On the Importance of Dispersion and Heterogeneity in the Compositional Simulation of Miscible Gas Processes
Authors: Haajizadeh M. , Fayers F. J. , Cockin A. P. , Roffey M. , Bond D. J. 
Published: December 2007

Abstract
Compositional simulation of miscible gas displacement at the reservoir scale is mostly undertaken neglecting physical dispersion mechanisms such as capillary pressures, molecular diffusion, dispersive mixing, etc. The necessity to use large grid block sizes implies that numerical dispersion will dominate any attempts to include physical dispersion effects. The numerical dispersion causes loss of miscibility and increases the dependence on the relative permeability behavior. Improvements in computing power and in stochastic reservoir description are beginning to enable very fine grid simulations to be run. Thus this paper provides quantitative evidence of possible magnitudes of physical dispersion effects and the degree to which these might be partially replaced by an appropriate size of numerical grid.
We first discuss results from 1D simulations and show that the potential influences of dispersive effects depends on the type of drive mechanism. In a condensing drive, the condensation and saturation smearing due to dispersion occur in the leading part of the transition zone, while near-miscibility develops at the tail end. In contrast, in a vaporizing drive, the vaporization and saturation smearing occur in the tail part of the transition zone, while near-miscibility develops at the leading edge. The commonly occurring condensing/vaporizing drive exhibits a mixture of the above dispersion properties. Depending on the degree of dispersion, loss of miscibility causes the condensing drive to produce a dry gas bank ahead of the transition zone, resulting in earlier gas breakthrough. We investigate the potential relative magnitudes of effects associated with physical dispersion/diffusion, capillary pressure, and relative permeability adjustment due to varying interfacial tensions. For these 1D cases it proves possible to broadly emulate the physical dispersion effects by using instead a correctly chosen grid size. In the condensing drive, the characteristics of the leading dry gas tongue, caused by dispersion, are influenced by the relative permeability and capillary pressure data at high IFT.
In regard to the effective longitudinal dispersion coefficient, it is believed that the contribution due to dispersive mixing in small scale heterogeneities will usually dominate any influences due to molecular diffusion. We illustrate this by studying rectilinear displacement in finely gridded heterogeneous 2D models. The heterogeneities are represented as log normal distributions with short correlation lengths. Effective longitudinal dispersion coefficients are found which give the appropriate average effects in 1D for the dispersion/phase behavior of the 2D heterogeneous systems. The heterogeneity triggers viscous fingering/channeling, and this causes the effective dispersion coefficient to be larger than would be associated with a Gelhar and Axness theory for single phase flow. Thus we are able to demonstrate that for this idealistic class of heterogeneity there is a choice of 1D grid size to approximate omitted physical dispersion effects in multi-contact "miscible" displacement.