(60b) Simultaneous Integration of Machine Learning in a Mixed-Integer Nonlinear Programming Formulation to Optimize Gas Production and Water Management in Shale Gas Reservoirs

The considerable use of freshwater and wastewater discharge in shale gas production necessitate the development of effective water-management strategies. Many optimization methodologies have been elaborated for the efficient use of available water and the reuse of flowback water. However, these methodologies have presented different assumptions such as considering fixed parameters or uncertain factors the total water needed to perform hydraulic fracturing and the amount of flowback water obtained in each well. Furthermore, they have not considered the simultaneous optimization of gas production and water management, nor have they considered other aspects such as the optimal selection of well locations, well size (depth and lateral length) and the amount of proppant used in the working fluid, which are important variables during hydraulic fracturing.

On the other hand, one of the complicating factors in the management of wastewater from shale gas production is the spatiotemporal variability of its quantity and composition. Hybrid methods have been described in which Monte Carlo simulation, autoregressive integrated moving average (ARIMA) model, different index analogy methods, polynomial models, and the response surface approach have been evaluated to predict shale gas production. On the other hand, machine learning is a widely used alternative in several areas of study due to its high accuracy in the development of highly complex models, so some machine learning models have been described to make predictions in shale gas wells from real well production data information. These studies have focused on machine learning models to predict shale gas production. In addition, the prediction of gas production and flowback water have been addressed separately.

In addition to the above, there is a need for decision-making approaches for shale gas exploitation that are accurate and can provide solutions that reduce environmental pollution. Therefore, this study presents a novel mathematical programming approach that simultaneously incorporates a mixed-integer nonlinear programming (MINLP) formulation with machine learning models to determine operating conditions, gas production, and the optimal water management for the completion phase in shale gas fields. The dataset collected for the development of the artificial neural network (ANN) model takes into account well (i.e., geological location), hydraulic fracturing, and production information; this dataset has been collected in the Eagle Ford formation. The total cumulative gas production and flowback water generated in shale gas wells are selected as output variables. Optimization of the hyperparameters associated with the ANN model is carried out to obtain a competitive model. The proposed MINLP mathematical optimization model includes machine learning models for each well, material balances, temporal generation of flowback water with its respective treatment, storage, reuse, and disposal options, location constraints, capital and operating costs, drilling and completion costs as well as revenues from the sale of shale gas. Maximizing total annual profit (TAP) and minimizing total freshwater consumption are the economic and environmental objectives established in this study.

A case study located in Mexico has been presented to illustrate the benefits of the proposed approach. It has been proven that it is possible to reduce the consumption of freshwater where up to 29% (41,498 m³) of the total fracture water can be reused (solution A) to carry out hydraulic fracturing of other wells; different papers have been reported in the literature where the same case study is considered by fixing the amount of total fracture water and have reached percentages of total water reused of between 20-22%. Moreover, an average drilling and completion cost per well of 7,917,047 $/well, 8,700,973 $/well, and 8,630,239 $/well have been obtained for solutions A, B, and C respectively; these per-well costs are among the costs reported in the Eagle Ford Formation. The compromise solution offers a water consumption per produced energy of 6.71 L/GJ in addition to the fact that 27% of the total fracture water required can be obtained by reusing the flowback water with attractive economic indicators. Furthermore, some wells were fractured only with reused water while almost all wells have a good production of shale gas.