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A second‐order approach for the modeling of dispersive transport in porous media: 3. Application to two porous media problems
Author(s) -
Tompson Andrew F. B.,
Gray William G.
Publication year - 1986
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/wr022i013p01959
Subject(s) - porous medium , péclet number , aquifer , porosity , dispersion (optics) , mechanics , work (physics) , mathematics , tracer , line source , groundwater , geotechnical engineering , thermodynamics , geology , physics , optics , nuclear physics
The second‐order dispersion model developed by A. F. B. Tompson and W. G. Gray (1986 a, b ) is applied to two porous media problems: one‐dimensional solute transport in a packed column and two‐dimensional transport in a relatively uniform groundwater aquifer. The importance of the convective source q in the model is recognized, and estimates for its constitutive coefficients β 1 and β 2 are found through a series of numerical experiments. For the slow‐flow problems considered, the diffusive source s seems best represented through a one‐term source ( K 0 F ) relationship only, instead of a general three‐term approximation found earlier. Use of K 0 in the column test as predicted from the pipe tests of A. F. B. Tompson and W. G. Gray (1986 b ) works well if the characteristic length for the Peclet number is chosen to be a typical pore diameter. This procedure did not work well in the aquifer test because of the inconsistency of applying a parameter found in a one‐dimensional experiment to a two‐dimensional problem. Both the second‐order model and the traditional first‐order (Fickian) approximation were satisfactory in the tracer tests considered, the former verifying the latter.