Pore Structure Evaluation of Quaternary Highly Vuggy Limestone by a Combination of X-ray CT Images of Differently Sized Cores

Abstract

Groundwater storage in an atoll that is facing water shortage is a crucial issue for freshwater supply and agricultural practices. As a solution to increase the volume of freshwater in an atoll, a floating-type underground dam is proposed. Precipitation, which displaces brine in underground reservoirs, is stored as a freshwater resource in the underground dam. However, the aquifer in an atoll consists of vuggy limestone, such as Ryukyu limestone, which possesses a wide range of pore sizes and heterogeneous pore structure such that the retardation of salinity reduction in the aquifer is of concern when considering freshwater reservoirs. To understand the pore structure of such vuggy limestone, X-ray computed tomography scans were conducted for eighteen cylindrical Ryukyu limestone cores 100, 50, and 6 mm in diameter. Cluster analysis of the three-dimensional distributions of the pores revealed that the Quaternary vuggy Ryukyu limestone has a binary fractal with a wide size distribution of at least 12 orders for the pore volume and 10 orders for the pore surface area. To model the Ryukyu limestone numerically, a simplified method for pore structure modeling is required. Our numerical approach suggests that the three-dimensional pore structure of Ryukyu limestone aquifer can be modeled using a binary fractal aggregation of spheres of various sizes.

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Abbreviations

y :

The logarithm of \(N\).

N :

The number of pore clusters with attributes that are larger than \(V\) or \(S\).

N b :

The number of pore clusters with attributes that are larger than \(V\) or \(S\) in one cubic meter.

\(\overline{y}\) :

The arithmetical mean of \(y\).

i :

An integer used to indicate the section with the largest volume/surface area.

m :

The number of sections used to determine \(V\) or \(S\).

f :

The logarithm of the number of pore clusters predicted by the fitted line in the measured plots \((f = a + b\log x)\).

a :

Constant.

b :

Constant.

x :

The volume (\(V\)) or surface area (\(S\)) of a pore cluster.

R 2 :

Coefficient of determination for the fitted line.

\(\overline{{V_{j} }}\) :

The volume of a small sphere used to calculate the surface area of a simplified pore.

V j :

The volume for interval classification used in the frequency distribution of the volume of the pore clusters.

V min :

The smallest volume for interval classification used in the frequency distribution of the volume of the pore clusters.

α :

An arbitrary number representing shape complexity extent of a pore cluster against the sphere

Nss :

The number of the small spheres among a reference pore volume.

S sp :

The surface area of the simplified pore.

S r :

The surface area of the small reference spheres

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Acknowledgements

This research was supported by a Grant-in-aid for Science Research, numbers 17H03310 from the Japanese Ministry of Education, Science, Sports and Culture.

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Correspondence to Kentaro Masuoka.

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Masuoka, K., Nakaya, S. Pore Structure Evaluation of Quaternary Highly Vuggy Limestone by a Combination of X-ray CT Images of Differently Sized Cores. Rock Mech Rock Eng (2021). https://doi.org/10.1007/s00603-020-02352-4

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Keywords

  • X-ray computed tomography
  • Ryukyu limestone
  • Pore structure
  • Binary fractal
  • Quaternary stratum
  • Atoll limestone