Steady-State Two-Phase Flow in Porous Media: Laboratory Validation of Flow-Dependent Relative Permeability Scaling

Abstract

The phenomenology of steady-state two-phase flow in porous media is recorded in SCAL relative permeability diagrams. Conventionally, relative permeabilities are considered to be functions of saturation. Yet, this has been put into challenge by theoretical, numerical and laboratory studies that have revealed a significant dependency on the flow rates. These studies suggest that relative permeability models should include the functional dependence on flow intensities. Just recently a general form of dependence has been 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 that 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. In this work, we present the preliminary results of a systematic laboratory study using a high throughput core-flood experimentation setup, whereby SCAL measurements have been taken on sandstone core across different flow conditions -spanning 6 orders of magnitude on Ca and r. The scope is to provide a preliminary proof-of-concept, to assess the applicability of the model and validate its specificity. The proposed scaling opens new possibilities in improving SCAL protocols and other important applications, e.g. field scale simulators.

Estimation of Capillary‐Associated NAPL‐Water Interfacial Areas for Unconsolidated Porous Media by Kinetic Interface Sensitive (KIS) Tracer Method

“…As the capillary pressure is a function of saturation according to Brooks and Corey's theory (Equation ), the FIFA here reduces to be only a function of saturation. It is worth noting that this closed form function may not necessary hold true when the flowrate dependency of the interstitial flow structure, the associated size distributions of fluidic elements of the disconnected non‐wetting phase, and their effects on the FIFA are taking into consideration (Armstrong et al., 2016; Aursjo et al., 2014; Valavanides et al., 2020).…”