(712d) Handling Economic and Practical Considerations in Feedback Control of Hydraulic Fracturing in Ultra-Low Permeability Reservoirs
In ultra-low permeability formations, horizontal wells are typically drilled and for each well, multiple hydraulic fractures are generated for enhanced recovery of oil and gas. Based on the assumption that the propped fracture has practically infinite conductivity, in this work, we will use a section based method  to calculate the optimal number of horizontal wells, number of fractures, the length of the fracture and the drainage area aspect ratio that maximize the overall productivity of the well-fracture system. Economic considerations are represented in the form of fixed total length of all the fractures that can be created from the available resources. With a reasonable additional technical constraint (maximum length of fracture that can be placed repeatedly and reliably from any point of the horizontal well) there is a unique solution to the optimization problem.
Once the fracture design parameters are determined, it is also important to achieve uniform proppant concentration at the end of pumping, because it is directly related to the overall efficiency of hydraulic fracturing processes . From a control engineering viewpoint, hydraulic fracturing treatments have been traditionally operated in an open-loop manner. However, such an open-loop operation may lead to poor performance if there is a plant-model mismatch and uncertainties in the process model parameters. While some attempts to employ model-based control schemes have been made , they did not consider economics as well as practical and safety considerations in the design of pumping schedules. Motivated by these considerations, we initially focus on the development of a first-principle model of a hydraulic fracturing process. Second, a novel numerical scheme is developed to efficiently solve the coupled partial differential equations (PDEs) defined over a time-dependent spatial domain. Third, a reduced-order model is constructed and used to design a Kalman filter to accurately estimate unmeasurable variables such as proppant concentration inside the fracture. Lastly, model predictive control (MPC) theory is applied for the design of a feedback control system to achieve uniform proppant concentration across the fracture and to realize the optimal fracture geometry obtained by the open loop optimization. Within the controller, we explicitly take into account the practical considerations such as the actuator limitations and safety issues. We demonstrate that the proposed control scheme is able to generate the required fracture extent and the spatial concentration profile within which is closer to the target compared to other state-of-the-art pumping schedules.
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