A fully-coupled gas-water two phase productivity equations for low-permeability CBM wells

To date, much attention has been focused on the high-permeability CBM reservoirs, which results in ignorance of pressure and saturation gradients in the coal seams of previous productivity equations. However, for the low-permeability CBM reservoirs (< 1 mD), the pressure and saturation gradients are too large to be neglected during the production process. The CBM reservoirs exhibit stress-dependent permeability changes during early dewatering operation and a strong matrix-shrinkage effect once below the desorption pressure. Thus, considering the pressure profile will enable us to capture the absolute permeability profile in the coal seams. In addition, the gas-water two phase flow will further aggravate the complexity of this issue. Similarity, considering the saturation profile will enable us to capture the relative permeability profile of gas/water phase in the coal seams. Hence, the objective of this research is to develop the productivity equations for low-permeability CBM wells considering both pressure and saturation gradients. Firstly, the previous gas/water phase pseudo-pressure is modified by considering the gas/water phase effective permeability. Secondly, on the basis of gas-water two phase conservation equations of mass and momentum, the relationship between pressure and saturation is established through rigorously derivation. Subsequently, combined with gas-water two phase relative permeability curve, we present an iterative algorithm to obtain the pressure-saturation relationship. As a result, the gas/water phase effective permeability can be described as the unique function of pressure. Finally, according to the relationship between gas/water phase effective permeability and pressure, the fully-coupled productivity equations for low-permeability CBM wells are developed. The reliability of the proposed equations is successfully validated through comparisons with commercial numerical simulation and previous productivity equations. After that, the analysis of sensitive factors is implemented to quantify the corresponding effects on production performance and several key implications are drawn.