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"On the Misuse of the Simplest Transport Model" by Ernesto Baca, July-August 1999 issue, v. 37, no. 4: 483.
DISCUSSION by P. Binning, Department of Civil, Surveying, and Environmental Engineering, The University of Newcastle, Callaghan, N.S.W. 2308, Australia.
The Technical Commentary, "On the misuse of the simplest transport model" by E. Baca, erroneously states that by finding the distance L and time t at which C/C^sub 0^ = 1/2, the Ogata-Banks solution can provide the containment velocity as v = L/t. While this statement is approximately correct and useful innmany cases, it is derived by neglecting the second term of the nalytical solution. In come cases this second term is important and must be included in the analysis. The circumstances when it was valid to neglect the second term were described in a paper by Sauty (1980). For the purpose of clarification, this result is briefly recounted and elaborated here.
The analytical solution of Ogata nad Banks (1961) describing containment transport with velocity v and dispersion D for the initial and boundary conditions
References
Ogata, A., and R.B. Banks. 1961. A solution of the differential equation of longitudinal dispersion in porous media. U.S. Geological Survey Paper 411 -A.
Sauty, J.-P. 1980. An analysis of hydrodispersive transfer in aquifers. Water Resources Research 16, no. 1: 145-158.
AUTHOR's REPLY by Ernesto Baca, Environmental Consultant, 3216 Georgetown, Houston, TX 77005.
The comments by Binning relate to the phrase "mid-level concentration" or, algebraically, the C/C0 = 0.5 point of the solution (using the notation presented in my Technical Commentary). Notice that in my Technical Commentary I refer to the "estimated" location of this point. The reason for this wording is that, although I am well aware that the location of the mid-level concentration is not exactly at vc * t (i.e., contaminant travel velocity times travel time), the focus of the paper was on the difference of the location of a point at or near the middle of the plume versus a point at the tip of the plume. Binning is absolutely correct in stating that there are differences between the location of the mid-level concentration point and that predicted using vc * t. Binning's detailed explanation of these differences around the mid-level concentration point are welcomed. In fact,...