Well placement and design under geological uncertainties defines a major risk for field development processes. Including alternative geological realizations in a manually optimized development plan has been cumbersome and time consuming. In practical cases, a single reference model was often used as a basis for the flow simulation model which included a major risk on underestimating geological uncertainties. Optimization approaches and related optimization methods applied in this field previously included an objective function definition which aggregates multiple objectives, e.g. cumulative well rates or economical indicators. These optimization methods do not allow distinguishing easily between correlated and uncorrelated objectives which defines a major limitation for efficiency. This paper presents a novel approach individually linking objectives and design parameters to multiple optimization processes which operate in parallel on a single simulation case. This approach increases the efficiency of stochastic optimization processes for complex application scenarios with multiple objectives. The extension to an uncertainty workflow including multiple geological models in the optimization processes is discussed.Well placement optimization of horizontal wells in independent target formations of the gas condensate field is used to verify the optimization methodology. Alternative geological models are included in the optimization workflow representing geological uncertainties. The specific objective of the case study is to find optimum well trajectories by maximizing cumulative gas production over the life cycle of the field. Performance indicators for all well candidates (design parameters) are related to individual objectives (regional production). Robustness criteria for well candidates are implicitly fulfilled on the basis of risk weighted geological realizations.

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History Matching in Reservoir Simulation, well location and production optimization etc. is generally a multi-objective optimization problem. The problem statement of history matching for a realistic field case includes many field and well measurements in time and type, e.g. pressure measurements, fluid rates, events such as water and gas break-throughs, etc. Uncertainty parameters modified as part of the history matching process have varying impact on the improvement of the match criteria. Competing match criteria often reduce the likelihood of finding an acceptable history match. It is an engineering challenge in manual history matching processes to identify competing objectives and to implement the changes required in the simulation model. In production optimization or scenario optimization the focus on one key optimization criterion such as NPV limits the identification of alternatives and potential opportunities, since multiple objectives are summarized in a predefined global objective formulation. Previous works primarily focus on a specific optimization method. Few works actually concentrate on the objective formulation and multi-objective optimization schemes have not yet been applied to reservoir simulations. This paper presents a multi-objective optimization approach applicable to reservoir simulation. It addresses the problem of multi-objective criteria in a history matching study and presents analysis techniques identifying competing match criteria. A Pareto-Optimizer is discussed and the implementation of that multi-objective optimization scheme is applied to a case study. Results and consequences for the uncertainty quantification are presented. Introduction In recent years there has been more and more attention given to workflows for uncertainty assessment in reservoir management. Structured approaches exist for assessing the impacts of uncertainty on investment decision-making in the oil and gas industry.1 These approaches mostly rely on simplified component models for each decision domain such as G&G models, production scenarios, drilling models, processing facilities, economics and related costs. Because of its complexity, the integration of dynamical modelling is only gradually entering this domain of decision-making processes. It is generally accepted that any model reliably predicting future quantities should be able to reproduce known history data. This requires a model validation process2 (History Matching) which is traditionally cumbersome and time consuming. The consistent inclusion of production data calls for computation-intensive processing. This requires new approaches in the application of experimental design and optimization methods which is supported by the use of high-performance computing facilities3,4 . One crucial change in the mind set within reservoir engineering is the accepted importance of including multiple realizations of dynamical reservoir models into the forward modelling process to account for uncertainties in the prediction phase.5,6 Although several studies on deriving multiple solutions to a History Matching problem6–9 have been published recently there are nevertheless no structured workflows or optimization methods applicable to reservoir simulation which address the problem of multi-objective optimization MOO.10–13 Recent analysis of the TDRM6 workflow within the context of History Matching has identified single-objective optimization techniques as one weakness vis-à-vis manual history matching.7 This work extends the application of MOOs which are already applied in other industry areas and focuses on an implementation of a multi-objective optimization technique with applications in reservoir simulation. Multi-objective optimization criteria in reservoir simulation are not just addressing the problem statement of History Matching. Other examples include production optimization, portfolio optimization, etc. The methodology used in this work is described in the next chapter. Readers interested only in principal capabilities of the multi-objective optimization technique and results should refer to the implementation chapter and the application to History Matching.

Water flooding schemes introduced as part of redevelopment projects in mature fields are more often built on smart completions with multiple control valves (ICVs) in wells to be drilled. Decision processes for the implementation and operation of ICVs is supported by reservoir simulations to investigate the upside potential of technical production rates. The robustness of any presented solution is difficult to prove and requires workflows which integrate alternative geological scenarios for capturing uncertainties. In this work the employment of smart well technologies is modeled to investigate the potential for increasing o il recovery over the life time of a reservoir. Challenges exist on different levels. The number of control variables increases significantly as the number of wells, perforation sections per well and injection time intervals with varying injection constraints increases. Uncertainties related to different geological modeling concepts are taken into account for verifying the robustness of any optimized production scenario. The starting point for this paper is an ensemble of history matched simulation models. Ensemble-based production optimization including stochastic methods is applied for the optimization of water injection scenarios by individually adjusting ICVs. A novel concept for a time dependent target function is introduced. This reduces the number of control parameters adjusted at a time by focusing on incremental contributions to economic indicators. The workflow is applied to a complex reservoir model with production history. The optimization process is successfully improving economic indicators over the life time of the reservoir including a full risk evaluation based on alternative geological realizations.

Data assimilation techniques are on the verge of being employed in real field history matching processes in a production environment. In a previous publication on "Stochastic Optimization using EA and EnKF - A Comparison" (cf. Pajonk 2008) similarities between data assimilation techniques (EnKF) and stochastic optimizers (Evolutionary Algorithm - EA) were analyzed. Both algorithms are population based, they have similar implementation properties but differing optimization characteristics. A hybrid optimizer which couples an EnKF approach and the advantages of an Evolutionary Algorithm was introduced and applied to a synthetic test function. In this paper the formulation of a hybrid optimization approach with application to a history matching process is presented. Techniques are applied to the Brugge field simulation model which was taken from a recent SPE benchmark study. Production data is assimilated via a continuous update of 3D porosity and permeability fields. Global parameter uncertainties are included in a parameter estimation process guided by an evolutionary optimization method. In this paper we will concentrate on an Evolution Strategy with local and global search properties. It is shown that an EnKF workflow can be effectively coupled to other stochastic optimization schemes with complimentary optimization features. The EnKF formulation reduces a non-linear optimization problem in a large parameter space to a statistical optimization problem in ensemble space. An Evolution Strategy (ES) gradually modifies individual parameters and can be applied to mixed-integer parameter types. The case example shows that an EnKF ensemble can be combined with a population of individual realizations from a generational update scheme using an Evolution Strategy. Benefits are seen in alternative performance properties and the use of mixed-integer parameter types. This paper will include the first example of a hybrid EnKF-ES approach with application to reservoir simulation. Practical implications for history matching processes with mixed-integer parameter types which have not been used in a standard EnKF approach are discussed. Introduction In recent years more and more attention has been given to workflows for uncertainty assessment in reservoir management. It is generally accepted that any model reliably predicting future quantities should be able to reproduce known history data. This requires a model validation process (History Matching) which is traditionally cumbersome and time consuming. Most optimization methods described in the literature that have relevance for history matching in reservoir simulation use an objective function definition based on the overall simulation period. This applies to gradient techniques, evolutionary algorithms or combinations of experimental design and proxy modeling techniques, i.e., methods which are commonly used in modern history matching and uncertainty quantification workflows in the oil and gas industry. The integration of a sequential data assimilation process is not included as an integral part of such optimization methods. Frequent model updates would also incur high computational costs since existing concepts of an error function or objective function require computation of the entire simulation period. The Ensemble Kalman Filter method (EnKF) is a data assimilation technique that was developed for use in complex and highly non-linear simulation models (Evensen 1994). The EnKF technique was first applied to reservoir simulation in order to estimate lesser known rock properties as part of a history matching process (Nævdal 2003).