Optimizing Multiple-Field Scheduling and Production Strategy With Reduced Risk
Authors: Cullick Stan , Heath David , Narayanan Keshav , April Jay , Kelly James 
Published: June 2014

Distinguished Author Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized to be experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: to inform the general readership of recent advances in various areas of petroleum engineering.

Abstract
Developing large E&#x0026;P assets requires long-term commitments of capital that are tied to decisions on facilities, wells, scheduling, and production strategy. The decisions often must be made in the project-planning phase when large uncertainties exist that can lead to project risks. We present an optimization system and method that enables finding more-optimal reservoir-planning and management-decision alternatives under conditions of uncertainty, such that the associated risks can be managed. The system integrates a global, stochastic search-optimization algorithm, finite-difference reservoir simulation, and economics. The optimization problem is posed with the business goal stated as the objective and includes economic, reservoir, and production constraints and statistical requirements. The optimization is illustrated in an example E&#x0026;P asset with multiple oil fields produced through a common surface-pipeline network with uncertainties in reservoir volume, fluid quality, deliverability, and costs. Decision solutions seeking to maximize the mean net present value (NPV) while managing risk are presented. The example includes multiperiod decisions on scheduling of reservoir units, number of wells, and production-process capacity.

Background for Planning With Uncertainty
Making good investment decisions, which account for uncertainties in major components of an E&#x0026;P asset over a planning horizon, continues to be a significant challenge for the industry. There are many planning alternatives (e.g., numbers and types of wells and platforms, processing facilities, drainage strategies, gas management, and scheduling). There also are many uncertainties. These uncertainties lead to uncertainties in outcomes, such as NPV, rate of return, cumulative oil production, and gas-plateau period. If the uncertainty can have a negative outcome, it is refered to as risk. Fig. 1 illustrates a decision-making process that considers uncertainties and provides decision makers an uncertainty and risk perspective of field-development-planning alternatives.
The components of a decision-making process in the illustration are objectives, state parameters, decision variables, and decision processes. An objective is the statement of the goal, such as &#x0022;maximize NPV&#x0022; or &#x0022;maximize recovery.&#x0022; State parameters cannot be controlled and often are uncertain (e.g., volume, deliverability, or faulting). Decision variables are controllable choices (e.g., number and location of wells). In addition, constraints can be imposed as limitations on the variables (e.g., a maximum process capacity).
With such processes as decision trees, the decision maker evaluates all possible decision alternatives, with probabilities assigned to uncertainties. With stochastic simulation, the decision maker assigns probabilities to uncertain parameters and scenarios, then generates solutions with random sampling. Solutions are not driven by the objective or potential risk. An E&#x0026;P planning problem typically has such a large number of alternatives that one cannot simply search exhaustively for solutions, particularly when uncertainties exist. Thus, decision trees cannot be evaluated, and often only a small fraction of potential solutions is considered use of a case-study approach, with the result being that the best solutions may never be evaluated.
An alternative process, that is optimization, systematically finds the best solutions by evaluating a relatively small number of candidate alternatives. Optimization frames the problem differently (i.e., from the perspective of the objective, the set of decision alternatives, and constraints). A global, stochastic search optimizer is appropriate for planning problems that include discrete variables, are nondifferentiable, and are highly nonlinear. Uncertainty and risk are included explicitly through statistical requirements on the objective. An example problem statement of an optimization objective with requirements is &#x0022;maximize the mean NPV, subject to the variance of the NPV being no greater than 10&#x0025; of the mean and an 80&#x0025; probability of maintaining plateau for 7 years.&#x0022;

Previous Work and Current Approach
Previous work in field-development planning under uncertainty1,2 emphasized the importance of workflows that integrate subsurface information, well locations, well configurations and operations, surface configuration, and economics with stochastic analysis. However, industry continues to make many field-development decisions primarily on the basis of flow-simulation-sensitivity cases or simplified models that use simplifying constraints, which can underestimate uncertainty. Simulation tools, such as flow simulators, provide high-fidelity physics, but they give little guidance by themselves in identifying good planning alternatives.
Davidson and Beckner3 and Wang et al.4 have presented optimization examples. They optimize coupled reservoir/surface-network response and well-rate allocations within simulator timesteps. Eng and Herring5 and Iyer et al.6 present extensive mathematical programming formalisms for oilfield planning. These linear and nonlinear mathematical programming formulations have not been adopted in practice because of limitations in reproducing nonlinear-flow responses through tuned proxy equations and their requirements for problem-specific, very complex formulations. Harding et al.7 used a genetic algorithm as a global stochastic search engine for a production-planning problem with tank models.
There has not been an optimization framework that fully integrates rigorous reservoir modeling, flow simulation, and economics while explicitly managing risk. Here, we present a flexible approach for planning reservoir-development alternatives that accounts explicitly for uncertainty by requiring that the objective meet a requirement on its statistical risk,8 using an optimizer. We incorporate a simulation-optimization approach described by Kelly,9 which uses a global stochastic search algorithm in conjunction with flow simulation and uncertainty analysis.