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Comment on “An Analytical Solution for One‐Dimensional Transport in Heterogeneous Porous Media” by S. R. Yates
Author(s) -
Chrysikopoulos Constantinos V.
Publication year - 1991
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/91wr01389
Subject(s) - laplace transform , constant (computer programming) , laplace's equation , dispersion (optics) , mathematical analysis , boundary value problem , flux (metallurgy) , function (biology) , boundary (topology) , physics , mathematics , materials science , computer science , optics , evolutionary biology , programming language , metallurgy , biology
The solution to the deterministic one-dimensional advectiondispersion equation with distance-dependent dispersion coefficient derived by Yates [ 1990) has many advantages due to its analytical nature. The proposed model is interesting with potential practical applications in laboratory heterogeneous packed column solute transport experiments and possibly in some field studies where the assumption of one-dimensional flow under constant velocity is-valid. The author should be commended for the useful analytical results presented. The objective of this comment is to report a simpler solution than the one given b y Yates (1990) for the case of zero initia l concentration and constant flux boundary condition. The notation employed here is identical t o Yares (1990). The correct general Laplace time solution to the governing advection-dispersion model is given by Yates [1990. equation (9)]. assuming that the division of C(,$, s) by C,, on the left-hand side is in error. In order to satisfy the downstream boundary condition. the Laplace time solution reduces IO c([. s) = Ats)(‘K Y [2y(s + /3)“*(]. (1) The Laplace-transformed integration function, A(s). is evaluated from the constant flux boundary conditio n [Yates. 1990. equation (15)]