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The production performances of fractured tight gas wells are closely related to several complex and unknown factors, including the formation properties, fracture parameters, gas–water two-phase flow, and other nonlinear flow mechanisms. The rate transient analysis (RTA) results have significant uncertainties, which should be quantified to evaluate the formation and fracturing treatment better. This paper provides an efficient method for uncertainty quantification in the RTA of fractured tight gas wells with multiple unknown factors incorporated. The theoretical model for making forward predictions is based on a trilinear flow model, which incorporates the effects of two-phase flow and other nonlinear flow mechanisms. The normalized rates and material balance times of both water and gas phases are regarded as observations and matched with the theoretical model. The unknowns in the model are calibrated using the ensemble Kalman filter (EnKF), which applies an ensemble of multiple realizations to match the observations and updates the unknown parameters step by step. Finally, a comprehensive field case from Northwestern China is implemented to benchmark the proposed method. The results show that the parameters and rate transient responses have wide ranges and significant uncertainties before history matching, while all the realizations in the ensemble can have good matches to the field data after calibration. The posterior distribution of each unknown parameter in the model can be obtained after history matching, which can be used to quantify the uncertainties in the RTA of the fractured tight gas wells. The ranges and uncertainties of the parameters are significantly narrowed down, but the parameters are still with significant uncertainties. The main contribution of the paper is the provision of an efficient integrated workflow to quantify the uncertainties in RTA. It can be readily used in field applications of multi-fractured horizontal wells from tight gas reservoirs. [ABSTRACT FROM AUTHOR]

Energy models require accurate calibration to deliver reliable predictions. This study offers statistical guidance for a systematic treatment of uncertainty before and during model calibration. Statistical emulation and history matching are introduced. An energy model of a domestic property and a full year of observed data are used as a case study. Emulators, Bayesian surrogates of the energy model, are employed to provide statistical approximations of the energy model outputs and explore the input parameter space efficiently. The emulator's predictions, alongside quantified uncertainties, are then used to rule out parameter configurations that cannot lead to a match with the observed data. The process is automated within an iterative procedure known as history matching (HM), in which simulated gas consumption and temperature data are simultaneously matched with observed values. The results show that only a small percentage of parameter configurations (0.3% when only gas consumption is matched, and 0.01% when both gas and temperature are matched) yielded outputs matching the observed data. This demonstrates HM's effectiveness in pinpointing the precise region where model outputs align with observations. The proposed method is intended to offer analysts a robust solution to rapidly explore a model's response across the entire input space, rule out regions where a match with observed data cannot be achieved, and account for uncertainty, enhancing the confidence in energy models and their viability as a decision support tool. [ABSTRACT FROM AUTHOR]

Copyright of Geology & Exploration is the property of Geology & Exploration Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

ABSTRACT Reservoir models for predicting subsurface fluid and rock behaviors can now include upwards of billions (and potentially trillions) of grid cells and are pushing the limits of computational resources. History matching, where models are updated to match existing historical data more closely, is conducted to reduce the number of simulation runs and is one of the primary time‐consuming tasks. As models get larger the number of parameters to match increases, and the number of objective functions increases, and traditional methods start to reach their limitations. To solve this, we propose the use of Bayesian optimization (BO) in a hybrid cloud framework. BO iteratively searches for an optimal solution in the simulations campaign through the refinement of a set of priors initialized with a set of simulation results. The current simulation platform implements grid management and a suite of linear solvers to perform the simulation on large scale distributed‐memory systems. Our early results using the hybrid cloud implementation shown here are encouraging on tasks requiring over 100 objective functions, and we propose integrating BO as a built‐in module to efficiently iterate to find an optimal history match of production data in a single package platform. This paper reports on the development of the hybrid cloud BO based history matching framework and the initial results of the application to reservoir history matching.

Abstract The calibration of reservoir models using production data can enhance the reliability of predictions. However, history matching often leads to only a few matched models, and the original geological interpretation is not always preserved. Therefore, there is a need for stochastic methodologies for history matching. The Ensemble Kalman Filter (EnKF) is a well-known Monte Carlo method that updates reservoir models in real time. When new production data becomes available, the ensemble of models is updated accordingly. The initial ensemble is created using the prior model, and the posterior probability function is sampled through a series of updates. In this study, EnKF was employed to evaluate the uncertainty of production forecasts for a specific development plan and to match historical data to a real field reservoir model. This study represents the first attempt to combine EnKF with an integrated model that includes a genuine oil reservoir, actual production wells, a surface choke, a surface pipeline, a separator, and a PID pressure controller. The research optimized a real integrated production system, considering the constraint that there should be no slug flow at the inlet of the separator. The objective function was to maximize the net present value (NPV). Geological data was used to model uncertainty using Sequential Gaussian Simulation. Porosity scenarios were generated, and conditioning the porosity to well data yielded improved results. Ensembles were employed to balance accuracy and efficiency, demonstrating a reduction in porosity uncertainty due to production data. This study revealed that utilizing a PID pressure controller for the production separator can enhance oil production by 59% over 20 years, resulting in the generation of 2.97 million barrels of surplus oil in the field and significant economic gains.

Breaking atmospheric gravity waves (GWs) in the tropical stratosphere are essential in driving the roughly 2‐year oscillation of zonal winds in this region known as the Quasi‐Biennial Oscillation (QBO). As Global Climate Models (GCM)s are not typically able to directly resolve the spectrum of waves required to drive the QBO, parameterizations are necessary. Such parameterizations often require knowledge of poorly constrained physical parameters. In the case of the spectral gravity parameterization used in this work, these parameters are the total equatorial GW stress and the half width of phase speed distribution. Radiosonde observations are used to obtain the period and amplitude of the QBO, which are compared against values obtained from a GCM. We utilize two established calibration techniques to obtain estimates of the range of plausible parameter values: History matching & Ensemble Kalman Inversion (EKI). History matching is found to reduce the size of the initial range of plausible parameters by a factor of 98%, requiring only 60 model integrations. EKI cannot natively provide any uncertainty quantification but is able to produce a single best estimate of the calibrated values in 25 integrations. When directly comparing the approaches using the Calibrate, Emulate, Sample method to produce a posterior estimate from EKI, history matching produces more compact posteriors with fewer model integrations at lower ensemble sizes compared to EKI; however, these differences become less apparent at higher ensemble sizes. Plain Language Summary: Atmospheric gravity waves (GWs) are buoyancy driven oscillations which propagate through the atmosphere and deposit momentum where they break. This momentum exchange plays a significant role in setting various large‐scale atmospheric phenomena, of which a prominent example is the Quasi‐Biennial Oscillation (QBO), a roughly 2‐year oscillation of winds in the tropical stratosphere. Many of the waves responsible for creating these large scale patterns are too small to be simulated by climate models. Thus, we use parameterizations to estimate their impact on the large scale. These parameterizations have settings that require tuning, to enable the model to produce variability that matches the observed climate. In this work, we utilize and compare two techniques: History matching and Ensemble Kalman Inversion. These methods are combined with observations of the QBO to tune the settings for the GW parameterization. Key Points: History matching and Ensemble Kalman Inversion (EKI) were used to calibrate two parameters in a gravity wave parameterization to Quasi‐Biennial Oscillation observationsHistory matching was found to rapidly and compactly produce an estimate of the plausible space of parameters when compared to EKIEKI was found to be strong at single best estimates of the calibrated parameters at low ensemble sizes requiring few iterations [ABSTRACT FROM AUTHOR]

Coalbed methane (CBM) pilot wells typically exhibit a short production period, necessitating evaluation of their estimated ultimate recovery (EUR) through numerical simulation. Utilizing limited geological data from the pilot areas to finish history matching and subsequent production forecasting presents substantial challenges. This paper introduces a comprehensive numerical simulation workflow for CBM pilot wells, encompassing the following steps. Initially, geological parameters are categorized into two groups based on their statistical distribution trends: trend parameters (i.e., gas content, permeability, Langmuir volume, and Langmuir pressure) and non-trend parameters (i.e., fracture porosity, gas–water relative permeability, and rock compressibility). The probability method is employed to ascertain the probable high and low limits for trend parameter distributions, while empirical or analogous methods are applied to define the boundaries for non-trend parameters. Subsequently, the parameter sensitivity analysis is conducted to understand the influence of varying parameters on cumulative gas and water production. Conclusively, experimental design algorithms generate over 100 simulation cases using the identified sensitive parameters, from which the top ten optimal cases are chosen for EUR prediction. This workflow features two technological innovations: (1) considering the most comprehensive set of reservoir parameters for uncertainty and sensitivity analyses, and (2) considering the matching accuracy of both cumulative production and dynamic production trends when selecting optimal matching cases. This approach was successfully implemented in the C pilot area of the Bowen Basin, Australia. In addition, it offers valuable insights for numerical simulation of unconventional natural gases, such as shale gas. [ABSTRACT FROM AUTHOR]

Abstract Breaking atmospheric gravity waves (GWs) in the tropical stratosphere are essential in driving the roughly 2‐year oscillation of zonal winds in this region known as the Quasi‐Biennial Oscillation (QBO). As Global Climate Models (GCM)s are not typically able to directly resolve the spectrum of waves required to drive the QBO, parameterizations are necessary. Such parameterizations often require knowledge of poorly constrained physical parameters. In the case of the spectral gravity parameterization used in this work, these parameters are the total equatorial GW stress and the half width of phase speed distribution. Radiosonde observations are used to obtain the period and amplitude of the QBO, which are compared against values obtained from a GCM. We utilize two established calibration techniques to obtain estimates of the range of plausible parameter values: History matching & Ensemble Kalman Inversion (EKI). History matching is found to reduce the size of the initial range of plausible parameters by a factor of 98%, requiring only 60 model integrations. EKI cannot natively provide any uncertainty quantification but is able to produce a single best estimate of the calibrated values in 25 integrations. When directly comparing the approaches using the Calibrate, Emulate, Sample method to produce a posterior estimate from EKI, history matching produces more compact posteriors with fewer model integrations at lower ensemble sizes compared to EKI; however, these differences become less apparent at higher ensemble sizes.

Considering the pore deformation and permeability changes during dilation-recompaction in cyclic steam stimulation (CSS), an existing geomechanical model is improved and thermo-mechanically coupled with the flow equations to form a coupled flow-geomechanical model. The impacts of dilation-recompaction parameters can be quantified through sensitivity analysis and uncertainty assessment utilizing the synergy between Latin hypercube designs and response surface methodology. The improved coupled flow-geomechanical model allows a more reasonable history-matching of steam injection pressure and volume and oil/water production volume. In both the linear and quadratic models, the rise in recompaction pressure has the most significant effect on the rise in the volumes of steam injection and water production, both rock compressibility and recompaction pressure are positively correlated with steam injectivity and oil/water production, and the dilation pressure is negatively correlated with steam injectivity and oil/water production. In the linear model, dilation pressure has the most significant negative impact on the cumulative oil production, and compressibility and recompaction pressure are positively correlated with oil production. In the quadratic model, the rise in recompaction pressure has the most significant effect on the rise in the cumulative volumes of oil/water production and steam injection. The interactions between the dilation/recompaction pressures and spongy-rock compressibility negatively affect the cumulative volumes of oil/water production and steam injection.

Energy models require accurate calibration to deliver reliable predictions. This study offers statistical guidance for a systematic treatment of uncertainty before and during model calibration. Statistical emulation and history matching are introduced. An energy model of a domestic property and a full year of observed data are used as a case study. Emulators, Bayesian surrogates of the energy model, are employed to provide statistical approximations of the energy model outputs and explore the input parameter space efficiently. The emulator’s predictions, alongside quantified uncertainties, are then used to rule out parameter configurations that cannot lead to a match with the observed data. The process is automated within an iterative procedure known as history matching (HM), in which simulated gas consumption and temperature data are simultaneously matched with observed values. The results show that only a small percentage of parameter configurations (0.3% when only gas consumption is matched, and 0.01% when both gas and temperature are matched) yielded outputs matching the observed data. This demonstrates HM’s effectiveness in pinpointing the precise region where model outputs align with observations. The proposed method is intended to offer analysts a robust solution to rapidly explore a model’s response across the entire input space, rule out regions where a match with observed data cannot be achieved, and account for uncertainty, enhancing the confidence in energy models and their viability as a decision support tool.

The use of 4D seismic data in history matching has been a topic of great interest in the hydrocarbon industry as it can provide important information regarding changes in subsurfaces caused by fluid substitution and other factors where well data is not available. However, the high dimensionality and uncertainty associated with seismic data make its integration into the history-matching process a challenging task. Methods for adequate data reduction have been proposed in the past, but most address 4D information mismatch from a purely mathematical or image distance-based standpoint. In this study, we propose a quantitative and flow-based approach for integrating 4D seismic data into the history-matching process. By introducing a novel distance parametrization technique for measuring front mismatch information using streamlines, we address the problem from a flow-based standpoint; at the same time, we maintain the amount of necessary front data at a reduced and manageable amount. The proposed method is tested, and its results are compared on a synthetic case against another traditional method based on the Hausdorff distance. The effectiveness of the method is also demonstrated on a semi-synthetic model based on a real-case scenario, where the standard Hausdorff methodology could not be applied due to high data dimensionality. [ABSTRACT FROM AUTHOR]

Copyright of Iraqi Journal of Chemical & Petroleum Engineering is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Rapid technological advances have accelerated offshore and onshore tight oil extraction to meet growing energy demand. Reliable tools to carry out production prediction are essential for development of unconventional reservoirs. The existed tri-linear analytical solutions are verified to be versatile enough to capture fundamental flow mechanisms and make accurate production predictions. However, these solutions are obtained in Laplace space with the Laplace transform and numerical inversion, which may lead to uncertainty in the solution. In this paper, a general analytical solution is derived in real-time space through integral transform and average pressure substitution. Namely, the partial differential equations describing subsurface fluid flow are firstly triple-integrated and then the obtained volume average pressure are replaced with the rate-dependent expressions. Furthermore, the ordinary differential equations related to oil rate are solved analytically in real-time space. To validate our model, this derived solution is verified against two numerical models constructed with two typical physical configurations. The great match indicates the accuracy and applicability of the analytical solution. According to the developed workflow, two field cases including offshore and onshore tight oilfield data are selected for history matching and production prediction. This new approach not only makes the obtained solution more simplified, but also helps field engineers diagnose flow patterns more quickly to better optimize production schemes. [ABSTRACT FROM AUTHOR]

Characterization of large reservoir models with a great number of uncertain parameters is frequently carried out by ensemble-based assimilation methods, due to their computational efficiency, ease of implementation, versatility, and non-necessity of adjoint code. In this study, multiple ensemble-based assimilation techniques are utilized to characterize the well-known PUNQ-S3 model. Accordingly, actual measurements are employed to determine porosity, horizontal and vertical permeabilities, and their associated uncertainties. In consequence, the uncertain parameters of the model will gradually be adapted toward the true values during the assimilation of actual measurements, including bottomhole pressure and production rates of the reservoir. Monotonic reduction of root-mean-squared error and capturing the key points of the maps (such as direction of anisotropy and porosity/permeability contrasts) verify successful estimation of the geostatistical properties of the PUNQ-S3 model during history matching. At the end of the assimilation process, the RMSE values for Deterministic Ensemble Kalman Filter, Ensemble Kalman Filter, Ensemble Kalman Filter with Bootstrap Regularization, Ensemble Transform Kalman Filter Symmetric Solution, Ensemble Transform Kalman Filter Random Rotation, and Singular Evolutive Interpolated Kalman filter are 1.120, 1.153, 1.132, 1.132, 1.129, and 1.113, respectively. In addition to RMSE, the quality of history match as well as prediction of future performance are looked into in order to assess the performance of the assimilation process. Obviously, the results of the ensemble-based assimilation methods closely match the true results both in the history match section and in the future prediction section. Besides, the uncertainty of future predictions is quantified using multiple history-matched realizations. This is due to the fact that Kalman-based filters use a Bayesian framework in the assimilation step. Accordingly, the updated ensemble members are samples of the posterior distribution through which the uncertainty of future performance is assessed.

This paper proposes a methodology for an alternative history matching process enhanced by the incorporation of a simplified binary interpretation of reservoir saturation logs (RST) as objective function. Incorporating fluids saturation logs during the history matching phase unlocks the possibility to adjust or select models that better represent the near wellbore waterfront movement, which is particularly important for uncertainty mitigation during future well interference assessments in water driven reservoirs. For the purposes of this study, a semi-synthetic open-source reservoir model was used as base case to evaluate the proposed methodology. The reservoir model represents a water driven, highly heterogenous sandstone reservoir from Namorado field in Brazil. To effectively compare the proposed methodology against the conventional methods, a commercial reservoir simulator was used in combination with a state-of-the-art benchmarking workflow based on the Big Loop™ approach. A well-known group of binary metrics were evaluated to be used as the objective function, and the Matthew correlation coefficient (MCC) has been proved to offer the best results when using binary data from water saturation logs. History matching results obtained with the proposed methodology allowed the selection of a more reliable group of reservoir models, especially for cases with high heterogeneity. The methodology also offers additional information and understanding of sweep behaviour behind the well casing at specific production zones, thus revealing full model potential to define new wells and reservoir development opportunities.

In recent years, Machine Learning (ML) has become a buzzword in the petroleum industry, with numerous applications which guide engineers in better decision making. The most powerful tool that most production development decisions rely on is reservoir simulation with applications in multiple modeling procedures, such as individual simulation runs, history matching and production forecast and optimization. However, all of these applications lead to considerable computational time and computer resource-associated costs, rendering reservoir simulators as not fast and robust enough, and thus introducing the need for more time-efficient and intelligent tools, such as ML models which are able to adapt and provide fast and competent results that mimic the simulator's performance within an acceptable error margin. In a recent paper, the developed ML applications in a subsurface reservoir simulation were reviewed, focusing on improving the speed and accuracy of individual reservoir simulation runs and history matching. This paper consists of the second part of that study, offering a detailed review of ML-based Production Forecast Optimization (PFO). This review can assist engineers as a complete source for applied ML techniques in reservoir simulation since, with the generation of large-scale data in everyday activities, ML is becoming a necessity for future and more efficient applications. [ABSTRACT FROM AUTHOR]

Characterization of large reservoir models with a great number of uncertain parameters is frequently carried out by ensemble-based assimilation methods, due to their computational efficiency, ease of implementation, versatility, and non-necessity of adjoint code. In this study, multiple ensemble-based assimilation techniques are utilized to characterize the well-known PUNQ-S3 model. Accordingly, actual measurements are employed to determine porosity, horizontal and vertical permeabilities, and their associated uncertainties. In consequence, the uncertain parameters of the model will gradually be adapted toward the true values during the assimilation of actual measurements, including bottomhole pressure and production rates of the reservoir. Monotonic reduction of root-mean-squared error and capturing the key points of the maps (such as direction of anisotropy and porosity/permeability contrasts) verify successful estimation of the geostatistical properties of the PUNQ-S3 model during history matching. At the end of the assimilation process, the RMSE values for Deterministic Ensemble Kalman Filter, Ensemble Kalman Filter, Ensemble Kalman Filter with Bootstrap Regularization, Ensemble Transform Kalman Filter Symmetric Solution, Ensemble Transform Kalman Filter Random Rotation, and Singular Evolutive Interpolated Kalman filter are 1.120, 1.153, 1.132, 1.132, 1.129, and 1.113, respectively. In addition to RMSE, the quality of history match as well as prediction of future performance are looked into in order to assess the performance of the assimilation process. Obviously, the results of the ensemble-based assimilation methods closely match the true results both in the history match section and in the future prediction section. Besides, the uncertainty of future predictions is quantified using multiple history-matched realizations. This is due to the fact that Kalman-based filters use a Bayesian framework in the assimilation step. Accordingly, the updated ensemble members are samples of the posterior distribution through which the uncertainty of future performance is assessed. [ABSTRACT FROM AUTHOR]

The objective of this study is to evaluate the potential for History Matching (HM) to tune a climate system with multi‐scale dynamics. By considering a toy climate model, namely, the two‐scale Lorenz96 model and producing experiments in perfect‐model setting, we explore in detail how several built‐in choices need to be carefully tested. We also demonstrate the importance of introducing physical expertise in the range of parameters, a priori to running HM. Finally we revisit a classical procedure in climate model tuning, that consists of tuning the slow and fast components separately. By doing so in the Lorenz96 model, we illustrate the non‐uniqueness of plausible parameters and highlight the specificity of metrics emerging from the coupling. This paper contributes also to bridging the communities of uncertainty quantification, machine learning and climate modeling, by making connections between the terms used by each community for the same concept and presenting promising collaboration avenues that would benefit climate modeling research. Plain Language Summary: Climate models are computer simulation codes that incorporate centuries of human knowledge of the physics of planet Earth. They are used to understand the past, the present and make projections about the future of our climate. To validate a climate model, scientists tune a number of its parameters so that it yields a simulated climate resembling real‐life observations as much as possible. The main challenge in this tuning task is the extreme cost of climate models which limits a lot the number of tuning experiments scientists can run. In this paper we are interested in a technique that uses artificial intelligence in order to replace the expensive climate model with a cheaper surrogate. We experiment on a simplified model to assess the strengths and weaknesses of this semi‐automatic technique, and show that it can be more efficient when combined with human expertise. Key Points: The History Matching method is explained in detail then used for tuning a toy coupled model: the Lorenz 96 modelThe importance of several design choices is demonstrated, especially when considering forced experiments such as Atmospheric Model Intercomparison Protocol and Ocean Model Intercomparison ProjectWe argue that this tuning method is semi‐automatic & highlight the importance of human expertise when considering it for real coupled models [ABSTRACT FROM AUTHOR]

Abstract The objective of this study is to evaluate the potential for History Matching (HM) to tune a climate system with multi‐scale dynamics. By considering a toy climate model, namely, the two‐scale Lorenz96 model and producing experiments in perfect‐model setting, we explore in detail how several built‐in choices need to be carefully tested. We also demonstrate the importance of introducing physical expertise in the range of parameters, a priori to running HM. Finally we revisit a classical procedure in climate model tuning, that consists of tuning the slow and fast components separately. By doing so in the Lorenz96 model, we illustrate the non‐uniqueness of plausible parameters and highlight the specificity of metrics emerging from the coupling. This paper contributes also to bridging the communities of uncertainty quantification, machine learning and climate modeling, by making connections between the terms used by each community for the same concept and presenting promising collaboration avenues that would benefit climate modeling research.

This paper describes testing of the INSIM-FT proxy simulation method (interwell-numerical-simulation model improved with front-tracking method) to assess the dependencies between production and injection wells, as well as to assess the forecast of oil/liquid production by wells depending on their operation parameters. The paper proposes the approach of taking into account the influence of various production enhancement operations. The method was tested on a synthetic hydrodynamic model and on a sector of a real field. The results show a good match between historical data and simulation results and indicate significant computational efficiency compared to classical reservoir simulators. [ABSTRACT FROM AUTHOR]

Reformulating the history matching problem from a least-square mathematical optimization problem into a Markov Decision Process introduces a method in which reinforcement learning can be utilized to solve the problem. This method provides a mechanism where an artificial deep neural network agent can interact with the reservoir simulator and find multiple different solutions to the problem. Such a formulation allows for solving the problem in parallel by launching multiple concurrent environments enabling the agent to learn simultaneously from all the environments at once, achieving significant speed up. [ABSTRACT FROM AUTHOR]

Reservoir simulation is the combination of physics, mathematics, reservoir engineering, and computer programming for predicting the performance of a hydrocarbon reservoir under various operating conditions. The necessity of optimizing oil extraction methods is to increase the efficiency of a hydrocarbon reservoir under various operating conditions. Therefore, in a hydrocarbon recovery project that may involve hundreds of millions of dollars in investments, the risk associated with using the best method for the desired outcome must be evaluated and minimized. Finding an optimal model for static reservoir simulation through fluid flow model is the main goal of this paper. For this purpose, first of all, artificial data of porosity and permeability was generated, and then these data were used for geostatistical simulation. Sequential Gaussian Simulation (SGS) method was used for static simulation of a region and for each of two static parameters, 25 realizations were obtained. The realizations of SGS were randomly entered in the dynamic model of the reservoir. Dynamic model was coded by Python for slightly-compressible fluid flow equations in three dimensions and the pressure in each of the blocks in the oil production reservoir was determined. For each category, the least Sum of Squared Errors (SSE) was determined and then the corresponding static model was selected as the desired static model. With a reliable static model, it is possible to define different locations for designing injection and oil production wells, potential intelligent wells areas, as well as optimizing the management of a reservoir, which leads to costs reduction and, at the same time, increase in oil production. [ABSTRACT FROM AUTHOR]

The use of 4D seismic data in history matching has been a topic of great interest in the hydrocarbon industry as it can provide important information regarding changes in subsurfaces caused by fluid substitution and other factors where well data is not available. However, the high dimensionality and uncertainty associated with seismic data make its integration into the history-matching process a challenging task. Methods for adequate data reduction have been proposed in the past, but most address 4D information mismatch from a purely mathematical or image distance-based standpoint. In this study, we propose a quantitative and flow-based approach for integrating 4D seismic data into the history-matching process. By introducing a novel distance parametrization technique for measuring front mismatch information using streamlines, we address the problem from a flow-based standpoint; at the same time, we maintain the amount of necessary front data at a reduced and manageable amount. The proposed method is tested, and its results are compared on a synthetic case against another traditional method based on the Hausdorff distance. The effectiveness of the method is also demonstrated on a semi-synthetic model based on a real-case scenario, where the standard Hausdorff methodology could not be applied due to high data dimensionality.

Rapid technological advances have accelerated offshore and onshore tight oil extraction to meet growing energy demand. Reliable tools to carry out production prediction are essential for development of unconventional reservoirs. The existed tri-linear analytical solutions are verified to be versatile enough to capture fundamental flow mechanisms and make accurate production predictions. However, these solutions are obtained in Laplace space with the Laplace transform and numerical inversion, which may lead to uncertainty in the solution. In this paper, a general analytical solution is derived in real-time space through integral transform and average pressure substitution. Namely, the partial differential equations describing subsurface fluid flow are firstly triple-integrated and then the obtained volume average pressure are replaced with the rate-dependent expressions. Furthermore, the ordinary differential equations related to oil rate are solved analytically in real-time space. To validate our model, this derived solution is verified against two numerical models constructed with two typical physical configurations. The great match indicates the accuracy and applicability of the analytical solution. According to the developed workflow, two field cases including offshore and onshore tight oilfield data are selected for history matching and production prediction. This new approach not only makes the obtained solution more simplified, but also helps field engineers diagnose flow patterns more quickly to better optimize production schemes.

Ninety percentage of newly proven natural gas reservoirs of China are mainly unconventional resources, which can be typically developed by multi-stage fracturing horizontal well technology. Two regions typically occur near each fracture after hydraulic fracturing, in which the lower permeability region is considered as the storage source and the higher permeability region as the flow channel. The existed analytical models so far are mainly derived by Laplace transforming. In this paper, an improved practical analytical solution is derived for unconventional gas reservoirs bypassing the Laplace transform and numerical inversion. Through solving material balance equation and adopting the integration, a rate vs. pseudo-time solution in real-time domain can be directly obtained. Five numerical cases are created to verify the accuracy of the proposed analytical solution and the ratio of regular/irregular region pore volume is also proved to be derived reversely by the output parameters, which is significant for the field engineers to evaluate the effect of hydraulic fracturing. Moreover, a field example of a multi-fractured horizontal well in a tight gas reservoir is provided for demonstrate application.

Proxy-model is a popular reservoir modeling tool in the oil and gas industry due to its computational efficiency. This paper proposes and evaluates a proxy-model for reservoir history matching using extreme learning machines. The model does not require many computational resources when it is necessary to perform a large number of iterations. The proposed reservoir proxy-model is based on extreme learning machines with three hidden layers and the SPOCU activation function. It calculates the mismatch between the observed and simulated data. The experiments are carried out on a UNISIM-I-H reservoir reference model with 11 years of production data. The model outperforms the radial basis function neural network and polynomial regression proxy-models. The approach is assessed using the root mean squared error, the mean absolute percentage error, the normalized root mean squared error, and R2 metrics. The metrics prove the reliability and efficiency of the proposed proxy-model based on extreme learning machines. The experimental results demonstrate a sufficiently high accuracy (R2 = 98.7%) of the proxy-model in reservoir testing. It is expected that this study will draw researchers' attention to applying the proposed model to the history matching of oil reservoirs. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach based on deep learning to improve oil reservoirs' history matching problem. Deep autoencoders are widely used to solve the oil industry problems. However, as the input data increases, the autoencoder parameters increase exponentially. Our model is based on a convolutional variational autoencoder using AlexNet and bi-directional gated recurrent units. It parameterizes large-scale oilfield reservoirs. The proposed model is integrated into an ensemble smoother with multiple data assimilation to perform history matching. The proposed approach is validated on two reservoir models: PUNQ-S3 and Volve field. The root mean squared error, R2, and mean absolute error are calculated to verify the effectiveness of the proposed approach. The results show that the proposed model can effectively study the complex geological features of oil fields and be used in expert systems for reservoir modeling.

In recent years, Machine Learning (ML) has become a buzzword in the petroleum industry, with numerous applications which guide engineers in better decision making. The most powerful tool that most production development decisions rely on is reservoir simulation with applications in multiple modeling procedures, such as individual simulation runs, history matching and production forecast and optimization. However, all of these applications lead to considerable computational time and computer resource-associated costs, rendering reservoir simulators as not fast and robust enough, and thus introducing the need for more time-efficient and intelligent tools, such as ML models which are able to adapt and provide fast and competent results that mimic the simulator’s performance within an acceptable error margin. In a recent paper, the developed ML applications in a subsurface reservoir simulation were reviewed, focusing on improving the speed and accuracy of individual reservoir simulation runs and history matching. This paper consists of the second part of that study, offering a detailed review of ML-based Production Forecast Optimization (PFO). This review can assist engineers as a complete source for applied ML techniques in reservoir simulation since, with the generation of large-scale data in everyday activities, ML is becoming a necessity for future and more efficient applications.

Abstract Polymer flooding is a mature chemical enhanced oil recovery method employed in oilfields at pilot testing and field scales. Although results from these applications empirically demonstrate the higher displacement efficiency of polymer flooding over waterflooding operations, the fact remains that not all the oil will be recovered. Thus, continued research attention is needed to further understand the displacement flow mechanism of the immiscible process and the rock–fluid interaction propagated by the multiphase flow during polymer flooding operations. In this study, displacement sequence experiments were conducted to investigate the viscosifying effect of polymer solutions on oil recovery in sandpack systems. The history matching technique was employed to estimate relative permeability, fractional flow and saturation profile through the implementation of a Corey-type function. Experimental results showed that in the case of the motor oil being the displaced fluid, the XG 2500 ppm polymer achieved a 47.0% increase in oil recovery compared with the waterflood case, while the XG 1000 ppm polymer achieved a 38.6% increase in oil recovery compared with the waterflood case. Testing with the motor oil being the displaced fluid, the viscosity ratio was 136 for the waterflood case, 18 for the polymer flood case with XG 1000 ppm polymer and 9 for the polymer flood case with XG 2500 ppm polymer. Findings also revealed that for the waterflood cases, the porous media exhibited oil-wet characteristics, while the polymer flood cases demonstrated water-wet characteristics. This paper provides theoretical support for the application of polymer to improve oil recovery by providing insights into the mechanism behind oil displacement. Graphic abstract Highlights The difference in shape of relative permeability curves are indicative of the effect of mobility control of each polymer concentration. The water-oil systems exhibited oil-wet characteristics, while the polymer-oil systems demonstrated water-wet characteristics. A large contrast in displacing and displaced fluid viscosities led to viscous fingering and early water breakthrough.

• History matching of CO2/SF6 core flooding in Berea sandstone using PSO algorithm. • Assessing uncertainty of constitutive parameters and saturation function types. • Assessment of the effect of geological heterogeneity type on tracer BTC and mixing. • Assessment of the effect of capillary heterogeneity on tracer BTC and mixing. • Assessing impact of injection-to-monitoring distance on tracer BTC and mixing. Co-injection of conservative tracers with carbon dioxide (CO 2) is a viable tool for monitoring subsurface processes during geological CO 2 storage (GCS). This research investigates the simulation and history-matching of a gas tracer (sulfur hexafluoride, SF 6) during CO 2 flooding, employing a core flooding result in Berea sandstone. Four extensively used saturation functions are assessed for their efficacy in history matching of CO 2 /SF 6 injection at the core scale. The history-matching process incorporates particle swarm optimization (PSO) to fine-tune constitutive relationships parameters. Next, employing transport models at the aquifer scale, we interrogate the impact on tracer transport and mixing of saturation function uncertainties, arising from the non-uniqueness of constitutive relationships parameters and saturation function types. To assess the effects of geological heterogeneity on behavior of tracer breakthrough curves (BTCs), we employ two normalized parameters assessing the degree of mixing and SF 6 breakthrough time. The aquifer-scale investigation encompasses both homogeneous and heterogeneous systems with and without capillary heterogeneity effects. Our findings underscore the critical importance of addressing saturation function uncertainties, emphasizing the significance of auxiliary experiments and innovative methodologies to enhance predictive accuracy. The findings highlight significant disparities in arrival times, BTC peaks, tails, and mixing levels, even under optimal conditions. Heterogeneity, with or without capillary heterogeneity, plays a crucial role in shaping BTC variations, resulting in accelerated SF6 breakthrough times and reduced BTC peaks. Evaluation of monitoring points distant from the injector reveals a dampening effect on the SF 6 BTC peak, particularly in heterogeneous systems with capillary heterogeneity, where the peak is halved. These insights underscore the challenges associated with tracer monitoring and the necessity for enhanced methodologies to improve predictive accuracy in subsurface processes during GCS. [ABSTRACT FROM AUTHOR]

In power systems modelling, optimization methods based on certain objective function(s) are widely used to provide solutions for decision makers. For complex high-dimensional problems, such as network hosting capacity evaluation of intermittent renewables, simplifications are often used which can lead to the ‘optimal’ solution being suboptimal or nonoptimal. Even where the optimization problem is resolved, it would still be valuable to introduce some diversity to the solution for long-term planning purposes. This paper introduces a general framework for solving optimization for power systems that treats an optimization problem as a history match problem which is resolved via statistical emulation and uncertainty quantification. Emulation constructs fast statistical approximations to the complex computer simulation model in order to identify appropriate choices of candidate solutions for given objective function(s). Uncertainty quantification is adopted to capture multiple sources of uncertainty attached to each candidate solution and is conducted via Bayes linear analysis. It is demonstrated through a hosting capacity case study involving variable wind generation and active network management. The proposed method effectively identified not only the maximum connectable capacities but also a diverse set of near-optimal solutions, and so provided flexible guides for using the existing network to maximize the benefits of renewable generation.

Uncertainty quantification is a formal paradigm of statistical estimation that aims to account for all uncertainties inherent in the modelling process of real-world complex systems. The methods are directly applicable to stochastic models in epidemiology, however they have thus far not been widely used in this context. In this paper, we provide a tutorial on uncertainty quantification of stochastic epidemic models, aiming to facilitate the use of the uncertainty quantification paradigm for practitioners with other complex stochastic simulators of applied systems. We provide a formal workflow including the important decisions and considerations that need to be taken, and illustrate the methods over a simple stochastic epidemic model of UK SARS-CoV-2 transmission and patient outcome. We also present new approaches to visualisation of outputs from sensitivity analyses and uncertainty quantification more generally in high input and/or output dimensions.

Agent-based models (ABMs) can be found across a number of diverse application areas ranging from simulating consumer behaviour to infectious disease modelling. Part of their popularity is due to their ability to simulate individual behaviours and decisions over space and time. However, whilst there are plentiful examples within the academic literature, these models are only beginning to make an impact within policy areas. Whilst frameworks such as NetLogo make the creation of ABMs relatively easy, a number of keymethodological issues, including the quantification of uncertainty, remain. In this paper we draw on state-of-the-art approaches from the fields of uncertainty quantification and model optimisation to describe a novel framework for the calibration of ABMs using History Matching and Approximate Bayesian Computation. The utility of the framework is demonstrated on three example models of increasing complexity: (i) Sugarscape to illustrate the approach on a toy example; (ii) a model of the movement of birds to explore the efficacy of our framework and compare it to alternative calibration approaches and; (iii) the RISC model of farmer decision making to demonstrate its value in a real application. The results highlight the efficiency and accuracy with which this approach can be used to calibrate ABMs. This method can readily be applied to local or national-scale ABMs, such as those linked to the creation or tailoring of key policy decisions. [ABSTRACT FROM AUTHOR]

A review of field production data reveals that usually, it is very difficult to apply available decline models because of poor quality and often noisy character of initial data and also unrealistic assumptions of the models. This paper tries to introduce applicable procedures to correct initial data and reproduce missed data. Corrected data are analyzed and finally, the results for permeability and skin factor estimations are compared to results of transient well test analysis. Estimations for Initial Hydrocarbon In Place (IHIP) and reserve are also compared to the results of Material Balance Equation (MBE) and static model through field case studies. It is proved that the analysis can present acceptable estimations for radial permeability and skin values in naturally fractured reservoirs (NFR). Flowing material balance and Buba and Blasingame plotting function model give the best estimations for Original Gas In Place (OGIP) and gas reserve respectively. A simple but useful and applicable method is presented to determine reservoir fracture distribution mapping. It is also showed that the analysis can be used to distinguish water influx successfully.

This paper describes testing of the INSIM-FT proxy simulation method (interwell-numerical-simulation model improved with front-tracking method) to assess the dependencies between production and injection wells, as well as to assess the forecast of oil/liquid production by wells depending on their operation parameters. The paper proposes the approach of taking into account the influence of various production enhancement operations. The method was tested on a synthetic hydrodynamic model and on a sector of a real field. The results show a good match between historical data and simulation results and indicate significant computational efficiency compared to classical reservoir simulators.

Reformulating the history matching problem from a least-square mathematical optimization problem into a Markov Decision Process introduces a method in which reinforcement learning can be utilized to solve the problem. This method provides a mechanism where an artificial deep neural network agent can interact with the reservoir simulator and find multiple different solutions to the problem. Such a formulation allows for solving the problem in parallel by launching multiple concurrent environments enabling the agent to learn simultaneously from all the environments at once, achieving significant speed up.

In this study, the problem of water production in one of Iran's oil reservoirs will be examined. First, using the flow rate diagram of oil and water production, the water production problem will be examined according to time. Then, after confirming the occurrence of water production problem, the mechanism of water production will be investigated using Chan diagnostic diagrams and the created sector model. The results of this study indicate that firstly, the problem of water production in the well under study is observed, and secondly, according to the Decline-curve analysis diagrams, Recovery plot, Chan derivative diagram and schematic shape of the fluid flow movement, it shows the mechanism. Water production is a channel flow process, underwater injection. A gel treatment at early time with 25% of water cut was studied, for that it was modelled a gel treatment after 500 days of production. The main observation is that by increasing the concentration of injected gel, the rate of oil production increases and the rate of water production decreases. The concentration evaluated concentration was from 0 to 100 (lb/bbl) of solution, a stabilization concentration was not observed. Finally, first by identifying the type of water production mechanism for this reservoir in Iran, it has been determined that it has water production through the canal and then by using a simulation of gel injection, the water production rate has decreased and the oil production rate has increased. [ABSTRACT FROM AUTHOR]

Data-space inversion (DSI) is a data assimilation procedure that directly generates posterior flow predictions, for time series of interest, without calibrating model parameters. No forward flow simulation is performed in the data assimilation process. DSI instead uses the prior data generated by performing O(1000) simulations on prior geomodel realizations. Data parameterization is useful in the DSI framework as it enables representation of the correlated time-series data quantities in terms of low-dimensional latent-space variables. In this work, a recently developed parameterization based on a recurrent autoencoder (RAE) is applied with DSI for a real naturally fractured reservoir. The parameterization, involving the use of a recurrent neural network and an autoencoder, is able to capture important correlations in the time-series data. RAE training is accomplished using flow simulation results for 1,350 prior model realizations. An ensemble smoother with multiple data assimilation (ESMDA) is applied to provide posterior DSI data samples. The modeling in this work is much more complex than that considered in previous DSI studies as it includes multiple 3D discrete fracture realizations, three-phase flow, tracer injection and production, and complicated field-management logic leading to frequent well shut-in and reopening. Results for the reconstruction of new simulation data (not seen in training), using both the RAE-based parameterization and a simpler approach based on principal component analysis (PCA) with histogram transformation, are presented. The RAE-based procedure is shown to provide better accuracy for these data reconstructions. Detailed posterior DSI results are then presented for a particular “true” model (which is outside the prior ensemble), and summary results are provided for five additional “true” models that are consistent with the prior ensemble. These results again demonstrate the advantages of DSI with RAE-based parameterization for this challenging fractured reservoir case.

History matching is an important reservoir engineering process whereby the values of uncertain attributes of a reservoir model are changed to find models that have a better chance of reproducing the performance of an actual reservoir. As a typical inverse and ill-posed problem, different combinations of reservoir uncertain attributes lead to equally well-matched models and the success of a history-matching approach is usually measured in terms of its ability to efficiently find multiple history-matched models inside the search space defined by the parameterization of the problem (multiple-matched models have a higher chance of better representing the reservoir performance forecast). While studies on history-matching approaches have produced remarkable progress over the last two decades, given the uniqueness of each reservoir's history-matching problem, no strategy is proven effective for all cases, and finding alternative, efficient, and effective history-matching methodologies is still a research challenge. In this work, we introduce a learning-from-data approach with path relinking and soft clustering to the history-matching problem. The proposed algorithm is designed to learn the patterns of input attributes that are associated with good matching quality from the set of available solutions, and has two stages that handle different types of reservoir uncertain attributes. In each stage, the algorithm evaluates the data of all-available solutions continuously and, based on the acquired information, dynamically decides what needs to be changed, where the changes shall take place, and how such changes will occur in order to generate new (and hopefully better) solutions. We validate our approach using the UNISIM-I-H benchmark, a complex synthetic case constructed with real data from the Namorado Field, Campos Basin, Brazil. Experimental results indicate the potential of the proposed approach in finding models with significantly better history-matching quality. Considering a global misfit quality metric, the final best solutions found by our approach are up to 77% better than the corresponding initial best solutions in the datasets used in the experiments. Moreover, compared with previous work for the same benchmark, the proposed learning-from-data approach is competitive regarding the quality of solutions found and, above all, it offers a significant reduction (up to 30 × less) in the number of simulations. [ABSTRACT FROM AUTHOR]

In this study, simulation of low salinity polymer flooding in the core scale is investigated using Eclipse-100 simulator. For this purpose, two sets of data are used. The first set of data were adopted from the results of experimental studies conducted at the University of Bergen, performed using Berea sandstone and intermediate oil. The second data set, related to sand pack and heavy oil system, was obtained from experiments performed at Sahand Oil and Gas Research Institute. To obtain relative permeability and capillary pressure curves, automatic history matching is implemented by coupling Eclipse-100 and MATLAB software. Three different correlations are used for relative permeability. The parameters of each model are calculated using four different optimization algorithms, including Levenberg-Marquardt, Trust-region, Fminsearch, and Pattern search. The results showed that regardless of the optimization algorithm being used, applying relative permeability model of Lomeland et al., known as LET model, best matches the experimental oil recovery data in comparison with those of Corey and Skjeaveland et al.’s relative permeability correlations. The LET model and the Trust-region algorithm were selected for simulation of low salinity polymer flooding process. Simulation of the first set of data showed that using low salinity water flooding before polymer flooding, oil recovery was increased about 16%. In addition, using the second set of data, simulation of low salinity polymer flooding scenario is investigated in a long core model, taken from one of the southwestern fields of Iran. Simulation results show an increase of about 34% in the recovery of low salinity polymer flooding compared to the water flooding scenario.