Abstract

Molecular diffusion and mechanical dispersion are the main mechanisms responsible for gas-oil mixing that occurs in a miscible flood process. Most of the conventional reservoir simulators do not account for the these physical mechanisms and presume it to be compensated by the numerical dispersion arising out of the finite-difference scheme with single-point upstream weighting of mobilities for the sizes of gridblocks normally used in field-scale simulations. Numerical dispersion is artificial and non-physical and the assumption that it can compensate for physical dispersion can lead to erroneous results.

The multipoint flux approximation (MPFA) scheme developed in recent years provides an improved method for modelling tensorial permeabilities in non-uniform and skewed grids that are often required for proper representation of the reservoir geometry. The physical dispersion coefficient in the dispersive flux is tensorial in nature and amenable to a treatment similar to that of the permeability tensor in the convective flux. We have applied a multipoint control-volume scheme to the dispersive flux in a compositional simulator with a two-point upstream weighting and total variation diminishing (TVD) implementation to minimize the effect of front smearing caused by numerical dispersion.

In this paper we present salient features of the proposed formulation and the basic results for miscible displacements in a linear model, and in a quarter of a five-spot pattern with non-orthogonal grids.

Introduction

Dispersive mixing plays an important role in the performance of a miscible displacement process. It determines how much of the solvent will mix with the in-situ oil to promote miscibility under favorable conditions.

Dispersion is the process of distributing or spreading concentration profiles due to mechanisms in which the flux is proportional to the concentration gradient. Diffusion is a special case of dispersion when the velocity of the fluid is zero. The diffusion process was first recognized by Fick. Perkins and Johnston1 suggested that dispersion in porous media is Fickian in nature and the dispersive flux can be obtained by reducing the crosssectional area by multiplying it with porosity.

Two basic elements of dispersive mixing are molecular diffusion and mechanical dispersion2. For mechanical dispersion to occur variation in convective velocity field is required, which is created by the tortuous flow paths of the porous network and/or by imposed changes in the strength of sources or sinks. The inhomogeneity in porous medium promotes mechanical dispersion. Molecular diffusion, however, takes place solely due to concentration gradient, with or without the presence of motion.

A number of crossflow mechanisms3,4 are responsible for mass transfer in a gas displacement process, viz., diffusion, dispersive mixing, capillary pumping, interfacial tension effects and relative permeability modification. The present paper deals primarily with the first two factors i.e. molecular diffusion and mechanical dispersion.

Young5 used the convection-diffusion equation and a one-dimensional grid to model the multi-contact miscible process by treating the dispersion coefficient as a function of the viscosity gradient. The formulation used centered differences for evaluating convective and dispersive fluxes.

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