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RESEARCH PAPERS

# Optimal Allocation of Lift-Gas Rates Under Multiple Facility Constraints: A Mixed Integer Linear Programming Approach

[+] Author and Article Information
Eduardo Camponogara

Department of Automation and Systems Engineering, Federal University of Santa Cantarina, P.O. Box 476, 88040-900 Florianópolis, SC, Brazilcamponog@das.ufsc.br

Paulo H. R. Nakashima

Department of Automation and Systems Engineering, Federal University of Santa Cantarina, P.O. Box 476, 88040-900 Florianópolis, SC, Brazilcamponog@das.ufsc.br

The lift-gas allocation problem with multiple facility constraints is a generalization of the single constrained knapsack problem (15), a widely known NP-Hard problem.

The superscript 5 denotes the number of facility constraints represented by the formulation.

The dimension of a polyhedron $P$ is the number of affinely independent elements of $P$ minus 1. If the null vector belongs to $P$, then its dimension equals the number of linearly independent elements.

The multiplying factor 1 is used in place of $βn,k(Cy)$ for all $xn,k,(n,k)∊E(Cy)−Cy$, while the remaining variables are multiplied by zero.

Notice that there are $2m$ possibilities when $m$ wells are given the minimum injection rate.

We explicitly use the superscript 1 in $Pcpl1$ to indicate that the lift-gas allocation problem is limited only by constraint 3, that is, the problem is devoid of constraints 4,5,6,7.

J. Energy Resour. Technol 128(4), 280-289 (Feb 15, 2006) (10 pages) doi:10.1115/1.2358143 History: Received January 28, 2005; Revised February 15, 2006

## Abstract

The effective application of continuous gas lift entails solving the combinatorial optimization problem of optimally allocating limited resources. This work proposes a mixed integer linear formulation for the problem of maximizing oil field profit under multiple facility constraints such as limited lift gas, fluid handling, and storage capacities. Families of valid inequalities are identified and introduced into the basic model to render a stronger formulation. Numerical experiments using commercial and non-commercial software, and comparisons with published results, show that the proposed method yields fast solution with significant average increase in oil production rate and profit.

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## Figures

Figure 1

Schematic of an oil well operated via continuous gas lift (1)

Figure 2

Piecewise-linear performance curve

Figure 3

Well performance curves of well types A, B, C, and D (5)

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