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This paper presents an innovative data-integration that uses an iterative-learning method, a deep neural network (DNN) coupled with a stacked autoencoder (SAE) to solve issues encountered with many-objective history matching. The proposed method consists of a DNN-based inverse model with SAE-encoded static data and iterative updates of supervised-learning data are based on distance-based clustering schemes. DNN functions as an inverse model and results in encoded flattened data, while SAE, as a pre-trained neural network, successfully reduces dimensionality and reliably reconstructs geo-models. The iterative-learning method can improve the training data for DNN by showing the error reduction achieved with each iteration step. The proposed workflow shows the small mean absolute percentage error below 4% for all objective functions, while a typical multi-objective evolutionary algorithm fails to significantly reduce the initial population uncertainty. Iterative learning-based many-objective history matching estimates the trends in water cuts that are not reliably included in dynamic-data matching. This confirms the proposed workflow constructs more plausible geo-models. The workflow would be a reliable alternative to overcome the less-convergent Pareto-based multi-objective evolutionary algorithm in the presence of geological uncertainty and varying objective functions.

With the development of machine learning technology, research cases for spatial estimation through machine learning approach (MLA) in addition to the traditional geostatistical techniques are increasing. MLA has the advantage that spatial estimation is possible without stationary hypotheses of data, but it is possible for the prediction results to ignore spatial autocorrelation. In recent studies, it was considered by using a distance matrix instead of raw coordinates. Although, the performance of spatial estimation could be improved through this approach, the computational complexity of MLA increased rapidly as the number of sample points increased. In this study, we developed a method to reduce the computational complexity of MLA while considering spatial autocorrelation. Principal component analysis is applied to it for extracting spatial features and reducing dimension of inputs. To verify the proposed approach, indicator Kriging was used as a benchmark model, and each performance of MLA was compared when using raw coordinates, distance vector, and spatial features extracted from distance vector as inputs. The proposed approach improved the performance compared to previous MLA and showed similar performance compared with Kriging. We confirmed that extracted features have characteristics of rigid classification in spatial estimation, on this basis, we conclude that the model could improve performance.

Reservoir models are generated by geostatistics using available static data. However, there is inherent uncertainty in the reservoir models due to limited information. A number of reservoir models with equivalent probabilities are created to quantitatively assess model uncertainty. The easiest way to evaluate the uncertainty is to perform a reservoir simulation for hundreds of reservoir models, but the simulation cost is too high. Recently, distance-based clustering (DBC) has been used as a means of efficient uncertainty assessment. DBC classifies similar reservoir models into the same group. Because models belonging to the same group have similar reservoir performances, simulating a representative model for each group will give a comparable uncertainty range from simulating all models. For DBC to be successful, the definition of distance, which represents non-similarity between models, is the key factor. In this research, after the main information from a reservoir model is extracted through a stacked autoencoder (SAE), which is one of deep learning algorithms, the 2-norm of feature vectors for two models is defined as the distance. First, the hyperparameters for SAE are analyzed by sensitivity analysis in order to optimize the feature vector from reservoir facies model. Similar to other artificial neural network algorithms, uncertainty results are sensitive to the number of neurons and the number of hidden layers but are stable for the number of clusters. After SAE-based clustering, only 20 representative models can realize the uncertainty range present in 800 individual initial models. If there are observed dynamic data, the best representative model can be determined by a misfit between the simulated production from the representative models and the observed data. The best model and its 9 closest models in feature space are selected as qualified models from among the entire 800 models. Additional reservoir simulations for the closest models can dramatically improve the uncertainty range of the prior models without inverse algorithms. The 10 qualified models can be utilized for generating pseudo-static data or can be used as initial models for inverse algorithms for further improvement of reservoir characterization.

This paper develops a reliable and efficient data-integration method, based on artificial neural networks (ANN) incorporated with a stacked autoencoder (SAE) in a deep neural network's framework. To handle scale-different static and dynamic data of heterogeneous channel reservoirs, the workflow suggests an unsupervised pre-training process coupled with ANN-based inverse modeling. The performances of the proposed neural network, i.e. the training efficiency, the predictability of future production rates and the computing time, are compared to those with an optimal ANN and the impact of hidden neurons are discussed. The pre-trained neural network demonstrates a reliable estimation of reservoir properties with the spatial characteristics of a true channel reservoir while the ANN fails with respect to the spatial heterogeneity. The pre-trained neural network decreases the mean absolute error of future oil production rates up to 9.1% which is less than 25% of the comparison case's level, i.e. the optimal ANN model. Its efficiency is validated by a computing time 14 times faster than that of the optimal ANN workflow. The pre-trained neural network evaluates the spatial characteristics of reservoir properties and facies models in a reasonable manner and is thus able to predict the water production rates and also the breakthrough time accurately. This pre-trained neural network manifests its applicability with robustness as an efficient method to integrate static and dynamic data.

This paper develops a reliable deep-learning framework to extract latent features from spatial properties and investigates adaptive surrogate estimation to sequester CO2 into heterogeneous deep saline aquifers. Our deep-learning architecture includes a deep convolutional autoencoder (DCAE) and a fully-convolutional network to not only reduce computational costs but also to extract dimensionality-reduced features to conserve spatial characteristics. The workflow integrates two different spatial properties within a single convolutional system, and it also achieves accurate reconstruction performance. This approach significantly reduces the number of parameters to 4.3% of the original number required, e.g., the number of three-dimensional spatial properties needed decreases from 44,460 to 1920. The successful dimensionality reduction is accomplished by the DCAE system regarding all inputs as image channels from the initial stage of learning using the fully-convolutional network instead of fully-connected layers. The DCAE reconstructs spatial parameters such as permeability and porosity while conserving their statistical values, i.e., their mean and standard deviation, achieving R-squared values of over 0.972 with a mean absolute percentage error of their mean values of less than 1.79%. The adaptive surrogate model using the latent features extracted by DCAE, well operations, and modeling parameters is able to accurately estimate CO2 sequestration performances. The model shows R-squared values of over 0.892 for testing data not used in training and validation. The DCAE-based surrogate estimation exploits the reliable integration of various spatial data within the fully-convolutional network and allows us to evaluate flow behavior occurring in a subsurface domain.

This paper develops a novel approach of deep neural network (DNN)-based inverse modeling with selecting more reliable supervised-learning datasets with distance-based maps allocated at individual well levels. To mitigate divergence and overshooting in multi-scaled data assimilation, the DNN-based inverse model introduces a stacked autoencoder (SAE) that reduces the dimension of the training data. The proposed workflow also implements k-medoids clustering by selecting geo-models that have dynamic performances close to the true responses of producers to obtain plausible supervised-learning datasets. History-matching accuracy and forecasting performance are investigated in comparison of typical ensemble Kalman filter (EnKF)-based data assimilation for a waterflooding problem of heterogeneous fluvial channel reservoirs. The proposed approach is capable of matching the oil production rates of all producers in the range of 1.1–11.3% mean absolute percentage error (MAPE) and can forecast the future performances within 15.5% errors, while the errors of the EnKF method are up to six times higher. The proposed workflow can estimate the water-breakthrough time and the water productions accurately by generating more reliable geo-models with geological realism.