In a present scenario the applications of numerical reservoir simulators are very wide and extensive. Simulation is the only tool to describe quantitatively multi-phase flow in a heterogeneous reservoir. But, nowadays most of the users of reservoir simulators are becoming the hostages of computer-generated results, even though, many incorrect analysis techniques, mathematical models and computational approaches are used extensively in reservoir simulation study. This paper reveals such incorrect but commonly accepted approaches and presents alternate and correct mathematical approaches for the advancement of new generation reservoir simulators.

Firstly, wide literature survey is done and presented to show the mathematical approaches that are applied presently to the simulators. Then various examples (e.g. fracture and shale flow solutions where fine mesh discretization technique may lead to erroneous results due to singular velocities at the fracture and shale tips, fracture flow modeling using discrete point source which is replaced by continuous line source, etc.) of incorrect models are shown and proved to be the source of erroneous results and numerical instability.

After revealing such incorrect models, the solutions for eliminating this incorrect techniques and models are presented and proved numerically and analytically. Mathematical techniques and formulations used in this paper are advanced conformal mapping, streamfunction and streamline tracing, modern singular integral equation approaches, moving boundary value problems technique, artificial viscosity analysis, generalization of coordinate system, curvilinear grid generation, integral transformations, etc. which stabilize the mentioned simulation models.

In recent years the technological innovations in drilling and production and complicated reservoir studies have challenged the existing simulators so is the key target of this paper is to move in direction of the next generation simulators that can solve the various mentioned inaccuracies. Various accurate mesh generation algorithms are developed in this paper to revolutionize the modern petroleum engineering.

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