Implementing pore size distribution into saturation height function modelling of reservoir rock types: A case study on a carbonate gas reservoir

The accurate determination of saturation-height functions for modeling multiphase fluid flow in porous media is critical for applications, such as hydrocarbon recovery and subsurface CO2/H2 storage. The challenges associated with water saturation distribution in carbonate reservoirs arise from their inherent heterogeneity and complex pore systems. Addressing such challenges, this study aims to introduce a robust saturation-height function model that considers a non-linear relationship between capillary pressure and saturation, leading to more reliable es-timates of fluid saturations. To achieve this, modifications were performed on a saturation height model based on the relationship between porosity, permeability, and pore size distribution (PSD). First of all, the capillary pressure model implemented in the previously introduced PSD-based approach was replaced by a model suitable for heterogeneous reservoirs, fitting the available mercury injection capillary pressure (MICP) data with higher accuracy. Additionally, the derivation of the relations between the optimum pore throat radius and matching parameters of the capillary pressure model was conducted by finding the best correlation among all the available data in the previous approach. For the first time in this study, considering the resemblance in rock properties like capillary pressure and PSD within each rock type, individual correlations among these parameters were estab-lished for each reservoir rock type. The predicted saturation height model was cross-checked against the log and core-derived saturation heights, demonstrating a high level of consistency, particularly along the gas-saturated regions. The obtained results were also compared with the conventional saturation height models, including the Leverett J-Function, Johnson's method, and Cuddy's approach. The significance of the modifications was underscored through a comparison of results with those achieved by the previous approach in which the rock typing was ignored. Although the PSD method, which ignored rock types, exhibited high consistency with log data, our modifications yielded far better predictions by improving the coefficient of determination from 0.68 to 0.84.