Methods for calculating reserves, average reservoir pressure and gas recovery ratio for under-saturated coalbed methane reservoirs

Original gas in place (OGIP) is the material foundation for coalbed methane (CBM) development, while the average reservoir pressure and recovery factor are the primary evaluation metrics for CBM extraction. Currently, the evaluation methods for OGIP in undersaturated CBM reservoirs predominantly rely on material balance principles incorporating both gas and aqueous phases, considering changes in porosity and saturation. These conventional approaches employ pseudo-deviation coefficient Z* to equivalate adsorbed gas to free gas, requiring numerous parameters and involving complex calculations. Traditional average pressure calculation methods additionally consider aqueous phase production, necessitating iterative computations of gas deviation factor Z, making the process cumbersome. In reality, for undersaturated CBM reservoirs, neither numerous parameters nor iterative calculations of the gas deviation factor are fundamentally required. This study first establishes a material balance equation for undersaturated CBM reservoirs based on the adsorbed gas material balance principle, directly utilizing the relationship between remaining adsorbed gas reserves and pressure. This includes the Langmuir-Freundlich (L-F) adsorption model and the Dubinin-Astakhov (D-A) adsorption model based on micropore filling. Subsequently, the material balance equation is linearized to develop evaluation methods for OGIP, average reservoir pressure, and recovery factor in undersaturated CBM reservoirs. Finally, the methods are validated and applied in case studies. Research demonstrates: The proposed methods for calculating reserves and average reservoir pressure in undersaturated CBM reservoirs require only a few adsorption model parameters, along with pressure data from two or more well tests and corresponding cumulative gas production data. These methods enable the evaluation of OGIP and average reservoir pressure, as well as the prediction of recovery factor at a given abandonment pressure. The calculation process is simple, requires fewer parameters, saves computational time, and meets field accuracy requirements, making it suitable for widespread application. Using production data generated from a conceptual numerical simulation model, the relative error between the reserves evaluated by the proposed method and the numerical simulation results is –0.762 577%. The relative error for the evaluated average reservoir pressure during the pseudo-steady state phase falls within –0.6% to 0.25%, confirming the rationality and reliability of the method. Application and analysis of real-world wells with different adsorption models show that the reserve evaluation results align with field observations. The calculated average reservoir pressure curve passes through the actual shut-in pressure measurement points. At abandonment pressures of 2, 1.5, 1 MPa, the calculated recovery factors for Well A are 46.65%, 55.54%, and 66.65%, respectively, while for Well B, they are 57.49%, 65.05%, and 73.96%, providing significant guidance for field development. For undersaturated CBM reservoirs with known OGIP, the average reservoir pressure can be calculated without actual pressure measurement data. Compared to conventional methods, this approach significantly improves computational efficiency. The research findings can be applied to assess remaining CBM reserves, evaluate well productivity, and diagnose inter-well interference. They hold substantial theoretical and practical significance for production performance analysis, development strategy optimization, and production system adjustment.