Upscaling the porosity–permeability relationship of a microporous carbonate for Darcy-scale flow with machine learning

Abstract The permeability of a pore structure is typically described by stochastic representations of its geometrical attributes (e.g. pore-size distribution, porosity, coordination number). Database-driven numerical solvers for large model domains can only accurately predict large-scale flow behavi...

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Autores principales:	H. P. Menke, J. Maes, S. Geiger
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/0c2de835e3b64b44a545df75d6cf7758
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spelling	oai:doaj.org-article:0c2de835e3b64b44a545df75d6cf77582021-12-02T14:16:16ZUpscaling the porosity–permeability relationship of a microporous carbonate for Darcy-scale flow with machine learning10.1038/s41598-021-82029-22045-2322https://doaj.org/article/0c2de835e3b64b44a545df75d6cf77582021-01-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-82029-2https://doaj.org/toc/2045-2322Abstract The permeability of a pore structure is typically described by stochastic representations of its geometrical attributes (e.g. pore-size distribution, porosity, coordination number). Database-driven numerical solvers for large model domains can only accurately predict large-scale flow behavior when they incorporate upscaled descriptions of that structure. The upscaling is particularly challenging for rocks with multimodal porosity structures such as carbonates, where several different type of structures (e.g. micro-porosity, cavities, fractures) are interacting. It is the connectivity both within and between these fundamentally different structures that ultimately controls the porosity–permeability relationship at the larger length scales. Recent advances in machine learning techniques combined with both numerical modelling and informed structural analysis have allowed us to probe the relationship between structure and permeability much more deeply. We have used this integrated approach to tackle the challenge of upscaling multimodal and multiscale porous media. We present a novel method for upscaling multimodal porosity–permeability relationships using machine learning based multivariate structural regression. A micro-CT image of Estaillades limestone was divided into small 603 and 1203 sub-volumes and permeability was computed using the Darcy–Brinkman–Stokes (DBS) model. The microporosity–porosity–permeability relationship from Menke et al. (Earth Arxiv, https://doi.org/10.31223/osf.io/ubg6p , 2019) was used to assign permeability values to the cells containing microporosity. Structural attributes (porosity, phase connectivity, volume fraction, etc.) of each sub-volume were extracted using image analysis tools and then regressed against the solved DBS permeability using an Extra-Trees regression model to derive an upscaled porosity–permeability relationship. Ten test cases of 3603 voxels were then modeled using Darcy-scale flow with this machine learning predicted upscaled porosity–permeability relationship and benchmarked against full DBS simulations, a numerically upscaled Darcy flow model, and a Kozeny–Carman model. All numerical simulations were performed using GeoChemFoam, our in-house open source pore-scale simulator based on OpenFOAM. We found good agreement between the full DBS simulations and both the numerical and machine learning upscaled models, with the machine learning model being 80 times less computationally expensive. The Kozeny–Carman model was a poor predictor of upscaled permeability in all cases.H. P. MenkeJ. MaesS. GeigerNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-10 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q H. P. Menke J. Maes S. Geiger Upscaling the porosity–permeability relationship of a microporous carbonate for Darcy-scale flow with machine learning
description	Abstract The permeability of a pore structure is typically described by stochastic representations of its geometrical attributes (e.g. pore-size distribution, porosity, coordination number). Database-driven numerical solvers for large model domains can only accurately predict large-scale flow behavior when they incorporate upscaled descriptions of that structure. The upscaling is particularly challenging for rocks with multimodal porosity structures such as carbonates, where several different type of structures (e.g. micro-porosity, cavities, fractures) are interacting. It is the connectivity both within and between these fundamentally different structures that ultimately controls the porosity–permeability relationship at the larger length scales. Recent advances in machine learning techniques combined with both numerical modelling and informed structural analysis have allowed us to probe the relationship between structure and permeability much more deeply. We have used this integrated approach to tackle the challenge of upscaling multimodal and multiscale porous media. We present a novel method for upscaling multimodal porosity–permeability relationships using machine learning based multivariate structural regression. A micro-CT image of Estaillades limestone was divided into small 603 and 1203 sub-volumes and permeability was computed using the Darcy–Brinkman–Stokes (DBS) model. The microporosity–porosity–permeability relationship from Menke et al. (Earth Arxiv, https://doi.org/10.31223/osf.io/ubg6p , 2019) was used to assign permeability values to the cells containing microporosity. Structural attributes (porosity, phase connectivity, volume fraction, etc.) of each sub-volume were extracted using image analysis tools and then regressed against the solved DBS permeability using an Extra-Trees regression model to derive an upscaled porosity–permeability relationship. Ten test cases of 3603 voxels were then modeled using Darcy-scale flow with this machine learning predicted upscaled porosity–permeability relationship and benchmarked against full DBS simulations, a numerically upscaled Darcy flow model, and a Kozeny–Carman model. All numerical simulations were performed using GeoChemFoam, our in-house open source pore-scale simulator based on OpenFOAM. We found good agreement between the full DBS simulations and both the numerical and machine learning upscaled models, with the machine learning model being 80 times less computationally expensive. The Kozeny–Carman model was a poor predictor of upscaled permeability in all cases.
format	article
author	H. P. Menke J. Maes S. Geiger
author_facet	H. P. Menke J. Maes S. Geiger
author_sort	H. P. Menke
title	Upscaling the porosity–permeability relationship of a microporous carbonate for Darcy-scale flow with machine learning
title_short	Upscaling the porosity–permeability relationship of a microporous carbonate for Darcy-scale flow with machine learning
title_full	Upscaling the porosity–permeability relationship of a microporous carbonate for Darcy-scale flow with machine learning
title_fullStr	Upscaling the porosity–permeability relationship of a microporous carbonate for Darcy-scale flow with machine learning
title_full_unstemmed	Upscaling the porosity–permeability relationship of a microporous carbonate for Darcy-scale flow with machine learning
title_sort	upscaling the porosity–permeability relationship of a microporous carbonate for darcy-scale flow with machine learning
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/0c2de835e3b64b44a545df75d6cf7758
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Upscaling the porosity–permeability relationship of a microporous carbonate for Darcy-scale flow with machine learning

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