Summary Variability in production predictions caused by geologic heterogeneity and uncertainty was examined with a new method. The experimental design maximized the information derived from the flow simulation of various geologic models. Empirical response surface models were fit to simulation results to assess the consequences of varying several geologic factors. Posterior distributions of geologic parameters were estimated from flow responses. Improvements in the accuracy of the reservoir model were quantified by computing changes in factor uncertainties resulting from response measurements. Monte Carlo simulations with prior and posterior factor distributions illustrate uncertainty reduction. This approach can be used for model comparison, sensitivity analysis, and estimation of probability distributions of geologic model parameters. Introduction Reservoir simulation is used widely to investigate the effects of geologic heterogeneity and engineering parameter variability on reservoir production performance. Because many geologic and engineering factors interact to affect recovery predictions, an exhaustive examination of recovery behavior for all possible parameter combinations is prohibitively time-consuming and expensive. The factors that most strongly influence production behavior should be identified to focus analyses and measurements. If reservoir-simulation studies are conducted with an experimental design, response surface models can estimate how the variation of input factors affects reservoir behavior with a relatively small number of reservoir-simulation models. Response surface models can test the relative importance of the factors in experimental designs statistically. Because response surfaces are accurate and simple to evaluate, they are efficient proxies for reservoir simulators. A method based on response surfaces, Monte Carlo simulation, and Bayes' theorem (RSMCB) was used to examine the effects of geologic variability and different models for permeability fields. The method was demonstrated in an analysis of outcrop data from a heterolithic tide-influenced deltaic sandstone. The data set includes probe permeameter measurements, detailed bedding maps, shale diagrams, cement maps, facies maps, facies-specific rock properties, and variograms. Because of the importance of geostatistical methods for reservoir model construction, designed simulations examined the effects of varying geostatistical parameters and compared stochastic and deterministic geologic models. Methods Experimental Design. Experimental design1,2 has been used in reservoir engineering applications, including performance prediction,3 uncertainty modeling,4–6 sensitivity studies,7–9 upscaling,10,11 history matching,12 and development optimization.13 The first step in a designed simulation study is to identify the factors that may influence flow responses. These factors may be geologic (e.g., cement nodule permeability) or engineering (e.g., skin factor) parameters; they may be deterministic (e.g., well spacing), stochastic (e.g., permeability fields), or controllable (e.g., injection rate). Factor ranges should include all feasible factor values. Factors are usually scaled to span the range of −1,1. Factor-response relationships should be as linear as possible. However, linear factor-response relations are difficult to guarantee a priori and are impossible to obtain when many responses are modeled. This scaling difficulty is a motivation for using quadratic rather than linear models.7,11 Factor scaling should reflect the range of factor variability. For example, although a permeability range from 1 md to 1 darcy could be mapped linearly to the range of −1,+1, a logarithmic scaling to the same range gives a more nearly linear response in most cases. A design is a set of factor-value combinations for which responses are measured.1,2 In a two-level factorial design, each factor is assigned to its maximum or minimum value (±1) in all possible combinations with other factors (Fig. 1). For three factors, this requires eight experiments; for K factors, 2K experiments are needed. Similarly, three-level factorial designs assign each factor its minimum, centerpoint, or maximum value (−1,0,+1) in all possible combinations with other factors (Fig. 1b); this design requires 27 experiments for three factors, or 3K experiments for K factors. Box-Behnken14 designs are modified three-level factorials (Fig. 1c). This design requires 15 experiments for three factors, including three at the factor centerpoint (all factors assigned to their centerpoint values). Centerpoint replicates make the design more nearly orthogonal, which improves the precision of estimates of response surface coefficients. There is no simple formula relating the number of required experiments to the number of factors for Box-Behnken designs; however, the number of experiments needed will always be between 2K and 3K. Box-Behnken designs were used in this study. This design has several advantages relative to alternatives. Compared with a three-level full-factorial design, a Box-Behnken design reduces the number of required experiments by confounding higher-order interactions. This reduction becomes more significant as the number of factors increases. For five factors, a Box-Behnken design requires 41 experiments, compared to 243 experiments required for a full three-level factorial and 32 for a full two-level factorial. Box-Behnken designs have the desirable qualities of being nearly orthogonal and rotatable for many cases.14 Unlike D-Optimal designs,1,2,4 Box-Behnken designs neither require nor depend on prior specification of the model. Further, unlike first-order (e.g., two-level factorial) designs,8,9 Box-Behnken designs allow estimation of quadratic terms and do not imply constant sensitivities of responses to factors. Most two-level designs do not include experiments at the design centerpoint. By including the centerpoint, Box-Behnken designs reduce estimation error for the most likely responses. Box-Behnken designs require only a few more experiments than two-level designs and allow construction of more versatile and accurate models.

Large, multiple-field Exploration & Production (E&P) assets require long-term commitments of capital that are tied to decisions on facilities, wells, scheduling, and production strategy. The decisions often must be made when there are high uncertainties, leading to risks. This paper presents a system which integrates finite-difference reservoir simulation, an economics model, and a Monte Carlo algorithm with a global optimization search algorithm to identify more optimal reservoir planning and management decision alternatives under conditions of uncertainty, such that the associated risks are managed. The optimization problem is posed with the business goals stated as a general objective function and includes all constraints (economic, reservoir, production, and statistical) that need to be honored. The method is illustrated with an example of an E&P asset with multiple oil fields produced through a common surface network. The formulation of the example problem includes decision variables for the scheduling of reservoir units, the number of wells, and production rate capacities. It incorporates the nonlinear response of the objective to reservoir performance and surface pressure constraint through a flow simulator. The analysis is multi-period, evaluating the impact of predicted performance over time for each decision alternative. The individual reservoir units have uncertainties in hydrocarbon volumes and quality, reservoir deliverability, and costs. Decision solutions for objective functions of net present value (NPV) that mitigate risks are presented. Introduction Making better decisions, which take into account uncertainty in all the components of an E&P asset's value chain over the time horizon of interest, continues to be a significant challenge for the industry. There are many alternatives in the development of large E&P assets. For example, in a new development of multiple fields there are decisions on numbers and types of wells, numbers and types of platforms, processing facilities, drainage strategies, gas management, scheduling, use of capital, etc. Flow simulation packages give little guidance in identifying good alternatives. An E&P planning problem has such a large number of alternatives that one cannot simply search exhaustively for the best solutions, particularly when uncertainties are present. The literature of the last few years has emphasized the importance of workflows that integrate and include formal quantification of uncertainties across subsurface, well locations, well configurations and operations, surface interconnections, and economics. However, the industry continues to make many field development decisions based primarily on flow simulation 'sensitivity cases or from simplified models, using simplifying constraints, which can have the effect of underestimating the full uncertainty and yielding much less than the full potential value of the asset. There has not been a single technology that fully integrates rigorous reservoir modeling, flow simulation, and economics within a decision optimization framework and explicitly manages risk. The problems are highly nonlinear with numerous linear and nonlinear constraints, dependence on time, and multiple local optima. The decision variables can be continuous or discrete, and the number of solution combinations explodes exponentially with the number of discrete variables, which can make common practices such as developing decision trees and running a few case studies virtually useless in guiding engineers to more optimal solutions. Because the difficult computational challenge, much of the previous literature has focused on an individual aspect of the decision optimization process. Narayanan et al1 presented a case and scenario analysis system for evaluating uncertainties in the value chain of the E&P system, and they framed the problem for uncertain state parameters and decision variables. They used Monte Carlo analysis to span the parameter space of decision alternatives and used a flow simulator for the production response, including multiple well plans and surface networks. Floris et al2 presented a decision scenario analysis framework, focused on scenario and probabilistic analysis also using Monte Carlo, and they suggested proxy models be used for the production response.

The paper presents a process for determining optimal subsurface locations for producing and injecting wells in a field to improve reservoir performance and value. The process is illustrated by optimizing well locations in an initial development planning context. The process involves planning a set of wells on a static reservoir model using an automated well planner. These locations are then optimized with dynamic flow simulation to achieve higher recovery or economic benefit. In this work, we present the framework for optimizing many well locations simultaneously, with reservoir simulation and economic analysis. This method is demonstrated byapplying it to a field-scale simulation model with water injection. Introduction Forecasting optimal number, type, subsurface locations, and design parameters for a new set of wells, considering field uncertainty, is a complex and often a time-consuming set of challenges for field development planning. But it is a necessary and critical part of the field development planning workflow. Sub-optimal decisions on the number of wells, the size and configuration of platforms, the processing capacity of facilities, etc which are made early in the field life may constrain field operations for years. The problem is often addressed through a tedious process of locating one well at a time in a static model, and then validating a set of well locations through case studies with reservoir simulation; then repeating this process until some convergence to a "good" set of wells is reached. With only a small number of cases investigated, there may be little confidence by an asset team that an overlooked alternative could be more attractive. Previous reseachers have proposed using mathematical optimization on this problem. All previous work recognized that the well location problem is a highly combinatorial, nonlinear optimization problem with integer variables. Early work experimented with integer programming[1,2] and ranking on static reservoir models[3]. Beckner and Song[4] used simulated annealing optimization with reservoir simulation, and Seifert et al[5] used exhaustive sampling and uncertainty analysis with simulation. More recent advances,[6,7,8,9] have shown that a genetic algorithm or a hybrid genetic algorithm coupled with flow simulation can be used to optimize and configure well plans. The more recent work demonstrated locating a small number of new wells or configuring a complex well, such as a multilateral well. The problem of locating many wells simultaneously when formulated as an optimization problemis that it can result in innumerable solution combinations. Thus, a practical procedure for locating many wells in a full-field development plan has been elusive. In this current work, we present a framework for optimizing many well locations with design constraints simultaneously. Rather than solve the full problem all at once, the method identifies a set of target and well plan locations based on the static reservoir model and then uses the locations to "seed" the global optimization as initial guesses. The method locates initial target perforation intervals using static reservoir properties, e.g., porosity, pore volume, or saturation, with a greedy-search algorithm.These locations are used as initial decision varaiables by the optimizer, which tunes the variables using a global, metaheuristic optimizer and flow simulation. The locations are risked, based on subsurface uncertainty, through analysis of the statistical character of the oil recovery or net present value within the optimization procedure. The mean recovery can be maximized with requirements on the statistical risk, e.g., the standard deviation. A key to the success of the optimization is efficiently running optimizer simulations on a computer cluster or grid. The paper discusses the architecture that enables efficient execution of hundreds or thousands of full-field simulations and the nature of the parallel optimizer We demonstrate the methodby applying it on a field-scale simulation model with water injection. We show that dynamic simulation was critical to improving well locations for this example.

Making better decisions, which take into account uncertainty in all the components of an exploration and production (E&P) asset's value chain, drainage strategies with and without injection, and scheduling are included. Ultimate recoveries, profiles, and ultimate economics for the range of possibilities are evaluated.

Developing large E&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 managementdecision 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 This is paper SPE 88991. 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 as 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.

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TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractIncreasingly, the industry is aware of the need to improve field development planning decisions with more rigorous risk analysis. A key is to have technology and work processes supporting the complex evaluation of projects as a whole, i.e. from subsurface to processing with economics, while preserving physical fidelity and interdependent uncertainties. This paper will illustrate how an integrated stochastic approach with scenario analysis, sensitivity analysis, and Monte Carlo simulation assisted an asset team to understand overall project uncertainties and sensitivities for a large gas project. This understanding gave a better basis for the planning decisions.The richness and speed of the integrated stochastic approach is compared with more conventional case study analysis. The latter requires manual iteration to investigate how variations of input variables as e.g. reservoir properties impact reserves and production. It is followed by manual input to the economic model and manual analysis.Outputs presented from hundreds of simulations from the integrated stoachastic approach include distributions and histograms of original fluids in place, cumulative production, plateau period, net present value, production rate, discounted cash flows, and rates of return etc. Correlation coefficients between input uncertainties and output uncertainites indicate which input uncertainties give the major contribution to the output uncertainties. This helps the asset team to focus on the important factors for major decisions, and use less time on the less important issues.

TX 75083-3836, U.S.A., fax 01-972-952-9435.