Thermodynamic Analysis of Phase Behavior at High Capillary Pressure
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Summary High capillary pressure has a significant effect on the phase behavior of fluid mixtures. The capillary pressure is high in unconventional reservoirs because of the small pores in the rock, so understanding the effect of capillary pressure on phase behavior is necessary for reliable modeling of unconventional shale-gas and tight-oil reservoirs. As the main finding of this paper, first we show that the tangent-plane-distance method cannot be used to determine phase stability and present a rigorous thermodynamic analysis of the problem of phase stability with capillary pressure. Second, we demonstrate that there is a maximum capillary pressure (Pcmax) where calculation of capillary equilibrium using bulk-phase thermodynamics is possible and derive the necessary equations to obtain this maximum capillary pressure. We also briefly discuss the implementation of the capillary equilibrium in a general-purpose compositional reservoir simulator. Two simulation case studies for synthetic gas condensate reservoirs were performed to illustrate the influence of capillary pressure on production behavior for the fluids studied.Keywords:
Capillary pressure
Petroleum reservoir
Experiments were performed on transparent two‐dimensional microfluidic porous systems to investigate the relationships among capillary pressure and the interfacial areas per volume between two fluid phases and one solid phase. Capillary pressures were calculated from the observed interfacial curvature of the wetting‐nonwetting interface, and these correlated closely to externally measured values of applied pressure. For each applied pressure, the system established mechanical equilibrium characterized by stationary interfaces, uniform curvatures across the model, and random surface normals. To study the relationships among capillary pressure and the interfacial areas, we compare the curvature‐based capillary pressure with the differential change in interfacial areas per volume as a function of wetting‐phase saturation. The differential pressure contributions calculated from the experimental measurements are found to be nearly independent of the measured capillary pressure. These results suggest that other contributions to the capillary pressure must be significant when imbibition and drainage processes result in saturation gradients.
Capillary pressure
Imbibition
Capillary length
Saturation (graph theory)
Capillary surface
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Summary Current study of fractured petroleum reservoirs often is based on the assumption of capillary discontinuity between matrix blocks. Both theoretical analysis and examination of the field performance of some fractured reservoirs, however, indicate a degree of capillary interaction between matrix blocks. Experiments performed to gain an understanding of the capillary continuity across a stack of matrix blocks are described. Three matrix blocks with a total length of 3 ft [90 cm] were stacked and placed in a transparent core holder. Before the experiments with stacked blocks were conducted, rock properties, capillary pressure, relative permeabilities, and the aperture/overburden relationship were measured. Drainage capillary pressure data showed a threshold height of the same size as each of the individual matrix blocks. Experimental results showed a strong capillary interaction (capillary continuity) between the neighboring blocks. Recovery from the top two matrix blocks far exceeds that from the same blocks when the assumption of capillary discontinuity is used. We believe that incorporation of the capillary-continuity concept in dual-porosity models will result in more realistic simulation of fractured reservoirs.
Capillary pressure
Discontinuity (linguistics)
Matrix (chemical analysis)
Overburden
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Capillary pressure
Hysteresis
Capillary surface
Capillary length
Pressure angle
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The Green–Ampt model describes infiltration of water into soil. A sharp front separates the saturated from the unsaturated zones, and capillary pressure is assumed to remain constant during infiltration. We generalized this model to account for a capillary pressure that depends on the flow velocity. Based on dimensional analysis and physical considerations, we posited a functional form for dynamic capillary pressure and assumed the nonequilibrium capillary pressure to depend on the capillary number in the form of a power law. Our model for dynamic capillary pressure describes measurements of capillary pressure versus Darcy velocity by D.A. Weitz et al. and S.L. Geiger and D.S. Durnford. Moreover, the dimensional analysis allows us to collapse three dynamic capillary pressure curves that Geiger and Durnford measured for sands of different grain size onto one curve. Furthermore our model describes capillary rise experiments performed by T. Tabuchi well. We also derived an implicit analytical solution for the front velocity.
Capillary pressure
Infiltration (HVAC)
Capillary fringe
Capillary length
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Capillary pressure
Multiphase flow
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Abstract High capillary pressure has a significant effect on the phase behavior of fluid mixtures. The capillary pressure is high in unconventional reservoirs due to the small pores in the rock, so including the effect of capillary pressure on phase behavior is necessary for reliable modeling of unconventional shale gas and tight oil reservoirs. We show that the tangent plane distance method cannot be used to determine phase stability and present a rigorous thermodynamic analysis to determine phase stability with capillary pressure. We then demonstrate that there is a maximum capillary pressure (Pcmax) where capillary equilibrium is possible and derive the necessary equations to obtain this maximum capillary pressure. We also discuss the implementation of the capillary equilibrium in a general purpose compositional reservoir simulator and the numerical challenges involved with its application to unconventional reservoirs. Three simulation case studies for gas condensate and tight oil reservoirs were performed to illustrate the influence of capillary pressure on production behavior. These results clarify the influence of capillary pressure on production behavior in low-permeability reservoirs. We show that the choice of the capillary pressure function and parameters significantly affects the results.
Capillary pressure
Relative permeability
Petroleum reservoir
Reservoir Simulation
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Citations (34)
Summary High capillary pressure has a significant effect on the phase behavior of fluid mixtures. The capillary pressure is high in unconventional reservoirs because of the small pores in the rock, so understanding the effect of capillary pressure on phase behavior is necessary for reliable modeling of unconventional shale-gas and tight-oil reservoirs. As the main finding of this paper, first we show that the tangent-plane-distance method cannot be used to determine phase stability and present a rigorous thermodynamic analysis of the problem of phase stability with capillary pressure. Second, we demonstrate that there is a maximum capillary pressure (Pcmax) where calculation of capillary equilibrium using bulk-phase thermodynamics is possible and derive the necessary equations to obtain this maximum capillary pressure. We also briefly discuss the implementation of the capillary equilibrium in a general-purpose compositional reservoir simulator. Two simulation case studies for synthetic gas condensate reservoirs were performed to illustrate the influence of capillary pressure on production behavior for the fluids studied.
Capillary pressure
Petroleum reservoir
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Citations (14)
Capillary pressure
Multiphase flow
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Since the pore radius is very tiny in the low permeability porous media, the capillary pressure should be taken into account. A phase equilibrium calculation model in consideration of the capillary pressure was built. The capillary pressure, dew point pressure and retrograde liquid volume of the constant compositional expansion of a practical gas condensate system were calculated by using this model. The effects of capillary pressure on the phase equilibrium of gas condensate system were discussed. The results show that the affecting mode on the phase equilibrium of gas condensate system is determined by the wettability. The capillary radius and the interfacial tension determine the affecting degree. The upper dew point pressure rises, and the retrograde liquid volume of the constant compositional expansion increases while the wetting angle changes from 0° to 90°. The variation is inversed when the wetting angle is from 90° to 180°. When the capillary radius is below 0.1 micrometers, the effect of the capillary pressure will be obvious.
Capillary pressure
Dew point
Dew
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Capillary pressure
Saturation (graph theory)
Centrifuge
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