Grid Refinement Study of a Hydrocarbon Miscible Gas Injection Reservoir
Authors: Lim Min T. , Pope Gary A. , Sepehrnoori Kamy , Soni Yogi 
Published: December 2007

Abstract
A grid refinement study of an actual hydrocarbon miscible gas injection improved oil recovery project was made using an equation-of-state compositional reservoir simulator developed at The University of Texas (UTCOMP). A vertical cross- section of this massive carbonate reservoir was simulated using up to 95 permeability layers based upon an extensive characterization program done by Conoco Inc. The primary motivation of this study was to determine the dependence of the predicted oil recovery on the gridblock size. The initial expectation based upon the literature was that if very large gridblock sizes were used in a study planned to be done with a commercial reservoir simulator using conventional one-point upstream weighting and no physical dispersion, then the results would not be very accurate. This is because of numerical dispersion, especially since this was a multiple contact miscible (MCM) process requiring flash calculations in large gridblocks UTCOMP has a third-order-correct finite-difference approximation option and both this option and one-point upstream weighting were used so that comparisons could be made and plans made for what gridblock size to use with the commercial simulator. Contrary to what is in the literature, our results show that the effect of numerical dispersion is very problem dependent and not always large even for an MCM process. For the reservoir studied, our simulations show that the oil recovery is quite insensitive to mesh refinement at both low pressure, below minimum miscibility pressure (MMP), and high pressure. UTCOMP showed very nice linear convergence when the grid was refined. This is not true for all simulators and must be checked, and it is very important. We also found that surprisingly large gridblocks (up to 100 feet in the flow direction) can be used in this case before the errors in oil recovery become large, and that there was not very much difference between third-order and first-order approximations. We think that this is due to the dominance of the layering, and so both an accurate reservoir description and a careful grid refinement must be made on each problem. This has new and very important implications with respect to how field studies of miscible floods should be done and how accurate they will be in predicting the oil recovery.

Introduction
It is well recognized that physical dispersion is important in miscible gas displacements. Most of the commercial finite-difference compositional simulators currently available for miscible flood predictions and designs use either the one-point or two-point upstream weighting scheme to evaluate the coefficients of the convective terms and thus are subject to large truncation errors resulting in what is commonly known as numerical dispersion. However, the artificial numerical dispersion introduced by the one-point upstream weighting scheme, which in one-dimensional problems is approximately equivalent to a physical dispersivity of x/2, is often larger than the true physical dispersion unless very small gridblocks are used. Consequently, in reservoir-scale problems, gridblock size would have to be intractably small for the numerical dispersion to be on the order of realistic physical dispersion. In addition to grid size, the magnitude of this numerical dispersion is also sensitive to grid orientation. The two-point upstream method produces more accurate results than the one-point upstream method, but the numerical dispersion and grid orientation effects are not eliminated.
The effects of numerical dispersion and related issues on miscible gas floods have been an active subject of investigation. This is because inaccuracies arising from numerical dispersion can lead to erroneous solutions and misrepresent the physics of the displacement process.
P. 359^