Description of the oil recovery process implies creation of an adequate simulation model. One of the such models, the Dynamic Invasion Percolation with Trapping (DIPT) model, has been recently developed. This model is based on two independent steps.
The first step is to describe the oil reservoir saturated and/or unsaturated porous media in terms of the integer lattice models. In these models the lattice sites and bonds are identified with pores and capillary channels, respectively. It was suggested in to describe n possible different states (empty, filled with displacing fluid or displaced one, etc.) of each lattice site j (j [1, N]) in terms of the time-dependent n-component spinor functions Xj m(j) (t), where N is the total number of lattice sites and m(j) [1, n]. In such an approach the time-dependent state function (t) of the entire lattice modelling oil reservoir porous medium can be introduced as the following direct product:
(1)
The second step is to describe evolution of the oil reservoir subjected to the recovery process. It was done within the DIPT model. In this model it was suggested to describe evolution of the oil reservoir state function (t) with the help of the following Schrodinger-like equation:
(2)
where is the average time between consecutive displacing acts taking place in neighboring sites and H is the operator which governs evolution of the oil reservoir state function (t). This operator has the form:
(3)
where the local term Hj describes microphysics of displacement from a single pore whereas the non-local term Hji is responsible for correlation between displacements in neighboring pores. The summation in this expression is taken over the subset -<J>1 N of the particular sites which are displacement available under given physico-chemical conditions. These sites are supposed to be randomly distributed over the entire lattice. Their relative number P gives the probability that the arbitrary taken site j belongs to the subset <J>1 N. When P Pc there exists percolation phenomenon between any two arbitrary taken sites (Pc is the percolation threshold).
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