A Linear Programming Model for Optimum Development of Multi-Reservoir Pipeline Systems
Authors: Bohannon John M. 
Published: December 2007

Optimum drilling and facility expansion schedules for multi-reservoir pipeline systems are usually found by intuitive trial and error. The model pipeline systems are usually found by intuitive trial and error. The model and optimizing techniques described here give the manager a powerful planning tool, and a consistent basis for evaluating the effects of planning tool, and a consistent basis for evaluating the effects of external factors on the system.

Introduction
The term "multi-reservoir pipeline system" is used to designate a system composed of many oil reservoirs producing into one or more gathering systems. The producing into one or more gathering systems. The reservoirs differ in capacity, state of development, operating costs, and product value. Managing such a system is complicated by many constraints and interrelationships. If total production levels are fixed and are less than the total production of the completely developed reservoirs, the manager hopes to find the optimum "combination" of development drilling, secondary recovery projects, and other facility improvements that will enable him to meet the specified production goals. If total production levels are not fixed, the problem is compounded by his uncertainty of the optimum problem is compounded by his uncertainty of the optimum maximum producing level, and the optimum number of years to produce at this level. In either case, he usually finds that his alternative courses of action are many - too many to evaluate and compare individually. The final plan is usually determined by evaluating a subset of the many courses of action available, and picking the most attractive of these. Such a plan may picking the most attractive of these. Such a plan may or may not be the optimum one. If the manager could be freed of uncertainty as to the optimum course of action in a particular system and environment, he could more confidently evaluate the effect of changes in those factors. The major aim of the computer model and optimizing techniques described here is to find the optimum 15-year development plan for a specified multi-reservoir pipeline system, operating within a specified framework of costs, product prices, sales levels, and other factors. The product prices, sales levels, and other factors. The main variables in such a plan are
annual production rate from each reservoir, number of development wells to be drilled each year in each reservoir, and timing of major capital investments such as tying in unconnected fields, initiating secondary recovery projects, and expanding pipeline facilities.

Theory
The problem is formulated as a mixed 0–1 (or binary) integer, continuous-variable linear programming problem. Linear programming (LP) techniques are problem. Linear programming (LP) techniques are well established and are described extensively in many books and articles. Ref. 1 gives a detailed explanation of LP techniques, with examples. Ref. 2 discusses the mixed-integer problem. To use linear programming, the physical system that we wish to describe must be defined by a set of linear relationships in the following form:
Here, each a(ij) represents a constant coefficient, each x(j) represents an unknown variable, and each b(i) represents a constant. The relationships can be equalities or inequalities as indicated. They are the constraints of the problem.
JPT
P. 1429