Maximizing Seasonal Withdrawals from Gas Storage Reservoirs
Authors: Wattenbarger Robert A. 
Published: December 2007

Maximization of total withdrawals from a gas reservoir during a producing season depends upon the optimal selection of producing wells during the early part of that season. Presented here is a method for formulating the optimization as a linear programming problem, linearizing real gas flow and using transient influence matrices for superposing finite-difference solutions.

Introduction
It is common to store natural gas in underground storage reservoirs during the summer months and then produce the gas during the winter months to meet the seasonal demand. This same situation occurs in other gas reservoirs that are produced at low rates during the summer and then subjected to high demand in the winter. During the producing phase, the desired producing schedule often cannot be met phase, the desired producing schedule often cannot be met because of the limited producing capacity of the wells. The operator then faces a problem: to maximize the production from the wells during the producing season. production from the wells during the producing season. The seasonal production can be maximized through the optimal scheduling of withdrawals from the individual wells. The total reservoir withdrawal rates are limited at any time to the demand rate. The problem is further constrained by requiring that the wellbore pressure of each well not fall below a minimum value. Both the demand rate and the minimum wellbore pressures may change with time. When the wells "stabilize" immediately to pseudosteady-state flow, the scheduling problem is physically simple because the well behavior is not affected by past history. However, when the reservoir is relatively "tight", the transient nature of the reservoir flow becomes important and complicates the problem. It then becomes necessary to consider the transient wellbore pressure behavior of each well and the interference effect pressure behavior of each well and the interference effect that each well's flow has on the pressure behavior of every other well. The problem of optimizing withdrawals from a gas storage reservoir was described by Henderson et al. They presented a method for solving an actual gas storage problem presented a method for solving an actual gas storage problem through the use of finite-difference simulation and by trial-and-error selection of withdrawal schedules. They claimed only approximate optimization and indicated that further work was required. Here, a method is proposed for putting the withdrawal scheduling problem into a linear programming (LP) format. Once the problem is set up, the optimum withdrawal schedule may be found through the LP solution. The withdrawal schedule is optimized in the sense that no discretized withdrawal schedule can be specified for the finite-difference model that will give greater total seasonal production while still meeting the constraints placed on the problem. In the case of very large LP problems, an approximation to the solution will be necessary. The formulation presented in this paper fits the gas storage problem, but the method could be applied to a variety of problem, but the method could be applied to a variety of optimization problems.

Finite-Difference Superposition
Before formulating the LP problem, it is necessary to discuss how the well pressures can be expressed in terms of the well rates. This is done on the basis of straightforward superpositions in time and space. When a well is produced at a constant rate, its wellbore pressure decreases in a transient fashion, which describes the pressure decreases in a transient fashion, which describes the well's drawdown curve.
JPT
P. 994