energies Article Adaptive Surrogate Estimation with Spatial Features Using a Deep Convolutional Autoencoder for CO 2 Geological Sequestration Suryeom Jo 1 , Changhyup Park 2, * , Dong-Woo Ryu 1 and Seongin Ahn 1   Citation: Jo, S.; Park, C.; Ryu, D.-W.; Ahn, S. Adaptive Surrogate Estimation with Spatial Features Using a Deep Convolutional Autoencoder for CO 2 Geological Sequestration. Energies 2021, 14, 413. https://doi.org/10.3390/ en14020413 Received: 26 November 2020 Accepted: 10 January 2021 Published: 13 January 2021 Publisher’s Note: MDPI stays neu- tral with regard to jurisdictional clai- ms in published maps and institutio- nal affiliations. Copyright: © 2021 by the authors. Li- censee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and con- ditions of the Creative Commons At- tribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Geo-ICT Convergence Research Team, Korea Institute of Geoscience and Mineral Resources, Daejeon 34132, Korea; suryeom@kigam.re.kr (S.J.); dwryu@kigam.re.kr (D.-W.R.); seongin@kigam.re.kr (S.A.) 2 Department of Energy and Resources Engineering, Kangwon National University, Chuncheon 24341, Korea * Correspondence: changhyup@kangwon.ac.kr; Tel.: +82-33-2506259 Abstract: This paper develops a reliable deep-learning framework to extract latent features from spatial properties and investigates adaptive surrogate estimation to sequester CO 2 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 CO 2 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. Keywords: deep convolutional autoencoder; deep learning; spatial parameter; latent feature; surro- gate model; data integration 1. Introduction Data science has revolutionized engineering analytics in the oil and gas industry. Data- driven analyses are now assisting the decision-making process making it more reliable as well as more efficient [1–5]. Despite these high-end computer-assisted methods delivering efficient solutions, establishing reliable standard forms has been challenging. Uncertainty quantification requires reliable integration of all available scale-dominant spatiotemporal properties. Rock properties are heterogeneous spatially, which makes fluid-flow uncertain in subsurface domains. A grid in a heterogeneous geo-model contains a lot of scale-variant, non-linearly-connected, and spatiotemporal information that influences flow behavior, e.g., porosity, permeability, capillary pressure, and fluid saturations. These properties are assigned to an individual grid but are non-linearly linked so that the governing equations integrate them closely. Quantifying the non-linearity of grid properties is essential to simu- late flow behavior in a realistic manner. Integrating all available scale-dependent, uncertain, and spatiotemporal properties requires large amounts of computing resources; thereby, the Energies 2021, 14, 413. https://doi.org/10.3390/en14020413 https://www.mdpi.com/journal/energies