A semi-analytical model for the relationship between pressure and saturation in the CBM reservoirs

At present, analyzing and predicting CBM production performance remains challenging, which can be attributed to the complex gas-water two phase flow and dynamic nature of petro-physical properties. For the sake of simplicity, the saturation distribution in coal seams is generally overlooked and characterized by average water saturation in previous literature, which one can easily handle analytically, semi-analytically, and numerically. However, average water saturation is inadequate to obtain the precise value of pseudo pressure for water/ gas phase, which may generate large deviation compared with actual production behavior. To our best knowledge, the relationship between pressure and saturation in coal seams is still lacking in the petroleum industry. Thus, the main objective of this research is to gain a clear understanding of this issue. In this work, on the basis of rigorous derivation, a semi-analytical model for the relationship between pressure and saturation is developed, which comprehensively accounts for the presence of free gas at the early production stage, matrix shrinkage and gas desorption. Notably, the stress dependence effect is incorporated during the entire production process of CBM wells. Subsequently, employing the gas-water two phase relative permeability data, we present an iterative numerical algorithm to solve the model. Moreover, the proposed semi-analytical model is successfully verified against a numerical reservoir simulator. After that, we shed light on the influences of physical parameters upon the saturation distribution versus pressure and achieve a variety of new insights. This research, for the first time, presents a semi-analytical model to quantify the relationship between pressure and saturation, which fills the gap for the theory of gas-water two phase flow in CBM reservoirs. The proposed model is less data-intensive than performing a numerical simulation and turns out to be simple and powerful in the application. In addition, the new model can significantly contribute to the obtainment of precise pseudo pressure for water/gas phase, therefore lays the theoretical basis for the accurate production prediction for CBM wells.