Ohmic voltage losses

Figure 3.3.7 Theoretical (dashed dotted) and real (solid) cell voltage (V) - current density (I) performance characteristics of a fuel cell. Overpotentials are responsible for the difference between theoretical and real performance and cause efficiency losses. They split into (i) activation polarization overpotentials at anode and cathode due to slow chemical kinetics, (ii) ohmic polarization overpotential due to ohmic voltage losses along the circuit, and (iii) concentration polarization overpotentials due to mass-transport limitations. The activation overpotentials of the cathode are typically the largest contribution to the total overvoltage.

To conclude this section, I estimate the voltage components of the bubble layer in circumstances roughly appropriate to oxygen evolution in 1 N sulfuric acid and carbon dioxide evolution in Hall-Heroult electrolysis. The values chosen should be taken as approximations designed to show upper bounds of the individual components for the purposes of illustration. Equation (26) represents the ohmic voltage loss associated with the presence of the... 

The classical anode material was graphite. It is slowly oxidized to carbon dioxide, due to the formation of small amounts of oxygen (reaction 3), and the anode loses material. Thus, electrode gap and ohmic voltage losses increase, or anodes have to be mechanically readjusted. 

In any synthesis where electricity costs are important it is vital to minimize ohmic voltage losses. In addition to those covered by Eq. 2.41, namely in the electrolyte and the diaphragm, one must add losses caused by resistance in the current leads or bus bars. Of these, electrolyte resistance is usually the most important it is affected by several parameters. 

The effect of electrolyte composition on conductivity is complex. Typically, in relatively dilute solutions conductivity increases with concentration. Above a certain value of concentration the effect is reversed typical conductivity maxima result. This is true of electrolyte solutions of strong electrolytes such as NaCl, KOH, and HCl at temperatures approaching 100°C, they have conductivities of lOOmho/m at molarities of 4-6 M. Such conditions are typical of water and chlorine electrolyzers and mean that ohmic voltage losses are of the order of lOmV/mm interelectrode gap/(kAm" ). 

THE PROBLEM Estimate the ohmic voltage loss in the electrolyte between two cylindrical electrodes of diameters 0.05 m and 0.065 m and length 0.2 m. The conductivity is 200mho/m and the cell current is 200 amp. 

The evolution of a gas during an electrolytic reaction produces a dispersion of bubbles in the electrolyte. Since the bubbles have virtually zero electrical conductivity the current flow path becomes restricted and ohmic voltage losses become greater than those for the electrolyte. The usual way to deal with bubbles is to assign to the electrolyte an effective conductivity which is typically correlated as a function of gas voidage There are a number of correlations of this type one of the most reliable is the so-called Bruggeman equation ... 

Electrode materials employed in industrial reactors often have relatively poor electrical conductivities. If cost requirements require thin electrodes, appreciable ohmic voltage loss may occur across the electrode, especially if large electrodes are used. Potential and current distribution may suffer. This results from having to make a mechanical connection between the bus bars and the electrode, usually at one point (Fig. 5.27) or, preferably, distributed along one edge. As current flows through the electrode structure a variation... 

Figure 1.30. Voltage transient (thin line) and fitted average voltage (bold hue) for the whole stack. Extrapolation is indicated with a dotted hne. Air supply free convection i = 200 mA cm 171. (Reprinted from Journal of Power Sources, 112(1), Mennola Tuomas, Mikkola Mikko, Noponen Matti, Hottinen Tero and Lund Peter, Measurement of ohmic voltage losses in individual cells of a PEMFC stack, 261-72, 2002, with permission from Elsevier.)...

Meimola T, Mikkola M, Noponen M. Measurement of ohmic voltage losses in individual cells of a PEMFC stack. J Power Sources 2002 112 261-72. 

Using the methods described below in Section 3.10, it is possible to distinguish this particular irreversibility fi om the others. Using such techniques it is possible to show that this ohmic voltage loss is important in all types of cell, and especially important in the case of the solid oxide fuel cell (SOFC). Three ways of reducing the internal resistance of the cell are as follows ... 

Average voltage of one cell in a stack Activation overvoltage Ohmic voltage loss Work done... 

Equations 7.60 and 7.61 are the general representation of the ohmic resistance and ohmic voltage loss, respectively. The total ohmic voltage loss is the sum of all ohmic loss components owing to electronic resistances in interconnects and electrodes, and ionic conductivity in the electrolyte as shown in Figure 7.7. 

As we have discussed in Chapter 7, ohmic voltage loss in a fuel cell takes place owing to the resistance of the material to charge transport. This includes electron transport from the anode side to the cathode side of the cell through the electrodes and interconnects, and ion transport through the electrolyte. The net ohmic voltage loss is expressed as... 

The other four tunable parameters are presented in the equation of activation and ohmic voltage losses ... 

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