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

Abstract

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 non-wetting phase (NWP) 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 comprises a kernel function accounting for the transition between capillarity- and viscositydominated flow phenomena. In a follow-up systematic laboratory study SCAL measurements provided a preliminary proof-of-concept on the applicability of the model and validated its specificity. In the laboratory study presented here, we examine the applicability of the basic flow-rate dependent relative permeability scaling model in immiscible two-phase flows in an artificial two-dimensional microfluidic network, across different flow regimes. In particular, we assess the applicability of the flowdependent relative permeability scaling model in a microfluidic pore-network and we correlate the form of the associated kernel function with the interstitial structure of the flow across different flow regimes. The scope is to assess the applicability and/or universality of the aforementioned scaling function and to examine the forensic character of the kernel function, i.e. the potential for revealing the interstitial flow structure. The proposed scaling opens new possibilities in improving SCAL protocols and other important applications, e.g. characterization of systems and flow conditions, rock typing, assessment of end-effects during R/SCAL, as well as the development of more efficient field-scale simulators.