# Browsing by Subject "Rocks--Fracture--Mathematical models"

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Item Discrete element modeling of rock fracture behavior: fracture toughness and time-dependent fracture growth(2006) Park, Namsu; Olson, Jon E.Show more Understanding the mechanics of fracture is important in oil and gas reservoirs. Applications range from the characterization of natural fractures that enhance fluid flow to the prediction of fracturing around a wellbore that can affect its integrity and stability. Two parameters that are of particular importance in the fracturing process are fracture toughness and subcritical index. There is a fair amount of experimental data on different rock types for these parameters but it is not well-known what petrographic properties control their magnitude. Also, because of sample preparation difficulty, fracture mechanics testing of weakly cemented sandstone is very challenging. In order to better understand the micro-mechanics of fracturing of clastic rocks (sandstones of various cementation), a numerical study was performed using the Discrete Element Method (DEM). DEM was employed in order to model laboratory test behavior, vii by assessing individually the sensitivity of results to volume of cement, time-dependent cement properties, grain/cement mineralogy, temperature, and confining pressure. The micro-mechanical properties of DEM (stiffness and friction of grains and stiffness, strength, and volume of cement) were determined using macroscopic uniaxial and triaxial compression tests. The time-dependent properties of subcritical crack growth were implemented by incorporating stress corrosion of inter-particle bonds. The stress corrosion rate was quantified by the activation energy and volume of quartz. The fracture toughness and subcritical index of Berea sandstone was measured and the results were extended to weaker rock by reducing the cement volume. The DEM results generally agree with laboratory experiments. As intergranular cement volume is reduced, fracture toughness and subcritical index decrease. Based on this relationship, the fracture mechanics properties of weak rocks, which are difficult to measure in the laboratory, can be predicted. Using the DEM model constrained by laboratory results, the importance of subcritical crack growth in wellbore stability problems was investigated. Wellbore instability in shale can be an immediate result of stress redistribution and increasing formation pore pressure following the removal of the rock mass in the wellbore. Additionally, because of large clay content and the potentially high chemical reactivity with drilling fluids, shale can be susceptible to time-dependent failure. Previous studies (mostly based on continuum modeling using poroelasticity) have concentrated on predicting the onset of failure. However, the use of DEM makes it possible to evaluate the progression of failure over time by tracking the propagation of the damage zone boundaryShow more Item Incorporating subcritical crack growth mechanics into natural fracture characterization for improved reservoir simulation(2003) Philip, Zeno George; Olson, Jon E.Show more In conventional reservoir simulation, grid block permeabilities must frequently be assigned values systematically larger than those observed in core measurements to obtain reasonable history matches. Although part of the discrepancy might be due to improper 3-D scaleup, part of it might be due to substantial flow through natural fractures unaccounted for in the simulation. Here, a method to obtain equivalent permeabilities from fracture networks generated by a geomechanical model, constrained by geologic deformation and mechanical properties of the reservoir rock, is presented. A fracture mechanics based crack growth simulator, using laboratory measured subcritical indices and reservoir rock properties, rather than a purely stochastic method, was used to generate fracture networks with realistic clustering, spacing and fracture length distributions. The effects of subcritical index and bed-thickness on fracture attributes such as mean and total lengths were observed. These fracture networks were represented in a finite-difference simulator explicitly by using enhanced grid cell permeabilities and implicitly by using non-neighbor connections. Coupled fracture-matrix fluid flow simulations of the fracture networks, under uniform pressure boundary conditions, were performed to obtain equivalent permeabilities. Permeability enhancements by factors of between 2 and 10 were observed. The results also indicate that even though the permeability of individual fractures is highly sensitive to the fracture aperture, the computed equivalent permeabilities of a weakly-connected fractured region are not. They are more sensitive to the total and mean fracture lengths, as well as the nature of the fracture pattern, which include connectivity and clustering attributes. Superposing diagenetic effects (mineralization) on a fracture network can also reduce overall equivalent permeabilities. Equivalent permeability estimates made on the fracture networks under uniform flow rate boundary conditions generate lower values than those obtained with uniform pressure boundaries. Comparison of the equivalent permeabilities and flow behavior for fractured networks embedded in a larger homogeneous unfractured matrix indicate that uniform flow rate boundaries yield more reliable estimates of the equivalent permeability than uniform pressure boundaries.Show more Item Modeling naturally fractured reservoirs: from experimental rock mechanics to flow simulation(2005) Rijken, Margaretha Catharina Maria; Olson, Jon E.Show more Fractures have a big impact on reservoir production but are inherently difficult to quantify. This study gives a robust and practical workflow to obtain a mechanically consistent naturally fractured reservoir model without direct sampling of the fracture network. The three tiers of the workflow are: 1) subcritical testing, 2) geomechanical modeling, and 3) flow modeling. Subcritical fracture index, a rock property, has been shown to influence fracture attributes such as length, spacing and connectivity. Subcritical tests show that the average subcritical index for sandstones in ambient air is around 62, whereas the average value for microstructurally comparable carbonates samples is 120. Thin-section analysis shows that an increase in cement content increases the subcritical index. Furthermore, sandstone samples containing more than 15% carbonate cement, sandstone samples containing more than 40% clay, and pure carbonate samples exhibit a large drop in subcritical index when the environment is changed from ambient air or oil to fresh water or brine. Geomechanical modeling has shown that the mechanical bed thickness has a large influence on fracture pattern characteristics and has the potential to overshadow fracture pattern changes due to strain level, strain anisotropy and subcritical index. Furthermore, an increase in strain anisotropy reduces the number of dominant through-going fracture sets and decreases the fracture spacing between the through-going fractures. This spacing variation not only influences the preferential drainage direction, it can also enhance the drainage efficiency, because more rock is exposed to the through-going fractures which are more likely to be intersected by a borehole. The level of detail provided by the geomechanical model greatly exceeds the level of detail normally used in reservoir simulation. Therefore, upscaling of the geomechanically generated fracture patterns is necessary for practical flow modeling. This study shows that different upscaling methods can lead to large variations in permeability prediction. A Local Grid Refinement around the well should be maintained, because it will almost always ensure accurate production prediction. This method is preferred over the dual permeability approach, which can be calibrated to match production data in some cases, but often requires using an unrealistic representation of the fracture pattern.Show more Item Natural fracture modeling and characterization(2002) Qiu, Yuan; Olson, Jon E.Show more The production of oil and gas from a naturally fractured reservoir requires an understanding of fracture connectivity and fracture pattern geometry. To study fracture connectivity, it is important to know fracture path. Pseudo-threedimensional numerical simulations in linear elastic materials show that fracture growth geometry is affected by not only the ratio of remote differential stress to driving stress but also by bed thickness and fracture propagation environment. Fractures will propagate straight if either the remote differential stress ratio or fracture spacing to bed thickness ratio is above one. Fractures are more planar if the propagation condition is subcritical. A cumulative fracture length distribution is derived based on mechanical principles. The mechanical interaction between two mode-I cracks is a function of fracture length, spacing, overlap and bed thickness. Crack propagation is enhanced when the en echelon cracks slightly underlap, but it is impeded when the cracks overlap. If a small crack is close enough to a large crack, it can suppress the large crack’s propagation and capture it. The probability of a large crack passing close to a small crack depends on the large crack’s length and the density of small cracks. Putting the mechanics together with the probability analysis results in a negative exponential distribution for two-dimensional map view sampling. A semi-analytical geomechanical model is developed to simulate a single set of parallel fracture network. In this model, only a few cracks are modeled explicitly and other cracks are treated as a continuum through an effective elastic modulus controlled by crack density. The semi-analytical model simulates fracture patterns similar to a more rigorous displacement-discontinuity boundaryelement model. Compared to the boundary element numerical model, the semianalytical model computes faster and can deal with thousands fractures. A sensitivity study of fracture pattern development shows that the initial flaw density, subcritical index, bed thickness and elastic modulus affect fracture length, spacing and the degree of fracture clustering. The systematic relationship between the model inputs (boundary conditions and rock properties) and final fracture geometry indicates that this high-speed semi-analytical model can be used for the further investigation of fracture pattern inversion from observed data.Show more