Preprint E11/2008
APPROXIMATE SOLUTIONS FOR THE FILTRATION PROBLEM IN RADIAL GEOMETRIES.

Dan Marchesin | Silva, Julio M.

**Keywords: **
deep bed formation | perturbed explicit solutions | high order box scheme

The oil recovery process goes through different stages during the life of a reservoir. For a small fraction of this time the natural pressure of the compressed oil, under the top layers
of the terrestrial crust, suffices to expel the oil under production. However, during most of the time, the production is performed by the injection of water in one well, forcing the oil to be expelled at another well. The ratio between the injected flux and the pressure required to sustain this flux is called injectivity. The loss of injectivity by the deposition of particles brought by the water in the porous medium is called deep bed formation damage. To remedy this damage is costly, therefore it is important to predict the damage. Mathematical models are used for this purpose. We describe an approximate solution for the filtration problem in radial geometries, constructed using perturbation analysis on the equations governing the model. The availability of simple explicit solutions is very important for engineers, which have to make decisions without waiting for numerical computations. Until now, exact solutions have been reported for two cases: the first one corresponds to one-dimensional flows; the second occurs for cylindrical or spherical geometry when there is a linear relation between the filtration function and the suspended particle mass. We have extended the solution for the latter geometries in a model where the deposition depends linearly on the suspended particle mass and weakly on the deposited mass. We also developed a stable implicit second order finite difference scheme. This is the first such scheme for the filtration problem. We show results for flow in cylindrical coordinates.