A Logic Branch and Bound Algorithm for Petroleum Production Optimization Based on Generalized Disjunctive Programming

A new solution method for solving the real time production optimization (RTPO) problem for a petroleum production system is presented in this thesis. The objective function of the problem maximizes oil production and the RTPO handles decision variables at operational level. Including routing of production flows, lift gas allocation, and pressure configurations of the system. It is aimed to give decision support in a time horizon of days to weeks. Such problems require solution methods able to obtain solutions swiftly, as production planners adjust network components frequently to maintain optimal production.The problem contains binary decision variables combined with nonlinear expressions and is mathematically classified as a nonconvex mixed integer nonlinear problem (MINLP). MINLPs are in general known as computationally expensive and hard to solve to optimality, and when nonconvexities are present, few solvers can guarantee global optimality. The solution method presented deviates from traditional optimization techniques applied to such problems, and introduces logic disjunctions to substitute the binary variables of the MINLP. A specialized branch and bound algorithm (LBB) is developed to utilize the structure of these disjunctions, and as time is of paramount importance for the RTPO, it is aimed to reduce demanded computational effort for the problem. The LBB is given a high degree of user flexibility to be able to tailor the algorithm to different problems.Results of the LBB show substantial variation in solution efficiency when applied to a real petroleum production system. Only when specific problem knowledge is utilized to customize the algorithm to the current system, the algorithm provides solid reduction in computational effort compared to a recognized commercial solver. Also when applied to variations in system structure the LBB clearly outperforms the applied solver, and the effectiveness and robustness of the proposed algorithm when utilizing problem specific knowledge is confirmed. The fact that the LBB provides the same solution to the problem as the applied solver might also indicate that the nonconvexities of the problem are not as complex as expected, and that the solver is in fact able to find the global optimal solution

Comparing radiopaque markers and 13C-labelled breath test in diabetic gastroparesis diagnostics

Dag A Sangnes,1–3 Eirik Søfteland,1,4 Tonje Teigland,1,5 Georg Dimcevski1,31Department of Medicine, Haukeland University Hospital, Bergen, Norway; 2The National Centre for Functional Gastrointestinal Disorders, Haukeland University Hospital, Bergen, Norway; 3Clinical Institute 1, University of Bergen, Bergen, Norway; 4Hormone Laboratory, Haukeland University Hospital, Bergen, Norway; 5Faculty of Health and Social Sciences, Western Norway University of Applied Sciences, Bergen, NorwayPurpose: Determining gastric emptying is mandatory in the diagnosis of diabetic gastroparesis. Several methods of investigation exist, but none has proven reliable, inexpensive and accessible. In this study, we aimed to compare gastric emptying of radiopaque markers (ROM) and 13carbon-labelled gastric emptying breath tests for solids (GEBT). We also aimed to determine any association between gastric emptying and patient-reported symptoms, glycemic control and the patients’ age, diabetes duration and occurrence of other late complications.Patients and methods: Forty-five patients (30 women, 15 men) with diabetes mellitus types 1 or 2 (40, 5) and symptoms of gastroparesis were examined with ROM and GEBT. All were interviewed, filled out symptom questionnaires and had HbA1c levels measured.Results: Forty percent of patients had delayed gastric emptying of ROM, while 55% had delayed gastric emptying of GEBT. Correlation between ROM and GEBT was not significant. Compared to GEBT, sensitivity for a positive ROM test was 0.52, while specificity was 0.74. In women, we found a higher specificity of 0.92, sensitivity 0.47. Difference in HbA1c between patients with positive and negative results was of borderline significance for both tests. GEBT (r=0.41, P=0.008) correlated with HbA1c. Patients with any late complications of diabetes had higher gastric retention of ROM (P=0.028), while patients with polyneuropathy (P=0.014) and diabetic wounds (P=0.004) had slower emptying with GEBT. None of the methods identified significant associations between gastric emptying and symptom scores, age or diabetes duration.Conclusions: As a measure of gastric emptying, the ROM test has benefits of being affordable and available. Compared to GEBT, the method has low diagnostic reliability. Before continued use, we recommend additional studies validating the test in diabetes patients.Keywords: diabetes mellitus, gastroparesis, gastric emptying, radiopaque markers, 13carbon-labelled gastric emptying breath tests, patient-reported outcome