A double-cycle production splitting method and its application to gas wells

The production splitting coefficient is a key parameter for predicting gas production and reserves, evaluating gas recovery efficiency, and guiding the optimization of well patterns in multilayer commingled gas reservoirs. Therefore, developing a reliable splitting method to calculate this coefficient is critical for the development of multilayered commingled gas reservoirs. The gas drainage radius emerges as a key parameter in determining the production splitting coefficient grounded in the physical concept of production splitting. This coefficient is influenced by several factors—such as the wellbore radius, production layer thickness, porosity, initial gas saturation, gas deviation coefficient, reservoir temperature, gas drainage radius, and average formation pressure. Usually, calculating the gas drainage radius and average formation pressure cannot be performed in actual applications. Combining the gas well deliverability and material balance equations forms a closed-loop model for calculating the production splitting coefficient. This model features three equations with three unknowns—gas drainage radius, average formation pressure, and the production splitting coefficient. It introduces a double-cycle calculation method to solve the model. Specifically, the internal cycle computes the gas drainage radius, whereas the external cycle determines the production splitting coefficient, each offering unique solutions and employing alternating forward recursion and reverse recursion rules. The establishment of a double-cycle calculation process—defined by specific cycle step sizes and an error threshold—ensures that the external cycle progresses only upon the convergence of the internal cycle. Moreover, it determines whether the internal cycle can converge. Numerical simulations demonstrate that the production splitting coefficient exhibits different patterns across different production stage layers, highlighting the accuracy and mechanism soundness of the double-cycle method compared with direct numerical simulations. Moreover, it has good feasibility in field application because it can calculate the production splitting coefficient even without known values for gas drainage radius. Comparing gas-producing profiles indicates that the dual-cycle calculation method has reliable accuracy in field applications when the gas drainage radius and average formation pressure are unknown. Ultimately, the double-cycle calculation method offers a comprehensive solution for a three-element equation system, enabling simultaneous estimations of the production splitting coefficient, gas drainage radius, and average formation pressure.