ANALYTICAL SOLUTIONS FOR ONE-DIMENSIONAL COLLOID TRANSPORT IN SATURATED FRACTURES

Closed-form analytical solutions for colloid transport in single rock fractures with and without colloid penetration into the rock matrix ar e derived for constant concentration as well as constant flux boundary conditions. A single fracture is idealized as two semi-infinite paral lel plates. It is assumed that colloidal particles undergo irreversibl e deposition onto fracture surfaces and may penetrate into the rock ma trix, and deposit irreversibly onto rock matrix solid surfaces. The so lutions are obtained by taking Laplace transforms to the governing tra nsport equations and boundary conditions with respect to time and spac e. For the case of no colloid penetration into the rock matrix, the so lutions are expressed in terms of exponentials and complimentary error functions; whereas, for the case of colloid, penetration into the roc k matrix, the solutions are expressed in terms of convolution integral s and modified Bessel functions. The impact of the model parameters on colloid transport is examined. The results from several simulations i ndicate that liquid-phase as well as deposited colloid concentrations in the fracture are sensitive to the fracture surface deposition coeff icient, the fracture aperture, and the Brownian diffusion coefficient for colloidal particles penetrating the rock matrix. Furthermore, it i s shown that the differences between the two boundary conditions inves tigated are minimized at dominant advective transport conditions. The constant concentration condition overestimates liquid-phase colloid co ncentrations, whereas the constant flux condition leads to conservatio n of mass.