Moment theory of breakthrough curves for fixed-bed adsorbers and reactors

Razavi, Mohammad; McCoy, Benjamin J.; Carbonell, Ruben G.

doi:10.1016/0300-9467(78)85058-8

Cited by 18 publications

(11 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This is a common technique, especially when an explicit solution to the model is not available (Wiedemann et a]., 1978; Razavi et al, 1978). Using only the first two moments in x to represent a nonreacting porous bed: coefficient.…”

Section: F ( T ) D T / J a K T K F ( T ) D T (5)mentioning

confidence: 99%

“…Moment analysis is a frequently used tool in the characterization of unsteady reactor processes (Ramachandran and Smith, 1978;Razavi et a]., 1978;Wiedemann et al, 1978). It is especially popular in the analysis of chromatographic or reacting beds and the estimation of parameters in models describing such systems (Grubner and Underhill, 1970;Suzuki and Smith, 1971;Razavi et al, 1978).…”

Section: Introductionmentioning

confidence: 99%

“…It is especially popular in the analysis of chromatographic or reacting beds and the estimation of parameters in models describing such systems (Grubner and Underhill, 1970;Suzuki and Smith, 1971;Razavi et al, 1978). The principles of moment analysis (as well as the drawbacks) have been discussed by these authors.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimation of true moments from truncated data

Skopp¹

1984

AIChE Journal

View full text Add to dashboard Cite

Moment analysis is a powerful tool in reactor bed analysis. Weighted moments is a technique which has been introduced to increase the accuracy of moment estimation. The supposed advantage of weighted moments is reevaluated utilizing an optimum truncation point. The resulting coefficient of variation in the moment estimates is shown to be superior to an arbitrary truncation point for all weighting factors. When an optimum truncation pcint is used, little advantage is observed for weighted moments.

show abstract

Section: F ( T ) D T / J a K T K F ( T ) D T (5)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Estimation of true moments from truncated data

Skopp¹

1984

AIChE Journal

View full text Add to dashboard Cite

show abstract

“…Time moments are often used to analyze BTC for determining the mean breakthrough time, Ž . and the degree of spreading and tailing Razavi et al, 1978;Jury and Sposito, 1985 The first, second, third, and fourth moments of the concentration distribution of the BTC can be used to characterize the mean, variance, skewness, and kurtosis, respectively. The skewness characterizes the degree of asymmetry of the distribution around its mean.…”

Section: Calculating Effluent Btcmentioning

confidence: 99%

Characterization of preferential flow in undisturbed, structured soil columns using a vertical TDR probe

Lee

Horton

Noborio

et al. 2001

Journal of Contaminant Hydrology

View full text Add to dashboard Cite

Rapid movement of agricultural chemicals through soil to groundwater via preferential flow pathways is one cause of water contamination. Previous studies have shown that time domain reflectometry (TDR) could be used to characterize solute transport in soil. However, previous studies have only scarcely addressed preferential flow. This study presents an extended application of TDR for determining preferential flow properties. A TDR method was tested in carefully controlled laboratory experiments using 20-cm long and 12-cm diameter undisturbed, structured soil columns. The method used a vertically installed TDR probe and a short pulse of tracer application to obtain residual mass (RM) breakthrough curves (BTC). The RM BTC obtained from TDR were used to estimate mobile/immobile model (MIM) parameters that were compared to the parameter estimates from effluent data. A conventional inverse curve fitting method (CXTFIT) was used to estimate parameters. The TDR-determined parameters were then used to generate calculated effluent BTC for comparison with observed effluent BTC for the same soil columns. Time moments of the calculated and observed BTC were calculated to quantitatively evaluate the calculated BTC. Overall, the RM BTC obtained from TDR were similar to the RM BTC obtained from effluent data. The TDR-determined parameters corresponded well to the parameters obtained from the effluent data, although they were not within the 95% confidence intervals. Correlation coefficients between the parameters obtained from TDR and from effluent data for the immobile water fraction (θ im /θ), mass exchange coefficient (α), and dispersion coefficient (D m ) were 0.95, 0.95, and 0.99, respectively. For three of the four soil cores, θ im /θ ranged from 0.42 to 0.82, indicating considerable preferential flow. The TDR-calculated effluent BTC also were similar to the observed effluent BTC having an average coefficient of determination of 0.94. Time moments obtained from calculated BTC were representative of those obtained from observed BTC. The vertical TDR probe method was simple and minimally destructive and provided representative preferential flow properties that enabled the characterization of solute transport in soil. RightsWorks produced by employees of the U.S. Government as part of their official duties are not copyrighted within the U.S. The content of this document is not copyrighted. AbstractRapid movement of agricultural chemicals through soil to groundwater via preferential flow pathways is one cause of water contamination. Previous studies have shown that time domain Ž . reflectometry TDR could be used to characterize solute transport in soil. However, previous studies have only scarcely addressed preferential flow. This study presents an extended application of TDR for determining preferential flow properties. A TDR method was tested in carefully controlled laboratory experiments using 20-cm long and 12-cm diameter undisturbed, structured soil columns. The method used a vertically installed TDR probe and ...

show abstract

“…Outra forma de descrever parametricamente uma curva de avanço é por meio dos seus primeiros três momentos temporais (Razavi et al, 1978) que descrevem, respectivamente, o tempo médio de avanço, o grau de espalhamento e o grau de assimetria da curva. Na descrição clássica da curva de avanço pelos modelos descritos anteriormente, esses três momentos encontram seus equivalentes no fator de retardação (R), no coeficiente de dispersão hidrodinâmica (D) e na manifestação de "tailing", respectivamente.…”

Section: Análise De Momentos De Curvas De Avançounclassified

Parametrização do transporte dispersivo de solutos em solos estruturados: heterogeneidade do meio, percurso de transporte e modelagem

Schlindwein

1998

Rev. Bras. Ciênc. Solo

View full text Add to dashboard Cite

RESUMOO transporte dispersivo de solutos no solo é parametrizado por meio de equações difusivas e de modelos que partem da existência de uma relação de causalidade entre as características físicas do meio poroso, da sua condição de umidade e da manifestação macroscópica do processo nele ocorrente. A validade dessa proposição, como critério na elaboração de modelos dos processos que governam o transporte de solutos no solo, é discutida heuristicamente. Com base em índices obtidos a partir de uma análise de momentos de curvas de avanço (BTCs), é possível avaliar objetivamente o vínculo que as características do sistema estabelecem com o atendimento do pressuposto do equilíbrio local e, assim, com o sucesso ou não da adoção de uma abordagem de modelagem. Assim, BTCs assimétricas nada mais são do que a manifestação macroscópica de um processo incompleto, e o alcance de uma distribuição simétrica da concentração de solutos só pode ser garantido com a adoção de um "comprimento mínimo de mistura". Termos de indexação: transporte dispersivo, solos estruturados, modelagem. SUMMARY: PARAMETER IDENTIFICATION OF DISPERSIVE SOLUTE TRANSPORT IN STRUCTURED SOILS: SPATIAL HETEROGENEITY OF POROUS MEDIA, TRANSPORT DISTANCE AND MODELINGThe dispersive transport of solutes in soils is described by diffusive equations and by models that assume the existence of a causal relationship between physical characterisitcs of porous media, its water content and the macroscopic manifestation of processes that take (1) Recebido para publicação em maio de 1996 e aprovado em março de 1998.

show abstract

Moment theory of breakthrough curves for fixed-bed adsorbers and reactors

Cited by 18 publications

References 15 publications

Estimation of true moments from truncated data

Estimation of true moments from truncated data

Characterization of preferential flow in undisturbed, structured soil columns using a vertical TDR probe

Parametrização do transporte dispersivo de solutos em solos estruturados: heterogeneidade do meio, percurso de transporte e modelagem

Contact Info

Product

Resources

About