Refined ensemble-based waterflooding optimization subject to field-wide constraints

• Published in: Computational geosciences Vol. 24; no. 2; pp. 871 - 887
• Main Authors: Tueros, Juan Alberto Rojas, Horowitz, Bernardo, Willmersdorf, Ramiro Brito, de Oliveira, Diego Felipe Barbosa
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.04.2020; Springer Nature B.V
• Subjects: Capacitance; Coefficients; Competitiveness; Constraints; Covariance matrix; Earth and Environmental Science; Earth Sciences; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Injectors; Localization; Mathematical Modeling and Industrial Mathematics; Objective function; Optimization; Original Paper; Procedures; Quadratic programming; Sampling error; Sensitivity; Smoothing; Soil Science & Conservation; Statistical methods; Trans-Neptunian objects; Wells; Refined sensitivity matrix; Waterflooding optimization; Ensemble-based method; Sequential quadratic programming; Large-scale algorithm; Constrained optimization
• ISSN: 1420-0597; 1573-1499
• DOI: 10.1007/s10596-019-09866-z

In this work, we present a modification (refinement) of the ensemble-based method for constrained waterflooding optimization. The problem of determining life-cycle rate controls for both producer and injector wells that maximize the net present value, NPV, subject to well and field-wide capacity constraints is formulated and solved using sequential quadratic programming, SQP. The required gradient is approximately computed by an ensemble-based method. Field NPV is decomposed as the sum of the NPVs of each well. Sensitivity matrix of well NPVs with respect to controls of all wells is obtained from ensemble-based covariance matrices of controls and of well NPVs to controls. For efficiency reasons, ensemble size should be kept small which results in sampling errors. The approximate gradient is the sum of the columns of the refined sensitivity matrix. Using small-sized ensembles introduces spurious correlations that degrade gradient quality. Novel nondistance-based localization technique is employed to mitigate the deleterious effects of spurious correlations to refine the sensitivity of NPV of production wells with respect to injector controls. The localization technique is based on the connectivity of each injector/producer pair using a producer-based capacitance resistance model (CRMP). Competitiveness coefficients are developed to refine sensitivity of NPV of production wells with respect to producer controls, obtained using an interference test. A new procedure is proposed for consideration of maximum water-cut limit resulting in producer shut-in during the optimization process. Smoothing techniques are also introduced to avoid excessive abrupt jumps in well controls and to improve the overall optimization efficiency. Procedures and refinements are applied to a realistic reservoir taken from the literature, TNO Brugge Field, to demonstrate the resulting level of objective function improvement and variability reduction of the obtained solutions. NPV solution statistics are obtained for 20 independent runs. Using proposed refinements, smoothing and water cutting techniques, NPV is improved by up to 25.4% above the traditional ensemble-based methods.