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Abstract

Summary

In reservoir management optimization techniques are used to improve production and support new field development decisions. The waterflooding problem is based on determining optimal well control trajectories: rate, bottom hole pressure (BHP), valve openings, or a combination of them. The problem can be express as a typical nonlinear optimization problem. The objective function can be net present value (NPV) or cumulative oil production.

Linear constraints involve controls themselves, but nonlinear constraints involving state variables may also be imposed. For example, producer and injector wells controlled by BHP may be subject to flow control or vice versa. In optimization, constraints are imposed and respected at each control cycle, but not necessarily within control cycle due to discontinuity of rates due to control changes. The alternative to impose constraints at each time step of the simulation results in a high computational cost making the optimization process time-consuming. We propose correction points based on a time series within the control cycle to impose state constraints thus reducing the computational effort.

The algorithm of choice to solve the optimization problem is the sequential quadratic programming (SQP). The refined ensemble-based method is used to approximate gradient of the objective function and constraints. The sensitivity matrix is obtained as the product of pseudo-inverse of the covariance and cross-covariance matrices. The sum of the columns of the sensitivity matrix is the approximate gradient vector. The proposed refinements are based on connectivity between injector/producer wells and competitiveness coefficients between producers. The strategy aims to reduce spurious correlations in the sensitivity matrix when using small-size ensembles. Two synthetic models, Egg and Brugge, are used to validate the proposed strategy. Results are shown in different box plots, generated by performing ten optimization processes. We observe that the strategy of imposing correction points helps to impose state restrictions in the different steps of the simulation, reducing the computational cost during the optimization process.

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/content/papers/10.3997/2214-4609.202035040
2020-09-14
2024-04-25

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Refined Ensemble-Based Method for Waterflooding Problem with State Constraints
Conference Proceedings 2020, 1 (2020); https://doi.org/10.3997/2214-4609.202035040
/content/papers/10.3997/2214-4609.202035040
/content/papers/10.3997/2214-4609.202035040
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