Search

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]

The challenge in modeling complex-heterogeneous reservoirs is to accurately represent dimensions, trends, and quality for each facies type and to avoid overestimating or underestimating the reservoir elements. NEAG-2 Field has a highly heterogeneous reservoir system of the Albian-Cenomanian age; it is the main reservoir system in the East Abu Gharadig Basin, and it is the main oil contributor in the north Western Desert of Egypt. Therefore, developing a water-tight model for such a complex system can act as an analog for any similar complex-heterogenous system worldwide. In the NEAG-2 Field, a representative reservoir model and dynamic simulation for its reservoir are required to restore the field's production. The field has an excellent yet unique performance, and it recorded an average production rate of 9000 bbl/d from five producer wells in 2018. Since that peak, production has been declining, with a current total of 1390 bbl/d from four wells. This production behavior was not modeled nor predicted in the previous modeling trials. Therefore, we introduce a mature model to improve production forecasts and optimize recovery while giving an example of how the complex heterogeneous reservoirs should be properly modeled. An object-based geostatistical algorithm was applied in modeling the reservoir facies, and a truncated Gaussian algorithm was applied for the background (non-reservoir) facies. The property models were distributed using Gaussian simulation algorithms, with the guidance of variogram analysis. Three reservoir facies were distinguished, with specific geometry, orientation, and porosity–permeability characteristics to model their flow behavior. The highest-quality facies (type 1) were tidal channels, followed by moderate-quality (type 2) tidal sand bars, which had smaller lateral dimensions compared to the channels. The lowest quality sand facies (type 3) were embodied as mixed tidal flats. Each facies body, reservoir zone, and field segment was modeled distinctly to ensure a representative statistical range for each. The integrated workflow developed a flow-unit-based model that preserved the reservoir heterogeneity and fluid flow complexity, which improved the forecasting for reviving the field production. The final results of this static model were validated by the production data and the history matching of each well. [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]

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]

The accuracy and robustness of numerical models of geologic CO 2 sequestration are almost never quantified with respect to direct observations that provide a ground truth. Here, we conduct CO 2 injection experiments in meter-scale, quasi-2D tanks with porous media representing stratigraphic sections of the subsurface, and compare them to numerical simulations of those experiments. We evaluate (1) the value of prior knowledge of the system, expressed in terms of ex situ measurements of the tank sands' multiphase flow properties (local data), with respect to simulation accuracy; and (2) the forecasting capability of history-matched numerical models, when applied to different settings. We match three versions of a numerical simulation model—each with access to an increasing level of local data—to a CO 2 injection experiment in Tank 1 ( 89.7 × 47 × 1.05 cm). Matching is based on a quantitative comparison of CO 2 migration at different times from timelapse image analysis. Next, use the matched models to make a forecast of a different injection scenario in Tank 1 and, finally, a different injection scenario in Tank 2 ( 2.86 × 1.3 × 0.019 m), which represents an altogether different stratigraphic section. The simulation model can qualitatively match the observed free-phase and dissolved CO 2 plume migration and convective mixing. Quantitatively, simulations are accurate during the injection phase, but their concordance decreases with time. Using local data reduces the time required to history match, although the forecasting capability of matched models is similar. The sand–water– CO 2 (g) system is very sensitive to effective permeability and capillary pressure changes; where heterogeneous structures are present, accurate deterministic estimates of CO 2 migration are difficult to obtain. [ABSTRACT FROM AUTHOR]

In this study, we conduct a comprehensive history matching study for the FluidFlower benchmark model. This benchmark was prepared and organized by the University of Bergen, the University of Stuttgart, and Massachusetts Institute of Technology, for promoting understanding of the complex physics of geological carbon storage (GCS) through in-house experiments and numerical simulations. This paper synthesizes the experiences of history matching the benchmark data encountered by the Delft-DARTS and CSIRO participants. History matching is first performed based on a low-dimensional-zonated structured model using a simple Poisson-like solver. The permeability of six facies and two faults is inferred in this stage to match the digitized concentration data. The history matching is then further enhanced to richer spatial and physical models to capture the spatial variation of permeability and buoyancy effects, using an unstructured grid. Efficient adjoint methods are used to evaluate the gradient used in the optimization of data misfits or equivalent Bayesian log-likelihoods. With efficient optimization methods available for both maximum a posteriori model inference and Randomized Maximum Likelihood methods for model uncertainty, we perform history matching using both binary and continuous concentration observations. The results show that the tracer plumes in the enriched model match the experimental plumes more accurately compared with the results from the parsimonious-zonated model. The history matching results based on the concentration observations provide more similar plume shapes compared with the case based on the binary observations. The permeability difference between the model before and after history matching reveals that the tracer plume zone and the high permeable zone are the regions of high sensitivity in terms of data misfit between the model response and observations. Surprisingly, CO 2 concentration plume forecasts based on these history-matched models were not especially sensitive to the improvements observed in the enhanced model. [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]

History matching, as an essential part of reservoir development, aims to infer high-dimensional geological parameters of a reservoir with a small amount of observation. Despite the rapid development of optimization algorithms, finding optimal solutions for history matching is still challenging because of the large number of parameters that depend on the grid blocks of the numerical simulation model. Motivated by the divide-and-conquer strategy, in this work a novel probabilistic cooperative coevolutionary framework based on local parameterization (LP-PCC) is constructed to improve the convergence of the history matching of large-scale problems. First, the high-dimensional model parameters are decomposed based on smooth local parameterization, in which the divided low-dimensional parameters can reconstruct smooth boundaries of the geological structure during optimization. After that, a contribution-based cooperative coevolutionary algorithm is adopted to optimize the low-dimensional parameters in a round-robin fashion and allocate the computational resources reasonably. To further improve the performance of cooperative coevolution, a new probabilistic method integrated with contribution information is presented to select the subcomponents to be optimized. This framework incorporates domain knowledge for decomposition and a probabilistic mechanism to select subcomponents with large probability, which enhances both convergence and exploration in cooperative coevolution. Two synthetic reservoir cases are designed to validate the effectiveness and efficiency of the proposed method. The numerical results indicate that, compared with traditional strategies, the method can obtain better history-matching results and be adapted to large-scale reservoir problems. [ABSTRACT FROM AUTHOR]

This article explores methods for resolving two practical issues in reservoir engineering: discovering an optimal position for the production well on a grid, and recovering unknown fracture position based on the historical production data. To speed up the conventional approach (numerical simulation and the full grid search), we assess application of optimization techniques from the Hyperopt package as well as several machine learning models. [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]

Data assimilation is an important tool in many geophysical applications. One of many key elements of data assimilation algorithms is the measurement error that determines the weighting of the data in the cost function to be minimized. Although the algorithms used for data assimilation treat the measurement uncertainty as known, it is in many cases estimated or set based on some expert opinion. Here we treat the measurement uncertainty as a hyperparameter in a fully Bayesian hierarchical model and derive a new class of iterative ensemble methods for data assimilation where the measurement uncertainty is integrated out. The proposed algorithms are compared with the standard iterative ensemble smoother on a 2D synthetic reservoir model. [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]

Various types of geophysical measurements have been made available to illuminate different characteristics of subsurface reservoir formations. It becomes crucial to both efficiently and effectively utilize the information contained in these measurements for enhanced reservoir characterization and more informative decision-making support. To address the problem, image-oriented history matching approaches were proposed, which have shown promising results in efficiently assimilating multiple types of geophysical measurements. Relying on the interpretability of geophysical measurements, image-oriented strategies seek to match the extracted features or patterns (e.g., water front positions from the inverted saturation field) instead of the original data in the model update step. Consequently, the quality of the extracted features directly impacts the performance of these methods. However, extracting reliable features from related geophysical data is not straightforward. It requires not only in-depth domain knowledge but also appropriate image processing techniques. This study explores the use of deep learning (DL) based image segmentation techniques as an alternative to assist the feature extraction for an image-oriented ensemble-based history matching workflow. Accounting for the special characteristics of the considered application, a fast unsupervised DL segmentation model based on the convolutional neural network (CNN) is used together with an image denoising algorithm. The developed workflow separates the history matching of geophysical data into two sequential steps. It starts with a (joint) geophysical inversion step for saturation mapping, followed by a featured-oriented assimilation step to match the inverted saturation field, in which water front positions are extracted using the DL-based segmentation model. We test the proposed workflow on a synthetic reservoir model to history match electromagnetic (EM) and seismic data, which illustrates its promising performance in extracting relevant information from the data for efficient history matching. [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]

Because the geological conditions of the reservoir are complicated and involve many factors, the inversion of reservoir parameters is realized by using numerical simulation technology and history matching method. At present, Ensemble Kalman Filter method is widely used in history matching. But in the fact, the Ensemble Kalman Filter has problem such as inaccurate gradient calculation and pseudo correlation. In this paper, the Ensemble Kalman Filter based on shrinkage covariance matrix estimation is used to construct the localization matrix. By gradually matching production performance, the gradient of data assimilation method is corrected, the pseudo correlation is weakened, the reservoir model is updated, and the optimal estimate is obtained. By an example, we compare the Ensemble Kalman Filter and Ensemble Kalman Filter based on shrinkage covariance matrix estimation. The results show that Ensemble Kalman Filter based on shrinkage covariance matrix estimation is superior to Ensemble Kalman Filter in the accuracy of model production dynamic matching. [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.

Reservoir history matching refers to the process of continuously adjusting the parameters of the reservoir model, so that its dynamic response will match the historical observation data, which is a prerequisite for making forecasts based on the reservoir model. With the development of optimization theory and machine learning algorithms, automatic history matching has made numerous breakthroughs for practical applications. In this perspective, the existing automatic history matching methods are summarized and divided into model-driven and surrogate-driven history matching methods according to whether the reservoir simulator needs to be run during the automatic history matching process. Then, the basic principles of these methods and their limitations in practical applications are outlined. Finally, the future trends of reservoir automatic history matching are discussed. [ABSTRACT FROM AUTHOR]

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]

Comprehensively considering the migration law of air and foam in porous media, various physical and chemical phenomena, and the change of gas phase mobility are researched, then mathematical models of air-foam flooding are established. Based on air-foam flooding experiments, the relevant parameters of empirical model for numerical simulation of air-foam flooding were obtained. Matching of parallel core displacement experiment and air foam test flooding in Wuliwan Oilfield is completed with total fitting degree of more than 90%, and the reliability of empirical model of numerical simulation for air-foam flooding is verified. [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]

History matching is crucial for reliable numerical simulation of geological carbon storage (GCS) in deep subsurface aquifers. This study focuses on inferring highly complex aquifer permeability fields with multi- and intra-facies heterogeneity to improve the characterization of CO 2 plume migration. We propose a deep learning (DL)-based parameterization strategy combined with the ensemble smoother with multiple data assimilation (ESMDA) algorithm to formulate an integrated inverse framework. The DL model is employed to parameterize non-Gaussian permeability fields using low-dimensional latent variables in a Gaussian distribution, thereby mitigating the non-Gaussianity issue faced by the ensemble-based ESMDA inverse method and simultaneously alleviating the computational burden of high-dimensional inversion. The efficacy of the integrated DL-ESMDA inverse framework is demonstrated using a 3-D GCS model, where it estimates the non-Gaussian permeability field characterized by multi- and intra-facies heterogeneity. Results show that the DL model is able to represent the highly complex and high-dimensional permeability fields using low-dimensional latent vectors. The DL-ESMDA framework sequentially updates these low-dimensional latent vectors instead of the original high-dimensional permeability field to obtain posterior estimations of the permeability field. The resulting CO 2 plume migration closely matches historical measurements, suggesting a significantly improved model reliability after history matching. Additionally, a substantial reduction in uncertainty for future plume migration predictions beyond the history matching period is observed. The proposed framework provides an effective approach for reliable characterization of CO 2 plume migration in highly heterogeneous aquifers, enhancing GCS project operation and risk analysis. • We propose a deep learning-enabled, data assimilation method for history matching CO 2 storage in non-Gaussian aquifers. • The deep learning algorithm is trained to represent permeability fields in low-dimensional space. • Non-Gaussianity of permeability is preserved while reducing the parameter dimension. • Predictive uncertainty of CO 2 plume migration is significantly reduced using our method. [ABSTRACT FROM AUTHOR]

High computer power has long been a critical ingredient that affects the effectiveness and efficiency of history matching. Data-driven surrogate modeling as an efficient strategy can accelerate the history-matching process by constructing machine learning-based models with high computing speed but reduced accuracy. However, the applicability of surrogate models for different history-matching problems is uncertain due to the influence of data quality and quantity, model architectures, and hyperparameters. To overcome this issue, an offline data-driven dual-surrogate framework (ODDF) that considers the prediction error of surrogate models for history matching is proposed, where one surrogate model predicts the production data of reservoirs and the other one learns the prediction error of the former surrogate. The first surrogate model considers the time-series characteristics of production data using a recurrent neural network, while the second surrogate model regards the two-dimensional spatial correlation characteristics of multivariate prediction error using a fully convolutional neural network. Furthermore, an enhanced error model is applied to incorporate the prediction error into the objective function to reduce the influence of the prediction error on inversion results. Based on this hybrid framework, one can improve the prediction accuracy of surrogate models in history matching when the architectures or hyperparameters of surrogate models are not optimal. Additionally, one can obtain satisfactory results for history matching and uncertainty quantification based on surrogate modeling. The proposed framework is validated on the history matching of two- and three-dimensional reservoir models. The results show that the proposed method is robust in constructing the surrogate models and predicting the production data of reservoirs, which improves the efficiency and reliability of history matching. • A dual-surrogate framework is proposed for history matching to deal with the prediction error of imperfect surrogates. • Considering the time series and correlation of production data, the accuracy and robustness of surrogates are improved. • The prediction error of surrogates is incorporated into the objective function of history matching. • Combining the dual-surrogate framework with an adaptive differential evolution algorithm, the results are satisfactory. [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.

We analyze JUNE: a detailed model of COVID-19 transmission with high spatial and demographic resolution, developed as part of the RAMP initiative. JUNE requires substantial computational resources to evaluate, making model calibration and general uncertainty analysis extremely challenging. We describe and employ the uncertainty quantification approaches of Bayes linear emulation and history matching to mimic JUNE and to perform a global parameter search, hence identifying regions of parameter space that produce acceptable matches to observed data, and demonstrating the capability of such methods. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'. [ABSTRACT FROM AUTHOR]

In heavy oil displacement by fluid injection, severe instability can occur due to the adverse mobility ratio, gravity segregation or compositional effects. However, when estimating relative permeability, most analytical methods assume a stable front in the displacement, which may be highly erroneous when used with unstable displacements. Quite often in such cases, history matching using a high-resolution model is preferred, however, it is computationally inefficient or impractical in some cases. This work describes a relatively fast methodology for estimating relative permeability from displacement with instability and compositional effect. It involves defining a set of 2-dimensional (2D) coarse-grid models and the tuning of a three-parameter correlation. By this approach, an attempt is made to resolve the fine-scale information without direct solution of the global fine-scale problem. The results of the coarse-grid history matching corrected by the proposed approach in this study showed that the improved methodology is three times faster, and required less than half the memory of a high-resolution 2D model. [ABSTRACT FROM AUTHOR]

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.

The presence of protein aggregates in cells is a known feature of many human age‐related diseases, such as Huntington's disease. Simulations using fixed parameter values in a model of the dynamic evolution of expanded polyglutaime (PolyQ) proteins in cells have been used to gain a better understanding of the biological system. However, there is considerable uncertainty about the values of some of the parameters governing the system. Currently, appropriate values are chosen by ad hoc attempts to tune the parameters so that the model output matches experimental data. The problem is further complicated by the fact that the data only offer a partial insight into the underlying biological process: the data consist only of the proportions of cell death and of cells with inclusion bodies at a few time points, corrupted by measurement error. Developing inference procedures to estimate the model parameters in this scenario is a significant task. The model probabilities corresponding to the observed proportions cannot be evaluated exactly, and so they are estimated within the inference algorithm by repeatedly simulating realizations from the model. In general such an approach is computationally very expensive, and we therefore construct Gaussian process emulators for the key quantities and reformulate our algorithm around these fast stochastic approximations. We conclude by highlighting appropriate values of the model parameters leading to new insights into the underlying biological processes. [ABSTRACT FROM AUTHOR]