Flow-Dependent Relative Permeability Scaling for Steady-State Two-Phase Flow in Porous Media: Laboratory Validation on a Microfluidic Network

Conventionally, the relative permeabilities of two immiscible fluid phases flowing in porous media are considered and expressed as functions of saturation. Yet, this has been put into challenge by theoretical, numerical, and laboratory studies of flow in artificial pore network models and real porous media. These works have revealed a significant dependency of the relative permeabilities on the flow rates, especially when the flow regime is capillary to capillary-viscous dominated, and part of the disconnected nonwetting phase remains mobile. These studies suggest that relative permeability models should include the functional dependence on flow intensities. However, revealing the explicit form of such dependence remains a persistent problem. Just recently, a general form of dependence was inferred based on extensive simulations with the DeProF model for steady-state two-phase flows in pore networks. The simulations revealed a systematic dependence of the relative permeabilities on the local flow rate intensities. This dependence can be described analytically by a universal scaling functional form of the actual independent variables of the process, namely, the capillary number, Ca, and the flow rate ratio, r. The proposed scaling incorporated a kernel function, the intrinsic dynamic capillary pressure (IDCP) function, describing the transition between capillarity- and viscosity-dominated flow phenomena. In a parallel laboratory study, SCAL measurements provided a preliminary proof-of-concept on the applicability of the model. In the laboratory study presented here, we examine the applicability of the scaling model by taking extensive, ex-core measurements of relative permeabilities for steady-state co-injections of two immiscible fluids within an artificial microfluidic pore network, across different flow regimes in Ca and r. From these measurements, we calculate the values of the mobility ratio, and we compare these to the corresponding values of the flow rate ratio. We also extract the IDCP curve, the locus of critical flow conditions, whereby the process is more efficient in terms of energy utilization – accounted by the nonwetting phase flow rate per unit of total power provided to the process, as well as the locus of flow conditions of equal relative permeabilities. We show that the degree of consistency between flow rate ratio and mobility ratio values, the IDCP curve, the locus of critical flow conditions, and the locus of equal relative permeabilities, as well as some associated invariant characteristic values, can be used for assessing the extent of end effects and for characterizing the flow as capillary- or viscous-dominated. The proposed scaling introduces new opportunities for enhancing SCAL protocols and their associated applications. These include the characterization of systems and flow conditions, dynamic rock typing, evaluation of capillary end effects, as well as the advancement of more efficient field-scale simulators. Additionally, it paves the way in designing more energy-efficient EOR interventions.