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Abstract

A new method for generating pseudo relative permeability curves and its applications in a high accuracy front tracking simulator is presented.

The method is applied on 3 different cases, which all gave good results. The different cases consisted of homogenous and inhomogeneous horizontal reservoir models.

The results using a front tracking simulator were more accurate than the results presented by Nyronning (1], using a finite difference simulator.

Introduction

An eternal problem in reservoir simulation is that three-dimensional (3D) simulation models expand so much that there is never sufficient computer capacity. A lot of research has been done investigating techniques to simplify 3D models.

A common way to do this is to use pseudo relative permeability curves. They reduce 3D simulation models to 2D simulation models that reproduce the results from 3D simulations quite accurately. Several methods have been developed, see e.g. Lake et. a]. [2], Stone [3], Kossach et. al. [4], Aziz [5]. A good and well known method is developed by Kyte and Berry [6]. The method used here, extracted from the paper by Hewett and Behrens [7], uses a similar process is Kyte and Berry, but the method applied is different.

With traditional pseudo relative permeability curves it is often a problem to get an accurate reproduction of the production profiles for inhomogeneous reservoirs. Often some tuning must be performed on the curves to improve the results. A weakness which is common for most methods (not for Kyte and Berry [6] or Hewett and Behrens [7]), is that they only use the solution of the saturation equation from the cross section simulation as input. The presented method uses both the pressure and the saturation solution, and it generates pseudo relative permeability curves that can be used directly.

Description of the Front Tracking Simulator

In this paper, both a traditional finite difference simulator (FDS) and a new front tracking simulator (FTS) is used. The FTS, which is currently under development, needs a brief introduction.

The FTS is based on the same mathematical foundation as traditional black-oil simulators.

The equations describing the flow are split into an equation for pressure and an equation for saturation. For each timestep, the pressure equation is solved first by a finite element method.

The saturation equation is solved by a front tracking method, which makes it almost grid independent. The saturation fronts are tracked along the streamlines defined by the pressure calculation.

In this way the simulator is to a large extent independent of the grid system. Numerical dispersion is avoided, mid the simulator is very CPU efficient.

A more detailed presentation of the FTS call be seen e.g. in the papers by Bratvedt et. al. [8], Bratvedt et. d. [9], Riail and You [10] or Soreide et. al. [11].

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