基于双循环的气井产量劈分方法及应用

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

产量劈分系数是多层合采气藏动态预测的基础,建立产量劈分系数动态跟踪计算方法具有重要意义.基于产量劈分的物理意义,明确了产量劈分系数的求解关键参数为泄气半径,但泄气半径在实际应用中通常未知.结合产能方程和物质平衡方程,建立了闭环的产量劈分系数计算模型,计算模型包含泄气半径、平均地层压力和产量劈分系数等三个未知参数,为求解计算模型提出了双循环计算法,内循环求解泄气半径,外循环求解产量劈分系数,内循环和外循环均存在唯一解,循环规则包括正向递归和反向递归,内循环与外循环的循环规则始终相反,通过设定循环步长和误差上限,建立了双循环的计算流程,外循环包含内循环,内循环收敛时外循环才能进行,外循环决定了内循环能否收敛.数值模拟验证显示,产量劈分系数在不同产层、不同阶段、不同时间表现出不同的变化规律,双循环计算法不仅机理正确且精度很高.产气剖面对比显示,双循环计算法在现场应用中亦具有可靠的精度.双循环计算法属于三元方程组的求解方法,实现了产量劈分系数、泄气半径和平均地层压力的同时计算.

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.