Analytical model for CO2-water displacement with rate-dependent phase permeability for geological storage

Abstract

Analytical modelling is an effective tool for predicting reservoir behaviour under high uncertainties, like CO₂ storage in aquifers, where multiple simulation runs are necessary for stochastic modelling and risk assessment. This paper formulates the Buckley-Leverett problem with x-dependent fractional flow. We derive a new analytical model for displacement of brine by CO₂ accounting for (i) rate-dependent phase permeability during radial flows and (ii) radial flows of Forchheimer's high-rate gas injection; this analytical model is also valid for (iii) linear flows during flooding in micro heterogeneous or composite cores and (iv) CO₂-water flow upscaling in reservoirs where layering is perpendicular to flux direction. An exact solution of the flow equation is based on the observation that the flux of each phase conserves along the characteristic trajectories. We discuss S-shape fractional flow function, which is typical for reservoir rocks. The solution includes formulae for phase saturations and fluxes and trajectories of the displacement CO₂-water front and of the forward and rear mixture zone boundaries. The fast analytical model can be used for multivariate sensitivity study and sweep efficiency prediction.