About one test

September 8, 2008
Model blocks

My scientific work becomes more intensive and there is no time to devote to something else. I'll try to defend thesis in time. I'm adding some pictures with computing results now. Here is the one that I want to show you.

I'm not sure whether to put this test into the text, but I think about including it into presentation. That should clear the air.

Testing full permeability tensor for filtration problem

For those who is interested in this picture (in simple words). Consider three-dimentional hydrodynamic model of underground reservoir that is divided by homogeneous mesh. The liquid consists of three phases: water, oil and gas. The injector well is placed to the center and pumps water into reservoir. Four producer wells are drilled at corners to stabilize pressure. They pump liquid out of reservoir to the surface. The picture shows saturation of oil, i.e. relation of oil amount to total liquid amount in every grid block. The color means the value of saturation after a period of time since wells were opened. Blue zone — there is almost no oil (saturation is near to zero), red zone — there is almost solid mass of oil (saturation is near to one). The boundary (so called front line) is supposed to be circle in homogeneous media (when liquid flows equally in all directions). But I set up anisotropic tensor with main axis that is directed along one diagonal on the left side and along other diagonal on the right side (note that liquid flows faster along main axis than in other directions). The result is fully complied with theory. By the way, the shape and the size of the front are not depended on mesh partition. I could setup more intricate mesh and result will be the same. This is just a special test for the non-diagonal permeability tensor.

That is the thing I have to deal with.

Nikita Melnichenko.

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