Modeling Flow and Solute Transport in Packed Beds : Applications in On-site Wastewater Treatment Systems

Abstract: The use of separate phosphorus (P) filter units containing replaceable filter materials with a high P binding capacity have been suggested as an appropriate passive method to treat the P from pre-treated domestic wastewater in on-site facilities. A large number of materials have been identified and suggested as being potentially suitable for such filters. Despite the numerous experimental works with these P filter materials there is still a lack of systematic effort to model the P transport and removal in a packed-bed column experiment filled with such materials. Such a methodology is useful for assessing the performance and longevity of a material. Such a model could also have the potential to be used for scale-up and optimization of operational parameters.The overall objective of this thesis is to investigate and develop methods that can be used to model the flow and solute transport in packed beds in general, as well as dissolved P transport and removal in a laboratory-scale packed bed that is filled with P filter materials. Two different model approaches are investigated: discrete and continuum modeling. In the discrete modeling approach, a packed bed is modeled as a porous medium that consists of thousands of discrete particles. In the continuum modeling approach, a packed bed is considered as a single continuum model with effective parameters such as average pore-water velocity and dispersion coefficients describing the movement of a solute in the packed-bed model.In the discrete modeling approach, two- and three-dimensional randomly packed beds of inert cylinders and spheres are considered, respectively. The flow and nonreactive solute transport are modeled in packed-bed models. Voronoi diagrams are applied to discretize the system into cells that each contains one particle. The whole flow pattern for packed-bed models at low particle Reynolds number is obtained by minimization of the dissipation rate of energy. The effective dispersion coefficients that are derived from packed-bed models are in excellent agreement with the previous data in the literature, showing that these methods can successfully model the flow and solute transport in packed beds. One main advantage of the present method is to make it possible to perform pore-scale simulations of flow, mass and heat transfer in porous media and packed beds with many particles. Moreover, these models facilitate the study of the effects of different packing parameters, such as particle-size distribution, porosity and packing structure on the dispersion coefficients. For example, one result is that an increase in the width of the particle-size distribution increases the dispersion coefficients at high velocities. This discrete modeling approach to solve transport problems in porous media is generic and is applicable for studying heat transfer, drying processes, internal erosion in embankment dams, etc.In the continuum modeling approach, the Langmuir isotherm is fitted to measurements obtained from batch experiments. This Langmuir isotherm is further coupled with the one-dimensional advection-dispersion equation and can successfully model the dissolved P effluent curve of a laboratory- scale column experiment. In the next step, the hydro-geochemical transport code PHREEQC is used to model the transport of dissolved P, dissolution of reactive minerals from a calcium-silicate sorbent and precipitation of P- products in a laboratory-scale column experiment. This methodology can successfully simulate the possible dissolved P removal scenario that occurs in the laboratory-scale column containing the calcium-silicate sorbent.