Specified adaptive implicit method for unstructured grids in compositional reservoir simulation

Abstract

Compositional reservoir simulation is an important tool for predicting oil and gas production and it has been largely used in the last decades. Since compositional reservoir simulation, in general, involves solution of a large number of coupled partial differential equations representing the physical system, the numerical implementation of such model is a complex step. Different numerical approaches have been proposed in literature to optimize the CPU time of the numerical formulations. These formulations present many similarities; therefore, they are organized in major groups, which share some basic features. Two of these groups are of interest in this work: IMPEC (Implicit Pressure/Explicit Composition) and FI (Fully Implicit). In the IMPEC formulation, the pressure is evaluated implicitly, and the remaining variables explicitly. Fully Implicit (FI) methods, in the other hand, compute all the primary variables implicitly. Both techniques present advantages and disadvantages. In this work, a new formulation is proposed that combine features of both IMPEC and FI approaches. We call the new formulation the Specified Adaptive Implicit Method (SAIM), since the grid blocks that are treated as FI are fixed during the whole simulation. Herein the well grid blocks are always treated as FI; the neighbors of these grid blocks can also be treated as FI, and also the neighbors of the last set of grid blocks that were treated as FI can also be treated as fully implicit as well. The performance of SAIM is compared with the FI and IMPEC approaches in terms of average time step and total CPU time required for each simulation. The results obtained indicate the SAIM formulation is able to outperform the IMPEC in many situations.