Nonlinear Model Predictive Control of the Hydraulic Fracturing Process

Abstract

Hydraulic fracturing has drawn significant attention over the past decade, as it can recover crude oil and natural gas from shale deposits previously considered inaccessible, which brings considerable economic benefits. However, hazardous operating conditions of extremely high pressure and environmental concerns require us to control this process carefully. Unfortunately, nonhomogeneous rock properties make this process difficult to control. Therefore, an accurate dynamic model and a well-designed controller are needed. In this work, we use the well-known Perkins-Kern-Nordgren (PKN) model with reformulation to solve the moving boundary problem. Next, the process is controlled by a standard Nonlinear Model Predictive Controller (NMPC) and multistage NMPC. We find that the process performance deteriorates under the influence of uncertainty with standard NMPC. When we control the process with standard NMPC, the pressure violation happens in one of the parameter mismatch cases. Nonetheless, when we apply multistage NMPC and consider the uncertainty evolution with a scenario tree, no constraint violations occur for all cases for both time-invariant and time-varying uncertainties. We also discuss the computational performance of different robust horizons for multistage NMPC. Our results demonstrate that the multistage NMPC is a promising approach to handle uncertainty caused by nonhomogeneous rock properties in the hydraulic fracturing process.