Equilibrium gravity segregation in porous media with capillary heterogeneity.

*(English)*Zbl 1460.76764Summary: We study the equilibrium of two phases following gravity segregation under the influence of capillary heterogeneity. Such processes are important in a number of porous media applications, e.g. determining reservoir composition, secondary migration, gravity drainage enhanced oil recovery and CO\(_2\) storage in aquifers. Solutions are derived for three-dimensional saturation distribution \(S_w(x,y,z)\) and given as an analytical formula apart from a constant \(P_c^0\) which is determined by numerical integration. The first solution assumes hydrostatic pressure and applies to cases without capillary entry pressure \((P_c(S_w=1)=0)\). The solution can be used for validation of numerical simulations and we show a close match for a number of cases. A second analytical solution is derived, extending the first, to cases of random log-normally distributed permeability fields. A formula for ensemble average saturation solution is presented and a comparison to solutions of various realizations is discussed. When capillary entry pressure is present, the solution based on hydrostatic pressure may be inaccurate due to entry pressure trapping which occurs when regions of \(S_w=1\) are present. Using numerical simulation, we extend the solution to include estimations of entry pressure trapping for a range of parameters and show its applicability. The comparison of analytical and numerical results helps illustrate and draw insight on the trapping mechanism.

##### MSC:

76S05 | Flows in porous media; filtration; seepage |

76B45 | Capillarity (surface tension) for incompressible inviscid fluids |

##### Keywords:

porous media##### Software:

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\textit{A. Rabinovich} and \textit{K. B. Cheng}, J. Fluid Mech. 890, Paper No. A3, 30 p. (2020; Zbl 1460.76764)

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