Reduced order modeling of subsurface multiphase flow models using deep residual recurrent neural networks

We present a reduced order modeling (ROM) technique for subsurface multi-phase flow problems building on the recently introduced deep residual recurrent neural network (DR-RNN) [1]. DR-RNN is a physics aware recurrent neural network for modeling the evolution of dynamical systems. The DR-RNN architecture is inspired by iterative update techniques of line search methods where a fixed number of layers are stacked together to minimize the residual (or reduced residual) of the physical model under consideration. In this manuscript, we combine DR-RNN with proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM) to reduce the computational complexity associated with high-fidelity numerical simulations. In the presented formulation, POD is used to construct an optimal set of reduced basis functions and DEIM is employed to evaluate the nonlinear terms independent of the full-order model size. We demonstrate the proposed reduced model on two uncertainty quantification test cases using Monte-Carlo simulation of subsurface flow with random permeability field. The obtained results demonstrate that DR-RNN combined with POD-DEIM provides an accurate and stable reduced model with a fixed computational budget that is much less than the computational cost of standard POD-Galerkin reduced model combined with DEIM for nonlinear dynamical systems

Multi-fidelity deep residual recurrent neural networks for uncertainty quantification

Effective propagation of uncertainty through a nonlinear dynamical system is an essential task for a number of engineering applications. One viable probabilistic approach to propagate the uncertainty from the high dimensional random inputs to the high-fidelity model outputs is Monte Carlo method. However, Monte Carlo method requires a substantial number of computationally expensive high-fidelity simulations to converge their computed estimations towards the desired statistics. Hence, performing Monte Carlo high-fidelity simulations becomes computationally prohibitive for large-scale realistic problems. Multi-fidelity approaches provide a general framework for combining a hierarchy of computationally cheap low-fidelity models to accelerate the Monte Carlo estimation of the high-fidelity model output. The objective of this thesis is to derive computationally efficient low-fidelity models and an effective multi-fidelity framework to accelerate the Monte Carlo method that uses a single high-fidelity model only. In this thesis, a physics aware recurrent neural network (RNN) called deep residual recurrent neural network (DR-RNN) is developed as an efficient low-fidelity model for nonlinear dynamical systems. The information hidden in the mathematical model representing the nonlinear dynamical system is exploited to construct the DR-RNN architecture. The developed DR-RNN is inspired by the iterative steps of line search methods in finding the residual minimiser of numerically discretized differential equations. More specifically, the stacked layers of the DR-RNN architecture is formulated to act collectively as an iterative scheme. The dynamics of DR-RNN is explicit in time with remarkable convergence and stability properties for a large time step that violates numerical stability condition. Numerical examples demonstrate that DR-RNN can effectively emulate the high-fidelity model of nonlinear physical systems with a significantly lower number of parameters in comparison to standard RNN architectures. Further, DR-RNN is combined with Proper Orthogonal Decomposition (POD) for model reduction of time dependent partial differential equations. The numerical results show the proposed DR-RNN as an explicit and stable reduced order technique. The numerical results also show significant gains in accuracy by increasing the depth of proposed DR-RNN similar to other applications of deep learning. Next, a reduced order modeling technique for subsurface multi-phase flow problems is developed building on the DR-RNN architecture. More specifically, DR-RNN is combined with POD and discrete empirical interpolation method (DEIM) to reduce the computational complexity associated with high-fidelity subsurface multi-phase flow simulations. In the presented formulation, POD is used to construct an optimal set of reduced basis functions and DEIM is employed to evaluate the nonlinear terms independent of the high-fidelity model size. The proposed ROM is demonstrated on two uncertainty quantification test cases involving Monte Carlo simulation of subsurface flow with random permeability field. The obtained results demonstrate that DR-RNN combined with POD-DEIM provides an accurate and stable ROM with a fixed computational budget that is much less than the computational cost of standard POD-Galerkin ROM combined with DEIM for nonlinear dynamical systems. Finally, this thesis focus on developing multi-fidelity framework to estimate the statistics of high-fidelity model outputs of interest. Recently, Multi-Fidelity Monte Carlo (MFMC) method and Multi-Level Monte Carlo (MLMC) method have shown to significantly accelerate the Monte Carlo estimation by making use of low cost low-fidelity models. In this thesis, the features of both the MFMC method and the MLMC method are combined into a single framework called Multi-Fidelity-Multi-Level Monte Carlo (MFML-MC) method. In MFML-MC method, MLMC framework is developed first in which a multi-level hierarchy of POD approximations of high-fidelity outputs are utilized as low-fidelity models. Next, MFMC method is incorporated into the developed MLMC framework in which the MLMC estimator is modified at each level to benefit from a level specific low-fidelity model. Finally, a variant of deep residual recurrent neural network called Model-Free DR-RNN (MF-DR-RNN) is used as a level specific low-fidelity model in the MFML-MC framework. The performance of MFML-MC method is compared to Monte Carlo estimation that uses either a high-fidelity model or a single low-fidelity model on two subsurface flow problems with random permeability field. Numerical results show that MFML-MC method provides an unbiased estimator and show speedups by orders of magnitude compared to Monte Carlo estimation that uses a single high-fidelity model

Advancing Carbon Sequestration through Smart Proxy Modeling: Leveraging Domain Expertise and Machine Learning for Efficient Reservoir Simulation

Geological carbon sequestration (GCS) offers a promising solution to effectively manage extra carbon, mitigating the impact of climate change. This doctoral research introduces a cutting-edge Smart Proxy Modeling-based framework, integrating artificial neural networks (ANNs) and domain expertise, to re-engineer and empower numerical reservoir simulation for efficient modeling of CO2 sequestration and demonstrate predictive conformance and replicative capabilities of smart proxy modeling. Creating well-performing proxy models requires extensive human intervention and trial-and-error processes. Additionally, a large training database is essential to ANN model for complex tasks such as deep saline aquifer CO2 sequestration since it is used as the neural network\u27s input and output data. One major limitation in CCS programs is the lack of real field data due to a lack of field applications and issues with confidentiality. Considering these drawbacks, and due to high-dimensional nonlinearity, heterogeneity, and coupling of multiple physical processes associated with numerical reservoir simulation, novel research to handle these complexities as it allows for the creation of possible CO2 sequestration scenarios that may be used as a training set. This study addresses several types of static and dynamic realistic and practical field-base data augmentation techniques ranging from spatial complexity, spatio-temporal complexity, and heterogeneity of reservoir characteristics. By incorporating domain-expertise-based feature generation, this framework honors precise representation of reservoir overcoming computational challenges associated with numerical reservoir tools. The developed ANN accurately replicated fluid flow behavior, resulting in significant computational savings compared to traditional numerical simulation models. The results showed that all the ML models achieved very good accuracies and high efficiency. The findings revealed that the quality of the path between the focal cell and injection wells emerged as the most crucial factor in both CO2 saturation and pressure estimation models. These insights significantly contribute to our understanding of CO2 plume monitoring, paving the way for breakthroughs in investigating reservoir behavior at a minimal computational cost. The study\u27s commitment to replicating numerical reservoir simulation results underscores the model\u27s potential to contribute valuable insights into the behavior and performance of CO2 sequestration systems, as a complimentary tool to numerical reservoir simulation when there is no measured data available from the field. The transformative nature of this research has vast implications for advancing carbon storage modeling technologies. By addressing the computational limitations of traditional numerical reservoir models and harnessing the synergy between machine learning and domain expertise, this work provides a practical workflow for efficient decision-making in sequestration projects

Exploring the adoption of a conceptual data analytics framework for subsurface energy production systems: a study of predictive maintenance, multi-phase flow estimation, and production optimization

Als die Technologie weiter fortschreitet und immer stärker in der Öl- und Gasindustrie integriert wird, steht eine enorme Menge an Daten in verschiedenen Wissenschaftsdisziplinen zur Verfügung, die neue Möglichkeiten bieten, informationsreiche und handlungsorientierte Informationen zu gewinnen. Die Konvergenz der digitalen Transformation mit der Physik des Flüssigkeitsflusses durch poröse Medien und Pipeline hat die Entwicklung und Anwendung von maschinellem Lernen (ML) vorangetrieben, um weiteren Mehrwert aus diesen Daten zu gewinnen. Als Folge hat sich die digitale Transformation und ihre zugehörigen maschinellen Lernanwendungen zu einem neuen Forschungsgebiet entwickelt. Die Transformation von Brownfields in digitale Ölfelder kann bei der Energieproduktion helfen, indem verschiedene Ziele erreicht werden, einschließlich erhöhter betrieblicher Effizienz, Produktionsoptimierung, Zusammenarbeit, Datenintegration, Entscheidungsunterstützung und Workflow-Automatisierung. Diese Arbeit zielt darauf ab, ein Rahmenwerk für diese Anwendungen zu präsentieren, insbesondere durch die Implementierung virtueller Sensoren, Vorhersageanalytik mithilfe von Vorhersagewartung für die Produktionshydraulik-Systeme (mit dem Schwerpunkt auf elektrischen Unterwasserpumpen) und präskriptiven Analytik für die Produktionsoptimierung in Dampf- und Wasserflutprojekten. In Bezug auf virtuelle Messungen ist eine genaue Schätzung von Mehrphasenströmen für die Überwachung und Verbesserung von Produktionsprozessen entscheidend. Diese Studie präsentiert einen datengetriebenen Ansatz zur Berechnung von Mehrphasenströmen mithilfe von Sensormessungen in elektrischen untergetauchten Pumpbrunnen. Es wird eine ausführliche exploratorische Datenanalyse durchgeführt, einschließlich einer Ein Variablen Studie der Zielausgänge (Flüssigkeitsrate und Wasseranteil), einer Mehrvariablen-Studie der Beziehungen zwischen Eingaben und Ausgaben sowie einer Datengruppierung basierend auf Hauptkomponentenprojektionen und Clusteralgorithmen. Feature Priorisierungsexperimente werden durchgeführt, um die einflussreichsten Parameter in der Vorhersage von Fließraten zu identifizieren. Die Modellvergleich erfolgt anhand des mittleren absoluten Fehlers, des mittleren quadratischen Fehlers und des Bestimmtheitskoeffizienten. Die Ergebnisse zeigen, dass die CNN-LSTM-Netzwerkarchitektur besonders effektiv bei der Zeitreihenanalyse von ESP-Sensordaten ist, da die 1D-CNN-Schichten automatisch Merkmale extrahieren und informative Darstellungen von Zeitreihendaten erzeugen können. Anschließend wird in dieser Studie eine Methodik zur Umsetzung von Vorhersagewartungen für künstliche Hebesysteme, insbesondere bei der Wartung von Elektrischen Untergetauchten Pumpen (ESP), vorgestellt. Conventional maintenance practices for ESPs require extensive resources and manpower, and are often initiated through reactive monitoring of multivariate sensor data. Um dieses Problem zu lösen, wird die Verwendung von Hauptkomponentenanalyse (PCA) und Extreme Gradient Boosting Trees (XGBoost) zur Analyse von Echtzeitsensordaten und Vorhersage möglicher Ausfälle in ESPs eingesetzt. PCA wird als unsupervised technique eingesetzt und sein Ausgang wird weiter vom XGBoost-Modell für die Vorhersage des Systemstatus verarbeitet. Das resultierende Vorhersagemodell hat gezeigt, dass es Signale von möglichen Ausfällen bis zu sieben Tagen im Voraus bereitstellen kann, mit einer F1-Bewertung größer als 0,71 im Testset. Diese Studie integriert auch Model-Free Reinforcement Learning (RL) Algorithmen zur Unterstützung bei Entscheidungen im Rahmen der Produktionsoptimierung. Die Aufgabe, die optimalen Injektionsstrategien zu bestimmen, stellt Herausforderungen aufgrund der Komplexität der zugrundeliegenden Dynamik, einschließlich nichtlinearer Formulierung, zeitlicher Variationen und Reservoirstrukturheterogenität. Um diese Herausforderungen zu bewältigen, wurde das Problem als Markov-Entscheidungsprozess reformuliert und RL-Algorithmen wurden eingesetzt, um Handlungen zu bestimmen, die die Produktion optimieren. Die Ergebnisse zeigen, dass der RL-Agent in der Lage war, den Netto-Barwert (NPV) durch kontinuierliche Interaktion mit der Umgebung und iterative Verfeinerung des dynamischen Prozesses über mehrere Episoden signifikant zu verbessern. Dies zeigt das Potenzial von RL-Algorithmen, effektive und effiziente Lösungen für komplexe Optimierungsprobleme im Produktionsbereich zu bieten.As technology continues to advance and become more integrated in the oil and gas industry, a vast amount of data is now prevalent across various scientific disciplines, providing new opportunities to gain insightful and actionable information. The convergence of digital transformation with the physics of fluid flow through porous media and pipelines has driven the advancement and application of machine learning (ML) techniques to extract further value from this data. As a result, digital transformation and its associated machine-learning applications have become a new area of scientific investigation. The transformation of brownfields into digital oilfields can aid in energy production by accomplishing various objectives, including increased operational efficiency, production optimization, collaboration, data integration, decision support, and workflow automation. This work aims to present a framework of these applications, specifically through the implementation of virtual sensing, predictive analytics using predictive maintenance on production hydraulic systems (with a focus on electrical submersible pumps), and prescriptive analytics for production optimization in steam and waterflooding projects. In terms of virtual sensing, the accurate estimation of multi-phase flow rates is crucial for monitoring and improving production processes. This study presents a data-driven approach for calculating multi-phase flow rates using sensor measurements located in electrical submersible pumped wells. An exhaustive exploratory data analysis is conducted, including a univariate study of the target outputs (liquid rate and water cut), a multivariate study of the relationships between inputs and outputs, and data grouping based on principal component projections and clustering algorithms. Feature prioritization experiments are performed to identify the most influential parameters in the prediction of flow rates. Model comparison is done using the mean absolute error, mean squared error and coefficient of determination. The results indicate that the CNN-LSTM network architecture is particularly effective in time series analysis for ESP sensor data, as the 1D-CNN layers are capable of extracting features and generating informative representations of time series data automatically. Subsequently, the study presented herein a methodology for implementing predictive maintenance on artificial lift systems, specifically regarding the maintenance of Electrical Submersible Pumps (ESPs). Conventional maintenance practices for ESPs require extensive resources and manpower and are often initiated through reactive monitoring of multivariate sensor data. To address this issue, the study employs the use of principal component analysis (PCA) and extreme gradient boosting trees (XGBoost) to analyze real-time sensor data and predict potential failures in ESPs. PCA is utilized as an unsupervised technique and its output is further processed by the XGBoost model for prediction of system status. The resulting predictive model has been shown to provide signals of potential failures up to seven days in advance, with an F1 score greater than 0.71 on the test set. In addition to the data-driven modeling approach, The present study also in- corporates model-free reinforcement learning (RL) algorithms to aid in decision-making in production optimization. The task of determining the optimal injection strategy poses challenges due to the complexity of the underlying dynamics, including nonlinear formulation, temporal variations, and reservoir heterogeneity. To tackle these challenges, the problem was reformulated as a Markov decision process and RL algorithms were employed to determine actions that maximize production yield. The results of the study demonstrate that the RL agent was able to significantly enhance the net present value (NPV) by continuously interacting with the environment and iteratively refining the dynamic process through multiple episodes. This showcases the potential for RL algorithms to provide effective and efficient solutions for complex optimization problems in the production domain. In conclusion, this study represents an original contribution to the field of data-driven applications in subsurface energy systems. It proposes a data-driven method for determining multi-phase flow rates in electrical submersible pumped (ESP) wells utilizing sensor measurements. The methodology includes conducting exploratory data analysis, conducting experiments to prioritize features, and evaluating models based on mean absolute error, mean squared error, and coefficient of determination. The findings indicate that a convolutional neural network-long short-term memory (CNN-LSTM) network is an effective approach for time series analysis in ESPs. In addition, the study implements principal component analysis (PCA) and extreme gradient boosting trees (XGBoost) to perform predictive maintenance on ESPs and anticipate potential failures up to a seven-day horizon. Furthermore, the study applies model-free reinforcement learning (RL) algorithms to aid decision-making in production optimization and enhance net present value (NPV)

Progressive reduced order modeling: empowering data-driven modeling with selective knowledge transfer

Data-driven modeling can suffer from a constant demand for data, leading to reduced accuracy and impractical for engineering applications due to the high cost and scarcity of information. To address this challenge, we propose a progressive reduced order modeling framework that minimizes data cravings and enhances data-driven modeling's practicality. Our approach selectively transfers knowledge from previously trained models through gates, similar to how humans selectively use valuable knowledge while ignoring unuseful information. By filtering relevant information from previous models, we can create a surrogate model with minimal turnaround time and a smaller training set that can still achieve high accuracy. We have tested our framework in several cases, including transport in porous media, gravity-driven flow, and finite deformation in hyperelastic materials. Our results illustrate that retaining information from previous models and utilizing a valuable portion of that knowledge can significantly improve the accuracy of the current model. We have demonstrated the importance of progressive knowledge transfer and its impact on model accuracy with reduced training samples. For instance, our framework with four parent models outperforms the no-parent counterpart trained on data nine times larger. Our research unlocks data-driven modeling's potential for practical engineering applications by mitigating the data scarcity issue. Our proposed framework is a significant step toward more efficient and cost-effective data-driven modeling, fostering advancements across various fields