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The average global recovery factor of a typical oil and gas field is approximately 40% at after secondary recovery processes such as gas lifting and water flooding. The low recovery factor is often a result of by passing a considerable amount of oil in the reservoir due to unknown reservoir heterogeneity and incomplete understanding of the geology. Enhanced oil recovery (EOR) methods will play a key role in increasing recovery factors from existing reservoirs. Heterogeneous reservoir sands often show permeability contrast between layers and therefore lead to early water breakthrough when water flooding. In such situations, polymer flooding can potentially be a suitable EOR technique that helps to lower water cut and increase recovery. The addition of polymers to the injected water lowers the mobility ratio, thereby reducing viscous fingering and delaying water breakthrough. This study investigates how a polymer flood design can be optimized while considering geological uncertainty in the reservoir models as well as modelling decisions. We applied an adjoint based technique to match data from a prolonged waterflood in the Watt Field, a synthetic but realistic clastic reservoir that is based on real data and captures a wide range of geological heterogeneities and uncertainties through a range of different model scenarios and model realizations. We apply Latin hypercube experimental designs with the Particle Swarm Optimization algorithm in CMOST. This was used to build a proxy model employing polynomial regression for the optimization of the engineering parameters to maximize NPV. The optimization were performed for both history-matched models (constrained optimization) and the original, non-history-matched models (unconstrained optimization). The aim of this work is to analyse how geological uncertainties inherent to a heterogeneous clastic reservoir as well as modelling decisions impact the design and performance a polymer flood. We further investigate how the different optimization methods impact the predicted reservoir performance and optimal design of the polymer flood. Our findings show that both, geological and engineering uncertainties, impact polymer flooding and that designing the right well controls is essential for successful polymer flooding. Shale cut-offs are identified as a key petrophysical uncertainty when optimizing a polymer flood in a heterogeneous clastic reservoir. Furthermore, forecasts using constrained optimization yielded a much narrower range of incremental oil recovery and NPV during polymer flooding and may underestimate both, risk and opportunities for polymer flooding because the history matching of the water flood emphasizes different geological features compared to the way geology interacts with a more viscous polymer solution.

Produced Water Chemistry data (PWC) is the main source of information to monitor scale precipitation in oil field operations. Chloride concentration is used in order to evaluate the seawater fraction of the total produced water per producing well and is included as an extra history matching constraint to revaluate a good conventionally history matched reservoir model for the Janice field. Generally PWC is not included in conventional history matching and this approach shows the value of considering the nature of the seawater injection front and the associated brine mixing between the distinctive formation water and injected seawater. Adding the extra constraint resulted in the re-conceptualization of the reservoir geology between a key injector and two producers. The transmissibility of a shale layer is locally modified within a range of geologically consistent values. Also, a major lineament is identified which is interpreted as a NW-SE trending fault, whereby the zero transmissibility of a secondary shale in the Middle Fulmar is locally adjusted to allow cross-flow. Both uncertainties are consistent with the complex faulting known to exist in the region of the targeted wells. Other uncertainties that were carried forward to the assisted history matching phase included: water allocation to the major seawater injectors; thermal fracture orientation of injectors and the vertical and horizontal permeability ratio (kv/kh) of the Fulmar formation. Finally, a Stochastic Particle Swarm Optimization (PSO) algorithm is used to generate an ensemble of history matched (HM) models using seawater fraction as an extra constraint in the misfit definition. Use of addition data in history matching has improved the original good history matched solution. Field Oil Production Rate is interpreted as improved over a key period and although no obvious improvement was observed in Field Water Production Rate, Seawater fraction in a number of wells was improved.

Conventionally, automated history matching methods operated on a single number (the misfit or match quality) which is obtained by summing the least square misfits for all the quantities of interest in a history match. Multi-objective history matching allows the algorithm to be guided by (usually groups of) match quality components, with the overall history match probability determined by summing the components at the end. This feature encourages diversity in the history match, as the algorithm can trade off matches in one area against good fits elsewhere, and has also been shown to speed up history matching in some cases. This paper describes a comparison of single and multi-objective history matching of a medium-sized field in Western Siberia with nearly 100 wells and over 10 years of history. We compared the performance of both single and multi objective versions of Particle Swarm Optimization. We also assess the effectiveness of various different choices of history match parameters chosen based on reservoir engineering knowledge. Using these techniques, we are able to obtain a high-quality group level match with a relatively low number of simulation runs. The paper also describes trade-offs between the parallelism of the history matching process and that of the simulator on a 12 core windows workstation. This is an important trade-off as the extreme choices of using of all the cores by the simulator or limiting each simulation to a single core and using each core for a separate history matching run may not be optimal.

Produced Water Chemistry (PWC) has been included in the history matching of reservoir simulations. Generally, in conventional history matching, the water chemistry is not considered as an extra constraint. The chemistry of the different types of water in a reservoir, such as aquifer, connate and seawater is very different, and can be traceable. Produced Water Chemistry is the main source of information to monitor scale precipitation in oil field operations. The objective of this paper is to evaluate the effect of adding produced water chemistry information as an extra constraint history matching a modified version of the PUNQ-S3 reservoir model. The PUNQ-S3 model is a synthetic benchmark case that has been used previously for history matching and uncertainty quantification. Conventional historical production data (gas, oil rates and pressure) from six production wells are supported by the water chemistry tracer data from the wells that produce water in the history period. The different types of water are traced through their distinctive chemistries, namely aquifer, connate (formation) and sea (injection) water. Geological model is matched by varying porosity and permeability, both horizontal (kh) and vertical (kv) according to the prior beliefs about the reservoir geology (layering, spatial correlation and anisotropy). Two history matching (HM) scenarios are considered: including and not-including the Produced Water Chemistry (PWC) as an extra matching constraint. Stochastic Particle Swarm Optimization (PSO) algorithm is used to generate ensembles of history matched models, which characterise the uncertainty of the reservoir prediction. Comparison of the two scenarios reveals potential value of adding PWC data in history matching that allows achieving better matched models and ensuring diversity of HM models, which is essential for robust uncertainty quantification of the predictions.

Quantifying uncertainty in hydrocarbon production forecasts is critical in the petroleum industry because of the dominant role uncertainty quantification plays in reservoir management decisions. An efficient application of global optimisation methods to history matching and uncertainty quantification of real complex reservoirs has been an extensively an active area of research. The goals of these methods are to navigate the parameter space for multiple good fitting models quickly and identify as many different optima as possible. Obtaining multiple optima can result in an ensemble of history matches that has divergent prediction profiles for more accurate and reliable predictive uncertainty estimates. The present study extends the application of particle swarm optimisation to handle multi-objective optimisation in reservoir history matching context. Previous research studies in assisted history matching primarily focused on optimising a single objective function in which all the production data coming from the wells are aggregated into a single misfit value. The single misfit value is constructed by summing the weighted squared differences between historical and simulated production data. In the multi-objective optimisation scheme, multiple objectives can be defined representing each or some of the weighted squared difference of a production type. By constructing multiple objectives that measure the contribution of each objective in the multi-objective optimisation scheme, it can be possible to find a set of solutions which optimally balances the different objectives simultaneously while maintaining solution diversity. The advantage of this construction is that the tradeoffs between the objectives can be explored and explicitly exploited in the course of optimisation to find all possible combination of good fitting model solutions that have similar match quality. In history matching, it is desirable to have various solutions that map to relatively similar low misfit values that can represent all the possible geological scenarios. The new multi-objective particle swarm optimisation uses a crowding distance mechanism jointly with a mutation operator to preserve the diversity of solutions. In this paper, the multi-objective particle swarm optimisation scheme has been investigated on history matching a well-known synthetic reservoir simulation model and the results were compared with a single objective methodology. Analyses of history matching quality and predictive uncertainty estimation based on the resulted models have been conducted to obtain the uncertainty predictions envelopes for both strategies. The comparative results suggest that, for the reservoir under consideration, the multi-objective particle swarm approach obtains better history matches and has achieved over twofold faster convergence speed than the single objective approach. The benefits of using multi-objective scheme by comparison with the single objective scheme to obtain a diverse set of history matches while reducing the number of simulations required for achieving a similar matching performance have led to more reliable predictions.

Today we have 50 years of research in assisted history matching that bring us many fascinating frameworks to obtain multiple history matched models. Recently the evolutionary optimization algorithms for history matching have enjoyed an increasing popularity in our community. However these methods are often criticized for their high computational demands. We are looking to improve the convergence speed of these algorithms while maintaining their ability to obtain multiple history-matched models to have realistic uncertainty quantification. In this paper, we discuss a new approach to history matching and uncertainty quantification using multiobjective stochastic population-based optimization. The current practice in industry is to sum the individual match results from wells and minimize a global misfit value in order to get a history matched model. This work proposes a methodology where we can handle different objectives of history matching separately. We extend original differential evolution (DE) algorithm to optimize multiple objectives. The new algorithm is called differential evolution for multiobjective optimization using Pareto ranking (DEMOPR). We couple this algorithm with Bayesian uncertainty quantification framework to estimate the uncertainty in future recovery. The DEMOPR algorithm is tested for history matching and uncertainty quantification of the PUNQ-S3 reservoir. We have discussed the benefits of new multiobjective approach in fulfilling the targets of PUNQ-S3 problem: obtaining good history matching results and accurate prediction of the ultimate oil recovery. Results are very promising and show better final misfit values and simultaneously, two times increase in the speed of history matching in comparison with the original DE algorithm. We also study the number of models required to reach a stable Bayesian credible interval in quantifying the production uncertainty. We show that multiobjective approach stabilizes faster than original DE which means we need fewer simulations to have a reliable uncertainty estimate in the proposed workflow.

In modern field management practices, there are two important steps that shed light on a multimillion dollar investment. The first step is history matching where simulation model is conditioned to production and/or seismic data. In this inverse problem, we calibrate our model to reproduce the historical observations from the field. In second step we quantify uncertainty of the predictions made by calibrated models. These two steps are tied together; multiple history matched models are essential for a realistic uncertainty estimate of the future field behavior. Stochastic population-based optimization methods have been used in the last two decades as popular tools in history matching frameworks. Stochastic sampling algorithms explore/exploit the parameter space to find diverse good-fitting models. Recently two innovative algorithms were proposed to tackle history matching problem; ant colony optimization [Hajizadeh et al. 2009] and differential evolution [Hajizadeh et al. 2010]. However these algorithms were applied for history matching of a simple reservoir model with few unknown parameters. The question is the capability of these new methods for solving complex history matching problems and estimation of the uncertainty associated with these models. This paper compares the application of ant colony, differential evolution and neighbourhood algorithms for history matching and uncertainty quantification of the PUNQ-S3 reservoir. PUNQ-S3 model is a synthetic benchmark case with challenging parameterization, history matching and uncertainty quantification steps. We compare performance of the above algorithms in sampling the parameter space and obtaining multiple history-matched models. The paper also includes comparison of convergence properties of these algorithms for this high dimensional problem. We show that novel stochastic population-based optimization algorithms can be successfully applied for history matching problems with large number of unknown parameters. The algorithms are integrated with a Bayesian framework to quantify uncertainty of the predictions. Results confirm that the proposed methodology provides reliable predictions of the future reservoir recovery.

Reservoir modelling is frequently used in the oil industry to measure the risk associated with alternative production scenarios. However, reservoir models themselves contain a high level of uncertainty because of the typically very limited, sparse and multi-scaled reservoir knowledge. The effect of this uncertainty can be assessed by producing a set of diverse models that match the production data reasonably well and using these models to quantify uncertainty in predicting the future performance of the reservoir. Evolutionary and swarm intelligence algorithms have become very popular for history matching due to their simplicity and parallel implementation capacity. This paper focuses on the application of Particle Swarm Optimisation (PSO) for history matching the Brugge field (a recent SPE benchmark case study). The parameterisation of the model is based on principal component analysis (PCA) for modelling spatially correlated random fields (e.g. porosity, net-to-gross and permeability) applied to the set of initial realisations which describe the range of prior beliefs. The PSO is then used to find the set of possible combinations of parameters, represented by the PCA eigenvalues, which match the historical data and honour the static data from the wells present in the initial realisations. We show that PSO is able to find multiple good and diverse history matched models for the Brugge reservoir without exhaustive sampling of the parameter space. Uncertainty of production forecasts are quantified by P10-P50-P90 uncertainty envelope obtained from the ensemble of PSO models. The history matching results are compared with the ones obtained with Ensemble Kalman Filter data assimilation method. These results show the ability of PSO to handle large history matching problems and obtain results comparable to the EnKF for this case study.

History matching and uncertainty quantification are two important aspects of modern reservoir engineering studies. Finding multiple history matched models for uncertainty quantification with fast and efficient optimization algorithms are the focus of research in assisted history matching methods. Recently a new approach for history matching has been proposed based on differential evolution optimization algorithm. Differential evolution is a very powerful optimization method with a simple structure and few tuning parameters which makes it easy to use in automatic history matching frameworks. In this paper we are looking at three new search strategies as alternates to the proposed method in previous publication for obtaining multiple history-matched reservoir models. These strategies of differential evolution are different in the way that new models are generated during automatic history matching process. The comparative study presents the differences between performances of new search schemes for a simple reservoir simulation case in Gulf of Mexico. We compare the best history matching results and sensitivity of algorithms to starting conditions. Tradeoff between speed of convergence to good fitting regions and coverage of the search space is also demonstrated for different variants of differential evolution. We show that some variants of differential evolution exhibit global searching characteristics, while other ones quickly obtain good results, saving time and computational resources in reservoir engineering studies. Final part of this paper focuses on the uncertainty of production forecasts, discussing the prediction capability of applied differential evolution algorithms.

History matching optimisation in Bayesian framework is a fairly recent approach to quantify uncertainty in oil industry. Currently some innovative global optimisation approaches such as evolutionary algorithms and swarm intelligence methods have gained popularity for tackling history matching problems.Particle swarm optimisation (PSO) is a swarm intelligence approach for solving optimisation problems. In this approach particles are moving points in parameter space. The position of a particle is a candidate solution to the optimisation problem. Each particle searches for better positions in parameter space by updating its velocity according to rules originally inspired by behavioural models of the movement of flocks of birds.Recently the PSO algorithm has shown to be a promising tool for finding acceptable multiple history matched models quickly (Mohamed et al., 2009). However, the algorithm control parameters which balance between exploitation–exploration trade–off are to be studied for history matching problems. In this paper we investigate some basic PSO variants for updating the control parameters using a real–life case study.It is shown that PSO could be improved by optimising the PSO control parameters. Some variants converge faster to good fitting regions in parameter space leading to a fewer number of reservoir simulation runs though others maintain diversity of the reservoir models better for this reservoir example. This study helps better employing the PSO algorithm for reservoir model history matching and uncertainty quantification.

This paper presents a novel approach in automatic history matching using a differential evolution algorithm. Differential evolution is becoming a popular global optimization method and has been widely applied in many challenging engineering problems outside the oil industry. Some advantages of differential evolution are its simplicity in structure which leads to ease of coding and straightforward parallelisation, and its few control parameters making it easy to use in an operational context. These advantages make it important to evaluate differential evolution for use in automatic history matching frameworks where reservoir engineers require a powerful, yet easy to work tool with little effort to find optimum algorithm parameters. We have applied differential evolution approach to obtain history matched models of a reservoir simulation case in Gulf of Mexico. The effect of different tuning parameters on the performance of differential evolution has been studied and the algorithms sensitivity to initial starting conditions investigated. Results confirm that differential evolution is a good optimization tool in obtaining multiple good history matched models. We have also compared the match quality of models obtained using differential evolution with the Neighbourhood Algorithm (NA). This comparison shows that differential evolution obtains comparable or better models in terms of matching misfit. Finally, we studied the effect of the number of observation data points used in history matching with differential evolution algorithm. We show how additional information helps the algorithm in finding the promising regions of the search space and narrowing down the uncertainty intervals of the predictions.

Well performance prediction is a key Petroleum Engineering task. However, large discrepancies between Petroleum Engineering models and reality still frequently occur; despite the continuous increase in the complexity and predictive quality of reservoir models. To-day's field development decisions are still made with a high level of uncertainty in the underlying data and its economic impact. The degree of data uncertainty is greatest during the exploration stage, but decreases as the reservoir development plan is executed and production data is obtained. Standard, probabilistic workflows have been developed to quantify this uncertainty. These workflows are usually framed by the reservoir scale development plan and end prior to the well's detailed completion design. This is despite the fact that expensive, advanced completions have become common during recent years and the additional investment in such completions can only be justified if it is shown to be paid-back by improved overall project economics which is subject to a significant level of uncertainty. This paper illustrates the quantification of the long-term benefits of advanced completions using the probabilistic approach. It will be shown how choice of the optimum advanced completion design will reduce the impact of geostatistical uncertainty on the production forecast. Geostatistical realisations of a benchmark reservoir model were generated with a suitable level of data uncertainty. The reservoir was developed by a single horizontal well in a fixed location. The well could be equipped with a variety of completions – an Open Hole with a sand control screen or a perforated pipe, Inflow Control Devices (ICDs) and Interval Control Valves (ICVs). The probabilistic (P10, P50, P90) oil-recovery distribution was then used to identify the optimum completion design. This completion not only achieved the largest recovery, but also showed the least uncertainty in this value.