Unconventional plays such as tight gas and shale gas reservoirs have potential of becoming the main source of cleaner energy in the 21th century. Development of unconventional fields requires engineered hydraulic fracturing that facilitates access to larger volumes of the reservoir rock and delivers more hydrocarbon to the production wells. While hydraulic fracturing technology has advanced considerably in application of materials, equipment, and procedures in the last thirty years, design of fracture systems still primarily relies on heuristic judgment of geoscience experts. This study closes the existing gap in computational tools and explores advantages of numerical optimization techniques in automatic design of hydraulic fracture systems. In this work we implement and analyze several optimization algorithms that allow obtaining nearly optimal solutions with reasonable computational time, achieving short- and long-term production goals of unconventional projects, and improving their revenue. In particular, we solve the problem of hydraulic fracture placement with the gradient-based finite difference method (FD), discrete simultaneous perturbation stochastic approximation (DSPSA), and genetic algorithm (GA). Although all presented algorithms approach global optimal solutions for selected test cases, our numerical experiments indicate higher efficiency of DSPSA and GA. We illustrate our findings with a suit of simulation runs based on synthetic field data.
Commercial development of unconventional reservoirs such as shale and tight formations became possible with advances in hydraulic fracturing widely used in North America since the 1950s. This technology allows to create fractures along a horizontal wellbore in the reservoir of interest and to produce natural gas from tight rock matrix (Holditch, 2007). Further improvement of the technology has led to invention and application of multi-stage HF that made many unconventional plays potentially exploitable assets (King, 2010). Due to costly operations, including HF equipment and materials, optimization of fracture placement and operation scheduling has drawn attention of researchers and oil production companies in the last years.
Optimization of multi-stage hydraulic fracture (HF) placement is a challenging problem not only in terms of the multidisciplinary tasks involved, but also in relation to its numerical issues, especially when automatic optimization algorithms are used. Its complexity stems out of requirement to achieve maximum revenue while minimizing operating costs that are subject to geological and economic constraints. In addition, the highly uncertain environment in which the HF jobs take place, may lead to numerical optimization problems that need to take into account uncertainty in the parameter spaces, and in turn, large number of parameters to be optimized. Thus, without a solid optimization approach, knowledge of experienced engineers and large suites of simulations will yield suboptimal and inefficient results.