Consider the following 1D reservoir, where unsteady-state, single oil phase is taking place. The homogeneous properties of the reservoir, φ=30%, and kx=178 md. Figure shows the dimensions. The boundary conditions at the extreme ends are specified as no flow boundary conditions and the wells in grid-blocks 2 and 6 produce at a rate of 2000 STB/D. Each gridblock has an initial specified pressure of 4000 psia.
1. Obtain the system of equations whose solutions give the pressure distribution in the reservoir at the end of 10 days. Use a time step of 5 days to generate the system of equations. Use the implicit backwarddifference scheme to generate the finitedifference equations. Also note that μ1 = 1.0 cp, c1 = 5x10-6 psi-1.
2. Solve the system of equations to get the pressure distribution using
(a) Gaussian Elimination Method
(b) Thomas Algorithm
