Simulation and interpretation of formation-tester measurements acquired in the presence of mud-filtrate invasion, multiphase flow, and deviated wellbores
This dissertation implements three-dimensional numerical simulation models to interpret formation-tester measurements acquired at arbitrary angles of wellbore deviation. Simulations include the dynamic effects of mud-filtrate invasion and multi-phase flow. Likewise, they explicitly consider the asymmetric spatial distribution of water-base and oil-base mud filtrate in the near-wellbore region due to the interplay of viscous, gravity, and capillary forces. Specific problems considered by the dissertation are: (a) estimation of permeability from formation-tester measurements (pressure and fractional flow) affected by multi-phase flow and mud-filtrate invasion, (b) quantification of the spatial zone of response of transient measurements of pressure and fractional flow rate, (c) prediction of fluid-cleanup times during sampling operations in vertical and deviated wells, (d) joint inversion of formation-tester and resistivity measurements to estimate initial water saturation and permeability of multi-layer models, and (e) estimation of saturation-dependent relative permeability and capillary pressure using selective measurement weighting and Design-of-Experiment (DoE) methods to secure a reliable initial guess for nonlinear inversion. Using realistic tool and formation configurations, field measurements validate the reliability of the proposed methods. In one example, multi-layer rock formations are modeled using electrofacies derived from nuclear magnetic resonance logs, thereby reducing the number of unknown layer permeability values from 22 to 6. In the same example, non-uniqueness in the estimation of permeability is reduced with the quantitative integration of resistivity and formation-tester measurements. A second field example undertakes the estimation of permeability by history matching both pressure and gas-oil ratio (GOR) measurements acquired with a focused-sampling probe in a 27° deviated well. Because the latter measurements are affected by partial miscibility between oil-base mud and in-situ oil, Equation-of-State (EOS) simulations are used to account for variations of fluid viscosity, fluid compressibility, fluid density, and GOR during the processes of invasion and fluid pumpout. Results indicate that gravity-segregation and capillary-pressure effects become significant with increasing angles of wellbore deviation. If not accounted for, such effects could substantially degrade the estimation of permeability. Synthetic and field examples confirm that standard formation-tester interpretation techniques based on single-phase analytical solutions lead to biased estimations of permeability, especially in deviated wells or when complete fluid cleanup is not achieved during sampling. In addition, it is found that gravity-segregated invaded formations strongly affect predictions of fluid sampling time. Reliable and accurate estimations of petrophysical properties are only possible when both the angle of wellbore deviation and the process of mud-filtrate invasion are included in the interpretation methods.