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Analytical solutions for one-dimensional colloid transport in saturated fractures

Chrysikopoulos Constantinos, Assem Abdel-Salam

Πλήρης Εγγραφή

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Περίληψη

Closed-form analytical solutions for colloid transport in single rock fractures withand without colloid penetration into the rock matrix are derived for constantconcentration as well as constant flux boundary conditions. A single fracture isidealized as two semi-infinite parallel plates. It is assumed that colloidal particlesundergo irreversible deposition onto fracture surfaces and may penetrate into therock matrix, and deposit irreversibly onto rock matrix solid surfaces. Thesolutions are obtained by taking Laplace transforms to the governing transportequations and boundary conditions with respect to time and space. For the caseof no colloid penetration into the rock matrix, the solutions are expressed in termsof exponentials and complimentary error functions; whereas, for the case ofcolloid penetration into the rock matrix, the solutions are expressed in terms ofconvolution integrals and modified Bessel functions. The impact of the modelparameters on colloid transport is examined. The results from several simulationsindicate that liquid-phase as well as deposited colloid concentrations in thefracture are sensitive to the fracture surface deposition coefficient, the fractureaperture, and the Brownian diffusion coefficient for colloidal particles penetratingthe rock matrix. Furthermore, it is shown that the differences between the twoboundary conditions investigated are minimized at dominant advective transportconditions. The constant concentration condition overestimates liquid-phasecolloid concentrations, whereas the constant flux condition leads to conservationof mass.

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