Impact of relative permeability and capillary pressure parameterization on the inversion results of unsteady-state core flooding data

Relevance. Simultaneous estimation of relative permeability and capillary pressure-saturation functions from unsteady-state core flooding experiments is considered a promising way to reduce the scope of laboratory measurements. However, practical application of this approach is complicated by the non-uniqueness of the inverse problem, the limitation of experimental data, and the dependence of the result on the selected representation of the target curves. Under these conditions, the type of parameterization of relative permeability and capillary pressure curves becomes one of the key factors controlling both the quality of curve reconstruction and the uncertainty assessment. Aim. To evaluate the impact of the parameterization of relative permeability and capillary pressure on the results of numerical inversion and on the subsequent uncertainty quantification. Methods. Two approaches for describing the target functions were considered: analytical parameterization based on the Corey–Brooks and Skjaeveland models, and pointwise parameterization at saturation nodes. The analysis was performed on three two-phase computational experiments of unsteady-state oil displacement by water: a baseline synthetic case with smooth curves, a more complex synthetic case with variable curvature of the functions, and a digital LBM-based experiment at the pore scale. The inverse problem was solved using gradient-based optimization combined with an ensemble-based uncertainty analysis over multiple initial models. Results and conclusions. It was shown that analytical parameterization provides fast inversion and acceptable reconstruction for simple smooth curves, but leads to biased solutions and underestimated uncertainty bounds when the true saturation functions have a complex shape. In some cases, analytical models fail to reproduce complex saturation profiles and yield non-physical capillary pressure estimates. Pointwise parameterization is computationally more expensive, but it allows a wider class of functional shapes to be represented, provides a better match to complex experimental data, and produces more realistic confidence intervals. It is concluded that analytical parameterization is suitable for rapid estimates and simple cases, whereas the pointwise approach is a more reliable tool for reconstructing complex relative permeability and capillary pressure curves and for consistent uncertainty assessment. For citation: Dzharkinov R.B., Fokin M.I., Duchkov A.A., Krutko V.V., Avdonin A.S. Impact of relative permeability and capillary pressure parameterization on the inversion results of unsteady-state core flooding data. Bulletin of the Tomsk Polytechnic University. Geo Assets Engineering, 2026, vol. 337, no. 7, pp. 228-246. https://doi.org/10.18799/24131830/2026/7/5739