Stochastic modeling of fluid displacement in porous media and its impact in oil recovery engineering

Resumen

The displacement of a viscous fluid by another that preferentially wets a porous medium is modeled with the aim to simulate cooperative invasion processes found in experiments of immiscible wetting displacement. In our model we consider the non-local effects on it of the Laplacian pressure field and the capillary forces. This is achieved with Diffusion Limited Aggregation DLA-type Montecarlo computations that simulate both the hydrodynamic equations in the Darcy regime with a boundary condition for the pressure at the interface. The boundary condition contains two different types of disorder: the capillary term which constitutes an additive random disorder, and a term containing an effective random surface tension which couples to a curvature (it constitutes a multiplicative random term that carries non-local information of the whole pressure). This multiplicative random disorder together with the non-local coupling causes a short range scaling regime that reveals itself in a roughness exponent α ≈ 0.80. Additionally, we find a DLA-type scaling regime with a roughness exponent α ≈ 0.60 at the largest scales. Our results sheds the following strategy for oil recovery: in order to minimize trapping of oil in the fingers, oil has to be displaced by a liquid that preferentially wets the porous rock.