A Mixed-Wet Hysteretic Relative Permeability and Capillary Pressure Model for Reservoir Simulations
- M. Delshad (The U. of Texas at Austin) | R.J. Lenhard (Idaho Natl. Environmental Engineering Laboratory) | Mart Oostrom (Pacific Northwest Natl. Laboratory) | G.A. Pope (The U. of Texas at Austin)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- October 2003
- Document Type
- Journal Paper
- 328 - 334
- 2003. Society of Petroleum Engineers
- 5.4.1 Waterflooding, 4.3.4 Scale, 5.3.4 Reduction of Residual Oil Saturation, 5.3.1 Flow in Porous Media, 2.4.3 Sand/Solids Control, 5.5 Reservoir Simulation, 5.2.1 Phase Behavior and PVT Measurements, 1.6.9 Coring, Fishing, 5.3.2 Multiphase Flow, 5.1 Reservoir Characterisation, 4.6 Natural Gas, 5.4.7 Chemical Flooding Methods (e.g., Polymer, Solvent, Nitrogen, Immiscible CO2, Surfactant, Vapex), 1.2.3 Rock properties, 5.6.5 Tracers
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A crucial component of all multiphase flow models is the relationship among relative permeabilities, fluid saturations, and capillary pressures. Relative permeability and capillary pressure parametric models can be very useful for predicting fluid behavior in porous media. However, relative permeabilities and capillary pressures used in oil reservoir simulators are commonly determined through interpolation between laboratory measurements. A problem with this approach is that the relations are valid only for the specific saturation path measured. Therefore, simulations of oil production using different saturation paths from those measured are likely to be in error and can limit the investigation of alternative production scenarios. In this paper, saturation-history-dependent relative permeability and capillary pressure functions for two-phase flow in mixed-wet rocks are discussed. Relative permeabilities are predicted by integrating a pore-distribution model between limits that reflect how oil and water are distributed in mixed-wet porous media. The proposed model was tested against mixed-wet capillary pressure data. The model then was incorporated in the U. of Texas Chemical Compositional Simulator (called UTCHEM) to compare waterflood simulations in water- and mixed-wet reservoirs. The simulation results agree qualitatively with laboratory core and field observations. The model and its implementation also were validated against a sandpack experiment.
Significant emphasis and efforts have been directed toward better geological reservoir descriptions and numerical solutions of reservoir simulators, but relatively little attention has been paid to better fluid-flow description in the simulation models. Petrophysical properties such as relative permeability and capillary pressure are generally dependent on saturation and saturation history. Reservoir wettability also plays an important role in relative permeability and capillary pressure and their hysteretic behavior.1-3 The majority of hysteretic relative permeability and/or capillary pressure functions have been developed for strongly water-wet porous media.4-8 However, it is now generally accepted that many oil reservoirs are mixed-wet.1,9-11 The definition of mixed wettability is adopted from Salathiel.11 The oil-wet pores correspond to the largest pore in the rock, and the small pores are water-wet. Despite these findings, there are only a few capillary pressure and relative permeability models developed for mixed-wet porous media,3,12-14 and only two have actually been incorporated in reservoir simulators.3,14 In this paper, we briefly describe a hysteretic two-phase oil/water model developed for both capillary pressure and relative permeabilities for mixed-wet rocks.15 We successfully implemented the model in UTCHEM.16,17 We have tested and validated the model and its implementation in the simulator against laboratory results.
Lenhard and Oostrom15 developed a hysteretic relative permeability and capillary pressure model for two-phase flow of oil and water in a mixed-wet porous medium based on pore-scale processes. The model described and applied in this paper, however, is a simplified version of the original model. The model requires primary drainage and main imbibition capillary pressure data. By main imbibition capillary pressure, we mean an imbibition curve starting from any point on the primary drainage curve. In addition to the primary curves, a method of developing secondary scanning curves for saturation paths inside the primary curves is also developed. The basic assumption is that the water saturation cannot become less than the water saturation that corresponds to reversal from main drainage to main imbibition paths.
Key features of the capillary pressure-saturation model are that (1) the main drainage is modeled using a Brooks and Corey function18; (2) the scanning curves are modeled using an S-shaped function19,20 that approaches asymptotes at either end; (3) the model is capable of predicting negative capillary pressures observed in mixed-wet rocks; and (4) residual oil saturations are computed using a relation that takes into account the size of the pores that are oil-wet. The relative permeability-saturation function is based on Burdine's pore-size-distribution model21 using the main drainage capillary pressure parameter. The wettability effects in the relative permeabilities are accounted for by using an index that distinguishes those pore sizes that are water-wet from those that are oil- or mixed-wet.
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