For the 1D governing equation used in the reservoir problem, the stability criterion is: or Note: Stability depends on the ratio of t to (x)2 Maximum t allowed increases as x increases.

t Implicit Solution: Traditional Approach n+1 m+3 Iteration planes

x t Implicit Solution Spreadsheet Model: a different view of iteration Time as a spatial dimension t

Solution of the Reservoir Problem using a direct (matrix solution) as coded in the FORTRAN programs in Figures 5.1 and 5.2 in Wang and Anderson.   16.00 16.00 16.00 15.99 15.98 15.96 15.89 15.72 15.27 14.09 11.00 10.00 16.00 16.00 15.99 15.98 15.94 15.87 15.70 15.35 14.62 13.24 11.00 20.00 16.00 15.99 15.97 15.94 15.87 15.74 15.48 14.98 14.13 12.79 11.00 30.00 16.00 15.98 15.95 15.89 15.79 15.59 15.24 14.67 13.77 12.52 11.00 40.00 16.00 15.96 15.91 15.83 15.68 15.43 15.03 14.40 13.50 12.34 11.00 50.00 16.00 15.95 15.87 15.76 15.57 15.28 14.83 14.17 13.30 12.21 11.00 60.00 16.00 15.92 15.83 15.68 15.46 15.13 14.65 13.98 13.13 12.11 11.00 70.00 16.00 15.90 15.78 15.60 15.35 14.99 14.49 13.82 13.00 12.04 11.00 80.00 16.00 15.88 15.73 15.52 15.24 14.86 14.34 13.68 12.88 11.97 11.00 90.00 16.00 15.85 15.67 15.45 15.14 14.74 14.21 13.56 12.79 11.92 11.00 100.00 t = 10