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Evaluation of Empirical Models for Viscous Fingering in Miscible Displacement
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, IOR 2019 – 20th European Symposium on Improved Oil Recovery, Apr 2019, Volume 2019, p.1 - 17
Abstract
The performance of miscible gas injection projects can be significantly affected by viscous fingering. This is further complicated by the presence of heterogeneities, as depending on the scale of the heterogeneity, there can be a diffusive, advective or channelling effect. To assess the economic feasibility of a miscible gas injection project, reservoir simulations are needed but very fine grids are required for the fingers to be modelled explicitly. This requires a large amount of computational power and time. To get around this issue, many empirical models have been proposed which model the average behaviour of the viscous fingers, allowing predictions of performance, thus reducing grid size and computational time.
Many previous studies have investigated the ability of empirical models to represent fingering in line drives but none have considered flow in a quarter five spot pattern. In this study, a two phase, three component higher-order simulator is used to simulate miscible injection in square line drive and quarter five spot models, with and without heterogeneities. The results of the detailed fingering simulations were compared to the Todd & Longstaff and Fayers empirical models. To account for the effect of heterogeneities, the mixing parameter, w, in the Todd & Longstaff was adjusted using Koval's heterogeneity factor, H_k. The growth rate of the fingers, α, and the final fraction of the cross section occupied by the fingers, a+b, were adjusted in the Fayers model to account for heterogeneities and bypassed oil. The empirical models were implemented in a commercial immiscible reservoir simulator, Eclipse-100 using pseudo relative permeabilities.
The detailed simulations indicate that the growth rate of the fingers varies non-linearly with mean concentration in radial flows and this is not captured by either of the empirical models. A modification of the Fayers model is proposed to capture this. For both heterogeneous line drive and quarter five spot models, the Todd & Longstaff model consistently overestimates recovery after solvent breakthrough as it cannot account for bypassed oil. The Fayers model underestimates recovery whereas the modified Fayers model tends to overestimate the breakthrough time, but after this point, it can accurately reproduce the effluent profile from simulations. However, this requires production data or detailed fingering simulation data to calibrate b, the constant which defines bypassed oil, as this depends on the heterogeneity, the mobility ratio and the time scale of interest