Abstract In reducing the grid orientation effect for the numerical solution of partial differential equations, interpolation functions play an important role when the advective transport of the governing equations is considered. This is due to the fact that, in general, the unknowns are evaluated in the vertices of the elements and such properties must be extrapolated to inner parts of the elements. First-order schemes, such as upwind, are the easiest methods to use for performing the extrapolation of the properties. However, such methods introduce a large amount of numerical diffusion in the solution. A few higher-order interpolation schemes, on the other hand, are capable of providing solutions free of numerical diffusion, increasing the accuracy of the method and reducing the computational efforts required. In this work, we investigate the TVD interpolation scheme for three-dimensional unstructured grids in conjunction with Element-based Finite Volume Method (EbFVM) using four types of elements: hexahedron, tetrahedron, prism and pyramid.

Abstract In the last decade, unstructured grids have been a very important step in the development of petroleum reservoir simulators. In fact, the so-called third generation simulators are based on Perpendicular Bisection (PEBI) unstructured grids. Nevertheless, the use of PEBI grids is not very general when full anisotropic reservoirs are modeled. Another possibility is the use of the Element based Finite Volume Method (EbFVM). This approach has been tested for several reservoir types and in principle has no limitation in application. In this paper, we implement this approach in an in-house simulator called UTCOMP using four element types: hexahedron, tetrahedron, prism, and pyramid. UTCOMP is a compositional, multiphase/multi-component simulator based on an Implicit Pressure Explicit Composition (IMPEC) approach designed to handle several hydrocarbon recovery processes. All properties, except permeability and porosity, are evaluated in each grid vertex. In this work, four case studies were selected to evaluate the implementation, two of them involving irregular geometries. Results are shown in terms of oil and gas rates and saturated gas field.

In compositional reservoir simulation, a set of non-linear partial differential equations must be solved. In this work, two numerical formulations are compared. The first formulation is based on an implicit pressure and explicit composition (IMPEC) procedure, and the second formulation uses an implicit pressure and implicit saturation (IMPSAT). The main goal of this work is to compare the formulations in terms of computational times for solving 2D and 3D compositional reservoir simulation case studies. In the comparison, both UDS (Upwind difference scheme) and third order TVD schemes were used. The computational results for the aforementioned formulations and the two interpolation functions are presented for several case studies involving homogeneous and heterogeneous reservoirs. Based on our comparison of IMPEC and IMPSAT formulations using several case studies presented in this work, the IMPSAT formulation was faster than the IMPEC formulation.