Feedback control of proppant bank heights during hydraulic fracturing for enhanced productivity in shale formations

Multi-Size Proppant Pumping Schedule of Hydraulic Fracturing: Application to a MP-PIC Model of Unconventional Reservoir for Enhanced Gas Production

Slickwater hydraulic fracturing is becoming a prevalent approach to economically recovering shale hydrocarbon. It is very important to understand the proppant’s transport behavior during slickwater hydraulic fracturing treatment for effective creation of a desired propped fracture geometry. The currently available models are either oversimplified or have been performed at limited length scales to avoid high computational requirements. Another limitation is that the currently available hydraulic fracturing simulators are developed using only single-sized proppant particles. Motivated by this, in this work, a computationally efficient, three-dimensional, multiphase particle-in-cell (MP-PIC) model was employed to simulate the multi-size proppant transport in a field-scale geometry using the Eulerian–Lagrangian framework. Instead of tracking each particle, groups of particles (called parcels) are tracked, which allows one to simulate the proppant transport in field-scale geometries at an affordable computational cost. Then, we found from our sensitivity study that pumping schedules significantly affect propped fracture surface area and average fracture conductivity, thereby influencing shale gas production. Motivated by these results, we propose an optimization framework using the MP-PIC model to design the multi-size proppant pumping schedule that maximizes shale gas production from unconventional reservoirs for given fracturing resources.

Experimental and Theoretical Study on Dynamic Hydraulic Fracture

Hydraulic fracturing is vital in the stimulation of oil and gas reservoirs, whereas the dynamic process during hydraulic fracturing is still unclear due to the difficulty in capturing the behavior of both fluid and fracture in the transient process. For the first time, the direct observations and theoretical analyses of the relationship between the crack tip and the fluid front in a dynamic hydraulic fracture are presented. A laboratory-scale hydraulic fracturing device is built. The momentum-balance equation of the fracturing fluid is established and numerically solved. The theoretical predictions conform well to the directly observed relationship between the crack tip and the fluid front. The kinetic energy of the fluid occupies over half of the total input energy. Using dimensionless analyses, the existence of equilibrium state of the driving fluid in this dynamic system is theoretically established and experimentally verified. The dimensionless separation criterion of the crack tip and the fluid front in the dynamic situation is established and conforms well to the experimental data. The dynamic analyses show that the separation of crack tip and fluid front is dominated by the crack profile and the equilibrium fluid velocity. This study provides a better understanding of the dynamic hydraulic fracture.

Approximate Dynamic Programming Based Control of Proppant Concentration in Hydraulic Fracturing

Hydraulic fracturing has played a crucial role in enhancing the extraction of oil and gas from deep underground sources. The two main objectives of hydraulic fracturing are to produce fractures with a desired fracture geometry and to achieve the target proppant concentration inside the fracture. Recently, some efforts have been made to accomplish these objectives by the model predictive control (MPC) theory based on the assumption that the rock mechanical properties such as the Young’s modulus are known and spatially homogenous. However, this approach may not be optimal if there is an uncertainty in the rock mechanical properties. Furthermore, the computational requirements associated with the MPC approach to calculate the control moves at each sampling time can be significantly high when the underlying process dynamics is described by a nonlinear large-scale system. To address these issues, the current work proposes an approximate dynamic programming (ADP) based approach for the closed-loop control of hydraulic fracturing to achieve the target proppant concentration at the end of pumping. ADP is a model-based control technique which combines a high-fidelity simulation and function approximator to alleviate the “curse-of-dimensionality” associated with the traditional dynamic programming (DP) approach. A series of simulations results is provided to demonstrate the performance of the ADP-based controller in achieving the target proppant concentration at the end of pumping at a fraction of the computational cost required by MPC while handling the uncertainty in the Young’s modulus of the rock formation.