Hydraulic fracturing plays a crucial role for economic production from unconventional resources. Especially development of shale gas resources is highly dependent on this evolving technology. Meanwhile, advanced logging tools, microseismic mapping and well testing analysis revealed the presence of abundant natural fractures and the complex induced fracture network in their presence. Natural fractures may open during fracturing treatments and change the direction of fracture growth. Despite the significance of natural fractures in formation evaluation, reservoir modeling, fracturing design and notable advances in numerical modeling of fractured reservoirs, these modeling require a description of natural fractures, which is often impossible to obtain from seismic. This paper proposes an innovative optimization technique to estimate the geometry of natural fractures based on geophysical data. A constrained mixed-integer nonlinear programming (MINLP) model is developed to compute and define possible optimal realizations of natural fractures from selected double-couple microseismic events, which will provide both geologist and reservoir engineers a robust tool for evaluating and modeling naturally fractured reservoirs. The objective of the MINLP problem was to minimize the total least squared errors of distance between microseismic events under different geodesic and technical design constraints. The performance and efficiency of the MINLP problem is tested through several instances. Computational results confirm to the expected numerical results obtained manually. An real example with field data is presented to show the model's computational capability.
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