Analytical model of sedimentation process based on the equation of continuity of settling polydisperse suspension flow (to be discussed)

Summary

In the well-known studies on the precipitation of polydisperse suspension the latter is identified with suspended (fluidized) bed. However all currently used mathematical models of natural and wastewater sedimentation processes do not take this circumstance into account and sometimes contradict it. Models of the processes of sedimentation in the strict sense have not yet been developed; instead separate methods are used with the help of which the process of sedimentation implemented in laboratory cylinders is carried out in industrial clarifiers. In this simulation the value of the main parameter of the sedimentation process (hydraulic size or sedimentation rate) always decreases with time. In the proposed model the flow of settling suspension is presented as fluidized bed. Moreover this flow has the properties of integrity and continuity of the values of its physical characteristics; whereas the flow rate in this case remains constant. In the process of the model design it was suggested that the concentration of suspended solids in the flow remained average by volume of the clarifier. Taking into account the continuity equation the sedimentation rate is proposed to be understood as the sedimentation rate of polydisperse suspension in the selected flow section that corresponds to the mass flow of suspension through the given section. Based on the above prerequisites a balance differential equation has been compiled that describes the process of sedimentation in a batch clarifier including laboratory cylinders. The solution of the differential equation provides for the formulas for calculating the clarification efficiency both for batch and flow-through clarifiers with time. In order to check the adequacy of the mathematical model the results of calculating the clarification efficiency using the obtained formulas were compared with the results of experiments carried out by other authors and with the typical project solutions. From the analysis of graphs it was concluded that the values of the clarification efficiency calculated theoretically have good convergence with the experimental data given in typical projects.

Key words

clarification , batch clarifier , flow-through clarifier , precipitation of polydisperse suspension , concentration of nonsettleable solids , clarification efficiency , analytical model , equation of continuity , balance differential equation