Multicomponent flows of miscible fluid mixtures through packed beds of spherical particles are studied in this thesis. An algorithm for the simulation of randomly packed beds of spherical particles with different ranges of diameters is developed. Using a linear optimization routine, statically unstable particles inside the strucre are detected. To simulate the flow inside such a complicated geometry, a model based on the lattice Boltzmann method is investigated. Recovery of Navier-Stokes and Stefan-Maxwell equations is proved for this model. The application of boundary conditions for these simulations is also discussed. Based on a detailed analysis for the mass and momentum conservations on the inlet and outlet, a new in-out flow boundary condition for multicomponent flows is also developed. Radial point interpolation technique is utilized to deal with the multiple grid requirements of the lattice Boltzmann model for mixtures. Using this technique, the deficiencies of previous simulations in complicated geometries are resolved. Applicability of the discussed methods is studied for a number of test cases. Numerical results for the multicomponent flows are in very good agrrement with those of single component flows. A grid study has also been conducted for all test cases.