Variations of Longitudinal Moments for a Contaminant Transport in Physically and Chemically Heterogeneous Media

물리.화학적 불균질 특성을 지닌 매질 내 오염운 이동시 보이는 종적률 변화

  • Published : 2009.03.31

Abstract

Two dimensional Monte-Carlo simulations of a non-reactive solute plume in isotropic porous media which are physically and chemically heterogeneous are conducted to determine the variations of moment. Retardation factors of 1, 2 and 5 are given to ascertain how the second moments are changed as adsorption increased. Retarded longitudinal second spatial moment, ${Z_{11}}^{'R}(t',l')$, increased during the transport process and as the dimensionless lengths of line plume source, $l_2'$, increased. ${Z_{11}}^{'R}(t',l')$ decreased as the retardation factors increased, and the simulated moments fit well to the first-order analytical results. Retarded longitudinal plume centroid variance, ${Z_{11}}^{'R}(t',l')$, decreased as the dimensionless lengths of line plume source, $l_2'$, increased and as the retardation factor increased. The result indicates that the uncertainty about the plume center decreased, and the ergodic condition for the second spatial moments is far from reaching. Simulated longitudinal one particle displacement covariance, ${Z_{11}}^{'R}(t')$, well consistent with the first-order analytical results for the three degrees of retardation factors of 1, 2 and 5 respectively. It is, consequently, concluded that the retarded longitudinal second moments could be produced by stochastic simulation, and that the first-order analytical results definitely provides very close values of the longitudinal retarded moments.

물리 화학적 불균질 특성을 가진 매질 중 K 임의장과 $K_d$ 임의장이 정(+)의 상관관계를 가지는 경우, 매질 내 이송되는 오염운이 보이는 적률변화를 알아보기 위해 등방매질 내 이송되는 비반응성 오염운에 대한 2차원 몬테카를로 시뮬레이션이 시행되었다. 흡착성이 증가함에 따라 변화하는 이차적률들을 관찰하기 위해 1, 2, 5의 지연요소가 설정되었다. 지연된 종이차공간적률, ${Z_{11}}^{'R}(t',l')$은 오염운의 이송이 진행됨에 따라 증가하며 초기 오염운의 크기가 증가함에 따라 증가한다. 또한 지연요소가 증가함에 따라 감소하며, 일차분석해에 의한 이론적 결과와 비교적 잘 일치함을 보인다. 지연된 종오염운중심분산, ${Z_{11}}^{'R}(t',l')$은 초기오염원의 크기, $l_2'$가 증가할수록 감소하며 설정된 시뮬레이션에 의해서는 아직 에르고딕 이송상태에 도달하지 않았음을 지시해준다. 지연요소가 증가함에 따라 현저히 감소하여 오염운 중심점에 대한 불확실성이 감소함을 보인다. 지연된 단일입자종이송분산, ${X_{11}}^{'R}(t')$은 세 가지 다른 등급의 지연요소에 대해서 모두 일차근사법에 의한 이론적 결과와 비교적 잘 일치한다. 따라서 종방향의 지연된 이차적률들은 추계론적 시뮬레이션에 의해 산출될 수 있으며, 일차근사법에 의한 분석해는 종방향의 지연된 적률들에 대해 상당히 정확한 근사값을 제공하고 있음을 결론지을 수 있다.

Keywords

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