This paper presents a methodology for the optimal hydraulic fracture treatment design. The methodology includes, the construction of a "fast surrogate" of an objective function whose evaluation involves the execution of a time-consuming computational model, based on neural networks, DACE modeling, and adaptive sampling. Using adaptive sampling, promising areas are searched considering the information provided by the surrogate model and the expected value of the errors.

The proposed methodology provides a global optimization method, hence avoiding the potential problem of convergence to a local minimum in the objective function exhibited by the commonly Gauss-Newton methods. Furthermore, it exhibits an affordable computational cost, is amenable to parallel processing, and is expected to outperform other general purpose global optimization methods such as, simulated annealing, and genetic algorithms.

The methodology is evaluated using two case studies corresponding to formations differing in rock and fluid properties, and geometry parameters. From the results, it is concluded that the methodology can be used effectively and efficiently for the optimal design of hydraulic fracture treatments.

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