Hydrodynamic Behavior of a Filter-Press Electrochemical Reactor with

Ind. Eng. Chem. Res. 1998, 37, 4501-4511

4501

Hydrodynamic Behavior of a Filter-Press Electrochemical Reactor with Carbon Felt As a Three-Dimensional Electrode Jose´ Gonza´ lez-Garcıá, Vicente Montiel,* and Antonio Aldaz Grupo de Electroquı´mica Aplicada, Departamento de Quı´mica Fı´sica, Universidad de Alicante, Ap. Correos 99, 03080 Alicante, Spain

Juan A. Conesa Departamento de Ingenierıá Quı´mica, Universidad de Alicante, Ap. Correos 99, 03080 Alicante, Spain

Jose´ R. Pe´ rez and Guillermo Codina I. D. Electroquı´mica S. L. Poligono de Carru´ s, Elche, Alicante, Spain

The implementation of three-dimensional electrodes in electrochemical reactors provides an effective method to improve the efficiency of some electrochemical processes, such as wastewater treatment, electrosynthesis, and energy storage. The increase of the surface area due to the high porosity of these materials is of special interest in diffusion-convection controlled processes. The flow distribution inside the reactor compartments is highly influenced by the characteristics of the porous material. The hydrodynamic behavior of a filter-press electrochemical reactor assembled with three-dimensional electrodes made of carbon felt has been studied in this paper. The felt thickness/cell thickness ratio has been optimized on the basis of flow distribution and energetic considerations, such as pumping power and electrode-collector contact losses. 1. Introduction One of the most common electrochemical procedures for heavy-metal recovery is cathodic electrodeposition.1 This process is usually controlled by the diffusiveconvective mass transport to the electrode. The limiting current is given by the following equation:

IL(t) ) nFkmAc(t)

(1)

where, for a given effluent, the limiting current IL(t) depends on two design factors of the electrochemical reactor: the mass-transport coefficient km and the electrode area A. For the cases where the concentrations of the electroactive species are extremely low, the reactor design must be modified in such a way that the availability of electroactive species to the cathode is enhanced. Based on eq 1, this modification may be done via convection enhancement, km (Pletcher and Walsh2), or electrode area increase, A (Coeuret3). Following this last possibility, the implementation of three-dimensional electrodes in electrochemical reactors has been widely treated in the past few years.4 A great diversity of materials has been used as three-dimensional electrodes.5-8 The scope of application of these materials is continuously extending.9-12 The common feature of all these materials is their high active surface to electron transfer. Moreover, the high porosity of these materials results in the enhancement of convection mechanisms through them. In this way, eq 1 may be transformed in eq 2 (Walsh13).

IL(t) ) nFAeVekmc(t)

(2)

* Corresponding author. Phone: +34-965903628. Fax: +34965903537. E-mail: [email protected].

where Ae is the specific surface area (m2 surface/m3 electrode) and Ve is the electrode volume. The strategy for electrochemical reactor characterization, proposed in the literature consulted, is the establishment of mass balances assuming well-known reactor models (plug flow, stirred tanks, etc.) and the obtaining of analytical expressions describing the reactor behavior.14 The recording of the concentration (of the electroactive species) versus time during an electrolysis in conditions of mass-transport control allows the analysis of the validity of these models. Once the validity of each model has been checked, it is possible to make a quantitative determination of the design factor kmAe. Nevertheless, there are some limitations in the design and scale-up of three-dimensional electrodes when implemented in an electrochemical reactor. These limitations may be purely hydrodynamic, such as the appearance of preferred paths and great stagnant areas in the electrode bulk, high-pressure drops, and bad gas evacuation.15,16 These limitations are also related to the nonuniform potential distribution on the electrode, limiting its effective thickness, especially when the electrolyte has low electrical conductivity, the flow is very high, or the concentration of the electroactive species is very high.17 These limitations imply the need for the development of experimental studies to evaluate the hydrodynamic behavior of these materials. In this paper, the hydrodynamic behavior of a filterpress electrochemical reactor in which a three-dimensional electrode made from carbon felt has been implemented has been studied. The main objective of this paper is to optimize the ratio between the thickness of the felt and the cell regarding the energetic considerations and contact losses. In this way, the influence of the ratio felt/cell thickness on some cell operating parameters, such as pressure drop and pumping power, has been studied. Moreover, a residence time distribu-

10.1021/ie980144a CCC: $15.00 © 1998 American Chemical Society Published on Web 09/24/1998

4502 Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998

Figure 1. Diagram of experimental setup (a): (1) reservoir; (2) thermometer; (3) centrifugal pump; (4) reactor UA200.08; (5) flowmeters; (6) valve; (7) U-tube manometer; (8) nitrogen inlet; (9) heat exchanger; (10) pressure taps. (b): (11) Injection of tracer; (12) conductivity probe. Table 1. Carbon Felt Properties carbon felt thickness/mm density/g‚cm-3 carbon content/% specific surface area(N2)/m2‚g-1 electrical resistivity/Ω‚cm

10 0.1 96 1.1 perpendicular, 20 parallel, 2

tion (RTD) analysis has been performed modeling the cell hydrodynamic behavior as a function of the ratio between felt and cell thicknesses. Finally, a study of the influence of the felt thickness/cell thickness ratio on the contact resistance between the current collector and the electrode felt has been carried out. This influence has been studied through an application of this kind of electrode in the Fe/Cr redox flow battery.18,19 The Fe/Cr redox flow battery is an electrical energy storage system based on the redox process: 3+

Fe

discharge

2+

+ e 98 Fe charge

79 discharge

Cr2+ 98 Cr3+ + e charge

79 The use of three-dimensional electrodes (carbon felts) in a redox flow battery will increase the value of the charging and discharging velocity. Nevertheless, the selection of the ratio between felt and cell thicknesses must be appropriate to obtain a good flow dispersion and a good electrode conductivity that will involve the absence of undesired reactions (water oxidation and/or H+ reduction) and low values of the internal resistance of the accumulator. 2. Experimental Details 2.1. Three-Dimensional Electrodes. Some physical properties of carbon felt RVC 4002 as provided by Le Carbonne Lorraine are shown in Table 1. This material has a very high compressibility when compared to other porous materials usually used as threedimensional electrodes. 2.2. Flow Circuit and Chemicals. Pressure drop measurements were carried out with the experimental arrangement shown in Figure 1, equipped in each case with different kinds of pressure gauges. The injection tracer and the conductivity probe for the RTD experiments substituted the pressure taps. An analogous flow

Figure 2. (I) View of compartment (or chamber) showing details of flow distributors and geometric dimensions, in mm. (II) Exploded view of the UA200.08 reactor in the divided mode showing (a) backplate; (b) polypropylene block with flow channels; (c) flat plate; (d) compartment (or chamber); (e) separator. Table 2. Electrolyte Properties

(F)/kg‚m-3

density dynamic viscosity(µ)/kg‚m-1‚s-1 kinematic viscosity (ν)/m2‚s-1

Na2SO4 0.5 M @ pH 2

water

1056 1.12 × 10-3 1.06 × 10-6

995.2 0.942 × 10-3 0.947 × 10-6

circuit was arranged to feed a second reactor compartment to obtain the polarization curves. The electrolyte was fed into the reactor with an MSEEP-R (March May) model centrifuge pump. Variable area flowmeters and polypropylene membrane valves were used to control the electrolyte flow. All-glass heat exchangers and Pt-100 probes were used to control the electrolyte temperature. The electrolyte used for pressure drop measurements was a 0.5 M sodium sulfate solution. Some of its properties are shown in Table 2. Water was used for RTD tests. A KCl-saturated solution was used as the tracer. A 1.25 M FeCl2 + 1.25 M CrCl3 in 3 M HCl solution was used for the recording of the polarization curves of the redox flow cell, using Bi3+ (6 mM) as a catalyst. The use of Bi3+ is necessary in order to catalyze the Cr3+ reduction process to Cr2+ in the process of charging the accumulator and to avoid the undesired reaction of the reduction of H+ to hydrogen.20 All chemicals were analytical grade. 2.3. Cells. The test cell was a filter-press electrochemical reactor model UA200.08 (built “in house”). Figure 2 shows (I) a detailed description of the cell compartment and flow distributor and (II) a typical dual-compartment configuration. Table 3 displays the characteristic dimensions of the compartment. It must be remarked that the flow channels have a thickness of 2 mm versus the compartment thickness of 8 mm. The cell compartments and the blocks with flow

Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998 4503 Table 3. Characteristic Dimensions for Reactor UA200.08 (See Notation for the Meaning of the Symbols) B L s de Le γ

Reactor UA200.08 0.18 m 0.12 m 8 × 10-3 m 1.53 × 10-2 m 1.28 × 10-2 4.44 × 10-2

channels were made of polypropylene. Gaskets (not included in the figure) were made of EPDM. JP845 graphite plates (Le Carbonne Lorraine) were used for the registration of the polarization curves. Felt plates with different thicknesses were introduced in both a cathodic and anodic compartment. A NAFION 117 ion-exchange membrane (DuPont) was used for cell division. 2.4. Additional Equipment. Various commercial differential pressure gauges were used for the pressure drop measurement of the reactor. An Ingold conductivity probe connected to a Crison 522 conductimeter and a Philips PM8133 X-t analogic recorder were used to register the system conductivity. An UA200.08 model electrochemical reactor and an E.T.I. 100/40 (0-40 V/030 A d.c.) power supply were used as the redox flow system for the recording of the polarization curves. All the system parameters were recorded with a digital data logger connected to a control computer. 2.5. Experimental Procedures. Due to the high hydrophobic behavior of carbon felts, the samples were immersed in an ultrasound bath (0.5 M Na2SO4) for 2 h to achieve a complete material deaeration and hydration. After this treatment, samples showed a volume increase. Before each experiment, the electrolyte was deaerated by N2 bubbling. JP845 graphite samples (Le Carbonne Lorraine) were treated with the activation process described in the literature.21,22 Before each experience, the electrolytes of the redox flow cell were deaerated by nitrogen bubbling. The electrolyte temperature was maintained at 40 °C.

Figure 3. Pressure drop measurements against lineal flow rate for different felt thicknesses at reactor UA200.08. (Details in figure.)

3. Results and Discussion 3.1. Pressure Drops Tests. Associated Energy Consumption. Figure 3 shows the variation of the pressure drop versus the electrolyte linear velocity. The cases represented comprise empty cell and felt-assembled compartments. Different felt thicknesses have been considered. As can be seen, a gradual increase of the pressure drop with felt thickness exists. However, two families of curves can be differentiated, separated when the felt thickness is greater than the compartment thickness. When choosing the ratio felt/cell thickness, a compromise between the electrochemical efficiency and a suitable internal cell distribution with no considerable energy consumption must be established. These kinds of electrodes are usually applied to processes where the energy consumption is of vital importance (wastewater treatment, energy production and storage, etc.). Figure 4 shows the specific energy consumption per mole of product due to the pumping cost Eb (W‚h/mol) is shown. Eb is defined by eq 3 (Stankovic16). The values of j (10 A‚m-2) and ηp (0.8) are arbitrary. As a consequence of the high-pressure drop in the cell compartments, pressure data have been corrected to achieve a suitable representativeness of the results in relation to the influence of felt thickness.

Figure 4. Specific energy comsumption for fluid pumping against lineal flow rate for different felt thicknesses at reactor UA200.08. (Details in figure.)

Eb )

nF∆Pvs jLηp

(3)

An expected behavior has been found on the basis of the experimental results shown in Figure 3. A considerable rise in energy consumption may be observed when the felt thickness is greater than the compartment thickness. These consumptions are highly differentiated from the values obtained for smaller felt thicknesses. For all the thicknesses studied, pumping consumption has been found to be considerable in relation to the energy consumption associated to the electrochemical process (for example, 160 W‚h/mol, for n ) 2 and V ) 3 V), especially for flow rates greater than 0.01 m‚s-1. Nevertheless, for lower flow rates, no remarkable differences were found for the different felt thicknesses studied. 3.2. Distribution of Residence Times. An experimental recording of RTD for the UA200.08 reactor was carried out for the following felt/cell thickness ratios: 7/8, 8/8, 9/8, 10/8, and 13/8. The experimental recording was carried out for different flows: 33, 70, 104, and 144


Figure 5. Experimental RTD obtained for different thickness ratios at reactor UA200.08: (A) 7/8; (B) 8/8; (C) 9/8; (D) 10/8; (E) 13/8. Volumetric flow rate: 104 dm3 h-1 (v ) 2.04 × 10-2 m s-1).

dm3 h-1. Figure 5 shows the RTD obtained at 104 dm3 h-1 for each cell configuration. In the experiments, the RTD obtained for the same sequence of felt thickness shows a similar behavior independently of the applied flow. For every flow, the RTD for the ratio 7/8 splits into two different peaks when the ratio is 8/8. For the relation 9/8, the RTD response presents a characteristic shape that is consolidated for the 10/8 ratio and higher, those presenting a great similarity. To develop a model for the observed behavior, different nonideal flow models have been tested. These models are based on the combination of the dispersed plug-flow reactor model and models for stirred tank reactors in a series. Levich et al.23 consider the hydro-

dynamic mixing in a porous medium with the help of a model containing a series of perfect mixers with stagnant areas and studied the relationship between this model and the usual diffusion one. They concluded that the distribution (for a run with only one peak in the RTD) can be represented as the sum of two distributions, a normal distribution and an exponentially decaying one, and determined the parameters of the porous medium from the experimental results. In our case, and due to the existence of two peaks in the RTD, the model proposed considers two possible paths by where the electrolyte may flow. A scheme of this model is shown in Figure 6. For one of the paths (path 2, occupying a volume V2), the dispersed plug-flow model, assuming a small disper-

Ind. Eng. Chem. Res., Vol. 37, No. 11, 1998 4505

Figure 6. Sketch of the model for flow characterization. (Details in figure.)

sion grade, is applied. The curve representing the distribution of residence times for path 2 (E2) is

( ) (

)

t 1τ 2 1 E2 ) exp 4 π 2 Pe2 Pe2

x

Vtot ) V1 + V2

(8)

Q ) Q1 + Q2

(9)

2

(4)

And the mean residence times will be given by the following equations:

In this equation, Pe2 is the Peclet number for path 2, t is time from the injection of a tracer, and τ2 is the mean residence time for path 2. For the other path (path 1, occupying a volume V1), it is assumed that the electrolyte flows following a dispersed plug-flow model, and that there exists a stagnant area. The electrolyte in the stagnant areas is slowly refreshed by the freely flowing electrolyte that can be considered in axially dispersed plug flow. The electrolyte hold-up in this zone, βtot ) m3 liquid/m3 column, is divided into a dynamic hold-up, βdyn and a static or stagnant hold-up, βstat (see Figure 6). The local rate of exchange between the dynamic and static holdup is assumed to be proportional to the concentration difference in the dynamic and static phases, and it can be characterized by an exchange coefficient, Rm (s-1), defined by

JR ) (number of moles exchanged)/(m3 liquid‚s) ) Rm(cdyn - cstat) (5) where cdyn and cstat are the concentrations in the dynamic and static phase, respectively. Rm can be considered as the product of a mass-transfer coefficient and the specific interfacial area between the flowing and the stagnant zones, kLa. The model equations can be found from a mass balance for the dynamic (dyn) and the static (stat) phases over a thin slice perpendicular to the direction of the flow, whereas we assume the density and other variables to be constant over the length coordinates:24 2 ∂Cdyn 1 ∂ Cdyn ∂Cdyn ΘB ) - Na(Cdyn - Cstat) (6) ∂θ Pe1 Z2 ∂Z

(1 - ΘB)

t/τ, with τ ) L/(ΘBvl); Cstat ) cstat/c; Cdyn ) cdyn/c; S ) cross-sectional area of volume Vl (m2); vl ) velocity in dynamic phase of volume V1 ) Ql/Sβdyn; Ql ) electrolyte flow through volume Vl (m3 s-1); Dax ) dispersion coefficient in dynamic phase (m2 s-1). In this way, NR is the number of mass-transfer units for the mass exchange between the dynamic and the static phase and Pel is the Peclet number for the dynamic phase. The equations system proposed before has been solved by Villermaux and Van Swaaij25 using the Laplace transformation. Due to the high complexity to attain an analytical solution, in this paper the equations system has been solved numerically using the CrankNicholson method.26 Considering that the model proposed for path 1 may be applied to a volume, V1, that has a flow rate, Q1, and the model for path 2 may be applied to a volume, V2, with a flow rate, Q2, the following is done:

∂Cdyn ) -Na(Cstat - Cdyn) ∂θ

(7)

where Z ) z/L, L being the total length of the reactor; ΘB ) βdyn/βtot; NR ) (RmL)/(ΘBvl); Pe1 ) (vlL)/Dax; Θ )

τi ) Vi/Qi

i ) 1,2

(10)

For the different felt thicknesses, the values of ΘB and βtot will be different, but for the experiments carried out with the same felt thickness at different flows, both values must be equal. Thus, the experiments carried out with the same felt thickness have been optimized simultaneously, using as the objective function

O.F. )

∑r ∑k

(

dEk,cal dt

-

)

dEk,exp dt

2

(11)

In this equation, r represents each run at a different flow rate, k represents the data collected at each time, and the subindexes cal and exp correspond to the calculated and experimental data, respectively. It must be pointed out that the small changes observed in the slope of the experimental curves cannot be fitted if this objective function is not used (i.e., small changes in the experimental curve are best observed when using the derivative objective function). The model parameters for each group of the experiments carried out with the same felt thickness are the following: (1) ΘB and βtot, valid for all the flows. (2) Peclet numbers for each flow (Pe1, Pe2). (3) Mean residence time in path 2 (τ2) for each flow. (4) NR value for each flow. (5) Ratio between the volume occupied in path 1 and the total volume for each flow. So, for the fitting of four experiments (at different flow rates) carried out with the same felt thickness there are 22 parameters. These parameters are valid for four experiments of 250 points each. In the literature, models with less parameters that may explain the existence of the two peaks in the RTD curve can be found, but the model proposed in this paper is the only one that justifies all the experimental results. It may be observed that a minimum number of parameters have been used. Unnecessary values, such as ΘB and βtot for all the flows, have been suppressed. All the


13/8 70 0.9703 0.9137 2.56 1.11 10.01 102.44 0.264 0.35 0.65 24.87 1.13 2.80 13/8 33 0.9703 0.9137 2.46 0.21 19.99 134.41 0.360 0.40 0.60 46.10 1.06 2.45 10/8 144 0.9755 0.8254 1.12 2.15 5.63 179.09 0.185 0.38 0.62 11.23 1.30 2.60

(12)

10/8 70 0.9755 0.8254 4.90 1.13 9.04 252.40 0.450 0.46 0.54 18.86 1.02 2.12 10/8 33 0.9755 0.8254 4.37 1.43 19.28 259.96 0.469 0.48 0.52 37.87 1.03 2.02 9/8 134 0.9800 0.8455 3.26 1.95 6.10 44.53 0.113 0.33 0.67 13.97 1.31 3.01 9/8 104 0.9800 0.8455 4.54 1.25 7.63 56.56 0.335 0.48 0.52 12.25 1.28 2.05 9/8 70 0.9800 0.8455 7.79 1.58 9.12 76.95 0.599 0.61 0.39 14.31 1.03 1.61 9/8 33 0.9800 0.8455 5.57 1.37 21.50 47.55 0.422 0.49 0.51 37.43 1.14 1.99 8/8 144 0.9838 0.4431 56.05 1.90 10.33 192.26 0.663 0.86 0.14 4.95 2.39 1.15 8/8 104 0.9838 0.4431 51.35 1.67 13.01 217.38 0.742 0.88 0.12 6.68 2.17 1.12 8/8 70 0.9838 0.4431 24.54 1.55 16.85 203.88 0.762 0.87 0.13 10.00 1.90 1.12 8/8 33 0.9838 0.4431 20.13 1.66 33.79 227.49 0.798 0.89 0.11 20.90 1.79 1.11 7/8 144 0.9956 0.3971 37.76 4.07 2.48 44.34 0.874 0.78 0.22 5.51 0.57 1.28 7/8 104 0.9956 0.3971 24.20 2.03 2.37 38.30 0.891 0.72 0.28 8.23 0.40 1.38

where N is the total number of points, P the number of parameters to be fitted, and (dE/dt)exp the mean value of the experimental data used in the O.F. (eq 11). The values of this V.C. are between 2 and 4% for all the cases. The parameters βtot and ΘB present no dependence on flow. However, dependence on felt thickness has been observed. Parameter βtot gradually decreases with felt compression and it may be correlated to felt porosity. Parameter ΘB suddenly increases with felt compression in the transition from 8/8 to 9/8, and higher. At first, path 1 with the flow inside the felt and path 2 with the flow in the felt limits and outside the felt could be identified. This must be rejected because, for high ratios of felt/cell, the value of V1/Vtot and Q1/Q are 0.5, and it is very improbable that thickness relations of 10/8 or 13/8 leave more than a half of the cell compartment unoccupied by the porous material. The analysis of the results of maintaining a constant flow and increasing the thickness ratio presents a very interesting discussion. We will analyze the thickness ratio 7/8. In the first place, we may assume that the porous material for this thickness ratio does not occupy a portion of the compartment. However, it has been experimentally observed that this material expands in the pretreatment, so this assumption is not so evident. From the results shown in Table 4, it may observed that the fraction of the total volume occupied by path 1 is around 0.9 and the fraction of the total flow circulating through it is 0.75. For this thickness ratio, the parameter βtot provided by the model is 0.996. However, it must be remarked that the fraction of this volume in the dynamic movement is only 0.4. All these observations seem to indicate that felt acts as a “sponge” for this thickness ratio, where the greater part of the liquid is slowed down. Path 2 shows a ratio of τ2/τtheor less than 1 for all the flows. This value of τ2/τtheor may indicate that a portion of this path is located outside the porous material, appearing to be a bypass phenomenon.

7/8 70 0.9956 0.3971 10.88 6.03 2.93 50.44 0.932 0.79 0.21 11.16 0.33 1.26

( )

7/8 33 0.9956 0.3971 9.06 0.78 13.51 8.07 0.609 0.45 0.55 41.28 0.72 2.19

(13)

dE dt exp

Table 4. Results of Modelization for Different Thickness Ratios and for Different Volumetric Flow Rates

O.F. x N-P V.C.(%) )

10/8 104 0.9755 0.8254 3.33 1.15 6.92 229.46 0.388 0.47 0.53 12.38 1.16 2.07

In Table 4, the parameters obtained and the relationships between flows and τi calculated from them, as well as the ratio τi/τtheor(τtheor ) Vtot/Q), are shown. In Figure 7, a calculation for each felt thickness at a flow of 70 L‚h-1 is shown. Both calculated and experimental curves are presented, as well as the RTD for the two constituent paths. The O.F. values in eq 11 have been smaller than 3 × 10-5 for fits of four simultaneous experiments, each one formed of 250 experimental points. A variation coefficient can be defined in order to quantify the quality of the fitting:

Q (L/h) βtot ΘB Pe1 NR τ2 (s) Pe2 V1/Vtot Q1/Q Q2/Q τ1 (s) τ2/τteor τ1/τteor

Q1 Q2 E ) E1 + E2 Q Q

13/8 104 0.9703 0.9137 3.24 1.46 7.12 146.28 0.266 0.38 0.62 15.14 1.19 2.53

remaining values, such as Q1, Q2, and τ1, are determined by the optimized parameters, the mass equations (8) and (9), and the relationships (10). The optimization of the parameters is carried out using the flexible simplex method.27 The total RTD is calculated using the following equation28:


Figure 7. Experimental and simulated RTD curves obtained for different thickness ratios at reactor UA200.08: (A) 7/8; (B) 8/8; (C) 9/8; (D) 10/8; (E) 13/8.s, experimental; calculated; +, E1; O, E2. Volumetric flow rate: 70 dm3 h-1 (v ) 1.38 × 10-2 m s-1).

When the felt thickness is increased to 8 mm (i.e., ratio of 8/8), the values of V1/Vtot are slightly smaller, though the values for the flow ratio Q1/Q are slightly greater. The dynamic fraction of path 1 slightly increases while the parameter βtot slightly decreases. Nevertheless, it may be deduced that the situation has not changed much. The highest difference is that the value τ2/τtheor is now higher than 1. This implies absorption of the tracer on the material, so now path 2 is fully located inside the porous material. For the ratio 9/8 and higher, the compression of the porous material begins to be significant. It may be observed that the reactor volume occupied by path 1 (stagnant area) still decreases. However, the flow ratio begins to decrease. This decrease is greater at higher

Table 5. Total Dynamic Volume Ratio for Different Thickness Ratios and Different Volumetric Flow Rates 33 L/h 70 L/h 104 L/h 144 L/h

7/8

8/8

9/8

10/8

13/8

0.63 0.44 0.47 0.48

0.55 0.57 0.59 0.63

0.94 0.91 0.95 0.98

0.92 0.93 0.93 0.97

0.97 0.97 0.97

flows. Nevertheless, the more important observation is that the percentage of stagnant areas has suddenly decreased from the thickness ratio. Table 5 shows the moving portion of the total volume (sum of the contribution of the two paths ) (1 - (V1/ Vtot)) + V1B/Vtot) for all the studied flows. From these results, it may be deduced that the major effect of material compression is the decrease of the stagnant areas.


Figure 8. Polarization curves obtained for different thickness ratios at the reactor UA200.08: (A) 7/8; (B) 8/8; (C) 10/8; (D) 12/8. +, 50% charge state; [, 50% discharge state; 0, 70% charge state; O, 70% discharge state; 2, 90% charge state; 90% discharge state. EFe3+/Fe2+ and ECr3+/Cr2+ are the electrode potentials for Fe3+/Fe2+ and Cr3+/Cr2+. I is the current passed and Rinternal is the internal resistance of the cell.

For a fixed thickness ratio, the values of V1/Vtot show a general decreasing tendency when the flow increases. However, a clear influence on the Q1/Q ratio is not observed and remains constant. A flow pattern explaining the proposed analysis would be the identification of path 2 as a part of the felt with relatively easy electrolyte circulation, path 1 being located on areas with difficult electrolyte percolation. Only these areas maintain their behavior when the porous material is compressed. The values of βtot and ΘB obtained for each thickness ratio are uniform and representative of the felt in these conditions. Moreover, this flow pattern is able to explain the following aspects: (i) The behavior observed in Figure 3 shows that the gradual decrease of the material porosity with the decrease of the thickness ratio implies a rise in the cell

pressure drop for each flow. The appearance of two families of curves separated in the transition 8/8 to 9/8 is explained by the sudden rise of the moving portion of the total volume (from 0.50 to 0.95). The electrolyte flowing by path 2 circulates through a porous medium and, moreover, the electrolyte flowing by path 1 leaves the stagnant areas (ΘB varies from 0.44 to 0.85). This fact implies a sudden increase of the cell pressure drop because a greater quantity of electrolyte is circulated. (ii) The Pe values associated to each path present very different values. The Pe values for path 2 are high and relatively independent of the thickness ratio. This result would be expected for a flow path with no difficult circulation. The Pe value for path 1 undergoes a major variation when the material is compressed. For the ratios 7/8 and 8/8, there is a great portion of stagnant areas and the electrolyte flowing by path 1 only circu-


lates through nonwinding zones, smaller dispersion and high Pe values being observed. When the material is compressed, it may be observed that the fraction of the stagnant area in path 1 decreases, and therefore, the electrolyte is forced to circulate through winding areas, thus the dispersion observed in the decrease of Pe values. (iii) The analysis of the values of τi/τtheor reveals that path 1 always presents values greater than 1, being closer to this value when the felt is not compressed and being closer to 2 when the felt is compressed. The proportion of the stagnant volume is very low when the porous material is compressed. However, the material presents a difficult percolation, producing a difficult evacuation of the adsorbed tracer. On the other hand, path 2, which does not consider slowed areas, presents values very close to 1 when the material is compressed, circulating more than a half of the flow through it. In this way, the adsorption of the tracer is not favored. For the relation 8/8, the proportion of flow is low, favoring the adsorption of the tracer, and values for the ratio τ1/ τtheor close to 2 are obtained. 3.3. Electrical Resistance. For the moment, the influence of the ratio felt/compartment thickness on the pumping power and internal flow distribution has only been taken into account. However, due to the special characteristics of electrochemical reactors, the influence of this ratio on the electrical parameters of the reactor must also be studied. Thus, a three-dimensional electrode must present low-resistive electrical connections to the current collector, achieving a homogeneous potential distribution in its bulk. In this way, the appearance of undesired parallel reactions is avoided. One of the most common applications of three-dimensional electrodes is the redox flow cells for power accumulation systems. The introduction of these kinds of materials as electrodes considerably decreases the value of the internal resistance of the cell, increasing the energetic efficiency of the overall system. For this particular case, it is evident that the study of the contact resistance collector-electrode is of special relevance. In the configuration used for this paper, the electrical connection felt-collector is made by direct contact, the contact resistance being influenced by the felt/compartment thickness ratio. To evaluate this influence, a series of experiments using the UA200.08 reactor as the redox flow cell have been carried out. Charge-discharge cycles starting from identical initial conditions have been established for each felt thickness (7, 8, 10, and 12 mm). The evaluation of the redox cell performance was made from the polarization curves obtained at different state-of-charge levels, representing the cell voltage versus the current density. The state of charge of the Fe/Cr redox flow battery is given by the state of charge of the solutions that constitute it (Fe3+/Fe2+ and Cr3+/Cr2+). The state of charge of the solutions are defined as29

% state of charge (Fe3+/Fe2+) ) 100 mol of Fe3+/(mol of Fe3+ + mol of Fe2+) % state of charge (Cr3+/Cr2+) ) 100 mol of Cr2+/(mol of Cr3+ + mol of Cr2+) In Figure 8, the polarization curves for different felt thicknesses have been represented (see details in figure). The representation of the cell voltage versus

Figure 9. Electrical resistance against the state of charge (%) for different thickness ratios at the reactor UA200.08 used as the redox battery. (Details in figure.)

current density must be a straight line in the absence of electrode overvoltages. From the slope of this line, the internal resistance of the cell can be calculated. It may be observed that the linear response of the polarization curve increases when the felt/compartment thickness ratio rises. From this observation, it may be concluded that the increase of the felt/compartment thickness ratio improves the contact collector-electrode, achieving a better potential distribution in the electrode bulk. Very good linear responses have been obtained for felt thicknesses of 10 and 12 mm. In Figure 9, the values of the internal resistance have been represented. The great degree of linearity of these graphical representations confirms the uniformity of the potential distribution in the three-dimensional electrode. 4. Conclusions The optimization of the felt/compartment thickness ratio of a three-dimensional electrode has been carried out by different techniques. In a first approximation, the information given by the pressure drop measurements and by the voltage has limited the possible range of optimum values of the ratio. Nevertheless, more detailed information about the hydrodynamic behavior of the system is proportioned by the RTD analysis. This analysis yields an optimum ratio close to 10/8. The model presents a good fit of the experimental data, and accurate information of the flow permits one to establish the necessary bases in order to apply the mass balances and kinetics for the characterization of the electrochemical reactors cited in the literature. It is also important to remark that an alternative method for the structural characterization of porous materials is proposed, since the porosity is optimized in the model. However, this paper gives useful information concerning the adequate configuration to be used in a bench or industrial scale (ratio close to 10/8, with the possibility of optimization using the same technique). In these conditions, a dispersed plug-flow model, with almost no dead zones, can represent the hydrodynamical behavior obtained. A good electrical connection between the collector and the three-dimensional electrode is also obtained.


With the specific finding obtained, high values of conversion when passing through the reactor are expected and also no parallel reactions are being produced due to a good distribution of the electrical current (i.e., a good electrical connection). It is also expected that no accumulation or retention of the liquid or gas phase inside the reactor, due to its hydrodynamical behavior, will occur. Acknowledgment One of the authors (J.G.-G.) is grateful to the “Consellerıá de Cultura, Educacioń y Ciencia, de la Generalitat Valenciana” for his research grant. Support for this work was provided by CYCIT-Spain, research project QUI97-1086. Notation a ) specific interfacial area between the flowing and stagnant zones for stream 1, m2/m3 A ) electrode area, m2 Ae ) specific superficial area for three-dimensional electrode, m2/m3 b ) breadth of the compartment, m (perpendicular to the direction of flow) c ) concentration, mol/m3 cdyn ) concentration in the dynamic phase for stream 1, mol/m3 cstat ) concentration in the static phase for stream 1, mol/ m3 Cdyn ) normalized concentration in the dynamic phase for stream 1, mol/m3 Cstat ) normalized concentration in the static phase for stream 1, mol/m3 Dax ) dispersion coefficient in the dynamic phase, m2/s de ) equivalent (hydraulic) diameter of the compartment, m ()2bs/(b + s)) E1 ) residence time distribution (RTD) for stream 1 E2 ) residence time distribution (RTD) for stream 2 Eb ) specific energy consumption for fluid pumping, W‚h/ mol F ) faraday constant, 96485 C/mol IL ) limiting current, A j ) current density, A/m2 J ) rate of exchange between the static and dynamic holdup of stream 1, mol/(m3‚s) kL ) mass-transport coefficient between the flowing and stagnant zones for stream 1, m/s km ) mass-transport coefficient, m/s L ) length of the compartment in the direction of flow, m Le ) dimensionless length group ()de/L) n ) number of electrons per mol ∆P ) pressure drop, Pa Pe ) Peclet number Pe1 ) Peclet number for stream 1 Pe2 ) Peclet number for stream 2 Q ) volumetric flow rate, m3/s Q1 ) volumetric flow rate for stream 1, m3/s Q2 ) volumetric flow rate for stream 2, m3/s R ) resistance, m2 s ) thickness of compartment, m S ) cross-sectional area of volume 1, m2 t ) time, s v ) lineal flow rate, m/s v1 ) lineal flow rate for stream 1, m/s v2 ) lineal flow rate for stream 2, m/s V ) cell voltage, V or total volume of reactor m3 V1 ) volume of reactor for stream 1, m3 V2 ) volume of reactor for stream 2, m3

Ve ) three-dimensional electrode volume, m3 Vtot ) total volume of reactor, m3 z ) coordinate in the direction of flow, m Z ) normalizated coordinate in the direction of flow Greek Letters Rm ) exchange coefficient between dynamic and static holdup for stream 1, s-1 ΘB ) fraction of dynamic zone for stream 1 βtot ) liquid hold-up for stream 1 βdyn ) dynamic hold-up for stream 1 βstat ) static hold-up for stream 1 ηP ) pumping power efficiency factor µ ) dynamic viscosity, kg/(m s) F ) density, kg/m3 ν ) kinematic viscosity, m2/s ()µ/F) γ ) aspect ratio of the compartment θ ) dimensionless time τ ) averaged residence time, s τ1 ) averaged residence time for stream 1, s τ2 ) averaged residence time for stream 2, s τteor ) averaged residence time for the compartment, s (dV/Q)

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Received for review March 3, 1998 Revised manuscript received July 15, 1998 Accepted July 24, 1998 IE980144A

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