Worst‐case design of subsea production facilities using semi‐infinite programming

Abstract

The problem of designing novel process systems for deployment in extreme and hostile environments is addressed. Specifically, the process system of interest is a subsea production facility for ultra deepwater oil and gas production. The costs associated with operational failures in deepwater environments are prohibitively high and, therefore, warrant the application of worst-case design strategies. That is, prior to the construction and deployment of a process, a certificate of robust feasibility is obtained for the proposed design. The concept of worst-case design is addressed by formulating the design feasibility problem as a semi-infinite optimization problem with implicit functions embedded. A basic model of a subsea production facility is presented for a case study of rigorous performance and safety verification. Relying on recent advances in global optimization of implicit functions and semi-infinite programming, the design feasibility problem is solved, demonstrating that this approach is effective in addressing the problem of worst-case design of novel process systems. Given a process model, and taking into account the uncertainty in the model and disturbances to the inputs of the system, do there exist control settings such that, at steady state, the physical system will always meet performance/safety specifications? This question will be formulated mathematically later and its application to subsea production facilities will be the primary focus of this article. In the following section, the subsea process system model will be presented and the case study will be set up. Model and Case StudyThe subsea separator is considered to be at the heart of subsea production facilities because it is the key process system for performing upstream phase separation as material is being produced from the wellhead. In the steadystate model presented here, it is considered that a threephase mixture of oil/water/gas is being sufficiently separated to allow for reinjection of the water back into the environment and the production of separate oil and gas Pointwise numerical simulation was performed using a Windows 7 machine with Intel Core2 Quad Q9450 CPU to study the behavior of the model over a range of uncertainty

Semi-Infinite Optimization with Hybrid Models

“…An LHC sampling procedure was then performed over a range of valid values given in Table to generate 10 5 data points used to train the DDM. As noted in Stuber et al, the implicit function characterized by eq may not exist for some realization of uncertainty and control variables. Values that yielded a locally infeasible result were labeled accordingly, while the solutions of the feasible problems were saved.…”

“…In Stuber et al., a method of forward–backward interval constraint propagation on the DAG, , interval contractor methods, a novel convex/concave relaxation algorithm, and a novel algorithm for solving SIPs were all necessary to solve this problem. While these methods adequately address the problem in question, the broad and robust applicability of this approach to more general SIPs is lacking.…”

“… a Bounds directly specified by Stuber et al were used if available. Otherwise, natural interval extensions of known quantities were used to compute necessary values.…”

“…Due to downstream equipment specifications, the oil product stream gas mass fraction may not exceed the value G max = 0.05. The full model can be found in Stuber et al with the analysis of the DAG in Stuber et al (section 8.1).…”

“…However, it is worth noting that the method proposed by Stuber et al has an early termination criterion whereby the algorithm terminates with a feasible suboptimal solution as soon as robustness is verified. Thus, the solution value obtained by Stuber et al is an upper bound on the global solution. Despite this, we notice that η* > −5.77 × 10 –3 , seemingly in violation of the upper bound for the full mechanistic model .…”