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This paper describes a new general purpose three - dimensional multi-phase reservoir simulator that uses fully unstructured curvilinear meshes and employs dynamic mesh adaptivity based on a flow solution. The simulator is based on an unconventional finite element framework called hp finite elements (where h refers to the local mesh size and p refers to the order of the local polynomial approximation). The simulator is coded as an application layer on top of a general-purpose solution-adaptive hp-finite element kernel. This kernel incorporates advanced object-based data structures that allow simultaneous manipulation of h (via refinement/unrefinement) as well as p (via enrichment/ unenrichment).

The simulator supports both IMPES as well as fully implicit schemes. It offers an automatic time stepping strategy. The numerical difficulties associated with advection terms and presence of solution near-discontinuities are overcome using SUPG (Stream-wise Upwind Petrov Galerkin) method with a discontinuity capturing (DC) operator. The simulator achieves higher computational efficiency by anisotropic hp-type mesh adaptation. It does not use a predetermined well model (such as Peaceman's well model). Instead the wells are represented exactly and modeled right up to (and sometimes including) the well bore. The simulator is equipped with both direct and iterative solvers. The iterative solvers are also parallelized. Several validation and demonstration cases solved using this simulator are presented in the paper. It is anticipated that this simulator will provide unprecedented computational advantages when handling geologically complex reservoirs with non-trivial and nontraditional well shapes and perforations.

1.0 Introduction
1.1 Foreword

Emerging challenges for practicing reservoir engineers include the ability to produce more reliable predictions in less turn-around time. With increasing attempts to produce hydrocarbons from relatively difficult fields (for example, highly viscous heavy oils in unconsolidated strata) by using more expensive methods such as enhanced recovery, better predictive tools for reservoir engineering are a must. Such tools need to be not only capable of handling complex physics but also able to handle complex reservoir features adequately, both structural and mechanical. The tools must also be user-friendly and have tunable accuracy (i.e. have the ability to accept user-specified accuracy parameters). It is clear that such a tool will have to be based on robust mathematical algorithms, will employ fully unstructured meshes and have static and dynamic mesh adaptivity.

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