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Title: Approximate solutions for diffusive fracture-matrix transfer: Application to storage of dissolved CO 2 in fractured rocks

Abstract

Analytical solutions with infinite exponential series are available to calculate the rate of diffusive transfer between low-permeability blocks and high-permeability zones in the subsurface. Truncation of these series is often employed by neglecting the early-time regime. Here in this paper, we present unified-form approximate solutions in which the early-time and the late-time solutions are continuous at a switchover time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the first coefficient dependent only on the dimensionless area-to-volume ratio. The last two coefficients are either determined analytically for isotropic blocks (e.g., spheres and slabs) or obtained by fitting the exact solutions, and they solely depend on the aspect ratios for rectangular columns and parallelepipeds. For the late-time solutions, only the leading exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic rectangular blocks. The optimal switchover time is between 0.157 and 0.229, with highest relative approximation error less than 0.2%. The solutions are used to demonstrate the storage of dissolved CO 2 in fractured reservoirs with low-permeability matrix blocks of single and multiple shapes and sizes. These approximate solutions are building blocks for developmentmore » of analytical and numerical tools for hydraulic, solute, and thermal diffusion processes in low-permeability matrix blocks.« less

Authors:
ORCiD logo [1];  [1];  [2];  [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Energy Geosciences Division
  2. Montana State Univ., Bozeman, MT (United States). Big Sky Carbon Sequestration Partnership
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Montana State University
Sponsoring Org.:
USDOE Office of Science (SC); USDOE Office of Fossil Energy (FE)
OSTI Identifier:
1393610
Alternate Identifier(s):
OSTI ID: 1430906
Grant/Contract Number:  
AC02-05CH11231; FC26-05NT42587; FE0023323
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Water Resources Research
Additional Journal Information:
Journal Volume: 53; Journal Issue: 2; Journal ID: ISSN 0043-1397
Publisher:
American Geophysical Union (AGU)
Country of Publication:
United States
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES; diffusion; mass transfer; analytical solutions; approximate solutions; fractured rocks; solubility trapping

Citation Formats

Zhou, Quanlin, Oldenburg, Curtis M., Spangler, Lee H., and Birkholzer, Jens T. Approximate solutions for diffusive fracture-matrix transfer: Application to storage of dissolved CO2 in fractured rocks. United States: N. p., 2017. Web. doi:10.1002/2016WR019868.
Zhou, Quanlin, Oldenburg, Curtis M., Spangler, Lee H., & Birkholzer, Jens T. Approximate solutions for diffusive fracture-matrix transfer: Application to storage of dissolved CO2 in fractured rocks. United States. doi:10.1002/2016WR019868.
Zhou, Quanlin, Oldenburg, Curtis M., Spangler, Lee H., and Birkholzer, Jens T. Thu . "Approximate solutions for diffusive fracture-matrix transfer: Application to storage of dissolved CO2 in fractured rocks". United States. doi:10.1002/2016WR019868. https://www.osti.gov/servlets/purl/1393610.
@article{osti_1393610,
title = {Approximate solutions for diffusive fracture-matrix transfer: Application to storage of dissolved CO2 in fractured rocks},
author = {Zhou, Quanlin and Oldenburg, Curtis M. and Spangler, Lee H. and Birkholzer, Jens T.},
abstractNote = {Analytical solutions with infinite exponential series are available to calculate the rate of diffusive transfer between low-permeability blocks and high-permeability zones in the subsurface. Truncation of these series is often employed by neglecting the early-time regime. Here in this paper, we present unified-form approximate solutions in which the early-time and the late-time solutions are continuous at a switchover time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the first coefficient dependent only on the dimensionless area-to-volume ratio. The last two coefficients are either determined analytically for isotropic blocks (e.g., spheres and slabs) or obtained by fitting the exact solutions, and they solely depend on the aspect ratios for rectangular columns and parallelepipeds. For the late-time solutions, only the leading exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic rectangular blocks. The optimal switchover time is between 0.157 and 0.229, with highest relative approximation error less than 0.2%. The solutions are used to demonstrate the storage of dissolved CO2 in fractured reservoirs with low-permeability matrix blocks of single and multiple shapes and sizes. These approximate solutions are building blocks for development of analytical and numerical tools for hydraulic, solute, and thermal diffusion processes in low-permeability matrix blocks.},
doi = {10.1002/2016WR019868},
journal = {Water Resources Research},
number = 2,
volume = 53,
place = {United States},
year = {Thu Jan 05 00:00:00 EST 2017},
month = {Thu Jan 05 00:00:00 EST 2017}
}

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Works referenced in this record:

CO2-H2O mixtures in the geological sequestration of CO2. I. Assessment and calculation of mutual solubilities from 12 to 100°C and up to 600 bar
journal, August 2003

  • Spycher, Nicolas; Pruess, Karsten; Ennis-King, Jonathan
  • Geochimica et Cosmochimica Acta, Vol. 67, Issue 16, p. 3015-3031
  • DOI: 10.1016/S0016-7037(03)00273-4