Comment on “Convergent radial dispersion in a double‐porosity aquifer with fracture skin: Analytical solution and application to a field experiment in fractured chalk” by Allen F. Moench

Moench [1995] has recently presented a new model for the interpretation of tracer tests in fractured rocks and interpreted a multitracer test of Garnier et al. [1985] in a fractured chalk formation, which had earlier been shown to be dominated by matrix diffusion effects, including reactions of some tracers in the matrix [Maloszewski and Zuber, 1990].Moench's approach differs from the earlier one in several aspects: (1) new and more detailed geological information is given; (2) the solution to the transport equation is obtained for resident concentration whereas the previous one was for flowing (flux) concentration [Brigham, 1974; Kreft and Zuber, 1978, 1986]; (3) the model is developed for divergent radial flow whereas the previous one for the unidimensional approximation; (4) the model is developed for sphere-shaped blocks whereas the previous one was represented by the single fissure approximation of the parallel fissure model (slab blocks); (5) the model may account for an instantaneous reversible reactions in the matrix and fissures whereas the previous one may also account for reversible kinetic reactions in the matrix; (6) the skin effect is taken into account; and (7) a different fitting procedure is applied.Item 1 is an evident improvement and needs no discussion.Item 2 is ditticult to judge on the basis of available solutions.Moench [1995] is right in stating that the resident concentration is consistent with the concentration in the matrix where there is no flow.However, it is the flux concentration which is measured in the outflowing water [Brigham, 1974; Kreft and Zuber, 1978, 1986].Item 3 is a theoretical improvement, though it is not clear if the accuracy of that improvement is essential.Item 4 is questionable because instead of parallel fissures between slab blocks (which can be approximated for short-term experiments by a single fissure [e.g., Grisak and Pickens, 1981; Maloszewski and Zuber, 1985, 1990, 1993]), equal-sized sphere-shaped blocks are used.Some of these blocks must be partly concave (see Figure 1 of Moench [1995]); this is not taken into account in the model.Item 5 is better developed in the previous model, and Maloszewski and Zuber [1990, p. 1525] concluded that "for a proper description of sorbable solute transport an adequate formulation of the reaction model is probably more important than the formulation of a fissure network".Item 6 can perhaps be regarded as an improvement for rocks in which fissures are covered by very thin less permeable coating, though it results in an additional fitting parameter which cannot be confirmed by an in&pen-

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