Development and Application of an Efficient Assisted History Matching Workflow Using Novel Algorithms

The significant increase in using reservoir simulation models poses significant challenges in the design and calibration of models. Moreover, conventional model calibration, history matching, is usually performed using a trial and error process of adjusting model parameters until a satisfactory match is obtained. In addition, history matching is an inverse problem, and hence it may have non-unique solutions. In typical reservoir simulation problems with a large number of unknown parameters, the problem could be ill-posed. In recent years, assisted history matching approach has been offered to solve this problem hopefully. In this paper, proposes an efficient assisted history matching workflow is recommended, and its application in a full field reservoir simulation model of a mature gas-cap reservoir is presented. In addition, Sobol sequence experimental design technique, Kriging proxy modeling, and three novel metaheuristic optimization algorithms are used to assist the history match of 28 years of historical production and pressure data. Finally, the results are compared with those obtained using a manual history matching procedure and with those obtained using the most widely used assisted history matching workflow. Also, in the proposed workflow, a significant improvement in terms of match quality and solution time is shown.

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.

Seismic data incorporation in reservoir simulation models history matching (HM) studies has been continuously growing. 4D seismic data, in contrast with well production data, can provide a very good scenario of fluids arrangement along reservoir. In this work we describe how 3D and 4D seismic data gathered in acquisitions performed in Campos Basin was incorporated in Marlim Sul deep water field geological model reconstruction and in assisted HM (AHM). It is taken advantage of both 3D and 4D seismic data in several stages of the study, for instance, in the construction of a new porosity – most influential in impedance – model by using a methodology based on the inversion of synthetic seismic (calculated by petro-elastic model) in porosity through an optimization process that aims to reduce the difference between observed and synthetic impedance, and when defining influential parameters based on fluids displacement registered by seismic signal, by using a technique based on the creation of transmissibility multipliers parameters regions that considers the fluids displacement shown in 4D signal. Another relevant point is the use of information from reservoir and 3D seismic data when weighting the 4D data in the objective function. Combining the above mentioned techniques with the knowledge of the field – supported by the 3D seismic data – which allowed, for instance, identification of faults – where fault transmissibility multipliers were used as parameters in the HM process – a fairly good agreement on the observed well and seismic production data was achieved. HM studies using AHM tools have been shown a much more time-efficient technique when compared to manual HM. The incorporation of 4D seismic data can considerably improve the HM quality by improving the reservoir description, once it increases the ability of describing fluids arrangement and pressure distribution. The techniques successfully applied in the Marlim Sul field HM support these conclusions.

Quantifying the uncertainty of reservoir models has always been considered as a major concern. Uncertainty and sensitivity analyses provide us with information about how "incorrect" a proposed prediction scenario is. One effective approach to quantify reservoir uncertainties is to apply the concept of Experimental Design. As the name indicates, experimental design is the technique used to guide the choice of the experiments to be conducted in an efficient way. Samples are selected in the design space of the uncertain parameters in order to obtain the maximum amount of information using low number of experiments. Geoscientists and engineers are building larger models to address reservoir heterogeneity and hence reservoir simulation is usually expensive (takes significant time to run). Experimental design techniques became very useful in assisted history matching. Several experimental design techniques are introduced in literature, some must be more effective than others in typical reservoir simulation problems. The objective of this paper is to compare different experimental design techniques and to introduce two efficient ones (Halton and Sobol sequences) to reservoir engineering problems. To show the potentiality and efficiency of the Halton and Sobol sequences design techniques, a comparative study is conducted to compare between their performance in solving assisted history matching problems and the performance of the most widely used experimental design technique, Latin hypercube. Other conventional techniques were compared too, but found to be less efficient than Latin hypercube. Two different scale reservoir models are used as test problems. A performance indicator is developed to compare between the three studied techniques in terms of the relative error between the estimated values of history matching parameters calculated using the proposed assisted history matching procedure and their exact solutions. The results of this work indicate that the Sobol and Halton sequences experimental design techniques are superior to Latin hypercube method.

Chapter 4 - Shale-gas well in Longmaxi Shale with bi-wing hydraulic fractures

Reservoir simulation plays an important role in managerial decisions during the life of a reservoir. Thus, it is vital that the simulations present an accurate prospect of real reservoir performance. The main goal of the History Matching (HM) process is to improve the quality of numerical models by contrasting simulated with observed data. A typical HM process evaluates a chosen objective function (OF) comprised by non-linear functions on the uncertain reservoir properties that measure the current mismatch. Thus, the HM problem is a minimization problem where the decision variables are reservoir characterization properties and the goal is to find a set of values for the decision variables that minimize the OF. This paper focuses on the use of an optimization technique called Scatter Search (SS) to perform the HM. The main feature of SS is that it works on a set of solutions called the reference set. The goal is to improve the overall quality of the reference set after each new iteration. New solutions are generated by a non-convex combination of reference solutions. The proposed methodology was used in both automatic and assisted HM processes and the analyzed reservoir models presented increasing challenges to the algorithm. This paper describes how the HM problem was solved with the SS framework, the expected performance of the methodology in dealing with complex solution spaces and also points how it can be expanded to better scale to a growing number of optimization parameters. The application of the SS methodology to the HM problem is a recent trend. Unlike most metaheuristics, SS can be effective even when the simulation time of each instance of the problem is long. Most of the current HM methodologies do not perform well when the solution space is both large and complex.

Over the past decades, Assisted History Matching has been the new norm for history matching that leverages the rapid advancement in digital computational performance. Continuous advancements such as parallel computing and GPU accelerates numerical simulation which overcomes the cumbersome experience of working with large fine-scaled model that mainly concerns the simulation time and intervention of engineers. As more interest emerges around artificial intelligence in the optimisation process, this paper explores the Artificial Intelligence algorithm to optimize two proxy modelling techniques: Quadratic Polynomial and Artificial Neural Network proxy model. These techniques are compared with stochastic optimisation method known as Differential Evolution algorithm on their efficiency of optimizing the objective functions, time taken, and knowledge investment needed by engineer, given today's hardware technology. This paper starts off by using Latin hypercube experimental design to generate first ensemble of simulation cases to generate proxy models to match the historical cumulative oil and water production by well level. The quality of both proxy modelling techniques is evaluated using R2 coefficient and proxy plot. Proxy models are then further validated by creating real simulation models from variants generated via Monte Carlo Analysis. The history matching quality and practicality were compared between the AI algorithm that runs optimizer on top of existing proxy models, and Differential Evolution algorithm in optimizing the regional porosity and permeability multipliers. The ANN proxy model prevailed over quadratic proxies to mimic the numerical reservoir model output with high degree of accuracy. The black-box nature of the ANN proxies limits the interpretability of predicted model when compared quadratic proxies where the formula for the proxy model can be obtained. Quadratic approximations are more flexible, simplistic in nature, and requires less computational cost to be constructed. Despite that, its prediction quality maybe subjected to the degree of non-linearity in the simulation model. The use of AI algorithm vastly reduces the number of full reservoir simulation required to achieve the minimum objective function at a shorter timeframe, which is proved to be the strength of such method. However, AI optimisation is highly susceptible to be trapped in local minimum. This paper proved the superiority of Differential Evolution algorithm over AI, that it may avoid being trapped in local minimum to achieve high degree of prediction accuracy for the history matching given the larger number of iterations required. This paper provides a preliminary understanding of optimisation workflow and how to go about each optimisation strategies: quadratic polynomial proxy, ANN proxy, stochastic optimisation, artificial intelligence techniques, and a novel approach of converting proxy predicted variants into real simulation cases to evaluate proxy quality. Hence establishes engineers’ expectation by appraising the pros and cons of each optimisation strategies.

This article, written by Technology Editor Dennis Denney, contains highlights of paper SPE 101933, "Improved and More- Rapid History Matching With a Nonlinear Proxy and Global Optimization," by A.S. Cullick, SPE, W.D. Johnson, SPE, and G. Shi, Landmark Graphics, prepared for the 2006 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 24–27 September. Generating reservoir-simulation models that match field production data has been a long-time industry challenge. Two workflows are presented for assisting history match. One workflow minimizes the misfit between simulated and historical data with a global optimizer. Another workflow trains a comprehensive nonlinear-proxy model with a small set of numerical simulations from experimental design to reduce the number of numerical simulations. Introduction History matching is, by its nature, an ill-posed optimization problem with many unknown reservoir parameters that could be adjusted to achieve a match against a relatively small amount of measured data at wells. The most common method of history match is to execute many simulations one at a time, changing a few parameters in a trial-and-error fashion. Often, a reservoir-simulation history match might require months of effort and many simulations to achieve a single model that neglects model nonuniqueness and often may not be a good predictor of future field performance. Many automated history-match algorithms have been investigated. Early assisted history matching emphasized deterministic gradient-optimization algorithms that require complete derivatives of the production response with respect to reservoir parameters. Subsequently, the emphasis evolved to faster methods to compute the sensitivity coefficients, such as streamline simulation, with emphasis on preserving uncertainty through the integration of geostatistics. Recent developments with adjoint models have renewed interest in sensitivity-based algorithms. However, none of these methods have been taken up widely by practitioners. With black-box optimization, the number of required simulations to achieve a match can be very large, numbered in the hundreds of simulations. If a single simulation model takes many hours to execute, there is good incentive to reduce the number of simulations for the optimization, even with the use of a distributed-computing system. This study used a global optimizer, while seeking to reduce the number of simulations with a fast proxy model. The use of proxy-regression models has been suggested to reduce the number of required simulations, but analytical-response models may not be sufficiently robust to represent the nonlinear reservoir production and pressure vs. time profile data. The use of neural networks as nonlinear-proxy models also has been suggested. In this paper, a history-match workflow is presented that has a robust, nonlinear neural-network proxy model to improve a history match and reduce the number of finite-difference simulations required.

Traditional reconciliation of geomodels with production data is one of the most laborious tasks in reservoir engineering. The uncertainty associated with the great majority of model variables only adds to the overall complexity. This paper describes the conceptualization, implementation, and visualization characteristics of the multilevel assisted history matching (AHM) technique that captures inherent model uncertainty and allows for better quantification of production forecasts. The workflow is applied to history matching of the pilot area in a major, structurally complex Middle East (ME) carbonate reservoir. The simulation model combines 49 wells in five waterflood patterns to match 50 years of oil production and 12 years of water injection and to predict eight years of production. Initially, the reservoir model was calibrated to match oil production by modifying permeability and/or porosity at well locations and by fine-tuning rock-type properties and water saturation. The second level history match implemented two-stage Markov chain Monte Carlo (McMC) stochastic optimization to minimize the misfit in water cut on a well-by-well basis. The inversion process is dramatically accelerated by the efficient parameterization of permeability, constraining the proxy model using streamline-based sensitivities and using parallel and cluster computing. The optimal number of representative history-matched models was identified to capture the uncertainty in reservoir spatial connectivity using rigorous optimization and dynamic model ranking based on forecasted oil recovery factors (ORFs). The reduced set of models minimized the computational load for forecast-based analysis, while retaining the knowledge of the uncertainty in the recovery factor. The comprehensive probabilistic AHM workflow was implemented at the operator's North Kuwait Integrated Digital Oilfield (KwIDF) collaboration center. It delivers an optimized reservoir model for waterflood management and automatically updates the model quarterly with geological, production, and completion information. This allows engineers to improve the reservoir characterization and identify the areas that require more data capture.

History matching is a challenging reverse problem due to the inherited uncertainty from Earth modeling. History matching process mandates building one or more sets of representative reservoir models with minimum misfit between the reservoir models and observed field data. There are several commercial assisted history matching tools and workflows to facilitate and orchestrate this process. This paper provides performance assessment and process evaluation between two of the commonly used optimization algorithms: the Evolutionary Algorithm (EA) and the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) in an automated and closed loop workflows. The workflow starts with a parametrization step to identify and quantify the static and dynamic uncertainties in the reservoir model. The objective function is then constructed to guide and measure the convergence of the optimization process. The workflow is then executed to start the model calibration and history matching process. The algorithms, EA and ES-MDA, take different routes during the optimization process. EA works by selecting the best cases (i.e. most fitting genes that resulted in a minimum misfit) in each cycle, and generates a number of simulation cases (new generation) based on the predefined gene selection criteria. The iterative ES-MDA algorithm maintains the same number of simulation cases in each iteration (as many as in the initial Ensemble) throughout the assimilation process. The EA and ES-MDA optimization algorithms have their advantages and disadvantages to the history matching process. For instance, both workflows preserve the geological consistency with the dynamic reservoir models. The automation that both workflows provide incorporates G&G (Geological and Geophysical) workflows to capture, and carryover the static uncertainty to ensure consistency throughout the history matching process. In addition, in both cases, multiple simulation models are generated to cover reservoir static and dynamic uncertainties, which are crucial to the predictive capabilities of the history matched models. Both algorithms, as known, are stochastics in nature (i.e. cannot guarantee one deterministic solution) and, therefore. the results are highly dependent on the initial ensemble. EA is highly effective in searching the solution space, it requires a large number of simulation runs to converge a solution. On the other hand, ES-MDA does not exceed the number of initial ensembles in each iteration regardless of the number of iterations. This paper presents an automated workflow that leads to multiple reliable history matched simulation models. All of the generated models are geologically consistent and capture all model uncertainties that are needed to be preserved and carried forward in prediction. Moreover, this helps in updating the models seamlessly whenever new data is available by simply re-running the workflow with the model updates.

Technology Focus Many reservoir engineers dislike the very idea of automatic history matching applied to real full-field studies. They believe there is no artificial substitute for experienced reasoning, deep understanding of the reservoir mechanisms, and attention to real-life practical aspects of the problem. Some use terms such as art and intuition. For them, even if computers long ago learned to play chess, computers will never be able to perform real-case history matching on their own or at least they are still too far from this achievement. Very often, during technical sessions, immediately following an advanced mathematical presentation on history matching, someone in the audience makes his or her point about the limits of automatic approaches. To avoid disputes, experienced speakers prefer less pretentious expressions such as assisted or semiautomatic history matching. Indeed, history matching can be seen as a two-step iterative process, normally requiring many cycles to be completed. Broadly speaking, the first step is about analysis and setting the problem parameters, and the second step is about searching for and computing solutions. We start our discussion with the second part, which has a more obvious algorithmic nature. There has being a great deal of research and progress in this area. The ensemble Kalman filter is dominating the scene, but gradient-based methods and global-optimization stochastic methods are attracting merited attention. Most published contributions come from universities, and, typically, papers include examples to demonstrate successful algorithm application. These examples can be simple synthetic or somewhat-more-realistic cases, but the discussion is naturally focused on the solution method and not on the entire problem as found in the field. The first part of the problem is less mathematized, for now, and involves essential tasks such as to be clear about the practical purposes and requirements in the particular context; to have a full understanding of the quality of the reservoir model and the production data; to design or redesign well-justified objective functions; to set adequate parameterization, considering the main uncertainties and their effect on the simulation results; to represent properly and sample the uncertainty space; and to evaluate results from the previous steps of the history-matching process judiciously. Unfortunately, the strategies used to consider this part of the problem are much less discussed and documented. In fact, many of these tasks are open to further formalization and, ultimately, can be automated also. We definitely need more papers illuminating these other aspects of the reservoir-engineering problem, instead of relying on intuition. Recommended additional reading at OnePetro: www.onepetro.org. SPE 146292 Practical Assisted History Matching and Probabilistic Forecasting Procedure: A West Africa Case Study by B.O. Dujardin, SPE, Chevron, et al. SPE 141929 An Ensemble Smoother for Assisted History Matching by J.-A. Skjervheim, Statoil, et al. SPE 142497 Advanced History-Matching Techniques Reviewed by R. Rwechungura, Norwegian University of Science and Technology, et al. SPE 143067 History Matching and Uncertainty Quantification: Multiobjective Particle-Swarm-Optimization Approach by Linah Mohamed, SPE, Heriot-Watt University, et al.

History matching a field's performance to understand the reservoir behavior and characterize its static and dynamic properties has been a key activity for reservoir engineers for a long time. Recently, significant effort has been made to devise techniques that allow this process to be automated. These techniques suffer with a number of limitations and often yield History Match (HM) solution points in the uncertainty space that carry certain bias inherent to the algorithm used. Common limitations include:Techniques more often failing to yield any realization with acceptable HM quality at the well levels,Large number of iterations and simulation runs required to minimize the HM errors to acceptable values and,Significant volume of information generated during this iterative process, which becomes unmanageable to interpret and reconcile. Consequently, the assisted HM unfortunately becomes just an iterative process of minimizing the objective function, and the main goal of understanding the reservoir performance gets diluted. When these techniques are applied for Enhanced Oil Recovery (EOR) studies, the list of uncertainty parameters becomes very extensive due to the addition of parameters defining the EOR process itself. As a result, the number of scenarios increases in addition simulations tend to become slower due to incorporation of EOR module and model requirements for space and time resolution to simulate physio-chemical phenomena. Traditional HM techniques then become cumbersome which might lead to inadequate characterization of the potential upside and downside scenarios. This in turn could adversely impact business decisions involving huge capital investments for any field (re-)development opportunities. This paper will discuss a technique that evolved during the HM exercise for an EOR pilot area in the Middle East. The methodology preserves the idea of Assisted History Match (AHM) to generate multiple HM realizations, however, the solution points are found much quicker eliminating large number of iterations, thereby minimizing the computational expense. The devised methodology is based on the combination of Design of Experiment (DoE) based Stochastic Uncertainty Management (SUM) workflow with the gradient based calculation (Adjoint) approach to find multiple HM realizations. First, a complete stochastic uncertainty management workflow is applied sampling the entire uncertainty space and multiple realizations are screened ensuring enough variability in parameters and acceptable HM error. The gradient based calculations are then applied on each of these selected realizations to further minimize the HM error. The Adjoint method yields final set of improved HM realizations with different starting points in the solution space that were obtained via DoE. This helps in two ways – firstly, it covers the entire uncertainty space for better characterization of upside and downside cases and secondly, provides a focused view of the reservoir characteristics. Additionally, the paper would also offer insights gained from the HM exercise into water coning behavior in a viscous oil reservoir and illustrate the reservoir parameters and their significance that need to be addressed to adequately capture the coning phenomenon.

One of a key responsibility for oil and gas industry is to ensure the balance between energy sustainability and minimizing the net carbon footprint to the environment. PTTEP, Thai national oil and gas company, has aligned this goal to achieve net zero greenhouse gas emission in 2050. Therefore, the scope of this project is to utilize carbon capture and storage (CCS) technology by injecting CO2 into the depleted reservoirs in the Gulf of Thailand. To evaluate the feasibility of the project, the simulation model was required to mimic the physics behaviors, including free gas structural storage, residual trapping, soluble gas in water and mineralization, when the CO2 was injected into many layers of depleted reservoirs. This is to obtain the optimized scenario for CO2 injection. However, the key step for reservoir simulation is the history matching by calibrating the model with production data. First, the static model was built by integrating geological understanding, well data, logging data and petrophysical interpretation, core data, and quantitative interpretation (QI) from seismic data. Then, the subsurface uncertainties were captured and transferred to dynamic model for history matching step. The sensitivity analysis was performed to understand causes and effects and determine the significant uncertain parameters. Then, the assisted history matching was performed to explore the possible solutions using evolutionary algorithm. Lastly, multiple realizations of history matching solutions were obtained. From sensitivity analysis, the key parameters to be calibrated with production data and routine shut-in bottomhole surveys are gas-water contacts, porosity and permeability correlation and relative permeability endpoint parameters. From history matching solutions, we narrowed down the range of uncertainty of uncertain parameters during history matching. The pressure, gas and water production could be matched. Obtaining the calibrated model from history matching is the critical step because this will determine the feasibility of the project in terms of injection strategy and CO2 storage volume. This study was the first history matching task performed for Thailand CCS project. The practical and robust history matching workflow used in this CCS project could be set as a milestone and provides the guideline how to implement assisted history matching technique for any future CCS projects.

The current practices of assisted and automated history matching refer only to specific methods to address the optimization problem in history matching, but never span over the complete workflow. Computational power and the development of sophisticated software should allow us today to capture the whole workflow and automate it rather than just a piece of it (usually the regression method). The approach presented in this paper is based on the principle of domain decomposition. The reservoir history matching (HM) problem is decomposed into smaller and smaller pieces (from reservoir to region, from region to layer) to allow a refinement of the final result and hence the HM quality. The decomposition of the problem can be commenced by introducing time dependent well influence areas. These areas are sub-divisions of previous decomposition processes, as there are lithofacies types, clusters, flow units and vintage intervals. For the time dependent "influence areas", the success of the optimization can be tracked over the sequential iterations as well as across the different realizations. The progress of the most sensitive parameters can be tracked and successful strategies can be applied to other, similar areas of each realization. Finally, the interference of the influence areas has to be accounted for in the selection of the parameter values in each of the regression loops. A smart expert system that includes machine-learning techniques (cognitive agents) is used to drive the global history matching process, control the sub-domains and find the best parameter combination amongst all influence areas. The approach presented in this paper allows an automated history matching process, which is scalable for very large reservoir models. Relying on smart run selection and cluster technology even large models (many hundreds to thousands of wells) can be successfully matched in a reasonable amount of time. As the system is reservoir independent and learning from human experts, less and less user input is necessary over time leading to an autonomous history-matching agent.

The applications of numerical simulation modeling such as assisted history matching, production optimization, and reservoir performance forecasting usually lead to significant time, computer resources, and accordingly huge associated costs. To overcome these circumstances, proxy modeling is the suggested approach to deliver a cheap alternative and approximate nonlinear oil and gas reservoir responses such as recovery factor and reservoir operating parameters and characteristics. Proxy modeling is considered a powerful tool for optimization and uncertainty analysis alike. Conventionally, the reservoir simulation is solved by tuning selected uncertain reservoir parameters one at a time. While, the most important feature of proxy modeling is the ability to determine the combined effect of uncertain parameters at the same time. Petroleum engineering field usually requires a wide variety of parameter estimation problems, and proxy modeling can satisfy this demand. Proxy modeling can be developed based on different methods; the current paper presents a comprehensive review of the methods of developing of proxy modeling and their applications in reservoir simulation since proxy modeling is becoming more widely used as a simplify highly complex substitution to reservoir simulation with reasonable accuracy. This article reviews the methods used in recent years to develop proxy models as a successful replica of complex numerical flow simulation models. This will shed the light of different proxy models, their uses, and how to judge on their efficiencies.