Accounting for viscous fingering in relative permeability estimation of special core analysis measurements
Pereira, Bruno Miguel Ferreira
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Relative permeability (kr) is a critical input data for any calculation involving multiphase flow in petroleum reservoirs. Normally, kr curves are obtained by performing coreflood experiments as part of SCAL measurements or EOR studies. The results of the experiments are then used to obtain kr values often by either analytical models (e.g. JBN) or history matching techniques. Most of these models are based on the Buckley-Leverett displacement theory and are not applicable to unstable displacements. Therefore, using these models to describe a core flood experiment involving viscous fingering will result in potentially large errors in the estimation of kr curves. This study focused on the estimation of relative permeability curves for unstable experiments, more specifically in unfavourable mobility corefloods with a tendency to develop viscous fingering. Refined 2D coreflood simulations were used to evaluate the effect of viscous fingering in kr estimation methods. The simulations were performed as immiscible corefloods in homogeneous cores using a Black-oil model in a commercial simulator. The first part of this study, describes the methodology used to generate viscous fingering in numerical corefloods. Instability triggering methods were used with high resolution simulation to generate the viscous fingering. This methodology was then used to generate different numerical experiments with viscous fingering formation. In the second part, the currently widely used oil industry approaches for relative permeability estimation (1D history matching and JBN method) were evaluated for cases with unfavourable mobility. The errors were quantified in order to understand the effect of fingering on these methods and the amount of error one can incur when using them for these cases. In the latter part of the thesis, two novel methods are proposed for estimating relative permeabilities for unfavourable mobility coreflood experiments, namely viscous fingering. These methods are based on the proposed model called ‘stable equivalent model’. This model proposes a correction to the velocity of the fluids in a coreflood affected by viscous fingering, allowing to account for viscous fingering in relative permeability estimation. The model is used to modify the JBN method and 1D history matching, allowing these methods to tackle viscous instability. The integrity of these techniques was validated against published experimental data and numerical data.