The modified gas-water two phase version flowing material balance equation for low permeability CBM reservoirs

The flowing material balance (FMB) equation is a frequently-utilized engineering tool to extract reservoir information according to production performance of producing wells. At present, it is still significantly challenging to adapt the FMB equation to CBM reservoirs due to the existence of gas-water two phase flow, stress dependence, matrix shrinkage and gas desorption. With all my respect to previous FMB equations for CBM reservoirs, a great deal of attention has been drawn to the single water/gas flow, which can only be applied for early production stage or cannot capture the gas-water two phase flow features of general CBM reservoirs. The most recent and comprehensive research effort of FMB equation for CBM reservoirs is performed by Clarkson and Salmachi (2017), which takes the aforementioned characteristics into account. However, suffering the limitation that the pressure-saturation relationship is not available, Clarkson and Salmachi (2017) assume the saturation and pressure gradients in coal seams are negligible, i.e., the relative permeability is not incorporated in the pseudo-pressure calculation, which will inevitably lead to large deviation compared with the precise results. Notably, during the depressurization development process of low-permeability CBM reservoirs, the pressure and saturation gradients are large enough and cannot be overlooked. Thus, a robust FMB equation for gas-water two phase flow in low-permeability CBM reservoirs is still lacking in the petroleum industry and is significantly necessary to be developed. In this study, the important pressure-saturation relationship is rigorously derived in terms of the conservation of mass and momentum equations, in which the gas desorption, matrix shrinkage and stress dependence are fully coupled. Next, the developed relationship is used to calculate the gas/water phase pseudo-pressure and subsequently the previous FMB equation for CBM reservoirs is modified. Finally, reliability of proposed FMB equation is successfully verified against the numerical simulation with excellent agreements compared with the input reservoir properties. In addition, with the intent of further solidifying the field applicability of the modified FMB equation, the production performance of an actual low-permeability CBM well in Hancheng field, China is analyzed through the proposed FMB equation and desirable interpretation results are achieved. Incorporating the pressure-saturation relationship for the first time, the modified FMB equation can serve as a practical and robust tool to extract valuable information regarding the low-permeability CBM reservoirs.