• Title/Summary/Keyword: non-ergodic transport

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Numerical Simulajtions of Non-ergodic Solute Transport in Strongly Heterogeneous Aquiferss (불균질도가 높은 대수층내에서의 비에르고딕 용질이동에 관한 수치 시뮬레이션)

  • Seo Byong-Min
    • The Journal of Engineering Geology
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    • v.15 no.3
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    • pp.245-255
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    • 2005
  • 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.

Monte-Carlo Simulations of Non-ergodic Solute Transport from Line Sources in Isotropic Mildly Heterogeneous Aquifers (불균질 등방 대수층 내 선형오염원으로부터 기원된 비에르고딕 용질 이동에 관한 몬테카를로 시뮬레이션)

  • Seo Byong-min
    • Journal of Soil and Groundwater Environment
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    • v.10 no.6
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    • pp.20-31
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    • 2005
  • 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.

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)

  • Seo, Byong-Min;Jung, Joon-Oh;Kim, Young-Woo;Hwang, Seung-Min
    • The Journal of Engineering Geology
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    • v.19 no.1
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    • pp.81-88
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    • 2009
  • 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.