Two-Dimensional Flow Through Porous Media

We now want to develop the equations that describe the two-dimensional flow of oil, water, and gas through porous media. The material balances for water and oil are 

We can normalize these equations by dividing by the phase densities at standard temperature and pressure conditions 

The ratios Po/Po Pw/p can be given in terms of the formation volume factors and where 

For the water and oil phases, we have assumed that water and oil are only found in their respective phases. This is not the case for gas. There is a solubility of gas in both the water and oil phases given by the solubility coefficients Rgy, and Rgg. These are defined at standard conditions as 

We can normalize this equation by dividing by the gas phase density at standard conditions. This gives 

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This chapter discusses finite-difference techniques for the solution of partial differential equations. Techniques are presented for pure convection problems, pure diffusion or dispersion problems, and mixed convection-diffusion problems. Each case is illustrated with common physical examples. Special techniques are introduced for one- and two-dimensional flow through porous media. The method of weighted residuals is also introduced with special emphasis given to orthogonal collocation. 

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