• Monte-Carlo Simulations of Non-ergodic Solute Transport from Line Sources in Isotropic Mildly Heterogeneous Aquifers
  • Seo Byong-min;
  • Research Institute of Basic Sciences, Chungnam National University;
  • 불균질 등방 대수층 내 선형오염원으로부터 기원된 비에르고딕 용질 이동에 관한 몬테카를로 시뮬레이션
  • 서병민;
  • 충남대학교 기초과학연구소;
Abstract
Three dimensional Monte-Carlo simulations of non-ergodic transport of a lion-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 tile simulation uncertainties. Ensemble averages of the second spatial moments of the plume and plume centroid variances were simulated with 1600 Monte Carlo runs for three variances of log K, ${\sigma}_Y^2=0.09,\;0.23$, and 0.46, and three dimensionless lengths of line plume sources 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 generally larger than the first order results. The first order theoretical results significantly underestimated the simulated dimensionless transverse moments for the aquifers of large ${\sigma}_Y^2$ and large dimensionless time. The ergodic condition for the second spatial moments is far from reaching in all cases simulated, and transport In transverse directions may reach ergodic condition much slower than that in longitudinal direction. The evolution of the contaminant transported in a heterogeneous aquifer is not affected by the shape of the initial plume but affected mainly by the degree of the heterogeneity and the size of the initial plume.

일정한 평균 지하수 유속을 가진 불균질한 등방성 삼차원 대수층 내에서 정류상태로 흐르는 지하수의 흐름과 함께 이동해가는 비반응성 오염물질에 대한 몬테카를로 시뮬레이션이 시행되었다. 대수-정규적으로 분포되어 있는 수리전도도 K(x)가 임의장으로 설정되었으며 시뮬레이션 동안에 발생할 수 있는 불확실성을 감소하기 위해 여러 가지 방법들이 시도되었다. 1600개 오염운들에 대한 이차공간적률의 집합적평균(ensemble average) <$S_{ij}'(t',\;l')$>(i,\;j=1,2,3), 그리고 오염운중심분산 $R_{ij}'(t',\;l')$이 각기 다른 세 가지 불균질도${\sigma}_Y^2=0.09,\;0.23$ 및 0.46에 대해서 시뮬레이션 되었으며 또한 각기 다른 크기의 평균속도에 수직방향인 선형초기오염원(l': 1, 2, 4)에 대해서 입자추적이 행하여 졌다. 시뮬레이션 된 무차원 종적률들은 일차근사법에 의한 비에르고딕 이론적 결과와 비교적 잘 일치하나 시뮬레이션 된 무차원 횡적률들은 일차근사법에 의한 이론적 결과들 보다 더 큰 값을 보인다. 일차근사법에 의한 비에르고딕 이론적 결과는 특히 불균질도가 큰 대수층에 대해서 그리고 큰 무차원 시간에 대해서 시뮬레이션 된 무차원 횡적률들을 과소평가 했다 시뮬레이션 된 집합적 평균이차적률은 에르고딕 상태에 도달하지 못했으며 횡방향으로의 오염운 확장이종방향보다 훨씬 느리게 에르고딕 상태에 접근하는 것으로 관찰되었다. 불균질한 대수층 내에서의 오염운의 진화는 초기 오염원의 모양이나 배열상태 보다는 주로 대수층의 불균질도와 초기 오염원의 크기에 영향을 받는 것으로 밝혀졌다.가 정신의 숭고한 고유-독창성(Originality)이 피드백의 경로를 투과하면서 자신을 남에게 투영시켜 얻어내는 것이 고유성의 변종이다. 피드백은 단순한 작품의 일부가 아니라 작품을 이루는 뼈대이다 기술의 과시만으로는 예술의 행위가 될 수 없다. 작가의 예술성이 관객의 감성에 피드백 되도록 노력해야 한다 그러기 위해서는 예정된 피드백이란 느낌을 관객이 갖지 않도록 하여야 한다. 인터렉티브 미디어 아트는 초기의 형태에서 벗어나 새로운 집적된 피드백 기술로 전환하여야 할 시기가 온 것이다.료된다.시한 개체의 수술 전 방사선학적 평균 고관절 등급은 양측 모두 $3.2\pm0.9$이었고 수술 직후의 좌 우측 평균 고관절 등급은 각각 $2.7\pml.1,\;2.7\pm0.9$ (n=36) 이었다. 수술 직후와 2, 4, 8, 12, 24주 후의 고관절 등급이 수술 전에 비하여 유의적으로 개선된 것을 확인하였다.(P<0.01). 수술 후 정기적인 검사 시에 측정한 Norberg angle, percentage of femoral head coverage도 수술 전과 비교해 유의성 있게 증가하였다(P<0.01). 변형 3중 골반 절골술 직후의 평균 골반직경은 수술 전의 골반직경보다 유의적으로 증가하였으며(P<0.01)(n=36) 수술 후 평균 9.3L2.7주에 절골선 유합이 종료되었다(n=21). 반면 편측 3중 골반 절골술을 실시한 경우에는 수술 후 골반경이 수술 전과 비교해 증가하지 않았다. 변형 3중 골반 절골술후에 장액종 형성(1마리), 스크류 변위(4마리), 스크류 부러짐(1마리), 편측성 신경마비(1마리) 등의 부작용이 발생하였다. 이상의 결과를 토대로,

Keywords: Groudwater;Isotropic;Monte-Carlo;Non-ergodic transport;

Keywords: 지하수;등방성;몬테카를로;비에르고딕 이동;

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This Article

  • 2005; 10(6): 20-31

    Published on Dec 1, 2005