Interpretation of Gas/Water Relative Permeability of Coal Using the Hybrid Bayesian-Assisted History Matching: New Insights

The relative permeability of coal to gas and water exerts a profound influence on fluid transport in coal seams in both primary and enhanced coalbed methane (ECBM) recovery processes where multiphase flow occurs. Unsteady-state core-flooding tests interpreted by the Johnson–Bossler–Naumann (JBN) method are commonly used to obtain the relative permeability of coal. However, the JBN method fails to capture multiple gas–water–coal interaction mechanisms, which inevitably results in inaccurate estimations of relative permeability. This paper proposes an improved assisted history matching framework using the Bayesian adaptive direct search (BADS) algorithm to interpret the relative permeability of coal from unsteady-state flooding test data. The validation results show that the BADS algorithm is significantly faster than previous algorithms in terms of convergence speed. The proposed method can accurately reproduce the true relative permeability curves without a presumption of the endpoint saturations given a small end-effect number of <0.56. As a comparison, the routine JBN method produces abnormal interpretation results (with the estimated connate water saturation ≈33% higher than and the endpoint water/gas relative permeability only ≈0.02 of the true value) under comparable conditions. The proposed framework is a promising computationally effective alternative to the JBN method to accurately derive relative permeability relations for gas–water–coal systems with multiple fluid–rock interaction mechanisms.