Optimal Resource Allocation in a Subsea Oil Production Network Using Distributed Feedback-Based RTO

This work considers the problem of steady-state optimal resource allocation in an industrial symbiotic subsea oil production system, where the different wells are operated by different organizations. System-wide optimal operation requires information in the form of models, real time measurements, constraints etc. However, the different companies may not wish to share such information across the different companies due to various reasons such as market competitiveness and intellectual property rights.

Distributed real-time optimization using the dual (Lagrangian) decomposition approach is a potential solution that facilitates industrial symbiosis [3], where the different subproblems are locally optimized for a given shadow price of the shared resource, which is updated by a master coordinator. In the traditional distributed RTO approach, this involves solving numerical optimization problems online for each subproblem iteratively, which can be computationally intensive. Although different approaches have been recently proposed to speed up the convergence of the distributed optimization problem (see [4] and the references therein), solving the numerical optimization problem online in itself may be a fundamental limiting factor in many applications. Furthermore, many traditional oil and gas companies also prefer to use simple feedback controllers as opposed to model-based RTO tools.

In order to avoid the need for solving numerical optimization problems, this work considers a distributed feedback-based real-time optimization framework introduced in [2], where each subproblem is locally optimized for a given shadow price using feedback controllers. Here, the key idea is to convert the Lagrangian decomposition framework into a feedback control problem. For the stationarity condition of the different subproblems, we need the gradient of the Lagrange function in each subproblem to be equal to zero. Based on this idea, we propose an “optimizing" controlled variable for each subproblem, which is given as a function of the shadow price. By controlling the proposed controlled variable to a constant setpoint of zero in each subproblem independently, the different subproblems can locally optimize their processes for a given shadow price. Since the gradient is a function of the Lagrange multipliers, by using a standard master coordinator that updates the Lagrange multipliers using the subgradient method, the proposed approach leads to system-wide optimal operation.

We apply the proposed distributed feedback-based RTO approach on a large-scale subsea gas-lifted oil production well network with 10 wells producing from four different subsea manifolds (clusters), each operated by different companies [1]. We use a model-based gradient estimation scheme to estimate the local cost gradient and use PI controllers in each subsystem. The simulation results are compared with centralized model-based RTO, which shows that the proposed approach can optimally allocate the shared resources in a distributed manner without the need to solve numerical optimization problems.

References

[1] Dirza, R., Skogestad, S., Krishnamoorthy, D. (2021). Optimal Resource Allocation using Distributed Feedback-based Real-time Optimization. IFAC ADCHEM (accepted).

[2]Krishnamoorthy, D., 2021. A distributed feedback-based online process optimization framework for optimal resource sharing. Journal of Process Control, 97, pp.72-83.

[3] Wenzel, S., Paulen, R., Stojanovski, G., Kramer, S., Beisheim, B., and Engell, S. (2016). Optimal resource allocation in industrial complexes by distributed optimization and dynamic pricing. Automatisierungtechnik, 64(6), 428-442

[4] Wenzel, S., Riedl, F., and Engell, S. (2020). An efficient hierarchical market-like coordination algorithm for coupled production systems based on quadratic approximation. Computers & Chemical Engineering, 134, 106704.