Summary Field development and control optimization aim to maximize the economic profit of oil and gas production. Mathematically, this results in a complex optimization problem with a large number of correlated decision (also known as control) variables of various types at different levels (e.g., at the level of well location variables or at the level of well production/injection control also know as well control or control settings variables) and a computationally expensive objective function (i.e., a reservoir simulation model). Current multilevel optimization frameworks provide only a single optimal scenario for a field development and control problem. However, unexpected problems that commonly arise during field development and operations can impose extra constraints, resulting in operators having to eventually select an adjusted, and most-likely, nonoptimal scenario. This work proposes a novel multisolution optimization framework, based on sequential optimization of control variables at multiple levels, providing the flexibility for operators to make optimal decisions while considering operational constraints. An ensemble of close-to-optimum solutions is selected from each level (e.g., from the well location optimization level) and transferred to the next level of optimization (e.g., to the control settings optimization), and this loop continues until no significant improvement is observed in the objective value. Fit-for-purpose clustering techniques are also developed to systematically select an ensemble of solutions, with maximum differences in well locations and control settings but small variation in the objective values, at each level of the optimization. The developed framework has been tested on two benchmark case studies. The results demonstrate high economic and operational efficiency of the developed multisolution framework as compared to the traditional approaches that rely on single-solution optimization. It is shown that suboptimal solutions from an early optimization level could approach the optimal solution at the next level(s), highlighting the value of the developed multisolution framework to deliver operational flexibility by a more efficient exploration of the search space.

Capacitance-resistance model (CRM) is a nonlinear signal processing approach that provides information about interwell communication and reservoir heterogeneity. Several forms of CRM have been introduced; however, they would deliver erroneous model parameters if production history involves shut-in period. To address this issue, this study presents a dynamic capacitance-resistance model (D-CRMP), a comprehensive formulation that is capable of handling multiple shut-in periods in different producers. CRM model parameters are representative of the geological information. Accordingly, two geologically identical synthetic examples are used to validate D-CRMP; one including shut-in periods in historical production data of some producers and the other one with all continuously operating wells. Obtaining the same model parameters and the high quality of fitting in both cases proved the reliability of D-CRMP, which allows the utilization of historical data to characterize the reservoir behavior in real cases. Investigation of uncertainty on the fitted model parameters was also performed to demonstrate that confidence intervals are affected mostly by two aspects; permeability distribution and interwell distance. It is shown that though the confidence intervals in the heterogeneous fields are relatively higher than the homogeneous examples, higher permeability and lower producer-injector distance reduce the uncertainty of model parameters in both cases. This study also applies the proposed model in reservoirs with horizontal wells and further examines the impact of well direction and length of the productive interval on the connectivities between wells. Keywords Capacitance-resistance model • Reservoir characterization • History matching • Waterflood • Shut-in well • Horizontal well Abbreviations BHP Bottom-hole pressure CMG Computer modeling group Ltd. CRM Capacitance-resistance model CWI Cumulative water injection D-CRMP Dynamic capacitance-resistance model ICRM Integrated capacitance-resistance model IMEX Implicit-explicit black oil simulator IWC Interwell connectivity MLR Multivariate linear regression MSHW Multi-segmented horizontal well List of symbols L, F, t Mean length, force, and time, respectively c t Total compressibility (L 2 /F) f ij Interwell connectivity between injector i and producer j , dimensionless I Water injection rate (L 3 /t) J Productivity index (L 5 /F − t) N p Cumulative liquid production rate (L 3 /t) n P Total number of producers n T Total number of historic time periods n I Total number of injectors P wf Well bottom-hole pressure (F/L 2) q Total liquid production rate (L 3 /t) R 2 Correlation coefficient Time constant, t

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