Effect of Permeability Distribution On Miscible Displacement In a Heterogeneous Carbonate Core
Authors: Hicks P.J. , Deans H.A. 
Published: March 2010

Abstract
Three-dimensional miscible brine displacement simulations have been performed for flow through a 10.2 cm (4 inch) diameter heterogeneous core containing a residual oil phase. The displacement front, as expected, is found to be a strong function of the permeability distribution assumed for the core.
The porosity and residual oil saturations were measured previously using X-ray CT. These experimental distributions were used as input for the simulations. Since the permeability distribution cannot be measured directly in three dimensions for the core, two different empirical relationships were used to estimate the permeability distribution based on the experimental porosity and residual oil saturation distributions. The position of the saturation from is calculated and shown for various injection volumes for simulations using the two porosity-permeability relationships. Semi log and exponential porosity-permeability models were tested. For our case the semi log relationship tends more toward the piston-like displacement, with only a couple of fingers developing. The exponential fit has a more irregular front.
The two porosity-permeability models yield significantly different in-situ saturation distributions with roughly equivalent matches of the experimental effluent profiles from the displacement experiments. Through the use of CT measured in-situ saturations, the porosity-permeability relationships were evaluated. The semi log relationship performed slightly better for the core studied even though both models gave equivalent results for the effluent profiles. This demonstrates the importance of developing techniques such as CT which will monitor the in-situ saturations as well as the effluent saturations when attempting to develop and validate flow models.

Background

Experimental
Details of the experimental equipment and procedures were reported earlier(1,2). The experiment was the displacement of brine by lagged brine in the presence of a residual oil phase. The porosity and concentration data used in this work were obtained using a forth generation medical CT-scanner. The scanner gantry was rotated 90 ° to make the scan plane horizontal. The displacement were conducted in the vertical direction, minimizing gravity effects by eliminating gravity induced underrides and overrides.
A 10.2 cm (4 inch) diameter San Andres dolomite core from The Taylor-Link Field in Pecos County, Texas was used. It had an average porosity of 11.4% and an average residual oil saturation of 24.9%. The average superficial velocity during the displacements was about 0.11 m/day (0.36 ft/day). The flow was stopped periodically to scan the core.

Modeling
The experimental miscible displacements were modeled assuming single phase miscible flow: unit mobility ratio; porosity, permeability and residual oil saturation are functions only of position: incompressible fluids: Darcy's law applies,. capillary and gravitational effects are negligible: and the dead-end pore model(3,4) can be used to represent the convective and dispersive transport in the core. The dead-end pore model divides a saturation (in this case the brine saturation) into two fractions. One fraction is flowing and the other is the dead-end pore or non-flowing fraction. Convection takes place in the flowing fraction, f, and the nonflowing fraction, I-f, communicates with the flowing fraction only via diffusion. The diffusion is proportional to the dimensionless diffusion parameter.