Influence of the diffusion pattern of the liquid phase flow on ion exchange in a continuously operated countercurrent apparatus

Summary

Physical and mathematical models of a continuously operated ion-exchange apparatus with plug flow of ionite granules and diffusion flow pattern of processed liquid are compiled. It is shown that in this case the operating line becomes curved and inverted to the direction of the equilibrium line. The algorithm of ion-exchange apparatus calculations is presented. Linear approximation of the equilibrium line was carried out that provided for obtaining a differential equation of second order which had an analytical solution. The comparative results of designing an ion-exchange apparatus with plug flow of both phases with different flow patterns are presented.

Key words

linear approximation , ion-exchange apparatus , plug flow , diffusion model of flow pattern , ion exchange , countercurrent , operating and equilibrium lines

Optimal upgrade of sewers

Summary

Choosing the optimal structures and parameters of new and upgraded wastewater disposal systems has been a determining factor in designing their prospective development schemes. This task is suggested to be fulfilled on the basis of preliminary designed redundant schemes that are formed by overlapping pre-engineered options of wastewater system development. On the basis of the redundant scheme a transportation network scheme is designed to determine the maximum flow at minimum costs. For this purpose the flow-through capacity limits of the existing sewers are assigned on the basis of self-cleansing velocities (lower limits) and impermissibility of gravity sewer operation under pressure (upper limits). The cost of the flow units is determined for every network section on the basis of the capital and operation cost data. From the optimization results the route and parameters of the new network sections, options of the existing sewers upgrade (open cut or trenchless relaying, parallel pipeline construction) are determined. The suggested method can be useful when designing prospective development schemes of wastewater systems, and can be used by wastewater services providers for developing investment programs.

Key words

water disposal system , optimization method , maximum flow at minimum cost , flow unit , cost function , linear approximation