Nonlinear Optimization of Well Production Considering Gas Lift and Phase Behavior
Authors: Palke Miles R. , Horne Roland N. 
Published: December 2007

Abstract
This paper describes numerical techniques developed to determine the wellbore configuration that will optimize the life-time value of a property. The production history of a reservoir can be predicted by integrating a reservoir model, a well-bore flow model, a choke model, and a separator model. Changes in any production parameter, including the gas-lift configuration, will cause changes in the predicted production history. The numerical methods can find the combination of production parameters that optimizes the net present value of the flowstream. The control parameters sampled in this work include tubing diameter, separator pressures, depth of gas injection, and volume of gas injected. Each of these parameters can be variable with time. The influence of these parameters upon the net present value is complicated by the feed-back nature of the gas-injection loop. This nonlinearity requires robust, efficient routines for optimization. Genetic Algorithm optimization techniques are shown to be both stable and efficient when used to optimize these sorts of nonlinear problems.

Introduction
Petroleum engineers face a wide variety of parameter estimation and optimization problems. Every time a transient test is analyzed or a location for a well is chosen, an optimization or parameter estimation problem has been solved. Yet it is surprising how rarely a formal optimization technique is used to solve these problems. Mathematical and heuristic methods are available which can find optimal solutions for a given model. This paper describes the application of formal optimization techniques to a realistic petroleum engineering problem. With the improvement of computer modeling over time, it is now feasible to apply optimization techniques to petroleum engineering models.
In 1990, Carroll and Horne applied multivariate optimization techniques to a model of a field produced by a single well. However, only the separator model was compositional, and no wellbore parameters were allowed to vary with time. Carroll and Horne used two types of optimization routines, gradient methods and polytope methods. In 1992, Ravindran followed and allowed engineering parameters to be varied with time. Fujii continued this line of study in 1993, by including a network of wells connected at the surface. Fujii also studied the utility of genetic algorithms for petroleum engineering optimization.
This project expands on Ravindran's work by replacing all black-oil components with fully compositional models. In addition, all three major types of optimization techniques were considered.

Model Construction
The model developed for this project was designed to test optimization algorithms for petroleum engineering problems. In addition to being robust, the model is a simplification of a real petroleum engineering problem. If the tested optimization algorithms are to be useful for real applications, the test problem should include challenging nonlinear relationships. The field model constructed for this work provides these challenges.
The field model is an integration of smaller components. The complete model represents an oil reservoir with a single gas-lifted well. The individual components include:reservoir model;well model with gas lift;choke model;and separator model.
Fig. 1 illustrates the fashion in which these components are combined.
In the integrated model, each component influences the other components. Produced fluid flows into the tubing. At the point where the lift gas enters the tubing, the two streams commingle, and the flow continues up the wellbore. At the surface, the commingled fluid passes through the choke into the first separator. Gas from the first separator goes into the gas line and the liquid phase moves into the second separator. Gas from the second separator passes into the gas line, and the liquid goes into the third separator. The gas in the third separator goes into the gas line, and the liquid goes into stock tanks to be sold. Some of the separated gas is compressed, and injected into the tubing-casing annulus for gas lift. The remainder of the gas is sold.
Notice the nonlinear relationships between the various components.
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