Individual well modeling with r-z geometry is often done with a small number of radial cells (e.g. 6 or 7). This usually leads to small space truncation error for black oil systems. for power law fluids a finer grid is required. An example problem is readily solved using 20 radial cells. Coarser definition leads to unacceptable truncation error.
A method is shown to improve finite difference accuracy by space differencing the time derivative. An analytical solution to the difference equation is developed, and used to validate approximate numerical solutions.
Three figures, five tables illustrate results.
A small number of radial cells (e.g., 6 or 7) is usually adequate for individual well models using r-z geometry. Our results indicate that solution errors are small for such models when the fluid is a black oil. But errors are not small for power law fluids. The problem discussed here requires 20 radial cells to reduce truncation errors to be acceptable levels. Improved accuracy in the space dependent approximation can be obtained by a suitable space differencing of dp/dt. With such improved accuracy it becomes tenable to use a reduced number of radial cells to model power law behavior. power law behavior. II.
Recent papers, developed the following equation describing radial flow of a non-Newtonian power law fluid in a porous medium: power law fluid in a porous medium:
........(1)
