Efficient Global Optimization For Hydraulic Fracturing Treatment Design

Abstract

Abstract 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. Introduction Hydraulic fracturing is one of the most common stimulation strategies used to enhance the production from oil and gas wells. During a hydraulic fracturing treatment, fluids are injected to the formation at a pressure high enough to cause tensile failure of the rock, and propagate the fracture. As a result of a successful treatment, a path with much higher permeability than the surrounding formation is created from the well. Each of the fluids injected during the treatment execution performs a significant and specific task. The initial fluid, known as pad, initiates and propagates the fracture. The following stages of the treatment involve the injection of a fracturing fluid with varying concentrations of proppant. The fluid is intended to continue the fracture propagation and the proppant will keep the fracture open, even though the formation stresses will try to close the fracture, after the fluid injection ceases. For a given formation, the design of a hydraulic fracture treatment involves the selection of appropriate fracturing fluids and proppants, the number of treatment stages, the concentrations and the rates and pressures of injection of each stage. Each design will result in a specific fracture geometry and conductivity, which is related to the production increase obtained from the fractured well. This means that, due to the several possible combinations of the parameters involved, and their non-linear interactions, there are a significant number of possible fracture geometries, each of which will result in a different post-fracture well production performance. Ralph and Veatch1 presents the general concepts of hydraulic fracture treatments economics and introduced the net present value as a valuable tool for the optimal design of hydraulic fracture treatment. An optimal hydraulic fracture treatment design maximizes the net present value of the revenue after the treatment, considering the post-fracture production performance and the treatment costs.