Open Access

ARTICLE

A New Solution Algorithm for Multi-Dimensional Reservoir Simulation

Boyun Guo¹, Yin Feng²

1 University of Louisiana at Lafayette.
2 Louisiana State University.

Structural Longevity 2013, 10(2), 85-94. https://doi.org/10.3970/sl.2013.010.085

Abstract

A new numerical procedure, called Semi-Alternating Direction Implicit (SADI), was developed for solving the Diffusivity Equation (DE) using the Finite Difference Method (FDM) in this study. The SADI procedure was compared with the Simultaneous Sweep (SS) procedure and the Alternating Direction Implicit (ADI) procedure in terms of numerical stability and computing speed in a 3-dimensional oil reservoir simulator. Results from the model-testing indicate that, due to different degrees of numerical dispersion, the function values generated by the SADI procedure are slightly greater than that by the SS procedure and the ADI procedure. The SADI procedure is as stable as the SS procedure, and is much more stable than the ADI procedure. The maximum stable time-step size with SADI is at least twice that with ADI. The SADI procedure is as fast as the ADI procedure and over a thousand times faster than the SS procedure. SADI’s nature of increasing speed of computation does not diminish quickly as the time step size increases. The advantage of the SADI procedure in speeding up computation is more pronounced in large scale (large number of grid blocks) systems than in small scale systems. Although the SADI procedure was tested in an oil reservoir simulator that is used in the petroleum industry, the procedure is equally valid for any numerical simulations that involve solving the DE using the FDM.

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