Montecarlo DLA type simulation of non-wetting (Drainage) stable displacement in porous media
Resumen
We study immiscible fluid-fluid displacement in a porous media in a regime where the displaced fluid has negligible viscosity. In our model we consider the interplay between viscosity forces and capillary forces; the ratio is denoted by the parameter r, the inverse of the capillary number. We use a DLA type algorithm and consider a boundary condition at the interface of the two liquids, which takes into account the viscous, and the capillary pressure drop at the interface. This boundary condition makes the problem nonlinear. We make computer simulations and generate patterns of displacement. The roughness exponent a and the dynamic exponent b are calculated for each interface of the pattern obtained. We find that the roughness exponent depends on r and ranges from a value around 0.5 for small r to a saturation value 0.8 for large r. We also find strong fluctuations of these values during the simulations because of cascade similar processes at the interface. Our results compare well with the experiments of Pon-zeng Wong et. al. We further extend our model and introduce a parameter, which considers the relative preference of the wetting properties of the two liquids to the porous media. We find that this parameter controls the amount of trapped liquid behind the front.
