A Numerical Technique for Tracking Sharp Fronts in Studies of Tertiary Oil-Recovery Pilots

Abstract

Summary A numerical front-tracking technique, based on a transformation of the governing equations into a moving coordinate system (MCS), is applied to a finite-element reservoir simulator. The method is especially suited for studies of tertiary oil-recovery pilots with chemical flooding and other miscible displacement processes. The new front-tracking technique is compared to conventional finite-element formulations with a uniform grid over the entire domain. Comparisons with other methods show that computer time can be greatly reduced with the same accuracy. Introduction Accurate simulation of EOR processes (such as chemical and polymer flooding) is very important for the design and appraisal of pilots and the prediction of full-field performance. The most prediction of full-field performance. The most serious limitation on making predictions is the inability to simulate these processes with a large enough number of gridblocks to reduce the numerical dispersion to an acceptable level. Lake et al. studied the Benton stage chemical flood project with two-dimensional (2D) simulation (cross section) and a stream tube program to account for areal and confinement effects. With this procedure the effect of dispersion is not accounted for properly. The MCS is a numerical method that performs three-dimensional (3D) simulation without numerical dispersion in a symmetric flooding pattern. The method can be used in EOR studies pattern. The method can be used in EOR studies as shown in Fig. 1. Coreflood and cross-sectional models are used to study the physical process and reservoir layering, as well as other components crucial for the design of the flood. The streamtube simulator and the 3D symmetric pattern simulator (where the MCS-is applied) study simultaneously the sensitivity to parameter variation and full-field performance. The symmetric pattern simulation performance. The symmetric pattern simulation can provide response functions of individual streamtubes through the detailed simulation of a small area. Many studies were conducted to develop methods for reducing numerical dispersion. The basic numerical methods-finite-difference and weighted-residual methods-show either oscillations close to the sharp front(s) or a smearing of the front.

Numerical modelling of multiphase flow in porous media

“…Jensen and Finlayson (85,86) introduce an alternative scheme for fronttracking that gives good results in convection-dominated species-transport problems. This method defines a set of moving coordinates based on the method of characteristics €or the hyperbolic, or purely convective, part of the partial differential equations.…”

Front Tracking in Two Dimensions Without a Grid

“…Between these two smooth solutions will be a function that can vary from being quite smooth to being a near discontinuity. We would expect, therefore, that a basis of the form (10) might suffice. Here the Qi are polynomials in space and H(z) is a function that can vary from being smooth to being a near discontinuity.…”