CURRENT EFFICIENCY MODEL

Sterten, A., Solli, P.A., An electrochemical current efficiency model for aluminium electrolysis cells. Journal of Applied Electrochemistry, 26, pp. 187-193, 1996. 

Heat and mass balance equations are used in all aspects of process modelling however, what is key to this model is an understanding of the electrolytic process behind the cell. For example, the model must be able to predict current efficiency and k-factor if it is to predict electricity consumption. Most of these electrolytic parameters are calculated using empirical relationships derived from experimental data both from test cells and the full-scale plant. Considering k-factor, this is primarily a function of brine strength and temperature. Figure 20.5 illustrates the experimentally derived function used in the model. 

Less than 10% of the reports on pyridine electrochemistry deal with anodic reactions. The mechanisms of these reactions are rarely known and, as a result, yields or current efficiencies have not always been optimized. Many of the anodic reactions were studied in beaker cells, which are simply not good models for modern flow cells moreover, uncontrolled power supplies were often used. Consequently, anode overpolarization caused ring degradation in many cases. 

Boyaval et al. (1993), Weier et al. (1992), and Zhang et al. (1993) attempted to optimize the electrodialytic recovery of propionate from model or real solutions by resorting to a few performance indicators (i.e., current efficiency, solute recovery yield, solute and water fluxes). Despite such parameters were found to be dependent on the feed solutions used, that is, model sodium propionate and/or sodium acetate media and real fermentation broths, Weier et al. (1992) were able to estimate the membrane surface area required to guarantee low propionate levels (0. KUO.32 kmol/m3) during the fermentation as a function of the fermenter size. 

Lillebuen and Mellerud [223] developed a model for the current efficiency as a function of various parameters. The variation with the alumina concentration showed a curve with a minimum at about 4% A1203. The authors showed that the reoxidation reaction rates may be limited by gas dissolution at low alumina contents. The presence of rather large gas bubbles reduces the gas-bath interfacial area to such a degree that the reoxidation reaction rates are being reduced and the current efficiency increased, in spite of the fact that metal solubility is increased at lower alumina concentrations [195,196,223], The current efficiency increases for alumina concentrations over 4% due to the decrease of the metal solubility in the electrolyte [195],... 

In general, current efficiency [tj in (8.3)] has to be determined by laboratory experiments. However, for such compounds as phenol which are susceptible of a fast reaction with OH radicals, the model proposed by Iniesta et al. (2001) may be used. Following this model, when the galvanostatic electrolysis is performed in a batch reactor and the process is only limited by the mass transfer of the reactant to the electrode surface, r] is equal to 1 when the applied current density is lower than the initial limiting current density for mineralization of the reactant ... 

The next group of materials comprises conducting polymers (ICP). Systems with identical polymers have often been reported for polyacetylene. It is known that this ICP forms insertion compounds of the A and D types (see Section 6.4, and No. 5 in Table 12). Cells of this Idnd were successfully cycled [277, 281-283]. However, the current efficiency was only 35% heavy losses were observed due to an overoxidation of the PA [284]. In other cases as for polypyrrole (PPy), the formation of D-PPy was anticipated but did not occur [557, 558]. Entry (6) in Table 12 represents some kind of ideal model. A PPy/PPy cell with alkyl or aryl sulfates or sulfonates rather than perchlorates is claimed in [559]. Similar results were obtained with symmetric polyaniline (PANI) cells [560, 561]. Symmetric PPy and RANI cells yield about 60% current efficiency, much more than with PA. An undoped PPy/A-doped PPy combination yields an anion-concentration cell [562, 563], in analogy to graphite [47], (cf. No. 7). The same principle can be applied with the PPy/PT combination [562, 563] (cf. No. 8). Kaneto et al. [564] have reported in an early paper the combination of two pol54hiophene (PT) thin layers (< 1 pm), but the chargeability was relatively poor (Fig. 40, and No. 9 in Table 12). A pronounced improvement was due to Gottesfeld et al. [342, 343, 562, 563], who employed poly[3-(4-fluoro-phenyl)thiophene], P-3-FPT, in combination with a stable salt electrolyte (but in acetonitrile cf. Fig. 40 and No. 10 in Table 12). In all practical cases, however, Es.th was below 100 Wh/kg. 

Another study carried out by these authors [93] modeled the collapsing motion of a single bubble near an electrode surface, and equations for the motion of a spherical gas bubble were obtained. The jet speed and water hammer pressure during jet flow (liquid jet) were calculated, and when the jet speed was 120 m/s, the water hammer pressure was approximately 200 MPa upon the electrode surface. This pressure played an important part in the fineness of the crystal deposits. Mass transfer during the electrode reaction was by turbulent diffusion. The diffusion layer thickness was reduced to approximately 1/10th its size in the presence of the ultrasonic field. The baths contained the ions Cl-, SO -, and Zn2+. The ultrasonic frequency employed in the experiments was 40 kHz and it was seen that ultrasound considerably increased the deposition rate and current efficiency, as well as the smoothness and hardness of the deposit. Microscopy studies showed that the... 

The current efficiency in modern cells of aluminum electrolysis may exceed 95%. It is generally accepted that the major part of loss in current efficiency is due to the reaction between dissolved metal and electrolyte. Model studies by 0degard et al. (1988) indicates that sodium dissolves in the electrolyte in the form of free Na, while dissolved Al is predominantly present as the monovalent species ALF. Any electronic conductivity is most likely associated with the Na species, which may form trapped electrons and electrons in the conduction band. Morris (1975) ascribed the loss in current efficiency during Al production to electronic conduction. In a theoretical and experimental study. Dewing and Yoshida (1976) subsequently maintained that the electronic conductivity was too low to account for the loss in current efficiency in industrial aluminum cells. However, the existence of electronic conduction in NaF-AlF3 melts was demonstrated later by Borisoglebskii et al. (1978) also. 

Since the conductivity of electrolytes and the cross section and thickness of the membrane are known, a can be determined from the voltage drops across the three pairs of probe electrodes 1-2, 3-4 and 5-6. The sodium current efficiency (CE) can also be determined by titrating the amount of caustic soda generated over a given period of time. The confinement chambers around the working electrodes are used to eliminate free bubbles near the membrane. Our normalized transport data for sulfonate, carboxylate and sulfonamide ionomers are plotted In Figure 5 the universal percolative nature of perfluorinated ionomers can be clearly eeij. The prefactor sulfonate ionomers. The exponent t is 1.5 0.1 in reasonable agreement with theory and the thresholds are between 8 to 10 vol. %, which are consistent with the bimodal distribution in cluster size postulated by the cluster-network model (5.18). This theory has also been applied recently to delineate sodium selectivity of perfluorinated ionomers (20). 

Figure 6. Schematic potential seen by a hydroxyl ion as it moves across a Nafion perfluorinated membrane in a chlor-alkali cell. This potential consists of two parts a constant sloping portion that arises from the voltage drop across the membrane and an oscillating part that arises from electrostatic restriction of the hydroxyl ions. Physically, the hills and troughs correspond to the channel and cluster regions, respectively. For simplicity, a one-dimensional, periodic, model potential is used to evaluate the membrane current efficiency although the real potential is three-dimensional and aperiodic.

Figure 7. Computed current efficiency as a function of EW according to the absolute reaction rate theory. The closed circles and open squares are results of the Cluster-Network (CN) model and classical Donnan equilibrium (DE), respectively. In comparison the experimental trend (----------) is also shown. The adjustable param-...

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