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Title: Scaling Behavior of Thermally Driven Fractures in Deep Low‐Permeability Formations: A Plane Strain Model With 1‐D Heat Conduction

Abstract

Abstract Injection of cold fluids through/into deep formations may cause significant cooling, thermal stress, and possible thermal fracturing. In this study, the thermal fracturing of low‐permeability formations under one‐dimensional heat conduction was investigated using a plane strain model. Dimensionless governing equations, with dimensionless fracture length , aperture , spacing , time , and effective confining stress , were derived. Solution of single thermal fracture was derived analytically, while solution of multiple fractures with constant (or dynamic) spacing were obtained using the displacement discontinuity method (and stability analysis). For single fracture, increases nonlinearly with and then transitions to scaling law , indicating that late‐time fracture length increases linearly with the square root of cooling time. For constantly spaced fractures, deviates from the single‐fracture solution at a later for a larger , showing slower propagation under inter‐fracture stress interaction . For dynamically spaced fractures, fracture arrest induced by stress interaction was determined by the stability analysis; the fully transient solution provides evolution of dimensionless fracture length, spacing, aperture, and pattern; a similar scaling law, with , obtained shows the effect of both stress interaction and fracture arrest. The solution and scaling law provide fast predictions for all reservoir and cooling conditions usingmore » (single) model parameter . Application to a geothermal site with demonstrates that thermal fractures reach 0.67, 6.25, and 78.00 m in length, 0.49, 2.30, and 13.00 m in spacing, and 0.43, 2.09, and 12.19 mm in aperture at 1, 100, and 10,000 days.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]
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  1. Division of Energy Geosciences Lawrence Berkeley National Laboratory Berkeley CA USA
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Biological and Environmental Research (BER)
OSTI Identifier:
1846323
Alternate Identifier(s):
OSTI ID: 1846324; OSTI ID: 1890995
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Published Article
Journal Name:
Journal of Geophysical Research. Solid Earth
Additional Journal Information:
Journal Name: Journal of Geophysical Research. Solid Earth Journal Volume: 127 Journal Issue: 3; Journal ID: ISSN 2169-9313
Publisher:
American Geophysical Union (AGU)
Country of Publication:
United States
Language:
English

Citation Formats

Chen, Bin, and Zhou, Quanlin. Scaling Behavior of Thermally Driven Fractures in Deep Low‐Permeability Formations: A Plane Strain Model With 1‐D Heat Conduction. United States: N. p., 2022. Web. doi:10.1029/2021JB022964.
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Chen, Bin, & Zhou, Quanlin. Scaling Behavior of Thermally Driven Fractures in Deep Low‐Permeability Formations: A Plane Strain Model With 1‐D Heat Conduction. United States. https://doi.org/10.1029/2021JB022964
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Chen, Bin, and Zhou, Quanlin. Thu . "Scaling Behavior of Thermally Driven Fractures in Deep Low‐Permeability Formations: A Plane Strain Model With 1‐D Heat Conduction". United States. https://doi.org/10.1029/2021JB022964.
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@article{osti_1846323,
title = {Scaling Behavior of Thermally Driven Fractures in Deep Low‐Permeability Formations: A Plane Strain Model With 1‐D Heat Conduction},
author = {Chen, Bin and Zhou, Quanlin},
abstractNote = {Abstract Injection of cold fluids through/into deep formations may cause significant cooling, thermal stress, and possible thermal fracturing. In this study, the thermal fracturing of low‐permeability formations under one‐dimensional heat conduction was investigated using a plane strain model. Dimensionless governing equations, with dimensionless fracture length , aperture , spacing , time , and effective confining stress , were derived. Solution of single thermal fracture was derived analytically, while solution of multiple fractures with constant (or dynamic) spacing were obtained using the displacement discontinuity method (and stability analysis). For single fracture, increases nonlinearly with and then transitions to scaling law , indicating that late‐time fracture length increases linearly with the square root of cooling time. For constantly spaced fractures, deviates from the single‐fracture solution at a later for a larger , showing slower propagation under inter‐fracture stress interaction . For dynamically spaced fractures, fracture arrest induced by stress interaction was determined by the stability analysis; the fully transient solution provides evolution of dimensionless fracture length, spacing, aperture, and pattern; a similar scaling law, with , obtained shows the effect of both stress interaction and fracture arrest. The solution and scaling law provide fast predictions for all reservoir and cooling conditions using (single) model parameter . Application to a geothermal site with demonstrates that thermal fractures reach 0.67, 6.25, and 78.00 m in length, 0.49, 2.30, and 13.00 m in spacing, and 0.43, 2.09, and 12.19 mm in aperture at 1, 100, and 10,000 days.},
doi = {10.1029/2021JB022964},
journal = {Journal of Geophysical Research. Solid Earth},
number = 3,
volume = 127,
place = {United States},
year = {Thu Feb 24 00:00:00 EST 2022},
month = {Thu Feb 24 00:00:00 EST 2022}
}
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