A Conjugate Gradient-Truncated Direct Method for the Iterative Solution of the Reservoir Simulation Pressure Equation

Abstract This paper describes a way of solving the reservoir simulation pressure equation using preconditioned conjugate gradients. The preconditioning is based on an approximate inverse using a diagonal ordering of the difference equations. The new method has been tested and compared with the strongly implicit procedure (SIP) on a number of problems in both two and three dimensions. In two dimensions, it is generally faster than SIP; in three dimensions, it is much slower than SIP when SIP works well but can be many times faster than SIP when SIP works poorly. Use of the new method generally does not require the selection of an iteration parameter, which is a significant advantage over SIP. Furthermore, it is much more reliable than SIP. In other words, it is far less likely to be unable to solve a given problem than SIP is.