## Electrodialysis Process Costs

The economics of an electrodialysis process are usually expressed as cost per unit product. These costs are the sum of fixed charges associated with amortization of the investment and operating costs such as energy and labour.

Investment costs include items such as the electrodialysis stacks, pumps, electrical equipment and membranes and are proportional to the required membrane area. The minimum required membrane area for a certain plant capacity is

Here a and b are constants, the values of which are determined by a series of parameters such as the cell and spacer geometry, the solution viscosity and the transference numbers of ions in the membrane and the solution.

Eqn [25] shows that the limiting current density is proportional to the diluate concentration. However, the diluate concentration is changing during the desalting process from the concentration of the feed to that of the product. Thus, the limiting current density is decreasing along the flow path through the stack. The average limiting current density is proportional to the average concentration in the diluate cell and

Figure 7 Membrane, energy and total costs of the actual desalination process in electrodialysis.

given by:

Co bdf'p s Cs bdco

logw4

Combining eqns [24] and [26] leads to:

log b^p

bdco

Cs Cs

The constant a' is determined by the feed flow velocity, the stack design, etc.

The operating costs of an electrodialysis plant are mainly determined by the energy consumption which is the sum of the electrical energy required for the ion transfer and the energy necessary for pumping the solution through the stack, as indicated in eqns [17] and [18]. The energy required for the desalting process is a function of the feed solution concentration. The pumping energy depends on the flow velocities in the stack.

It should be noted that, according to eqn [12], the energy costs increase with increasing current density, while the required membrane area decreases with increasing current density. Thus the total desalination cost - which is the sum of capital, energy and operating costs - will reach a minimum at a certain current density, as illustrated in Figure 7, where the total cost of an electrodialysis process is shown schematically as a function of the applied current density.

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