Immiscible Displacement in a Porous Medium Simulated by a Statistical Model
Invasion percolation theory is here applied to the simulation of immiscible displacement of two phases in well-defined porous media. A model has been developed that takes not only the influence of the capillary number into account but also the wettability of the system and the viscosity ratio of the immiscible phases. The porous medium in this model is described by a network of pores of equal length. Their size (radius) follows a selected distribution function. Four different distribution functions have been tested in this work: the even distribution function f(r) = c, the χ2 function (with n equal to 4 and 10) and a function f(r) =2r · exp(− r 2), which was also used by Heiba et al. (1986). The influence of the distribution functions on the simulation results was investigated. A method to generate the corresponding network model based on the properties of a given medium is also proposed. The simulation results show that the displacement results cannot be described by the capillary number alone, and the influence of the viscosity ratio between the two phases varies with the capillary number. The larger the capillary number, the larger the influence. The wettability of the system also changes significantly the dependence of the residual oil saturation (both for the oil-wet and the water-wet cases) on the capillary number. This is most dominant when the capillary number is relatively small. The critical capillary number is determined for porous media with different wettabilities. The simulated results are compared with experimental results published by other investigators and this laboratory.
KeywordsPorous Medium Interfacial Tension Capillary Pressure Relative Permeability Capillary Number
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