Optimizing Production Schedule of Coalbed Methane Wells Using a Stochastic Evolution Algorithm

Abstract

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.