Production optimization of coalbed methane (CBM) is a complex constrained nonlinear programming problem. Finding an optimal decision is challenging since the coal seams are generally heterogeneous with widespread cleats, fractures, and matrix pores, and the stress sensitivities are extremely strong; the production of CBM wells needs to be adjusted dynamically within a reasonable range to fit the complex physical dynamics of CBM reservoirs to maximize profits on a long-term horizon. To address these challenges, this paper focuses on the step-down production strategy, which reduces the bottom hole pressure (BHP) step by step to expand the pressure drop radius, mitigate the formation damage, and improve CBM recovery. The mathematical model of CBM well production schedule optimization problem is formulated. The objective of the optimization model is to maximize the cumulative gas production and the variables are chosen as BHP declines of every step. BHP and its decline rate constraints are also considered in the model. Since the optimization problem is high dimensional, nonlinear with many local minima and maxima, covariance matrix adaptation evolution strategy (CMA-ES), a stochastic, derivative-free intelligent algorithm, is selected. By integrating a reservoir simulator with CMA-ES, the optimization problem can be solved successfully. Experiments including both normal wells and real featured wells are studied. Results show that CMA-ES can converge to the optimal solution efficiently. With the increase of the number of variables, the converge rate decreases rapidly. CMA-ES needs 3 or even more times number of function evaluations to converge to 100% of the optimum value comparing to 99%. The optimized schedule can better fit the heterogeneity and complex dynamic changes of CBM reservoir, resulting a higher production rate peak and a higher stable period production rate. The cumulative production under the optimized schedule can increase by 20% or even more. Moreover, the effect of the control frequency on the production schedule optimization problem is investigated. With the increases of control frequency, the converge rate decreases rapidly and the production performance increases slightly, and the optimization algorithm has a higher risk of falling into local optima. The findings of this study can help to better understanding the relationship between control strategy and CBM well production performance and provide an effective tool to determine the optimal production schedule for CBM wells.

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随机进化算法优化煤层气井生产进度

煤层气（CBM）的生产优化是一个复杂的约束非线性规划问题。由于煤层通常是非均质的，具有广泛的夹板，裂缝和基质孔隙，并且应力敏感性极强，因此找到最佳决策是一项挑战。煤层气井的产量需要在合理范围内动态调整，以适应煤层气储层复杂的物理动力学，从而在长期内最大化利润。为了应对这些挑战，本文重点关注逐步生产策略，该策略逐步降低了井底压力（BHP），以扩大压降半径，减轻地层损害并提高煤层气采收率。建立了煤层气井生产进度优化问题的数学模型。优化模型的目的是使累积的天然气产量最大化，并随着BHP每步下降而选择变量。模型中还考虑了必和必拓及其下降率约束。由于优化问题是高维的，具有许多局部最小值和最大值的非线性，因此选择了协方差矩阵自适应演化策略（CMA-ES），它是一种随机的，无导数的智能算法。通过将储层模拟器与CMA-ES集成在一起，可以成功解决优化问题。研究了包括正常井和实际特征井在内的实验。结果表明，CMA-ES可以有效地收敛到最佳解决方案。随着变量数量的增加，收敛速度迅速下降。CMA-ES需要功能评估的3倍甚至更多倍才能收敛到最佳值的100％（而99％）。优化的调度方案可以更好地适应煤层气储层的非均质性和复杂的动态变化，从而达到更高的产量峰值和更高的稳定期产量。优化计划下的累计产量可以增加20％甚至更多。此外，研究了控制频率对生产进度优化问题的影响。随着控制频率的增加，收敛速度迅速降低，生产性能略有提高，优化算法陷入局部最优的风险较高。