Wednesday, November 7, 2007 - 4:45 PM
468d

Decomposition Method For Solving Mixed Integer Nonlinear Model For Oilfield Exploration And Production Operations Under Uncertainty

Bora Tarhan, Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213 and Ignacio E. Grossmann, Dept of Chemical Engineering, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213.

Oilfield exploration and production operations consist of four major steps: exploration, appraisal, development and production. In each step, many decisions have to be taken that affect the overall performance of the operation. In the beginning of exploration phase, many uncertainties exist and depending on the decisions taken at each step, the uncertainty reduces gradually. Unfortunately, many crucial decisions related to development planning have to be taken in the early steps where the uncertainty level is high. The quality of these important decisions affects the overall profitability of the operation. Most of the available literature for exploration and planning of petroleum fields is based on deterministic models (Haugland et al. (1988), Iyer & Grossmann (1998), Van den Heever & Grossmann (2000), Lin & Floudas (2000), Carvalho et al. (2006)), while there are only few papers that deal with uncertainty (Jonsbraten (1998), Lund (2000), Begg et al. (2002), Cullick, Heath, Narayanan (2003), Aseeri, Gorman & Bagajewicz (2004), Goel & Grossmann (2004), Ulstein, Nygreen & Sagli (2007), Ozdogan & Horne (2006)).

In this paper, we consider a multistage stochastic programming approach for the design and planning of an oilfield infrastructure over a planning horizon under gradual uncertainty resolution. The main uncertainties considered are in the sand quality, size of the reservoir and breakthrough time, which are represented by discrete distributions. Furthermore, it is assumed that these uncertainties are not immediately revealed but are revealed gradually as a function of design and operation decisions. In order to account for these uncertainties, we propose a multistage stochastic programming model that captures the complex economic objectives and nonlinear reservoir behaviour, and simultaneously optimizes the investment and operation decisions over the entire project horizon. Furthermore the model assumes discrete distribution functions and takes into account the fact that the resolution of uncertainty is decision dependent.

Specifically, we consider an oilfield consisting of a number of reservoirs where each reservoir contains several possible well sites. Some of these well sites have to be drilled and exploited for oil over a planning horizon. The oilfield infrastructure can be composed of Floating Production Storage and Offloading (FPSO) and/or Tension Leg Platform (TLP) facilities. There are two options for drilling wells. Each well can be drilled either as a sub-sea or as a TLP well. The aim of the model is to select the type, location of facilities, time to build them, select wells to drill, the time to drill each well, time to connect each well to the facilities, and production from the wells. The goal is to maximize the expected net present value of the project, calculated by revenues, capital and operating expenditures. In order to solve this difficult problem, we propose an aggregated problem in order to find the optimum number of wells to drill, facilities to build (instead of which well, facility to build) as well as timing of these decisions. This aggregate problem is a stochastic nonconvex mixed integer nonlinear model and can be solved by a duality-based branch and bound algorithm (Tarhan and Grossmann 2007) to give an upper bound on the optimal solution. The decision variables found from the aggregate model can be used in the original model to find the exact wells to drill or facilities to build. This feasible solution for the original problem is a lower bound for the problem. This iterative approach finds optimal solution in finite number of iterations. We describe results on several test problems to illustrate the capabilities of the proposed model.