The efficiency of electrodialysis is determined to a large extent by the properties of the membranes. But it is also affected by the process and system design, which determine the limiting current density, the current utilization, the concentration polarization, etc. Therefore, the process design has a significant effect on the overall efficiency and costs [22,23] in electrodialysis.

4.1.1 The electrodialysis stack and process parameters

A key element in electrodialysis is the so-called stack, which is a device to hold an array of membranes between the electrodes that the streams being processed are kept separated. A typical electrodialysis stack used in water desalination contains 100-300 cell pairs stacked between the electrodes. The electrode containing cells at both ends of a stack are often rinsed with a separate solution, which does not contain Cl_ ions to avoid chlorine formation.

The membranes in an electrodialysis cell are separated by spacer gaskets as indicated in Fig. 9, which shows schematically the design of a so-called sheet-flow electrodialysis stack. The spacer gasket consists of a screen, which supports the membranes and controls the flow distribution in the cell and a gasket that seals the cell to the outside and also contains the manifolds to distribute the process fluids in the different compartments. To minimize the resistance of the solution in the cell, the distance between two

Ion-exchange Electrode membrane

Ion-exchange Electrode membrane

membranes is kept as small as possible and is in the range of 0.5—2 mm in industrial electrodialysis stacks. A proper electrodialysis stack design ensures uniform flow distribution and mixing of the solutions to minimize concentration polarization at the membrane surfaces at minimized pressure loss of the solution flow in the stack.

Concentration polarization and limiting current density. The limiting current density is the maximum current that may pass through a given cell pair area without detrimental effects. If the limiting current density is exceeded, the electric resistance in the diluate will increase and water dissociation may occur at the membrane surface, which affects current utilization and can lead to pH changes in the solutions.

The limiting current density is determined by concentration polarization at the membrane surface in the diluate containing compartment, which is determined by the diluate concentration, the compartment design, and the feedflow velocity. Concentration polarization in electrodialysis is also the result of differences in the transport number of ions in the solution and in the membrane. The transport number of a counterion in an ionexchange membrane is generally close to 1 and that of the co-ion close to 0 while in the solution the transport numbers of anions and cations are not very different. At the surface of a cation-exchange membrane facing the diluate solution, the concentration of ions in the solution is reduced due to a transport number of the cations that is lower in the solution than in the membrane. Because of the electroneutrality requirements, the number of anions is reduced in the boundary layer by migration in the opposite direction. The net result is a reduction of the electrolyte concentration in the solution at the surface of the membrane and a concentration gradient is established in the solution between the membrane surface and the well-mixed bulk. This concentration gradient results in a diffusive electrolyte transport. A steady-state situation is obtained when the additional ions, which are needed to balance those removed from the interface due to the faster transport rate in the membrane, are supplied by the diffusive transport. The other side of the cation-exchange membrane faces the concentrate solution where the electrolyte concentration at the membrane surface is increased. The effect of concentration polarization is illustrated in Fig. 10, which shows the salt concentration profiles and the fluxes of cations and anions in the concentrate and diluate solution at the surface of a cation-exchange membrane.

The symbols J and C in Fig. 10 denote the fluxes and the concentration of ions, the superscripts mig and diff refer to migration and diffusion, the

Jmig

Cathode

Cathode

Anode idiff Js

Figure 10 Schematic drawing illustrating the concentration profiles of a salt in the laminar boundary layer on both sides of a cation-exchange membrane and the flux of ions in the solutions and the membrane.

Anode idiff Js

Figure 10 Schematic drawing illustrating the concentration profiles of a salt in the laminar boundary layer on both sides of a cation-exchange membrane and the flux of ions in the solutions and the membrane.

superscripts d and c refer to diluate and concentrate solution, and the superscripts b and m refer to bulk phase and membrane surface, respectively, the subscripts a, c, and s refer to anion, cation, and salt, respectively.

The concentration polarization occurring in electrodialysis can be calculated by a mass balance taking into account all fluxes in the boundary layer and the hydrodynamic conditions in the flow channel between the membranes. To a first approximation, the salt concentration at the membrane surface can be calculated by applying the so-called Nernst film model, which assumes that the bulk solution between the laminar boundary layers has a uniform entrance to the exit. In a practical electrodialysis stack, there will be entrance and exit effects and the idealized model hardly exists. Nevertheless, the Nernst model provides a very simple approach to the mathematical treatment of the concentration polarization, which results in an expression for the current density as a function of the bulk solution concentration, the transport number of the ions, the diffusion coefficient of the electrolyte and the thickness of the laminar boundary layer.

where i is the current density, T the transport number of the counterion, DC the concentration difference between the solution in the diluate at the membrane surface and in the bulk, D the diffusion coefficient, F the Faraday constant, z the charge number, Zb the boundary layer thickness, the subscript i refers to cations or anions, and the superscripts d, m, and s refer to diluate, membrane, and solution, respectively.

When the flow conditions are kept constant, the boundary layer will be constant and the current density will reach a maximum value independent of the applied electrical potential gradient. This maximum current density, which is referred to as the limiting current density, is reached when the counterion concentration at the membrane surface becomes 0. Thus, i - ilim for m Cd ! 0.

where ilim is the limiting current density and b Cd is the salt concentration of the diluate in the bulk solution. All other symbols have the same meaning as in Eq. (17).

The assumptions made in the Nernst film model are often not permissible in an electrodialysis stack. Therefore, the limiting current density in practical applications is generally experimentally determined and described as a function of the feedflow velocity in the electrodialysis stack by the following relation [23]:

where Cd is the concentration of the solution in the diluate cell, u the linear flow velocity of the solution through the cells parallel to the membrane surface, F the Faraday constant, and a and b are characteristic constants for a given stack design and must be determined experimentally. This is done in practice by measuring the limiting current density in a given stack configuration at constant feed solution salt concentrations as a function of the feedflow velocity.

Current utilization. In practical applications, electrodialysis is affected by incomplete current utilization. The reasons for the incomplete current utilization are poor membrane permselectivity, parallel current through the stack manifold, and water transport by convection and due to osmosis and electroosmosis. In a well-designed stack with no pressure difference between diluate and the concentrate, the convective water transport is negligibly low and also the current through the manifold can be neglected.

Under these conditions, the overall current utilization is given by

X - n(Ccm Ta + camT0[1 -(rwm + Twm) Vw(csnd - coutd)] (20)

where X is the current utilization; C is the membrane permselectivity; T is the transport number; n is the number of cell pairs in the stack; Vw is the partial molar volume of water; and c is the concentration; a, c, s, and w refer to anion, cation, solution, and water, respectively; and the superscripts cm, am, ind, and outd refer to cation-exchange membrane, anion-exchange membrane, and diluate at the inlet and outlet of a stack, respectively.

Electrodialysis equipment and plant design. In most commercially used electrodialysis stacks, the membranes are arranged in parallel between two electrodes and are separated by spacers, which also hold the manifolds for the distribution of the individual flow channel as indicated in Fig. 11. There are two major concepts as far as the construction of the spacers is concerned. One is the so-called sheet-flow spacer concept, which is illustrated in Fig. 11a and the other is the so-called tortuous path concept, which is illustrated in Fig. 11b. The main difference between the sheet-flow and the tortuous path flow spacer is that in the sheet-flow spacer the compartments are vertically arranged and the process path is relatively short. The flow velocity of the solutions in the cells formed by two membranes and a spacer

Concentrate or diluate outlet

Concentrate or diluate outlet

Feed inlet

Figure 11 Schematic drawing illustrating the sheet-flow and a tortuous path spacer concept.

Feed inlet

Figure 11 Schematic drawing illustrating the sheet-flow and a tortuous path spacer concept.

is between 2 and 4cms_1 and the pressure loss is 0.2-0.4 bar. In the tortuous path flow stack, the membrane spacers are horizontally arranged and have a long serpentine cut-out, which defines a long narrow channel for the fluid path. The feedflow velocity in the stack is relatively high, that is, between 6 and 12cms1, which provides a better control of concentration polarization and higher limiting current densities, but the pressure loss in the feedflow channels is quite high, that is, between 1 and 2 bar.

In the practical application of electrodialysis, there are two main process operation modes. The first one is referred to as the unidirectional electrodialysis and the second one electrodialysis reversal [24]. In a unidirectional-operated electrodialysis system, the electric field is permanently applied in one direction and the diluate and concentrate cells are also permanently fixed over the period of operation. Unidirectional-operated electrodialysis plants are rather sensitive to membrane fouling and scaling and require periodical rinsing of the stack with acid or detergent solutions. In desalination of brackish or surface waters, generally electrodialysis reversal is applied. In the electrodialysis reversal operating mode, the polarity of the electric field applied to the electrodialysis stack is reversed in certain time intervals. Simultaneously, the flow streams are reversed, that is, the diluate cell becomes the concentrate cell and vice versa with the result that matter being precipitated at the membrane surface will be redissolved and removed with the flow stream passing through the cell. The principle of the electrodialysis reversal is illustrated in Fig. 12.

Fig. 12 shows an electrodialysis cell unit formed by a cation- and anion-exchange membrane between two electrodes and a feed solution containing negatively charged large "fouling" components. If an electric field is applied, these components will migrate to the anion-exchange membrane and be deposited on its surface to form a so-called fouling layer, which affects the efficiency of the electrodialysis process. If the polarity is reversed, the negatively charged components will now migrate away from the anion-exchange membrane back into the feed stream and the membrane properties are restored. This procedure, which is referred to as "clean in place,'' is very effective not only for the removal of colloidal fouling materials but also for removing precipitated salts and is used today in almost all electrodialysis water desalination systems.

However, reversing the polarity of a stack has to be accompanied by a reversal of the flow streams. This requires a more sophisticated flow control. The flow scheme of an electrodialysis plant operated with reversed polarity is shown in Fig. 13. In the reverse polarity operating mode, the hydraulic

Colloidal deposition Cathode

Colloidal displacement Anode

Flow

Colloidal deposition Cathode cm

Colloidal displacement Anode

Flow

Figure 12 Schematic drawing illustrating the removal of deposited negatively charged colloidal components from the surface of an anion-exchange membrane by reversing the electric field in the electrodialysis reversal operating mode.

flow streams are reversed simultaneously, that is, the diluate cell will become the brine cell and vice versa. In this operating mode, the polarity of the current is changed at specific time intervals ranging from a few minutes to several hours.

While reversing the polarity and the flow streams, there is a brief period when the concentration of the desalted product exceeds the product quality specification. Therefore, the product water outlet has a concentration sensor, which controls an additional three-way valve. This valve diverts high concentrated product to waste and then, when the concentration

returns to the specified quality, directs the flow to the product outlet. Thus, in electrodialysis reversal, there is always a certain amount of the product lost to the waste stream.

The degree of desalination that can be achieved in passing the feed solution through a stack is a function of the solution concentration, the applied current density, and the residence time of the solution in the stack. If the degree of desalination or concentration that can be achieved in a single path through the stack is insufficient, several stacks are operated in series or part of the diluate or concentrate is fed back to the feed solution as shown in Fig. 14.

In the so-called feed and bleed operating mode, both the brine and the product concentration can be determined independently and very high recovery rates can be obtained.

The total costs in electrodialysis are the sum of fixed charges associated with the plant investment costs and the plant operating costs. Both the capital costs as well as the plant operating costs per unit product are a function of the feed solution and the required product and brine concentration. But they are also strongly affected by the plant capacity and the overall process design [23].

Investment-related costs. The investment costs are determined mainly by the required membrane area for a certain plant capacity. Other items such as pumps and process control equipment are considered as a fraction of the required membrane area. The required membrane area for a given capacity plant can be calculated from the current required to remove a certain number of ions from the feed solution. Thus, the total current required for the desalination process is proportional to the concentration difference between the feed and diluate solution, the total volume flow of the diluate through the stack, and the Faraday constant. It is inversely proportional to the number of cell pairs in the stack and the current utilization. The total current passing through the stack is given by

NcellX N cell X c£11

Thus

Ncell Qcell - Qst and NcellAcell - Ast and A« - ---- (22)

where I and i represent the electric current and the current densities, A is the cell pair area, Ncell refers to the number of cell pairs in the stack, Q is the volume flow, C is the concentration expressed in equivalent per volume, F is the Faraday constant, and X the current utilization. The subscripts st and cell refer to the stack and cell pair, and the superscripts outd and ind refer to diluate at stack outlet and inlet.

The voltage drop across the stack is constant over the entire cell length of a stack while the resistance changes from the feed inlet to the product outlet due to an increase of the resistance of the diluate as a result of the concentration change. Therefore, the current density also decreases from the feed entrance to the diluate exit. The current density is related to the resistance and the voltage by

Ust - Ncell iRRAcell (23)

where is Ust the voltage drop across the stack, Acell is the cell pair area, and RR is the average resistance of a cell pair.

The average resistance RR can be calculated from the average con-

dc centrations in the diluate and concentrate cells C and C [23] and is given by

cell

Aeq(Clnd - COUtd)

where RR is the average resistance, Ncell and Acell are the number of cell pairs in a stack and the Cind and Coutd are the salt concentrations ofthe diluate at the inlet and outlet of the cells, Cinc and Coutc are the salt concentrations of the concentrate at the inlet and outlet, Aeq is equivalent conductivity of the solutions in the cells, D is the cell thickness, and ram and rcm are the membrane area resistances.

The voltage drop in an electrodialysis stack is the result of the resistances of the membranes and the solutions, the concentration potential difference between the concentrate and diluate streams, and the voltage drop related to the electrode reaction. Most electrodialysis stacks used in practical applications consist of several hundred geometrically identical cells, which are operated in co-current flow, and it can be assumed that the concentration potentials as well as the electrode reactions can be neglected and that in the concentration range of interest, the equivalent conductivity is independent of the concentration [23]. Since the voltage drop is proportional to the current density, which should not exceed the limiting current density, there is a maximum voltage drop that may be applied. The relation between maximum voltage drop and the limiting current density is given by

im x

Leq(Cind - Coutd)

where Umax is the maximum applied voltage across the stack and tlim is the limiting current density. All other symbols are identical to that of Eq. (24).

The membrane area required for a certain plant capacity as function of the feed and product concentrations is obtained by combination, and rearranging of Eqs. (21)—(25) gives

ln(Cind/Cinc)(Coutc/Coutd) + [Aeq(ram + rcm)(Cind - Coutd)/A]

d outd v QdtFC

where Ast is the total membrane area in a stack and Nceu is the number of cell pairs in a stack. All other symbols are the same as the ones in the Eqs. (24) and (25).

The total investment-related costs depend on the price of the membranes and their useful life under operating conditions, which is in practical application 5-8 years, and on the price of the additional plant components and their life.

Operating costs. The operating costs are composed of labor cost, the cost of maintenance of the plant, and the energy cost. The labor and maintenance costs are proportional to the size of the plant and calculated as a percentage of the investment-related costs. The energy required in an electrodialysis process is an additive of two terms: (1) the electrical energy to transfer the ionic components from one solution through membranes into another solution and (2) the energy required to pump the solutions through the electrodialysis unit. The energy consumption due to electrode reactions can generally be neglected since in a modern electrodialysis stack more than 200 cell pairs are placed between the two electrodes. The energy required for operating the process control devices can generally also be neglected.

The total energy required in electrodialysis for the actual desalination process is given by the current passing through the electrodialysis stack multiplied with the total voltage drop encountered between the electrodes:

where Edes is the energy consumed in a stack for the transfer of ions from a feed to a concentrate solution, Ist the current passing through the stack, Ust the voltage applied across the stack, that is, between the electrodes, and t the time of operation.

The total current through the stack is given by Eq. (21) and the voltage across the stack is given by Eq. (24). Introducing the two equations into Eq. (26) and dividing by the produced diluate gives the desalination energy per volume product:

Ede,spc

N cellt

Acell V, pro

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