Prashanth Siddhamshetty

Optimal pumping schedule design to achieve a uniform proppant concentration level in hydraulic fracturing

Abstract We present a novel design framework of an optimal and practical pumping schedule to achieve uniform proppant concentration across fracture at the end of pumping. By using the average viscosity to approximate concentration dependence of fracture propagation, a set of constant-concentration pumping schedules is applied to the developed dynamic model, each of which is carefully chosen by taking into account the practical constraints such as the limit on the change of proppant concentration between pumping stages and the desired fracture geometry that has to be satisfied at the end of pumping for maximum productivity. Then, a practically-feasible target concentration profile is obtained via linear combinations of the generated spatial concentration profiles, and mass balance is applied to the practically-feasible target concentration to calculate the duration of each pumping stage. We apply the generated pumping schedule to the high-fidelity hydraulic fracturing model, and the performance is compared with Noltes pumping schedule.

Modeling of hydraulic fracturing and designing of online pumping schedules to achieve uniform proppant concentration in conventional oil reservoirs

Abstract We present a novel control framework for the closed-loop operation of a hydraulic fracturing process. Initially, we 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 defined over a time-dependent spatial domain. Third, a reduced-order model is constructed, which is used to design a Kalman filter to accurately estimate unmeasurable states. Lastly, model predictive control theory is applied for the design of a feedback control system to achieve uniform proppant concentration across the fracture at the end of pumping by explicitly taking into account the desired fracture geometry, total amount of proppant injected, actuator limitations, and safety considerations. We demonstrate that the proposed control scheme is able to generate a spatial concentration profile which is uniform and close to the target concentration compared to that of the benchmark, Noltes pumping schedule.

Model order reduction of nonlinear parabolic PDE systems with moving boundaries using sparse proper orthogonal decomposition: Application to hydraulic fracturing

Abstract Developing reduced-order models for nonlinear parabolic partial differential equation (PDE) systems with time-varying spatial domains remains a key challenge as the dominant spatial patterns of the system change with time. To address this issue, there have been several studies where the time-varying spatial domain is transformed to the time-invariant spatial domain by using an analytical expression that describes how the spatial domain changes with time. However, this information is not available in many real-world applications, and therefore, the approach is not generally applicable. To overcome this challenge, we introduce sparse proper orthogonal decomposition (SPOD)-Galerkin methodology that exploits the key features of ridge and lasso regularization techniques for the model order reduction of such systems. This methodology is successfully applied to a hydraulic fracturing process, and a series of simulation results indicates that it is more accurate in approximating the original nonlinear system than the standard POD-Galerkin methodology.

Modeling of hydraulic fracturing and developing a new pumping schedule to achieve uniform proppant concentration

In this work, we initially focus on modeling of hydraulic fracturing processes. Then, we present a methodology for the design of a pumping schedule to achieve uniform proppant concentration at the end of pumping. The pumping schedule is designed by taking into account the effect of proppant particles on fracture propagation. We generate multiple spatial concentration profiles and approximate the target concentration by the piecewise combination of the generated spatial concentration profiles. As a result, a piecewise concentration profile that best describes the target concentration is obtained, and an inverse problem is formulated based on the law of conservation of mass to calculate the duration of each pumping stage with a specific proppant concentration. We show that the produced concentration profile is closer to the target concentration compared to Noltes pumping schedule, which is one of the most commonly used pumping schedules. Furthermore, the proposed design scheme is optimal because it directly takes into account practical constraints such as the limit on the change of the proppant concentration between pumping stages and the desired fracture geometry that has to be satisfied at the end of pumping.