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Analytical and Approximate Solutions to Radial Dispersion From an Injection Well to a Geological Unit With Simultaneous Diffusion Into Adjacent Strata
Author(s) -
Chen ChiaShyun
Publication year - 1985
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/wr021i008p01069
Subject(s) - aquifer , laplace transform , dispersion (optics) , mechanics , geology , advection , hydraulic conductivity , diffusion , permeability (electromagnetism) , leakage (economics) , soil science , groundwater , geotechnical engineering , mathematics , mathematical analysis , physics , chemistry , thermodynamics , membrane , biochemistry , optics , macroeconomics , soil water , economics
Analytical and approximate solutions are developed for radial dispersion in aquifers with simultaneous diffusion into adjacent strata. Contaminants from the injection well are transported within the main aquifer by advection and mechanical dispersion, assuming a steady state and radially diverging ground‐water flow field. The leakage of contaminants from the main aquifer to the aquitards is accounted for by molecular diffusion. A mathematical model consisting of two coupled differential equations is proposed to investigate concentration distributions in the main aquifer as well as in the adjacent aquitards. By making use of Laplace transforms, analytical solutions valid for small time periods are obtained without difficulty. To complement these analytical solutions, concentration distributions for intermediate and large time intervals are determined approximately by numerically inverting the appropriate transformed solution in the Laplace domain with the Stehfest algorithm. Excellent agreement exists between analytical solutions and approximate solutions for small time intervals, supporting the validity of approximate solutions for intermediate and large time periods. It is shown that the diffusive leakage may significantly delay contaminant movement within the main aquifer at relatively large time periods. The solutions can be applied to study radial dispersion in granular aquifers bounded by relatively low permeability aquitards, or in planar fractures contained in porous formations.