Laplace Transform Finite Difference (LTFD) numerical method for simulation of compressible fluid flow in reservoirs
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abstract
A new numerical method, the Laplace Transform Finite Difference (LTFD) method, was developed for the simulation of single-phase compressible liquid flow in one, two or three dimensions. The major advantage of LTFD is that it eliminates time dependency, the need for time discretization, and of the problems stemming from the treatment of the time derivative in the nonlinear equation of flow by employing a Laplace transform formulation. LTFD 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 one-, two- and three-dimensional test cases obtained from a standard Finite Difference (FD) simulator, as well as from analytical models. For a single time-step, 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 in the LTFD scheme 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, a problem in standard FD format may require several hundred timesteps and matrix inversions between the initial condition and 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 the conventional FD.
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Proceedings - SPE Annual Technical Conference and Exhibition
