Abstract
Abstract
Highlights
The flow of immiscible fluids in heterogeneous porous media has widespread applications in energy and the environment
We consider the flow of a non-wetting phase driving out a wetting phase in a two-dimensional aquifer of length L, height H, and whose intrinsic properties vary in the vertical direction z
We summarise the steps for modelling the transition between the viscous and capillary limits as follows: first the capillary number must be calculated for some initial saturation data (e.g. (3.8)) using the implicit equation (3.11); if shocks are present, the shock saturation value ss must be calculated using (3.5), where the advection velocity V (3.2) and flux J use the composite expressions (2.61) for the equivalent relative permeabilities; if no shocks are present, the flooding front corresponds to saturation value s∞; the solution is calculated for all time via the characteristic equation (3.7), where V (3.2) contains the composite expressions (2.61)
Summary
The flow of immiscible fluids in heterogeneous porous media has widespread applications in energy and the environment. The ultimate goal is to be able to study a vast range of scenarios to provide ensemble forecasts for the migration of immiscible fluids in porous media This tool needs to be computationally inexpensive, and needs to be able to predict where and when heterogeneities affect the flow in the aquifer via the transition between viscous and capillary limiting regimes. We use our simplified semi-analytical expressions to address the dynamics of this transition, showing that regions of the aquifer near the injection point (or at early times) lie within the viscous limit, whereas regions far away from the injection point (or at late times) lie within the capillary limit We use this approach to quantify the effect of heterogeneities on the injection of CO2, making comparisons with field data from the Salt Creek case study (Bickle et al 2017).
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