Research Reports from the Department of Operations
Document Type
Dissertation
Publication Date
8-27-1975
Abstract
Three optimization models for offshore oil field development are studied: the platform location problem, the dual completion problem, and the scheduling problem in the drilling operation. Either more efficient procedures are proposed, or a better characterization for the optimal policy is obtained. The decision variables in the platform location problem are: the number, size and location of drilling platforms, and the allocation of targets to platforms so as to develop a field at a minimum cost. The "exact" solution for this problem is found when the platform cost is an increasing convex function of its size, via a linear programming formulation. Under this assumption, two special cases are studied: when the platform cost is independent of the location and when it is uniform over regions. Two formulations of the problem are also investigated: as a complete set partitioning problem and as a minimum concave cost flow problem. The problem of dual completion is to determine which targets to complete as a single and which pairs to complete as a dual, so as to minimize cost. It is shown that the problem can be solved by finding the maximum weighted matching on a suitable graph, without changing the size of the problem. The scheduling problem in the drilling operation refers to calculating the number of feet between changes of bits as well as the number of bits so as to minimise cost. The problem is formulated as a dynamic programming problem, via a renewal functional equation. Existence and uniqueness of solutions for this functional equation are proved when a general drilling cost function is used. Under both convexity and concavity assumptions, the optimal policy as a function of the well length is completely characterized. A more general class of functional equations with the same solution structure as the scheduling problem in drilling is also described, together with one special example of it in inventory theory.
Keywords
Operations research, Offshore oil well drilling, Petroleum engineering, Mathematical optimization, Linear programming, Dynamic programming
Publication Title
Dissertation/Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 386 ; Submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy.
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Ferreira da Costa, Luiz Roberto, "Optimization Models for Offshore Oil Field Development" (1975). Research Reports from the Department of Operations. 403.
https://commons.case.edu/wsom-ops-reports/403