Approximate solutions for diffusive fracture-matrix transfer: Application to storage of dissolved CO₂ in fractured rocks

Journal Article · 05 January 2017 · Water Resources Research

DOI: https://doi.org/10.1002/2016WR019868 · OSTI ID:1393610

Zhou, Quanlin  ^[1]; Oldenburg, Curtis M. ^[1]; Spangler, Lee H. ^[2]; Birkholzer, Jens T. ^[1]

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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

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.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Montana State Univ., Bozeman, MT (United States)
• Sponsoring Organization: USDOE Office of Science (SC); USDOE Office of Fossil Energy (FE)
• Grant/Contract Number: AC02-05CH11231; FC26-05NT42587; FE0023323
• OSTI ID: 1393610
• Alternate ID(s): OSTI ID: 1430906
• Journal Information: Water Resources Research, Vol. 53, Issue 2; ISSN 0043-1397
• Publisher: American Geophysical Union (AGU)Copyright Statement
• Country of Publication: United States
• Language: English