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Faraday's Law

In a continuous electrodeionization device the DC current is the driving force for the removal of ions, while the applied DC voltage is the means of obtaining the required current. Faraday's Law states that the electric charge required to liberate one gram-equivalent of a substance by electrolysis is 96,487 coulombs (a coulomb is the amount of electric charge that crosses a surface in one second when a steady current of one ampere is flowing across the surface). In both electrodialysis and electrodeionization, Faraday's Law is used to relate the transfer of salts through the membranes and the amount of current flowing through the membranes. A common form of this relationship is given in Equation 2:


Eq. 2

 

This shows that the amount of DC current required is directly proportional to the flow rate through the diluting compartments and the amount of ionic equivalents to be removed, and inversely proportional to the current efficiency.

Current Efficiency and E-factor

Current efficiency can be defined as the ratio of the theoretical minimum current predicted by Faraday's law (at 100% efficiency) to the actual current applied to the electrodes of the device, as shown in Equation 3:


Eq. 3

 

In a EDI device, current that does not cause the transfer of salt will cause water (HOH) to split into hydrogen (H+) and hydroxyl (OH-) ions, allowing electrochemical regeneration of the ion exchange resins within the device. For example in a module that is operating at 25% current efficiency and drawing 4 amps of DC current, 1 amp is causing the transfer of salt and 3 amps are causing water splitting that is unrelated to ion transfer. Cross-leakage and back diffusion can also cause some current loss, but these are normally small compared to the water splitting.

In order to produce high purity water (over 1 megohm-cm resistivity) with a EDI system, it is generally necessary to feed the system with low TDS water such as RO permeate (normally less than 0.0005 equivalents/liter) and to operate at a current efficiency of less than 35%. For optimal removal of weakly ionized solutes such as silica and boron, current efficiencies as low as 5% are sometimes employed.

Some authors prefer to use the term E-factor. This is defined as the ratio of the applied current to the theoretical current, and is therefore the reciprocal of the current efficiency:


Eq. 4

 

Ohm's Law and Module Resistance

Ohm's law states that the direct current flowing in an electric circuit is directly proportional to the voltage applied, and inversely proportional to the resistance of the element:


Eq. 5

 

Most manufacturers of EDI devices limit the applied voltage to 600 VDC, in order to avoid the need for the more expensive wiring construction that is required for higher voltages. Given such a voltage limitation, the electrical resistance of the module therefore controls how much current can be passed through the cells. Since the DC current determines how much water can be processed for a given product quality (or what the quality will be for a given flow rate), it is important to optimize the electrical resistance of the module.

The overall resistance of the EDI module can be affected by the following:

  • Resistance of the anion-selective membranes
  • Resistance of the cation-selective membranes
  • Resistance of the ion exchange resins
  • Resistance of the concentrate stream
  • Resistance of the anolyte
  • Resistance of the catholyte
  • Feed water temperature
  • Ionic composition of the feed water

In addition to proper selection of resin and membranes, there are several methods that reduce the electrical resistance of the cell and therefore allow greater passage of DC current. The first technique used to accomplish this was to increase the water recovery and therefore the amount of salt in the concentrate compartments. This is generally done by incorporating a feed-and-bleed arrangement, using a pump to recirculate the concentrate stream and ensure adequate flow distribution, while decreasing the flow rate of the bleed that is sent to drain.

An alternative method of reducing the cell resistance is to inject a conductive salt such as NaCl into the feed to the concentrate compartments using a dosing pump. There are several possible drawbacks to this method. Increasing the TDS may prevent reclaiming the concentrate stream for other uses, and may increase the possibility of salt bridging and stray DC currents. If the concentrate is used to feed the electrode compartment, this can also lead to generation of chlorine gas at the anode.

A third method is to incorporate resin filler into the concentrate (and in some cases, electrode) compartments, which eliminates the need for injection of a conductive salt. It has also been seen that the resin helps ions transfer away from the surface of the concentrate side of the ion exchange membrane. This reduces the ion concentration in the boundary layer, reducing the driving force for back-diffusion and improving salt removal.

 

 
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