Summary

When using a reservoir simulator to predict future field production, one must determine objectives and apply constraints to manage wells and surface facilities. Sequential Quadratic Programming (SQP) methods are used to set well rates in a facility network of a reservoir simulator so that production objectives are maximized (or minimized) subject to constraints on pressures, flow rates, and stream compositions. Actions taken for infeasible conditions are discussed. This method is called Optimized Rate Allocation (ORA). Black-oil and compositional examples are given.

Introduction

When modeling a hydrocarbon reservoir, one must clearly define the constraints of both the reservoir and the attached facilities, as well as the objectives of the production. An objective might be based on economics or on maximizing oil production. Often, there are numerous constraints imposed on a reservoir model, such as the gas-delivery pressure, water-handling restrictions, flaring limitations, and optimal flow-stream compositions. Networks, platforms, pipes, and individual wells may each have their own set of operating constraints. The processes of modeling, developing, or managing a reservoir can be thought of as optimizing an objective while simultaneously satisfying all constraints by adjusting well and facility settings.

Traditionally, the setting of operating conditions in reservoir simulators has been handled by the modeler setting individual well rates based on his or her experience, or by programming a set of operating rules and actions that must be tuned for each field and for each phase of production.1 It can be very time-consuming and difficult to implement and maintain a well-management algorithm that is able to simultaneously satisfy all operating constraints.

Several papers have discussed the use of optimization algorithms in determining the best facility settings.2,3 Some have looked at determining optimal settings over a period of time.4 The focus of this paper is the optimization of facility settings at a particular time. How this relates to optimization over time will also be discussed.

In the 1990s, Lo et al.5,6 used linear programming methods to optimize oil production subject to the capacity constraints of the facilities. Their facilities model was coupled with a simplified representation of the reservoir. Each well or well group was represented by a rate stream that was calculated from well histories determined by full-field simulation runs. Similarly, to optimize production at Prudhoe Bay's E-Field, Litvak et al.7 modeled the reservoir with well inflow-performance curves and used mixed integer optimization to determine the set of wells to be open for every timestep.

Hepguler et al.8 connected a commercial facility network model with a separate commercial black-oil simulator through a software interface using a nonlinear sequential quadratic programming optimizer. For each timestep, the facility model and the reservoir model are solved iteratively until the reservoir outflow matches the network inflow.

Building on work done previously at the former Mobil Corp.,9 nonlinear SQP methods have been implemented in a black-oil and compositional reservoir simulator, EMpower.10 Reservoir modelers may use ORA to optimally determine well-rate settings so that network objectives and constraints are satisfied simultaneously. This paper will discuss how this method has been formulated, how individual well rates are set, and how infeasible conditions are handled. Differences in technique and formulation from previous work will be noted in the body of this paper.

The Model

The production of fluids from an underground reservoir is modeled numerically using a reservoir simulator. Given the state of the reservoir at some initial time, the purpose of the simulator is to predict the state of the reservoir at some future time and thereby calculate quantities and rates of produced and injected fluids. The reservoir is modeled using a finite-difference approximation in time and space of the diffusivity equation. During the course of each timestep, properties are computed, boundary conditions are set, and the predicted future state of the model is computed. This model is divided into two parts: the facilities (the wells, flow lines, separators, and chokes) and the reservoir (see Fig. 1).

At the boundary between the reservoir and the facilities, conditions must be specified so that the state of the reservoir and facilities may be calculated. At the beginning of each timestep, the reservoir conditions (pressure, saturations, and composition) are considered constant so that the flow rate of each well to the facilities becomes only a function of the pressure of the bottomhole nodes.

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