Ensemble Smoother Research Articles

Flow-dependent observation errors for greenhouse gas inversions in an ensemble Kalman smoother

Abstract. Atmospheric inverse modeling is the process of estimating emissions from atmospheric observations by minimizing a cost function, which includes a term describing the difference between simulated and observed concentrations. The minimization of this difference is typically limited by uncertainties in the atmospheric transport model rather than by uncertainties in the observations. In this study, we showcase how a temporally varying, flow-dependent atmospheric transport uncertainty can enhance the accuracy of emission estimation through idealized experiments using an ensemble Kalman smoother system. We use the estimation of European CH4 emissions from the in situ measurement network as an example, but we also demonstrate the additional benefits for trace gases with more localized sources, such as SF6. The uncertainty in flow-dependent transport is determined using meteorological ensemble simulations that are perturbed by physics and driven at the boundaries by an analysis ensemble from a global meteorology and a CH4 simulation. The impact of direct representation of temporally varying transport uncertainties in atmospheric inversions is then investigated in an observation system simulation experiment framework in various setups and for different flux signals. We show that the uncertainty in the transport model varies significantly in space and time and that it is generally highest during nighttime. We apply inversions using only afternoon observations, as is common practice, but also explore the option of assimilating hourly data irrespective of the hour of day using a filter based on transport uncertainty and taking into account the temporal covariances. Our findings indicate that incorporating flow-dependent uncertainties in inversion techniques leads to more accurate estimates of GHG emissions. Differences between estimated and true emissions could be reduced more effectively by 9 % to 82 %, with generally larger improvements for the SF6 inversion problem and for the more challenging setup with small flux signals.

Deep learning-based geological parameterization for history matching CO2 plume migration in complex aquifers

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 CO2 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 CO2 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 CO2 plume migration in highly heterogeneous aquifers, enhancing GCS project operation and risk analysis.

A sequential ensemble smoother for multiple data assimilation in hydrogeological modeling

A sequential ensemble smoother for multiple data assimilation in hydrogeological modeling

Numerical experiment on data assimilation for geothermal doublets using production data and electromagnetic observations

The data assimilation process for geothermal reservoirs often relies on well data, which primarily offer insights into the immediate vicinity of the borehole. However, integrating geophysical methods can provide valuable information beyond well proximity, possibly enhancing reservoir predictions. Current methods of monitoring geothermal reservoirs struggle to maintain a good signal-to-noise ratio for deep reservoirs. Diffusive electromagnetic (EM) methods can be sensitive to the decreasing conductivity from heat extraction in geothermal reservoirs and offer promising additional value. To test their potential effectiveness, numerical examples are simulated. A scheme to incorporate diffusive EM observations into a data assimilation process for geothermal reservoirs is presented and implemented in this study. First, an ensemble of prior models representing the reservoir uncertainty is used to determine the moments of the resulting temperature field using a forward geothermal simulation. Subsequently, a conductivity model is calculated from the temperature field using an empirical relationship. The expected electric field response can then be simulated using an EM forward model. EM sources are placed on the surface around the expected cold plume location. The receiver is placed at reservoir depth. To assimilate the data, the ensemble smoother with multiple data assimilation method is used. The findings demonstrate that the incorporation of EM data provides valuable information regarding the temperature field. This improves the accuracy of the temperature forecast of the entire reservoir when combined with the localized data from the production well and, therefore, helps to resolve the complex migration of the cold front. These results highlight the monitoring potential of EM observations for geothermal reservoirs.

A combined data assimilation and deep learning approach for continuous spatio-temporal SWE reconstruction from sparse ground tracks

Our understanding of the impact of climate change on water availability and natural hazards in high-mountain regions is limited due to the spatial and temporal scarcity of ground observations of precipitation and snow. Freely available, satellite-based information about the snowpack is currently mainly limited to indirect measurements of snow-covered area or very coarse-scale snow water equivalent (SWE), but only for flat areas in lowlands without vegetation cover. Novel space-based laser altimeters, such as ICESat-2, have the potential to provide high-resolution snow depth data in worldwide mountain regions where no ground observations exist. However, these space-based laser altimeters come with spatial gaps between ground tracks, obtained without repetition at a give location. To overcome these drawbacks, here, we present a combined probabilistic data assimilation and deep learning approach to reconstruct spatio-temporal SWE from observations of snow depth along ground tracks, imitating ICESat-2 tracks in view of a potential future global application.Our approach is based on assimilating SWE and snow cover information in a degree-day model with an iterative ensemble smoother (IES) which allows temporally reconstructing SWE along hypothetical ground tracks separated by 3 km. As input, the degree-day model uses daily precipitation and downscaled air temperature from the ERA5 reanalysis. A feedforward neural network (FNN) is then used for spatial propagation of the daily mean and standard deviation of the updated SWE ensemble members obtained from the IES. The combined IES-FNN approach provides uncertainty-aware spatio-temporally continuous estimates of SWE.We tested our approach in the alpine Dischma valley (Switzerland) using high-resolution snow depth maps obtained from photogrammetric techniques mounted on airplanes and unmanned aerial system observations. Our results show that the IES-FNN model provides reliable estimates at a resolution of approximately 100 m. Even assimilating only one SWE observation during the year (combined with satellite-based melt-out date estimates) produces satisfying results when evaluating the IES-FNN SWE reconstructions on independent dates and smaller (<4 km2) areas: mean absolute error of 86 mm (78 mm) at Schürlialp (Latschüelfurgga) for average SWE of 180 mm (254 mm), and average spatial linear correlation with the reference SWE of 0.51 (0.48). However, the assimilated SWE observation must not be too early in the accumulation season or too late in the melt season when the snowpack is starting or ending to accumulate or melt, respectively. Smaller distances between ground tracks (1500 m and 500 m) show improved performance of the IES-FNN approach in space, with no significant improvement in terms of temporal reconstruction.Applying the IES-FNN approach to e.g., real ICESat-2 data, remains challenging due to the higher uncertainties associated with these data. However, the approach we propose remains potentially very helpful in addressing the problem of scarcity of ground observations of precipitation and snow in high-mountain regions.

Better stopping through cross validation in an iterative ensemble smoother: A perspective from supervised machine learning

Iterative ensemble smoothers (IES) are among the popular reservoir data assimilation (RDA) algorithms for reservoir characterization. The actual deployment of an IES algorithm requires implementing certain stopping criteria, normally adopted for runtime control (e.g., by stopping the IES when it reaches the maximum number of iterations) and/or safeguarding the RDA performance (e.g., by preventing the simulated data from overfitting the actual observations). In practice, for various reasons, it is often challenging for existing stopping criteria to simultaneously achieve both purposes. One noticeable issue, as illustrated in this work, is that in many situations, the qualities of the estimated reservoir models may already start to deteriorate before a conventional stopping criterion activates to terminate the iteration process. Following this observation, one practically important question arises: Is it possible to further improve the efficacy of the IES algorithm by designing a different stopping criterion so that the IES can stop earlier, saving computational costs while achieving better RDA performance?As one of the rare attempts in the community, this work aims to investigate the use of a new IES stopping criterion that has the potential to provide an affirmative answer to the above question. In this regard, our main idea is based on the concept of cross validation (CV), routinely adopted in supervised machine learning (SML) problems for early stopping to prevent SML models from overfitting the training data. Despite the noticed similarities between RDA and SML problems, some fundamental differences exist, making it fail to work well if one directly extends a vanilla CV procedure from SML to RDA. To tackle this identified challenge, we design an efficient CV procedure tailored for RDA problems, and inspect the performance of an IES algorithm equipped with this CV procedure (IES-CV) in both synthetic and real field case studies. Our numerical investigation indicates that the IES-CV algorithm achieves promising RDA performance in all case studies, confirming the possibility that with the aid of a proper stopping criterion, an IES algorithm can terminate at an appropriate iteration step with near-optimal RDA performance. Beyond these numerical findings, it is also our hope that the current work may help improve the best practices of applying IES to RDA problems, taking advantage of the effective, CV-based stopping criterion.

Calibrating high-dimensional rock creep constitutive models for geological disaster prevention: An application of data assimilation methods

The study of rock creep phenomena is of paramount importance due to its potential to trigger geological disasters, such as landslides. To predict and prevent such disasters, creep constitutive models are widely employed to comprehend the time-dependent deformation of rocks. These models encompass various mechanical parameters that describe the intricate stress-strain behaviors. Nevertheless, significant challenges persist in achieving accurate and consistent parameter estimation and state prediction. In this study, we introduce three advanced data assimilation (DA) methods, including one Markov chain Monte Carlo method, DREAM(KZS), and two ensemble smoother methods, ESMDA and ILUES. This marks the first application of such methods for calibrating rock creep models in the scenario of geological disaster prevention. We conducted numerical simulations under both low- and high-dimensional conditions to assess the performance of these DA methods. For the single partition model, all three DA methods demonstrated promising results. In the high-dimensional case, DREAM(KZS) displayed inefficiency, while both ESMDA and ILUES proved to be still effective. ESMDA offered improved data matching but tended to underestimate parameter uncertainties, whereas ILUES excelled in addressing the issue of equifinality. In a real-world case focusing on characterizing creep deformation at the Mogu tilting deformation body near the Lianghekou Dam, China, we employed all three DA methods, and they collectively demonstrated satisfactory performance. Particularly noteworthy is the enhanced performance of the DREAM(KZS) method during the accelerated creep phase, even in the presence of limited data. The findings of this research bear significant importance in reducing uncertainties associated with model parameters in the realm of rock mechanics, thereby advancing our capabilities in predicting and preventing disasters.

Advanced attention-based spatial-temporal neural networks for enhanced CO2 water-alternating-gas performance prediction and history matching

This study combines convolutional neural networks, spatial pyramid pooling, and long short-term memory networks (LSTM) with self-attention (SA) mechanisms (abbreviated as CSAL) to address the problem of production dynamics prediction in tight reservoirs during the CO2 water-alternating-gas (CO2-WAG) injection process. By integrating DenseNet and SPP modules, this method effectively captures and processes complex spatial features in tight reservoirs. Concurrently, the LSTM enhanced with SA mechanisms improves the prediction capability of temporal data during the CO2-WAG process. Experimental results demonstrate that the CSAL model performs excellently in both the training and testing phases, achieving a coefficient of determination (R2) exceeding 0.98, significantly enhancing the model's prediction accuracy. Compared to models without attention mechanisms, the CSAL model increases the R2 value in time series prediction by 10%. Furthermore, employing the Ensemble Smoother with Multiple Data Assimilation algorithm, the CSAL model achieves high-precision history matching, significantly reducing the error between predicted values and actual observations. This study validates the application potential and superiority of the CSAL model in the CO2-WAG process in tight reservoirs.

Improving fault zones hydrodynamic characterization and simulation in karstified carbonate environments with GLM and IES invers methods

A quantitative and qualitative estimation of groundwater resources is a challenge for water management in the world, especially in carbonated and karstified aquifers. Within these aquifers, fault zones exert a significant influence on groundwater hydrodynamics and transport. Improving the management of this type of aquifer involves better assessment of its hydrodynamics properties. Sustainability and management solutions can be estimated through numerical modeling. In this study hydrodynamic parameter of fault zone in karstified carbonate environments are estimated from cross-hole pumping test data. These estimations allow the simulation and forecasting of fault zone flow and transport. For this purpose, a flow and transport model has been set up using MODFLOW6 and MODPATH7 codes. Inverse modeling of hydrodynamic parameters is performed with the PEST++ code suite, with both the Gauss-Levenberg-Marquardt algorithm (GLMA) and the iterative ensemble smoother (IES) which is a recent approach with few applications so far. Simulation, parameter estimation, and forecasts of drawdown and pollutant travel time through the fault zone have been first evaluated on a synthetic fault zone and are eventually applied to a real-world fault zone of interest in karst carbonate environments. A comprehensive comparison and analysis of GLMA and IES results are performed for parameter estimation, parametric and predictive uncertainties, ensuring a thorough assessment of results. The findings reveal satisfactory levels of uncertainty associated with the hydraulic conductivity field and both flow and transport forecasts. This approach demonstrates its ability to estimate the hydrodynamic parameter field with a high level of accuracy within the internal structures of the fault zone. This study constitutes valuable and reproducible insights into the simulation and forecasts of fault zones in karst carbonate aquifers. The findings are a step forward in groundwater flow and transport simulation of fault zones and provide relevant practical help for the management and protection of water resources in these critical areas of interest.

Coupled hydrogeophysical inversion through ensemble smoother with multiple data assimilation and convolutional neural network for contaminant plume reconstruction

In the field of groundwater, accurate delineation of contaminant plumes is critical for designing effective remediation strategies. Typically, this identification poses a challenge as it involves solving an inverse problem with limited concentration data available. To improve the understanding of contaminant behavior within aquifers, hydrogeophysics emerges as a powerful tool by enabling the combination of non-invasive geophysical techniques (i.e., electrical resistivity tomography—ERT) and hydrological variables. This paper investigates the potential of the Ensemble Smoother with Multiple Data Assimilation method to address the inverse problem at hand by simultaneously assimilating observed ERT data and scattered concentration values from monitoring wells. A novelty aspect is the integration of a Convolutional Neural Network (CNN) to replace and expedite the expensive geophysical forward model. The proposed approach is applied to a synthetic case study, simulating a tracer test in an unconfined aquifer. Five scenarios are compared, allowing to explore the effects of combining multiple data sources and their abundance. The outcomes highlight the efficacy of the proposed approach in estimating the spatial distribution of a concentration plume. Notably, the scenario integrating apparent resistivity with concentration values emerges as the most promising, as long as there are enough concentration data. This underlines the importance of adopting a comprehensive approach to tracer plume mapping by leveraging different types of information. Additionally, a comparison was conducted between the inverse procedure solved using the full geophysical forward model and the CNN model, showcasing comparable performance in terms of results, but with a significant acceleration in computational time.

A Fast History-Matching and Optimization Tool and Its Application to a Full Field with More than 1,000 Wells

Summary In this work, we study a waterflood field containing more than 1,000 wells, and the modern field management techniques with full-fidelity 3D geocellular reservoir models become computationally prohibitive. To overcome the difficulty, we developed a novel flow-network data-driven model—the general-purpose simulator-powered network (GPSNet) model—and used it for rapid history matching and optimization. GPSNet includes physics, such as mass conservation, multiphase flow, and phase changes, while maintaining a good level of efficiency. To build such a model, a cluster of 1D connections among well completion points is constructed and forms a flow network. Multiphase fluid flow is assumed to occur in each 1D connection, and the flow in the whole network is simulated by our in-house general-purpose simulator. Next, to effectively reduce the uncertainty, a hierarchical history-matching workflow is adopted to match the production data. Ensemble smoother with multiple data assimilation (ESMDA) plays an important role in reducing the error at each history-matching step. After that, the best-matched candidate is selected for numerical optimization to maximize field oil production with constraints satisfying field conditions. Excellent history-matching results have been achieved on the field level, and good matches have also been observed for key producers. It is also worth mentioning that the history-matching process took a mere 4 hours to finish 1,100 simulation jobs. The successful application of the GPSNet to this waterflood field demonstrates a promising workflow that can be used as a fast and reliable decision-making tool for reservoir management.

Parameter ESTimation With the Gauss-Levenberg-Marquardt Algorithm: AnIntuitive Guide.

In this paper, we review the derivation of the Gauss-Levenberg-Marquardt (GLM) algorithm and its extension to ensemble parameter estimation. We explore the use of graphical methods to provide insights into how the algorithm works in practice and discuss the implications of both algorithm tuning parameters and objective function construction in performance. Some insights include understanding the control of both parameter trajectory and step size for GLM as a function of tuning parameters. Furthermore, for the iterative Ensemble Smoother (iES), we discuss the importance of noise on observations and show how iES can cope with non-unique outcomes based on objective function construction. These insights are valuable for modelers using PEST, PEST++, or similar parameter estimation tools.

Impact of 4D Seismic Data Assimilation in the Production Forecasting of a Heavy Oil Turbidite Sandstone Field Offshore Brazil

The incorporation of 4D seismic data can be done at model characterization and data assimilation steps, the latter applying the observed data to update the model properties. In this work, we evaluate the impact of 4DS data in the production forecasting results investigating the influence on these distinct steps. We employ a prior model set generated without 4DS data and another prior set with 4DS in the characterisation. We perform, then, the DA in three different ways: (1) using only well history data with a prior set without 4DS; (2) using well history and 4DS data with this same prior set; and (3) using well history and 4DS data with the prior set generated with 4DS data. We employ the Ensemble Smoother with Multiple Data Assimilation method for data assimilation and implement a procedure to adjust the well productivities and injectivities after DA. This work assesses the differences among the three DA cases in terms of field oil production forecasting, model attributes and model misfits, the latter evaluated in terms of the assimilated data set and of a different data set for validation purposes only. We apply the work to a real heavy oil turbiditic field located offshore Brazil. The case application demonstrates a successful data assimilation study on a real field integrating well history and 4DS data. The results show that the utilisation of 4DS in both model characterisation and DA steps brought value to the final uncertainty reduction results. The posterior model ensemble with 4DS data in model characterization and DA provided the lowest model misfits overall to the full data set, being the best choice for application in field production forecasting studies. The case without 4DS data provided significantly more pessimistic field oil production than the cases with 4DS, making very evident the importance of employing 4DS at uncertainty reduction workflows.

Strategic Geosteering Workflow with Uncertainty Quantification and Deep Learning: Initial Test on the Goliat Field Data

Continuous integration of real-time logging-while-drilling data into a subsurface model with relevant geological uncertainties enables strategic geosteering: a field-level optimization of the well-placement strategy. Model errors arising from oversimplified conceptual geological models and imperfect simulation of measurements result in unreliable subsurface-model updates. The model errors are particularly pronounced when synthetic measurements are approximated with a fast but imperfect model, such as a deep neural network (DNN).#xD;We present a practical data-assimilation workflow consisting of offline and online phases. The offline phase involves DNN training and building an uncertain prior near-well geo-model. The online phase utilizes the flexible iterative ensemble smoother (FlexIES) to perform real-time assimilation of extra-deep electromagnetic data while accounting for the model errors in the approximate DNN model. We demonstrate the proposed workflow on historic well-log data from the Goliat Field (Barents Sea). #xD;The median of our probabilistic estimation is on par with proprietary inversion, regardless of the number of layers in the chosen prior or the approximate DNN model. By estimating model errors, FlexIES automatically quantifies the uncertainty in the boundaries and resistivities of layers, which is not standard in proprietary inversion. #xD;This capability allows us to capture uncertainties more efficiently, thus providing input for future quantitative decision support methods. We demonstrate the potential of quantitive decision support by visually estimating the ahead-of-bit risk of reservoir exit that has occurred during the considered operation.

Groundwater Contamination Source Recognition Based on a Two-Stage Inversion Framework with a Deep Learning Surrogate

Groundwater contamination source recognition is an important prerequisite for subsequent remediation efforts. To overcome the limitations of single inversion methods, this study proposed a two-stage inversion framework by integrating two primary inversion approaches—simulation-optimization and simulation-data assimilation—thereby enhancing inversion accuracy. In the first stage, the ensemble smoother with multiple data assimilation method (a type of simulation-data assimilation) conducted a global broad search to provide better initial values and ranges for the second stage. In the subsequent stage, a collective decision optimization algorithm (a type of simulation-optimization) was used for a refined deep search, further enhancing the final inversion accuracy. Additionally, a deep learning method, the multilayer perceptron, was utilized to establish a surrogate of the simulation model, reducing computational costs. These theories and methods were applied and validated in a hypothetical scenario for the synchronous identification of the contamination source and boundary conditions. The results demonstrated that the proposed two-stage inversion framework significantly improved search accuracy compared to single inversion methods, with a mean relative error and mean absolute error of just 4.95% and 0.1756, respectively. Moreover, the multilayer perceptron surrogate model offered greater approximation accuracy to the simulation model than the traditional shallow learning surrogate model. Specifically, the coefficient of determination, mean relative error, mean absolute error, and root mean square error were 0.9860, 9.72%, 0.1727, and 0.47, respectively, highlighting its significant advantages. The findings of this study can provide more reliable technical support for practical case applications and improve subsequent remediation efficiency.

Effective Characterization of Fractured Media With PEDL: A Deep Learning‐Based Data Assimilation Approach

AbstractGeological formations with fractures are frequently encountered in various research fields. Accurately characterizing these fractured media is of paramount importance when it comes to tasks that demand precise predictions of liquid flow and solute transport within them. Since directly measuring fractured media poses inherent challenges, data assimilation (DA) techniques are typically employed to derive inverse estimates of media properties using observable state variables. Nonetheless, the considerable difficulties arising from the strong heterogeneity and non‐Gaussian nature of fractured media have diminished the effectiveness of existing DA methods. In this study, we formulate a novel DA approach known as parameter estimator with deep learning (PEDL) that harnesses the capabilities of DL to capture nonlinear relationships and extract non‐Gaussian features. To evaluate PEDL's performance, we conduct three case studies, comprising two numerical cases and one real‐world case. In these cases, we systematically compare PEDL with three widely used DA methods: ensemble smoother with multiple DA (ESMDA), iterative local updating ES (ILUES), and ES with DL‐based update (ESDL). Notably, in the problems characterized by highly non‐Gaussian features, ESMDA and ILUES produce significantly divergent results. Conversely, employing the DL‐based update, ESDL demonstrates improved performance. However, its estimation uncertainty remains high, potentially attributable to ESDL's updating mechanism. Comprehensive analyses confirm PEDL's validity and adaptability across various ensemble sizes and DL model architectures. Moreover, even in scenarios where structural difference exists between the accurate reference model and the simplified forecast model, PEDL adeptly identifies the primary characteristics of fracture networks.

A Deep Learning‐Based Data Assimilation Approach to Characterizing Coastal Aquifers Amid Non‐Linearity and Non‐Gaussianity Challenges

AbstractSeawater intrusion (SI) poses a substantial threat to water security in coastal regions, where numerical models play a pivotal role in supporting groundwater management and protection. However, the inherent heterogeneity of coastal aquifers introduces significant uncertainties into SI predictions, potentially diminishing their effectiveness in management decisions. Data assimilation (DA) offers a solution by integrating various types of observational data with the model to characterize heterogeneous coastal aquifers. Traditional DA techniques, like ensemble smoother using the Kalman formula (ESK) and Markov chain Monte Carlo, face challenges when confronted with the non‐linearity, non‐Gaussianity, and high‐dimensionality issues commonly encountered in aquifer characterization. In this study, we introduce a novel DA approach rooted in deep learning (DL), referred to as ESDL, aimed at effectively characterizing coastal aquifers with varying levels of heterogeneity. We systematically investigate a range of factors that impact the performance of ESDL, including the number and types of observations, the degree of aquifer heterogeneity, the structure and training options of the DL models. Our findings reveal that ESDL excels in characterizing heterogeneous aquifers under non‐linear and non‐Gaussian conditions. Comparison between ESDL and ESK under different experimentation settings underscores the robustness of ESDL. Conversely, in certain scenarios, ESK displays noticeable biases in the characterization results, especially when measurement data from non‐linear and discontinuous processes are used. To optimize the efficacy of ESDL, attention must be given to the design of the DL model and the selection of observational data, which are crucial to ensure the universal applicability of this DA method.

A dual-porosity flow-net model for simulating water-flooding in low-permeability fractured reservoirs

The physics-based data-driven flow-network models with high computational efficiency have received great attention as the promising surrogate models for reservoir numerical simulation. However, the existing flow-network models developed for water-flooding reservoirs fail to consider different seepage characteristics of matrix and fractures and cannot be straightly applied to simulate the water-flooding process in low-permeability fractured reservoirs. In this study, we combine the flow-network model with the dual-porosity model to propose a new physics-based data-driven surrogate model, namely the Dual-Porosity Flow-Network Model (Flow-Net-DP), which can consider the non-Darcy flow in tight matrix and the stress-sensitive effects and preferential flow characteristic in fractures. Specifically, we refer to the dual-porosity model and use two channels to represent the connections between wells: one indicates the fracture system, the other represents the matrix system, and the fluid exchange between these two systems is considered by using a transfer function. Besides, each channel is discretized into one-dimensional grids, and a fully implicit scheme with Newton iteration is used to calculate pressure and saturation. Moreover, we establish an automated history matching method by using the Ensemble Smoother with Multiple Data Assimilation (ESMDA) algorithm to calibrate model parameters of Flow-Net-DP, and develop a production optimization method by using the Differential Evolution (DE) algorithm. Finally, the numerical simulation, history matching, and production optimization are conducted on different numerical examples to validate the capability of Flow-Net-DP. The results indicate that the Flow-Net-DP can provide a better description of water flooding process in low-permeability fractured reservoirs compared with the existing flow-network model, especially the rapid water breakthrough caused by the preferential flow characteristic in fractures. Furthermore, both history matching and production optimization based on the Flow-Net-DP yield satisfactory outcomes. For instance, when the optimization results are similar to the full-order simulation model, the optimization speed of Flow-Net-DP is increased by more than five times.

Evaluating parameter inversion efficiency in Heterogeneous Groundwater models using Karhunen-Loève expansion: a comparative study of genetic algorithm, ensemble smoother, and MCMC

Evaluating parameter inversion efficiency in Heterogeneous Groundwater models using Karhunen-Loève expansion: a comparative study of genetic algorithm, ensemble smoother, and MCMC

Application of latent variable evolution for channel reservoir characterization using generative adversarial networks and particle swarm optimization

When characterizing channel reservoirs, ensemble-based methods may compromise channel features due to the conflict between the Gaussian distribution assumption of the methods and bimodality of channel reservoirs. To overcome this challenge, one effective approach involves leveraging generative models. Specifically, a generative model trained with channel reservoir models has ability to generate bimodally distributed values from latent vectors whose elements are intentionally designed to conform a Gaussian distribution. Therefore, it resolves the conflict, allowing the ensemble-based methods to update the latent vectors.However, generating initial latent vectors randomly poses an additional challenge and can lead to a suboptimal quality of the initial ensemble. They can significantly influence the unreliability of characterizations, primarily because their impact is strongly tied to the quality of the initial models in the ensemble-based methods.To address this challenge, we propose a novel scheme for channel reservoir characterization using Latent Variable Evolution. In this study, we adopt Generative Adversarial Networks (GAN) and Particle Swarm Optimization (PSO). PSO explores the latent space of GAN trained with channel reservoirs in order to find ones that generate models resembling a true reservoir. Validation on simple and complex reservoir cases demonstrates our proposed method can efficiently provide reliable channel reservoir characterization regardless of the quality of the initial latent vectors. These results are compared to Ensemble Smoother with Multiple Data Assimilation with GAN.