Analytical Solutions for Colloid Transport in a Single UniformAperture Fracture Using Effective Parameters and Comparison with aParticle Tracking Algorithm

摘要

This work presents analytical solutions that describe the transport of finitely sized monodispersernand polydisperse particles of neutral buoyancy within a semi–infinite, uniform aperture fracturernsubject to several boundary and initial conditions. The transport of one monodisperse and threernpolydisperse plumes composed of spherical particles with equivalent mean but different log–rnnormally distributed diameters is investigated. Instantaneous as well as continuous particlerninjections are examined. Both reversible and irreversible particle–wall interactions arernconsidered. Both the finite particle size and the characteristics of the particle diameterrndistribution significantly affect the shape of the normalized particle concentration breakthroughrncurves. Furthermore, increasing the standard deviation of the particle diameter enhances particlernspreading and increases the number of sorbed particles when particle–wall interactions are takenrninto account. Excellent agreement between an analytical solution and a particle trackingrnalgorithm is demonstrated.