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The fully implicit coupling of surface facilities with a reservoir model can lead to a significant increase in computing time. The focus of this paper is on the development of methods that can minimize the impact of the facility model on the global solution procedure. A local grid refinement preconditioner is developed to accelerate convergence of the full flow field implicit simulation. P. 181

This paper was prepared for presentation at the 1999 SPE Reservoir Simulation Symposium held in Houston, Texas, 14-17 February 1999.

Summary Determination of the operating conditions of a field under a set of physical system constraints (e.g., compressor limits) and engineering preferences (e.g., voidage replacement) is a primary concern for petroleum engineers. Rule-based systems have been proposed for this, but the process is most suitably defined as an optimization problem. An optimization procedure that uses mixed-integer linear programming (MILP) is discussed in this study. Well rates that honor system and engineering constraints are handled simultaneously while the maximum for an objective is calculated (e.g., field oil rate or cash revenue). Optimal rates for the current conditions of the field are determined. Note that this results in instantaneous optimization and, thus, cannot account for recurrent events such as water breakthrough. Nevertheless, an efficient and robust instantaneous optimizer is useful within a grander optimization scheme, short forecast periods and, also, in real-time allocation situations. The approach is able to efficiently handle the nonlinearities in the system by way of piecewise linear functions. Also, as a result of the formulation, the exact optimal solution of the problem is guaranteed. Another property of the approach is that, in cases in which it is not possible to honor all the targets and limits of the system simultaneously, a scheme is introduced that enables the engineer to prioritize the constraints. This prioritization scheme proves to be of great practical significance because most real cases have conflicting targets and limits that result in optimization systems with no feasible solutions. Also, a heuristic is used that ensures realistic results by elimination of mathematical artifacts (rate oscillations in time) that often arise when the reservoir contains wells with similar properties [e.g., water/oil ratio (WOR) and gas/oil ratio (GOR)]. The optimization system is applied to synthetic cases and two real-field cases. The real-field cases pose problems that cannot be handled by conventional rule-based systems. Introduction Production and injection allocation with the objective of maximizing profits while simultaneously honoring all facilities limits, contractual targets, and engineering preferences, is a process that can best be addressed as an optimization problem. Optimization techniques have been applied to a variety of oil-field-development problems. Early approaches used linear programming (LP) techniques to solve rate-allocation problems with linear constraints, a linear objective, and continuous parameters (Brown et al. 1998; Bohannon 1970; Lang and Horne 1983; Lo et al. 1995). MILP methods, however, enable optimization on discrete and continuous variables in which discrete variables are commonly used to model decisions or approximate nonlinear functions. For example, Saif et al. (1987) were interested in determining production allocation when considering several reservoirs and used discrete variables to model selection of a production profile from a set of predefined profiles for each reservoir. The profiles were generated by use of aggregate production from all wells in the reservoir, which simplied well performance and interaction. Fang and Lo (1996) demonstrated how separable programming techniques can be used to optimize oil production during artificial lift with gas injection; for each well, flow performance vs. amount of lift gas was represented as a piecewise linear curve, and the optimizer determined the best allocation of gas lift under various facility constraints. For wells not under gas lift, the wellbore performance was represented with a simple linear relationship between the phase flowing rates that assumed equal scaling of phase flow rates. This approach is similar to that presented by Wang et al. (2002a) in which piecewise linear curves were used to model the well performance for all wells, not just those on gas lift. Nonlinear optimization methods, such as sequential quadratic programming, have also been used to optimize coupled reservoir-facility models in systems in which the gathering system has significant impact on individual well performance (Wang et al. 2002b; Davidson and Beckner 2003). These methods are capable of incorporating pipe and facility devices in the formulation and capturing gathering system impact of individual well performance. However, they lose the ability to incorporate discrete variables representing common well-management actions such as producing at a minimum flow rate or shutting in the well. Optimization is still not widely used and accepted as a best-practice approach for rate allocation in the reservoir-engineering community. Sequential rule-based heuristic systems are still the most common form of well-management systems (Wijesinghe et al. 1983). Apart from the engineer's familiarity with rule-based systems, one reason for their persistence might be that, although these systems often deliver suboptimal results, they are robust. The systems hardly fail in delivering a solution no matter how suboptimal it may be. Here, we present a similarly robust and easy-to-use allocation-optimization framework that is advantageous when compared to rule-based systems in several ways:Ability to define an objective to be maximized: This also brings in the ability to penalize the production of certain phases or components.Ability to handle all operating constraints simultaneously: Rule-based systems often deliver suboptimal solutions because they fail to capture the dependencies among the operating constraints as a result of their sequential nature.Ease of use: Removes the complexity of finding the correct allocation scheme, which, in rule-based systems, might involve defining convoluted logic with dependence among the allocation steps and iterations. The approach presented here focuses on optimization of allocation at a point in time rather than over time. The allocation is conducted in real time in the sense that the future behavior is not taken into consideration while allocating the rates for the current time. While this is a limitation, a robust instantaneous optimization framework works in many situations:Replace sequential rule-based allocation logic to deliver optimal allocation: The use of rule-based allocation systems is currently the common practice in the reservoir-engineering community.Use with a reactive operating strategy. This might be the case when we have confidence in our numerical models to represent the current or near-future situation in the reservoir but we may not have the same level of confidence in the models predictions. For instance, we might not want to proactively shut wells before we observe any water breakthrough despite the model's predictions indicating this would be beneficial over time.Use for real-time production optimization. This point is related to the previous one.Use as the inner loop in grander optimization schemes. As compared to previous allocation-optimization approaches, (Wang et al. 2002a; Davidson et al. 2003) we present a prioritization scheme that enables the prioritization of the operating conditions to deliver the desired allocation in the case of conflicting targets and limits. Additionally, techniques are developed that avoid unrealistic operating scenarios that result from continually solving for the optimal solution.

A comprehensive well model that exists within a next-generation parallel reservoir simulator is described. It incorporates a general formulation approach which handles global phase-component partitioning allowing any number of phases and components, where any component can exist in any phase. The model can run in either isothermal or thermal mode, the latter including special features for steam injection and production. A multisegment capability enables the wellbore to be divided into segments for improved accuracy when simulating horizontal and multilateral wells. This unified well model reduces to a ‘conventional’ model when a single segment is used.