Use of Mathematical Decomposition to Optimize Investments in Gas Production and Distribution
Authors: Dougherty E.L. , Lombardino E. , Hutchinson P. , Goode P.A. 
Published: December 2007

Summary
This paper presents an analytical approach based upon the decomposition method of mathematical programming for determining the optimal investment sequence in each year of a planning horizon for a group of reservoirs that produce gas and gas liquids through a trunk-line network and a gas processing plant. The paper describes the development of the simulation and investment planning system (SIPS) to perform the required calculations. Net present value (NPV) is maximized with the requirement that the incremental present value ratio (PWPI) of any investment in any reservoir be greater than a specific minimum value. A unique feature is a gas reservoir simulation model that aids SIPS in evaluating field development investments. The optimal solution supplies specified dry gas offtake requirements through time until the remaining reserves are insufficient to meet requirements economically. The sales value of recovered liquids contributes significantly to NPV, while the required spare gas-producing capacity reduces NPV.
SIPS was used successfully for 4 years to generate annual investment plans and operating budgets, and to perform many special studies for a producing complex containing over 50 reservoirs. This experience is reviewed. In considering this large problem, SIPS converges to the optimal solution in 10 to 20 iterations. The primary factor that determines this number is how good the starting guess is. Although SIPS can generate a starting guess, beginning with a previous optimal solution ordinarily results in faster convergence. Computing time increases in proportion to the number of reservoirs because more than 90% of computing time is spent solving the reservoir subproblems.

Introduction
SIPS's modularization reflects the structure of the solution process. The modules include the data input module (DATM), the systems integration module (SIM, the coordinator), the linearized field development module (LDFM), the field development module (FDM), the simple reservoir model (SRM), the trunkline optimization module (TOM), the reservoir/demand integration model (RDI), and the cash flow module (SIPSCF).
The technical advance presented is the adaptation and use of the decomposition method of mathematical programming to determine optimal gasfield development and production plans. We sketch SIPS's computer layout and examine its two operational modes, the optimization mode and the simulation mode. Then, we explain how the decomposition method is adapted in the optimization mode; mathematical details are given in the Appendix. The two primary functions of the simulation mode are to translate results of the optimization mode into useful planning reports and to allow sensitivity studies of minor variations to optimal plans to be carried out quickly.
SIPS is an effective planning tool because its cash flow projections are based on realistic predictions of deliverability vs. cumulative recovery in the gas reservoirs considered. Our experience shows that, with SIPS, knowledgeable planning personnel can generate annual budgets and plans, and derive answers to a variety of specific management questions in a timely manner.
SIPS's Architecture
The physical system for which SIPS determines activities over a planning horizon of 25 years extends from the raw gas in the reservoir to finished gas and liquids exiting from the gas processing plant. During each year, physical effects in three areas are accounted for.
In Reservoir j, SIPS considers pj (in each region) vs., cumulative production; gas production capacity (and rate) vs. nw, pj, and pwf; gas flow rate between regions vs. pj in adjacent regions; ?p across the field separator; separator overhead and bottoms flow rate vs,. total raw gas flow rate; separator overhead burned as field fuel; separator overhead rate vs. pwh, ?p, and pd (without compression); and separator overhead rate vs. ps, pd, PH1, and PH2 (with compression).
In the trunkline, SIPS considers gas flow rate vs. capacity in each segment; capacity vs. ds of new segments; capacity vs. fraction looped (existing segments only); flow direction in each segment; and total flow rate to provide gas sales, plant fuel, and spare capacity.