On the cumulant expansion up scaling of ground water contaminant transport equation with nonequilibrium sorption

ŞİRİN H., Marino M. A.

STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT, cilt.22, sa.4, ss.551-565, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 4
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1007/s00477-007-0174-6
  • Dergi Adı: STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.551-565
  • Anahtar Kelimeler: stochastic differential equations, cumulant expansion, ground water contaminant transport, nonequilibrium sorption, SOLUTE TRANSPORT, STOCHASTIC-ANALYSIS, REACTIVE TRANSPORT, POROUS-MEDIA, FLOW, UNSTEADY, VELOCITY, AQUIFERS, MODEL
  • Anadolu Üniversitesi Adresli: Evet

Özet

The laboratory-scale ground water transport equation with nonequilibrium sorption reaction subjected to unsteady, nondivergence-free, and nonstationary velocity fields is up-scaled to the field-scale by using the ensemble-averaged equations obtained from the cumulant expansion ensemble-averaging method. It is found that existing ensemble-averaged equations obtained with the help of the cumulant expansion method for the system of linear partial differential equations are not second-order exact. Although the cumulant expansion methodology is designed for noncommuting operators, it is found that there are still commudativity requirements that need to be satisfied by the functions and constants exist in the coefficient matrix of the system of ordinary/partial differential equations. A reversibility requirement, which covers the commudativity requirements, is also proposed when applying the cumulant expansion method to a system of partial differential equations/a partial differential equation. The significance of the new velocity correction obtained in this study due to the applied second-order exact cumulant expansion is investigated on a numerical example with a linear trend in the distribution coefficient. It is found that the effect of the new velocity correction can be significant enough to affect the maximum concentration values and the plume center of mass in the case of a trending distribution coefficient in a physically heterogeneous environment.