The semi-analytical productivity equations for vertically fractured coalbed methane wells considering pressure propagation process, variable mass flow, and fracture conductivity decrease

Abstract

As an unconventional gas resource, coalbed methane (CBM) reservoir has unique flow mechanism and production scheme compared with conventional and other unconventional gas reservoirs. At present, many investigators have done a lot of researches on CBM productivity prediction. However, few studies consider variable mass flow within hydraulic fracture and hydraulic fracture conductivity decrease in the model. Thus in order to accurately forecast gas productivity, the pressure propagation process, gas-water two phase flow in coal formation, stress sensitivity and coal matrix shrinkage in cleat system, variable mass flow within hydraulic fracture, and fracture conductivity decrease should be considered simultaneously when establishing gas production model of CBM wells.In this work, firstly the pressure propagation model is established for vertically fractured CBM wells and vertical CBM wells without fracturing. Secondly, the pressure drop model in the hydraulic fracture is developed considering variable mass flow and conductivity decrease in the hydraulic fracture. Thirdly, based on the pressure propagation model, the dynamic permeability model considering stress sensitivity effect and matrix shrinkage effect, the pressure drop model in the hydraulic fracture considering variable mass flow and conductivity decrease in the hydraulic fracture, a multi-factor coupled CBM well productivity equation is established and solved using numerical methods. Fourthly, the proposed models are validated by numerical simulation and compared with numerical simulation when variable mass flow and conductivity decrease in the hydraulic fracture are considered. Finally, the main factors influencing the productivity of CBM wells are analyzed. Excellent agreements between gas (water) production rate by the proposed models and simulations are obtained when variable mass flow and conductivity decrease in the hydraulic fracture are not considered, indicating that the degradation form of the proposed gas productivity model for CBM wells is rational and accurate to predict the gas production of CBM wells. More importantly, when variable mass flow and conductivity decrease in the hydraulic fracture are considered, the proposed model matches the actual data better than the commercial simulator, exhibiting the superiority of the proposed model in some cases. Preliminary study results show that: the cumulative gas production of CBM wells (CGPC) decreases sharply when permeability is less than 0.5 mD. CGPC increases with increasing the hydraulic fracture length but reaches a plateau after a given value. The stress sensitivity of the cleat system decreases early production, while, the matrix shrinkage improves the productivity of CBM wells at late production stage. The permeability decreasing index of the hydraulic fracture directly leads to the rapid decrease in gas production rate of CBM wells.Because the pressure propagation process, the dynamic permeability, the variable mass flow within the hydraulic fracture, and fracture conductivity decrease are accounted for in the productivity equation of CBM wells, it can predict the actual productivity of CBM wells more accurately and provide a theoretical basis for the development of CBM reservoirs.