Journal of the Mineralogical Society of Korea (한국광물학회지)

The Mineralogical Society of Korea (한국광물학회)
권호 표지

Geophysical Implications for Configurational Entropy and Cube Counting Fractal Dimension of Porous Networks of Geological Medium: Insights from Random Packing Simulations

지질매체 공극 구조에 대한 구성 엔트로피와 상자집계 프랙탈 차원의 지구물리학적 의미 및 응용: 무작위 패킹 시뮬레이션 연구

  • Lee, Bum-Han (School of Earth and Environmental Sciences, Seoul National University) ;
  • Lee, Sung-Keun (School of Earth and Environmental Sciences, Seoul National University)
  • 이범한 (서울대학교 지구환경과학부) ;
  • 이성근 (서울대학교 지구환경과학부)
  • Received : 2010.12.01
  • Accepted : 2010.12.21
  • Published : 2010.12.30
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Abstract

Understanding the interactions between earth materials and fluids is essential for studying the diverse geological processes in the Earth's surface and interior. In order to better understand the interactions between earth materials and fluids, we explore the effect of specific surface area and porosity on structural parameters of pore structures. We obtained 3D pore structures, using random packing simulations of porous media composed of single sized spheres with varying the particle size and porosity, and then we analyzed configurational entropy for 2D cross sections of porous media and cube counting fractal dimension for 3D porous networks. The results of the configurational entropy analysis show that the entropy length decreases from 0.8 to 0.2 with increasing specific surface area from 2.4 to $8.3mm^2/mm^3$, and the maximum configurational entropy increases from 0.94 to 0.99 with increasing porosity from 0.33 to 0.46. On the basis of the strong correlation between the liquid volume fraction (i.e., porosity) and configurational entropy, we suggest that elastic properties and viscosity of mantle melts can be expressed using configurational entropy. The results of the cube counting fractal dimension analysis show that cube counting fractal dimension increases with increasing porosity at constant specific surface area, and increases from 2.65 to 2.98 with increasing specific surface area from 2.4 to $8.3mm^2/mm^3$. On the basis of the strong correlation among cube counting fractal dimension, specific surface area, and porosity, we suggest that seismic wave attenuation and structural disorder in fluid-rock-melt composites can be described using cube counting fractal dimension.

지구물질로 이루어진 공극 구조와 이를 채우고 있는 유체의 상호작용에 대한 이해는 지표 및 지구내부의 다양한 지질학적 현상의 설명에 필수적이다. 본 연구에서는 지구물질과 유체의 상호작용을 보다 잘 이해하기 위해, 비표면적과 공극률이 다공성 매질의 공극 구조를 설명하는 매개변수에 미치는 영향을 살펴보고자 하였다. 이를 위해 입자의 지름과 공극률을 다양하게 하여 동일한 크기의 구형의 입자로 이루어진 다공성 매질에 대한 삼차원 공극 구조를 무작위 패킹 시뮬레이션으로 얻었고, 이에 대해 구성 엔트로피와 삼차원 상자집계 프랙탈 차원 분석을 하였다 구성 엔트로피 분석 결과, 엔트로피 길이는 비표면적이 2.4에서 $8.3mm^2/mm^3$으로 증가할 때 0.8에서 0.2 mm로 감소하고, 최대 구성 엔트로피는 공극률이 0.33 에서 0.46으로 증가할수록 0.94에서 0.99로 증가하는 뚜렷한 경향을 보인다. 구성 엔트로피와 공극률의 관계로부터 구성 엔트로피가 맨틀 용융체의 탄성과 점성도를 설명하는 변수로 사용될 수 있음을 제시한다. 삼차원 상자집계 프랙탈 차원은 비표면적이 같을 때 공극률이 증가함에 따라 증가하고, 비표면적이 2.4에서 $8.3mm^2/mm^3$으로 증가할 때 2.65에서 2.98로 증가한다. 이러한 삼차원 상자집계 프랙탈 차원과 비표면적, 공극률의 관계로부터 삼차원 상자집계 프랙탈 차원이 지진파 감쇠와 맨틀용융체를 포함한 다양한 지질매체의 구조와 무질서도를 설명하는 변수로 사용될 수 있음을 제시한다.

Keywords

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