The Laplace Transform Finite Difference (LTFD) Numerical Method for the Simulation of Compressible Liquid Flow in Reservoirs
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SUMMARYA new numerical method, the Laplace Transform Finite Difference (LTFD) method, was developed for the simulation of single-phase compressible liquid flow through porous media. The major advantage of LTFD is that it eliminates time dependency, the need for time discretization, and the problems stemming from the treatment of the time derivative in the flow equation by employing a Laplace transform formulation. The LTFD method yields a solution semi-analytical in time and numerical in space, and renders the effects of the time derivative on accuracy and stability irrelevant because time is no longer a consideration. The method was tested against results from three test cases obtained from a standard Finite Difference (FD) simulator, as well as from analytical models. For a single timestep, LTFD requires an execution time 6 to 10 times longer than the analogous FD requirement without an increase in storage. However, this disadvantage is outweighed by the fact that LTFD allows an unlimited timestep size. Execution times may be reduced by orders of magnitude because calculations are necessary only at the desired observation times, while in a standard FD method calculations are needed at all the intermediate times of the discretized time domain. Thus, FD may require several hundred timesteps and matrix inversions to reach the desired solution time, but LTFD requires only one timestep and no more than 6 to 10 matrix inversions. Moreover, LTFD yields a stable, non-increasing material balance error in addition to a more accurate solution than FD.
