One of the most important properties for understanding the dynamic behavior of multiphase flow in porous media is relative permeability. Particularly in two-phase flow, the relative permeability to a given phase is generally assumed to be only a function of the saturation of that phase, independent of the properties of fluids involved and/or flow conditions and ranging in value from zero to one.
In this work, experiments were conducted to determine the effect of viscosity ratio, flow rate and porous medium topology on two-phase relative permeabilities. Two different etchedglass micromodels and acrylic-made triangular capillary tubes were used as porous media. Three different pairs of fluids with viscosity ratios ranging from 0.005 to 202.3 were used. Primary drainage and secondary imbibition displacements were carried out at different injection flow rates and unsteady-state relative permeability curves were constructed.
It was found that relative permeability to both the wetting and the non-wetting phase varied with the viscosity ratio and the injection flow rate. It was also observed that relative permeability to the non-wetting phase took values larger than unity when viscosity ratio was larger than one. This "lubrication effect" observed in the non-wetting phase was affected by the topology of the porous medium.
Experimental relative permeabilities were compared to those predicted by the triangular capillary model presented by Ortiz- Arango and Kantzas [1]. Good agreement was observed in drainage displacements through the triangular capillary tubes at low Reynolds numbers and annular flow conditions.
Multiphase flow occurs in many fields of science. This type of flow is of particular interest in hydrocarbons production. The description of the involved physico-chemical mechanisms must be as precise as possible for optimizing recovery processes. Despite its great importance, multiphase flow is still not well understood and has not yet been properly described analytically, even for simple pipeline flow. The microscopic description of flow through porous media is even more complex because natural porous media have very complex geometry requiring boundary conditions to be specified at all grain surfaces as well as at the interfaces between the fluids contained within the pore space. For this reason, empirical macroscopic descriptions based on Darcy's pioneer work have been used extensively by petroleum engineers.
In single-phase flow, Darcy's law governs a fluid flow through a porous medium under the effect of gravity and viscosity forces. In multiphase flow, Darcy's law was extrapolated[2] inducing a notion of permeability also, but relative to each fluid. This notion does not yet have an obvious theoretical proof. Rose[3] underlines that Darcy's multiphasic law assumes that a porous medium in which two or more immiscible fluids flow, forms with one fluid a new porous medium for the others. Boundary conditions at fluid/fluid and fluid/solid interfaces are thus considered as similar, although this is not true. Another questionable assumption inherited by the conventional formulation for multiphase flow through porous media is the sole dependence of relative permeabilities on saturation, and that they are independent of the pressure, velocity and viscosity of the fluids.
