Fast modelling of gas reservoirs using non-intrusive reduced order modelling and machine learning

This work focussed on developing approximate methods for rapidly estimating gas field production performance. Proper orthogonal decomposition (POD) - Radial basis function (RBF) and POD-Autoencoder (AE) Non Intrusive Reduced Order Models (NIROMs) were considered. The accuracy and speed of both NIROMs were evaluated for modelling different aspects of gas field modelling including reservoirs with time-varying and mixed production controls, reservoirs with and without aquifer pressure support, and for wells that were (or not ) shut-in during production lifecycle. These NIROMs were applied to predicting the performance of four gas reservoir models: a homogeneous synthetic model; a heterogeneous gas field with 3 wells and structures similar to the Norne Field; a water coning model in radian grid; and a sector model of a real gas field provided by Woodside Petroleum. The POD-RBF and POD-AE NIROMs were trained using the simulation solutions from a commercial reservoir simulator (ECLIPSE): grid distributions of pressure and saturations as well as time series production data such as production rates, cumulative productions and pressures. Different cases were run based on typical input parameters usually used in field performance studies. The simulation solutions were then standardised to zero mean and reduced into hyperspace using POD. In most cases, the optimum number of POD basis functions (99.9% energy criterion) of the solutions (training data) were used to reduce the training data into a lower-dimensional hyperspace space. The reduced training data and their corresponding parameter values were combined to form sample and response arrays based on a cause and effect pattern. RBF or AE was then used to interpolate the weighting coefficients that represented the dynamics of the gas reservoir as captured within the reduced training data. These weighting coefficients were used to propagate the prediction of new unseen simulation cases for the duration of predictions. The simulation results from either or both NIROMs was then compared against the simulation solution of the same cases in ECLIPSE. It was found that the POD-RBF is a better predictive tool for gas field modelling. It is faster, more accurate and consistent than the POD-AE, giving satisfactory predictions with up to 99% accuracy and 2 orders of magnitude speed-up. No single POD-AE is sufficient for predicting different production scenarios, besides, the process of arriving at a suitable POD-AE involves finetuning several hyper-parameters by trial and error, which may be more burdensome for practising petroleum engineers. The accuracy of NIROM’s prediction of production variable is generally improved by using more than the optimal number of POD-basis functions, while predictions of grid distributed properties are satisfactorily predicted with the optimal number of POD-basis functions. NIROM’s accuracy is dependent on whether the range of parameters of the prediction, their duration and specific production scenarios (such as having mixed production controls or aquifer pressure support) reflect those of the training cases. Overall, the number of training runs, the size of the reservoir model as well as the number of time intervals at which simulation output data is required all affect the speed of training both NIROMs for prediction. Other contributions of this work include showing that the linear RBF is the most suitable RBF for gas field modelling; developing a novel normalisation approach for time-varying parameters; and applying NIROMs to seasonally varying production scenarios with mixed production controls. This work is the first time that the POD-AE has been developed and evaluated for petroleum field development planning.Open Acces

Numerical simulation of flooding from multiple sources using adaptive anisotropic unstructured meshes and machine learning methods

Over the past few decades, urban floods have been gaining more attention due to their increase in frequency. To provide reliable flooding predictions in urban areas, various numerical models have been developed to perform high-resolution flood simulations. However, the use of high-resolution meshes across the whole computational domain causes a high computational burden. In this thesis, a 2D control-volume and finite-element (DCV-FEM) flood model using adaptive unstructured mesh technology has been developed. This adaptive unstructured mesh technique enables meshes to be adapted optimally in time and space in response to the evolving flow features, thus providing sufficient mesh resolution where and when it is required. It has the advantage of capturing the details of local flows and wetting and drying front while reducing the computational cost. Complex topographic features are represented accurately during the flooding process. This adaptive unstructured mesh technique can dynamically modify (both, coarsening and refining the mesh) and adapt the mesh to achieve a desired precision, thus better capturing transient and complex flow dynamics as the flow evolves. A flooding event that happened in 2002 in Glasgow, Scotland, United Kingdom has been simulated to demonstrate the capability of the adaptive unstructured mesh flooding model. The simulations have been performed using both fixed and adaptive unstructured meshes, and then results have been compared with those published 2D and 3D results. The presented method shows that the 2D adaptive mesh model provides accurate results while having a low computational cost. The above adaptive mesh flooding model (named as Floodity) has been further developed by introducing (1) an anisotropic dynamic mesh optimization technique (anisotropic-DMO); (2) multiple flooding sources (extreme rainfall and sea-level events); and (3) a unique combination of anisotropic-DMO and high-resolution Digital Terrain Model (DTM) data. It has been applied to a densely urbanized area within Greve, Denmark. Results from MIKE 21 FM are utilized to validate our model. To assess uncertainties in model predictions, sensitivity of flooding results to extreme sea levels, rainfall and mesh resolution has been undertaken. The use of anisotropic-DMO enables us to capture high resolution topographic features (buildings, rivers and streets) only where and when is needed, thus providing improved accurate flooding prediction while reducing the computational cost. It also allows us to better capture the evolving flow features (wetting-drying fronts). To provide real-time spatio-temporal flood predictions, an integrated long short-term memory (LSTM) and reduced order model (ROM) framework has been developed. This integrated LSTM-ROM has the capability of representing the spatio-temporal distribution of floods since it takes advantage of both ROM and LSTM. To reduce the dimensional size of large spatial datasets in LSTM, the proper orthogonal decomposition (POD) and singular value decomposition (SVD) approaches are introduced. The performance of the LSTM-ROM developed here has been evaluated using Okushiri tsunami as test cases. The results obtained from the LSTM-ROM have been compared with those from the full model (Fluidity). Promising results indicate that the use of LSTM-ROM can provide the flood prediction in seconds, enabling us to provide real-time flood prediction and inform the public in a timely manner, reducing injuries and fatalities. Additionally, data-driven optimal sensing for reconstruction (DOSR) and data assimilation (DA) have been further introduced to LSTM-ROM. This linkage between modelling and experimental data/observations allows us to minimize model errors and determine uncertainties, thus improving the accuracy of modelling. It should be noting that after we introduced the DA approach, the prediction errors are significantly reduced at time levels when an assimilation procedure is conducted, which illustrates the ability of DOSR-LSTM-DA to significantly improve the model performance. By using DOSR-LSTM-DA, the predictive horizon can be extended by 3 times of the initial horizon. More importantly, the online CPU cost of using DOSR-LSTM-DA is only 1/3 of the cost required by running the full model.Open Acces

Machine Learning-based Generalized Multiscale Finite Element Method and its Application in Reservoir Simulation

In multiscale modeling of subsurface fluid flow in heterogeneous porous media, standard polynomial basis functions are replaced by multiscale basis functions, which are used to predict pressure distribution. To produce such functions in the mixed Generalized Multiscale Finite Element Method (GMsFEM), a number of Partial Differential Equations (PDEs) must be solved, leading to significant computational overhead. The main objective of the work presented in this thesis was to investigate the efficiency of Machine Learning (ML)/Deep Learning (DL) models in reconstructing the multiscale basis functions (Basis 2, 3, 4, and 5) of the mixed GMsFEM. To achieve this, four standard models named SkiplessCNN models were first developed to predict four different multiscale basis functions. These predictions were based on two distinct datasets (initial and extended) generated, with the permeability field being the sole input. Subsequently, focusing on the extended dataset, three distinct skip connection schemes (FirstSkip, MidSkip, and DualSkip) were incorporated into the SkiplessCNN architecture. Following this, the four developed models - SkiplessCNN, FirstSkipCNN, MidSkipCNN, and DualSkipCNN - were separately combined using linear regression and ridge regression within the framework of Deep Ensemble Learning (DEL). Furthermore, the reliability of the DualSkipCNN model was examined using Monte Carlo (MC) dropout. Ultimately, two Fourier Neural Operator (FNO) models, operating on infinite-dimensional spaces, were developed based on a new dataset for directly predicting pressure distribution. Based on the results, sufficient data for the validation and testing subsets could help decrease overfitting. Additionally, all three skip connections were found to be effective in enhancing the performance of SkiplessCNN, with DualSkip being the most effective among them. As evaluated on the testing subset, the combined models using linear regression and ridge regression significantly outperformed the individual models for all basis functions. The results also confirmed the robustness of MC dropout for DualSkipCNN in terms of epistemic uncertainty. Regarding the FNO models, it was discovered that the inclusion of a MultiLayer Perceptron (MLP) in the original Fourier layers significantly improved the prediction performance on the testing subset. Looking at this work as an image (matrix)-to-image (matrix) problem, the developed data-driven models through various techniques could find applications beyond reservoir engineering

Parametric Model Order Reduction For Optimization in Closed Loop Field Development Using Machine Learning Techniques

Field development workflows consist of production optimization and data assimilation procedures that require running large number of reservoir simulations for fine scale models. Recent advancements in parallel computing and accelerated solvers have reduced simulation times for such high-fidelity models, however, repeated simulations and underlying complex non-linearities involved in multiphase and multicomponent models still remain a bottleneck. This computational challenge has motivated the development of Model Order Reduction (MOR) techniques which provide low dimensional representation of high-fidelity models and thus provide significant computational savings with the efforts to preserve the accuracy of simulation outputs. The aim of my research is to develop projection based MOR workflows for optimization problems in closed loop field development procedure, which include well control optimization and well placement optimization. We pose the problem formulation as Parametric Model Order Reduction (PMOR) that allows for taking into consideration a system parameter for each optimization problem considered. For developing Reduced Order Models (ROMs) for such problems, we use projection based Proper Orthogonal Decomposition (POD) which enables representation of reservoir state variables in terms of highly reduced set of variables. First part of the research is based on developing ROMs for well control optimization problem, where we look for the optimal strategy to control the wells settings. Here we use DEIM in addition to POD for quick evaluation of non-linear functions. We introduce a novel training procedure for global ROM during control optimization, which proved to give accurate results when compared to optimization using fine scale simulations. We test the performance of POD-DEIM for different optimization parameterization methods like polynomial and piecewise polynomial approximations on a waterflooding scenario. Polynomial approximation of BHP control served as good training sets for POD-DEIM with the training strategy proposed leading to accurate and fast reduced model. The second part of my research, which is a major contribution of my work, is based on developing ROMs for changing well locations during well placement optimization problem. Here, we do not employ proposed MOR on well location optimization problem, rather develop MOR strategies as a precursor to be used for well location optimization in future. Projection based reduced order modeling methodologies for well control optimization have reached a good level of maturity, however, MOR development for changing well configurations, is unexplored. We first propose error based local PMOR for new well location using a Machine Learning (ML) framework with POD. ML algorithms like Neural Networks and Random Forests help us predict the ROM error that eventually will choose appropriate basis at a new well location from previously computed reduced models. We introduce geometry based features and physics based flow diagnostics features to train ML models. In efforts to tackle the issues with local PMOR technique proposed, we introduce a novel global non-intrusive PMOR technique based on machine learning. The idea here is to represent the entire parameter space of well location by a single global ROB and then using ML model to establish a relation between the input well location information and the POD basis coefficients of each state. We then also formulate the error correction model based on the reduced model solution, to account for solution discrepancies. The proposed method, that can make use of parallel resources efficiently, shows promising results on waterflooding case studies in predicting various quantities of interest (QoI) at new well locations such as oil production rates and water cut, and showed significant speedups of one to two orders of magnitude for the test cases