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Pressure drop, liquid holdup and mass transfer in a graphite fibre bed with upward co-current gas-liquid… Hodgson, Isaac O. A. 1993

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PRESSURE DROP, LIQUID HOLDUP AND MASS TRANSFER IN AGRAPHITE FIBRE BED WITH UPWARD CO—CURRENT GAS—LIQUIDFLOWByIsaac Owusu Afriyie HodgsonB. Sc (Hons) University of Science and Technolgy, GhanaA THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENT FOR THE DEGREE OFMASTER OF APPLIED SCIENCEINTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF CHEMICAL ENGINEERINGWe accept this thesis as conformingTHE UNIVERSITY OF BRITISH COLUMBIAAugust 1993© Isaac O.A. HodgsonIn presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of  CkketV■ • Ct--1^VoEIV-4 (\-)C)The University of British ColumbiaVancouver, CanadaDate 1 S-4"-^TDE-6 (2/88)AbstractThe pressure drop, liquid holdup and overall mass transfer capacityhave been studied in a graphite fibre electrode of porosity 0.90and fibre diameter 22 micrometer with cocurrent upward gas-liquidflow.A U-tube mercury manometer was used to measure the pressure dropin a graphite fibre bed 356 mm long by 38 mm wide by 3 mm thick.The gas and liquid were oxygen and water. For gas load 0 5 G 5 0.43kg/m2s and liquid load 1.46 5 L 5 7.30 kg/m2s, the pressuregradient ranged from 0.24 and 2.09 bar/m. The correlation for thepressure gradient isAP = L [ 0.36 + 1.182 (G/L ) 0.618 ]2where AP = pressure gradient^ bar/mL = liquid load^ kg/m2sG = gas load kg/m2sThe quick closing valve method was used to measure the totalliquid holdup in a graphite fibre bed 356 mm long by 38 mm wide by3mm thick. Oxygen and 1M aqueous sodium hydroxide were the fluidsused for the total liquid holdup measurements. For gas load 0 5 G5 0.35 kg/m2s and liquid load 1.53 5 L 5 7.62 kg/m2s the liquidholdup ranged from 0.44 to 1.0.The correlation for the total liquid holdup ishL = 1 - 0.907 L 0.362 G 0.301iiwhere hL = liquid holdupThe overall mass transfer capacity was determined by theelectrochemical reaction method with the electro-reduction ofoxygen to peroxide. The electrochemical reactor used consisted ofgraphite fibre cathode bed of dimension 89 mm long by 38 mm wide by3 mm thick. The cathode was separated from the anode by a cationmembrane. Oxygen gas and 1M aqueous sodium hydroxide were thefluids used. For gas load 0.04 5 G 5 0.36 and liquid load 3.05 5L 5 7.62 the overall mass transfer capacity ranged from 3.4 to 9.0-1s . The correlation for the overall mass transfer capacity isKa = 5 . 9 L0.371 G0.233where K = overall mass transfer coefficient^ m/sa = effective interfacial area for gas to solid^m-1L = superficial liquid load^ kg/m2sG = superficial gas load kg/m2siiiTable of ContentsAbstractTable of contents^ ivList of Tables viList of Figures^ viiAknowledgement viii1 Introduction^ 12 Literature Review^ 42:1 Hydrodynamics 42:2 Gas-Liquid Flow^ 52:3 Pressure drop 62:4 Liquid holdup^ 102:5 Gas-Liquid mass transfer for co-currentupward flow^ 122:6 Liquid-solid mass transfer^ 162:7 Porous electrodes^ 182:8 Electrochemical reaction method for determination- of mass transfer rates^ 203 Experimental Apparatus and Procedures^ 253:1 Pressure drop measurement^ 253:2 Total liquid holdup measurement^ 303:3 Measurement of mass transfer capacity^ 334 Results and Discussion^ 404:1 Pressure drop 40iv4:2 Liquid holdup^ 474:3 Overall mass transfer capacity^ 555 Conclusions and Recommendations 605:1 Conclusions^ 605:2 Recommendation 62Nomenclature^ 64Bibliography 69Appendix^ 73A Calibration Curve and Analytical Method^ 73B Experimental Results^ 76C Sample Calculations 93Sample Calculation One (Fuild load, pressure gradient) 94Sample Calculation Two (Liquid holdup)^ 97Sample Calculation Three (Peroxide concentration)^98Sample Calculation Four (Theoretical current)^99Sample Calculation Five (Current efficiences)^100Sample Calculation Six (Limiting current) 103Sample Calculation Seven (Mass transfer capacity)^103Sample Calculation Eight (Porosity of graphite felt) 106Sample Calculation Nine (Electrode potential)^107List of Tables1 Some experimental data cited in the literature for pressuredrop, liquid holdup and mass transfer in packed beds^212 Calibration of the gas rotameter, at R.T.P^ 733 Results of the pressure drop measurement in fibre bed^774 Results of the liquid holdup measurement in fibre bed^785 Results of the overall mass transfer capacity measurement^796 Results of the Reynolds number of gas and liquid and theirmass transfer capacity^ 807 Results of peroxide produced at various currents, run 1^818 Results of peroxide produced at various currents, run 2^829 Results of peroxide produced at various currents, run 3^8310 Results of peroxide produced at various currents, run 4^8411 Results of peroxide produced at various currents, run 5^8512 Results of peroxide produced at various currents, run 6^8613 Results of peroxide produced at various currents, run 7^8714 Results of peroxide produced at various currents, run 8^8815 Results of peroxide produced at various currents, run 9^8916 Results of peroxide produced at various currents, run 10^9017 Results of peroxide produced at various currents, run 11^9118 Results of peroxide produced at various currents, run 12^9219 Experimental errors^ 112viList of Figures1 Detailed sketch of the cell^ 282 Apparatus used for the pressure drop measurement^293 Apparatus used for the liquid holdup measurement 324 Detailed sketch of the graphite fibre trickle-bed reactor^365 Detailed sketch of the graphite fibre trickle-bed electrode 376 Apparatus used for the overall mass transfer capacitymeasurement^ 387 Peroxide concentration versus current^ 398 Pressure gradient versus gas load 449 Pressure gradient versus liquid load^ 4510 Experimental versus correlated pressure gradient^4611 Liquid holdup versus gas load^ 5012 Liquid holdup versus liquid load 5113 Effective electrolyte conductivity of 1 M aqueous sodiumhydroxide at 20 to 25 °C versus liquid holdup^ 5214 Experimental._versus correlated liquid holdup 5315 Experimental versus correlated liquid holdup by differentauthors^ 5416 Mass transfer capacity versus gas load^ 5817 Experimental versus correlated mass transfer capacity^5918 Calibration curve for the oxygen gas, at 760 mmHg and 21°C 75viiAknowledgementPraise be to God the Father of mankind who has given us Jesus andthrough Him we receive blessings upon blessings. It is in Him welive, move and have our being. Praise the Lord!I express my sincere appreciation to Professor Colin Oloman forhis guidance, continual encouragement, valuable assistance andpatience throughout the course of this project.I express my sincere gratitude to the staff of the workshop andstores for their assistance and advice.Also acknowledged are all those who through their prayers,advice, suggestions, help and encouragement have made this workpossible.Finally, I thank the N.S.E.R.C. for financial support.viiiCHAPTER 1IntroductionOver the years one of the aims of electrochemical technology hasbeen to increase the space-time yield of electrolytic cells. Theneed to design a cell with a high active surface area per unitvolume of reactor has led to the design of new electrodes whichdiffer from the classical plate electrodes.Presently, in some processes, the classical plate electrodes arebeing replaced by porous electrodes. This is because recent studieshave proved that porous electrodes have a higher active electrodearea per unit volume of reactor and also a higher overall masstransfer capacity when compared to the classical electrodes. Theseporous electrodes have commonly been applied in the reaction ofdilute species whose conversion depends on effective mass transfer.Typical examples are recovery or separation of dissolved metalions, the oxidation of dissolved organic wastes and surfactants andthe electrosynthesis of organic compounds. Also, they have beenemployed for separation of organic species by electrosorption, fuelcells and batteries [1], and peroxide synthesis. These porouselectrodes have been constructed from wire screens, expanded metal,packed beds, metallic foams and felts [2]. They have been found tohave high surface area per unit volume of electrode and to improvemass transfer by turbulent promotion when compared to the classicalplate electrodes [2].1Chapter 1. IntroductionA trickle-bed electrode is a porous electrode through which agas and an electrolyte solution are passed in cocurrent flow.Usually, the gas and liquid are passed cocurrently downward butsometimes the direction of the flow may be upward. For this studythe trickle-bed will refer to an upward flow system. Just like allother porous electrodes, the effective electrode thickness of thetrickle bed is limited to about one centimetre. This is because ofthe decrease in electrode potential which occurs in the directionof current flow. Usually a long electrode bed is required to beable to obtain useful chemical conversion per pass at high space-velocity and low voltage drop. The particle or fibre diameter forthese electrodes is about two millimetres or less. This is lowerthan the size generally employed in trickle-bed thermochemicalreactors [3].In trickle-bed electrochemical reactors there is a simultaneousabsorption of the reactive gas into the liquid phase followed by afurther electrochemical reduction or oxidation of the dissolvedgas. The reactant gas when introduced into the cell along with theelectrolyte phase helps to improve the availability of the reactantto the electrode surface. It also affects the hydrodynamics of theflow in the porous electrode and thus its mass transfer capacity.Usually, high gas loads used in trickle-bed electrodes cause adecrease in the liquid holdup but increase the pressure drop [3].2Chapter 1. IntroductionAccording to Takahashi and Alkire [4], the few data that existfor gas-liquid flow over small packing of about two millimetres indiameter or less, suggest that their mass transfer behaviour isdifferent from that of particles in the range of .2.6-76 mm. Thus,the many two-phase flow mass transfer correlations reported in theChemical Engineering literature do not apply to porous electrodes.There is therefore the need for a more accurate knowledge of thefluid dynamics and models to be developed to predict the behaviourof porous electrodes, for example the graphite fibre electrode.Since the fibre diameter (22 micrometer) of the graphite fibretrickle bed electrode is less than two millimetres it is likelythat its pressure drop, liquid holdup and mass transfer rate willbe different from the larger packings reported in the ChemicalEngineering literature.The objective of this study was to determine by experiment thepressure drop, the liquid holdup and the overall gas-solid masstransfer capacity for a range of gas-liquid co-current upward flowin a graphite fibre electrode. Also, to develop empiricalcorrelations for pressure drop, liquid holdup and mass transfercapacity to assist in designing graphite fibre trickle-bedelectrodes.3CHAPTER 22: Literature Review2:1 HydrodynamicsThe transport processes within a packed bed depend on theprevailing flow regime. The flow regime primarily depends on thethe flow loads of the gas and liquid phases, together with thenature, size and status of the packing material.The various flow regimes that exist for co-current gas-liquiddownflow are trickle flow which is gas continuous, pulsed flow,spray flow and bubble flow. The flow regime for cocurrent upflowthrough a packed column is composed of various modes such asliquid-continuous, gas-continuous and slug flow. In the gascontinuous regime, the liquid may flow partly as drops and partlyas a film over the packing.In the trickle-flow regime, the liquid trickles over thepacking in the discontinuous shape of films, rivulets, and dropsnear a stagnant continuous gas phase. The trickle flow regime indownward flow is usually referred to as the poor interaction regimebecause there is very little interaction between the gas and liquid[5].4Chapter 2. Literature Review2:2 Gas-Liquid FlowGas-liquid flow in fixed bed thermochemical reactors has beenwidely used over the years. Some of the applications include coalliquefaction, catalytic hydrodesulfurization, selectivehydrogenation, etc [6].Countercurrent flow is often used to provide effective gas-liquid contacting for distillation towers and gas absorptioncolumns. It is not usually applied in electrochemical cells becauseof the problem of flooding which limits the range of flowrates.Fixed-bed electrodes with simultaneous co-current flow of gasand electrolyte solution have been investigated for electrochemicalprocesses involving gaseous reactants like oxygen [7,8,9], sulphurdioxide [10], propylene [11]. Jansson and other workers haveinvestigated the use of bipolar trickle towers to solve pollutioncontrol problems (scavenging of copper, silver,lead and calciumfrom dilute streams, oxidation of cyanide concentration by directand indirect methods, etc.) [12-14].Compared to the co-current gas-liquid downflow reactor, theupflow reactor gives higher pressure drop, better wetting of thecatalyst and higher liquid holdup [15].5Chapter 2. Literature Review2:3 Pressure DropSince pumping costs could play a significant part of the totaloperating costs in an electrochemical process-it is important toconsider the pressure drop in the design of electrochemicalreactors. Significant pressure drop can also cause largeundesirable changes in the partial pressure of the reacting gaswithin the reactor and mechanical problems in cell construction.There is little literature on pressure drop in electrochemicalreactors.Two main approaches are usually adopted to correlate thepressure drop for a two phase flow in trickle-bed reactors.One is the empirical approach, the other involves the modificationof the single-phase flow Ergun equation to account for the two-phase flow.Single-phase flow:-The Ergun equation [16] has been widely acceptedand used to predict the pressure drop for single phase flow throughfixed beds. Ergun proposed universal constants of 150 and 1.75 forthe two parameters in his equation. He assumed that the constantshold for all types of packings. He also proposed the use of anequivalent spherical particle diameter.Macdonald et. al. [17] investigated the single phase flow modelpredictions by Ergun. After a thorough comparison of their data6Chapter 2. Literature Reviewwith the Ergun equation they concluded that the functional form ofthe Ergun equation represented their data well but discovered largeerrors which were up to two orders of magnitude with the use of theuniversal Ergun constants. They therefore suggested the need todetermine the constant for the packing of interest since theuniversal constants do not hold for all packings.Two-phase flow:- Sweeney [18] assumed the single-phase flow Ergunequation for each phase in the two-phase flow. He also assumed thatthe solid particle size remained unchanged and considered theliquid as a solid boundary relative to the gas. He also stressedthe need to determine the constants for the packing underconsideration instead of using the ones suggested by Ergun in hisequation.In arriving at their model for gas phase pressure drop in two-phase flow Specchia and Baldi [19] considered the effect of phaseinteraction in the trickle flow to be negligible. They recommendedthat the coeffitient in the Ergun equation be determined.Thd Pittsburgh Energy Research Centre (PERC) [20] obtained theirpressure drop data in highly-pulsed and spray-flow regimes in a10.2 cm internal diameter clear acrylic column. They obtained over300 pressure drop data points for both 6.35 mm by 6.35 mm and 3.2mm by 3.2 mm pellets. Their data fitted well with Tallmadge'scorrelation [21]. Sato et al [22] correlated their data using theLockhart-Martinelli type of relation. They also graphically7Chapter 2. Literature Reviewrepresented some pressure drop data in the bubble, pulse and spray(gas continuous) flow regimes. They used the Ergun equation todetermine the single-phase flow for each phase for the two-phaseflow. They assumed that the pressure drop of each phase flowthrough the restricted section is the same as that for a single-phase flow through the whole section. Thus they did not account forthe interaction effects between the gas and liquid.Empirical Correlations:-Turpin and Huntington [23] used dataobtained from an air-water flow system and 51, 102 and 153 mmdiameter columns. They used tabular alumina particles for theirpacking. The diameter sizes of the packings were 7.6 and 8.2 mm.They correlated their pressure drop data for co-current upflowempirically. They chose gas loads ranging from about 0.02 kg/m2s to38.3 kg/m2s. The range for the liquid load was from 6.52 to 54.33kg/m2s. Their correlation which is shown in Table 1 related thegas and liquid phase Reynolds numbers to the pressure gradients.Ford [24] ffeasured the pressure drop in beds packed withapproX'imately one millimeter diameter particles. He presentedempirical correlations for both two phase pore flow and single-phase pore flow. According to Ford [24] the transition from oneflow regime to the other could occur at a liquid holdup of 0.43.Before his correlation can be used knowledge of the liquid holdupis required. He suggested that if the liquid holdup is less than0.43 the equation for the two-phase pore flow should be used and8Chapter 2. Literature Reviewwhen the liquid holdup is greater than 0.43 then the correlationfor the single pore flow should be used to calculate the pressuredrop. Saada [25] discovered some inconsistencies in Ford'scorrelations. He repeated and extended part of Ford's work. Hestudied the air-water system in a 45-mm internal diameter, 400-mmlong column. For his examination he used three different sizepackings of glass-bottom spheres of nominal diameter 0.514-, 0.974and 2.064-mm. He came out with two different empiricalcorrelations one for the single-phase pore flow and the other forthe two-phase pore flow. He developed an empirical correlation(shown in Table 1) which related the pressure drop to the Reynoldsnumber for the gas and liquid, the diameter of the column andpacking. He arrived at a relation to determine the transition fromsingle-phase pore flow to two-phase pore flow. His equation showshow the Reynolds number of the liquid and the diameters of theparticle and the column can be used to obtain the minimum value ofgas Reynolds number (ReG*). ReG is the minimun value of gasReynolds number'above which the flow will be in the two-phase pore-flow regime. The pressure drop correlation derived by Turpin andHungtington [23] has been found suitable for calculation ofpressure drop in the bubble and pulse flow regimes. For small sizepacking the PERC [20] data or the data of Sato [22] for thepressure drop are recomended [5].There is has been no previous work done on pressure drops in co-current two-phase upward or downward flow in fibre beds.9Chapter 2. Literature Review2:3 Liquid HoldupThe liquid holdup can be defined as the volume of liquid containedper reactor volume. However, it is usually defined on the basis ofthe void volume of the reactor and not the total reactor volume.The liquid holdup is one of the factors used to evaluate theperformance of a reactor. The liquid holdup can be divided into twoparts :- dynamic holdup and the static holdup. The dynamic liquidholdup depends on the gas and liquid loads, the properties of thefluids and the packing material. The static holdup depends on thenature of the packing and the fluid properties. Quite a substantialnumber of studies on liquid holdup has been carried out ondifferent packings.Voyer and Miller [26] studied the liquid holdup in a columnwith screen packings. They observed that the liquid holdupdecreases with the increase in gas velocity. Unfortunately they didnot develop any correlation to represent their data.The liquid holdup in an air-water system and 51, 102 and 153 mmdiameter columns packed with tabular alumina particles of 7.6 and8.2 mm in diameter was measured by Turpin and Huntington [23]. Theycorrelated their total liquid holdup to the ratio of liquid to gasmass flux by an empirical relation. Their total liquid holdup wasbased on the column's void volume. The ratio of the liquid to gas1 0Chapter 2. Literature Reviewmass flowrate ranged from 1 to 6. Their correlation model has beenfound not to be valid for L/G greater than 5.69 since it gives atotal liquid holdup greater than unity.Sato et al [22] correlated their data to the Lockhart-Martinelli parameter for the pressure drop. They accounted for theporosity of the packing in their correlation.Hutton and Leung [27] proposed a theoretical model of the liquidholdup for cocurrent upflow through a packed column. They alsocorrelated their liquid holdup to the pressure drop. They assumedthe liquid holdup to be a function of the two-phase pressure dropand the superficial liquid velocity. Their theoretical predictionof the total liquid holdup by their model showed only a fairagreement when compared to the experimental data of Turpin andHuntington [23]. Hutton and Leung [27] also confirmed the fact thatco-current upflow operation gives higher liquid holdup under thesame gas and liquid loads. They arrived at this result using atheoretical model. This fact had earlier on been demonstratedexperimentally Sy Turpin and Huntington [23].The Pittsburg Energy Research Centre [20] studied the liquidholdup in a packed column with co-current gas-liquid upflow. Theyperformed their measurements on air-water flow through a 10.2 cminternal diameter acrylic column. Three different packing sizeswere examined. They are 19 mm x 19 mm, 6.35 mm x 6.35 mm and 3.2mm x 3.2 mm cylinders. Most of their experiments were obtained inthe bubble flow and pulsed flow regimes. They found the average11Chapter 2. Literature Reviewliquid holdup to be strongly dependent on the liquid velocity.Stiegel and Shah [28] studied the characteristics of the liquidholdup using an air-water system. The dimensions of their columnwere 168 mm long, by 20.6 mm wide and 1220 mm high. Polyethylenepacking with 3.18 mm diameter was used. The air load ranged from 0to 0.203 kg/m2 s. Their results indicated that under the same flowconditions, the liquid holdups in a rectangular column were ingeneral higher than those obtained in a cylindrical column ofequivalent section.Lamine et al [15] studied the liquid holdup using smallparticles of diameter one, two and three millimeters. The liquidload ranged from 1-11 kg/m 2 s and the gas load ranged from 0-0.3kg/m2 s. Achwal and Stepanek (29) also measured the liquid holdup.The diameter of the particles they used was about 6 mm. Both thecorrelations of Lamine et. al. and Achwal and Stepanek are shown inTable 1. The results of Achwal and Stepanek agree fairly well withthe results of Lamine et. al. The experimental results of Lamine etal deviate by ±20 % from the empirical correlation of Achwal andStepanek.No previous work has been done on liquid holdup measurement ingraphite fibre beds.12Chapter 2. Literature Review2:4 Gas-Liquid mass transfer for co-current upward flowQuite a number of interesting studies have been carried out todetermine the gas-liquid mass transfer capacity for upward co-current gas-liquid flow.Mashelkar and Sharma [30] used columns of diameters 66, and 200mm with a variety of packing to examine both the gas side andliquid side gas-liquid mass transfer coefficient. They measured theabsorption of carbon dioxide in various electrolytes and nonelectrolytes. Their results showed that the volumetric gas-liquidmass transfer coefficient increased with the superficial gasvelocity.Using an 80 mm diameter packed column with three differenttypes of packings:- glass spheres, Berl saddles, and ceramic rings,Specchia et. al. [31] measured the liquid-phase mass transfercoefficient. The superficial gas and liquid velocities they usedranged from 0.14 to 2.21 m/s and 0.0025 to 0.043 m/s respectively.They correlated their liquid-side mass transfer coefficient to theenergy parameter. This is shown in Table 1. Prior knowledge of thegas-liquid pressure drop is required before their correlation canbe used. Higher kr, values were obtained for upward compared todownflow for lower liquid velocities. Specchia et al [31] foundthat the kLaL values for upward flows were on the average 100 %greater than the downflow in pulsed and spray flow regime. This was13Chapter 2. Literature Reviewbecause of the gravitational force which gave higher liquid holdupand pressure drop [5].Snider and Perona [32] used a column packed with 2.9 mm aluminaspheres coated with palladium catalyst to study the mass transfercoefficient for the hydrogenation of alpha-methyl styrene. Theyfound that the mass transfer coefficient increased with the gasrate up to a gas-phase Reynolds number of about 50 and as the halfpower of the liquid load. The pulsating nature of the flow forhigher gas rates accounted for the strong decrease in the masstransfer coefficient for higher gas rates.Goto et. al. [33] measured the liquid-gas mass transfercoefficient for the desorption of oxygen from water into nitrogen.They used a 25.8 mm internal diameter glass tube packed with Cu0-ZnO particles with diameter of 0.541 or 2.91 mm. The condition atwhich the data were obtained are 1 atm pressure, and 25°Ctemperature. The gas load ranged from 0.0027 through 0.0082 and theliquid from 0.478 to 5.738 kg/m2s respectively. They obtained theirdata in the bubble-flow regime as defined by Specchia et. al.[31]. Their results showed that the liquid-side mass transfercoefficient increased with both gas and liquid load. Compared tothe co-current downflow data their results show that the upflowgave larger values of mass transfer coefficient only at high gasand liquid loads. They used the desorption of naphthalene fromwater to determine the gas side mass transfer. From their resultsthey deduced that the gas-side mass transfer was a strong function14Chapter 2. Literature Reviewof the gas load and only depended mildly on the liquid load.Ohsima [34] used a column packed with 1-, 2.8-, and 4.3 mm glassbeads to measure the liquid-phase mass transfer coefficient for theoxidation of sodium sulfite. The superficial liquid velocity rangedfrom 10 to 60 mm/s and that of the gas from 5 to 60 mm/s. Theycorrelated the kLaL to the dynamic gas holdup.Voger and Miller [26] studied the liquid-phase mass transfercoefficient by measuring the desorption of CO2 from water. Theyperformed their experiments in a column of internal diameter of140 mm and heights ranging from 2.04 to 2.38 m. The column waspacked with screens. The gas load ranged from 0.18 to 1.62 kg/m2sand the liquid from 5.5 to 30 kg/m2s. From their investigation theyfound that the mass transfer coefficient was independent of gasvelocity but increased with liquid velocity. Also, that at shortcolumn heights the average mass transfer coefficient and capacitydecreased with an increase in column height.Alexander and Shah [35] measured the desorption of oxygen fromwater in a 60-MM diameter column. They used different shapes ofpacking which are normally used in gas-liquid-solid catalystreactors. The gas load ranged from 2.14 to 44.3 kg/m2s. Theliquid load ranged from 0.9 to 6 kg/m2s. These flow rates are therates typically used in pilot scale catalytic hydrogenationprocesses. They correlated kLaL with the gas and liquid loads. Theyalso correlated their data with the energy correlation of Reiss[36]. Prior knowledge of the two-phase pressure drop is required15Chapter 2. Literature Reviewbefore their equation can be used.Charpentier [37] suggested that in the absence of any reliabledata or correlation a value of 0.15 s-1 could be used as a firstapproximation for the kLaL for pulse and spray flow regimes.It is generally recommended that the correlation by Specchiaet. al. [31] be used to determine the kLaL [5].2:5 Liquid-solid mass transferSnider and Perona [32] used 3-mm alumina spheres coated withpalladium catalyst to measure the volumetric liquid-solid masstransfer coefficient for the hydrogenation of alpha-methylstyrene. They performed their experiments in the bubble flowregime.Mochizuku and Matsui [38] used the diffusion-current method todetermine the liquid-solid mass transfer coefficient. The activeplatinium particle was 5 mm long and 5 mm in diameter. Thisparticle was placed in a dummy particle-packed bed. The diameter ofthe column was 87 mm. The measurement of the diffusion current fromthe platinium anode particle was determined by streaming anequimolar solution of potassium ferro and ferricyanides throughthe bed. They kept the Schmidt number constant at 1170.The validity of the equations above is questionable under theconditions of an actual reactor, where all particles are active and16Chapter 2. Literature Reviewunder the conditions where the Schmidt number is not equal to 1170.Goto et. al. [33] measured the liquid-solid mass transfercoefficient in the bubble flow regime for the dissolution rates ofnaphthalene in water. They used a glass column packed withparticles of sizes 0.54 to 2.4mm of naphthalene and CuO-ZnO. Thecolumn had internal diameter of 25.8 mm. The liquid load rangedfrom 0.5 to 5.74 kg/m2s while the gas load ranged from 1.8 to 7.2kg/m2s. Their correlation can be found in Table 1. The temperatureand pressure were 25°C and one atmosphere respectively. They foundthe mass transfer coefficient to be higher for upflow when comparedto the downflow.Takahashi and Alkire [4] used the electrochemical limitingcurrent method to measure both the liquid to solid mass transferand the overall gas to solid mass transfer capacity for a two phaseco-current upflow in a packed bed electrode. In both cases theyused 1.2 mm glassy carbon particles for their packing. They usedferricyanide reduction to measure the liquid-to-solid mass transfercapacity. Pure ditrogen was used as the inert gas. Oxygen reductionwas used to obtain the overall gas to solid mass transfer capacity.The Reynolds number for the gas and liquid they chose for theoverall gas to solid mass transfer capacity ranged from 10 to 300and 11.7 to 59.3 respectively. They observed that the liquid tosolid mass transfer rates depended mainly on the liquid flow rate.Surprisingly, their measurements showed that the mass transferrates increased with decreasing liquid flow rate. The overall mass17Chapter 2. Literature Reviewtransfer capacity they obtained ranged from 0.009 to 0.032 s-1.Unfortunately, they did not correlate their results for the gas tosolid mass transfer though they presented it graphically.Kinoshita and Leach [39] studied the mass transfer coefficientfor a single phase flow using the limiting current measurement forthe cathodic reduction of bromine. They used carbon felt electrode(fibre diameter about 25 micrometers) for their packing. TheReynolds number for the electrolyte ranged from 0.01 to 0.4. Theircorrelation related the Reynolds number of the liquid to theSherwoods number. They used two electrodes of thickness 0.25 cm and0.175 cm. The values of their mass transfer capacity for theelectrode of thickness 0.25 cm ranged from 0.011 to 0.157 s-1 andfor electrode of thickness 0.175 cm the Ka value ranged from 0.018to 0.170 s-1. The specific surface area for the electrode thicknessof 0.175 and 0.25 cm were 110 and 88 cm-1 respectively.No previous work has been reported on mass transfer for two-phase upward or downward flow in graphite fibre beds.2:4 Porous electrodesPorous electrodes or three dimensional electrodes have beenconsidered and studied because they yield high mass transferperformance. They help carry reactions to a high degree ofcompletion. This is significant for slow electrochemical reactions.18Chapter 2. Literature ReviewPorous electrodes are preferred when dealing with reactive gaseswhich have low solubility. These reactive gases may be dissolvedand forced through these electrodes and kept at the surface.Compared to classical plate electrodes they provide a largerinterfacial area per unit volume and higher space-time yield [40].Unfortunately, excessive ohmic voltage losses occur within theporous electrode. The potential difference of the electrode andelectrolyte varies through the electrode. This leads to non-uniformreaction rate distribution [40] thereby restricting the use of thewhole internal surface area of the electrode. To be able to usethe whole internal surface area of the electrode there is the needto minimize the ohmic influences. This can be achieved bymaximizing the equivalent conductivity of the electrode.The ohmic potential drop can be reduced by compressing theelectrode to reduce the distance through which the current mustflow and also increasing the electrode conductivity (i.e.increasing electronic conductivity of electrode).The models used for the three-dimensional electrodes account forthe esential features of the electrodes and not the very finegeometric details of the pores. Usually, the parameters used in themodel are those which can easily be obtained experimentally withoutmuch difficulty for example, flowrates, porosity, pressure drop,liquid holdup, etc.Knowledge of how the electrode processes occur and why theyoccur so non-uniformly through the depth of the electrode will be1 9Chapter 2. Literature Reviewa big step in designing porous electrodes with high performance.The general requirement of three dimension electrodes are higheffective conductivity, high porosity, high internal surface areaand adequate.mechanical strength.2:6 Electrochemical reaction method for determination ofmass transfer ratesThe electrochemical measurement of the reduction of ferricyanideions on a cathodic packed bed is commonly used to study the masstransfer characteristics of porous electrodes. The mass transfercoefficient is calculated from the limiting diffusion current.Cathodic reduction of bromine and oxygen have also been employed.Delaunay et. al. [6] found that the electrochemical technique,which is frequently used for a single phase flow is stillapplicable for two-phase flow with a large range of gas and liquidloads.2 0Chapter 2. Literature ReviewTable 1: Some experimental data cited in the literature forpressure drop, liquid holdup and mass transfer in packed beds[VARIABLES DEFINED IN NOMENCLATURE 21!Pressure drop correlationInvestigators:l. Turpin and HuntingtonSystem: Air-water^Column size 51 ,^102 and 153Particle size^7.6 to 8.2 mmmmGas load 0.02 to 38.3 kg /m2s^Liquid load 6.52 to 54.33 kg/m2sCorrelation:ln fLG = 8.0 - 1.12(ln z1)^- 0.0769^(lnz1)2+ 0.0152^(lnz1)3 0.3 5 z 5 500where^z1^=^(dpGg/p.g) 1.167/ (dpGripto 0.767fLG^=^(AP/Az)LG de gc/(2UG 2 PG)de^= eb Vp^/[Sp(1-610)]Investigator:2.^SaadaSystem: Air-water^Column diameter^45 mmParticle size:^0.514,^0.914 and 2.064 mmCorrelation: Single-phase pore flow1/gpi,^(AP/Az)LG = 0.024^Re 2.39 ReL0.60^(dp/dc) -1.1Correlation: Two-phase pore flow1/gpL^(AP/Az)LG = 0.027 ReGo.51 ReL0.35^(dp/dc) -1.1521Chapter 2. Literature ReviewReG *^= 0.44^ReL^2^(dio^hic^)^0.38Investigator:3.^Sato et.^al.System: Air-waterColumn:^65.8 and 122 mm internal diameterPacking: 6 different glass sheres of diameters ranging from2.59 - 24.3 mm.APLG^= APL^[1.3 + 1.85^(APG /APL).85]2Liquid holdupInvestigators: Lamine et. al.System : nitrogen-waterGas load:0 - 0.3 kg/m2s^Liquid load 1 - 11 kg/m2sParticle size:^1,^2,^3 4 and 5.9 mmCorrelation:^hi, =1^-^(1.3^+ 0.3 L 0.13 G -.563^)-1Investigators: 2 Achwal and StepanekSystem : air-waterGas load 0 - 0.65 kg/m2s^Liquid load 4 - 48 kg/m2sPorosity 0.4^Column diameter 50 mm^Packing diameter 6 mm..Correlation:^hi, = 1^-^(1 + 0.59 L013G-0563)-1Gas-Liquid mass transfer22Chapter 2. Literature ReviewInvestigators:1.^Specchia et. al.System for mass transfer measurement:-Desorption of oxygen with air from a 2N solution of causticsoda previous saturated with oxygenSystem for interfacial area:-Chemical absorption of CO2 in NaOH solutionsuperficial gas velocity 0.14 to 2.21 m/ssuperficial liquid velocity 0.0025 to 0.043 m sdiameter of packed column 80 mmPackings: glass spheres, berl saddles, and ceramic ringsPacking sizes: glass spheres 6mm^benl saddles^6mmceremic rings 6mm103 kLE/UL = 7.96[(- AP/Az)LG gc e/ (as pLuL ) } 0.275 _ 9.41al, /as^= 0.29^[(-AP/Az)LG cias^j1.17 + 0.61Investigators:2. Takahashi K.M. and Alkire R.C.System: Desorption of oxygen from an air-saturated 0.70 MNa2SO4 solution into nitrogen bubblesGas velocity^0.02 to 0.16 m/sLiquid velocity^0.0051 to 0.056 m/s_Packing: glassy carbon particles 1.2 mmCorrelation:^in^(kLaL )^= 73.5 UG + 32.4 UL - 3.49Liquid to solid mass transfer capacity23Investigators:l.Goto et. al.System: Air- water^Column diameter: 25.8 mmGas load 0-0.009 kg/m2s^Liquid load: 0.118 - 5.2 kg/m2sPorosity 0.44^Particle size 0.54, 1.08 and 2.41 mmCorrelation: j D = 1.31 ReL -0.436Chapter 2. Literature Review2 4CHAPTER 33 Experimental Apparatus and ProceduresThe experimental apparatus and procedure chosen to measure thepressure drop, liquid holdup and the overall mass transfer capacityfor the graphite fibre trickle-bed electrode were simple andreliable. These procedures have been used by other authors for thestudies of the parameters mentioned above in particulate beds.Other methods available for measuring the pressure drop, liquidholdup and overall mass transfer capacity are mentioned in thischapter.3:1 Pressure drop measurementStatic pressure gradients can be measured by means of- U-tube mercury manometer- differential'pressure gauge.The U-tube mercury manometer was used for the determination of thepressure gradients in this study.ApparatusCell:- A graphite fibre bed (UCAR 1/4" WDF Graphite Felt, UnionCarbide Corp.) of dimension 356 mm long by 38 mm wide by 6.4 mm25(before compression) thick with graphite fibres of about 22micrometer diameter packed to about 90% porosity after compressionwas used. This graphite felt was placed inside a neoprene gasket ofdimensions 460 mm long x 64 mm wide x 3.2 mm thick to hold it inplace. Details of the cell are shown in Figure 1. The gasket whichcontained the graphite felt was placed between two clear plexiglasssheets of size 505 mm long x 127 mm wide x 25 mmm thick, bolted andcompressed with a torque of 120 lb in. Sixteen stainless steelbolts (1/4") were used in all. Both the gasket and graphite bedwere compressed to a thickness of 3 mm. To obtain a uniform bedthickness and prevent bulging of the plexiglass, stainless steelmetal spacers of thickness 3 mm were placed on each side and thetop and bottom of the gasket before compression.The apparatus for measuring the pressure drop consisted of afeed tank, pump, rotameter, cell, U-tube mercury manometer, gascylinders, associated piping, etc. The experimental setup is shownin Figure 2.ProcedureThe liquid used was de-ionized water and the gas was pure oxygen.The flow of the water and the gas were obtained respectively by apositive displacement pump and an oxygen cylinder under pressure.The gas flow rate was adjusted with the valve above the rotameterand the liquid flow with the pump. The oxygen and water were mixedat a simple 'tee' before entering the cell. The arms of the U-tube26Chapter 3. Experimental Apparatus and Proceduresmercury manometer were connected to the manometer taps on the sideof the cell opposite to the side where the water and oxygen mixtureenters the cell. Since the maximum pressure drop was 40 % of theinlet pressure a linear pressure gradient was assumed indetermining the static pressure gradient for the different sets ofgas-liquid flowrates chosen. For each of the different liquid andgas flow rates the static pressure drop within the cell wasdetected by the change in the mercury levels in the U-tubemanometer. The difference in the level of mercury in the manometerwas equal to the pressure drop inside the cell for that flowcondition. Two readings were taken for each flow condition. Theaverage value of the two readings was taken as the pressure dropfor that condition. The gas loads ranged from 0 to 0.43 kg/m2s andthe liquid from 1.46 - 7.30 kg/m2s. This corresponds to gas andliquid flows of 0 - 739 ml/min at S.T.P and 10 - 50 ml/minrespectively. The temperature ranged from 20°C to 25°C. The outletpressure was one atmosphere absolute.27manometertapmanometertapgraphite-fibrebedNeoprenegasket\\\ \\\\plexiglassplate^outletstainlesssteelspacerinletbolt(1/4")Chapter 3. Experimental Apparatus and ProceduresFigure 1 Detailed sketch of the cellChapter 3. Experimental Apparatus and Procedures_Figure 2 Apparatus used for the pressure drop measurement29Chapter 3. Experimental Apparatus and Procedures3:2 Total liquid holdup measurementThe measurement of liquid holdup may be carried out by differentmethods:-(1) Weighing method(2) Tracer response method(3) Quick closing valve methodThere is always the possibility of obtaining different resultsdepending upon the method adopted for measurement. The methodadopted here for the measurement of the overall liquid holdup wasthe quick closing valve method.ApparatusThe equipment setup for this experiment is shown in Figure 3. Itconsisted of feedtanks, pump, rotameters, cell and oxygen cylinder.The cell used for this study was exactly the same as that used forthe pressure drop study as shown in Figure 1.ProcedureThe gas and liquid used for this experiment were pure oxygen and amolar solution of sodium hydroxide in water (the density of waterat 20°C is 998.2 kg/m3 and its viscosity is 1.04 kg/ms, the density30Chapter 3. Experimental Apparatus and Proceduresand viscosity of 1M NaOH hydroxide are 1042.8 kg/m3 and 1.11 kg/msrespectively, the surface tension of water is 73 dynes /cm and thatof a molar solution of sodium hydroxide is 76 dynes thus thedifference between the the surface tensions of these two liquid issmall such the switching from water to aqueous sodium hydroxidewill not likely affect the the fluid dynamics) respectively. Theaqueous solution of sodium hydroxide was pumped upward through thecell along with the oxygen gas. The oxygen and sodium hydroxidesolution were mixed at a 'tee' before entering the cell. The gas-liquid mixture was made to flow through the cell for about tenminutes to obtain a steady flow. After, which the inlet and outlet3-way valves were closed simultaneously. Water was used to wash outall the sodium hydroxide captured in the cell column. Tenmillilitres of the bulk washwater was taken and titrated with onemolar solution of hydrochloric acid to determine the concentrationof the washwater and thus the volume of sodium hydroxide solutiontrapped in the bed, channels, and inlet and outlet valves. Toaccount for the liquid trapped both in the inlet and outlet valvesand channels, the graphite felt was removed and the space itoccupied was covered with solid neoprene which was 356 mm long x 33mm wide x 3.0 mm thick after compression. This allowed a width of5 mm for the fluid to flow through when the procedure above wasrepeated. The volume occupied by the inlet and outlet valves andchannels was used to determine the volume of liquid that was heldby the graphite electrode bed alone. Different sets of gas-liquid31Chapter 3. Experimental Apparatus and Proceduresflows were metered through the cell and their liquid holdupsdetermined. For each flow condition two readings were taken. Thegas and liquid loads ranged from 0 to 0.35 kg/m2s and 1.53 to 7.62kg/m2s corresponding to 0 to 605 ml/min S.T.P. and 10 to 50 ml/minrespectively. The temperature ranged from 20°C to 25°C. The outletpressure was one atmosphere absolute.Figure 3 Apparatus used for the total liquid holdup measurement32Chapter 3. Experimental Apparatus and Procedures3:3 Measurement of mass transfer capacityElectrochemical reaction methodThe electrochemical reaction method was used for the overall masstransfer studies. The thickness of the electrode bed chosen for thestudy was 3 mm. It was assumed that the electrochemical reactionthrough the electrode volume was solely controlled by mass transferand the total volume of the bed was electroactive (calculation wascarried to support this -Appendix C (7)).ApparatusElectrolytic cellThe electrolytic cell consisted of a cathode bed of graphite fibrefelt (UCAR 1/4" WDF). Two layers of stainless steel mesh screens(8-mesh) were used for the anode. The thickness of the anolytechamber was about 3 mm. A cation selective membrane (Nafion 214)separated the anode from the cathode. The dimension of the cationmembrane was 454 mm long by 68 mm wide. The dimension of each ofthe stainless steel mesh screens was 89 mm long by 38 mm wide by1.5 mm thick. The graphite cathode bed dimension was 89 mm long by38 mm wide by 3 mm thick with graphite fibres about 22 mictometerdiameter packed to about 90% porosity.The experimental setup for measuring the overall mass transferrate is shown in Figure 6. It consisted of feedtanks, pumps33Chapter 3. Experimental Apparatus and Proceduresrotameters, pressure gauges, thermocouples, direct current powersupply source, ammeter, electrochemical cell, heat exchanger andgas-liquid separator.ProcedureA one molar solution of sodium hydroxide containing 0.02% DTPA andthe pure oxygen gas were metered into the cathode compartment ofthe electrolyte cell with the aid of the rotameter and pump. Thesodium hydroxide and the oxygen gas were mixed together at a 'tee'before entering the reactor as shown in Figure 6. The inlet andoutlet pressure and temperature were measured by pressure gaugesand thermometers respectively.A molar solution of aqueous sodium hydroxide was recycledthrough the anode compartment. The temperature of the catholyteproduct was kept in the range of 17 to 24 °C by the introduction ofa cooler in the anolyte loop.Various currents were applied to the top of the 3 mm thickstainless steel feeder electrodes. The ammeter measured the currentwithin the closed system. The alkaline hydrogen peroxide producedin the cathode compartment were sampled and the concentration ofthe sample determined using the potassium permaganate titrationmethod [41]. Two samples were taken and analysed for each conditionof gas and liquid flowrate chosen.Graphs of concentration of alkaline hydrogen peroxide versus34Chapter 3. Experimental Apparatus and Proceduresapplied current were plotted to determine the maximumconcentration. The current at the maximum peroxide concentrationwas assumed to correspond to the maximum rate of oxygen reduction.This current (called the applied current in Appendix 0-6 ) was usedto determine the limiting current and thus the mass transfercapacity. Figure 7 shows a typical plot of concentration ofalkaline hydrogen peroxide versus current.The concentration of the hydrogen generated for a typical gasand liquid load was determined using gas chromatography (AppendixC) .Calculation of the mass transfer capacity from the experimentaldata is detailed in Appendix C - sample calculations 4,5,6 and 7.35plexiglass platestainless steelmesh screens graphite fibre bedNafion cation membrane Neoprene gasketstainless steel plate(316ss)Chapter 3. Experimental Apparatus and ProceduresFigure 4 Detailed sketch of the graphite fibre trickle-bed reactor36Chapter 3. Experimental Apparatus and ProceduresFigure 5 Detailed sketch of the graphite fibre trickle-bed electrode37Figure 6 Apparatus used for the overall mass transfer capacity measurement2c0If r3-C'a)0C8 0.04 —a)73'5•<"2a)a_Chapter 3. Experimental Apparatus and Procedures10^15^20^25Current (A)Fig 7: Peroxide concentration vs current39CHAPTER 44:1 Results and DiscussionThe aim of this project was to determine the pressure drop, liquidholdup and the overall mass transfer capacity of a graphite fibretrickle-bed electrode with co-current upward flow. Also, to developsatisfactory empirical correlations based on the experimentalresults obtained for the above-mentioned parameters.This chapter reports the experimental results obtained,discusses results and their significance, and how well theempirical correlations fit the experimental results.4:1 Pressure dropThe results of the pressure drop measurement for different sets ofgas-liquid loads for the graphite fibre trickle-bed electrode aresummarised in Table 3 (Appendix B). The variation of the staticpressure gradients with the gas loads at constant liquid load ispresented in Figure 8. Figure 9 shows the variation of pressuregradient with liquid load at constant gas load.The general trend shows that the static pressure gradientsincrease with both the gas and liquid loads as shown in Figures 8and 9. There happens to be a point of inflection at gas loads of0.3 kg/m2s for the various liquid loads. Increasing the liquid load40Chapter 4. Results and Discussionscaused a big change in the pressure gradient for the same gas load.The pressure gradient obtained for both gas and liquid loadswere lower than that given by Oloman [3] and Delaunay et. al. [6].Oloman used downward flow in a fixed bed of graphite particles 0.1to 1 mm. Delaunay et. al. used an upward flow. They used packingsof diameter 4 mm. The graphite fibre bed used for the present studyhad a porosity of about 0.90 which is greater than that of theparticulate electrodes used by the authors mentioned above. Theporosity of the electrodes they used was 0.4. From the Ergunequation the pressure gradient decreases with the increase in theporosity. The results obtained confirmed this fact. The lowerpressure gradients obtained was mainly influenced by the highporosity of the graphite fibre. It is possible that even lowerpressure gradients could have been obtained if the flow system hadbeen downward since in general downflow yields lower pressuregradients than upward flow [15]. Increasing the pumping power leadsto an increase cost. Thus, by selecting a graphite fibre trickle-bed electrode instead of particulate electrode some savings can bemade on the pumping cost for equivalent mass transfer capacity.In developing an equation to fit the experimental resultsobtained it was assumed that the pressure gradient was a funtion ofthe liquid load and the gas load. Only the gas and liquid loadparameters were used for the correlation. A number of differentcorrelations were tried and the one that gave the highest rankcorrelation was chosen. This developed empirical correlation is of41Chapter 4. Results and Discussionsthe same form as that of Sato's [22] two phase pressure gradientcorrelation .The pressure gradient was correlated as a function ofliquid and gas load instead of as a function of the single phasepressure drop. The developed correlation from this study is shownbelow.AP = L[0.36 + 1.182 (G/L) 0.618]2^Eqn (1)where^AP - pressure gradient in bar/mG - superficial gas load in kg/m2sL - superficial liquid load in kg/m2sThe standard deviation is 0.10 bar/m and the rank correlationcoefficient for the above non-linear regression is 99.4 %. Thisshows a good fit between the predicted results and the experimentalresults. The relationship between the experimental results and thecorrelated results are graphically shown in Figure 10.The empirical correlation by Turpin and Huntington [23] wasfound to be unsuitable for the present experimental resultsobtained. Theft' correlation was suitable for values of1.167/Re10.767^ g1.167/Relo.767between 0.3 and 500. The Re^valuesobtained for this study were far below the required range (i.e.below 0.3). Their gas and liquid loads ranged from 0.02 kg/m2s to38.3kg/m2s and 6.52 to 54.33 kg/m2s respectively . For the presentstudy the gas and liquid loads ranged from 0 to 0.43 kg/m2s and1.46 to 7.30 kg/m2s respectively. The diameters of the aluminaparticles used by Turpin and Huntington [23] were far larger than42Chapter 4. Results and Discussionsthe diameter of the graphite fibres. The graphite fibre has adiameter of 22 micrometer while that of the alumina particlesstudied by Turpin and Huntington [23] were 7.6 and 8.2 mm.The correlation by Sato [22] which is generally recommended forsmall packings was also found to give a very poor fit of theexperimetal results obtained here.43Chapter 4. Results and Discussions2.0 -1.8 -1.6 -0.6 -0.4 -Liquid 1.46 kg/m2sLiquid 2.92 kg/m2sLiquid 4.38 kg/m2sLiquid 5.84 kg/m2sLiquid 7.30 kg/m2s0.2 -I^I^I^I^.^I0.0 OA 0.2 03 OAGas load (kg/m2s)Figure 8: Pressure gradient versus gas load05442.2  2.0 —1.8 —1.6 —1.4 —1.2 —1.0 —0.8 —0.6 —Chapter 4. Results and Discussions0.4 —0.2 —• Gas load 0.0 kg/m2s• Gas load 0.02 kg/m2sA Gas load 0.04 kg/m2s• Gas load 0.08 kg/m2s• Gas load 0.13 kg/m2s• Gas load 0.22 kg/m2s• Gas load 0.28 kg/m2s)4;^Gas load 0.35 kg/m2s- Gas load 0.43 kg/m2sI^'^I2^3 4I^'5^6^7^8Liquid load (kg/m2s)Figure 9: Pressure gradient versus liquid load45Chapter 4. Results and Discussionsi^ 1^,^I0 0^0.5^1.0^1.5 2.0^25Pressure gradient correlated (bar/m)Figure 10: Experimental versus correlated pressure gradient46Chapter 4. Results and Discussions4:2 Liquid holdupThe total liquid holdup for this study was defined as the totalvolume of liquid trapped divided by the void volume of the bed.The results of the experiments are summarised in Table 4 (AppendixB). Figure 11 shows the liquid holdup versus gas load at constantliquid load. The relationship between the liquid holdup versus theliquid load at constant gas load is shown in Figure 12. The liquidholdup decreases with increase in gas load but increases withincrease in liquid load. At constant liquid load the liquid holdupdecreases sharply at low gas loads (less than 0.1 kg/m 2/s) thengradually at high gas loads (greater than 0.1 kg/m2 /s). This can beseen in Figures 11 and 12.The highest total liquid holdup obtained for all the differentliquid loads chosen was 1.0. At the total liquid holdup of 1.0 thegas load was zero.From the Bruggeman equation the presence of gas bubbles decreasethe effective conductivity of the electrolyte which adverselyaffects the performance of an electrochemical cell. Thus,electrodes which are able to retain a lot of the solution leavingno or little space available for the gas will generally yieldhigher cell performance because of higher effective electrolyteconductivity. Also the equation by Neale and Nader [42] shows arelationship between the liquid holdup and the effective47Chapter 4. Results and Discussionselectrolyte conductivity. From their equation it can be impliedthat the higher the liquid holdup that can be achieved the higherthe effective electrolyte conductivity. Figure 13 shows a plot ofeffective electrolyte conductivity of 1 M aqueous sodium hydroxidewith temperature ranging from 20 to 25°C versus liquid holdup usingthe results obtained for the liquid holdup in present study and theequation by Neale and Nader to obtain the effective electrolyteconductivity.For gas loads ranging from 0 to 0.35 kg/m2s and liquid load from1.53 to 7.62 kg/m2s the liquid holdup obtained for present studyranged from 0.44 to 1.0 The empirical relationship between theliquid holdup and the superficial gas and liquid loads obtained inthis study is shown belowhi, =1_ 0.907 L-0.362 G0.301where^hL = liquid holdupL = superficial liquid load kg/m2sG = superficial gas load^kg/m2sEqn (2)The liquid holdup was taken to be a function of only the gas andliquid loads as done by Lamine et. al. [15] and Achwal and Stepanek[29]. Many different forms were tried and the one that gave thehighest rank correlation was chosen. For this chosen correlationthe standard deviation is 0.02 and the correlation coefficient forthe above non-linear regression is 100 %. This shows a good fitbetween the correlated results and the experimental results. The48Chapter 4. Results and Discussionsrelation between the experimental results and the correlatedresults have been graphically shown in Figure 14.The correlations by Lamine et. al [15] and Achwal and Stepanek[29] fit equation (2) quite well as shown in Figure 15. Thecorrelation by Lamine et. al. deviates by a maximun of ± 17 % whilethat of Achwal et. al. by ± 9 %. The empirical correlationobtained from present study deviates by ± 3 % from theexperimental results obtained. The standard deviations of thevalues obtained from Lamine et. al. and Achwal and Stepanek fromthe experimental results are 0.11 and 0.06 respectively.49Chapter 4. Results and DiscussionsFigure 11: Liquid holdup versus gas load501 2 4 5 6 7 8Gas load 0.0 kg/m2sGas load 0.40 kg/m2sGas load 0.08 kg/m2sGas load 0.20 kg/m2sGas load 0.35 kg/m2s2.0 —1.5 —0.5 —-Chapter 4. Results and DiscussionsLiquid load kg/m2sFig 12: Liquid holdup versus liquid load5114 -6 -I^I^I^I^•^I^•^I^i^I0.4^0.5^0.6^0.7^0.8^0.9^1.0Chapter 4. Results and DiscussionsLiquid holdup ■Figure 13: Effective electrolyte conductivity of 1M aqueoussodium hydroxide (20-25 °C )vs liquid holdup52Chapter 4. Results and Discussions0 4^0.5^0.6^0.7^0.8^0.9^10Correlated liquid holdupFig 14: Experimental versus correlated liquid -holdup0 4^0.5^0.6^0.7^0.8 0.9 10• Experimental results (this work)Chapter 4. Results and DiscussionsCorrelated liquid holdup.■Fig 15: Experimental vs correlated liquid holdup by different authors54Chapter 4. Results and Discussions4:3 Overall mass transfer capacityThe results showing the variation of the applied current and theconcentration of alkaline hydrogen peroxide have been summarisedin Tables 7 to 18 (Appendix B). Figure 16 shows the relationshipbetween the overall mass transfer capacity (Ka) versus the gas loadof the gas at constant liquid load. The Ka value increases bothwith the increase in gas and liquid loads.The overall mass transfer capacity (Ka) obtained was high. Thismay be due to the following reasons:-The graphite fibre increases the turbulence of the fluid. It hasa high surface area per unit volume and because of this it allowsfor high-space time yield. The high porous nature of thegraphite fibre trickle-bed allows for free flow of the solution.The reactive gas increases the mass transfer rates by increasingthe velocity of the liquid. When the electrolyte surface is wellwetted by the electrolyte the gases that reach the surface of theelectrode do not block the surface like inert gases but ratherreadily react. Thus, there is always a strong drive for the gasesto move to the electrode surface for reaction hence the high masstransfer.The gas and liquid loads were used correlate the overall masstransfer capacity. Different forms were tried and the one that gavethe highest rank correlation was chosen. Below is the empirical55Chapter 4. Results and Discussionscorrelation obtained from the experimental results.0.371^0.233Ka = 5 . 9 L^ Ekpa (3)^where Ka = mass transfer capacity^s -1L = Liquid load^ kg/m2sG = gas load kg/m2sThe standard deviation is 0.60 s-1 and the standard correlationcoefficient for the above non-linear regression is 99.5 % . Thisshows a good fit between the experimental results and thecorrelated results. The relationship between the experimentalresults and the correlated results has been graphically shown inFigure 17.The experimental technique used to determine the overall masstransfer capacity in this study was also used by Takahashi andAlkire. They used larger spherical packing diameters of about 1.2mm compared to 22 micrometer which was used for this study. Alsothe porosity of their packing was lower (0.4) than what was used inthis study (0.90). The Reynolds number for the gas and liquid theychose were mu&h higher than what was used in this study. TheReynOlds number of gas they used ranged from about 15 to 210 andthat of the liquid from 11.7 to 59.3. For the gas and liquid loadsthat they chose the Ka values they obtained ranged from 0.009 to0.032 s-1. The Ka values obtained in this study ranged from 3.4 to9 s-1.Comparatively the graphite fibre trickle-bed electrode is better56Chapter 4. Results and Discussionsthan the 1.2 mm glassy carbon particles since it yields lowerpressure gradients and higher mass transfer capacities. Thisqualities are necessary for high performance of an electrochemicalcell.The mass transfer capacity obtained by Kinoshita and Leach for asingle-phase flow ranged from 0.011 to 0.157 and 0.018 and 0.157 s-1 for electrode thickness of 0.175 and 0.25 cm respectively. Theyused carbon felt of fibre diameter 25 micrometer. Their Reynoldsnumber of the liquid ranged from 0.01 to 0.4. The range of masstransfer capacity obtained when the Reynolds number of the liquidfor the present study is fitted into their equation is 0.329 to0.593 s-1. The value of two phase mass transfer capacity obtainedin the present study is about ten times that of the single phase.The difference is due to reactive gas which enhances the masstransfer.57Chapter 4. Results and Discussions9—8—4-.Liquid load 3.05 kg/m2sLiquid load 4.57 kg/m2sLiquid load 7.62 kg/m2s3 i^1^.^10.00^0.05^0.10 0.15^0.20^0.25^0.30^0.35^0.40Gas load (kg/m2s)Fig 16: Mass transfer capacity versus gas load1^'^1^'^1^'^1^'^18 9I^.I.I.Iiiii4 5^6^71 09-M4 -33 10Chapter 4. Results and DiscussionsCorrelated mass transfer capacity (s-1)Fig 17 Experimental vs correlated mass transfer capacity59CHAPTER 55: Conclusion and Recommendations5:1 ConclusionThe pressure drop, liquid holdup and overall mass transfer capacityof a graphite fibre trickle-bed electrode have been determinedexperimentally. These experimental data have been correlatedempirically.For the gas load ranging from 0 to 0.43 kg/m2s and liquid loadranging from 1.46 to 7.30 kg/m2s the pressure gradient ranged from0.24 to 2.09 bar/m. The empirical correlation for the pressure dropfor the graphite fibre of porosity 0.90 and fibre diameter 22micrometer wasAP=L[0.36 + 1.182 (G/L) 0.618,2j (standard deviation=0.10 bar/m)This low range of pressure gradient obtained is due mainly to thehigh porosity (0.90) of the graphite fibre trickle bed electrode.Lower pressure gradient is advantageous to cell performance sincethe cost for pumping power will be less, compared to higherpressure gradients. The empirical correlation developed could beused to estimate the pressure gradient for graphite fibre trickle-bed electrode at porosity of 0.90 and fibre diameter of 22micrometer operating at 20-25°C near atmospheric pressure with gasand liquid loads within the ranges of this study.60Chapter 5. Conclusions and RecommendationsThe total liquid holdup determined for the gas and liquid loadof 0 to 0.35 kg /m2s and 1.53 to 7.62 kg/m2s respectively rangedfrom 0.44 to 1.00 Such a high liquid retaining ability allows forhigh reaction rates and effective electrolyte conductivity, thushigh cell performance. The developed empirical correlation for thegraphite fibre electrode of porosity 0.90 and fibre diameter of 22micrometer is shown belowhL = 1 - 0.9071.- 0.362e.301 (standard deviation= 0.03)This correlation could be used to estimate the total liquid holdupfor graphite fibre trickle-bed electrode operating at 20 - 25°Cnear atmospheric pressure with the same value of porosity and fibrediameter for the flow ranges of the study.For the gas load ranging from 0.04 to 0.36 and liquid loadranging from 3.05 to 7.62 the overall mass transfer capacity rangedfrom 3.4 to 9.0 s-1. This range of mass transfer capacity isremarkably high, suggesting the graphite fibre trickle-bedelectrode to be a more suitable porous electrode than graphiteparticles. The mass transfer rates are strongly influenced by thegas load at low liquid load. The developed empirical correlationobtained in this study for the overall mass transfer capacity shownbelowKa = 5.9 L 0.371e.232 ( standard deviation - 0.60 s-1)could be used for fibre beds of porosity of 0.90 and fibrediameter 22 micrometer operating at 17 - 26°C near atmospheric61Chapter 5. Conclusions and Recommendationspressure instead of those reported in the Chemical EngineeringLiterature which do not apply to these fibre beds.This study has been able to provide more knowledge about thefluid dynamics of the graphite fibre trickle-bed electrode and alsoits mass transfer properties. The empirical correlations developedwill assist in designing and evaluating the performance of suchelectrodes.5.2 RecommendationsThis knowledge now made available can be applied in theelectrosynthesis of alkaline hydrogen peroxide. One way ofobtaining alkaline hydrogen peroxide is by the cathodic reductionof oxygen using graphite fibre trickle-bed electrodes.Further studies need to be carried out to determine theindividual mass transfer coefficients as well as the interfacialareas for the gas-liquid and liquid-solid sides for a graphitefibre trickle-bed electrode. The effects of pressure on pressuredrop, liquid holdup and mass transfer capacity could also beinvestigated.Graphite fibre trickle-bed electrodes with different porositiescould be studied over a wider range of gas and liquid loads todetermine the optimum porosity that gives the best electrodeperformance.62Chapter 5. Conclusions and RecommendationsThe mechanical strength of these graphite fibre trickle-bedelectrodes needs to be considered more critically and determinedsince there may be some problems encountered when constructing aseries of these cells for industrial use.In order to make maximum use of the graphite fibre trickle-bedelectrode the thickness of fibre bed must be selected such that thewhole bed is electrochemically active. As a first estimate thedeveloped empirical correlations from this study could be used todetermine the thickness required.The measurement of pressure drop, liquid holdup and overall masstransfer capacity could be carried out for a two phase downflow todetermine how different it is from upward flow. This will help inevaluating the two different configurations so that the better ofthe two system could be selected.63Nomenclature 1A cross sectional area of fibre bed (width x thickness)a^specific surface area of fibre bed^ m2/m3CE1 current efficiency of hydrogen gas generatedCE2 current efficiency of peroxide producedCo^bulk concentration of reactive species, (oxygen)^moles/m3• fibre diameter• Faradays number, 96480^coulombs/mole of electron• superficial gas load kg/m2s• concentration of hydrogen peroxide^ moles/m3Hf^final concentration of peroxide moles/m3Hi^initial concentration of peroxide^ moles/m3hL liquid holdup• theoretical current^ AIi^current used in producing peroxide^ A12^current used in destroying peroxide A13 current used in producing hydrogen gas^ Alimiting current density^ A/m2interfacial electrochemical reaction current density^A/m2• overall mass transfer coefficient^ m/sKa^overall mass transfer capacity s-1• superficial liquid load^ kg/m2s• mass of graphite fibre felt kg• number of moles of electrons per mole peroxideAP pressure gradient^ bar/m64Qg^gas flow rate at 1 atm and 21°C^ 3/sQl^liquid flow rate^ 3/sconcentration of electrolyte (1M NaOH)^moles/m3• thickness of graphite fibre bed• final thickness of graphite fibre felt(after compression)to^initial thickness of graphite fibre felt(before compression)^ bulk volume of graphite fibre felt^ m3X^distance across the fibre bed• total length of the fibre bedZ+^charge on positive ion• working porosity of graphite fibre felt(after compression)initial porosity of graphite fibre felt0(before compression)effective conductivity of electrolyte (1M NaOH) mho/m0^conductivity of electrolyte^ mho/mA^equivalent conductance mole cm2/equivN4 number of positive ions in molecule^ kinematic viscosity of oxygen^ m2/sV1^kinematic viscosity of 1M NaOH m2/sdensity of graphite electrode^ kg/m3PL density of liquid^ kg/m3PG^density of gas kg/m365a^effective conductivity of graphite electrode^mho/ma^conductivity of graphite electrode^ mho/m00^electrode potential difference VoltOm electric potential in matrix^ VoltOs^electric potential in solution Volt00^electrode potential when x=0^ Volt66Nomenclature 2 (Specifically for the correlations in Table 1)aL^gas-liquid interfacial area^ m2/m3as^specific packing surface area m2/m3D diffusivity^ m2/sdc^column diameter mde^equivalent packing diameter^ md diameter of packing particle mPfLG two-phase friction factorG superficial gas load^ kg/m2sg acceleration due to gravity^ m/s2g^gravitational constant^ m/s2chL^liquid holdupChilton-Colburn factor Sc 2/3 Ks /ULjDK overall mass transfer coefficient^ m/sKL^liquid-side mass transfer coefficient m/sKs^liquid-solid mass transfer coefficientL superficial liquid load^ kg/m2sRe^Reynolds number dpG/vSc^Schmidt number gL/QLDS surface area of packing^ m2PU superficial velocity m/sVP^volume of packing particle^ M3Z^axial distance^ mZl^ReL 1.167 /Re G0'767Eb^bed porosity67V^kinematic viscosityPL^density of liquidPG^density of gasviscosity(AP/Az)LG two-phase pressure gradientAP^pressure gradientsubscriptG gas phaseL liquid phaseLG mixed phase flow condition68Bibliography[1] Takahashi K. M., "Mass Transfer Studies on Porous Electrodewith Gas-Liquid Flow," M. S. Thesis , University ofIllinois, Urbana, Illinois 1983[2] Piovono S., Bohn U., "Natural Convection Mass Transfer atFelt Electrodes," Latin American Applied Research 21, 151-156 (1991).[3] Oloman C., "Trickle-Bed Electrochemical Reactors," Journal ofthe Electrochemical Society., 126 , 1885 (1979)[4] Takahashi K. and Alkire R., "Mass Transfer in Gas-SpargedPorous Electrodes," Chemical Engineering Communicatons. 38209-227 (1985)[5] Shah Y.T., " Gas-Liquid-Solid Reactor Design  , "McGrawHill New York 1979[6] Delaunay G., Stock A., Laurent A. and Charpentier J. C."Electrochemical Study of Liquid-Solid Mass Transfer inPacked-Beds with Upward Co-current Gas-Liquid Flow,"Ind. Eng. Chem. Process Des. Dev. 19 514-515 (1980)[7] McIntyre and Phillips R.F. "Electrolyte Synthesis ofHydrogen Peroxide in a Trickle-Bed" U.S. Pat 4,406,758 (1983)[8] Oloman C. and Watkinson A.P. "Hydrogen Peroxide ProductionTrickle-bed Electrochemical Reactor," Journal of AppliedElectrochemistry ., 9, 117-123 (1979)[9] Lovrecek B., Batinic M. and Caja J., "The ElectrochemicalOxygen Rechjction on the Graphite Electrode," Electrochimica Acta 28 (5) 685-690 (1983)[10] Oloman C. Lee B., Leyten W. "Electrosynthesis of SodiumDithonite in a Trickle-Bed Reactor," Canadian Journal of Chemical Engineering. 68 1004 -1009 (1990)[11] Manji A. and Oloman C., "Electrosynthesis of Propylene in aBipolar Trickle-bed Reactor " Journal of AppliedElectrochemistry. 17 532 - 544 (1987)[12] Endaie S., Fleischman M. and Jansson R.E. W., "Applicationof the Trickle Tower to Problems of Pollution Control.-I TheScavenging of Metal Ions," Journal of AppliedElectrochemistry., 12, 59-69 (1982)69Bibliography[13] El-Ghaoui E A., Jansson R.E. W.and Moreland C., "Applicationof the Trickle Tower to Problems of Pollution Control -IIThe Direct and Indirect Oxidation of Cyanide."Journal of Applied Electrochemistry 12, 69 (1982)[14] El-Ghaoui E.A., and Jansson R.E.W., Moreland C.,"Applicationof the Trickle Tower to Problems of Pollution Control -IIIHeavy-metal Cyanide Solutions," Journal of Applied Electrochemistry 12 75 (1982)[15] Lamine A.S., Colli Berrano M. T. , Wild G. ," Hydrodynamicsand Heat Transfer in Packed Bed with Co-current Upflow"Chemical Engineering Science. 47 (13/14) 3493 1992[16] Ergun S., "Fluid Flow through Packed Columns," Chemical Engineering Progress 48, 89 (1952)[17] MacDonald I. F., El- Sayed M.S. , Mow K., Dullien F.A. L.,"Flow through Porous Media-The Ergun Equation Revisited,"Industrial and Engineering Chemistry Fundamentals., 18 199(1979).[18] Sweeney D.E.,"A Correlation for Pressure Drop in Two PhaseConcurrent Flow in Packed Beds," AIChE. J 13 663 (1967)[19] Specchia V. and Baldi G., "Pressure Drop and Liquid Holdupfor Two -Phase Concurrent Flow in Packed Beds, "  Chemical Engineering Science. 32 515 (1977)[20] Pittsburg Energy Research Centre Quarterly Reports 1975 -1976.[21] Tallmadge J. A., " Packed Bed Pressure Drop-An Extension toHigher Reynolds Numbers," AIChE J., 16 1092 , 1970[22] Sato Y., Hirose T., Takahashi F. and Toda M. "Pressure Lossand Liquid Holdup in Packed Bed Reactor with Cocurrent Gas-Liquid Downflow," Journal of Chemical Engineering (Japan), 6147 (1973a)[23]_ Turpin J. L. and Huntington R. L., "Prediction of PressureDrop for Two-Phase, Two Component Concurrent Flow in PackedBeds"  AIChE J., 13 1196 1967[24] Ford L. H., "Multiphase Flow through Porous Media, withSpecial Reference to the Turbulent Region" Ph.D. Thesis,University of London , 1960[25] Saada M. Y., "Fluid Mechanics of Co-current Two-Phase Flow70Bibliographyin Packed Beds: Pressure Drop and Liquid Holdup Studies"Periodica Polvtechnia-Chemical Engineering,  19, 317 1975[26] Voyer R. D., Miller A. I., "Improved Gas-Liquid Contactingin Concurrent Flow," Canadian Journal of Chemical Engineering., 46 335 (1968)[27] Hutton B. E. T., and Leung L.S., "Cocurrent Gas-Liquid Flowin Packed Columns," Chemical Engineering Science.  29, 1681(1974)[28] Stiegel G.J., Shah Y. T., "Axial Dispersion in a RectangularBubble Column." Canadian Journal of Chemical Engineering  553 (1977).[29] Achwal S.K.and Stepanek J.B. "Holdup profiles in packedbeds" Chemical Engineering Journal 12 69-75 (1976)[30] Mashelkar R.A., Sharma M.M., "Mass Transfer in Bubble andPacked Bubble Columns., Trans Instn. Chem.Eng.,  48 T 162,(1970)[31] Specchia V., Sicardi S., Gianetto A., "Absorption in PackedTowers with Co-current upward flow" AIChE. J. 20 646(1974)[32] Snider J. W., Perona J.J., "Mass Transfer in a Fixed-BedGas-Liquid Catalytic Reactor with Cocurrent Upflow" AIChE J. 20 1172 , (1974)[33] Goto S., Levec J., Smith J. M., " Mass transfer in packedBeds with Two-Phase Flow," Ind. Eng Chem. Pro Des. Dev., 14473 (1975)[34] Ohshima S. Takematsu T., Kuriki Y., Shimada K., Suzuki M.,Kato J., "Liquid Phase Mass Transfer Coefficients and GasHoldup in a Packed Bed Concurrent Upflow Column" Journal ofChemical Engineering (Japan), 9 29 , (1976)[35] Alexander B. F., Shah Y.T., "Gas-Liquid Mass TransferCoefficient for Cocurrent Upflow in Packed Beds-Effect ofPacking Shape at Low Flow Rates." Canadian Journal of Chemical Engineering., 54 556, (1976)[36] Reiss L. P., "Cocurrent Gas-Liquid Contacting in PackedColumns," I& EC Process Design Dev., 6 487, (1967)[37] Charpentier J. C., " Recent Progress in Two-Phase Gas-LiquidMass Transfer in Packed Beds" Chem Eng J. 11 161 (1976)71Bibliography[38] Mochizuku S. and Matsui T. "Solid-Liquid Mass Transfer Ratein Gas-Liquid Upward Cocurrent Flow in Packed Beds." ChemEng Sci., 29 1328, (1974)[39] Kinoshita K and Leach S.C., "Mass transfer study of carbonfelt ,flow through electrode " Journal of the Electrochemical Society 129 (16) 1993-1997 (1982).[40] Newman J.S.and Tobias W.T., J. "Theoretical Analysis ofCurrent Distribution in Porous Electrodes," J. ElectrochemSoc. 109 (12) (Dec. 1962).[41] Vogel A. I., Textbook of Ouantitative Inorganic Analysis 3r ed. Longman, London (1961)[42] Neale G.H. and Nader W.K., "Prediction of TransportProcesses within Porous Media: Diffusive-Flow Processeswithin a Homogeneous Swarm of Spherical Particles" AIChE J.,19, 112 (1973)[43] Perng Yuan-Shing, "Electrochemical Mediated Oxygen Bleachingof Pulp." Ph.D Thesis , U.B.C. (1992)[44] Perry's Chemical Engineers' Handbook Sixth Edition[45] Oloman C., Matte M. and Lum C., "Electronic Conductivity ofGraphite Fibre Fixed-Bed Electrodes" Journal of the Electrochemical Society 138 (8) 199172Appendix ACalibration Curve and Analytical MethodTable 2: Calibration of the gas rotameter, at R.T.PFloat ElevationStainless steelGas flow incm3/min R.T.P.10 3220 6840 14860 24880 376100 512120 652Analysis of Alkaline hydrogen peroxideThe reaction which occurs when potassium permaganate solution isadded to hydrogen peroxide solution and acidified with dilutesulphuric acid is2KMn04^3H2SO4^5H202^K2SO4^2MnSO4^8H20 ± 50273Appendix AProcedure- A two ml of the sample solution was collected.- 30 ml of distilled water was added.- Two ml of two molar sulphuric acid was then added to acidifythe solution. The solution was then shaken thoroughly.-The solution was then titrated with standard 0.1 N potassiumpermaganate to the first permanent, faint pink colour.74Appendix A0^20^40^60^80^100^120Stainless steel float elevationFig 18: Rotameter calibration for oxygen gas(at 20°C, 1Atm., absolute pressure)75Appendix BExperimental Results76Table 3: Results of pressure drop measurements in fibre bedBed dimensions : 356 mm x 38 mm x 3 mm thickLiquid: water^Gas: oxygen Configuration: Upward flowPorosity^: 0.90 Temperature 20-25 °C.Fibre diameter: 22 gm^Outlet pressure: 1 atm absoluteGas loadkg/m2sLiquidloadkg/m2s1.46liquidloadkg/m2s2.92Liquidloadkg/m2s4.38Liquidloadkg/m2s5.84Liquidloadkg/m2s7.30Pressure Gradient^(bar/m)'0.00 0.24 0.42 0.51 0.63 0.850.02 0.38 0.57 0.74 0.85 1.140.04 0.46 0.66., 0.81 1.01 1.290.08 0.64 0.82 0.89 1.20 1.480.13 0.76 0.93 1.03 1.33 1.610.22 0.88 1.06 1.14 1.48 1.840.28 1.04 1.27 1.33 1.63 1.940.35 1.16 1.38 1.52 1.80 2.090.43 1.23 1.48 1.71 1.9577Appendix B. Experimental ResultsTable 4: Results of the liquid holdup in fibre bedBed dimension: 356 mm long x 38 mm wide x 3 mm thickLiquid: 1 M NaOH^Gas: oxygen Configuration: Upward flowPorosity : 0.90 Temperature: 20-25°CFibre diameter 22 gm^Outlet pressure: 1 atm absoluteGas loadkg/m2sLiquid loadkg/m2s1.53Liquid loadkg/m2s3.05Liquid loadkg/m2s4.57Liquidloadkg/m2s7.62Liquid Holdup0.00 1.00 1.00 1.00 1.000.04 0.71 0.79 0.83 0.850.08 0.63 0.69 0.74 0.790.20 0.51 0.60 0.69 0.710.35 ,^0.44 0.57 0.65 0.6778Appendix B. Experimental ResultsTable 5:- Results of the overall mass transfer capacitymeasurements in fibre bed.Bed dimensions: 89 mm long x 3.8 mm wide x 0.3 mm thickPorosity: 0.90^Liquid: 1M NaOH^Gas: oxygenFibre diameter: 22 gm^Outlet pressure: 1 atm absoluteLiquidloadkg/m2sGasloadkg/m2sAppliedCurrentALim.CurrentAAverageTemp.°CSo1.02mol/m3MassTransf.(Ka)s-13.049 0.037 10 6.4 17.5 0.954 3.433.049 0.081 14 8.6 20.0 0.914 4.813.049 0.205 16 9.7 23.0 0.871 5.693.049 0.355 22 12.8 23.5 0.864 7.574.574 0.037 12 8.3 20.5 0.906 4.684.574 0.081 14 9.4 23.0 0.871 5.514.574 0.205 20 12.7 24.0 0.857 7.574.574 0.355 22 13.5 26.0 0.832 8.297.623 0.037 16 10.2 20.5 0.906 5.757.623 0.081 22 13.6 23.0 0.871 7.987.623 0.205 24 14.5 22.0 0.877 8.457.623 0.355 25 15.4 23.0 0.871 9.0379Appendix B. Experimental ResultsTable 6:- Results of the gas and liquid loads and mass transfercapacities.Bed dimension: 89 mm long x 38 mm wide x 3 mm thickLiquid: 1 M NaOH^Gas: oxygen Fibre diameter: 22 gmPorosity: 0.90 Outlet pressure 1 atm absoluteLiquid loadkg/m2sGas loadkg/m2sMass TransferCapacity^(Ka)^s-13.049 0.037 3.433.049 0.081 4.813.049 0.205 5.693.049 0.355 7.574.574 0.037 4.684.574 0.081 5.514.574 0.205 7.57..4.574 0.355 8.297.623 0.037 5.757.623 0.081 7.987.623 0.205 8.457.623 0.355 9.0380Appendix B. Experimental ResultsTable 7:- Results of peroxide produced at various currents,run 1Bed dimension: 89 mm long x 38 mm wide x 3 mm thickPorosity^: 0.90^Outlet pressure 1 atm abs.Liquid load : 3.049kg/m2s^Pressure drop 0.059 barsGas load : 0.037 kg/m2s^Fibre diameter 22 gmAverage Temp^(°C ) Current^(A) Concentration^(M)17.5 2 0.01918.5 4 0.02518.0 6 0.03018.0 8 0.03617.5 10 0.04319.0 12 0.04319.5 14 0.04820.5 .. 16 0.04981Appendix B. Experimental ResultsTable 8: Results of peroxide produced at various currents, run 2.Bed dimension:- 89 mm long x 38 mm wide x 3 mm thickPorosity : 0.90^ Pressure drop 0.073 barsGas load : 0.080 kg/m2s^Liquid load 3.049 kg/m2sFibre diameter 22 gm Outlet pressure 1 atm abs.Average Temp.^(°C) Current^(A) Concentration^(M)19.0 2 0.02018.5 4 0.02819.0 6 0.03318.5 8 0.03518.0 10 0.04318.5 12 0.04820.0 14 0.05020.5..16 0.05022.0 18 0.05322.0 20 0.05582Appendix B. Experimental ResultsTable 9: Results of peroxide produced at various currents, run 3Bed dimension: 89 mm long x 38 mm wide x 3 mm thickPorosity :^0.90^Outlet pressure 1 atm abs.Fibre diameter: 22 gm^Pressure drop: 0.094 barsGas flow:- 0.204 kg/m2s^Liquid flow:^3.049 kg/m2sAverage Temp^(°C) Current^(A) Concentration^(M)18.5 2 0.02318.5 4 0.03019.0 6 0.03520.5 8 0.03820.5 10 0.04021.0 12 0.04521.5 14 0.04823.0 .. 16 0.053.^22.0 18 0.05323.0 20 0.05524.0 22 0.05824.0 24 0.05883Appendix B. Experimental ResultsTable 10: Results of peroxide produced at various currents,run 4.Bed dimension: 89 mm long x 3.8 mm wide x 0.3 mm thickFibre diameter 22 gm^Porosity : 0.90Liquid load: 3.049 kg/m2s^Gas load: 0.3541 kg/m2sPressure drop 0.124 bars^Outlet pressure 1 atm abs.Average Temp. (°C) Current^(A) Concentration^(M)17.5 2 0.02417.0 4 0.02819.0 6 0.03019.5 8 0.03420.0 10 0.03820.5 12 0.04021.5 14 0.04421.0 16 0.04522.0 18 0.05023.0 20 0.05323.5 22 0.05824.0 24 0.05824.0 26 0.05884Appendix B. Experimental ResultsTable 11: Results of peroxide produced at various currents, run 5Bed dimension:- 89 mm long x 3.8 mm wide x 3 mm thickFibre diameter 22 gm^ Porosity : 0.90Pressure drop: 0.072 bars^Outlet pressure 1 atm abs.Liquid flow : 4.574 kg/m2s^Gas flow : 0.037 kg/m2sAverage Temp.^(°C) Current^(A) Concentration^(M)18.5 2 0.01918.5 4 0.02818.5 6 0.03520.0 8 0.04320.5 10 0.04620.5 12 0.04821.0 14 0.04522.0^' 16 0.04522.5 18 0.04685Appendix B. Experimental ResultsTable 12 :Results of peroxide produced at various currents, run 6Bed dimension:- 89 mm long x 38 mm wide x 3 mm thickFibre diameter 22 gm^Porosity^: 0.90Pressure drop 0.079 bars^Outlet pressure 1 atm abs.Liquid load : 4.574 kg/m 2 s^Gas load : 0.080 kg/m2 sAverage Temp. ( °C) Current^(A) Concentration^(M)19.0 2 0.02119.5 4 0.02921.0 6 0.03621.0 8 0.04122.0 10 0.04822.0 12 0.05023.0 14 0.05024.0 16 0.05023.5 18 0.05186Appendix B. Experimental ResultsTable 13: Results of peroxide produced at various currents, run 7Bed dimension: 89 mm long x 38 mm wide x 3 mm thickFibre diameter: 22 gm^Porosity: 0.90Pressure drop: 0:101 bars^Outlet pressure: 1 atm abs.-Liquid load: 4.574 kg/m2s^Gas load : 0.204 kg/m2sAverage Temp.^(°C) Current^(A) Concentration^(M)20.0 2 0.02020.0 4 0.03020.5 6 0.03821.0 8 0.04121.0 10 0.04621.5 12 0.04822.5 14 0.05022.5 .. 16 0.05323.0 18 0.05424.0 20 0.05524.5 22 0.05525.0 24 0.05587Appendix B. Experimental ResultsTable 14: Results of peroxide produced at various currents, run 8Bed dimension: 89 mm long x 38 mm wide x 3 mm thickFibre diameter: 22 gm^ Porosity : 0.90Pressure drop 0.135 bars Outlet pressure 1 atm abs.Liquid load : 4.574 kg/m2s^Gas load : 0.354 kg/m2sAverage Temp.^(°C) Current^(A) Concentration^(M)20.0 2 0.02320.0 4 0.03120.5 6 0.03520.5 8 0.04020.5 10 0.04321.0 12 0.04520.0 14 0.04620.5..16 0.04923.0 18 0.05026.0 20 0.05126.0 22 0.05323.5 24 0.05388Appendix B. Experimental ResultsTable 15: Results of peroxide produced at various currents, run 9Bed dimension : 89 mm long x 38 mm wide x 3 mm thickFibre diameter: 22 gm^Porosity : 0.90Pressure drop: 0.115 bars^Outlet pressure 1 atm.abs.Liquid Flow : 7.623 kg/m2s^Gas load : 0.037 kg/m2sAverage Temp.^(°C) Current^(A) Concentration^(M)19.5 2 0.01019.5 4 0.01522.0 6 0.01820.5 8 0.02021.0 10 0.02320.0 12 0.02520.0 14 0.02520.5..16 0.02820.0 18 0.02820.5 20 0.02822.0 22^_ 0.02889Appendix B. Experimental ResultsTable 16: Results of peroxide produced at various currents,run 10Bed dimension : 89 mm long x 38 mm wide x 3 mm thickFibre diameter: 22 AM^ Porosity : 0.90Pressure drop: 0.132 bars Outlet pressure: 1 atm abs.Liquid load: 7.623 kg/m2s^Gas load: 0.080 kg/m2sAverage Temp.^(°C) Current^(A) Concentration^(M)17.5 2 0.01318.5 4 0.01519.0 6 0.01819.5 8 0.01918.5 10 0.02119.0 12 0.02520.0 14 0.02820.0 16 0.02821.5 18 0.03022.0 20 0.03023.0 22 0.03323.5 24 0.03323.0 26 0.03390Appendix B. Experimental ResultsTable 17: Results of peroxide produced at various currents,run 11Bed dimension : 89 mm long x 38 mm wide x 3 mm thickFibre diameter: 22 gm^ Porosity^: 0.90Pressure drop: 0.164 bars Outlet pressure: 1 atm absLiquid load : 7.623 kg/m2s^Gas load: 0.204 kg/m2sAverage Temp. (°C) Current^(A) Concentration^(M)18.0 2 0.01417.0 4 0.01819.0 6 0.01820.0 8 0.02018.0 10 0.02118.5 12 0.02519.5 14 0.02520.0 16 0.02820.5 18 0.02921.5 20 0.03021.5 22 0.03022.5^, 24 0.03123.0 26 0.03191Appendix B. Experimental ResultsTable 18: Results of peroxide produced at various currents, run 12Bed dimension : 89 mm long x 38 mm wide x 3 mm thickFibre diameter: 22 gm^ Porosity: 0.90Pressure drop: 0.186 bars Outlet pressure: 1 atm absLiquid load: 7.623 kg/m2 s^Gas load:^0.354 kg/m2 sAverage Temp. ( °C) Current^(A) Concentration^(M)17.5 2 0.01417.5 4 0.01817.0 6 0.01917.0 8 0.02018.0 10 0.02318.5 12 0.02520.5 14 0.02820.0 16 0.02820.0 18 0.03121.0 20 0.03322.0 22 0.03522.5 24 0.03592Appendix CSample Calculations93Sample Calculation OneFLUID LOADS AND PRESSURE GRADIENT Liquid (water)Density of water at 20°C^ = 998.204 kg/m3Area of fibre bed^ = 3.0 E-3 x 38 E-3 m2Conversion of water flowrate from cc/min to kg/m2s(cc/min) (1 min/60s) (998.204 kg /m2s) (1/1.14 E-4 m2) (1 m3/1 E-6)1 cc/min^= 0.1459 kg/m2sflow rate (cc/min)^ liquid load(kg/m2s)10^ 1.4620 2.9230^ 4.3840 5.8450^ 7.30Gas (oxygen)Density of oxygen at 0°C, 1 atm^= 1.4289 kg/m3^[44]Density of oxygen at 21°C 1 atm = 1.33 kg/m3Flow area of electrode bed^ = 1.14 E-4 m2Conversion of the oxygen flowrate from cc/min at 760 mm Hg and 21°Cto kg/m2s1 cc/min =(cc/min) (1 min/60 s) (1.33 kg/m3) (1/1.14 E-4 m2) (1E-6)= 1.944 E-4 kg/m2sFrom the calibration curve for stainless steel float94Appendix C.Scale Reading^ cc/min at1020406080100120140The pressure of the gas in the rotameter= 100 lb/in2 gaugeThe pressure gauge=(100) (4.448) (1/2.54x2.54E-4^) (1/1.01325Sample Calculation760 mmHg and 21°C3268148248376512652792E5^)= 6.804 atmThe absolute pressure=6.804 + 1 atm= 7.804 atmThe adtual flowrate=(absolute pressure/atmospheric pressure)112 x calibrated= 2.794 x calibrated value-95Calibrated valueAppendix C. Sample CalculationActual flow rate^Gas load(cc/min,^760 mmHg and 21°C)^kg/m2s32 89.4 0.0268 199.0 0.04148 413.5 0.08248 692.9 0.13376 1050.5 0.20512 1430.5 0.28652 1821.7 0.35796 2224.0 0.431 in Hg (60°C)^= 3.37685 E3^N/m21 bar^ = 1 E 5^N/m21 atmosphere^= 1.01325 E5^N/m2Conversion of pressure from inches mercury to bars= (3.37685 E3)(E-5)1 inch Hg^= 3.37685 E-2 barlength' of graphite packing= 0.356 mConversion of pressure drop to pressure gradient1^bar^ = 9.4855 E-2 bar/m96Appendix C. Sample CalculationSample Calculation TwoLIQUID HOLDUP Liquid ( 1M NaOH)Density of 1M NaOH at 20°C^= 1.0428 g/ccCross sectional area of electrode= 1.14 E-4 m2Conversion of the flow rate of NaOH from cc/min to kg/m2s=(1/60)(1042.8)(1/1.14 E-4)(1 E-6)1 cc/min^= 0.1525 kg/m2sFlowrate (cc/min)^ Liquid load (kg/m2s)10^ 1.5320 3.0530^ 4.5750 7.62Calculation of liquid holdup for liquid and gas loads of 1.53kg/m2s' and 0.04 kg/m2s respectively.Volume of one molar aqueous sodium hydroxide trapped in graphitefibre bed, channels and inlet valves = 31 mlVolume of one molar aqueous sodium hydroxide trapped in channelsand valves^ = 5 ml97Appendix C. Sample CalculationTherefore the volume of one molar sodium hydroxide trapped ingraphite bed alone^ = 26 mlThe void volume of graphite electrode^= 0.9x3.8x0.3x35.6= 36.53 cm3Therefore the total liquid holdup which is equal to the volume ofliquid trapped in the bed divided by the void volume of bed for thegas and liquid load under consideration^=26/36.53=0.71Sample Calculation ThreePEROXIDE CONCENTRATIONCalculation of the concentration of the alkaline hydrogenperoxideBasis: 0.75 ml of 0.1N KMn04 used to titrate 2 ml of the samplesolution (peroxide)1 ml of 0.1 M kMn04^= 0.001701 g of H202^[41]therefore 0.75 ml of 0.1M kMn04 = 0.75 ml x 0.001701 g of H202since 2 ml of H202 was used for the titration analysis this impliesthat 2 ml of H202 will contain 0.75 x 0.001701 gtherefore1000 ml of H202 will contain^=1000 x 0.75 x 0.001701/2Molecular weight of H202^= 34 gtherefore 34 g of H202 = 1 mole /litre98Appendix C. Sample Calculation1000 x 0.75 x 0.001701/2 of H202 =1000x0.75x0.001701/(34 x 2)mole /litre= 0.0188 Mapproximately 0.019 E-3 moles/m3Sample Calculation FourTHEORETICAL CURRENT Calculation of the theoretical current required for peroxidegeneration02^+ H20 + 2e-^OH- + H02The theoretical current required for production of peroxide=^n F (Hf-Hi )where Q1= catholyte flowrate m3/sn = number of moles of electrons per mole peroxideF = Faradays number coulombs/mole of electronHf = final concentration of the H202 moles/m3Hi = initial concentration of the H202 moles/m3I = theoretical current^ ACatholyte flowrate = 20 ml/min= 20 ml/min x 1 min/ 60 s x 1 E-6 m3/m1= 3.333 x 1 E-7 m3/s99Appendix C. Sample CalculationHf= 0.0425 E 3 moles/m3Hi= 0 moles/m3I= 3.333 x 1E-7 x 2 x 96480 x 0.0425 x 1 E3= 2.73 A= 2.7 ASample Calculation FiveCURRENT EFFICIENCY Calculation of hydrogen generated and its currentefficiencyThe electrochemical reactions that takes place in the cell are:-Cathode :-02^+ H20 + 2e^0H- + H02-^IiH02- + H20 + 2e-^30H^122H20 +^2e-^H2 + 20H-^13Anode:-02^2H20 4- 4e-^40H-liquid flow rate = 10 ml/min= 1.667 x 10-4 l/sGas flowrate^= 20 rotameter readingFrom the gas rotameter calibration (Appendix A) this corresponds to100Appendix C. Sample Calculationa reading of 68 ml/minPressure within the gas rotameter = 100 psithe total pressure^ = 100 + 14.7= 114.7 psitherefore the gas flowrate^= 68 ( 114.7/14.7)°.5= 3.167E-3 l/s22.4 litres of gas is contained in one mole of a gas at STPat temperature of 21°C the number of litres will be 24.12The amount of hydrogen generated was 0.52 % by volumetherefore the amount of hydrogen in moles will be= 0.0052 x 3.167 E-3/24.12= 6.859 E-7 moles/sOne mole of hydrogen will be produced by 96480 x 2 Faradays.The amount of current that will generate 6.859 E-7 moles= 6.859 E-7 x 96480 x 2=0.13 Aapproximately 0.1 ACurrent efficiency (CE)= theoretical current required Applied currentthe theoretical current for hydrogen generation = 13applied current^ = Ii + 12 + 13CE 1 - the current efficiency for hydrogen generationCE 2 - the current efficiency for peroxide generation101Appendix C. Sample CalculationBelow are some typical results calculated for the different currentIi, 12 and 13 and the current efficiencies for the hydrogengenerated and the peroxide produced for a gas load of 0.04 kg/m2sand liquid load 1.53 kg/m2s.11+12+13(A)Ii(A)12(A)13(A)C.E.^1(%)C.E 2(%)2.2 1.9 0.2 0.1 4.5 734.4 3.3 0.9 0.2 4.5 488.8 6.1 1.8 0.9 10.0 3811.0 7.3 2.5 1.2 11.0 3213.2 8.4 3.3 1.5 11.4 27When 13 is neglected the calculated value of the mass transfercapacity will be higher than the true value by up to about 6 %.102Appendix C. Sample CalculationSample Calculation SixLIMITING CURRENT FOR OXYGEN REDUCTION Calculation of the limiting current for oxygenreduction. At thecathode some of the current applied to the system goes to destroythe perhydroxyl produced. The total applied current was taken to beequal to 11+12 (13 was neglected in this calculation)The theoretical current required to produce H202 will then beI1- 12For an applied current of 10 A^Ii + 12 = 10 A^(a)The theoretical current required for peroxide generation fromsample calculation Four^ 11-12 = 2.7A^(b)therefore^ 12 = 11 - 2.7Asubstituting (c) into eqn (a) gives211 -2.7A = 10 Atherefore^ I1^= (10A + 2.7A)/2= 6.35 Athe limiting current for oxygen reductionIi^= 6.4 ASample Calculation SevenMASS TRANSFER CAPACITYCalculation of mass transfer capacity (Ka)103Appendix C. Sample CalculationSince the electrochemical reaction is controlled by the masstransfer rates, the mass transfer coefficient will be related tothe current density by the equationi =nFK Cowhere^i = limiting current density involved in reaction 1.n = number of electrons involved in reactionK = overall mass transfer coefficientCo = bulk concentration of reactive species, that isthe oxygenThe pressure drop throughout the packing was less than 0.19 bars.The Co was considered to be a constant.A mass balance on a differential element in the flow direction (y)gives (discounting loss of peroxide by secondary reaction,decomposition or transfer to the anolyte.)d[H] /dy = Co K a A/Qwhere H = concentration of peroxide^moles/m3Hf = final concentration of peroxide^moles/m3Hi = initial concentration of peroxide^moles/m3Co = solubility of oxygen in 1M aqueoussodium sodium hydroxide^moles/m3Y = total length of fibre bedK = overall gas-solid mass transfercoefficient^ m/s104Appendix C. Sample Calculationa = effective interfacial area for gas-solid mass transferA = cross sectional area of bed (width timesthickness)Qi = liquid flow ratem- 1m2m3/sFor a plug flow of total length Y(Hf -Hi)/Y^- co K a A/QiFrom Faraday's lawI^ = n F Q [Hf - Hi]I/(nFQ1)^= II ^HiI/(nFQ1) = co K a A/41Ka^= I / ( Con F A Y)^n = 2 Faradays /mole peroxideF^= 96480 Coulombs/ mole electronA = 0.003 x 0.038 m2Y^= 0.089 mCo = 0.954 mole/m3^[44]I^= 6.4 A (sample calculation 6)Therefore Ka =6.4/(2x96480x0.003x0.038x0.089x0.954)= 3.43 s-1105Appendix C. Sample CalculationSample Calculation EightPOROSITY OF GRAPHITE FELT Determination of the porosity of the graphite fibre feltGraphite fibre felt with dimension 250 mm long by 76 mm wide by6.35 mm thick was used. The mass of the sheet when weighed was8.8868 g. The density of the fibre as given by the Manufacturer is1500 kg/m3. The initial porosity of this sheet was calculated usingthe formulae = (V-Mid) /V0where V = bulk volume of graphite fibre matrix m 3M = mass of the graphite fibre felt kgd = fibre density^kg/m3The fibre density was taken to be 1500 kg/m3= (250x76x6.35 E-9 - 8.8868 E-3/1500)/(250x76x6.35E-9)o= 0.951The working porosity was calculated using the equation below6^= 1 - to (1- s) /t= 1 - 6.35 E-3 (1- 0.951)/ 3 E-3= 0.90106Appendix C. Sample CalculationSample Calculation NineELECTRODE POTENTIAL Calculation of the electrode potential difference across a graphitefibre trickle-bed electrodeThe electrode potential difference is related to the conductivitiesof the electrolyte and electrode by the well known differentialequation given belowd2 (Om -^)^ = - aj ( 1/x + 1/a)dX2Let^0^= Om - OsThen^d20^= - aj (1/x + 1/a)dX2for pure mass transfer controlj =nFK CoTherefored20^a n K Co F (1/x + 1/a) + constantdX2at X = 0^dO = i/xdX^dO^a n K Co F (1/x + 1/a)X + i/xdXat X =XOx^= -anKC0F ( 1/x + 1/a)X2 + iX/K + 00107Appendix C. Sample Calculation00 - Ox= an K Co F(1/K + 1/a)X2 /2 -iX/K= ajTfor a graphite bed of thickness x = T where the potential at X=0 isdenoted by 00the electrode potential difference can be written as00 - Ox = anFKC0 (1/K + 1/a) X2 /2 -anFKC0 TX/KThe electrode conductivity for graphite fibre can be obtained usingthe correlation by Oloman et. al. [46]K = 10 + 2800 ( 1- e/s. ) 1.55the working porosity e of the graphite fibre trickle-bed electrodeis related to its thickness by the equation belowE = 1 - to (1- so ) /tSpecifications of the graphite fibre trickle-bed electrode used forthe study wereto = 6.35 E-3 m^t = 3 E-3 m E=0.90^so = 0.951therefore a = 10 + 2800 ( 1- 0.90/0.951) 1.55= 40.04 mho/mFrom Neale and Nader equation [42] the effective electrolyteconductivity can be determined by the relation belowK = 2 Ko shL /(3 -^0Ko =1E-4 Z N4 S A,where^= charge on positive ionN4 = number of positive ions in molecule= concentration of electrolyte (1M NaOH) moles/m3A, = equivalent conductance of electrolyte mole108Appendix C. Sample Calculationcm2 /equivAv for 1M NaOH = 158.4 mho equiv-1 cm2S =1E 3 moles/m3^Z+ =1^N4 =10 = 1E-4 x 1E3 x 1^1 x 158.4= 15.84 mho/mFrom this study the total liquid holdup was found to range from0.44 to 1.0choosing the least value of the liquid holdup ie 0.42= 2 x 15.84 x 0.90 x 0.44/(3 - 0.44 x 0.90)= 4.82 mho/mwhen the liquid holdup is 1.0= 13.58 mho/mElectrochemical ReactionsCathode:-Primary reaction:02 + H20 + 2e- ---z* H02- + OH-^V° = - 0.076V (1)Secondary reaction 2H20 + 2e-^H2^20H-^V° = -0.828 V (2)V^=^-(-0.076)^= -0.752 VFrom the study the mass transfer capacity ranged from 3.4 to 9.0 s-1.■■Recall00-(1)x^anEKC0(1/K + 1/a)X2/2 - anFKCJX/K109Appendix C. Sample Calculationcase 1 when lc = 4.82 mho/m^and^Ka = 3.4 s-1Co = 0.954 mole/m3 T= 3 E-3 mthen00^Ox^96480 x 3.4 x 0.954 X2/ (1/4.82 + 1/40.04)-2 x 96480x 0.954 x 3.4 x 3 E-3 X /4.8200 - Ox = 72741.58 X2 - 389.56 Xwhen X =0.003m4- Ox = -0.51 VThe potential difference obtained in this case is less than thereversible potential for peroxide production but greater than thatrequired for hydrogen generation thus only reaction (1) will occur.case 2when iz = 4.82 mho/m^ Ka = 9.0 s-1Co = 0.871 mole/m3 T =3 E-3 m00 -Ox = 96480 x 9 x 0.871 (1/4.82 + 1/40.04)X2- 2 x96480 x 0.871 x 9 x 0.003 X /4.82= 175798.89 X2 - 941.46 Xwhen X = 0.003 m00 - Ox = -1.24 VThe potential difference is less than the standard reversiblepotential for both reactions (1) and (2) thus hydrogen and peroxidewill be produced.110Appendix C. Sample Calculationcase 3 when I( = 13.58 mho/m^ Ka = 3.4 s-1Co = 0.954 mole/m3 T = 3 E-3 m00 - Ox = 96480 x 0.954 x 3.4 (1/13.58 + 1/40.04) X2-96480 x 0.954 x 3.4 x 0.003 X /13.58when X = 0.003 m00 - Ox^= -0.14 VUnder these conditions only reaction (1) will occur.case 4 when 1^= 13.58 mho/m^ Ka = 9.0 s -1Co^= 0.871 mole/m3 T = 3 E-3 m00 - Ox = 96480 x 0.871 x 9 (1/13.58 + 1/40.04 )X2- 2 x 96480 x 0.871 x 9 x 0.003 X /13.5800 - Ox = 74581.47 X2 - 334.16 Xwhen X^= 0.003 m00 -Ox^0.33 VOnly reaction 11) will occur for this case.111Appendix C. Sample CalculationTable 19  : Experimental errorsVariable ErrorTemperature^(°C) ± 0.5 °CCurrent^(A) ± 0.5 °CPressure drop^(inHg) ± 0.5 inHgBurrette reading^(ml) ± 0.05 mlBed^dimensions^(mm) ± 1 %Pressure gradient^(bar/m) ± 6 %Total liquid holdup ± 5 %Mass transfer capacity^(s-1) ± 12%KMn04 concentration ± 5%Peroxide concentration ± 2%Aqueous sodium hydroxide conc. ± 0.05M112

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