Relative Permeability During Cyclic Steam Stimulation of Heavy-Oil Reservoirs
Authors: Dietrich J.K. 
Published: December 2007

Introduction
Reliable relative permeability data are important to the overall planning for prospective thermal recovery projects. Empirically derived relative permeability functions presented here have characteristics quite different from those determined experimentally. The empirical functions emerged from simulations of numerous ongoing thermal projects in unconsolidated heavy-oil reservoirs from Trinidad, West Germany, Canada, and the U.S.The cyclic steam process involves strongly changing saturation and pressure conditions during alternating imbibition and drainage cycles. Three-phase flow effects are to be expected in this process, where both steam and mobile water are found in the presence of oil due to steam condensation.
Experimental procedures for determining relative permeability on a microscopic scale often ignore dependency on saturation history (hysteresis), changing pressure levels, and three-phase effects. Hence, relative permeability in this process (and in other thermal processes) often is considered a weakly determined parameter. The thermal simulator, which has been available since 1973, provides insight into the nature of relative permeability on a reservoir scale.

Thermal Reservoir Simulator
A volatile-oil steamflood simulator developed by Todd, Dietrich & Chase Inc. was used during analysis of the field thermal projects. This model is a fully implicit, finite-difference-based program that can treat up to four mass conservation equations and an energy balance. There are three phases: aqueous, liquid hydrocarbon, and vapor. The four mass species are water, a nonvolatile heavy oil, and two volatile components. Although only water and a dead-oil component were used in the majority of field projects, all four mass species were needed in some projects. The volatile components have been used to model (1) noncondensable-gas and CO2 additives to steam, (2) solution-gas and free-gas effects, and (3) distillation of hydrocarbon pseudocomponents.The model was employed in two-dimensional areal and vertical (cross section) simulations and in three dimensions, using Cartesian (x, y, z) and cylindrical (r, o, z) coordinates. Relative permeability functions were changed between the injection and production stages of the cyclic steam process to model the previously noted imbibition and drainage hysteresis effects.

Empirical Relative Permeability Functions
Relative permeability relationships shown in Fig. 1 are typical of those developed empirically (through simulation) to reproduce observed producing water/oil ratios in cyclic steam projects worldwide. In this work, two-phase data similar to those shown in Figs. 1a and 1b were used with a modified form of Stone's expression to generate three-phase oil relative permeability functions. These functions were used with adjustments for temperature dependency (Table 1) to match drainage production behavior. In each field application, very low water relative permeability curves (0.0025 is lesser than krwro is lesser than 0.25) were required to reproduce field performance. These empirically developed curves are much lower than those routinely measured (0.05 is lesser than krwo is lesser than 0.25) during imbibition water/oil relative permeability tests using unconsolidated core material.Experimentally determined imbibition water relative permeability curves often are used successfully to match observed steam injection pressures and rates.

Physical Basis
Several complementary conjectures are offered regarding a physical basis for the empirically derived relative permeability functions. Hysteresis of drainage and imbibition nonwetting-phase relative permeability curves is an established phenomenon. Only recently are experimental results appearing in the literature that indicate wetting-phase hysteresis. Jones and Roszelle showed that water relative permeability exhibits pronounced hysteretic behavior in water-wet sandstone, and Schneider and Owens demonstrated oil relative permeability hysteresis in oil-wet carbonate. These results support the speculation that water relative permeability (in water-wet sands) is much lower on the production cycle (drainage) than on the injection (imbibition) cycle during cyclic steam stimulation.A second complementary conjecture is related to mechanical stress.
JPT
P. 1987^