(610a) Multistage Nonlinear Model Predictive Control of the Hydraulic Fracturing Process

Hydraulic fracturing process is a well stimulation technique that has been playing an important role in the worldwide energy supply for several decades. The process begins with a perforation stage to create initial paths along a drilled well and then the fracturing fluid, composed of water, proppant, and chemical additives is injected into the well at a very high pressure to crack the rock formation underground. The pumped fluid continues to extend the fracture path and the substances are transported along the fracture as it propagates forward. After the pumping stage is completed, the proppant is trapped inside the fracture and keeps the induced channel open as the rock walls close because of the internal rock pressure. The created space provides high conductive channels that allow for the constrained natural gas or crude oil, which was once identified as inaccessible resources to flow out, increasing the well production and bringing significant economic benefits (Bartik et al., 2019). However, hazardous operating conditions of high pressure should be controlled carefully during the entire process to avoid the machine damage and the safety threat for onsite workers. In the current control strategy, the injection pressure is usually monitored on the ground level and the pump rate is adjusted manually according to the pressure measurements. Also, the spatially varying rock properties have significant effects on the process (Narasingam et al., 2018), making the process more difficult to control and sometimes even leading to undesired premature termination.

In this talk, we present a dynamic model that describes the hydraulic fracturing process considering the fracture propagation, mass transport of substances (Singh Sidhu et al., 2018), changing fluid properties, drag reduction due to friction reducer (Le Brun et al., 2016), and the wellhead pressure formulation. Next, the fracturing process is simulated with this first-principle model and controlled by Nonlinear Model Predictive Controller (NMPC) to fulfill a set of endpoint requirements and operating constraints. NMPC is known for its ability to deal with the constraints and the model nonlinearity explicitly for a multiple-input-multiple-output system. In our case studies, we compare the performance between standard NMPC and multistage NMPC. Standard NMPC performs well when there is no uncertainty in the rock properties. However, its performance deteriorates when parameter and model mismatch occur and standard NMPC fails to satisfy the final requirements for fracture geometry and maximum pressure specification. On the other hand, multistage NMPC, which considers possible realizations of rock uncertainties with a scenario tree, provides robust control for the fracturing process by satisfying all constraints, no matter if the uncertainty realization is time-invariant or time-variant in the process. We also compare the difference between different robust horizons, which include the branching to different stages for multistage NMPC. Our results show that multistage NMPC is capable of handling non-homogeneous rock parameters and providing a robust, high performance control strategy for the hydraulic fracturing process.

References

W. Bartik, J. Currie, M. Greenstone, C. R. Knittel, The local economic and welfare consequences of hydraulic fracturing, American Economic Journal: Applied Economics 11 (4) (2019) 105–55.

Narasingam, P. Siddhamshetty, J. S.-I. Kwon, Handling spatial heterogeneity in reservoir parameters using proper orthogonal decomposition-based ensemble Kalman filter for model-based feedback control of hydraulic fracturing, Industrial & Engineering Chemistry Research 57 (11) (2018).

Singh Sidhu, P. Siddhamshetty, J. S. Kwon, Approximate dynamic programming-based control of proppant concentration in hydraulic fracturing, Mathematics 6 (8) (2018).

Le Brun, I. Zadrazil, L. Norman, A. Bismarck, C. N. Markides, On the drag reduction effect and shear stability of improved acrylamide copolymers for enhanced hydraulic fracturing, Chemical Engineering Science 146 (2016) 135 – 143.