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

Marios S Valavanides,Olga Vizika,Souhail Youssef,Matthieu Mascle,J Schembre-Mccabe,H Ott

doi:10.1051/e3sconf/202014603002

Marios S Valavanides, Olga Vizika + Show 4 more

Open Access

https://doi.org/10.1051/e3sconf/202014603002

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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 a 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.

Highlights

The conventional use of saturation as the independent variable in two-phase flow in porous mediĂ (PM) is based on the oversimplifying assumption that disconnected fluidic elements of the non-wetting phase (NWP) do not move with the average flow but remain stranded in the pore medium matrix
Pairs of NWP and WP relative permeability values {kkrrrr, kkrrrr}ii, were computed using eqn (1) for each measurement i (ii = 1, 88). These were drawn into standard relative permeability diagrams in terms of the WP saturation, Swi, for each one of the 14 different core flood cycles
These diagrams are not presented here because of space limitation. They have been merged into a single diagram, see Fig. 6(a)

Summary

Introduction

The conventional use of saturation as the independent variable in two-phase flow in porous mediĂ (PM) is based on the oversimplifying assumption that disconnected fluidic elements of the non-wetting phase (NWP) (ganglia and droplets) do not move with the average flow but remain stranded in the pore medium matrix This situation arises when flow conditions of ‘relatively small values’ of the capillary number are maintained. For any one of those cases, the corresponding superficial velocity of the disconnected NWP would not necessarily attain the same value The latter would be the result of the ‘negotiation’ between the two factors inhibiting the transport of each phase, i.e. viscosity and capillarity, over the mass and momentum balances. This ‘negotiation’ takes place within the ‘regulatory framework' conformed by two critical ‘stakeholders’ or ‘regulators’, namely the particular structure of the PM and the externally imposed, flow conditions

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