A multiobjective dominance and decomposition algorithm for reservoir model history matching

It is well-known that history matching of reservoir models with production measurements is an ill-posed problem, e.g. different choices for the history matching parameters may lead to equally good history matches. We analyzed this problem using the system-theoretical concept of structural identifiability. This allows us to analytically calculate a so-called information matrix. From the information matrix we can determine an identifiable parameterization with a significantly reduced number of parameters. We apply structural identifiability analysis to single-phase reservoir simulation models and obtain identifiable parameterizations. Next, we use the parameterization in minimizing an objective function that is defined as the mismatch between pressure measurements and model outputs. We also apply the structural identifiability analysis to an object-based parameterization describing channels and barriers in the reservoir. We use the iterative procedure to determine for reservoir models with 2025 grid block permeability values a structurally identifiable parameterization of only 13 identifiable parameters. Next, we demonstrate that the parameterization leads to perfect history matches without the use of a prior model in the objective function. We also demonstrate the use of the identifiable object-based parameterization, leading to geologically more realistic history matches.

This paper presents a review of history matching and oil field development optimization techniques with a focus on optimization algorithms. History matching algorithms are reviewed as a precursor to production optimization algorithms. Techniques for history matching and production optimization are reviewed including global and local methods. Well placement, well control, and combined well placement-control optimization using both secondary and tertiary oil production techniques are considered. Secondary and tertiary recovery techniques are commonly referred to as waterflooding and enhanced oil recovery (EOR), respectively. Benchmark models for comparison of methods are summarized while other applications of methods are discussed throughout. No single optimization method is found to be universally superior. Key areas of future work are combining optimization methods and integrating multiple optimization processes. Current challenges and future research opportunities for improved model validation and large scale optimization algorithms are also discussed.

Technology Focus Production forecasting is one of the main tasks of engineers involved in reservoir management. To perform it, they resort to models, which vary from simple decline curves to complex numerical simulations. Regardless of the model’s level of complexity, uncertainty will always exist in the forecasts. Therefore, reservoir engineers devote significant efforts trying to incorporate data in these models (history matching), aiming to mitigate uncertainty and improve the reliability of the predictions. The reservoir-history-matching literature is quite extensive. The first works on automatic history matching were published in the 1960s. Nowadays, there is a wealth of history-matching methods. As a result, we observe that it is becoming a common industrial practice to generate multiple history-matched models, even for fairly complex problems with thousands of uncertainty variables and a large amount of data. However, we are still far from a definitive solution. Actually, it seems that there will be no single best history-matching technique. Instead, what we may have is the best method for the specific problem. Moreover, there are many challenges that are not completely addressed. In particular, most of the approaches seem overly simplistic to handle complex geology and structural uncertainties. Also, the computational demand for uncertainty quantification remains an issue. Therefore, industry and academia still have much work to do. Another point I want to mention is that, back in 2009, SPE promoted a forum meeting titled “Getting to Robust Production Forecasts.” This meeting became the startup of a Global Integrated Workshop Series on production forecasting. To date, there have been six meetings; the latest was held this year in Malaysia. These workshops have the ambitious goal of developing a production-forecasting guideline. I think we will hear more about this in the coming years. The papers summarized in this feature and the ones indicated in the additional-reading list are good examples of recent developments and field applications of history matching and forecasting. I hope you enjoy them. JPT Recommended additional reading at OnePetro: www.onepetro.org. SPE 163582 An Ensemble-Based Nonlinear Orthogonal Matching Pursuit Algorithm for Sparse History Matching of Reservoir Models by Ahmed H. Elsheikh, The University of Texas at Austin, et al. SPE 170622 Integrated Subsurface Uncertainty Study and Application—A Case Study of a Chalk Reservoir, Greater Ekofisk Area, North Sea by H.J. Yu, ConocoPhillips, et al. SPE 170945 Practical Considerations for Forecasting Production Data in Unconventional Reservoirs—Variable- Pressure Drop Case by P.W. Collins, Texas A&M University, et al.

Using commercial numerical reservoir simulators to build a full field reservoir model and simultaneously history match multiple dynamic variables for a highly complex, offshore mature field in Malaysia, had proven to be challenging, manpower intensive, highly expensive, and not very successful. This field includes almost two hundred wells that have been completed in more than 60 different, non-continuous reservoir layers. The field has been producing oil, gas and water for decades. The objective of this article is to demonstrate how Artificial Intelligence (AI) and Machine Learning is used to build a purely data-driven reservoir simulation model that successfully history match all the dynamic variables for all the wells in this field and subsequently used for production forecast. The model has been validated in space and time. The AI and Machine Learning technology that was used to build the dynamic reservoir simulation and modeling is called spatio-temporal learning. Spatio-temporal learning is a machine-learning algorithm specifically developed for data-driven modeling of the physics of fluid flow through porous media. Spatio-temporal learning is used in the context of Deconvolutional Neural Networks. In this article Spatio-temporal Learning and Deconvolutional Neural Networks will be explained. This new technology is the result of more than 20 years of research and development in the application of AI and Machine Learning in reservoir modeling. This technology develops a coupled reservoir and wellbore model that for this particular oil & gas field in Malaysia uses choke setting, well-head pressure and well-head temperature as input and simultaneously history matches Oil production, GOR, WC, reservoir pressure, and water saturation for more than a hundred wells through a completely automated process. Once the data-driven reservoir model is developed and history matched, it is blind validated in space and time in order to establish a reliable and robust reservoir model to be used for decision making purposes and opportunity generation to maximise the field value. The concepts and the methodology of history match of multiple wells, individual offshore platforms, and the entire field will be presented in this article along with the results of blind validation and production forecasting. Results of using this model to perform uncertainty quantification will also be presented. A case study of a highly complex mature field with large number of wells and years of production has been used to be studied and simulated by this data-driven approach. Time, efforts, and resources required for the development of the dynamic reservoir simulation models using AI and Machine Learning is considerably less than time and resources required using the commercial numerical simulators. It is validated that the TDM developed model can make very reasonable prediction of field behavior and production from the existing wells based on modification of operational constraints and can be a prudent complementary tool to conventional numerical simulators for such complex assets.

Even though the ensemble Kalman filter (EnKF) is widely used, history matching reservoirs with facies description has proven to be a major challenge. A preferred technique for estimating large-scale facies fields within the petroleum industry is still missing. In this paper we present a new approach to this problem. Instead of applying the EnKF directly on facies realizations, the approach applies a transformation of facies fields to a specific level-set function, representing distances between facies types. This ensures better agreement with the EnKF Gaussianity assumptions, and the method always returns facies realizations with geological authenticity. The method also offers large flexibility in generating the initial ensemble, which can be done using any geostatistical tool. Further, no modifications of the standard EnKF equations are needed. The methodology is evaluated on two synthetic examples with increasing complexity. In both examples we consider reservoirs with channel structure. The results presented show that the updated models give large improvements in matching the measurements, and the uncertainty of the models is decreased. Further, recovery of the true petrophysical parameters is highly dependent on sufficient information in the measurements, but in one of the examples considered we are able to completely recover the true channel structure. Additional improvements in the quality of the updated facies fields are obtained by proper handling of the distances close to the reservoir boundaries, and conditioning on specific statistical measures to better preserve prior information about channel properties. Introduction The ensemble Kalman filter (EnKF) (Evensen [1], Aanonsen et al. [2]) is one of the most promising tools for assisted history matching of reservoir models. The filter has in particular proven to work well on cases where petrophysical properties are modeled using Gaussian random fields with variogram models. However, many operative oil and gas reservoirs have challenging complex geological structures - channelized reservoirs being one example. These structures typically have rapid spatial variations in the petrophysical properties (e.g., permeability and porosity). The effect of applying the EnKF directly on such reservoirs is that the characteristics of the fields are lost, i.e., sharp gradients are smeared out (dissipated). Several approaches for using EnKF on complex reservoirs have been proposed. The goal is to ensure that the updated fields are facies realizations, or at least approximations of such, and that good history match is obtained. The methods involve use of truncated pluri-Gaussian methods (Liu and Oliver [3, 4]), Gaussian mixture models (Dovera and Della Rossa [5], Sun et al. [6]), discrete cosine transformations (Jafarpour and McLaughlin [7]), kernel methods (Sarma and Chen [8]), and level-set methods (Moreno et al. [9]). Many of the above mentioned methods give promising results, but there are still drawbacks related to e.g., flexibility in how the initial ensemble may be generated, or the method involves complex and large modifications of the standard EnKF implementation. Our goal is to develop a methodology which is both simple, flexible and able to preserve facies structure for the updated fields. To achieve this, we propose a method motivated by the work of Moreno et al. [9], in the sense that level-set functions are used to represent the facies fields. However, in Moreno et al. [9], only perturbations of a fixed "base case" are updated, and it is questionable whether the real uncertainty is properly described by the prior ensemble. The method we propose is not limited to updating perturbations, and the initial ensemble can be computed using any geostatistical tool. This means that using our methodology, the initial ensemble can be conditioned on the correct facies types at the well locations. The method relies on a transformation of the facies field to a specific level-set function - a signed distance function (representing distances between opposite facies types). The distances are then updated using the EnKF, and converted to petrophysical properties when the reservoir simulator is run to the next assimilation time. The advantage with this transformation is that the ensemble of parameters to be estimated is closer to a Gaussian distribution, which is in better agreement with the EnKF Gaussianity assumptions. In addition, we are guaranteed that the updated fields are facies realizations.

This paper describes a novel approach for creating an efficient, general, and differentiable parameterization of large-scale non-Gaussian, non-stationary random fields (represented by multipoint geostatistics) that is capable of reproducing complex geological structures such as channels. Such parameterizations are appropriate for use with gradient-based algorithms applied to, for example, history-matching or uncertainty propagation. It is known that the standard Karhunen–Loeve (K–L) expansion, also called linear principal component analysis or PCA, can be used as a differentiable parameterization of input random fields defining the geological model. The standard K–L model is, however, limited in two respects. It requires an eigen-decomposition of the covariance matrix of the random field, which is prohibitively expensive for large models. In addition, it preserves only the two-point statistics of a random field, which is insufficient for reproducing complex structures. In this work, kernel PCA is applied to address the limitations associated with the standard K–L expansion. Although widely used in machine learning applications, it does not appear to have found any application for geological model parameterization. With kernel PCA, an eigen-decomposition of a small matrix called the kernel matrix is performed instead of the full covariance matrix. The method is much more efficient than the standard K–L procedure. Through use of higher order polynomial kernels, which implicitly define a high-dimensionality feature space, kernel PCA further enables the preservation of high-order statistics of the random field, instead of just two-point statistics as in the K–L method. The kernel PCA eigen-decomposition proceeds using a set of realizations created by geostatistical simulation (honoring two-point or multipoint statistics) rather than the analytical covariance function. We demonstrate that kernel PCA is capable of generating differentiable parameterizations that reproduce the essential features of complex geological structures represented by multipoint geostatistics. The kernel PCA representation is then applied to history match a water flooding problem. This example demonstrates that kernel PCA can be used with gradient-based history matching to provide models that match production history while maintaining multipoint geostatistics consistent with the underlying training image.

As the role of reservoir flow simulation increasingly impacts existing operations and field development decisions, it follows that rigor, fitness and consistency should be imposed on the calibration of reservoir flow models to dynamic data through history matching. Although a wealth of history matching techniques exist in the petroleum literature that propose novel algorithms or share case studies, seldom does the content guide the modeler in fit-for-purpose reservoir model calibration for an operating asset. To evaluate the applicability of these diverse techniques against standards required for reservoir management, an internal study was performed to benchmark four assisted history matching (AHM) techniques commonly promoted in the oil and gas industry. The techniques were vetted against a comprehensive suite of modeling requirements for multiple asset classes, integrating a variety of historical dynamic data types through the calibration of reservoir properties that control flow behavior from the field to inter-well scale. The methods benchmarked were: (1) Design of Experiments (DoE)-based, (2) Ensemble Kalman Filter and Ensemble Smoother, (3) Genetic Algorithm and (4) Generalized Travel Time Inversion. This manuscript focuses solely on the DoE-based technique.In order to consistently benchmark the techniques, a set of standards was defined against which each was evaluated to determine its suitability for widespread history matching applications. The standards involve: the capacity to parameterize (and therefore calibrate) a diversity of reservoir flow model attributes, the capacity to integrate different types of dynamic data, the level of independence from the flow simulator and the capability to provide probabilistic outcomes for predictive uncertainty assessment. Of the four techniques, the DoE-based approach uniquely satisfied all requirements. Its history matching workflow has the flexibility to incorporate any form of reservoir model parameter and to assimilate a history matching error metric for any individual or group of historical data types; therefore, benchmarking established DoE-based techniques as unambiguously the most compliant with generic asset modeling requirements. The approach was also identified as the most straightforward, both theoretically and in practical computation, and therefore applicable to the broadest range of practitioners. Perhaps most importantly, the approach demonstrated the capacity for accurate quantification of uncertainty (or non-uniqueness) in reservoir quality resulting from an exhaustive, although approximate, exploration of model parameter space and the associated history matching error metric(s).This manuscript compiles the results and insights gained from benchmarking of the DoE-based techniques through the proposal of a comprehensive assisted history matching workflow. The workflow is designed for generality while providing best practices that guide the modeler in fit-for-purpose application. Limitations of the workflow are also recognized. Key components include: selection and screening of calibration parameters based on statistical significance, development of surrogate models to characterize the relationship between parameters and the simulated historical data being integrated into the reservoir model, use of the surrogate models for exhaustive yet efficient exploration of parameter space to identify (non-unique) history matched models, and (deterministic or probabilistic) discrete reservoir model selection for use in forecast-based decision making. Each step of the AHM workflow is presented from a conceptual and applied perspective, and field applications are provided to demonstrate key concepts. Although the applications presented include two deepwater Gulf of Mexico assets, the workflow and insights provided are developed from benchmarking across a diverse suite of asset types.

Hierarchical benchmark case study for history matching, uncertainty quantification and reservoir characterisation

The application of elastic stress simulation for fracture modeling provides a more realistic description of fracture distribution than conventional statistical and geostatistical techniques, allowing the integration of geomechanical data and models into reservoir characterization. The geomechanical prediction of the fracture distribution accounts for the propagation of fracture caused by stress perturbation associated with faults. However, the challenge lies in estimating the past remote stress conditions which induced structural deformation and fracturing, the limited applicability of the elasticity assumption, and the latent uncertainty in the structural geometry of faults. The integration of historical production data and welltest permeability into geomechanical fracture modeling is a practical way to reduce such uncertainty. We propose to combine geostatistical algorithms for history matching with geomechanical elastic simulation model for developing an integrated yet efficient fracture modeling tool. This paper presents an integrated approach to history matching of naturally fractured reservoirs which includes 1) fracture trend prediction through elastic stress simulation, 2) geostatistical population of fracture density based on fracture trend map, 3) fracture permeability modeling integrating fracture density, matrix permeability and welltest permeability, and 4) numerical flow simulation and history matching. All of these implementations are incorporated into a single forward modeling process and iterated in the automatic history matching scheme. To obtain a history match on a reservoir model, we jointly perturb the large-scale fracture trend and local-scale geostatistical fluctuations of fracture densities rather than perturbing permeability calibrated from fractures. This strategy enables us to preserve the geological/geomechanical consistency throughout the history matching process. The geomechanically simulated fracture trend model is calibrated to both production data and geological structure map (faults and horizons) by finding the optimum remote stress condition for elastic stress-field simulation. The latter is achieved by matching the actually observed structural deformation trend with the simulated one. The smaller-scale fluctuation of fracture density is simultaneously history matched through the probability perturbation method of Caers (2003)1,2. The result of synthetic reservoir application is presented.

The purpose of history matching is to achieve geological realizations calibrated to the historical performance of the reservoir. For complex geological structures it is usually intractable to run tens of thousands of full reservoir simulation to trace the most probable geological model. Hence the inadequacy of the history-matching results frequently leads to poor estimation of the true model and high uncertainty in production forecasting. Reduced-order modeling procedures, which have been applied in many application areas including reservoir simulation, represent a promising means for constructing efficient surrogate models. Nonlinear dimensionality reduction techniques allow for encapsulating the high-resolution complex geological description of reservoir into a low-dimensional subspace, which significantly reduces number of unknowns and provides an efficient way to construct a proxy model based on the the reduced-dimension parameters. Polynomial Chaos Expansions (PCE) is a powerful tool to quantify uncertainty in dynamical system when there is probabilistic uncertainty in the system parameters. In reservoir simulation it has been shown to be more accurate and efficient compared to traditional experimental design (ED). PCEs have a significant advantage over other response surfaces as the convergence to the true probability distribution is proved when the order of the PCE is increased. Accordingly PCE proxy can be used as the pseudo-simulator to represent the surface responses of the uncertain variables. When the objective and constraints of a reservoir model is described by multivariate polynomial functions, there are very efficient algorithms to compute the global solutions. We have developed a workflow at which incorporates PCE to find the global minimum of the misfit surface and assess the uncertainty associated with. The accuracy of the PCE proxy increases with the additional trial runs of the reservoir simulator. We conduct a two dimensional synthetic case study of a fluvial channel as well as a real field example to demonstrate the effectiveness of this approach. Kernel Principal Component Analysis (KPCA) is used to parameterize the complex geological structure. The study has revealed useful reservoir information and delivered more reliable production forecasts. PCE-based history match enhances the quality and efficiency of the estimation of the most probable geological model and improve the confidence interval of production forecasts.

Reservoir model history matching is a complex, time-consuming, and resource intensive process that needs to be carried out carefully for building reliable predictive tools to manage Oil & Gas assets. Reservoir models encompass detailed geological description representing subsurface heterogeneities that influence its dynamics. To intelligently manage and preserve the complexity of the reservoir models, an artificial intelligence, Progressive-Recursive Self-Organizing Maps (PR-SOM), algorithm was developed. PR-SOM is an unsupervised artificial intelligence neural network algorithm that classifies the reservoir grid cells into progressive reservoir parameters to identify similarly adjoining regions. The algorithm explores and identifies model geo-bodies with similarities and dissimilarities in a progressive and recursive manner. This allows history matching to be conducted on much smaller subsets of the reservoir model of similar geological features. In this work, an artificial intelligence (AI) algorithm was applied, first, to guide the reservoir-wide history match processes. Next, the algorithm was applied to fine-tune well performance using information form well testing and historical data. The algorithm uses both static properties (permeability, rock quality indices, porosity, flow zonation … etc.) and dynamic properties (pressure or saturation) to construct similarities matrix. The results show that the clusters’s growth is progressive, controlled and quality assured by accounting for the controlling reservoir parameters. The number of mapped regions (clusters) is determined by optimizing the similarity matrix recursively. The quality of the global reservoir history match shows the effectiveness of the algorithm, better quality matching for historical production data, and fewer iterations (i.e. less simulation runs). The process is repeated to calibrate the reservoir model near wellbores by limiting the AI algorithm to only the drainage regions seen from well tests and historical data. The results show that employed AI-guided history matching revealed similarities and dissimilarities in the reservoir model. That not only enhance field and well match, but also allowed us to maintain the heterogeneity contrasts inherited from the Earth model. The advanced algorithm was successfully used to assess the extent of geological heterogeneity and its impact on reservoir dynamics, to enhance history match quality, minimize human interaction, and to reduce computational requirements.

In current practice history matching is often performed on upscaled reservoir models without updating the original geological model. Taking into account new production data in an existing model is often problematic because of the lack of appropriate techniques. This problem becomes crucial when using geostatistical models. In such a case, the integration of new static and dynamic constraints requires the modification of an initial realization without destroying the initial history match and the overall geostatistical properties. This paper presents a new methodology based on advanced history matching techniques for updating dynamically 3D stochastic reservoir models to account for new production data. The proposed approach is based on the gradual deformation method. It allows local or global smooth transformations of the model while conserving the overall statistical characteristics. History matching is performed by coupling this method with an optimization process which integrates geostatistical modeling, upscaling, and fluid flow simulation in the same loop. This approach provides great flexibility in history matching various types of production data. In addition, inversion parameters can be selected throughout the entire modeling loop, from the facies spatial distribution, to petrochemical parameters and fluid flow parameters. Finally, local transformations may be performed to account for new wells or to update the reservoir model with new dynamic information. A successful application to a 3D stochastic reservoir model inspired from a real field is presented. The first step was to perform a history match using the production history available from an initial group of production wells. Then, new dynamic information is acquired from infill wells and over one year of additional production data. The heterogeneity distribution is locally modified by gradual deformation to update the model with this new information. The benefit of the proposed approach for improving the model characterization and reducing uncertainty on production forecasts is demonstrated.

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 193895, “Multilevel Strategies and Geological Parameterizations for History Matching Complex Reservoir Models,” by Yimin Liu, SPE, and Louis J. Durlofsky, SPE, Stanford University, prepared for the 2019 SPE Reservoir Simulation Conference, Galveston, Texas, 10–11 April. The paper has not been peer reviewed. The complete paper explores the use of multilevel derivative-free optimization for history matching, with model properties described using principal component analysis (PCA) -based parameterization techniques. The parameterizations applied are optimization-based PCA (O-PCA) and convolutional-neural-network-based PCA (CNN-PCA). Mesh adaptive direct search (MADS), a pattern search method that parallelizes naturally, is used for the optimizations required to generate posterior models. The use of PCA-based parameterization reduces considerably the number of variables that must be determined during history matching, but the optimization problem can still be computationally demanding. The multilevel strategy addresses this issue by reducing the number of simulations that must be performed at each MADS iteration. History-matching results demonstrate that substantial uncertainty reduction is achieved in all cases considered and that the multilevel strategy is effective in reducing the number of simulations required. Overview Parameterization has two key advantages in history matching: Far fewer parameters must be determined, which simplifies greatly the minimization in some cases. Posterior (history-matched) geomodels will be consistent with the geological scenario or training image for which the parameterization was constructed. PCA is the foundation for many geological-dimension-reduction parameterization methods. PCA is based on the eigen-decomposition of the prior geomodel covariance matrix and, thus, honors only two-point spatial statistics. History-matching algorithms largely can be classified as either optimization-based or ensemble-based procedures. Optimization-based algorithms generate one history-matched model at a time, while ensemble-based algorithms update a large set of models simultaneously. The resulting ensemble of posterior models is used to quantify uncertainty. In this study, only optimization-based history matching is considered, though the parameterizations applied also can be used with ensemble-based methods. Optimization-based history-matching algorithms can be classified further into gradient-based and derivative-free optimization (DFO) methods. Gradient-based algorithms often are combined with adjoint procedures that provide the required gradient efficiently. Unlike adjoint-based procedures, DFO algorithms (which are considered in this work) are nonintrusive. They treat the reservoir simulator as a so-called “black box,” and, as a result, they are much easier to implement and can be applied with any simulator. In this study, MADS, a pattern-search DFO, is applied for history matching. In pattern-search (or stencil-based) algorithms, the number of simulations required at each iteration scales with the number of parameters to be determined. Because the latter typically is much smaller than the number of grid-blocks in the model, geological parameterization leads to large computational savings when a pattern search, or other DFO, is used for history matching. The performance of DFO for history matching with non-Gaussian models, a primary topic in the complete paper, has not been studied extensively. The authors devise a multilevel strategy, applicable for PCA-based parameterization methods, to further reduce the computational cost of history matching using DFO. A multilevel strategy lends itself naturally to PCA-based parameterizations because the PCA representation can be ordered from the most-important to the least-important principal component. Thus, PCA parameters can be determined sequentially, level by level, in groups, rather than all at once.

History matching is the process of calibrating reservoir models with actual production and pressure data. The model is considered calibrated if it can reproduce the historical data of the reservoir it represents. Only history matched models can be used to predict the reservoir future performance under different scenarios. Traditional history matching is carried out through trial and error sequences of adjusting model parameters until a satisfactory match is obtained. History matching is an inverse problem, and hence it may have non-unique solutions. History matching process is an ill posed problem, and it is often very time consuming. In recent years, several approaches have been introduced to assist the history matching process. Assisted history matching concept is inspired by the optimization theory which has been first introduced by Kantorovich in the area of mathematical programming. The history matching problem is converted to an optimization problem with the objective of minimizing the difference between observed and simulated data. The workflow of assisted history matching is usually composed of three main procedures: experimental design, proxy modeling, and optimization. This work introduces a new assisted history matching workflow. The proposed workflow involves introducing a superior technique in each element of the typical assisted history matching workflow. Sobol sequence is the proposed experimental design technique whereas Kriging is used as the proxy modeling method. Three recently developed metaheuristic global optimization algorithms [firefly optimization (FFO), bee colony optimization (BCO), and harmony search optimization (HSO)] are used to optimize the created proxy model. The following part of this work presents the methodology followed to prove the superiority of the newly proposed technique(s) in each step of the three main steps of the assisted history matching procedure. To show the effectiveness of the proposed methods, their performance in solving assisted history matching problems is compared with the latest algorithms commonly used in commercial assisted history matching programs. Three synthetic history matching problems of different reservoir engineering applications with variable complexity are used as test problems to compare the results with each other and validate the work conclusions. A performance indicator is developed to quantify the relative error between the estimated values of history matching parameters using the studied algorithms and the exact solutions. The studied assisted history matching newly proposed techniques are applied on the three test problems and the results of each assisted history matching aspect are presented in the following section.

Assisted history matching (AHM) using Design of Experiments (DoE) is one of the most commonly applied history matching techniques in the oil and gas industry. When applied properly, this stochastic method finds a representative ensemble of history-matched reservoir models for probabilistic uncertainty analysis of production forecast. Although DoE-based AHM is straightforward in concept, it can be misused in practice because the workflow involves many statistical and modeling principles that should be followed rigorously. In this paper, the entire DoE-based AHM workflow is demonstrated in a coherent and comprehensive case study that is divided in seven key stages: problem framing, sensitivity analysis, proxy building, Monte-Carlo simulation, history-match filtering, production forecast, and representative model selection. Best practices of each stage are summarized to help reservoir management (RM) engineers understand and apply this powerful workflow for reliable history matching and probabilistic production forecasting. One major difficulty in any history matching method is to define the history-match tolerance, which reflects the engineer's comfort level of calling a reservoir model "history-matched" even though the difference between simulated and observed production data is not zero. It is a compromise to the intrinsic and unavoidable imperfectness of reservoir model construction, data measurement, and proxy creation. A practical procedure is provided to help engineers define the history-match tolerance considering the model, data-measurement, and proxy errors.