(184g) Simultaneous Uncertainty Reduction and Control of Hydraulic Fracturing

Accurate characterization of reservoir properties is of central importance to achieve a desired fracture geometry during a hydraulic fracturing process. However, the estimation of spatially varying geological properties in hydraulic fracturing is inherently ill-posed due to a limited number of measurements. One way to address this is to perform parametrization that reduces the dimensionality of reservoir properties (for example, spatially varying Young’s modulus profiles). In our previous work, we proposed an integrated framework that combines proper orthogonal decomposition (POD) with a data assimilation technique, ensemble Kalman filter (EnKF) [2], to estimate the parameter values in the reduced low-dimensional subspace [3]. Usually, the process and measurement noise information within the EnKF is assumed to be known and independent of inputs. However, unlike other industrial applications, for hydraulic fracturing processes that use microseismic monitoring technology, the occurrence of a measurement depends on the fluid injection rate into the fracture, which is an input to the process [4]. To be more precise, higher flow rates are likely to trigger a higher number of microseismic events as a result of increased stress caused by higher flow rates. A larger number of almost simultaneous microseismic events can effectively reduce measurement errors. This suggests the use of new control approaches based on the input dependent measurement error covariance to help reduce state and output estimation errors [5].

In this work, we explore the idea of using a controller for the purpose of simultaneous uncertainty reduction and set-point tracking of a nonlinear hydraulic fracturing process. More specifically, we propose to design a model-based feedback control system that will help in accurately identifying the spatially varying geological properties by reducing the measurement uncertainty, while at the same time accomplishing the original control tasks. Here, the objective function fed to the controller consists of both the estimation error covariance (uncertainty reduction) as well as the deviation from the desired target value (set-point tracking). The proposed closed-loop system is applied to a simulated model of a hydraulic fracturing process with synthetic spatially varying geological parameters.

Literature cited:

[1] Holmes, P., Lumley, J.L., Berkooz, G., 1996. Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press, New York.

[2] Evensen, G., 1994. Sequential data assimilation with a non-linear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. Journal of Geophysical Research, 99, 10143–10162.

[3] Narasingam, A., Siddhamshetty, P., Kwon, J. S., 2018. 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), 3977-3989.

[4] Maxwell, S. C., Rutledge, J., Jones, R., Fehler, M., 2010. Petroleum reservoir characterization using downhole microseismic monitoring. Geophysics, 75(5), 129–137.

[5] Sun, Z., Gu, Q., Dykstra, J., 2016. Uncertainty reduction of hydraulic fracturing process. In American Control Conference (ACC). 2135-2141.