Mathematical Modeling of Suspended Solids and Associated Pollutant Transport.

Abstract

The transport dynamics of particulate solids have been of long-st and ing concern from the perspectives of sedimentation operations in water and wastewater treatment, and bed-load movement and siltation processes in rivers, streams, and dredged channels. Only recently, however, has attention focused on detailed descriptions of the behavior of suspended solids in natural water systems from the perspective of water quality transformations. This interest is predicated largely on increased awareness of the role of suspended solids in the transport of certain pollutants in natural water systems. Pollutants absorbed on, or contained within, suspended solids constitute a separate phase in a heterogeneous system, and can be expected to behave quite differently -- chemically, biochemically, hydrodynamically, and toxicologically -- from dissolved pollutants. Yet most water quality models presently used to describe the behavior and fate of pollutants account only for the transport and distribution dynamics of the homogeneous phase, or dissolved pollutants. It has become increasingly clear that accurate description of the environmental distribution and accumulation of solids-associated pollutants, of the impact of these pollutants on the food webs of the aquatic environment, and of their toxicologic implications to man must take account of the dynamics of transport of suspended solids. This research focused on development of a rational approach to mathematically model the fate of these materials from an environmental engineering perspective. The rectangular open channel flume was used as the primary subsystem. A two-dimensional, steady-state, mass balance equation was formulated to describe particulate transport in the subsystem. Appropriate definitions were made for horizontal velocity and the turbulent diffusivity coefficient as functions of depth. The bottom boundary condition was formulated in terms of a resuspension function. The resultant subsystem modeling equation was solved using an explicit finite difference method. Fall velocity was defined for a given suspension in terms of a log-normal distribution resulting from quiescent settling column analyses. Results from several tests were presented demonstrating the efficacy of this approach. A correlation for the resuspension function was formulated from an analysis of cohesive sediment flume data. The resultant formulation was used to resimulate the data and exhibited good correlation. A finite segment approach was developed to apply the subsystem model to three-dimensional, time-variable natural systems. A conceptual approach within the finite segment framework implementing the resuspension function was developed for the consideration of sediment scour. The system model was applied to the Ford Lake-Belleville Lake (MI) system. A classical model application approach was used. First, an appropriate hydrodynamic model was constructed using conductivity as a tracer for calibration/verification. A steady-state model for suspended solids transport was constructed. A fecal coliform bacteria transport model was constructed using both sedimentation and die-off as independent removal mechanisms. The final step was the construction of rainfall related time-variable simulations. Three events were simulated, each possessing different characteristics. Most significant was the simulation of possible scour events occurring during Rain Events 1 and 2 in the Huron River reach between Ford and Belleville Lakes, where significant increases in flow indicated the possibility of scour within the framework of the conceptual framework developed previously.