Modeling Relative Permeability Variations in Three-Phase Space

Abstract

Three-phase relative permeability can vary greatly from two-phase relative permeability as mechanisms such as flow coupling, double displacement, and layer drainage flow regime play a role in three-phase flow. These are on top of the dependency of three-phase relative permeability on two saturations and saturation path/history. The net result is that it is difficult to model/predict relative permeabilities in three-phase space. In this work, we present three-phase oil relative permeability data measured along 11 saturation paths, in a water-wet consolidated (Berea sandstone) and unconsolidated (sandpack) porous media. These saturation paths cover a wide swath of the three-phase saturation space, providing a better physical understanding of the complete three-phase phase space. Three different oils (crude oil, mineral oil, and n-octane) are used in the experiments; the varying viscosities, spreading coefficients, and composition of the oils allows us to investigate the effect of different drainage mechanisms on relative permeability curves. Our data show that there are significant variations between the curves depending on the media, final water saturation, and fluids. In particular, when the media and fluids are held constant, oil relative permeability can vary an order of magnitude at the same oil saturation, depending on the initial condition and water saturation. We find that within each media, all the curves represent a similar shape, but reach to a different residual saturation. This suggests that residual oil saturation is the key parameter in observed relative permeability differences along different saturation paths. We examine this hypothesis with the most common three-phase relative permeability models, i.e. Saturation Weighted Interpolation, Stone I and II, where we vary residual oil saturation to fit the experimental data. We find that if residual oil saturation is used as a fitting parameter, the models predict experimental data well. Otherwise, without varying residual oil saturation, these relative permeability models perform poorly in predicting experimental data.

An extended JBN method of determining unsteady-state two-phase relative permeability

“…To our knowledge, there are two methods of calculating local fractional flow from the saturation profile at each injection time. One method is based on a fractional flow analysis (the fractional flow method) [ Chen and DiCarlo , ], and the other method is based on mass balance (the mass balance method) [ DiCarlo et al ., , ; Kianinejad et al ., ]. Both methods have the same boundary and initial conditions.…”

Measurements of CO2‐brine relative permeability in Berea sandstone using pressure taps and a long core

“…These methods, and variations of these methods, are colloquially known as bump test methods as the flow rate is increased or 'bumped up' for the final steps. 10,12,21,25,33,35,36 On the other hand, Chen et al 37,38 and Kianinejad et al [39][40][41][42][43] introduced new unsteady-state methods that can locally measure pressure gradient, phase flux and saturation during two-phase and three-phase flows, which experimentally avoid the capillary end effect particularly for gas and supercritical phases and give more accurate CO 2 relative permeability data than conventional unsteady-state methods.…”

“…21,25,35,36 Bennion et al proposed to measure endpoint CO 2 relative permeability at different flow rates and fit the two parameters with an exponential function; then they corrected the endpoint CO 2 relative permeability by extrapolating this function to infinite flow rate. 10,12,21,25,33,35,36 On the other hand, Chen et al 37,38 and Kianinejad et al [39][40][41][42][43] introduced new unsteady-state methods that can locally measure pressure gradient, phase flux and saturation during two-phase and three-phase flows, which experimentally avoid the capillary end effect particularly for gas and supercritical phases and give more accurate CO 2 relative permeability data than conventional unsteady-state methods. They fit the flow rate versus overall pressure drop with a function; and by taking the derivative of this function, CO 2 relative permeability was determined at the inlet of the core.…”

A new unsteady-state method of determining two-phase relative permeability illustrated by CO2-brine primary drainage in berea sandstone

“…The expression for oil relative permeability at the outlet is simplified from the original JBN expression to the oil production rate due to high mobility of air and low capillary pressure. DiCarlo et al [32,33] and Kianinejad et al [34][35][36][37][38] conducted gravity drainage experiments and measured local saturations and fluxes in-situ using CT scanning. The local pressure gradient was taken to be the gravitational gradient, which was shown to be a good assumption for the center portion of the column.…”