Consider a 2D reservoir with 7 by 7 grid blocks. Based on some simplifying assumptions, you know that you can use the steady state equation below to solve for pressure in the reservoir.
(?^2 P)/(?x^2 )+(?^2 P)/(?y^2 )=0
The equation above can be shown as below when finite difference approximation is used.
(P_(i+1,j)-2P_(i,j)+P_(i-1,j))/?(?x)?^2 +(P_(i,j+1)-2P_(i,j)+P_(i,j-1))/?(?y)?^2 =0
Solve for this equation to get pressure distribution in the reservoir. Make a 2D pressure map (contours) by using MATLAB plotting features. Do not forget about color bars and units. Pressure at the boundaries is 1000 psia (orange grid blocks) and the well block pressure (shown with blue color) is set at 100 psia.
Grid block are uniform and ?x=?y=100 ft. There are 24 grid blocks with unknown pressures. 24 equations are required to solve for 24 unknowns. Use i and j notations (shown for some grid blocks in the picture below) to write the required equations and solve the system of 24 unknown, 24 equations to solve for pressures.
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