843E-01 0.561E+O O 42.33 50.0 -60.0 45. -0 .133E+OO 0.570E+OO 52.44 60.0 -70.0 44. -0.843E-01 0 . 436E+OO 62.61 70.0 -80.0 96. 0.166E-02 0.428E+OO 70 .83 80 .0 -90 .0 34. 0.950E-01 0.502E+OO 82.50 90.0 -100.0 38. 0.218E-01 0. 575E+OO 92.37 100 .0 -110. 0 85. 0.123E+OO 0. 537E+OO 103.94 110.0 -120.0 20. 0. 777E+ OO 0. 675E+OO 112.75 120.0 -130. 0 23. 0.763E+OO 0.725E+OO 122.83 130.0 -140.0 22. 0.832E+ OO 0. 974E+OO 132.73 140.0 -150.0 61. 0.259E+ OO 0.379E+OO 140 .98 150 .0 -160.0 26. O.lOOE+OO 0.186E+OO 152.50 160 .0 -170.0 28. 0.202E+OO 0.245E+OO 162.32 170. 0 -180.0 54. -0. 921E-02 0. 296E+OO 173. 52 210.0 -220.0 24. -0.215E+OO 0.640E+OO 210 .00 240.0 -250 .0 9. -0 .132E+OO 0.372E+OO 245.00 RUN NUMBER 3 , DIRECTION 90 . 0 , WINDJW 0 . 0 , STEP 1.0 DISTANCE # PAIRS DRIFT GAMl-'i.A AVER DIST 1. 0 -2 . 0 190. -0 . 388E-01 0.313E+OO 1.00 2.0 3.0 175. -0 .418E-01 0.411E+OO 2.00 3.0 4.0 165. -0.619E-01 0 .446E+ OO 3.00 4.0 5. 0 152. -0.875E-01 0.446E+OO 4.00 5.0 -6.0 139. -0. 164E+OO 0.508E+OO 5.00 6.0 -7.0 128. -0.197E+ OO 0.427E+OO 6.00 7.0 -8.0 117. -0.246E+OO 0. 486E+OO 7.00 8.0 -9.0 105. -0. 339E+OO 0.549E+OO 8.00 9.0 -10. (1 94. -0 .427E+OO 0. 695E+OO 9.00 10.0 -11.0 84. -0 .510E+OO 0.805E+OO 10.00 11.0 -12.0 72. -0.570E+OO 0. 711E+OO 11.00 12.0 -13.0 61. -0. 671E+OO 0.721E+ OO 12.00 13.0 -14.0 52. -0.685E+OO 0:705E+OO 13. 00 14.0 -15.0 45. -0. 679E+OO 0.721E+OO 14.00 15.0 -16.0 36. -0.908E+OO 0. 845E+OO 15.00 16.0 -17.0 26. -0 .105E+Ol 0.899 E+OO 16.00 17.0 -18.0 23. -0.104E+Ol 0.799E+OO 17.00 18. (1 -19. 0 19. -0.970 E+OO 0.641E+ OO 18.00 19.0 -20.0 14. -0.113E+Ol 0.857E+OO 19.00 20.C• -21.0 10. -0 .113E+Ol 0.850E+OO 20.00 21. 0 -22. 0 7. -0.107E+Ol 0.752E+ OO 21.00 22.0 -23.0 3. -0.789E+OO 0.819 E+OO 22.00 23.0 -24.0 1. -0 .839£+00 0.352E+ OO 23.00 24.(: -25.0 1. -0 .568E+OO 0.161E+OO 24.00 STARTING PROGR~11 \IGCODE4 -RUN TITLED: GRID C/ final variograrn run / BEG: \IGCODE4 / M.2'F -6/ 25 /91 235 DATA SETS REJ..D FROM FILE IN PUT RUN NT.JMBER l , DIRECTIOH 0.0, WINIOW 0.0, STEP 1. 0 DISTJ.J-JCE # PAIPS DP.IFT GJIJ•1MA A\IEF, DIST 0.0 -1.0 40. 0.825E-01 0.171E+OO 0.50 1.0 -2.0 226 . 0.164E-01 0.191E+OO 1. 08 2.0 -3.0 206. -0 .355E-01 0.218E+OO 2. 07 3.0 -4.0 181. -0.264E-01 0.218E+OO 3.07 4.0 -5.0 155. -0.374E-01 0.269E+OO 4.05 5.0 -6.0 139. -0 .123E+OO 0.263E+ OO 5.06 6 . 0 -7.0 127. -0.941E-01 0.256E+ OO 6.06 7.0 -8.0 114. -0 .850E-01 0.244E+OO 7. 06 8.0 -9.0 104. -0 .842E-01 0.203E+OO 8. 06 9.0 -10.0 94. -0 .681E-01 0.204E+OO 9.05 10.0 -11.0 84. -0.937E-01 0.231E+ OO 10.05 11.0 -12.0 76. -0.143E+ OO 0.222E+OO 11.04 12. 0 -13. 0 62. -0.104E+OO 0. 212E+OO 12.02 13. 0 -14. 0 53. -0. 190E+ OO 0 . 252E+OO 13.02 14.0 -15 . 0 45. -0.2 07 E+OO 0 . 258E+OO 14.00 15.0 -16. 0 39. -0 .219E+OO 0.334E+OO 15.00 16.0 -17.0 29. -0.358E+OO 0.318E+OO 16.00 17.0 -18.0 23. -0 .376E+OO 0.208E+OO 17.00 18.0 -19.0 12. -0 .429E+OO 0.400E+OO 18.00 19.0 -20.0 9. -0.624E+OO 0.451E+OO 19.00 20. 0 -21. 0 5. -0 .484E+OO 0.153E+OO 20. 00 21.0 22.0 2. -0.585£+00 0.187E+ OO 21.00 RUN NUMBER 2, DIRECTION 90 . 0 , WINCOW 0 . 0 , STEP 1. 0 DISTANCE # PAIRS DEIFT GAMJ.1A AVER DIST 0.0 -1. 0 62. -0 .127E+OO 0.196E+OO 0.53 1.0 -2 . 0 215 . -0.346E-01 0.281E+OO 1.10 2.0 -3. 0 176. -0 .141E+OO 0.339E+OO 2. 07 3.0 -4.0 143. -0.222E+OO 0. 308E+OO 3.06 4.0 -5.0 127. -0.226E+OO 0 . 354E+OO 4.06 5.0 -6.0 104. -0.265E+OO 0.354E+OO 5.07 6.0 -7.0 89. -0.342E+OO 0.340E+OO 6.06 7.0 -8 . 0 65. -0.335E+OO 0 . 288E+ OO 7.02 8.0 -9.0 47. -0.338E+ OO 0.309E+OO 8.01 9.0 -10.0 30. -0.391E+OO 0.479E+OO 9.02 10.0 -11. 0 17 . -0.178E+ OO 0 . 354E+OO 10.03 11. 0 -12. 0 4. -0 .728E+OO 0.432E+OO 11. 00 STARTING PRCCRAM VGCODE4 -RUN TITLED: GRID DI final variograrn run/ BEG:VGCODE4/ MAF -6/25/91 191 DATA SETS READ FROM FILE I NPUT RUN NUMBER l , DIRECTION 0. 0, WINDOW 0. 0, STEP 1.0 DISTANCE # PAI PS DRIFT GAMMA AVER DIST 1. 0 -2.0 105. 0.154E-01 0.500E+OO 1.00 2.0 -3.0 102. -0.197E-01 0.516E+ OO 2.00 3.0 -4.0 100. -0.503E-02 0.604E+OO 3.00 4.0 -5.0 98. 0.436E-01 0.602E+OO 4.00 5.0 -6.0 94. 0.615E-01 0.504E+OO 5.00 6.0 -7.0 90. 0.406E-01 0.637E+OO 6.00 7.0 -8.0 87. 0.122E+OO 0.616E+OO 7.00 8.0 -9.0 85. 0.158E+OO 0.710E+OO 8.00 9.0 -10. 0 84. 0.114E+OO 0.557E+OO 9.00 10.0 -11.0 82. 0.172E+OO 0.688E+OO 10 .00 11. 0 -12.0 103. 0.208E+OO 0.601E+OO 11.00 12.0 -13 .o 102. 0.157E+OO 0.678E+OO 12.00 13.0 -14.0 99. 0.265E+OO 0.70 5E+OO 13 .00 14. 0 -15.0 74. 0. 965E-01 0.516E+OO 14.00 15.0 -16.0 72. 0.121E+OO 0.587E+OO 15.00 16.0 -17.0 69. 0.193E+OO 0. 613E+OO 16.00 17.0 -18.0 64 . 0.238E+OO 0.574E+OO 17.00 18.0 -19.0 E3 . 0.124E+OO 0. 491E+OO 18.00 19.0 -20.0 59. 0.177E+OO 0.518E+OO 19.00 20.0 -21. 0 57. 0.240E+OO 0.572E+OO 20. 00 RUl l !fU1·1BER 2, DIRECTION 90 . 0, WINDOW 0 . 0, STEP 1. 0 DISTAHCE # PAIRS DEIFT GAMMA AVER DIST 1. 0 -2.0 110. -0.199E-02 0.571E+ OO 1. 00 2.0 -3.0 106. 0.646E-01 0.759E+OO 2.00 3.0 -4.0 102. 0.103E+OO 0.793E+OO 3.00 4.0 -5.0 99. 0.108E+OO 0.878E+OO 4.00 5.0 -6.0 95. 0 .112E+OO 0.654E+OO 5.00 6.0 -7.0 87. 0.543E-01 0.802E+OO 6.00 7 .0 -8.0 83. 0.421E-01 0.665E+OO 7.00 8.0 -9.0 76. 0. lllE+OO 0.637E+OO 8.00 9.0 -10.0 72. 0.179E+OO 0.890E+OO 9.00 10.0 -11.0 68. 0.232E+OO 0.917E+OO 10.00 11. 0 -12.0 108. -0.319E+OO 0. 968E+OO 11.00 12.0 -13 .0 59. 0.382E+OO 0.670E+OO 12.00 13 .0 -14.0 55. 0.442E+OO 0.702E+OO 13.00 14.0 -15.0 50 . 0 .457E+OO 0 .745E+OO 14 . 00 15.0 -16.0 47. 0.354E+OO 0.733E+OO 15.00 16.0 -17.0 43. 0.302E+OO 0.660E+OO 16.00 17.0 -18.0 35. 0.340E+OO 0.866E+OO 17.00 18.0 -19. 0 31. 0 .178E+OO 0.838E+OO 18. 00 19.0 -20.0 24. 0.242E+OO 0.427E+OO 19.00 20.0 -21.0 20. 0.313E+OO 0.417E+OO 20. 00 VITA Malcolm Alexander Ferris was born November 2, 1961, on Long Island, New York, to John Burkam and Eileen M. Ferris. He was raised in Rye, New York and Nantucket, Massachusetts, and graduated from Rye Country Day School in 1979. He attended the University of Massachusetts, Amherst from 1980 to 1984, receiving a Bachelor of Science in Environmental Science with studies in Hydrology and Hydrogeology in May, 1984. After six months service in the Peace Corps followed by two and a half years working for the Town of Natick, Board of Health, he returned to attend the University of Texas at Austin. He returned to the University of Texas in Austin in June 1988 and finished the degree requirements for the degree of Master of Arts in January 1993. Permanent Address: 8408 Appaloosa Run Austin, Texas 78737 This thesis was typed by the author. A16 A17A18 A19 A20 A21 A22 A23 l l 00 1200 !300 1qoo 1500 !600 1700 1600 1900 2000 2100 zzao · 2300 zqoo 2500 2600 !·" 0 0 ~\.O l. 0 i·"" 0 ..... -----.. N 0 ... 0 N . • ..... '?.·· 0 I _,.o------­ ;;;---' ~:.. ---­ • 0 ~· '-o THESIS P LATE 1.H .. ...0 ~ "'·"" • "".:" • • DlsrRIBUTION OFP ERM8\BILIIT PATTERNS­UPPER SAN ANDRES fORMATION OUTCROP, GUADALUPE M OUNTAINS, N EWMEXICO '!-· •• Malcolm A. Ferris M.A., May 1993 -­• '+o ~­ '!" 1· ••• ' ... ,, " ".·" ..... ,.0 ~. ~ !: " ,~,, ~'~-"' ~,.,1 "!-" ·~-., ''}'" '!·,, 0 ·~·"' '"·" -• ":.·'"' ''!:"' --~~ . ::::=------,_-~-,---:,. ---· - ·o ..• " ----1.0 ----- -\.a •-"' ~ ... " .." ~­ .. • 1.o ­ • - 0 C_.) 0 ~-"' ~-0 • ~-·· '·'' 0 0 2300 Plate 1. Contoured map of log-transformedpermeability measurements collected on Lawyer Canyon outcrop of uSAl, first parasequence; GRID A sample data. Vertical and horizontal heterogeneities are observed in areas of concentrated sample points. Continuous patterns of high permeabilities are observed, but are contoured around relatively few data points.