지질공학 (The Journal of Engineering Geology)

  • 제15권3호
  • /
  • Pages.245-255
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  • 2005
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  • 1226-5268(pISSN)
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  • 2287-7169(eISSN)
대한지질공학회 (The Korean Society of Engineering Geology)
권호 표지

불균질도가 높은 대수층내에서의 비에르고딕 용질이동에 관한 수치 시뮬레이션

Numerical Simulajtions of Non-ergodic Solute Transport in Strongly Heterogeneous Aquiferss

  • 서병민 (충남대학교 기초과학 연구소)
  • Seo Byong-Min (Research Institute of Basic Sciences, Chungnam National University)
  • 발행 : 2005.09.01
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초록

균일한 지하수 유속을 가진 불균질한 등방성 대수층 내에서 정류상태로 흐르는 지하수의 흐름과 함께 이동해가는 비반응성 오염물질에 대한 삼차원 몬테카를로 시뮬레이션이 시행되었다. 로그-정규적으로 분포되어 있는 수리 전도도 K(x)가 임의 장으로 설정되었으며 시뮬레이션 동안에 발생 할 수 있는 불확실성을 감소하기 위해 여러 가지 방법들이 시도되었다. 3,200개 오염 운들에 대한 이차공간적률의 집합적평균 $$lt;S_{ij}'(t',l')$gt;$, 그리고 오염 운중심분산 $$lt;R_{ij}'(t',l')$gt;$이 각기 다른세가지 불균질도 $\omega^2_y1.0,$ 2.5 및 5.0에 대해서 시뮬레이션 되었으며 또한 각기 다른 크기의 평균속도에 수직방향인 선형초기오염원( l=1.5 및 10)에 대해서 입자추적이 행하여 졌다 시뮬레이션된 무차원 종적률들은 일차 근사법에 의한 비에르고딕 이론적 결과와 비교적 잘 일치 하나 시뮬레이션된 무차원 횡적률들은 일차근사법에 의한 이론적 결과들과 잘 일치하지 않으며 특히 불균질도가 큰 대수층에 대해서 그리고 초기 선형오염운의 크기가 작은 무차원 횡이차공간적률에 대해서 뚜렷하게 저평가 했다. 시뮬레이션된 집합적 평균이차적률은 에르고딕 상태에 도달하지 못했으며 일차근사법에 의한 에르고딕 용질 이동에 관한 횡이차공간적률은 시뮬레이션 결과를 저평가 했음을 보인다.

Three dimensional Monte-Carlo simulations of non-ergodic transport of a non-reactive solute plume by steady-state groundwater flow under a uniform mean velocity in isotropic heterogeneous aquifers were conducted. The log-normally distributed hydraulic conductivity, K(x), is modeled as a random field. Significant efforts are made to reduce the simulation uncertainties. Ensemble averages of the second spatial moments of the plume, $$lt;S_{ij}'(t',l')$gt;$ and plume centroid variances, $$lt;R_{ij}'(t',l')$gt;$ were simulated with 3200 Monte Carlo runs for three variances of log K, $\omega^2_y1.0,,2.5,$ and 5.0, and three dimensionless lengths of line plume sources ( l=,5 and 10) normal to the mean velocity. The simulated second spatial moment and the plume centroid variance in longitudinal direction fit well to the first order theoretical results while the simulated transverse moments are not fit well with the first order results. The first order theoretical results definitely underestimated the simulated transverse second spatial moments for the aquifers of large u: and small initial plume sources. The ergodic condition for the second spatial moments is far from reaching, and the first order theoretical results of the transverse second spatial moment of the ergodic plume slightly underestimated the simulated moments.

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