An Adaptive implicit compositional reservoir approach using 2D/3D unstructured grids

Abstract

One of the main aspects of compositional reservoir simulation concerns the algorithms, or formulations, to solve flow equations. A literature survey shows that several approaches have been developed in the last decades, always aiming increasing the accuracy of results and run performances. The choice of primary variables and applied implicitness level are two of the fundamental ways in which these methods differentiate themselves. Implicit Pressure, Explicit Composition models treat a single variable implicit, reducing the run time for each time step while becoming more vulnerable to numerical instabilities. On the other hand, Fully Implicit schemes evaluate all primary variables coupled within the Jacobian matrix, which confers great stability, but produces much larger linear systems and are, therefore, more expensive per time step. Herein, we develop a model that incorporates both formulations to produce an adaptive method with variable level of implicitness throughout the simulation. This is achieved by identifying the sources of instabilities in a reservoir and setting them implicit in a dynamic procedure. Two switching criteria are applied into establishing the correct amount of implicit unknowns for each grid volume and performing the required shifts. Additionally, this Adaptive Implicit Method (AIM) is combined with the EbFVM scheme for unstructured meshes, enabling the handling of more complex reservoir geometries. The accuracy of the Adaptive Implicit Method is compared with both IMPEC and Fully Implicit formulations for several case studies in terms of oil and gas production rate curves, while the CPU run times are applied into verifying performance.