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Foamed electrolyte in flow-by fixed-bed electrodes : study of fluid dynamics & transport processes Mohandes, Abdolhosein 1994

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FOAMED ELECTROLYTE IN FLOW-BY FIXED-BED ELECTRODESStudy of***** Fluid Dynamics & Transport Processes *****ByAbdoihosein MohandesB. Sc. (Faculty ofEngineering) University of Tehran 1965M. Sc. (Chemical Engineering) Oregon State University 1972A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF CHEMICAL ENGINEERINGWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAAugust 1994© Abdoihosein Mohandes, 1994In 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 Cit2cThe University of British ColumbiaVancouver, CanadaDate eiRi 19 jDE-6 (2/88)AbstractExperiments were carried out in bench scale electrochemical packed-bed cells to studythe “fluid dynamics and transport processes” with upward flow-by foamed electrolyte.Inthis context, the pressure gradient, liquid holdup, axial liquid dispersion coefficient, flowing foam electric conductivity, and overall mass transfer capacitywere measured in packed rectangular cells.All the runs were conducted at 22 degree Celsius inlet foam temperature. The cellswere packed with graphite fiber felt (comprised of 20 micron diameter fibers) and theliquid phase of the flowing foam was composed of water (for dispersion experiments) and1 N NaOH solution (for all other experiments) with 0.1 % v/v surfactant, Tergitol. Thegas phase of the foam was oxygen for mass transfer experiments and nitrogen for all otherexperiments. The studies were performed with respect to the three independent variablesof bed porosity (at three levels, except for the mass transfer measurements which weredone at two levels), liquid load and gas load (at numerous levels). Empirical second ordercorrelations including interaction terms were developed for each parameter, in terms ofthe three independent variables. The overall results are summarized as follows:I - Absolute value of the pressure gradient ranged from 20 to 80 bar.m , and is a factorof 50-100 higher than in nonfoaming systems with similar fluid loads.II - Liquid holdup ranged from 7 to 20 %, which is lower than the minimum of about•40 % observed in nonfoaming systems at similar fluid loads.III - Axial dispersion coefficient ranged from 0.01 to 0.46 cm2.s1,which is below previously reported values of packed bed processors with nonfoaming liquids.IV - The flowing foam effective electric conductivity ranged from 6.8 to 11.1 mho,m,Hwhich is equivalent to the effective electrolyte conductivity in nonfoaming gas/liquid flowat 3 to S times the liquid holdup, as estimated by the Neale and Nader correlation.V - Overall mass transfer capacity ranged from 4.7 to 7.6 s_i which is a factor of 1.8times the values in similar nonfoaming systems, assuming the total bed is electrochemically active.Apart from the high pressure gradient, the graphite fiber packed-bed cell with foamedelectrolyte shows promising performance for electrochemical processing involving gaseousreactants.111Table of ContentsAbstract iiList of Tables ixList of Figures xiiAcknowledgement xv1 INTRODUCTION258112 PREVIEW OF INVESTIGATED PARAMETERS2.1 PRESSURE DROP2.2 LIQUID HOLDUP2.3 DISPERSION COEFFICIENT2.4 ELECTRICAL CONDUCTIVITY2.5 GAS-LIQUID MASS TRANSFER2.6 LIQUID-SOLID MASS TRANSFER3 STATEMENT OF PURPOSE 264 EXPERIMENTAL APPARATUS ElectrodesFoam Characteristics[1,45,77]Foam Flow in Packed-Bed Chemical Reactors .Foam Flow in Packed-Bed Electrochemical Reactors12131516192224iv5 EXPERIMENTAL PROCEDURES5.1 GENERAL DISCUSSIONS 335.1.1 Preparation of the Liquid Solutions, Gaskets, Packing, Diaphragmand the Membrane 345.1.2 Setup of the Experimental Cell Block Consisting of the “basic cell”and the Associated Electronic and Non-Electronic Components. 355.1.3 Conduct of Experiments and the Post-Chemical Analysis 385.2 Case I- Pressure Drop Measurements 415.2.1 Conduct of Experiment: 435.3 Case II- Liquid Holdup Measurements 445.3.1 Conduct of Experiment 465.4 Case Ill-Dispersion Measurements. . . 475.4.1 Concepts and Means of Experiment 495.4.2 Conduct of Experiment 515.5 Case IV- Flowing Foam Electrical Conductivity Measurements 535.5.1 Conduct of Experiment 555.6 Case V - Overall Mass Transfer Capacity Measurements 575.6.1 Conduct of Experiment 606 EXPERIMENTAL RESULTS AND DISCUSSIONS 626.1 GENERAL 626.2 PRESSURE DROP . . 646.3 LIQUID HOLDUP 716.4 AXIAL DISPERSION 786.5 FLOWING FOAM ELECTRICAL CONDUCTIVITY. 856.6 MASS TRANSFER CAPACITY 92V7 CONCLUSIONS AND RECOMMENDATIONS7.1 CONCLUSIONS7.2 RECOMMENDATIONS7.2.1 Some Remarks on Scale-up[4,22]Nomenclature 108A Extension to the Preview of the Parameters InvestigatedA.1 Pressure DropA.2 Liquid HoldupA.3 Dispersion CoefficientA.4 Gas-Liquid Mass TransferA.5 Liquid-Solid Mass Transfer124124127129131132B Preparations and MeasurementsB.I Preparation of the Liquid SolutionsB.I.A Foaming 1 M Sodium Hydroxide SolutionB.I.B Foaming Water SolutionB.I.C 1 M Sodium Hydroxide SolutionB.II Preparation of Gaskets, 1/2” Graphite Felt Packing and Stainless SteelScreen PackingB.II.1 Preparation of GasketsB.II.2 Preparation of Graphite Felt and Stainlee Steel Screen PackingsB.III Preparation of Diaphragm and Membrane9999104105Bibliography 114Appendices 124133134134134134134134136136viB.IV Preparation of the Plexiglas Slabs 137B.V Preparation of the Electrodes and Current Collectors 138B.VI Measuring the Solid Volume of the Graphite Fiber Bed 140B.VI.1 Conduct of Measurements 141B.VII Specifications of Materials and Instruments Used in This Work 142B.VIIICell Configuration and the Experimental Design Parameters Values UsedThroughout this Research 143C Mathematical Treatment of Data 144C. 1 Porosity Measurement of Packed-Bed Cell 144C.1.1 Conduct of Experiment 144C.1.2 Sample Calculation of the Packed Bed Porosity Measurements. 146C.2 Sample Calculations for Each Case 149C.2J Calculation of the Flow Rates 149C.2.2 Calculation of Liquid Holdup from Washout Solution Obtained inHoldup Experiments 151C.2.3 Calculation of Liquid Axial Dispersion Coefficient 153C.2.4 Calculation of Flooded Bed and Flowing Foam Electrical Conductivities 155C.2.5 Calculation of Overall Mass Transfer Capacity 158D Experimental Design Tables and Results 166D.I Pressure drop 167D.II Liquid Holdup 172D.IllLiquid Axial Dispersion 175D.IV Foam Effective Electrical Conductivity 178D.V Overall Mass Transfer Capacity, Ka 181viiE Calibration of the InstrumentsE.I Calibration of Milton Roy Liquid Supply Pump with 1.N NaOH Solutionof 0.1 % v/v Tergitol Surfactant, at 21 °CE.II Calibration of the Gas Rotameters: Cole Parmer Ser No 015279, tube# 42-15 and Matheson Model no 7630-602E.III Calibration of Heath Power Supply System (including its associated poweramplifier)188188191193G The 196G.A 196G.B 197G.C 198G.D200G.E 201G.F 203G.G 205183183184186F Mathematical Modeling for Design and Scale-upF.1 GeneralF.1J Conservation of Mass[661P.1.2 Conservation of Charge[64]Computer RoutinesGlobal Variab1esGas and Liquid Flow Rate VariablesLiquid HoldupSetup of Computer Login Program, “NOTEBOOK”, in Dispersion MeasurementsDispersion CoefficientFoam Electrical Conductivity . . .Mass Transfer CapacityyinList of Tables1.1 Packing properties 101.2 Fluid properties and gas-liquid systems studied 105.1 Limiting current data for RUN ID EPL3G2 616.1 Three-dimensional correlation of pressuregradient 696.2 Three-dimensional correlation of liquid holdup 766.3 Three-dimensional correlation of axial dispersion coefficient 836.4 Three-dimensional correlation of foam effective electrical conductivity. 906.5 Three-dimensional correlation of mass transfer capacity 97B.1 Gasket dimensions corresponding to Figure B.1 135B.2 Dimensions of the Plexiglas slabs according to Figure B.2 137B.3 Dimensions of the current collectors and electrodes according to Figures(B.3-4) 138B.4 Parts and materials specifications used in this research work 142B.5 Cell configuration and operating parameters for all cases 143C. 1 Measured bed porosities along with contributed endline dimensions, for allcases 148C.2 Graphite fiber flooded bed effective electrical conductivity values 156C.3 The oxygen solubility integral for RUN ID EPL3G2 164D. 1 Pressure drop data and results for “LOW” level porosity bed 167ixD.2 Pressure drop data and results for “ZERO” level porosity bed 168D.3 Pressure drop data and results for “HIGH” level porosity bed 170D.4 Liquid holdup data and results for “LOW” level porosity bed 172D.5 Liquid holdup data and results for “ZERO” level porosity bed 173D.6 Liquid holdup data and results for “HIGH” level porosity bed 174D.7 Liquid axial dispersion data and results with 5.3-cm Neoprene gasket, for“LOW” level porosity bed 175D.8 Liquid axial dispersion data and results with 12-cm Neoprene gasket, for“ZERO” level porosity bed 176D.9 Liquid axial dispersion data and results with 12-cm Neoprene gasket, for“HIGH” level porosity bed 177D.10 Foam electrical conductivity data and results with 5.3-cm Neoprene gasket,for “LOW” level porosity bed 178D.11 Foam electrical conductivity data and results with 12-cm Neoprene gasket,for “ZERO” level porosity bed 179D.12 Foam electrical conductivity data and results with 12-cm Neoprene gasket,for “HIGH” level porosity bed 180D.13 Mass transfer capacity data for “ZERO” level porosity bed 181D.14 Mass transfer capacity data for “HIGH” level porosity bed 182E. 1 Calibration of Milton Roy (large plunger, 1/4” shaft) Liquid Supply Pumpwith iN NaOH Solution of 0.1 % v/v Tergitol Surfactant, at 21 °C. . . . 183E.2 Cole Farmer rotameter calibration with oxygen at PB =754.3 mm Hg andTB 21 °C, Toutiet2O.5 °C 184E.3 Matheson rotameter calibration with oxygen at PB =754.3 mm Hg andTB 21 °C, T,utiet20.5 °C 184xE.4 Cole Parmer rotameter calibration with nitrogen at PB =754.3 mm Hgand TB 21 °C, Toutiet2O.5 °C 185E.5 Matheson rotameter calibration with nitrogen at PB =754.3 mm Hg andTB = 21 °C, T,=2O.5 °C 185E.6 Parameters of the fit of the gas flow rate, G, of Cole Parmer and Mathesonrotameters, in term of rotameters reading, GCM, for nitrogen and oxygengases 185E.7 Calibration data for Heath power supply and its associated amplifier againstone Ohm standard resistance 186E.8 Prameters of the fit for correlation of the resistance efficiency in term ofV*I with two model 187E. 9 Comparison of the predicted and experimental values of resistance efficiency by models #1 and #2 187xiList of Figures1.1 Porous electrode configurations (Figure from Ref. [64]). (a) “Flow-through”two compartment reactor (b) “Flow-by” two compartment reactor (c)“Flow-through” single compartment reactor 31.2 a. Flow pattern diagram for nonfoaming liquids. b. Flow pattern diagramfor foaming liquids (keys in Tables 1.1 & 1.2). In this figure, G (kg/m2/s)is the superficial gas mass velocity, L (kg/m2/s) is the superficial liquidmass velocity A = and = [±L.(&)]1/3 9Pw Paw L U.w PL4.1 Experimental apparatus flow diagram 295.1 Schematic presentation of the basic cell 365.2 Cell block assembly for pressure drop measurements 425.3 Cell block assembly for liquid holdup measurements 455.4 Cell block assembly for axial dispersion measurements 485.5 Cell block assembly for foam electrical conductivity measurements. . 545.6 Cell block assembly for mass transfer capacity measurements 585.7 Typical saturation curve; consumed amount of 0.1 KMnO4 solution intitration of 2 mL of cell effluent electrolyte 616.1 Pressure gradient for”LOW” level porosity bed 666.2 Pressure gradient for”ZERO” level porosity bed 676.3 Pressure gradient for”HIGH” level porosity bed 686.4 Pressure gradient for foam flow in graphite fiber bed 70xii6.5 Liquid holdup for”LOW” level porosity bed 736.6 Liquid holdup for”ZERO” level porosity bed 746.7 Liquid holdup for”HIGH” level porosity bed 756.8 Liquid holdup for foam flow in graphite fiber bed 776.9 Liquid axial dispersion coefficient for”LOW” level porosity bed 806.10 Liquid axial dispersion coefficient for”ZERO” level porosity bed 816.11 Liquid axial dispersion coefficient for”HIGH” level porosity bed 826.12 Axial dispersion coefficient for foam flow in graphite fiber bed 846.13 Foam effective electrical conductivity for”LOW” level porosity fiber bed 876.14 Foam effective electrical conductivity for”ZERO” level porosity fiber bed 886.15 Foam effective electrical conductivity for”HIGH” level porosity fiber bed 896.16 Effective electrical conductivity for foam flow in fiber bed 916.17 Overall mass transfer capacity for”ZERO” level porosity fiber bed 956.18 Overall mass transfer capacity for”HIGH” level porosity fiber bed 966.19 Mass transfer capacity for foam flow in graphite fiber bed 98B.1 Drawings of the various gaskets 135B.2 Drawing of the Plexiglas slabs 137B.3 Drawings of the copper current collectors and the stainless steel flat sheetelectrodes 138B.4 Drawing of the 1/32” stainless steel electrodes with couplings 139B.5 Instrument to measure the graphite fiber-bed solid volume 140C. 1 Distribution of the captured electrolyte by quick closing valve method 145C.2 Cell Ohmic resistance analogy including diaphragms 155C.3 Concentration profile of species A in cathodic reduction 159C.4 Peroxide balance for a differential element of electrode 159xiiiD. 1. Pressure along the cell, for “ZERO” Level Porosity bed j69D.2 Pressure along the cell, for “HIGH” Level Porosity bed 171E. 1 Graphical presentation of Resistance efficiency for Heath power supplysystem 186F. 1 Coordinates for a three-dimensional flow-by lectrode.X = thickness Y = length Z = width 189xivAcknowledgementI wish to express my sincere gratitude and appreciation to my supervisor Professor CohnW. Oloman first for his valuable and skillful guidance in this work and secondly for twoyears of his financial support.Many thanks are due to my past and present professors, whose contribution to mybackground has been an essential factor during the course of this work.I would also like to express my sincere thanks to the professors and fellow students inthe Department of Chemical Engineering, whose suggestions, comments or even criticismhas, contributed to the success of this work. Also, I am grateful to my friends, Antonio,Igor, Marek, Eugene, Perng, Issac, Robin for their enthusiasm and support. May themany others, mostly overseas, forgive me for not mentioning them by name.The technical assistance and the kindness I received from the staff of the ChemicalEngineering Workshop, Stores, and main Office is highly appreciated.I feel particularly indebted to my sisters and my mother, for their continued encouragement, support, understanding and love. They are special, this work is dedicated tothem.xvChapter 1INTRODUCTIONIndustrial chemical processes are designed mainly based on three ultimate goals: highselectivity, high production rate, low capital and operating costs. Regarding the environmental considerations and today’s human need for better quality and minimal materialwaste, electrochemical methods are being explored as channels to most of these requirements. The application of electrochemical cells in the last two decades has progressedin many industrial areas: electro-refining, primary and secondary batteries, jet plating,electromachining, industrial synthesis, and fuel cells.Electrochemical reactors are devices by which the materials (reactants) are electrochemically converted to another sort (products) through the transfer of electrical energy.Other terms in common use for electrochemical reactor are ‘electrolyser’, ‘electrolyticcell’, or ‘electrochemical cell’. Chemical engineering reactor design involves the application of chemical engineering principles to kinetic and thermodynamic data. Electrochemical reactor design applies similar principles except that the existence of the electricfield adds complexity to the procedures.An electrochemical synthesis reactor essentially consists of two electronic conductorscalled electrodes, immersed in a bath of electrolyte solution. The electrodes are connectedoutside the bath to the terminals of a DC power supply. Application of sufficiently high•electromotive force (emf) results in electron transfer between electrodes and solution,causing flow of electricity in the external circuit, with the outcome of chemical reactionsat each electrode. Details of the charge transfer and reactions in an electrolytic cell arewell established in the literature and textbooks[50,87j.1Chapter 1. INTRODUCTION 21.1 Packed-Bed ElectrodesAccording to the outline above it is clear that reactions taking place in electrochemicalreactors are heterogeneous in nature and hence the increase in electrode specific surfacearea can raise the space time yield for an electro chemical reaction.To achieve high production rates with electrochemical reactors, porous electrodes areoften the proper choice, giving a high conversion per pass. Also by convenient controlof the applied emf to the cell and the cell current, high selectivity is achievable. In thiscontext, porous electrodes have found wide applications in the electrochemical industries,for example in, fuel cells and batteries and, more recently, in electrosynthesis.Porous electrodes offer about 100 times larger specific surface than plate electrodes.In addition, due to promotion of flow turbulence in porous electrodes, moderate valuesof the mass transfer coefficient, with the consequence of higher production rate, are attained for mass transfer limited processes. Hence, electrochemical reactors with porouselectrodes are expected to present highest performance when dealing with dilute reactants. Figure 1.J shows two basic and commonly used configurations of electrolysers withporous electrodes, which differ from each other mainly with respect to relative directionsof the electric current and fluid flow.1. Configurations (a) or (c), in which the electric current and fluid flow are parallel,are called ‘flow-through’. In this assembly the porous electrode is backed with aperforated solid plate, acting as current ‘collector’ or ‘feeder’.2. Configuration (b), in which the electric current and fluid flow directions are orthogonal, is called ‘flow-by’. In this assembly the porous electrode is shown supportedon the current collector.Electrical conduction in either configuration is accomplished via the motion of chargedChapter 1. INTRODUCTION 3Figure 1.1: Porous electrode configurations (Figure from Ref. [64]). (a) “Flow-through”two compartment reactor (b) “Flow-by” two compartment reactor (c) “Flow-through”single compartment reactor.species in the liquid phase to or from the liquid/solid electrode interface. Then in sequencethe discharge or generation of ions at the solid surface corresponds to the flow of electronsto the solid electrode, passing through the current collector, arriving in the externalcircuit as flow of electricity with the result of a chemical transformation at the electrodesurface. Thus, a Faradaic process is accomplished in the cell with the accompanied flowof electrons from anode (+) to cathode (-) through the external circuit.In the flow-through configuration, the bed thickness is limited by the potential dropwhich occurs in the electrolyte, restricting the fractional conversion per pass[64,89]. Theelectric potential and concentration distribution perpendicular to the current remains reasonably uniform. This simplifies modeling but it also limits scaling up and consequentlylowers the extent of its practical applications.In flow-by electrodes, fractional conversion per pass is high (up to 99 %), and suchChapter 1. INTRODUCTION 4electrodes can be scaled up by increasing the reactor width or, where possible, by increasing the length of the porous electrode.Applications of packed-bed electrodes span from organic synthesis to electrochemicalconversion of dilute gases, electrochemical winning of metals, etc. Practical applicationsof electrochemical processes involving gaseous reactants in packed-bed electrodes are forexample:1) The cathodic-reduction of oxygen to hydrogen peroxide[17], which has been cornercialised by H-D Tech. Inc. (Dow Chemical)02 + H20 + 2e H0 + 0H2) Electro-oxidation of sulphur dioxide to sulphuric acid[9,92], for generating electricpower and energy recovery, or in the treatment of stack gas to eliminate the toxic gascontents[57].SO2 + 2H0 == H2S04 + 2H + 2eThe last case as well as many other similar gaseous treatments with packed-bed electrodesare still under laboratory investigations with prospects for their future applications.The design parameters for packed-bed electro chemical reactor with gaseous reactantshave not been fully explored with many packing substances, especially graphite fiberfelts, and such systems have never before been studied with foamed electrolytes. Inthe conversion of gaseous reactants the application of porous electrodes with foamedelectrolyte may give improved performance over such systems with conventional nonfoamed electrolytes.Thus, the decision was made to study the”fiuid dynamics and transport processes”in flow-by electrochemical reactors packed with graphite felt with upward foam flow,expecting improved performance relative to similar but nonfoaming systems.In foam flow through packed beds, the liquid is the continuous phase and the gas phaseis in the form of side-by-side bubbles confined by the liquid film network in polyhedralChapter 1. INTRODUCTION 5packages. Also, it is supposed that the solid surface is covered by a liquid film. A foamyfluid consists of a gas phase and either a foaming liquid or an aqueous solution of afoaming agent (surfactant).The foamed fluid adopted in this research was generated from 1 M NaOH electrolytesolution of 0.1 % v/v surface active agent (surfactant), Tergitol (a non-ionic surfactant),and either nitrogen or oxygen gases. A brief discussion of the characteristics of the foammedium is given below.1.2 Foam Characteristics [1,45,77]Foam is a dispersed system of gas bubbles in an aqueous solution of a surface activeagent, called ‘surfactant’ (e.g., electrolyte solution of Tergitol, in this work). In analogywith conventional packed-bed processors, the foam flow may be identified more conveniently with the bubble flow regime based on their hydrodynamic similarities, and somestructural resemblances as follows:1. The liquid phase in the foam is continuous as in the bubble flow regime.2. The non-continuous gas phase ranges from the dispersed spherical gas bubbles,in the bubble flow regime, to the side-by-side bubbles confined by the liquid filmnetwork of polyhedral packages in the saturated foam flow regime.3. Gas bubbles in the foam are separated from each other by a liquid film with athickness of a few microns; whereas in the bubble flow regime, the liquid phaseconstitutes the main body of the flowing phases. In foam flow the interface liquidfilms of several gas bubbles meet each other and make a thicker liquid column calleda ‘Plateau border’.Chapter 1. INTRODUCTION 64. In foam flow, gas holdup is higher than liquid holdup whereas in the bubble flowregime, the liquid holdup is normally higher than gas holdup.The foam flow regime is, therefore, physically an extension of the bubble flow regimewith higher gas to liquid flux ratio causing greater interaction between the phases. Thelow liquid holdup in conjunction with the existence of the fine gas bubbles with diameterin the order of fractions of a millimeter (visually observed) in foam flow operation isexpected to have favorable mass transport effects.Foam stability against drainage, coalescence and breakage is classified as unstable ormetastable.(a) Unstable foam is made with a solution of short-chain fatty acids or alcohols. Althoughthe drainage and film rupture in this class of foams are retarded, those processes will notstop until complete collapse of the foam takes place.(b) Metastable foam is made with solutions of soaps, synthetic detergents, proteins,saponin, etc. In this class of foams the drainage of the liquid stops when a certainfilm thickness is reached and, in the absence of disturbing influences, these foams wouldpersist almost indefinitely.There are certain abilities and characteristics associated with the presence of thesurfactant. The surfactant tends to absorb in the gas/liquid interface layer, affectingthe inter-molecular force balance of the interfacial region. The surfactant lowers theliquid surface tension, and thus promotes a larger gas/liquid interfacial area, which is themain objective in generating foam. The proper amount of surfactant must be used so asto produce no more than a single molecule layer in the interface liquid film, otherwisemicelles of surfactant molecules are formed which reduce the effective concentration ofmonomers.Chapter 1. INTRODUCTION 7One main feature of the foamed liquids made with surfactants is the Gibbs-Marangonieffect. This effect appears when a bubble film is subjected to stretching as a result ofsome external disturbance. The consequent increase in surface area is accompanied by adecrease in the surface excess concentration of surfactant and, therefore, a local increasein surface tension (Gibbs’ effect). Now in this condition, if the film stays unruptured, thesurfactant molecules will diffuse back to the stretched film region to restore the originalsurface tension (Marangoni effect). When the surface tension restoration persists longenough, the film thickness will restore as well, with flow of liquid molecules to the liquidfilm. The effect confers elasticity to the film and helps to stabilize the foam againstmechanical deformation.Chapter 1. INTRODUCTION 81.3 Foam Flow in Packed-Bed Chemical ReactorsIn packed-bed chemical reactors, gas-liquid flowing phases are chosen in different relativedirections, for different reasons. The choice of flow direction is related to the throughput,the driving force for mass transfer and conversion of reactants [75]. For reactors of bothcocurrent and countercurrent two-phase-flow, several distinct flow patterns are observedwith constant liquid flux and increasing gas flux: trickling flow, foaming flow, foamingpulsing flow, pulsing flow, and sometimes spray flow for foaming systems; trickling flow,pulsing flow, and spray flow for nonfoaming systems.Flow patterns and transitions from one configuration to another have been presentedby Charpentier and Favier(1975) as functions of gas and liquid flux, Figure 1.1. Asingle transition line exists between the regimes of the feeble interaction (trickling flow)and others which are considered to be high interaction regimes. Another flow regime,called the ‘dispersed bubble’ regime, has been observed at high liquid flux by otherinvestigators[54,80], for non-foaming systems.In general, the flow regimes largely depend on the gas and liquid fluxes, their relativeflow directions, the nature, size and status of packing materials, the fluid properties, andthe type of gas/liquid distributor. Tables 1.1 and 1.2[46j give typical values of the systemparameters used in experiments and in generation of the flow maps of Figure 1.2. As thesevariables are numerous, many investigators have considered the different regimes: theeffect of gas and liquid flux on flow regimes[91], the influence of fluid physical properties onthe transition of flow regime[5,11}, the effect of packing characteristics and the structureof the medium on the flow regime(12,25,26]. An important point is that, contrary tothe foamed electrolyte used in the present work (surface tension of 30 dyne/cm anddensity of 1.05 gr/cm3, at 22°C), the foaming liquids used in generating the flow mapof Figure 1.2 were not made with the addition of surfactant to the liquid. Thus theChapter 1. INTRODUCTION 9Figure 1.2: a. Flow pattern diagram for nonfoaming liquids. b. Flow pattern diagram forfoaming liquids (keys in Tables 1.1 & 1.2). In this figure, G (kg/m2/s) is the superficialgas mass velocity, L (kg/m2/s) is the superficial liquid mass velocity, ? = [. &-J0.5 andIf) =‘rconditions corresponding to this work are not strictly identifiable on the flow map ofFigure 1.2.Foam flow in conventional packed bed chemical reactors has been investigated[1O,11,46,48]0.01 1 0.01 01 1previously. Under foam flow conditions in either conventional packed bed processors orChapter 1. INTRODUCTION 10110(1 Waterfoamtng- CyctohexancGasolinePetroleum etherFoaming Kerosene IKerosene ftDesulfurizedgas oilNort-desulfurizedgas oiLSphericalCylindrical ISphericalCylindricaL 22.7 CylindricaL 23.5 Cylindrical23.3 Cyliadrical23 2 SphericalCylindrical4.7 CylindricaL 2Table 1.2: Fluid properties and gas-liquid systems studied.foam bed processors, several hydro dynamic variables[3 ,11,46,71 ,79] and transport properties[6,32,53,76] have been investigated. However, no previous work has been reportedfor the use of foam in graphite fiber beds or in electrochemical cells, which is the maintopic of the present research.Type Spherical Glass Cylindrical catalyst I Cylindrical catalyst 2catalyst spheresd(rnm] - 3 3 1.8x6 L4x50.39 0.385 0.39 0.37a (mJ 2,000 2,000 2,560 3,260D(mI 0.05 0.10 0.05 0.05A’(seckg1 14,700 23,200 16,800 29,100’ 30,300’ 34,800’B(m’ScCkg9 0.633 0.571 1.38 1.00’ (•35b 1.35’packing used with the following liquid phasesGas oil and Petroleum ether, b Kerosene and Cyciahexane,’ GasolineTable 1.1: Packing properties.t’L. IL -O 2Liquid (g’cm (ci,] (dynescm9 Packing Gas (reported to Key. p=1 Atm)1.000.780.840.650.790.8050.860.861.10.930.570.310.991.04S5752525.21925.326.228.828.3airairN2CO:N2HeN.CotairN2CO:AirHeco±4.8 Cylindrical 2 AirHe0.880.871.130.900.340.790.990.890.881.140.930.341.140.930.340UA.U+±x,1*AChapter 1. INTRODUCTION H1.4 Foam Flow in Packed-Bed Electrochemical ReactorsIn packed-bed electrochemical reactors (PBECR’s) the aqueous foam flow regime maybe used in the following cases:1. A gas phase reactant, soluble in the liquid phase, undergoes an electrochemicalreaction on the solid electrode bed surface.2. A gas phase reactant dissolves in the liquid phase, and undergoes electrochemicalreaction with another reactant which is already present in the liquid phase.3. The reactant is. present in the liquid phase only and undergoes electrochemicalreaction on the electrode bed surface.The third case is not very relevant in foam flow and would normally be applied undernon-foaming conditions[24,85j. In foam flow there exists a stable liquid network structureand coherency between gas and liquid phases. Therefore, in foam flow, the enhancementof mass transfer to the electrode surface due to mixing and redistribution of reactantsin the liquid by the gas is weaker than non-foaming systems. Instead, there are twofavorable effects in compensation. One is the existence of “extremely large gas-liquidinterfacial areas[47,48]”, which would cause a proportional increase in gas-liquid masstransfer, and secondly, but not less important, would be reduction of liquid by-pass andother flow non-idealities which would result in lower dispersion effects.The work undertaken in this thesis was aimed at exploring these effects for the firsttime, and measuring several parameters which could be used in the design of continuousflow-by packed-bed electrochemical reactors with foamed electrolytes.Chapter 2PREVIEW OF INVESTIGATED PARAMETERSGas-liquid contacting systems are used to affect the transport of mass and heat, and todrive chemical reactions. In these systems, the packed bed is either catalytic or inert;this acts to provide a large interfacial area and intense mixing of phases. Successfulmodeling of such systems requires a careful study of hydrodynamic parameters, includingknowledge of the flow pattern of the phases, and transport properties, and eventuallyestablishment of correlations for predicting these quantities.In cocurrent gas-liquid flow in packed-beds, much of the effort devoted to obtaininghydrodynamic parameter correlations has been based on certain operating conditions,packing properties and flowing phase materials. Extensive literature reviews are available for packed bed reactors[lO,26,27,29,68,73,75]. There is no literature available forfoaming systems in packed-bed electrodes. In the following, fundamentals of some ofthe parameters in systems with foam flow which have been reported are reviewed. Inother cases where the information is lacking, similar available information for nonfoamirigpacked-bed electrodes or PBRs will be presented. Also, the following terminology willbe used throughout this chapter and Appendix A: feeble interaction regime for tricklingflow regime and high interaction regime for regimes other than trickling flow regime. Theflow regimes may be identified from the flow pattern diagram Figure 1.1, for surfactantfree foaming system. In this way, a foaming system may be located on the flow map,according to its flow coordinates.Some further information reported by other investigators is given for each parameterin Appendix A.12Chapter 2. PREVIEW OF INVESTIGATED PARAMETERS 132.1 PRESSURE DROPIn the design of three-phase systems, prediction of pressure drop through a packed-bed is important. The significance of the pressure drop is for the calculation of gas-liquid interfacial area, mass transfer coefficient and holdup. An equally important roleof pressure drop measurements is in the estimation of fluid pumping cost through thepacked-bed, especially in the foam flow regime, where the pressure drop is highest.Prediction of pressure drop in general is performed by four different approaches asfollows:1. The two-phase pressure drop is expressed in terms of the single phase pressuredrops, which was developed first by Larkins (1959) and was used thereafter bymany investigators [46].2. Pressure drop has been correlated to gas and liquid phase Reynolds numbers bymeans of friction factor type of relations[34,77].3. Two-phase pressure drop has been calculated with Ergun-type equations with adjustable parameters[36, 79].4. Application of traditional methods of relative permeabilities in analysis of hydrodynamics of trickling fiow[69].While most of the investigations have been performed on air-water systems, the behavior of organic systems is correlated in terms of the parameters ) and i’ , accountingfor deviation in physical properties from those of the air-water systems.All the above four prediction methods for two phase pressure drop fall in either oneof three categories of derivations: a) momentum balance, b) mechanical energy balance(which are looked upon, respectively, as the force per unit area of the cross sectionChapter 2. PREVIEW OF INVESTIGATED PARAMETERS 14required to overcome frictional forces and energy per unit volume lost due to dissipation),and c) totally empirical.Generally, pressure loss increases with increasing gas and liquid loads. Decreasing surface tension increases the gas-liquid interaction (rippling observations) and the foamingcharacteristic of the system with the consequence of higher pressure gradient. Pressureloss for foaming liquids has been observed to be as high as ten times that of nonfoamingsystems{48] when transition from trickling to foaming flow occurs, for similar gas andliquid loadings. Due to the importance of the pressure drop parameter in packed beds,one reported case of investigation of foaming systems is summarized below and numerousother cases are listed in Appendix A:Specchia and Baldi (1977) correlated two-phase pressure drop by using the Ergun-typeequation for free area available for gas flow for a system of air-glycerol and air-water plussurfactant, with packings of 6 mm spheres, and of cylinders 2.7x2.7 mm and 5.4x5.4 mm.In the high interaction regime, for 0.0016 < t1L < 0.025 m/s, 0.011 < UG < 2.46 m/s,810 < PL < 1070 kg/rn3, 0.7 < Pc < 1.2 kg/rn3, 0.001 < < 0.005 kg/m.s and0.027 < oj, < 0.072 kg/s2, (empirical basis):lnfw = 7.82 — l.31n(Z/’’) — 0.0573[ln(Z/’ç”’)]2— (PfLG/h)de , — 2jwuere. j— 2 U2 —rG aand Z = (Rec)1’67/( L)°767A detailed survey and numerous pressure drop correlations in foaming packed-bedprocessors are given in the literature[46,79].Chapter 2. PREVIEW OF INVESTIGATED PARAMETERS 152.2 LIQUID HOLDUPLiquid holdup is defined as the volume of liquid per unit volume of bed, where as liquidsaturation is the volume of liquid per unit volume of void space in the bed. Retentionof the liquid in the bed at certain operating conditions is usually interpreted as resultingfrom two different contributions: 1) a specific amount of liquid that remains in the bedafter it has been drained, called the static or residual holdup, and 2) the differencebetween total amount of liquid in the bed and the residual holdup, known as the dynamicholdup. Static holdup results from a balance between surface and gravitational effects.Liquid saturation has been reported either as total liquid saturation or dynamic liquidsaturation.Specchia and Baldi (1977) proposed empirical equations for prediction of dynamicsaturation based on defined parameters and routines introduced in the pressure dropsection for the same authors. For 0.005 < d, < 0.05 m and 0.3 < ReL < 3000, and in thehigh interaction regime, they introduced liquid dynamic saturation in terms of parameterZ/’?I’’:where Z = (Rec)’’67/(ReL)°767They also delineated that under the same fluid loads and other conditions of concern,the pressure drop in foaming systems is higher and the liquid holdup is lower than innon-foaming systems.A detailed survey and numerous holdup correlations for foam flow in fixed-beads canbe found elsewhere[7,12,40,70], (Appendix A).Chapter 2. PREVIEW OF INVESTIGATED PARAMETERS2.3 DISPERSION COEFFICIENTDispersion is a measure of deviation or non-ideality from the plug flow condition whichis caused by channeling and recycling of fluids, existence of stagnant regions, and bya nonuniform fluid velocity at different points in the bed macropores. The parameterdescribing the non-ideality of flow and the extent of the mixing of the fluid in the axialdirection is called the ‘axial dispersion coefficient’, or the ‘effective diffusivity’ and itseffect on the performance of the reactor as a whole is described in terms of the Pecletnumber, Pe.Dispersion phenomena tend to reduce the sharpness of the concentration gradientin the fluid which reduces the potential for mass transfer from the flowing fluid to thesolid, and hence, lowers the efficiency of the device. Therefore, those types of dispersiveflows should be avoided or suppressed to improve the overall performance of the unit.In the following, reported literature for nonfoaming systems is discussed, as there is noinformation for dispersion in foaming systems in the literature.The extent of the liquid axial dispersion in packed columns is essentially independentof gas flow rate and depends upon the liquid flow rate, liquid properties, and the natureand size of the packings[75. However, for the case of rectangular geometrical packed-beds, the liquid axial dispersion has also been reported to be an increasing function ofgas flux[81].In rectangular packed-bed electrodes, the dispersion values can be affected by thefollowing specifications and in some instances they might cause dispersion values to riseto an order of magnitude higher than the conventional TRs, under other similar conditions[47].1. for B/dr < 30, which can normally be the case for particle packing, dispersion ismagnified while for fiber packing with B/dr > 30, the general trend of packed-bedsChapter 2. PREVIEW OF INVESTIGATED PARAMETERS 17follows.2. Lack of even distribution of liquid feed and exit across the cell width.3. Variation of electrode packing density in the cell, especially for particle packing.4. Channeling created by bulging of electrode walls due to high operating pressure inthe cell (eg. up to 20 bars).5. Rectangular configuration of PBFEs, is another source of differences for enhancement of dispersion values of 2-2.5 times the dispersion values of conventional packed-bed cylindrical columns[71].Packed-bed electrodes (PBEs) which are the half-cell of packed-bed electrochemicalreactors, have a width to thickness ratio of about 50, whereas typically packed-bed processors have the width to thickness ratio of the order of 1. This results in large dispersioneffects in PBEs.In addition to the above, there exists radial dispersion in packed bed electrodes,perpendicular to the flow. Radial dispersion is normally caused by repeatedly dividedflowing streams as fluid flows around the packings, molecular diffusion, migration ofreactant ions due to potential field across the liquid phase and finally superimposedsecondary radial flow caused by temperature gradients across the bed.Based on the proposed assumptions of limiting current control, with small reactantconcentration, strong supporting electrolyte and isothermal operation, the effect of radialdispersion would be negligible. Also, gas dispersion effects in 3-phase reactors generallyare small, especially under the condition of the negligible gas-side mass transfer resistance. Axial dispersion of both phases in packed columns are practically smaller than thesame in unpacked bubble columns[54,75] (mentioned almost by all investigators). Pecletnumber is significantly lower in 2-phase than single-phase flow in packed-beds; but atChapter 2. PREVIEW OF INVESTIGATED PARAMETERS 18high ReL=100-l00they both appear to approach an asymptotic value of about 2.0[76j.This asymptotic value holds for packed-bed electrodes with single phase flow of eitherliquid or gas[51]. Based on this argument and the asymptotic Feclet number value of 2.0,at high Reynold’s numbers, Cianetto et al. (1973) concluded that ‘axial diffusion anddispersion’ do not have a dominant effect on the overall mass transfer rate in 2-phase flowpacked columns except at very low flow rates, which are likely to be outside the range ofindustrial interest. The following two studies in the nonfoaming electrochemical reactorsare worth mentioning:Fahidy (1985) obtained an approximate analytical solution to the equation of conservation of species in an annular porous bed electrolyser under essentially mass transfercontrol and single- phase liquid flow. He used axial dispersion coefficient values in therange Da =0-50 cm2/s or Fe = 3.7— 00, to obtain simulated relative conversion values forthe dispersed model of: 0.818-1.00 relevant to plug flow, for the parameters and variablesof: UL=5 cm/s, K8 = 0.001 cm/s, a8 = 1000 cm1, h =15 cm, = 0.8.Oloman (1979b) analyzed a nonfoaming 3D-trickle flow-by electrode (2 m high x 0.25m wide x 3 mm thick) packed with graphite particles of 0.30-0.99 mm diameter, with2-phase flow involving reacting and non-reacting gases. The operating range of gas andliquid loads were G = 0.1 — 1.0 kg/m2.s and L = 0.1 — 10 kg/m2.s, corresponding to gascontinuous flow (feeble interaction regime). Based on these flow regimes, he observed aliquid saturation range of /3 = 10 — 90% and decreasing trend of liquid axial dispersionupon increasing the gas load. The author also reported measured dispersion values ofDa = 1 — 4 cm2/s, equivalent to Fe = 10 — 22 in a separate experiment carried in abench scale packed-bed (0.5 x 0.05 x 0.003 m) with air- water system, L = 2.2 kg/m.sand C = 0— 0.14 kg/m2.s.Some other correlations of axial dispersion coefficients (in nonfoaming systems) arelisted in Appendix A.Chapter 2. PREVIEW OF INVESTIGATED PARAMETERS 192.4 ELECTRICAL CONDUCTIVITYFlowing fluid: In packed-bed electrodes with two-phase flow, depending upon the degreeof gas loading, the liquid saturation may range from about 5 to 90 percent. Increasingthe gas load, while increasing the mass transfer coefficients and pressure drop, lowers theeffective conductivity of the electrolyte.Neale and Nader (1973) and Maxwell (1892) investigated nonfoaming diffusive flowprocesses within a homogeneous swarm of spherical particles constituting the dispersiveporous media. They formulated and developed a predictive model for interstitial diffusionprocesses of mass and electric current in a homogeneous and isotropic porous medium,composed of non-conducting or/and impermeable spherical particles possessing arbitrarysize distribution. They derived a unique electrical conductivity and mass diffusivity factorcorrelation of A, with bed porosity c:3—cand claimed its validity over the entire range of 0 <c < 1. For the case of heat diffusionprocesses, due to extra transfer processes into the particle, namely fluid to solid interfacialheat transfer and interior solid phase conduction, the heat diffusivity factor correlationwith bed porosity is much more involved than the other two processes and contains extraresistance parameters.Lemlich (1978) studied the conductivity of 2-phase gas-liquid foam beds and presentedthe conductivity factor:A = EL/3for lean foams, where the structure of the foam was explained as a network of slenderrandomly oriented channels (Plateau border). For the other extreme where EL —* 1, theChapter 2. PREVIEW OF INVESTIGATED PARAMETERS 20author proposed Maxwell’s equation which has the same form as the Neale and Nadercorrelation.Later, Lemlich (1985) presented his correlation for liquid holdup, EL, in a 2-phasefoam bed, in terms of the conductivity factor:3A — 2.5A413 + 0.5A2Lemlich claimed that his later equation is valid for 0 < EL < 1, and at lower values of EL,A approaches his former equation.While this correlation satisfies the extreme values, its recommended applicability isin between the two extremes of 6L Based on experiments performed with different surfactants, the author concluded that there was no discernible effect due to the choice ofsurfactant or its concentration. Currently, no literature exists for the electrical conductivity of foam in foam flow through packed-beds.Solid matrix: The effective conductivity of the solid matrix, o, is highly dependent onthe physical structure of the electrode, as well as its material quality. Felt fiber bedshave porosity in the range of 0.95 for non-compressed bed to 0.7 for compressed bed[40].Hence from electrical conductivity point of view, felt and solid foam matrices may becomparable with liquid phase of flowing foam, with conductivity ranging up to 10 timesthat of the foam. A negative point to mention in simulation of felt matrix conductivityfactor, compared to solid foam matrix, is the non-continuous structure of solid fiberswith touching connections and hence, a contact resistance. Existence of this contactresistance on average and in macro-scale, will perhaps show some major differences fromthe conductivity factor correlation of solid foam matrix.Matte (1987) performed experiments to measure graphite felt matrix conductivityas a function of bed porosity. By applying pressure on stacks of multi-fibrous sheets, avariety of porosities were obtained. Applying electric potential to the porous matrices,Chapter 2. PREVIEW OF INVESTIGATED PARAMETERS 21as a dry cell, the author obtained correlations of matrix conductivity as a function of bedporosity:a) 11 micron fiber felt:U = 453 exp[—3(E’ — 0.586)/(1.3 — e°75)] 0.7< c < 0.95b) 20 micron fiber felt:U = 284 exp[—(E — 0.75)/(0.995 — 0.75 < E < 0.93After choosing proper models for u and ic, one can look into conditions where theoverall effective conductivity of the electrode matrix can be a maximum. This is equivalent to minimization of ohmic potential drop in the flowing phase and solid matrix, andhence increasing local electrode-electrolyte potential difference, or increasing electrodepotential and therefore increasing the space time yield of the ECR. In this context a caseof interest has been treated by Yg’al Volkman (1978), where the solid matrix and flowingphase conductivity factor correlations of Bruggeman were adopted.Chapter 2. PREVIEW OF INVESTIGATED PARAMETERS 222.5 GAS-LIQUID MASS TRANSFERA considerable amount of research has been conducted and published on gas-liquid masstransfer in packed-bed reactors and/or for gas absorption and desorption processes withpacking sizes as low as half millimeter[2,7,28,32].Based on the available literature in packed-beds, it has been found that the rate ofmass transfer increases sharply at the transition region from the low to high interactionflow regime and in this regime the liquid side mass transfer resistance becomes small.Gianetto et al. (1973) and Mahajani and Sharma (1979) suggested that the highrate of mass transfer is particularly due to the strong increase of the available gas-liquidcontact area in the pulsing flow regime. The value of KLa in the pulsing flow regimeis significantly higher than in the gas-continuous flow regime and its value is stronglydependent on the gas flow rate.For packing sizes up to 0.5 mm and fiber packing with foam flow, the objective ofthis study, there is no published information.Foam flow in packed-bed reactors is a fairly new area of investigation. Such reactorsoffer the highest gas liquid interfacial area per unit volume of the bed, about 8-10 timesthat of the conventional packed bed reactors, high gas holdup, low liquid holdup andhence less intruding homogeneous reactions. These specifications are all desirable fortreatment of gaseous reactants.Gas holdup, gas-liquid interfacial area and mass transfer coefficient are the mainparameters determining the rate of the mass transfer. In foam flow reactors, the liquidhas sufficiently low surface tension to produce high gas-liquid interfacial area. But inthe case of using a foaming agent, two opposing phenomena arise; 1) hydrodynamicalteration caused by surfactant due to increasing rigidity of the interface and causingreduction of interfacial turbulence, resulting in suppression of interfacial mass transfer;Chapter 2. PREVIEW OF INVESTIGATED PARAMETERS 232) the physico-chemical effects of changing the property at the interface film due toexistence of the surfactant molecules, which shows up in the form of intrinsic excessresistance to mass transfer at the interface.The advantage of high interfacial area is lowered partly or totally by opposing phenomena. Thus in the case of fast reactions, when the gas-liquid resistance is the controllingstep, advantage of higher interfacial area in a foam reactor may be completely lost andthese reactors are not suitable. In the case of slow reactions, however, the advantage ofincreased interfacial area is partially lost, such that the mass transfer rate will still be2-4 times higher than that in conventional reactors[76].After all, the operating cost due to surfactant may still overweigh the advantage ofhigh mass transfer rates. When the cost of surfactant is reduced and other side—effects arenot significant the foam reactors could be quite promising alternatives for electrochemicalprocesses with gaseous reactants.Biswas et al. (1987) conducted research to investigate the effect of surfactant in thermochemical foam bed reactors. They developed a model to determine the effect of surfaceresistance arising due to the presence of surfactant, on gas absorption accompanied bya chemical reaction in a foam bed. They found that surfactant molecules impose significant resistance to the rate of mass transfer at gas-liquid interface in an experiment ofabsorbing lean carbon dioxide gas in sodium hydroxide solution containing three differentsurfactants. In their formulation they assumed that surfactant molecules preferentiallyabsorb into the gas/liquid interface and constitute a very thin layer. This surface layeroffers a resistance to mass transfer, resulting in a drop in concentration across the interface film. After this transfer step they employed penetration theory for gas-liquid contacttime along the bed for the completion of penetration and absorption processes.The authors chose three surfactants of 10% TEEPOL, 240 PPM sodium lauryl sulfateand 1260 PPM Triton X-100. The fitted k1 values, some of which were consistent withChapter 2. PREVIEW OF INVESTIGATED PARAMETERS 24others’ experimental values, were reported as: 0.0305 , 0.157, and 0.375 cm/s, respectively. They also concluded that the variation of k1 values with surfactant concentrationwere negligible. Further, it was seen that the adverse effect of foaming agent on masstransfer could be minimized through a judicious choice of surfactant.Several other cases of the foaming systems for gas liquid mass transfer are given inAppendix A.2.6 LIQUID-SOLID MASS TRANSFERApplication of surfactants is accompanied by complex interfacial phenomena, affectingboth mass transfer coefficients and interfacial areas[19,59]. Based on the intrinsic qualityof surfactants, these materials after addition to the solution have the tendency to movetoward the liquid external surface, i.e., to gas-liquid interface region. This appearanceis the fundamental reason for excess mass transfer resistance at the gas liquid interfaceand the model adopted by Nguyen Ly et al. (1979) and others.Hence, based on the above argument, it is concluded that as far as liquid-solid interactions, mass transfer, and liquid phase dispersion are concerned, in modeling onecan assume that the solid electrode is flooded by bulk solution with all the liquid-solidmass transfer characteristics like the conventional PBRS with no surfactant in use, exceptfor the electric potential field effects, where applicable. This ideally predicted conditiondoes not exist in practice and surfactant substances have shown inverse effects due toadsorption and therefore, lowering the electroactive electrode surface efficiency[60].Addition of surfactant decreases the liquid surface tension, which increases liquidfoamability and solid matrix wettability, but causes an increase in the mass transferresistance for both the gas-liquid and liquid-solid interfaces. These circumstances willhave the least undesirable effects on mass transfer resistance, if there is an appropriateChapter 2. PREVIEW OF INVESTIGATED PARAMETERS 25amount of surfactant to produce a single layer at the interface. In addition, if the aboverequirements are met, the solid surface roughness will have a positive wetting effect, also.Hence, the proper amount of surfactant is crucial to the interfacial mass transfer rates.If excess surfactant is added, the aforementioned benefits of single layer adsorption maybe lost. In such a case excess layer adsorption and precipitation of waxy material mayresult; thus, lowering the electroactive surface efficiency[50].For a packed-bed reactor with foam flow, there is no literature available on the liquid-solid mass transfer coefficient. However, for nonfoaming PBRs much can be found inliterature[13,31,74], as is illustrated in the following report, by measuring the dissolutionrate of the slightly soluble benzoic acid tablets into the water.Satterfield et al. (1978) used cylindrical benzoic acid particles 0.3 x 0.6 cm, water system with UL=O.O5-2.cm/s andU0=O-l60 cm/s, and emphasis on flow pattern, proposedK3 correlation in pulsing flow regime in trickle-bed reactors:K3d=D a3 PLDwhere d is the diameter of a sphere having the same surface area as the particle underconsideration, K0 is the liquid phase Kolmogoroff number defined as:K0= (iXPw/h)pdULEL/ILChapter 3STATEMENT OF PURPOSEThe effect of configuration and electric potential gradient are the main features whichdifferentiate the PBECRs from PBRs. Associated with these two specific features, theremay be larger dispersion[56,80] and bad heat effects in PBECR[87] (due to ohmic potential drop).One of the desirable features of the packed-bed electrode is its high space-time yield.However, the achievement of this goal depends on the mass transfer process and theohmic potential drop in the working electrode.On the one hand, it is the mixing of the fluid in the flow direction, the longitudinaldispersion, that influences the axial concentration profiles of flowing liquid with subsequent decrease of mass transfer driving force. On the other hand, because of the ohmiclosses, the local electrode-electrolyte potential difference, which is the driving force forthe electrochemical reaction, varies through the electrode. This results in a wide rangeof surtension’, with consequent reduction of the electrochemically active portion of theelectrode.A judicious choice of supporting electrolyte may reduce electric potential gradienteffects, such as ohmic voltage drop, wide electrode surtension potential (and ionic migration, which complicates reactor modeling) [87]. These effects as well as dispersion, whichalso complicates reactor modeling, have a negative effect on reactor performance.The study of hydrodynamic parameters and transport properties at high gas holdup1Surtension, defined as the overpotential difference of the desired reaction from the face of the bedto the back of the bed.26Chapter 3. STATEMENT OF PURPOSE 27in packed-bed foam flow-by electrodes (PBFFEs) could be useful because of the positiveeffect of foaming on gas to liquid mass transfer, and in maintaining excess reactive gasto sustain the electrode reactions[69]. Foam flow also may decrease the axial dispersion[80,811 that always occurs in this type of ‘plug flow’ reactor, and this could improveprocess efficiency in electrosynthesis. The main feature of this research is to observethe effects of foam flow on the gas to solid mass transfer capacity and liquid-phase axial dispersion coefficient in packed bed electrodes. Using foam flow with an efficientpacking material, like carbon felt with fairly uniform texture, dispersion problems maybe reduced. While important dispersion relations have been explored for most cases ofsingle-phase flow electrodes in terms of Sherwood number-Peclet number correlations [511,there is no information available for electrochemical packed-bed systems, with foam flow.To design electrochemical reactors, one needs the values of the fluid dynamic parameters and transport properties for the specific conditions of operation throughout thereactor. In order to obtain such information, it was proposed to measure the pressuredrop, liquid holdup, foam effective electric conductivity, axial dispersion andoverall mass transfer capacity, in graphite fiber felt packed bed electrodes with foamflow. The three independent variables of this research were chosen as bed porosity, gasload and liquid load, which are the main factors affecting the performance of flow-bypacked-bed electrochemical reactors, through the hydrodynamic parameters and transport properties investigated in this research.Chapter 4EXPERIMENTAL APPARATUSFigure 4.1 shows the experimental flow diagram employed to measure the pressure drop,liquid holdup, axial liquid dispersion coefficient, flowing foam electrical conductivity andthe overall mass transfer capacity for graphite fiber bed electrodes, under foam flowconditions. Basically , the setup can be divided in two parts: (a) the experimental cellblock and (b) the remaining elements which are common in all the experiments. Detailsof the cell block setup, which varies in each case will be discussed in the next chapter.Description of the apparatus components, common to both parts of the setup are:1. A 20 liter electrolyte feed tank (polyethylene material), with supply line to thepump, gas exhaust line to fume hood and finally an inlet recycling line from thesystem, for those experiments permitting the electrolyte to be recycled, to avoidwaste.2. A Milton Roy pump with a pressure relief valve # 1 (set at 160 psig), to pump theelectrolyte from the supply tank to the experimental system. The electrolyte flowrate was regulated by the pump rotary percentage dial settings. The calibrationdetails of the pump is given in Appendix E.3. A LAUDA thermostatic water bath in series with the check valve # 2 to regulatethe cell inlet foam temperature at 22°C, for all the measurements of this study.The set point of the controller of the bath was regulated manually until the desiredinlet foam temperature was reached. Once the inlet foam temperature reached its28AChapter 4. EKPFJ?JMENTALAPPAPATUS 29RELIEF VALVEPNEUMATIC CONTROL VALVE118” NEEDLE VALVECHECK VALVEFOXBORO PRESSURE CONTROLLERGAS CYLINDER PRESSURE REGULATORTRANSMITTING LINE SWITCHTEE JOINT STREAMAT: AMBIENT THERMOMETERCR: COLE PARMER ROTAMETERGG: GAS ROTAMETER PRESSURE GAUGEIT: CELL INLET DIAL THERMOMETERIS: CELL INLET PURGE STREAMMR: MATHESON ROTAMETERP1,P2,P3,P4: PRESSURE GAUGES ALONG CELOS: CELL OUTLET PURGE STREAMP1: INLET PRESSURE GAUGEP0: OUTLET PRESSURE GAUGEPG: PRE-FOAMER PRESSURE GAUGE3-WAY VALVEPCL!HFigure 4.1: Experimental apparatus flow diagram.Chapter 4. EXPERIMENTAL APPARATUS 30desired value for the first run, the variations of the later runs were not significantand were quickly adjusted.4. An electrolyte bypass line which branches off the electrolyte supply line right afterthe check valve # 2 joined with the cell effluent recycled stream to the feed tank.This bypass line was used for fast system pressure relief at the end of the course ofthe operations or at the time of bed porosity measurements, to expedite the systemupstream gas purge trials (see details in the porosity measurement procedure, inAppendix C).5. A pre-foamer unit consisted of a basic cell (descriptions are given in next chapter)and the associated 3-way valve # 6, thermometer IT and the adjoined pressuretap, installed at the closest distance of the 3-way valve # 7, ahead of the cell block.The pre-foamer cell, which was aimed at producing quality foam from the gas-liquid stream supplied to the cell block, was assembled with 1/4” Neoprene gasketin which was embedded 1/2” graphite felt packing. Design details of the basic cellcomponents are given in Appendix B. The 3-way valve is a switch of the foam entrylevel either from the base or from the middle of the cell. The foam entry level iscritical to the foam quality and affects the cell upstream pressure, and consequentlythe pressure along the cell, by ± 10 psig. The thermometer reading was assumedfor the inlet foam stream temperature.6. The experimental cell block is separated from the flow stream by 3-way valves # 7& # 8. These valves enable the cell stream to be placed in either the experimentalsystem stream, the side out stream position or to be blocked and isolated. Theseline switch modes were extensively used at the time of the porosity and holdupmeasurements, and cell cleaning (before its removal for modifications and/or maintenance). For example, when the valve is in the outside stream position, the cellChapter 4. EXPERIMENTAL APPARATUS 3can be flushed with water (for cleaning) and blown with air. These treatments areessential parts of the porosity measurement experiments at each cell setup step, described in the next chapter. The experimental cell block composition differs for eachexperimental measurement, and the details will be given under the correspondingprocedure, in the next chapter.7. A pressure and flow synchronizer unit installed at the outlet of the cell block,consisted of a basic cell and the three associated outlet lines: a line with reliefvalve # 10 set at 100 psia; a line with air-to-close pneumatic control valve (Northern Columbia Processes Equipment); and the by-pass line with needle valve # 9,installed in order from bottom to the top. The cell in this unit has the same composition and configuration as the pre-foamer unit and is installed right after the3-way valve # 8. The role of this cell was to minimize the end effects caused byperiodic control valve discharges and hence provide less a disturbed flow pattern ofthe measurement cell, at the exit. The set point pressure transmitting line of theFoxboro controller (PID) and the outlet pressure gauge, P0, were jointly placedimmediately after the 3-way valve # 8, ahead of the synchronizer unit. The controller set point for most of the runs were chosen at 4 bar (40 psig). The reliefvalve # 10, was installed to assure the safety of the system’s pressure relief againstany discharge failure of the system.8. Finally, the effluent foam from the synchronizer unit, depending on the experiment,is either of the quality to be recycled directly to the feed tank or to be led to thewaste through the flow line switch # 12. Also a 3-way valve # 11 is installed oneffluent stream line to accomplish the stream samplings for post chemical benchanalysis, or other purposes.Chapter 4. EXPERIMENTAL APPARATUS 329. Two oxygen and nitrogen gas cylinder reservoirs equipped with the correspondingregulators.10. Two sets of precision Cole Parmer (No 42-15 Ser. No 015 279) and Matheson (modelNo 7630 - 602) rotameters, in series, to measure the gas supplied from pressurizedgas cylinder to the system. The gas flow rate is regulated through needle valve# 4 and check valve # 5 before joining the electrolyte stream to make up thetwo phase stream, heading to the pre-foamer unit. These rotameters were bothcalibrated with nitrogen and oxygen gases, separately, details of which are given inAppendix E.11. Mercury thermometer, AT, installed next to the gas rotameters, to measure theambient temperature, which was assumed to be equal to the pressurized inlet gasstream temperature. Dial thermometer IT, was used to monitor the inlet foamtemperature to the cell.12. Two stainless steel pressure gauges (4 1/2” dial CPW - 160 psig) installed at outletand inlet to the cell, before and after the three-way valves, respectively. Anotherstainless steel pressure gauge (4” dial MARSH - 200 psig) also was installed aheadof pre-foamer to safely monitor the possible highest pressure buildup on the system.A brass pressure gauge (2 1/2” dial WIKA - 200 psig) was installed just after therotameters, to measure the gas pressure at the rotameters reading.All the fluid and pressure transmitting lines were 1/4” tubing of either stainless steel orpolyethylene materials. Fittings were all of stainless steel, to protect from alkali corrosionand pressure effects. Detailed specifications of the parts utilized in this system are givenin Table B.4.Chapter 5EXPERIMENTAL PROCEDURES5.1 GENERAL DISCUSSIONS:In this section general experimental procedures are described in conjunction with thestudy and measurement of two hydrodynamic parameters and three transport properties:• pressure drop• liquid holdup• axial liquid dispersion• foam electrical conductivity• overall mass transfer capacityThe experiments were carried out in systems comprised of packed bed cells with two-phase up-flow of gas and liquid, under complete foaming conditions. In all experiments,1/2” Carborundum graphite felts with 20 micron fiber diameter were used as packingmaterial. The three independent variables chosen were the liquid load, the gas load, andthe porosity of the graphite fiber bed. Depending on the viability of the experiments,between 3 and 6 levels for gas and liquid variables and 3 levels of porosity have been testedthroughout the studies. The feasible operating ranges of the gas and liquid loads weredetermined by both the operating feasibility of the equipment (e.g. range of the pressuregauges) and the foam stability pressure limits (2.5 - 12 bar 20 - 160 psig). Thesecritical upper foam pressure limits were determined by early experiments with longer33Chapter 5. EXPERIMENTAL PROCEDURES 34cells, where pulsing patterns were noticed in the vicinity of 12 bar (160 psig) pressurezone. The lower limit was identified from observation of the stability of the foam frontlimit in the vicinity of the outlet section of the bed at different outlet pressures.In the following, the major common procedures of all case studies are described;where the specific procedures will be described later in the sections particular to eachcase study.5.1.1 Preparation of the Liquid Solutions, Gaskets, Packing, Diaphragm andthe Membrane.Three different aqueous solutions were utilized throughout the experiments: A-) 1 Msodium hydroxide solution of 0.1 % v/v of Tergitol, as surface active agent (surfactant),utilized as the liquid phase of the flowing foam in all experiments except for dispersionmeasurements; B-) solution of 0.1 % v/v Tergitol in water, utilized as liquid phase indispersion studies; C-) solution of 1 M sodium hydroxide, used in cell porosity measurement. Details of the preparation methods of the above solutions are given in Appendix B.The surface tension of of 1 M MaOH solution of 0.1 v/v % of Tergitol was measured as30 dyne/cm at 22°C. No measurements were made of contact angle of any of the abovesolutions on the graphite fibers. Howevere, observations of the capilary rise of the Tergitol solution into the hydrophobic graphite felt show that the graphite is rapidly andeffectively wetted by these solutions. Physical properties supplied by manufacturer ofTergitol and its water solution are:Pure Tergitol:molecular weight 682density at 20°C 1.062 gr.cm3viscosity at 20°C 338 cpChapter 5. EXPERIMENTAL PROCEDURES 35Water solution of 0.1 v/v % of Tergitol at 25°C:critical micelle concentration, cmc 0.24 mM ( 0.15 v/v %)surface tension 31 dyne/cmGaskets used in these experiments were cut from two different materials: Neopreneand Durabla. Three different Neoprene gasket thickness (1/8”, 3/16”, & 1/4”) were usedto accomplish three different porosity levels of the cell packing. Durabla gaskets of 1/16”were utilized in the anolyte compartment, to embed the stack of stainless steel screensanode. Cathode packing was cut from 1/2” Carborundum graphite felt composed of 20micron diameter fibers. Details of the procedures and the individual specific sizes aregiven in Appendix B.Diaphragms and membranes were prepared and treated with alkali solution of wetting agent, before placement in the cell for utilization. The details are explained inAppendix B.5.1.2 Setup of the Experimental Cell Block Consisting of the “basic cell” andthe Associated Electronic and Non-Electronic Components.The procedures belonging to this topic play the most significant role in each investigation;since the ease and correctness of the operation and hence the results, all depend on theprecision of the cell block setup. The basic element of the cell block in each one of fiveinvestigated systems, is the assembled cell itself, at which the simplest is named the “basiccell”. Here, the basic cell is defined to be a closed vessel composed of a sheet of graphitefelt packing placed in a Neoprene gasket which is sandwiched together between plexiglasslabs serving as the front and the back. The basic cell is tightened and held together by1/4” stainless steel bolts, under uniform 50 kg-cm torque, applied by a torque wrench.This amount of moment was the minimum requirement for the cell to be sealed with noleakage in all the experimental runs. In the assembled cell, the employed gaskets had aChapter 5. EXPERIMENTAL PROCEDURES 36front plexiglas slab cross sectional viewof basic cellback plexiglas slab andother partsstainlesssteelspacerplexiglasslabFigure 5.1: Schematic presentation of the basic cell.thickness, which did establish a porosity in the range of the experimental and practicalvalues. Three different adopted gasket sizes in this work were 1/8”, 3/16”, and 1/4”.Four 1/4” wide steel spacer bars were also placed surrounding the gasket to ensure thestability of the embracing gasket from possibility of creeping displacement or rupturingand bursting, since during the course of the operations the cell pressure can approach12 bar. The side spacers were supported by bolts from two sides, and the top and thebottom ones were aligned and mounted by 1/8” pins along the edges of the back slab (thegasket was in loose touch with the surrounding spacers, at the time of the assembly). Aschematic presentation of the basic cell is shown in Figure 5.1. Details of the technicaldrawings of the gasket and the plexiglas slabs are given in Appendix B. The basic celloutlined above corresponds to the real cell used in the holdup measurement case. Thecells used in any other experimental measurements are appropriately modified versionsNeoprenegasketgraphite—fiber bedChapter 5. EXPERIMENTAL PROCEDURES 37of the basic cell. As the other components of the cell block are numerous and vary foreach one of the five case studies, the details and the assembly procedures of each of themodified cells will be discussed in the related sections.A cell assembly was considered successful if it operated satisfactorily during the experiments. Such a cell demonstrated a fully developed foam flow with no visible bypassand channeling along the edges of the gasket or across the the packing. The existence ofoperating defects would lower the pressure drop along the cell, generating a false pressuregradient and no significant changes upon the variation of the gas and liquid loads wouldbe observed. For a successful assembly of a cell, i.e., a cell with a satisfactory operation,several points must be considered. One is the possession of a precisely cut Neoprenegasket; a second but not of less importance is the uniformity of the flow distribution, atthe entrance and exit of the packing. For this purpose, a gap of about 2-3 mm betweenthe gasket and the packing at each end of the packing was allowed by cutting the packingshorter, rather than an exact fit into the gasket. Also, in addition to the aforementionedgap allowance, a 1/8”X1/8” bore into the front slab at the exit and entrance was madeto further facilitate the uniformity of the foam distribution (in the case of the closing ofthe gaps by plugging or possible small upward packing shift). These bores were coveredby electrode in the cases of conductivity and mass transfer measurements, and henceare not in effect. The details of the layouts of the spacing gaps and the bores, can beobserved in Figure CJ.The assembled cell in the cell block was connected to the 1/4” tubing flow systemvia a pair of tapered 1/8” NPT Swagelok fittings installed on front Plexiglas slab, as theinlet-outlet to the cell, whence the whole system (including the modified cell block) wasready to proceed to the next stage of the experiment.Chapter 5. EXPERIMENTAL PROCEDURES 385.1.3 Conduct of Experiments and the Post-Chemical Analysis.Experiments were performed for determination of each one of the 5 aforementioned objective measurements on suitable experimental systems. In such systems the cell blockwas specially setup, including the modified cell for that particular measurement. Withreference to Figure 4.1, each measurement commenced with the following common startupsteps:1. Closed the bypass valve #‘s 3 and 9.2. Opened the air to outlet pneumatic control valve (air-to-close valve).3. Adjusted and started the electrolyte supply pump.4. Turned on and set the thermostatic bath at 22°C, and in approximately 10 minutes,a steady inlet temperature (thermometer IT) reading equal to 22°C could beenmaintained. Manipulation of the bath controller setting allowed for adjustment oftemperature should readings deviate from set point. The temperature 22°C hadbeen chosen as the fluid inlet temperature for all the experiments throughout thiswork.5. Opened the gas cylinder and regulated it at about 210 psig. This allowed for 10 to15 psia drop within the connecting lines to the rotameters.6. Opened the gas needle valve # 4 and regulated it simultaneously with rotameterback pressure, GO, in the vicinity of 195 psig target.7. After step 6, waited about 5 minutes and simultaneously watched the trend of thepressure value at inlet area, PT or P1. The magnitude of this pressure would suggesta proper setting of the 3-way valve # 6 for an optimum performance of the cell.Chapter 5. EXPERIMENTAL PROCEDURES 398. In about 10 minutes from the start of the opening of the gas to the system, a fullydeveloped foam flow was expected to be established and the steady state operationwas attained. Steady state operation is reached when the gas pressure and gasrotameter readings, all the gauge board readings are constant values at continuousoperation.The startup procedure is successfully concluded when fully developed foam flow (nochanneling or swirling) at steady state condition had been established. Normally, afterabout 5 to 10 minutes, steady state operation was observed and suitable conditions formaking the particular run based on the experimental program were achieved. At such anoperating condition, the system was said to be operating satisfactorily with a successfulsystem setup. If the cell foam flow condition was violated, the operation was pronouncedunsatisfactory; the cell was removed from the cell block and necessary adjustments toovercome the mal-operating behavior were tried. The adjustments in this stage werenormally on the maintenance of the gasket edges and the packing edges or sometimes byaddition of extra tiny spacers behind the main ones. After the readjustment, the cell wasput back into the system and its operation was tested by repeating the startup steps. Thetest and startup steps were carefully repeated until satisfactory operation was attained.After achieving satisfactory operation, the system was ready for the operator to measure the bed porosity and to make experimental runs.The bed porosity level of the successfully assembled cell, where the precise valueof the porosity defined as the percentage of the void space of the packed bed must bedetermined, is set with the size of the gasket already placed in the cell. The quick inletoutlet valve closing method of the flooded bed with electrolyte was employed for theporosity measurements in all experiments, except for mass transfer measurements wherethe porosity was estimated by the indirect mathematical method. The details of theseChapter 5. EXPERIMENTAL PROCEDURES 40methods are given in Section CJ.Experimental runs were performed according to the operating tables listed in Appendix Dand in the following order:1. Adjusted the gas flow rate.2. Adjusted the liquid flow rate.3. Waited until system steady state conditions, including cell block instruments, wasattained.4. Using experimental instruments of the modified cell block, the specific measurements were recorded5. Took all the samples for post chemical analysis, where applicable, Performed chemical analysis and carried out related and required mathematical analysis.6. Changed the gas and liquid rates to the next scheduled run settings.7. Repeated steps 3 to 7 until all the runs with the present gasket were satisfactorilycompleted.8. To obtain similar data for another bed porosity, removed the cell from the cellblock, dismantled the cell and reassembled it with the next scheduled gasket. Putthe cell back to its position in cell block and began again with instructions fromstartup steps of the conduct of the experiment. A case was completed when all theruns were made with all three gaskets.The next measurement started with modification to the cell block and continuedwith the instructions of this section from the beginning. In the following sections of thischapter, the five case measurements are discussed in series, with the details of proceduresspecific to each case.Chapter 5. EXPERIMENTAL PROCEDURES 45.2 Case I- Pressure Drop MeasurementsThe purpose of this investigation was to measure pressure drop for foam flow, in packedbed cells. The schematic drawing of the experimental cell block used in the pressuredrop studies is shown in Figure 5.2. The liquid and gas used were 1 M sodium hydroxidesolution of 0.1 % v/v Tergitol and nitrogen gas. In these measurements, the cell blockconsisted of a modified version of a large size basic cell. Modifications of the cell blockwere made as follows and in conjunction with Figure 4.1:1. The inlet and outlet fittings were replaced with tapered 1/8” NPT - 1/4” tubingSwagelok tees, and connected at the outlet to the pressure gauge P4 and at theinlet through the PI/Pi line switch #13, to pressure gauge P1.2. Two extra intermediate pressure taps along the cell were installed and connectedto the pressure gauges #2 and #3 via tapered 1/8” NPT Swagelok fittings. Thereadings from these taps, as their locations are specified on Figure 5.2, allowedfor judgment of the pressure variation along the cell (linear or otherwise). Theassembled modified cell was connected to the remainder of the flow system and inthis way the cell block setup was completed.modifiedbasic cell .—______Chapter 5. EXPERJMEW1AL PROCEDURES 42cellpressuregauges30050T.Figure 5.2: Cell block assembly for pressure drop measurements.Chapter 5. EXPERIMENTAL PROCEDURES 435.2.1 Conduct of Experiment:After the completion of the cell block setup the experiment commenced with the startupsteps. When startup was satisfactory, experimental runs were made according to theexperimental program listed in Table D.1. The recorded data included the readings ofthe pressure gauges P, P1 , P4, P0, the pump dial, the gas rotameter ball position,the rotarneter gas pressure, PG and its temperature, TG.After completion of all the runs with a gasket, the cell was removed from the cellblock to precisely measure the bed porosity. To do this, the inlet-outlet tees were replaced with male connector fittings and the middle pressure taps were filled up to slabinterior surface level with removable sealy putty and closed with 1/4” plugs. The cellwas then reconnected back to the flow system. The porosity of this prepared cell, whichin effect is a basic cell, was the porosity of the cell in pressure drop measurements forthat used gasket.Hence, by using three different gaskets in the modified cell and the above outlined procedures, three sets of measurement were conducted to obtain the complete pressure dropdata (listed in Tables (D.1-3)).No measurements of pressure drop were made without the surfactant. However,several observations were made of pressure drop with two phase flow under nonfoamingconditions and with single-phase gas or liquid flow. In these cases the pressure gradientshowed low values (of the order 1 bar/rn) for nonfoaming flow through a packed-bed.Chapter 5. EXPERIMENTAL PROCEDURES 445.3 Case II- Liquid Holdup MeasurementsThe purpose of this experiment was to measure the liquid holdup in packed bed cells.Liquid holdup is the liquid filled volume fraction of the bed under foam flow condition.The schematic drawing of the experimental cell block used in holdup studies is shown inFigure 5.3. The liquid and gas used in this case were 1 M sodium hydroxide solution of0.1 % v/v Tergitol and nitrogen gas.In holdup measurements, the large size basic cell was connected to the remainder ofthe flow system through a pair of tapered 1/8” NPT Swagelok male connector fittingsat inlet and outlet of the cell. The cell block consisted of the cell and the 1/4” tubingextension line from the 3-way valve #8 leading into a 25°C or 500 mL washout collectinggraduate cylinder.Chapter 5.E1YPERJMEtVT4L PROCEDURFS 45outletshout graduatecylinder///// / / / / ///in letbasic ceIl—Figure 5.3: Cell block assembly for liquid holdup measurements.Chapter 5. EXPERIMENTAL PROCEDURES 465.3.1 Conduct of Experiment:After the completion of the cell block setup, followed by satisfactory conclusion of thestartup steps, experimental runs were done according to the experimental design Tables(D.4-6). The quick closing valve method was adopted for holdup measurements.In each run the recorded data consisted of quick readings of the pressure gauges, P,P1, P0, the pump dial, the gas rotameter ball position, the rotameter gas pressure, PGand its temperature, TG. Immediately after these readings, the 3-way valves #7 and #8were simultaneously closed, (quick closing valve method) to isolate the foam content ofthe cell. This was followed by shut down of the supply pump and a full closure of theinlet gas valve # 4 to the system. Then the system’s pressure was released by openingthe needle valves #3 and # 9. Hence the system was idled and the foam entrapped inthe cell. The target of this method was to measure the electrolyte content of the packedportion of the cell. The total entrapped foam was first cleanly washed out with tap waterand collected in the 500 mL graduate cylinder. Then with pressurized air, the residualswere blown out and added to the washout. The collected washout volume was carefullyread and recorded and kept for electrolyte content analysis. Finally, the 3-way valveswere switched from washout loop to the flow system and the next run was ready to begin.The liquid holdup was obtained by titration of the collected washout solution in asimilar titration method to the porosity measurements. A sample calculation is given inAppendix C.Chapter 5. EXPERIMENTAL PROCEDURES 475.4 Case Ill-Dispersion MeasurementsLiquid longitudinal dispersion was investigated by the well established traditional dynamic method, which consisted of analysis of the response to an impulse tracer injection(Levenspiel, 1972) of foam flow in packed bed cells. The liquid and gas used in thiscase were an aqueous solution of 0.1 % v/v Tergitol and nitrogen gas. The tracer wasa 0.1 M solution of sodium hydroxide in distilled water. The schematic drawing of theexperimental cell block used in this study is shown in Figure 5.4. The cell block in thisexperiment consisted mainly of three parts as follows:1. The assembled modified cell, which was connected to the remainder of the flowsystem through a pair of tapered 1/8” NPT Swagelok fittings at inlet and outletto the cell. Startup steps were conducted on this cell before addition of the nexttwo parts until a satisfactory operation was achieved. For the high and zero levelsof porosity, large cells were used and for the low level of porosity a small cell wasused.2. The tracer injection system consisted of a 250 mL bottle tracer reservoir filled with0.1 M NaOH tracer solution connected to the bottom of a high pressure vertical5/8” boiler glass tube through the 1/4” stop-cock valve. The tracer solution wasled from the bottom of the glass tube to the injection port of the cell inlet througha precision 1/8” metering valve used for impulse tracer injection shots. A gasline connecting the gas cylinder to the top of the glass tube provided the requiredinjecting force at the time of each injection. The glass tube was fitted and sealedwith 0-rings and rubber cushions at each end with female 5/8” tubing - 1/8” NPTcoupled with a male 1/8” NPT - 1/4” tubing. This was all held in a 1/16” aluminumframe and fixed to the wall.Chapter 5. FXPERJMFJ’/TAL PROCEDURES 48Impulse TracerResponseI packed bed plus conductivity cell4fr“V 2: conductivity cellE 50J00-508apsed Time, secondHr220 40 60L.._411 11111POWER MAINSPOWER BAR3-way valvestop cock valvemetering valveneedle valveFigure 5.4: Cell block assembly for axial dispersion measurements.Chapter 5. EXPERIMENTAL PROCEDURES 493. The tracer detecting system consisted of the electrical conductivity flow cell installed at the cell outlet and wired to the conductivity meter which sent the signals to a 386 personal computer (IBM PC compatible) for data acquisition. ALABTECH NOTEBOOK menu driven software was installed to receive the signalsthrough an interface board (DAS-8PGA) and its terminal board.5.4.1 Concepts and Means of Experiment:The dispersion experiment was carried out by injecting a shot of tracer solution ( 0.1mL ) into the foam flow stream at the cell inlet from the injection port. As can beseen, the overall tracer path from inlet to the detecting point of the conductivity cellmay be considered to consist of two independent closed vessels in series, causing theresulting dispersion to be a convoluted value. The closed vessel assumption is justifiedfrom observation of the flow at the inlets and outlets of these vessels. At these locationsthe flow was viewed through transparent tubing and showed a continuous, smooth anduniform ‘plug flow’ pattern, regardless of the interior flow patterns of these vessels. Hence,the overall spread of the response detected by the conductivity meter (Through the WallMethod, Levenspiel, 1972) represents the sum of the variances of two vessels in series (firstvessel, the cell, to be from inlet to outlet and the second vessel, the conductivity cell,to be from outlet to the tracer detecting point). Therefore, deconvolution of the overalldispersion is the means of extracting the desired cell dispersion value. To this purpose,experiments were carried out to measure the overall dynamic parameters of two vesselsin series and the dynamic parameters of the second vessel, separately. This was usefulfor the deconvoluting process through additivity principles of the variances and meanresidence times. The cell block setup required for the overall parameter measurementswas described in the previous section and the cell block setup for measurements of thedynamic parameters of the second vessel is obtained by moving the injection port fromChapter 5. EXPERIMENTAL PROCEDURES 50cell inlet position to the cell outlet position. The dispersion measurement experimentsfor the second vessel (the conductivity cell) were performed in a similar way to the overalldispersion measurements.Having the cell block apparatus installed with a satisfactory operation, work enters itsfinal 3 steps of: a)- Preparation of tracer injection system; b)- Setup of the conductivitymeter; c)- Setup of the LABTECH NOTEBOOK logging program.a- The purpose of this phase was to purge the tracer transmitting lines of gas.1. The injecting metering valve was closed.2. The needle valve #1 was closed and needle valve #2 was opened for ventilation.3. The reservoir solution bottle top taken off and the bottom stop cock valve washeld open until the glass tube filled with tracer solution. It was then closed.4. Needle valve #2 was closed and needle valve #1 was opened to the pressurizedgas line.5. The metering valve was opened gradually and cautiously, letting the tracersolution transmitting line to the injection port to be purged of gas and filledwith tracer solution.6. The metering valve was closed and the tracer injecting system filled with tracersolution under pressure (about 210 psig) was ready for injection.b- By preliminary tests for each quick injection, and monitored by a multimeter, it wasfound that a signal with the strength range less than 150 mV could be obtainedfrom the conductivity meter (if the cell constant was set at the KC = 0.1). Thissetting produced an acceptable signal range to be logged into the terminal boardand had the highest operating precision for this instrument.Chapter 5. EXPERIMENTAL PROCEDURES 51c- The computer and the monitor were switched on. In NB sub-directory, the file NB.exewas executed. Thom the menu bar, SETUP, SAVE/RECALL and assignment of thename OVERALL DISPERSION (or SECOND VESSEL DISPERSION, dependingon the path under measurement) were performed for the logging program file to besetup. Details of setting up the program are listed in Appendix G.5.4.2 Conduct of Experiment:After the completion of the cell block setup, satisfactory conclusion to the cell startupsteps and the final three preparatory steps, experimental runs were performed, accordingto the experimental design Tables (D.7-9). The impulse tracer injection technique wascarried out in each run at the steady state conditions. The following steps outline theprocedures to measure the liquid axial dispersion coefficient.1. The computer and the monitor on, the cursor at NOTEBOOK sub-directory, theconductivity meter on, and the system running steady at some scheduled pumpand gas rotameter settings.2. The GO command was executed and the following appearance of the stand byblank monitor display, with coordinates systems of time (second) and signal (mV).3. The pressure gauges, P, P1, P0, the pump dial, the gas rotameter ball position,the rotameter gas pressure, PG and its temperature, TG, were recorded.4. The impulse tracer was injected and immediately the computer was triggered bypressing the keyboard space bar.5. The trend of the tracer image on the monitor was monitored until the tracer showedclose to a zero offset. This recovery period did not exceed more that several residence times of the vessels (less than 3 minutes in all cases).Chapter 5. EXPERIMENTAL PROCEDURES 526. By hitting the space bar, the image disappeared and cursor sat in NB sub-directory.At this time the signal and the elapsed time along with three other cumulatedmoments were recorded on the output file a:OUTPUT.PRN. This file was renamedto its corresponding experimental design table RUN ID (for example “EMUGI.”,at the first liquid and gas levels and low level porosity level).According to the experimental design Table D .7, the rest of the runs were made for thepresent cell, following the aforementioned 6-step procedure. Hence the overall dispersionmeasurement experiments were completed. The position of the tracer injection waschanged to the outlet of the cell, i.e., ahead of the conductivity cell. Similar runs basedon the same operating table were performed to obtain logged in response output files: say“L1G1”, corresponding to “EMIJG1” file. In this way a complete run was accomplishedand, the rest of the runs were made to completion, according to the experimental designTable D.7. By this way each pair of response output files (e.g. EML1G1 and L1G1)together contained the information needed in the deconvoluting analysis to obtain thecell variance and its dispersion coefficient. Typical tracer image pairs obtained in theseexperiments are presented on the monitor of Figure 5.4.The cell was removed from flow stream, the gasket was replaced, and the cell reconnected. The aforementioned procedures, starting with startup steps, were repeateduntil all the dispersion measurement data were obtained with three different size gaskets,according to the experimental design Tables (D.8-9).Chapter 5. EXPERIMENTAL PROCEDURES 535.5 Case IV- Flowing Foam Electrical Conductivity MeasurementsMeasuring the effective electrical conductivity of the flowing foam in packed bed cellswas the goal of this experiment. The schematic drawing of the experimental cell blockused in this study is shown in Figure 5.5. The liquid and gas used in this case, were1 M sodium hydroxide solution of 0.1 % v/v Tergitol and nitrogen. The cell block in thisexperiment consisted of two parts.1. The modified cell was made from the basic cell by addition of a pair of stainlesssteel electrode plates backed with a pair of 1/16” copper collector plates. The frontelectrode was installed with 1/8” NPT couplings at the inlet-outlet ports, whichalso served to eliminate utilization of the back sealing gaskets as well. A technical drawing of these electrodes is given in Figure B.4. Also in this cell sheetsof diaphragms were placed at the graphite fiber bed-electrode interface to preventthe electronic charge transfer across the bed-electrode interface. In this way thegraphite fiber bed was held in-between first the diaphragm sheets, second the electrodes, third current collector and finally the Plexiglas slabs. This all was tightenedand held together by 1/4” stainless steel bolts. The assembled cell was tested forpossible direct current leak through the electrode-packed-bed interface by way ofany rupture or other possible flows, at the dry condition under 5-10 DC volt. Iffailed, the cell was dismantled, adjusted and reassembled until correct. The correctly assembled cell was connected to the remainder of the flow system through apair of tapered 1/8” NPT Swagelok male connectors, at inlet and outlet to the cell.2. The power supply system and the electric measuring elements consisted of a Heathsignal generator coupled with a customized power amplifier (built in our departmentelectronic shop). It was used as the AC power source at high frequency (3000 Hz).Chapter 5. EXPERIMENTAL PROCEDURES 54r Imeter j CELLmeterHEATHsignal generatorMICRONTADIGITALMULTIMETERSelectrodecurrent-44modifiedbasic cell_________diaphragmsFigure 5.5: Cell block assembly for foam electrical conductivity measurements.Chapter 5. EXPERIMENTAL PROCEDURES 55At this frequency the Faradic current is zero in the cell and the capacitance effects werenegligible. Two Digital Multimeters were installed to measure the current and the appliedelectric potential across the cell.5.5.1 Conduct of Experiment:After the completion of the cell block setup and satisfactory conclusion to the startupsteps experimental runs were made, according to the experimental design Table D.1O.Preliminary tests with the one Ohm resistance in place of the cell measured unexpectedlydifferent values (less than one) for the one Ohm standard resistance. This unknown effectwas perhaps due to the internal effects of the power amplifier, signal generator, or theirinteractions. Therefore, it was decided to calibrate the power supply system at the cellpoint against the standard one Ohm resistance to obtain the resistance efficiency of theone Ohm standard measurements versus nominal applied power values, I*V. The detailsof the data and the related model correlations are listed in Appendix E.Experimental runs were made according to the following steps:1. The operation began with the startup steps until the satisfactory steady state operation was achieved.2. The signal generator and its amplifier were turned on and regulated to 15 mVelectric potential across the cell by the power generator adjusting sinusoidal knobset at 3000 Hz frequency while monitoring the multimeter connected across thecell.3. When steady state operation of the circuits was reached the readings of the currentand the flow stream indicators; pressure gauges, P, P1, P0, the pump dial, the gasrotameter ball position, the rotameter gas pressure, PG and its temperature, TG,were taken.Chapter 5. EXPERIMENTAL PROCEDURES 56Similar runs were made according to the experimental design Tables (D.11-12) for theother two porosity levels.The measurement of the electrical conductivity of the flooded cell with the sameelectrolyte was also carried out. This gave a basis for comparison to the predicted valuesof conductivity from correlations like that of Neale & Nader (1973).Chapter 5. EXPERIMENTAL PROCEDURES 575.6 Case V - Overall Mass Transfer Capacity MeasurementsThe electrochemical method was adopted to measure the overall mass transfer capacityof upward foam flow in the electrolytic cells packed with Carborundum graphite fiberbeds, at two porosity levels “ZERO” and “HIGH”. Electrolyte and gas used in this casewere 1 M sodium hydroxide solution of 0.1 % v/v Tergitol and oxygen. In this case, themeasurement of the pivotal reaction among some possible ones was the cathodic reductionof oxygen to hydrogen peroxide on the graphite electrode. A simple two-reaction modelinvolving the electro-reduction of 02 to HO and the parallel reduction of H20 to H2was realized among several other hypothetical multi-reaction models through extensivemodeling search tries on the data.The schematic drawing of the experimental cell block used in this study is shown inFigure 5.6. It basically consisted of three parts:1. The electrolytic cell was composed of anolyte and catholyte half cell compartmentsseparated by a Nafion 214 cationic membrane. The cathode compartment was madeof embedded graphite fiber bed in a Neoprene gasket, and the anode compartmentwas made of stacked stainless steel screens placed in two 1/16” Durabla gaskets.Stainless steel plates of 1/32” thickness were placed at both outer sides to serve asthe feeder electrodes. Two 1/16f Neoprene gaskets sheets were also utilized at theinterfaces of the feeder electrodes and at the exterior plexiglas slabs to secure thecell against the fluid leakage in the vicinity of the inlet and outlet bores. Spacerbars were not used around Durabla gaskets due to the low operating pressure ofthe anolyte compartment and high hardness of the gasket material, whereas thecustomary spacer bars were utilized in the catholyte compartment. The half cellswere held together and tightened by six 1/4” stainless steel bolts under 50 kg-cmtorque.outlet -graphitefiber bedDCR 40-25 BSorensenpower suppliesRAYTI-EON COM’ANYChapter 5. EXPERIMJiNTAL PROCEDURES 5825 AMPS MAX-T 4-I GNDss.s.s. screeninletpump controlerzNeoprenegasketdurablagasketssealing gasketsanolytefeed tankFigure 5.6: Cell block assembly for mass transfer measurements.Chapter 5. EXPERIMENTAL PROCEDURES 59A sampling port at the outlet of the cell was established by installing a 178” needlevalve and an ERTCO dial thermometer. Together these replaced the outlet tubingsection up to the 3-way valve # 8 (inclusive). In this way the sample of themost freshly produced cell effluent stream could be drawn conveniently for chemicalanalysis with the knowledge of its temperature. The temperature was detected bythe thermometer with its stem inserted right up to the packing head space.2. The anolyte fluid stream supply circuit consisted of a 20 liter feed tank, a tube heatexchanger, a tube pump and its associated Masterfiex controller. The anolyte circulation served several purposes: a)- removal of the generated oxygen gas bubblesfrom the anolyte compartment which otherwise caused poor electrolyte conductivity resulting in higher Ohmic potential drop and bad heat effects, b)- to supplythe anolyte 1 molar sodium hydroxide solution containing the transferring sodiumions, c)- to accomplish to some degree of cooling in the process of the catholytecompartment via heat transfer along the anolyte face of the membrane. Althoughthis heat transfer process was not effective to a high degree for the whole catholytecompartment, it was sufficient to cool the membrane body within a safer heat zone.The heat exchanger was a simple counterfiow concentric tube and shell with tapwater running as coolant. The anolyte outlet temperature read by the thermometerdid not exceed 25° C, under any run condition. The catholyte outlet temperaturewas ranging from 50 to 90 degree Celsius throughout the experiments.The anolyte solution was circulated at a rate of 80-90 percent of the controllerspeed (equivalent to 800-900 mL/min). After about 20 runs of operation a 5 %depletion of caustic concentration in the anolyte tank was observed. Hence, periodically make up amounts of concentrated 50 % caustic solution were added to thefeed tank.Chapter 5. EXPERIMENTAL PROCEDURES 603. The Sorensen power supply with volt and ampere ranges of, 50/30, was connectedto the feeder electrodes by strong spring loaded clips through one meter wires.5.6.1 Conduct of Experiment:After the completion of the cell block setup, preliminary runs were made with some gasand electrolyte flows to check for startup steps. In this case, a satisfactory startup wasjudged upon the following with zero applied electric potential across the cell.a- Reasonable pressure drop range in catholyte compartment.b- Good quality cell effluent foam.c- Clear and bubble free stream throughout the anolyte circulating loop.If any of the first two conditions failed, maintenance was required on the Neoprene gasketor adjustment on the graphite fiber packing dimensions or edges. The last failure was anindication for a rupture of the membrane and replacement was required. After correctingthe cell for the diagnosed defects and achievement of a satisfactory conclusion to thestartup steps, experimental runs were made, according to the experimental design Tables(D.13-14). The following was performed.1. The electrolyte and gas flow rates were adjusted; when steady state operation wasattained the anolyte loop operation was started (including its heat exchanger).2. The power supply was turned on. Various currents were applied to the cell in orderto search for the limiting current condition. At each current the generated alkalinehydrogen peroxide was sampled and analyzed immediately for its peroxide content.The searching process began scanning from low peroxide values and ending whenan optimum current for maximum peroxide content was found. For each run, theChapter 5. EXPERIMENTAL PROCEDURES 61limiting current was observed at the maximum of the plot of effluent hydrogenperoxide content versus current. This is called the saturation curve. A typicalsaturation curve for RUN ID EPL3G2, where the optimum condition was reachedat 18 Amperes current with 6.2 mL consumption of permanganate solution, ispresented in Figure 5.7.-JE00C/)0z03. At the limiting current, in addition to the current and milliliters of the titratedpermanganate, the readings of the pressure gauges, P, P1, P0, the pump dial, thegas rotameter ball position, the rotameter gas pressure, PG and its temperature,TG were taken.Bed porosities for this case were calculated from the bed length, width and the measuredbed thickness of the compressed cell. A description of this method is given in the SectionC.’.Table 5.1: Limiting currentdata for RUN ID EPL3G2.current 0.1 M KMnO4A mL2 0.854 1.656 2.507 3.108 3.409 3.9510 4.2511 4.6512 5.0014 5.3515 5.5016 5.7017 6.0018 6.2019 6.1520 6.20Figure 5.7: Typical saturation curve; consumed amount of 0.1 MKMnO4solution in titration of 2 niL of cell effluent electrolyte.7.RUN ID: EPL3G26-II-.5.ft.4.3/21•0 I I I5 10 15Applied Current, Ampere0 20Chapter 6EXPERIMENTAL RESULTS AND DISCUSSIONS6.1 GENERALIn this chapter the results of the experimental measurements of two hydrodynamic parameters — pressure drop and liquid holdup — and three transport properties — dispersioncoefficient, flowing foam electrical conductivity and mass transfer capacity — in cellspacked with graphite felt under foam flow conditions, are presented. The proceduresinvolved for each measurement are described in the previous chapter.The raw data recorded in rows for each run have been obtained by the variation ofthe three independent variables bed porosity, gas load and liquid load. The experimentaldesign tables for each set of measurements, containing the variable levels, other recordeddata and corresponding results, are presented in Appendix D, along with some associatedexplanatory plots. For each case, a Basic computer program was developed to analyzethe data, with regard to the principles of that objective. In each case the results werecorrelated to the independent variables by a second order polynomial. The resultingcorrelations, accompanied by the related statistical indices, are given in the ANOVAtables of the following sections of this chapter. In addition each correlation was testedwith Fisher’s factor[8] and it was found that the correlations fit well with the experimentaldata for a level of confidence of above 95 %.A RUN ID consists of six characters. The first two, EM, EZ, or EP represent theporosity level of LOW (low), ZERO (middle) and HIGH (high) levels, respectively. Thesecond pair starting with L, represents the level of liquid load, and similarly the third pair62Chapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 63starting with G represents the level of gas load. For example, a RUN ID like EML1GI.,represents a run made in a cell at low porosity, first liquid load and first gas load.The objective measured values are in the last column; where the various flow ratevariables, calculated under different conditions, were placed in intermediate columns ofthe result tables. The flow rate variables for all experimental measurements are presentedin the same terms of superficial velocities of liquid and gas average (along the packedbed) and were calculated by a single subroutine incorporated in every Main. The gasload, in terms of its average value, takes into account the compressibility of the fluid, andhence, indirectly the pressure effect on all the cases. A sample calculation of the flowrate variables for the RUN ID EML2G1 has been included in Appendix C. The results ofall the measurements are presented individually and in detail in the following sections.There is no literature reported for any one of the five parameters investigated in thisresearch, with foam flow and packed-bed electrochemical cells. None of the available datawith conventional packed-bed foaming systems used in thermochemical processing haveoperating ranges of variables anywhere close to the ranges used in this work (their rangesare higher). However, Hodgson (1993) investigated several parameters in a system ofsimilar configuration, but under trickling flow conditions with a nonfoaming electrolyte.The operating range of gas and liquid loads of the present work falls well within the lowerband portion of the same experimental variables of that author.The limitation on fluid loads in this research comes on the one hand from the extremely large pressure gradients in this system (LP/PL -40 to -70 bar/rn). On theother hand, by independent experiments it was found that the stability of the foam wasbracketed in the range of 2.5 - 12 bar (20 to 160 psig), within a 10 centimeter longgraphite felt bed. For pressures lower than 2.5 bar, the foam started to collapse, whereasfor pressures higher than 12 bar the foam flow regime changed to the pulsing foamingregime.Chapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 64The observed high pressure gradient, as well as other peculiar differences observed inthe measurements of other parameters of this work, are mainly attributed to the presenceof the surfactant (Tergitol), for the particular concentration (0.1 v/v %) applied in thiswork. This surfactant concentration, which was found to be the minimum requiredto attain an stable flowing foam was found through searches conducted with differentTergitol concentrations ranging from 0.01 to 0.2 v/v %, with 0.01 increments. Theresults of all the measurements, which differ substantially from values reported in theliterature both for nonfoaming systems and for foaming systems without surfactants, arepresented individually in the following sections.6.2 PRESSURE DROPPressure gradients were obtained at three porosity levels and numerous gas and liquidload levels, according to the experimental design Tables (D.1-3). A Basic computerprogram which carried out the analysis of the experimental data is listed in AppendixG, Part B.Plots of local pressure versus cell height showed the trend of the pressure variation along the cell to be approximately linear for all experiments. Example plots aredemonstrated on Figures (D.1,2) for “ZERO” and”HIGH” porosity levels, with the corresponding operating tables. The pressure gradient in each run was taken as the slopeof the straight line which best fitted the data points ( where the linear correlation coefficients ranged from 0.94 to 0.99 with a 95 % confidence limit).The data at all threeporosity levels were correlated by the “EXCEL” software and the results are given in thelast column of the Tables (D.1-3).The measured pressure gradient ranged from -40 to -70 bar/rn, which are a factor50-100 higher than in similar nonfoaming systems[33] (also see Section 5.2.1 for furtherChapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 65evidence of low pressure drop in nonfoaming systems obtained in this work). An explanation may be given due to the effects imposed by surfactant in excess to the classicalfrictional effects, cited in traditional fluid mechanic sources. It is speculated that thesurfactant role in increasing the pressure drop is mainly divided into two parts:a- Presence of surfactant (lowering liquid surface tension) and solid/liquid interfacialtension improves the wettability of the solid surface and hence raises the liquid/solidsurface frictional forces.b- As the foam passes through the porous bed, the bubbles of foam network are forcedto undergo frequent breakage and reformation processes. Accordingly, due to the“Gibbs’ - Marangoni” effect, there exist proportional energy losses of these processeswhich have been energized by the surface tension gradient in the liquid films.Plots of experimentally measured pressure gradients versus liquid and gas loads forthree bed porosity levels are presented in Figures (6.1-3).A visual inspection of these figures show that the pressure gradient increases withboth gas and liquid loads and decreases with increasing bed porosity. Also, observationof the figures reveals that a second order polynomial correlation (including interactionterms) of pressure gradient in terms of these variables should fit the data. The data forthe first liquid load (Li) at the ZERO level porosity do not fit the trends of Figure 6.2,because this was not a proper foaming condition. This could be due to low liquid loadlevel for these runs. The Li set of data of ZERO level porosity was therefore not includedin the correlation process.A three-variable second order polynomial was used to correlate the pressure gradientdata. The resulting equation 6.1 is listed, along with the associated significant statisticalindices, in Table 6.1.Chapter 6. EXPER!MEWTAL RESULTSAND DISCUSSIONS 66Figure 6.1: Pressure gradient fortLOWU level porosity bed.A - VS LIQUID LOAD-55 I I I I I I10 12 14 16 18 20 22 24AAAE A; -60 AC ..xA EM-Gix—LJ—- EM-G2 0-...---------EM-G3...-.--—X—EM-G4EM-G6-70Liquid Superficial Velocity, cm/mmB - VS GAS LOAD-55 I I I I6 7 8 9 10 11 12 13AE A A EM-X --. D-- EM-L3-60a) .-....... A- EM-LO-700Gas Avg Superficial Velocity, cmhninChapter 6. EXPERIMENTAL RESULTSAND DISCUSSIONS 67Figure 6.2: Pressure gradient for “ZERO” level porosity bed.a—0— EZ-G1a EZ-G2A EZ-G3EZ-G4EZ-GBA - VS LIQUID LOADI I7 9 11 13 15 17 19 21 23-15E25-35xa)A-45 .a,I-.-55a)A- x AI-75Lquid Superficial Velocity, cmlmiriaAxa a axIAxI-15B - VS GAS LOAD10 15-2520 25 30 35-35—0--— EZ-L1•o Z-L3Eb..a)Ia,Ia)-45o EZ-L4X EZ-L6-55IxV Ix-65I0xI0x0 0x-75Gas Avg Superficial Velocity, cm/mmChapter 6. FXPERJMENTAL RFSULTSAND DISCUSSIONS 68Figure 6.3: Pressure gradient for “HIGH” level porosity bed.7 9 13 15xO\\A - VS LIQUID LOAD-35.0 I I11 17EP-GI-40.0 - -X - EP-G22 -—-0—— EP-G3-----—A EP-G4—D---—EP-G6-45.0w\\\\\——-50.0 *- -x. - __-oU, .....0) O—-.0-55.0 -.-.—-..--60.0Liquid Superficial Velocity, cm/mm10 15 20 25 30 352I4JCa)(IIU,C’,a)cLB - VS GAS LOAD-35.0-40.0-45.0-50.0-55.0-60.0EP-L2—ê——— EP-L3-—--0—— EP-L4Gas Avg Superficial Velocity, cc/mma 0 C) H LiH 0C3Z 00-C3t’D3—QLi H Li Li U)ppIIH ..©--è3©C.3100)3cC)Li::•—p——U)p——-cC)oob130000QAIC3p.C)CD.VA d DD•_cJ1V0 1’) C” 1’.)t\)—.0D0CD C) oc’CDCD ooI-I-ICDI-ICDCDCD0Cl), -,Ct’CI)I-hCD cI. c’)‘-1C,)Cl)Q0p—.c-i--CDI-IH°apcrni-C) 0CD‘-1_CDjJCD00Hc-ICDU)0 LiU)C/)c U)Li U)C) C) 0 c-I- 0 c-ICD Cl) p c-i-C))c-i C) p C) CD.Cl)Cl)c-I-CD CD p 0 CD c-Ip C-’CD C) 0 CD C) CD c-i0 CD CDQU)HOLiCI) N 0© C)00 H Li CO —1Li Cl) U) 11C-’p.) H CD P*+1**+e1’.)* +*CA)* ** +Chapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 70Three-dimensional plots of the correlations (Eqn. 6.1) of measured pressure gradientwith liquid load and gas load, with bed porosity as a parameter, are shown in Figure 6.4.It is seen from the plot that the pressure gradient increases monotonically with liquidand gas loads but it decreases with increasing bed porosity.EP: High Level PorosityEZ: Zero Level PorosityEM: Low Level PorosityGas AVeIa SuperiialVelocitY, cmimiflFigure 6.4: Pressure gradient for foam flow in graphite fiber bed.Chapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 716.3 LIQUID HOLDUPLiquid holdups, defined as the liquid volume fraction of the packed bed under foam flowcondition, were obtained at three porosity levels and numerous gas and liquid loads.The corresponding results listed in Tables (D.4-6). A Basic computer program whichcarried out the analysis of the experimental data to produce the result tables is listed inAppendix C, Part C. A sample calculation of this routine for RUN ID EML2G1 is givenin Appendix C.The liquid holdup, which ranges from 7 to 20 %, is far less than for nonfoamingliquid in similar configuration systems (40 % at minimum)[33j. This result is due to thepresence of the surface active agent. The mechanisms of this effect may be explainedthrough the lowered liquid surface tension (by the added Tergitol) which facilitates theincrease of interfacial area, i.e., the foam generation, through the “Gibbs - Marangoni”effect.Plots of experimentally measured liquid holdup versus liquid and gas loads for threebed porosity levels are presented in Figures (6.5-7).Visual inspection of these figures shows that the liquid holdup increases with increasing gas and liquid loads and bed porosity. Also observation of the figures reveals thata second order polynomial correlation (including interaction terms) for liquid holdup interms of these variables should fit the data.A point of interest to mention in liquid holdup measurements is the increasing valueof this parameter with increasing gas load, which is opposite to what is observed innonfoaming systems. This phenomenon is speculated to be due to interfacial effectsrepresented by the “Young-Laplace” equation, relating the pressure difference acrossa concave gas/liquid interface to the liquid surface tension and the interface radius.According to that relation, the pressure difference is proportional to the liquid surfaceChapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 72tension and inversely proportional to the interface radius. Also, the sign of the pressuredifference is such that the pressure is less in the liquid than in the gas phase. By anincrease of gas load, the gas phase pressure rises and accordingly the gas/liquid interfacepressure difference rises. Meantime, with the assumption of no gas slippage, it is only thereduction of bubble radius that would keep the “Young-Laplace” equation in balance.This bubble size reduction results in increasing liquid holdup.A three-variable polynomial correlation for the liquid holdup, equation 6.2, also wasobtained, and it is listed along with its associated significant statistical parameters inTable 6.2.Chapter 6. FXPERJMENTAL RESULTSAND DISCUSSIONS 73Figure 6.5: Liquid holdup for ‘LOW’ level porosity bed13A - VS LIQUiD LOAD12A EM-Gi— EM-G2-EM-G3—X—EM-64—---GEM-G511zz-Jo-__••-:.—‘ .-- AAx.__._.___.-_.a A0 —A87 A68 11 14 17Liquid Superficial velocity, cm/mm20 23B - VS GAS LOAD13A EM-L212 EM-L3 ...--EM-M - -a—X—EM-L511 EM-L6 x-10 --4iGas Avg Superficial Velocity, cm/mmChapter 6. EKPERIMEJ’ITAL RESULTSAND DISCUSSIONS 74Figure 6.6: Liquid holdup for “ZERO” level porosity bed.A - VS LIQUID LOAD18--- 017o16 o15 .-----.- -.--.---.--.-.-.---.- — _—.4—.14 .-- .— .---— ---a-r.—_____--—--&----EZ-G113 .—- EZ-G2_-_-.- ...A... -—X— EZ-G4------0-—-- EZ-G6127.11 I I I8 11 14 17 20 23Liquid Superficial Velocity, cmkninB - VS GAS LOAD1817160’15141312110- ----:-.-B------0__ — --4 --—0 ——---7--/ —--7-__ __/ h7--.—__- EZ-L1—U—— EZ-L2_._..A..- EZ-L3EZ-L46 11-3616 21 26Gas Avg Superficial Velocity, cm/nun31Chapter 6. FJTERJA’IEATAL RESULTSAND DISCUSSIONS 75Figure 6.7: Liquid holdup for uIllGH level porosity bed.A - VS LIQUID LOAD* .0. —ID EP-G115 - •— —0— — EP.G2X •* — —O——--EP-G414013 I I I4 6 8 10 12 14 16 18Liquid Supeficial Velocity, cmhninB - VS GAS LOAD16—---x__ --15 --0 —1413- I6 11 16 21Gas Avg Superficial Velocity, cm/mmChapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 76Table 6.2: Three-dimensional correlation of liquid holdup.EL = AO+Al*UL+A2*Uc+A3*E+All*U+A22*U+33*E+A12*UL*Uc+A13*UL e+A23*UG*e (6.2)SOURCE SUM-OF- DF MEAN-SQUARESQUARESREGRESSION 11093 10 1109.3RESIDUAL 2.025 50 0.041TOTAL 11095 60CORRECTED 670 59RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.9998CORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.9970PARAMETER ESTIMATE A.S.E. < 95% > < 95% >LOWER UPPERAO 203.33 23.078 156.98 249.7Al 0.2513 0.1683 -0.087 0.6A2 1.4999 0.1694 1.1596 1.9A3 -5.617 0.5589 -6.739 4.5All -.0.004 0.0008 -0.005 -0.002A22 0.0044 0.0018 0.001 0.008A33 -0.013 0.002 -0.017 -0.009A12 -0.012 0.0012 -0.014 -0.009A13 -0.005 0.0005 -0.006 -0.004A23 0.0386 0.0034 0.032 0.045According to the statistical indices listed in the above table (coefficient of determination of 99.7 %), the fitted empirical correlation is a good estimating correlation. Theapplicable range of liquid and gas loads for this fit varies with respect to the bed porositylevel. The corresponding ranges of independent variables are given in Table B.5.Chapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 77E’& Lcm Level Porosity20 E18 —— —17 .- •— -..-._16 .. -I -. ‘p15 -14 ---— rn13 L112 ... ..—t--- L1ts —11 ..- .-.. - —-10.50Figure 6.8: Liquid holdup for foam flow in graphite fiber bed.It is seen from the plots that the liquid holdup is an increasing function of all threeThree-dimensional plots of the correlations (Eqn. 6.2) of measured liquid holdup,with liquid load and gas load, with bed porosity as a parameter, are shown in Figure 6.8.EP: Hii Level PorosityEZ: Zero Level Porosity001,LJqjVbocjj, criy,variables of liquid load, gas load and bed porosity.Chapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 786.4 AXIAL DISPERSIONLiquid axial dispersion coefficient and variance were measured at three porosity levels andnumerous gas and liquid loads, with the corresponding results listed in Tables (D.7-9).The basis of the formulation for the analysis of the data was discussed in Section5.4.1, where it was concluded that the additivity principle of the dynamic parameters:variances and residence time of the two independent closed vessels in series could be assumed. Therefore, from dispersion measurements, the cell variance was obtained bysubtracting the variance of the conductivity cell from the overall variance of the cell andconductivity cell in series. Also, the skewness of the tracer responses suggests that thereis no simple analytical solution for this goal. But, the closed vessel assumption couldfurther ease the solution method, and the available characteristic equation of such curves,relating the variance to the dispersion coefficient, can be used to calculate the dispersionnumber, and hence, the axial dispersion coefficient.A Basic computer program which carried out the analysis of the experimental datato produce the result tables is listed in Appendix G, Part E. A one data record samplecalculation for the RUN ID EZL4G3 is given in Appendix C, to demonstrate in detailthe routines involved.Dispersion, which has direct effect on the reactor performance, is of major concernin reactor assessment. The measured liquid axial dispersion coefficient ranged from 0.01to 0.45 cm2.s1,which falls by a factor of 2 below values in the conventional packedbed reactors[41,56j with nonfoaming fluids. In spite of some expected bad rectangularconfiguration effects[80], reduction of the dispersion must be due to the hydrodynamicalteration of the electrolyte caused by the surfactant. The mechanism may be explainedin terms of the increased rigidity of the interface (by the presence of the surfactant) whichresults in the reduction of turbulence and a decrease of liquid axial dispersion.Chapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 79Plots of experimentally measured axial dispersion coefficients versus liquid and gasloads for three bed porosity levels are presented in Figures (6.9-11).Visual inspection of these figures shows that the liquid axial dispersion coefficient hasa clearly increasing trend with increasing liquid load and porosity. But the trend withrespect to the gas load to some degree is not clear, for LOW and ZERO level porosities.For these porosity levels, corresponding to Figures (6.9-10), the data are scattered witha mild increasing behavior at LOW porosity, changing to a decreasing trend at ZEROlevel porosity. At HIGH porosity level, Figure 6.11, the data are less scattered anddispersion data shows a clear increasing trend with increase of the gas load. Consideringthe overall picture of the dispersion data from observation of the Figures (6.9-11), asecond order polynomial correlation (including interaction terms) for dispersion in termsof these variables was assumed to fit the data.Based on the observed variational trend of the data, a three-variable polynomialcorrelation for the dispersion coefficient, equation 6.3, was obtained, and it is listedalong with its associated significant statistical parameters in Table 6.3.Chapter 6. FXPERJMEWTAL RESULTSAND DISCUSSIONS 80Figure 6.9: Liquid axial dispersion coefficient for “LOW” level porosity bed.A - VS LIQUID LOAD0.60.5 XEMGIIEMG2 xEtEMG30.4 xC) 0.3CI0) X 00.2 x00.105 8 11 14 17 20 23Liquid Superficial Velocity, cm/mmB - VS GAS LOAD0.6DEML1OEML20.5 XEML3 XxAEML4 +2 ZEML5x0.4 +EML6++0)0.30.20,x0.100 D0 I7 9 11 13 15Gas Avg Superficial Velocity, cmkuinChapter 6. FXPERJMENTAL RESULTSAND DISCUSSIONS 81Figure 6.10: Liquid axial dispersion coefficient for “ZERO° level porosity bed.A - VS LIQUID LOAD0.2 0EZG2xEZG300.15 xEZG4 0+EZG5oEZG6D 0.1C) cC 0a0.05 + x0) Xx x+0 + C) CI + ÷-0.05 I I I I4 6 8 10 12 14 16 18 20 22Liquid Superficial Velocity, cm/mmB - VS GAS LOAD0.24C019 El+EZLIX AEZL2E a XEZL3OBZL40.14 XEZL5DEZL6C-)CC0.09 xa) XC.+x 00.04 0+ xX+ 4- D XC] + Xi—0.01 I I I I I8 11 14 17 20 23 26 29 32Gas Avg Superficial Velocity, cm/mmChapter 6. FXPERIMENTAL RESULTSAJJD DISCUSSIONS 82Figure 6.11: Liquid axial dispersion coefficient for “IIIGH” level porosity bed.A - VS LIQUID LOADEPG1 x0.225 oEPG2zEPG3xEPG4$2. +EPG5C%Js 0.175xa) ÷o xc_) 00.1250 AX A0) A0.0.075000.025 I I5 7 9 11 13 15 17 19 21Liquid Superficial Velocity, cm/mmB - VS GAS LOADEPL10.25 AEPL2DxEPL3OEPL4X XEPL50.2 DDEPL6E0.15 0a)O AcioI-0) +a0+0.050 I5 10 15 20 25 30Gas Avg Superficial Velocity, cm/mmChapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 83Table 6.3: Three-dimensional correlation of axial dispersion coefficient.D = AO+Al*UL+A2*Uc+A3*e+A1l*U!+A22*U+33 e2+A12*UL*UG+A13*UL*e+A23*UG*e (6.3)SOURCE SUM-OF- DFMEAN-SQUARESQUARESREGRESSION 5.5 10 0.55RESIDUAL 0.51 74 0.007TOTAL 6.0 84CORRECTED 2.04 83RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.915CORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) 0.750PARAMETER ESTIMATE A.S.E. < 95% > < 95% >LOWER UPPERAO 39.207 5.093 29.1 49.4Al 0.07 0.033 0.01 0.14A2 -0.062 0.062 -0.19 0.06A3 -99.834 13.134 -126 -73.7All -2.OOE-03 3.81E-04 -0.003 -0.001A22 -l.02E-04 2.29E-04 -5.6E-04 3.5E-04A33 62.686 8.395 46.0 79.4A12 4.54E-05 3.02E-04 -5.6E-04 6.5E-04A13 -0.012 0.038 -0.09 0.06A23 0.085 0.073 -0.061 0.23According to the statistical indices listed in the above table (coefficient of determination of 75.0 %), the fitted empirical correlation is not a good estimating correlation andindeed the data are widely scattered (see Figures (6.9-6.11)). Howevere, the dispersionvalues are so low that the error in the estimation of dispersion coefficient will have littleeffect on prediction of transport phenomena with foam flow in a packed-bed electrode.The applicable range of liquid and gas loads for this fit varies with respect to the bedporosity level. The corresponding ranges of independent variables are given in Table B.5.Chapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 84Three-dimensional plots of the correlations (Eqn. 6.3) of measured liquid axial dispersion coefficient with liquid load and gas load, with bed porosity as a parameter, areshown in Figure 6.12.Figure 6.12: Axial dispersion coefficient for foam flow in graphite fiber bed.It is seen from the plots that the liquid axial dispersion is an increasing function ofall three variables of liquid load, gas load and bed porosity.Chapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 856.5 FLOWING FOAM ELECTRICAL CONDUCTIVITYInvestigations were carried out to measure the effective flowing foam electrical conductivity in packed bed cells, at three porosity bed levels and numerous gas and liquid loads.The corresponding results listed in Tables (D.1O-12). Also, as mentioned in the chapteron experimental procedures, the power supply system was calibrated for its performancewith the standard one Ohm resistance. The measuring resistance efficiency, Reff, is defined as the ratio of the experimentally measured resistance divided by the real resistance.Resultant plots of Reff versus applied potential, through-current, and the total power,I * V, along with the experimental data tables are given in Appendix E, Part III.Correlation equations relating the resistance efficiency, Ref to the I * V have beenobtained, which were utilized in calculation of the real ohmic resistance of the foam fromV-I data. Two correlation models were tried, based on the appearance of the plots.Details of these correlations are given in the Tables (E.7-9) of the Appendix E.A Basic computer program which carried out the analysis of the experimental datato produce the result tables is listed in Appendix C, Part F. A sample calculation forRUN ID EPL2G3, demonstrating the routines involved is presented in Appendix C.The effective electrical conductivity of the flooded bed, K, and that with foam flow,were measured for three porosity levels. The measured K values for three porositylevels, LOW, ZERO and HIGH were 8.2, 14.4 and 15.0 mho/m, respectively. These values are about 15 % higher than values calculated from the Neale & Nader correlation, atthe two higher porosity levels, and is about 17 % lower at the LOW level porosity. Theimprovement at higher porosities may only be attributed to the surfactant effects whichare unknown at this time since the surfactant used (Tergitol) is a nonionic one. Considering the improvements at these two higher levels as normal operation, the reverse resultsfor the LOW level porosity may be explained by possible existence of some blockages ofChapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 86the packing at higher compression imposed at the LOW porosity level.The measured foam electrical conductivities ranged from 6.8 to 11.1 mho/m. Adopting the same method of comparison as for the flooded bed case, the predicted i valuesmay range from 0.7 to 2.2 mho/m (corresponding to the holdups ranging from 7 to 20%). Similar comparisons performed using other correlations[40,42], give even lower predicted values. This enormous improvement which is in order of 600 %, on average, isapparently due to the foam effects. It is speculated that the adsorbed Tergitol molecules(polyglycol ether) at the gas/liquid interface are polarized, under the electric potentialfield in the foam and may contribute to the charge transfer in the electrolyte. In this waya channel of charge transfer may be imagined through the polarized Tergitol molecules(possibly augmented by associated OH— ions), in the bubble films. By using the Neale &Nader correlation the porosities attributed to the measured conductivity ranges (6.8 to11.1 mho/m), correspond to liquid holdups of 54 to 80 %. These high estimated ranges,which are less than the three experimented bed porosities (71 to 87.2 %), support theexistence of the Tergitol polarized network.Plots of experimentally measured flowing foam effective electrical conductivity versusliquid and gas loads, for three bed porosity levels are presented in Figures (6.13-15).As is seen from Figure 6.13, at LOW level porosity bed, there is no significant variationof foam electrical conductivity with respect to gas load variation, while there is somevariation with respect to liquid load, although small. For the next two higher porositylevels, Kf varies with gas load to some degree, but it is difficult to judge precisely if it isa linear or a higher degree relation. With respect to liquid load, tc varies significantly.For ZERO porosity level, the variation shows a clear curvature effect. Hence a secondorder polynomial correlation (including interaction terms) was assumed and fitted to thedata.Chapter 6. EKPERJMENTAL RESULTSAND DISCUSSIONS 87Figure 6.13: Foam effective electrical conductivity for “LOW” level porosity bed.A - VS LIQUID LOAD7 0 XE6956.9 *•G20G3XG46 85 +G5AG6AG76.8 ÷ El AwLU6.756.7-0 I I I I I5 7 9 11 13 15 17 19 21Liquid Superficial Velocity, cmhninB - VS GAS LOAD7 EAAAA AX6.952 6.9 XX X ++>ED 0 00>I°’’I10L210L3CC) EM+L5w 6.8 000 0 + AL6 0LUE6.75Li6.7 I I I o—5 15 25 35 45 55Gas Avg Superficial Velocity, cm/mmFigure 6.14: Foam effective electrical conductivity for “ZERO” level porosity bed.Chapter 6. E?PERIMENTAL RESULTSA]TD DiSCUSSIONS 88Figure 6.14: Foam effective electrical conductivity for “ZERO” level porosity bed.A - VS LIQUID LOAD10.4* 00 ÷ +E10.A0 00209.6 003XG4+059.4A clG7*08U..929 I I I10 20 30 40 50 60Liquid Superficial Velocity, cm/mm10.4B - VS GAS LOAD+ A +A- A X - + AX A A OL1io + •L20L30 0 L49.8 0 +L50AL69.6 0 0Gew9.4 Vci ci9.2 V ci ci ci C cici9 I I I I4 7 10 13 16 19 22 25Gas Avg Superficial Velocity, cmhninChapter 6. FXPERJMFJ’JTAL RESULTSAND DISCUSSIONS 89Figure 6.15: Foam effective electrical conductivity for “HIGH” level porosity bed.A - VS LIQUID LOAD+11 0EAA0.= CE x10.5+5C CC A •G2g 10 A 0G3C-, XG4t +G5a) C AG6A9.5 uAG70 xL19. I I I15 25 35 45 55 65Liquid Superficial Velocity, cmhninB - VS GAS LOADA A11 AE.—A.2 + + +10.5 + + + +x xX •X 0 X 1J1 0g 10 0 0 C DL2ci13a) C I] L4LLi C C C C C I+L5lo o o [J o0 0 0 00LL9 I I I I4 7 10 13 16 19 22 25Gas Avg Superficial Velocity, cm/mmChapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 90A three-variable polynomial correlation for ,c,e, equation 6.4, has been obtained, andit is listed along with its associated significant statistical parameters in Table 6.4.Table 6.4: Three-dimensional correlation of foam effective electrical conductivity.Kf = AO+Al*UL+A2*UQ+A3*€+Al1*U-j-A22*U+33*E2+A12*UL*UG+A13*UL E-f-A23*UG*e (6.4)SOURCE SUM-OF- DF MEAN-SQUARESQUARESREGRESSION 11886 10 1188.6RESIDUAL 2.22 134 0.017TOTAL 11888.2 144CORRECTED 326.6 143RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.9998CORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.9932PARAMETER ESTIMATE A.S.E. < 95% > < 95% >LOWER UPPERAO -32.936 2.9 -38.7 -27.2Al -.2554 0.0258 -0.31 -0.20A2 0.0372 0.0259 -0.01 0.09A3 70.2702 5.5825 59.23 81.31All -0.001 0.0003 -0.002 -0.000A22 0.4762 0.0308 0.42 0.54A33 -0.0095 0.0266 -0.06 0.04Al2 -0.0023 0.0004 -0.003 -0.002A13 -0.0005 0.0002 -0.0009 0.000A23 -30.159 3.00 -36.1 -24.23According to the statistical indices listed in the above table (coefficient of determination of 99.3 %), the fitted empirical correlation is a good estimating correlation. Theapplicable range of liquid and gas loads for this fit varies with respect to the bed porositylevel. The corresponding ranges of independent variables are given in Table B.5.0E>0DCz000I—0w-jUi4:0LLChapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 91Three-dimensional plots of the correlations (Eqn. 6.4) of measured foam effectiveelectrical conducticity, with liquid load and gas load, with bed porosity as a parameter,are shown in Figure 6.16.If‘i (hOt•S(lpLe1oQfi\‘.JGSFigure 6.16: Effective electrical conductivity for foam flow in fiber bed.It is seen from the plots that the Kf is an increasing function of all three variables ofliquid load, gas load and bed porosity.Chapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 926.6 MASS TRANSFER CAPACITYInvestigations were carried out to measure the overall mass transfer capacity, Ka, inpacked bed electrolytic cells. Measurements were made at two porosity levels and numerous gas and liquid loads. The experimental results are listed in Tables (D.13-14).A Basic computer program which carried out the analysis of the experimental datato produce the result tables is listed in Appendix G, Part C. A sample calculation forRUN ID EPL2G3, demonstrating the routines involved is presented in Appendix C.Overall mass transfer capacity, Ka, which includes the effect of the overall masstransfer interfacial area, is the key parameter determining the mass transfer rate. Themeasured values of Ka, ranging from 4 to 7.5 s1, were obtained under the limitingcurrent condition, where the process is mass transfer controlled, with cathodic reductionof oxygen to hydrogen peroxide. These results surpass by far the results obtained innonfoaming packed-bed reactors[18,28] and a foam-bed reactor, used with three differentsurfactants[6], where the values of Ka were less than 1 s_i. In addition, the Ka obtained inthis work is by at least a factor of 1.8 higher than that of similar nonfoaming systems [33].In this context there are several important factors which account for this improvement,some with positive and some with negative effects.The positive effects are probably due to: 1) the enhanced gas/liquid interfacial areaof the foam, 2) the anisotropic field effects created by electric potential field and current (which is absent in non-electrochemical methods), 3) improved wetting of the solidsurface.The negative effects are probably due to: 1) the resistance to mass transfer raised viasurfactant monolayer in the gas/liquid interface, 2) the resistance to mass transfer dueto surfactant adsorption to the solid surface. The resultant interaction of different effectsis positive and has its roots in the sort and the amount of the used surfactant (0.1 v/vChapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 93% Tergitol).Also, the contribution of the stainless steel feeder electrode to any oxygen reductionwas considered to be negligible, due to the following:First, the feeder electrode potential does not vary much from solid matrix due tocompression of graphite felt against feeder electrode[62]. Second, if oxygen reductiondoes occur on the cathode feeder, its contribution to the process will be small becausethe ratio of the area of the porous electrode to the feeder electrode is about 100/1.After all the preceding, there are two fundamental factors that have been neglectedin processing of the data. The first one is the temperature factor, varying along thepacked-bed during the mass transfer measurements. The second one is the amount ofthe packed-bed which remains electrochemically active for the process of the oxygenreduction. This portioh of the bed is typically to 1-2 millimeter thickness of the bed [60].This is an important factor, when designing such systems. Hence considering the trueworking bed thickness’ in these measurements, the real Ka values could be a factor of 3higher than the calculated ones.The outlet temperature variation in these measurements ranged 50-90 °C. The heateffects consisted of heat of electrochemical reactions plus Joule heating. Steps were takento reduce heat effects as was explained in chapter 4, but were not completely successful.In general increased temperature increases the value of K, but decreases the solubility of02 in the electrolyte and thus lowers the driving force for 02 transfer. The contributionof each one of the heat effects is unknown at this time. The sum total of these effectsare reflected in the averaged calculated Ka.Plots of experimentally measured overall mass transfer capacity versus liquid and gasloads for two bed porosity levels, are presented in Figures (6.17-18).Visual inspection of these figures shows that the Ka increases with increasing gas andliquid loads and decreases with increasing bed porosity. Also, observation of the figuresChapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 94reveals that a second order polynomial (except bed porosity, with first order) correlationincluding interaction terms for overall mass transfer capacity in terms of these variablesfit the data.A three-variable polynomial correlating Ka to liquid superficial velocity, gas averagesuperficial velocity and fiber bed porosity, equation 6.5, has been obtained, and it is listedalong with its associated significant statistical parameters in Table 6.5.Chapter 6. FXPERJMENTAL RESULTSAND DISCUSSIONS 95Figure 6.17: Overall mass transfer capacity fortIZEROU level porosity bed.A-VS LIQUID LOAD87.5.0 +U 0 006.5IIG1lU) I I6 0 IoG2I xx I Io IoG3IU)++ 1xG4II I .•____5.4.5 I8 13 18 23 28Liquid Superficial Velocity, cmlminB - VS GAS LOAD8______L2 IIeL.3I7.5 . x IL4lU + 0+ 0 o06.5U)60I.- ciU)+U, e55. + D• C54.5 I I I5 10 15 20 25Gas Avg Superficial Velocity, cmlminChapter 6. EXPERIMENTAL RESULTSAND DISCUSSIONS 96Figure 6.18: Overall mass transfer capacity for hhl{IGHU level porosity bed.A - VS LIQUID LOAD60x0+ 0U 0 +(U(U xC)__‘RGI’x IoG21 +45 + I II.- + 10G31Ix G4 II I43.5 I I I6 11 16 21 26Liquid Superficial Velocity, cmlminB - VS GAS LOAD6 EJ LixL2X .L3+ 055. 0- . x 01-40 xL5>11 +U +L6(Uo 5. 0CU +C.) 00x +XXI- XU, xU,CU4C]3.5 - I I I3 8 13 18 23 28Gas Avg Superficial Velocity, cmlminChapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 97Table 6.5: Three-dimensional correlation of mass transfer capacity.Ka = AO+A1*UL+A2*Uc+A3*e+A11*UE-j-A22*(4+A12*UL*Uc+A13*UL*e-f-A23*UG*E (6.5)SOURCE SUM-OF- DF MEAN-SQUARESQUARESREGRESSION 1611 9 179RESIDUAL 6.5 43 0.15TOTAL 1617.5 52CORRECTED 41.3RAW R-SQUARED (1-RESIDUAL/TOTAL) = 0.9960CORRECTED R-SQUARED (1-RESIDUAL/CORRECTED) = 0.8425PARAMETER ESTIMATE A.S.E. < 95% > < 95% >LOWER UPPERAO -7.8601 5.748 -19.5 3.7Al 1.1923 0.2811 0.63 1.76A2 0.8881 0.2566 0.37 1.41A3 9.0374 6.88 -4.83 22.9All -.0022 0.0018 -0.006 0.0013A22 -0.8225 0.3169 -1.46 -0.18A33 -0.8219 8.395 46.0 79.42A12 4.54E-05 0.2934 -1.41 -0.23A13 -0.0132 0.0018 -0.02 0.00A23 -0.0065 0.0017 -0.01 0.00According to the statistical indices listed in the above table (coefficient of determination of 84.3 %), the fitted empirical correlation gives only a rough estimate of masstransfer capacity. The applicable range of liquid and gas loads for this fit varies withrespect to the bed porosity level. The corresponding ranges of independent variables aregiven in Table B.5.Chapter 6. EXPERIMENTAL RESULTS AND DISCUSSIONS 98Three-dimensional plots of the correlations (Eqn. 6.5) of measured mass transfercapacity with liquid load and gas load, with bed porosity as a parameter, are shown inFigure 6.19.30oo’Figure 6.19: Mass transfer capacity for foam flow in graphite fiber bed.It is seen from the plot that the mass transfer capacity is a weak increasing functionof liquid load and gas load but varies inversely with bed porosity.“quid supe,.fi.V9lOdlyon/miChapter 7CONCLUSIONS AND RECOMMENDATIONS7.1 CONCLUSIONSGENERALPressure gradients, liquid holdups, axial liquid dispersions, flowing, foam electrical conductivities and overall mass transfer capacity were measured in bench scale cells. Thecells were packed with graphite felt (fiber diameter 20 micron). The fluid used was foamgenerated from water (for dispersion case) or 1 N NaOH solution (for the rest of thecases) of 0.1 % v/v Tergitol surfactant. In all experiments the inlet temperature wasadjusted at 22 °C and outlet pressure was adjusted at 4 bar. There were three variablesfor each experiment: liquid load, UL, gas load, UG, and bed porosity, e.The results of these measurements are significantly different from the reported valuesof nonfoamed electrochemical cells with similar configurations. There is no literature ofprevious work on foamed electrolyte in fixed-bed electrodes.Correlations were obtained for each of the five dependent parameters of the study,(z\P/FL, EL, D, kf, Ka) as functions of UL, UG and 6. Inspection of the data revealedfunctionalities ranging from linear up to second order in all cases. Hence, for each correlation an empirical model with second order plus interaction effects was assumed. Correlation coefficients along with the corresponding statistical parameters, for each measuredparameter are listed in the chapter of experimental results. These empirical correlations99Chapter 7. CONCLUSIONS AND RECOMMENDATIONS 100can be used to estimate the relevant dependent parameters within the range of independent variables given in Table B.5, and for cell inlet temperature and outlet pressure sets,as stated above. Qualitative discussions are presented below along with comparisons toother packed-bed results.A. Pressure Gradient, L1F/PLThe pressure along the packed cell showed nearly a linear variation for all runs. Thecorrelation coefficients of the linear fits were in the range of 0.94-0.98. The measuredpressure gradient ranged from -39 bar/rn to -71 bar/rn, and increased monotonically withrespect to every one of the independent variables. It is speculated that this high pressuregradient range, which is 50 to 100 tirnes higher than the range for equivalent nonfoamingsystems [33], is due to the presence of the surfactant (explained in chapter 6) .This undesirable feature of the foaming system increases pumping and equipment costs of suchsystems as compared to nonfoaming ones. Details of the developed pressure gradientcorrelation are given in Table 6.1.B. Liquid Holdup, 6LThe measured liquid holdup in this research work ranged from 7 to 20 percent. Theliquid holdups for nonfoaming systems with similar fluid loads are a minimum of 40percent[33]. Liquid holdups, which are related to the cell space-time yield, are lowerfor foaming systems than for nonfoaming systems, but gas-liquid interfacial areas[47,48]are higher. According to the data, liquid holdup is a monotonically increasing functionwith respect to the three independent variables. A significant difference with nonfoamingsystems is the reverse behavior with gas load (an explanation is given in chapter 6). Thecoefficients of empirical correlation developed for liquid holdup along with the relatedChapter 7. CONCLUSIONS AND RECOMMENDATIONS 10statistical parameters are given in Table 6.2.C. Axial Liquid Dispersion, DLiquid axial dispersion coefficients in this research work ranged from 0.01 to 0.45 cm2.s1and fall below the values reported for the nonfoaming 2-phase flow conventional PBRsor electrochemical cells[41,56]. Also the variance of the tracer response curves was foundnot to exceed those of the conventional packed beds[41]. The low dispersion is one ofthe important desirable features of the foam system. As a result this system shouldhave better performance and achieve higher conversion of the species, from the gas phaseby reaction on the polarized electrode surface. This better performance is due to thesurfactant effect, which has overcome the high dispersion reported for the conventionalrectangular configuration reactors[80]. Although lower dispersion was observed in thisinvestigation, the trend with the gas load is not the same as that reported in the literature [71,76] for nonfoaming systems. Hence, it must be realized that it is the beneficialeffect of the foam (generated with surfactant) for foaming systems that has the mainrole in the reduction of dispersion in these cells. The empirical correlation developed fordispersion coefficient along with the related statistical parameters are given in Table 6.3.D. Flowing Foam Electrical Conductivity, IcfThe electrical conductivity of the flowing foam of 1 M NaOH in the packed-bed electrodes, ranged from 6.8 to 11.1 mho.m’. Also the effective conductivity of the flowingelectrolyte in the flooded cell was measured for comparison and verification of the surfactant effects. The effective conductivity in these media as well as the solid matrixhas an important role in the design of packed bed cells. A desirable design condition isachieved when the highest level of effective electrolyte conductivity is attained. In suchChapter 7. CONCLUSIONS AND RECOMMENDATIONS 102a condition, the ohmic potential drop in the electrolyte phase is reduced to a minimum.This is done for a solid matrix by proper choice of the material (i.e., graphite felt), andits porosity[93], whereas in the flowing phase it may be controlled via the use of a supporting electrolyte[78]. These two choices along with other necessities have been fixed forthis research and it is important to mention that in the flooded condition the measuredconductivity values were a factor of about 15 % higher than the value calculated by theNeale and Nader equation for nonfoaming cells. For the foam flow operation, the conductivity values are as high as those with four times higher liquid holdup (i.e. EL = 54-80 9’o)in nonfoaming systems, as calculated by the formula of Neale and Nader (1973). Sincethe surfactant used was non-ionic there is no conductance contributed by the ionizedsurfactant. Therefore, it is speculated that the increased effective conductivity is dueto the surface tension reduction effect of the added surfactant, Tergitol, and the surfaceconductivity of the liquid films in the foam matrix. The coefficients of empirical correlation developed for flowing foam electrical conductivity along with the related statisticalparameters are given in Table 6.4.E. Overall Mass Transfer Capacity, KaThe electrochemical method of direct absorption of oxygen gas from gas phase to the surface of the polarized solid graphite fiber, where the dissolved oxygen underwent cathodicreduction to hydrogen peroxide was adopted for overall mass transfer capacity measurements. Many experimental endeavors as well as mathematical analysis on the inlet andoutlet streams were carried out to identify the true reactions taking place in the cell,under the limiting current condition and in the flow-by mode. The conclusion was thatthe electrochemical reaction produced hydrogen peroxide and hydrogen gas. However,some peripheral tests showed, to a small degree, the possibility of thermal decompositionChapter 7. CONCLUSIONS AND RECOMMENDATIONS 103of the hydrogen peroxide along its passage out from the cell. Heat effects were seen tobe high, as the outlet temperature in some runs reached as high as 90 °C.Hence, the results of a mathematical analysis of the data based on a two—reactionmodel with the primitive assumption of total bed thickness being active, and averagingthe effect of the temperature variation in the porous electrode, gave mass transfer capacityranging from 4 to 7.5 s1. Comparing these values to the results of Hodgson (1993),obtained on similar cells but with nonfoaming flow, there is an 80 % increase. Consideringthat the active part of the bed may not exceed 30 % of the cell, the real values ofKa may be higher by a factor of three. In this work the porosity has been taken attwo levels and accordingly a polynomial degree of unity was chosen for the porosity.In general the results show that the mass transfer capacity is an increasing functionof the gas load and liquid load and a decreasing function of the bed porosity. Thecoefficients of empirical correlation developed for mass transfer capacity along with therelated statistical parameters are given in Table 6.5.In summary, comparing with nonfoaming systems in fixed-bed reactors under similarconditions, the foamed system of this work is characterized by:1. Higher gas-liquid interfacial area.2. Higher pressure gradient.3. Lower liquid holdup.4. Lower dispersion coefficient.5. Higher effective foam electrical conductivity compared with the values estimatedby literature correlations.6. Higher overall mass transfer capacity.Chapter 7. CONCLUSIONS AND RECOMMENDATIONS 1047.2 RECOMMENDATIONSThe new results obtained here reflect the significance and delicacy of this work. The improved values of the parameters D, Ka, obtained along with extremely high pressuregradient and observed high gas/liquid interfacial area (bubble diameters in order of fractions of millimeter), makes potential grounds for future investigations especially usefulin the field of packed-bed electro chemical systems dealing with the gas processing, utilizing foamed electrolytes. To enhance the knowledge and information useful in the designand application of such systems the following further determinations and assessments arerecommended:1. Measurement of the individual mass transfer coefficients of gas/liquid and liquid/solid, as well as gas/liquid interfacial area.2. Establish generalized relation of mass transfer coefficients with temperature alongthe porous electrode, as well as other temperature dependent parameters like dispersion coefficient, foam electrical conductivity and liquid holdup.3. Experiments with different nonionic surfactants (e.g. Triton X-100), to see theireffect on the parameter values.4. Experiments with graphite felt with different fiber diameters (e.g. 10 micron), aswell as graphite mat and cloth and with particulate packings.5. Having obtained the mass transfer relation with temperature, perform modeling totest the data and if successful, obtain the electro chemically active portion of theporous electrode.6. Measure pressure drop, liquid holdup and dispersion coefficient in electrolytic cellsto determine the electric potential and current field effects.Chapter 7. CONCLUSIONS AND RECOMMENDATIONS 1057. Perform experiments with downward foam flow to see the performance difference,compared to upward foam flow.8. After the aforementioned investigations, try for commercial scale-up and economicassessment based on the remarks given in the following section.7.2.1 Some Remarks on Scale-up[4,22]A broad approach in scale-up will require determination of the conditions under whichsimilitudes, i.e., similar objective values (like conversion of certain reactant, operablepressure limits, electroactive portion of the packed bed, etc.) are attained through theuse of the governing differential equations (established by proper modeling). This goalcould be achieved by duplicating the dimensionless coefficients of these equations betweenthe prototype and the model. The dimensionless coefficients are composed of values ofthe controllable and measureable quantities (These coefficients are give in Appendix F).Also, scale-up is achievable by applying the Buckingham Pi theorem, combined witha good knowledge in selecting the quantities affecting the process. The controllable andmeasureable quantities encountered during the course of this investigation are: Ka, a3,6, D, UL, U0, FL, d, packed-bed dimensions, cell applied potential. Ka is related tokLaL and k3a8 by=+ (the last term, which is the gas film resistance,is near zero for the present work, using pure reactant oxygen gas with water vapour).Having the preliminary information on the operable pressure limits for a persistantfoam flow (40 to 160 psig.) and with bed porosities the same as used in this work, thelimits for gas and liquid loads may be chosen. Here, it is worth mentioning that thelower porosity limit (with a gasket of 1/8” thickness), is the lowest possible because ofthe blockage of the packing at higher compressions. The upper porosity limit (with agasket of 1/4” thickness), is the highest possible, due to the shrinkage and bed movementChapter 7. CONCLUSIONS AND RECOMMENDATIONS 106caused by high pressure gradients.In the determination of the packed-bed dimensions (electrode dimensions), the widthof the electrode is limited only by the effectiveness of the electrolyte distribution acrossthe bed. The height of the reactor, Pb, mainly depends on the tolerable pressure limits(in this work the height is 10 cm). However, the thickness dimension, which is a criticalfactor in packed-bed operation, is identified corresponding to the desired electrochemicalreaction. This information will be available either by experimentally measuring the localelectrode potential in conjunction with the electrokinetic data of the reaction, or bysolving a model of the packed-bed. To this purpose, a model embracing a mass andpotential balance for a simplified case of isothermal and one electron-reaction has beenpresented in Appendix F, to explain the steps required by modeling.The last controllable quantity is the fiber diameter of the felt, which is related to thebed porosity and electrode/electrolyte interfacial area by: d = 4() So, by setting thebed porosity and fiber diameter, the specific surface, a, is defined.Appendix F presents a possible model to demostrate the power of the modeling inscale-up, with a simplified assumption of isothermal operation, in conjunction with thedata obtained in this workIn summary, the scale-up could be accomplished through the performance of thefollowing sets of experiments, in conjunction with reactor modeling:1. Experiment with other fiber diameters of the carbon felt (or with other types ofpackings).2. Experiments with varying the electrode length3. Experiments with different cell voltage, to investigate the effect on the electroactivethickness of the electrode.Chapter 7. CONCLUSIONS AND RECOMMENDATIONS 107Also, it is worthwhile mentioning the special place of the flow-through electrode incomparison to the flow-by electrode used in this work. It may be said that, in selecting a flow-through configuration packed-bed electrode, with a thickness in order of theelectroactive thickness of the desired reaction, coupled with a recycling ioop, one may beable to reach the same conversion at more suitable/practical operating pressures. Thedesired production rate may be achieved through adjustment of the inlet fluid load andthe inlet cross-sectional area within the constraints of effective distribution of the foamover the electrode surface.The correlations of pressure drop, liquid holdup, dispersion coefficient, effective foamconductivity and mass transfer capacity obtained in this work along with dimensionless coefficients introduced in Appendix F and the aforementioned sets of experimentswould be used to model the experimental system and to scale up electrochemical reactorsemploying foamed electrolyte in packed-bed electrodes.NomenclatureSymbol Description Dimensiona Overall gas-solid interfacial area L’a A/Aa Gas-liquid interfacial area per unit volume of L’reactor.External area of particles per unit volume of L’reactor(=4(1- e)/d = 4w/pd, cyliderical particles, like graphite fibers).A The liquid phase concentration of transferring kmole.L3species A.Saturation solubility of A in liquid. kmole.L3Liquid inlet concentration of species A. kmole.L3B Graphite fiber packing thickness. Lde Equivalent diameter of packing(= 2d6/3(1 — 6)). Ld Average nominal packing diameter (fiber Ldiameter).D Effective axial dispersion coefficient in this cm2.T’work(equals to the sum of the molecular diffusioncoefficient and axial dispersion coefficient).Da Effective axial dispersion coefficient(equals to the L2.T’sum of the molecular diffusion coefficient and axialdispersion coefficient).108Nomenclature 109symbol Description DimensionReactor column diameter. LE Electrode potential(= Em — E8). voltE° Standard electrode potential VEm, E Slid matrix and electrolyte potentials. VE, E80 Slid matrix and electrolyte potentials, at the cath- Vode face.F Faraday’s number(=965E5). AT. (kmole. equiv) -‘g Gravitational acceleration. LT2C Gas mass flux, gas volumetric flow rate(in this ML2T1,cm3.min1work).h Packed-bed heigh L/ —3ikmo1e.L of gasH,H3 Henry s constant of liquid phase electrolyte and(kmole.L of liq.)interfacial region, respectively.Bed superficial current density. AL2it Limiting or diffusion limited current density. AL2Electronic and ionic current densities. AL2I Total limiting electric current. AkGaG Liquid-gas side film true(local) mass transfer LT’coefficient.k1 Interfacial surfactant film mass transfer coefficient. LT1kLaL Gas-liquid side film true(local) mass transfer LT’coefficient.k3 Liquid-solid true(local) mass transfer coefficient. LTK Overall mass transfer coefficient. LT’Ka Overall mass transfer capacity. T’KL Overall gas-liquid mass transfer coefficient. LT’Nomenclature nosymbol Description DimensionKLaL Overall gas/liquid mass transfer capacity. T’K8a5 Overall liquid/solid mass transfer capacity. T’L liquid mass flux, liquid volumetric flowrate(in this ML2T’,cm3.minwork).L length, meterM mass, kilogram.N Superficial flux of species A. kmole.L2T’F Reactor pressure. ML2TFe Liquid phase Peclet number(—_ULFL/ELDa).FL Packed-bed length (in this work, graphite felt). cmR Ideal gas constant.RA Mass transfer rate of species A per unit volume of kmole.L3Treactor.Rf Total flowing foam phase media electric resistance. OhmRd Total diaphragm resistance. OhmReG,ReL Gas and liquid phase Reynolds numbers(=Upd/t).S Electrode cross sectional area. L2T Time, second., Kelvin temperatureU9,UG,UL Superficial gas and liquid velocities (STP). LT’Inlet-outlet gas average superficial velocity, liquid cm.min1superficial velocity (in this work).V Electric potential, VoltV.r Reversible electrode potential. Vw Mass of packing per unit volume of reactor. ML3Nomenclature 111symbol Description DimensionWe Weber number(=UGdepG/aL).x,y,z Coordinates. Lz Number of exchanged electrons.Abbreviationssymbol DescriptionANOVA Analysis of VarianceA.S.E. Associated Standard Errorcm, CM centimeterequiv equivalentGR gramIN inchkmole kilogram molem metermho Ohm’mm minuteml, mL milli-litermm, MM millimeterPBE Packed-Bed ElectrodePBECR Packed-Bed Electrochemical ReactorPBFFE Packed-Bed Foam Flow-By ElectrodeTR Thermochemical ReactorNomenclature 112Greek Symbolssymbol Description DimensionDimensionless gas-liquid mass transfer coefficient.Dimensionless liquid-solid mass transfercoefficient.Total liquid saturation (=EL/ c).13d,Is Dynamic and static liquid saturations.P Dimensionless mass transfer coefficient(= —B2RT( +—)a8kA).6G,LL Pressure drop due to friction for gas alone, for liquid alone, and 2-phase flow, meter of water per meter of reactor length(=LPf/pLgh , m.H20.m’).Pressure drop due to friction ,meter of water per meter of reactor length(=Pf/pLgh,m.H20.m’)./F/FL Pressure gradient (in this work). bar.m’/PfCL 2-phase pressure drop along the reactor. ML’T’E Matrix porosity(EC + EL).EC,EL Gas and liquid holdups.G,cL,cGL Volumetric energy dissipations for gas alone for,liquid alone, and for 2-phase flow; meter of waterper unit time(m.H20.s’).Overpotential(= E — VT). voltIG,KQ,Kf, Effective flooded bed, pure electrolyte, and effec- Ohm’.L’tive foam electric conductivities.Nomenclature 113symbol Description DimensionA Flow parameter (= Pwat PairA Electrical conductivity factor or mass diffusivityfactor.Elecrolyte equivalent conductance. Ohm’ .equiv’.L2Liquid dynamic viscosity. ML’T’Stoichiometric coefficients.Dimensionless height (y).p Dimensionless bed thickness (x).PG,PL Densities of gas, liquid electrolytes. ML3Pp,Pw Densities of solid matrix, and water. ML3cr,cr, Effective solid matrix and pure solid matrix Ohm’L1conductivities.Surface tensions of gas, liquid phase, and water. MT2cpL Lockhart-Martinelli parameter of correlation[=(öcL/5L)”21,in low interaction regime.Lockhart-Martinelli parameterof correlation [=((GL/CL)”2], in high interactionregime.x Lockhart-Martinelli parameter of correlation[=(SL/3)h/2], in low interaction regime.x’ Lockhart-Martinelli parameter of correlation[=(CL/c)”21,in high interaction regime.Dimensionless electrode potential (=zFE/RT).Flow parameter(=[(th)]h/3).0L I’w PLBibliography[1] Adamson, Arthur. W.Physical Chemistry of SurfacesJohn Wiley and Sons, Inc., N. Y., 5th ed., pp:777 1990[2] Alexander, B. F., Shah, Y. T.“Gas-liquid mass transfer coefficients for cocurrent upflow in packed-beds.”Can. J. Chem. Eng., 54, 556(1976)[3] Astarita, G.Mass Transfer With Chemical ReactionElsevier Publishing Co., N. Y., 1976[4] Astarita, G.Scaleup: Overview, Closing Remarks, and Cautions, in Scaleup of Chemical Engineering Processesedited by Bisio A. and Kabel R., L.John Wiley é4 Sons Inc., N. Y., pp:677 1976[5] Beimesch, W. 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(1976) presented a frictional pressure drop correlation based on themodified Lackhart-Martinelli parameters or energy variables and x’ in high interaction regime for air-hydrocarbon systems and packing of spheres, 3 mm and cylinders,1.8x6 mm.Also, they presented a frictional pressure drop correlation based on Lackhart-Martinelliparameters in the feeble interaction regime for the same system.feeble interaction regime:= 1 + x’ + 1.14°5 .1 < < 80high interaction regime:ço = 1 -1-- (x’Y1 + i-6.55(’)° 0.05 < < 100124Appendix A. Extension to the Preview of the Parameters Investigated 125= /PfL/pLgh = (/..H/h)LSc = t1Pfc/pgh = (IH/h)0tPfw/pLgh = (.H/h){(L/E)[(1/pL)(tH/h)L + l/pw]}= {(G/c)[(l/p)(iH/h)c +1/Pw]}LG = -b G/pG1(L)w + ‘-1H/h = A’uc(G/p0)+B’(G2/pa)Sai and Varma (1987) measured pressure drop of cocurrent gas-liquid downflow throughpacked-beds for Newtonian foaming liquids. The authors correlated pressure drop interms of two groups: a)flow rates, packing characteristics, fluid physical properties, andb)Lockhart-Matinelli parameters.a-foaming pulse flow: F-foaming flow: F-gas-continuous flow: F-pulse flow: Fwhere F = fRe°6/,°75 , =b-trickling flow regime: = + +-high interaction regime: = -i- + 1These authors also correlated their data on the basis of:c-modified geometric model of Sweeny (1967) by Rao et al. (1983), which presents alogical framework for the inclusion of the other dynamic interactions such as friction atthe interface and the entrainment. Rao et al. ‘s model is presented as a set of two coupledcorrelations for total liquid saturation 3 and dimensionless pressure gradient, 6LCwhere:andf L = (6W/SL)112 , with‘1 x = (SL/Sc)”2(1 9’’L =1.. x’=(w/L)h/2 Iwith(&/ec)”2 I= 3, 0LwJL1 “ILL1 Pw1= 3, 67O()°( L O.1O.12.O“wL1 1LL) Pw1= 1,L1 ‘ILL) “Pw1= 1,‘CL1 L1 “Pw1(1—e)/eAppendix A. Extension to the Preview of the Parameters Investigated 126— — +1 = 0SW — J +7j., +7c—+ ab(6JL/pLgd)2/3(1.5Sy!)’/(d0/d)]7c — aL7L = 0where model parameters c and cc are the ratios of the equivalent area of the contactbetween the liquid and gas phases in two phase flow to that in single-phase flow. 0b is anideality factor expressing the probability of bubble coalescence and reformation and isexpected to assume values between 0 and 1. Hence, at trickling flow regime 0L = crc = 1and cxb = 0. For other regimes and foaming systems, Sai and Varma presented theparameters as:cL*103 aG*103 abgas-continuous flow 1.00 1.00 0.0pulse flow 0.75 1.59 0.046dispersed bubble flow 2.80 0.122Sai et al. defined in their model 5 = LiPfc/pcg in contrast to S LPfc/pLg defined byRao et al. The authors also pointed out that pressure gradient varied along the bed in adecreasing manner. d0 is a characteristic length of bubble formation, the equivalent lengthdefined by the following equation in terms of column diameter, D: d0 = [D — Ndj/Mand M the integral part of the ratio D/d and7L = (L/pL)/[(L/pL) + (G/pc)1, 7G 1 — 7LAn interesting point to mention and to be aware of. in domain of pressure dropinvestigations is the existence of the multiple steady state or hystersis loop in pressuredrop measurements in trickling flow regime and non-foaming systemsj52,55,69]. Thisphenomenon has not been sensed in the high interaction regime.Appendix A. Extension to the Preview of the Parameters Investigated 127A.2 Liquid HoldupIn this section some frictional holdup correlations given by different authors which arevalid for two-phase flow with foaming liquids are presented.Charpentier and Favier (1975) proposed a correlation for total liquid saturation basedon 1500 data points, on 20 gas-hydrocarbonsystems(with an average variation of ±20%) for all flow regimes with catalyst packingsin trickle-bed reactor.logfl = P + Q 1og’ + R(logx’)2 0.05 < x’ < 100whereP Q Rspherical particles —0.280 0.175 —0.047cylindrical particles —0.363 0.168 —0.043and the energy concept parameter x’, being a measure of relative liquid to gas flow energydissipation through packing, defined in this case as:,L/G ji/2Xpg hAlso the authors in their conclusions recommended, for design purposes the correlationof Sato et al. (1973), developed with spherical packings 25.9 and 10.5 mm diameters:/3 0.4a/3x° 0.1 < x < 20where6(1—6)________a3= d =a’ ‘ 1J_ 44I 6D(1—e)Midaux et al. (1976) correlated liquid saturation to Lackhart-Martinelli parameters forsystems of air-hydrocarbons with spherical packings of 3 mm and cylinders of ]..8x6 mmand 1.4x5 mm as:Appendix A. Extension to the Preview of the Parameters Investigated 128-the feeble interaction regime:0 66 °‘= (1 ±O.66x°81)0.1 < < 80-the high interaction regime:fl Q)( I’\O.3a— \X) 005 ‘ 100“(1 + O.92(’)°3)°°5. XThey reported that liquid holdup increases with increasing liquid flux and decreases withincreasing gas flux. In a comparison, the liquid holdup in foaming systems is less thannon-foaming systems, except at high gas loads, where there probably exists a slip betweenthe liquid film and the gas phase. This comes from the inadequate character of foamingliquids to form droplets easily.Clement and Schmidt (1980) proposed dynamic liquid saturation for an air-siliconesystem of trickle-bed as:lid = 0.84(WeQRec/ReL)°34The system parameters were: L = 2280 — 89500 kg/m2hr, G = 200 — 2000 kg/m2hr,e = 0.320 — 0.361, PL = 900 — 920 kg/rn3, oL = 18 — 20 dyne/cm, = 3.2 — 8.2 c.p.Appendix A. Extension to the Preview of the Parameters Investigated 129A.3 Dispersion CoefficientFor 3-phase nonfoaming thermochemical processes, there are plenty of data and correlations, but there is no literature for foam flow in any chemical processor. Several examplesfor nonfoaming systems are given below.Stiegel and Shah (1977) measured the liquid phase axial dispersion coefficient in apacked rectangular (16.8 cm wide x 2.06 cm thick x 122 cm high) bubble bed withd=0.44 cm of polyethylene packings. Superficial water and air flow rates ranged 5.42-35.9 kg/m.s and 0-0.203 kg/m2.s, respectively. The liquid phase dispersion and Pecletnumber were correlated to the gas and liquid Reynolds numbers as:Da 4.75E — 5Re°8Rej’3Pc = 0.0775Re3Re97Based on the analysis and comparison, they also concluded that axial dispersion of theirreactor geometry is about 2-2.5 times larger than those obtained in cylindrical towerswith equivalent flow conditions.Chu and Ng (1985) conducted research in a pulsating trickle-bed column with nonporous spherical particles of 0.3 cm diameter and Reynolds number range of 300-700based on the interstitial liquid velocity. Based on the combination of the method ofcharacteristics and Monte Carlo simulation of liquid phase dispersion in the liquid richslug and gas rich pulse they developed a model to predict liquid dispersion. Their analysisshowed a decreasing trend of dispersion with increasing liquid flow rate (L=2.4E3-15.E4kg/m2.hr and G=.662E3-2.4E3 kg/m2.hr) from homogenous regime to fully developedpulsing regime. The simulated Peclet number for their pulsating regime varied from1.3 to 1.75. This result agreed well with data of most of the other investigators. Theyreported a negligible effect of the gas flow rate on liquid dispersion and or that no clearAppendix A. Extension to the Preview of the Parameters Investigated 130trend was observed for dispersion with gas flow rate. In contrast to trickling flow regime,the effect of gas flux on dispersion is signiflcant[54j.Chu and Ng concluded that Peclet number is relatively independent of gas and liquidflow rates in the fully developed pulsating flow regime and the pulsating phenomena,although complex, does not contribute to dispersion, significantly. Finally they recommended a single-phase dispersion correlation of the type presented by Chung and Wen(1968) to use with the pseudo-homogeneous model with average liquid saturation, :c/3Pe = .2 +ILwhich will offer adequate estimation of liquid phase dispersion.In the following two reported cases of information of systems with foaming liquid arelisted:Weber (1961) found that liquid phase surface tension has little effect on the extent ofaxial mixing.Zimmerman et al. (1987) measured the liquid phase axial dispersion in trickling flowwith liquids having surface tensions ranging 10 to 72 dyne/cm. They reported negligibleeffect of surface tension on either axial or radial dispersion, while the wetting efficiencydrops from 99 to 80 percent.Appendix A. Extension to the Preview of the Parameters Investigated 131A.4 Gas-Liquid Mass TransferNguyen Ly et al. (1979) proposed a relatively simple model for gas-liquid mass transfer, accounting for the interfacial resistance due to surface active agent, in a foam bedcolumns. They assumed an interfacial surfactant film region of finite thickness which separates the bulk liquid from gas phase. The film region has greater gas solubility for gasreactant, but a diffusion coefficient 3-4 orders of magnitude lower than the bulk phase,and obeys local equilibrium with bulk phase for gas phase reactant.Shah and Mahalingarn (1984) conducted experiments and analyzed their data basedon Nguyen Ly model, with a 10% GO2 in air in a 2-phase foam bed reactor with gas velocity of 1.5-5 cm/s, pressure gradient up to 500 Pa/rn with two alkali foamates of sodiurnhydroxide and buffer solution of sodium carbonate and bicarbonate. Three different wiremesh sizes, 20, 60 and 100 were used to generate different bubble sizes. Surfactants usedwere: a)nonionic, Triton X-100 as a 1% V/V solution in water containing the reactant;b)cationic, hexadecyl trimethyl ammonium bromide (HDTMAB) as a .5% W/W solutionin water containing the reactant. The respective concentrations were selected to obtainlimiting stable foam.The authors assumed a plug flow model of gas and liquid for the analysis of theirdata and they obtained three mass transfer parameters: gas holdup; gas-liquid interfacialarea; and modified interfacial mass transfer coefficient as the product of interfacial masstransfer, k1, and Henry’s constant for solute in the interfacial film region, H3. Theyderived many conclusions concerning mass transfer parameters in foam flow processes.Some of their conclusions, which are perhaps valid in packed-bed electrodes with foamflow, but have to be justified, are concerned with k1.H3 They mentioned k1.H3 tobe independent of; 1)gas flow rate; 2)gas bubble size, and confirmed the assumptionsAppendix A. Extension to the Preview of the Parameters Investigated 132made by Nguyen Ly et al. (1979) concerning physico-chemical effects of interface surfactant layer. The authors obtained numerical values of ki.H=1.27E-11 krnole/m2Pa.s forthe nonionic surfactant andk1.H8=1.4E-11 kmole/m2Pa.s for cationic surfactant, withH5=6.9E-6 kmole/m3Paand surfactant film thickness of 1500 2k. The calculated liquidphase CO2 diffusivities are 2.75E-13 m2/s and 3.1E-13 m2/s, respectively. For the caseof their study, they concluded that; 1)for slow reaction between CO2 and sodium buffera contribution of 40-70% of total resistance to gas-liquid mass transfer is due to interfacesurfactant film region mass transfer resitance; 2)gas holdup is insensitive to the type ofsurface active agent, but depends on bubble size and gas velocity; 3)liquid phase masstransfer coefficient, kL, increases with increasing gas velocity.A.5 Liquid-Solid Mass TransferHirose et al. (1976) used spherical benzoic acid particles, d=0.28-1.27 cm, water system,with UL=O.O5-25 cm/s and U=0.7-100 cm/s and proposed a generalized correlation fortrickle-bed reactors:rz, 13.5_____— 0 8(__0.333D — EL PLDAppendix B. Preparations &Measurements 133Appendix BPreparations and MeasurementsIn this appendix the following topics are presented:I- Preparation of the Liquid SolutionsII- Preparation ofGaskets, Graphite Felt Packing, Stainless Steel Screen Packingifi- Preparation ofDiaphragm and MembraneIV- Preparation of the Plexiglas SlabsV- Preparation of the Electrodes and Current CollectorsVI- Measuring the Solid Volume of the Graphite Fiber BedVII- Specifications ofMaterials and Instruments Used in This WorkVifi- Cell Configuration and the Experimental Design Parameter Values Used Throughoutthis ResearchAppendix B. Preparations &Measurements 1348.1 Preparation of the Liquid SolutionsThree different solutions were made throughout this research:B.I.A Foaming 1 M Sodium Hydroxide SolutionA 1 M NaOH solution of 0.1 % v/v Tergitol (surface active agent), was made with 1085mL of 50 % caustic soda (reagent) and 20 niL of Tergitol, to 20 liters of distilled water inthe feed tank. The Tergitol was dissolved in approximately 2 liters water of temperature 60-70 °C. This solution was added to the remaining distilled water. The mixture was agitated toensure a homogeneous solution. The accuracy of this prime hydroxide solution was testedwith 0.1 N standard HC1 solution, in the presence of phenolphthalein indicator [88]. Thecorrection of the hydroxide composition from 1 M for this prime solution was normally doneby dilution of the total container with about 100 mL of additional water. The solution wasagain mixed and a second test was performed. The solution used in the experiments werewithin two percent o the target concentration of 1 N.B.LB Foaming Water SolutionTwenty liter solutions of 0.1 % v/v Tergitol surfactant were made by adding 20 mL ofsurfactant to 20 liters of distilled water, in the feed tank. As in the previous case, Tergitolsurfactant was dissolved in a small portion of the total water at 70-80 C, mixed and thenadded to the rest of the water. The solution in container then was stirred manually to ensure awell mixed solution.B.I.C 1 M Sodium Hydroxide SolutionThese solutions were prepared following a similar method to Part A, except thatsurfactant was not added. The concentration of the solution also was tested and corrected to 1M as in Part A.B.!! Preparation of Gaskets, 1/2’ Graphite Felt Packing and Stainless SteelScreen Packing.8.11.1 Preparation of GasketsDurabla gaskets were used for the anolyte compartment whereas Neoprene gaskets wereused for the catholyte compartment and in all other positions. All the gaskets were manuallycut with a knife, to the specified dimensions with the accuracy of about ±0.1 mm. Theaccuracy of cutting was achieved by using a sharp knife applied along a steel ruler edge. Thiswork was accomplished with many wasted duplicates, until a satisfactory gasket, i.e., a gasketwith straight and accurately smooth edges was cut. At high cell pressures irregular gasketswould cause enormous fluid bypass or channeling along the edges resulting in a different fluidAppendix B. Preparations &Measurements 135dynamic pattern. A dimensional drawing of such gaskets are shown in Figure B. 1 and thecorresponding dimensions in Table B. 1.I- fornie&c tiwisfer ea’se ii- for a!! other easesFigure B.1: Drawings of the Various gaskets.Table B.1: Gasket dimensions corresponding to Figure B.1.Dimensions, mm—CI— CI Ibasket Type a b nominal size, in. 1 d e f.Teoprene:1- Mass Transfer 30 48 3/16, 1/4 166 15 59- Other Cases:a- large size 50 116 1/8,3/16, 1/4 166 15 25b-smallsize 40 57 1/8 105 10 24)urabla: 50 115 1/16 165 15 25Appendix B. Preparations &Measurements 136BiI.2 Preparation of Graphite Felt and Stainlee Steel Screen Packingsa- The 1/2” graphite felt packings were cut with a sharp knife accurately or each casemeasurement and according to the dimensions given in Table B.5. Then it was soaked in A 10drop ofMAKON F12 wetting agent per liter solution for more than 10 hours, before beingused in the cell. But for the case of mass transfer a prior treatment of the packing with 5 %nitric acid (soaked over 24 hours) was performed to eliminate traces of metal elements(especially iron) , which is believed to have adverse catalytic effects in electrolysisb- The stainless steel screen packings, used in anolyte compartments, were cut by presschopper to precisely fit into the Durabla gaskets, according to the sizes given in Table B. 1.Bill Preparation ofDiaphragm and MembraneThe sheets of diaphragm (0.1 mm thick macroporous polypropylene) were used asisolating substances between the graphite felt and the electrode. Prior to their use, thefollowing was done to the diaphragms to make them conductive.1- Cut to right size, to fit properly in its position (isolator) in the cell.2- Soaked for approximately 2 hours in 2 % solution ofMerpol in methanol.3- Removed from solution, rinsed with distilled water and soaked in iN NaOH solution of0.01 % Merpol or 0.1 % Tergitol for at least one hour, before utilization.The Naflon 214 membrane also underwent the same treatments as listed above, beforeutilization.Appendix B. Preparations &Measurements 137BJV Preparation of the Plexiglas SlabsThe holding plates of the cells were of 1 “thick Plexiglas material slabs (acrylic plastic),machined according to the following dimensional drawing. The numerical values ofdimensions for two large and small cells are given in Table B.2.Table B.2: Dimensions of the Plexiglas slabs according to Figure B.2.Dimensions, mmDimensions: a b I c ] d I e f I hLarge Cell: 130 140 70 20 15 110 35 46Small Cell: 100 70 -- 25 10 50 35 40Iron/slab back slab1- four of1/871/1”thjzunen/pinsIiI- lye of J/8”iYP? 2- lio of1/871/8”1io diWnbali.’sJolsY- ‘A” ckainc’ boles /bal/s)Figure B.2: Drawing of the Plexiglas slabs.Appendix B. Preparations &Measurements 138B.V Preparation of the Electrodes and Current CollectorsThe current collectors were made from 1/16” copper sheets, and the electrodes weremade from 1/32” stainless steel sheets. Two design options were machined for. One, simpleflat sheets, Figure B.3, were used in conjunction with rubber gaskets for sealing of the cell.The other design, with which the sealing gaskets were not needed, was made from the flatsheet electrode welded with 1/8” couplings at inlet and outlet, Figure B.4. Dimensions ofthese electrodes are given fri Table B.3.Table B.3: Dimensions of the current collectors and electrodes according to Figures (B.3-4).type & size a, mm [ b, mm B, degreecurrent collectors 30& electrodes: 20large cell: 110 80small cell: 50 69back piece front pieceA view8.5Figure B.3: Drawings of the copper current collectors and the stainless steel flat sheet electrodes.19Appendix B. Preparations &Measurements 139A viewback piece8.5A viewfront piece-28 -Figure B.4: Drawing of the 1/32” stainless steel electrodes with couplings.Appendix B. Preparations &Measurements 140B.Vl Measuring the Solid Volume of the Graphite Fiber BedDue to variation in the graphite packing from one cut to another of the same size, it wasconcluded that the packing density varied as well. Hence, a special solid volume meter for thispurpose was designed and made (of Plexiglas) to measure the solid volume of each packingutilized in this work. The schematic diagram of this instrument is shown in Figure B.5.This method is based on measuring the displacement of the liquid level in the top graduatedpipette, upon immersion of the prepared graphite fiber bed. The liquid was a solution ofdistilled water with 10 drops ofwetting agent, “MAKON P12”, per liter.mili-graduteburete‘aB I-7,.5-3;-2;-o.displacementplexiglas rodfittinglidttingdisplacementliquidFigure B.5: Instrument to measure the graphite fiber-bed solid volume.Appendix B. Preparations &Measurements 141B. VI. I Conduct ofMeasurements1- The cylinder was filled with the wetting solution to such a level that after closing andtightening the lid (including the fully inserted plunger to the bottom) the solution level(initial) in the graduated pipette was just above the zero level. This level was read with thehelp of a magnifying lens and was recorded.2- The 0-ring sealed plunger rod was carefully pulled out with no water loss from the systemand set aside.3- 20 mL of the solution from the reservoir solution with the help of a long 20 mL pipettewas taken and saved for later on re-addition. In this condition, the solution level in thereservoir was far enough below the tightening lid surface.4- The top lid was opened and set aside carefully with no solution being lost.5- The packing was gradually dropped into the cylinder and it was allowed to sink deep intothe solution and was fully flooded.6- The lid was put back in the same position and tightened. The 20 niL solution withdrawn inpart 3 was re-added and the plunger was placed back and pushed to the bottom of thereservoir.7- The solution level was observed in top graduate pipette and the value (final) was read. Thesolid volume of the packing was the difference of final and initial readings.The experimental values in solid volume of the packing used in the mass transfermeasurements areInitial reading of the graduate pipette (Part 1): 0.15 niLFinal reading (Part 7): 1.30 niLPacking bed solid volume: 1.15 mLAppendix B. Preparations &Measurements 142B. VII Specifications ofMaterials and Instruments Used in This WorkTable B.4: Parts and materials specifications used in this research work.Parts & Materials Supplier SpecificationsSodium hydroxide solution, 20 BDH Chemical Inc. 50 % w/w, reagent gradeL bucket Toronto, Canada R01928-86Tergitol, 500 mL bottle SIGMA Chemical Co. Polyglycol ether, (nonionic)St. Luis, Mo. USA surfactanttype NP-b [9016-45-9]Pressure gauges:41/2” dial CPW CPWHydro-Poise, Edmonton, 316 s.s., 0-160 psiCanada4 1/2” dial Marsh Marsh Instrument Company, Skoki. 316 s.s,. 0-200 psiUI. USA type 100-3ss, 316 s.s.,21/2” dial ‘WIKA WIKA 0-200 psi & 0-100 psi3 1/2” dial WiKA 0-160 psiFlow meters:Rotameter Cole-Parmer Tube No. 42-15Chicago, 111, USA Ser. No. 015279Rotameter Matheson Model No. 7630-602Valves:3-way valve Whitey & Hupro Co., Ohio, USA s.s. 1/4”Needle valve Swagelok s.s. 1/8” & 1/4”Stop cock valve “ s.s. 1/4”check valve “ s.s. 1/4”, 200 psiReliefvalvePneumatic control valve (air Research Control Valves s.s. 316, 3-15 psito close) Precision Products & controls Ser. No. 50936 Trim FInc., Tulsa, USA Female 1/4” NPTFoxboro 43AP Pneumatic Foxboro, Canada Ltd., La Salle, Model 43APcontroller Quebec, Canada Style BMilton Roy metering pump Milton Roy Company, Petersborough, Model M-75(positive displacement) Ontario, Canada 120 mL/min of liquid1/4’ piston shaftCole Parmer tube pump with Cole Parmer Instrument Company, PumpCat No 7553-20pump head tube size of 13 and Chicago, Ill,USA Controller Ser No 569867its Masterfiex controllerLAUDA Themostatic water MOW Wesgratte Werk LAUDA, Type NB-S 15bath Germany Ser. No 29442Sorensen DC power supply Raytheon Company, Manchester Model DCR4O-25-BN.H., USA output: 0-50 V, 0-30 AAppendix B. Preparations &Measurements 143Table B.4 continuedParts & Materials Supplier SpecificationsHeath built Heath Company Model EUW -27signal generator Benton Harbor, Michigan, USA Ser. No 9412667Cation exchange membrane Electrosynthesis Company, Inc. Nafion 214Amherst, New YorkGraphite felts (elctrode The Carborundum Company, Grade GF, density: 1.5 gr/cc,packing) Sanborn, New York fiber diameter: 20 micronDiaphragm Enka America, Inc. ACCUREL 1EAsheville, NC., USA Micro porous polypropylenewith 1 micron pore diameterB.Vlll Cell Configuration and the Experimental Design Parameters ValuesUsed Throughout this Research.Table B.5: Cell configuration and operating parameters for all cases.pressure drop holdup dispersion conductivity mass transferporosity levelwidth x heightU1 levelsrange, cm/mmUg levelsrange, cm/millporosity levelwidth x heightU1 levelsrange, cm/mmUg levelsrange, cmlminporosity levelwidth x heightU1 levelsrange, cm/mmUg levelsrange, cm/mm78%ScmxlO.7cm68.6 - 22.6529.5 - 67.287.6 %5 cmx 10.7cm55.5 - 16.5528 - 9589.7 %ScmxlO.7cm48.3 - 22328.9 - 6584.3 %5 cm x 10.7 cm68.6 - 22.6529.5 - 67.287.6 %5 cm x 10.7 cm55.5 - 16.5528 - 9590%5 cmxl0.7 cm48.3 - 22328.9 - 6575%4 cm x 4.7 cm65 - 20312 - 2184%5 cm x 10.7 cm65 - 20611.5 - 87.586.6 %ScmxlO.7cm65 - 20511.5 - 130.570.8 %4 cmx 4.7 cm65 - 20819.7 - 25784.7 %5 cm xlO.7 cm65 - 20811.5 - 14587.5 %5cmxlO.7cm65 - 20911.5 - 145N/A78%3 cm x 4 cm59.5 - 24.5529 - 148.584%3 cm x 4 cm66 - 24528 - 148Appendix C. Mathematical Treatment ofData 144Appendix CMathematical Treatment ofDataIn this appendix the porosity measurement procedure is discussed in conjunction with thecorresponding sample calculation, in the first section. In the second section the step by stepmathematical calculations are performed to demonstrate the routines involved in the analysisof the data for each case.C.1 Porosity Measurement of the Packed-Bed CellBed porosity of a satisfactorily assembled cell was obtained in two distinguished methods.A- Quick Closing Valve Method, for all measurements except for mass transfer..B- Mathematical method for mass transfer experiments.C.1.1 Conduct of ExperimentA- Quick Closing Valve Method, applied in all measurements except for mass transfer.The procedure suggests complete de-gasification of the cell first, ensuring a filly floodedcell, before applying the quick closing valves method. To achieve this goal, the following stepswere followed, referring to the Figure 4.1:1- Set the thermostat bath to 220 C and started pumping electrolyte to the cell.2- Set the cell inlet pressure to 80 psig, by adjusting the Foxboro controller set-point. Thispressure set was used, because it was close to the average cell operating pressure for allcases.3- After a few minutes running the electrolyte, when the system operated steadily, started degassi,ring the system, as follows.4- Quickly purged the upstream lines including the pre-foamer from gas bubbles by openingthe needle valve # 3. At this stage lots of foamy phase was by-passed. Held the valve for afew seconds, until the system pressure dropped to about 20 psig, then closed the valve andwaited about 5 minutes until the system reached its steady operation. Repeated purgingprocess from beginning of this step, until the foamy by-pass was disappeared.5- Moved to 3-way valves # 7 and # 8, in consecutive orders and performed the purgingprocess in the same manner as in step 4. The purged stream by these valves was notrecycled, as in the step 4, but it was led to the waste, by switching the 3-way valves to theopposite opening.6- Finally the system was purged by needle valve #9, to remove the last hidden gas bubblesleft in the top section and around the 3-way valve # 8.Appendix C. Mathematical Treatment ofData 145After passing the above steps, when the system was flooded with electrolyte, the quickclosing valves method was applied. The captured electrolyte was then flushed out with water.The washout was collected in a graduated cylinder for later hydroxide content titration, andthe cell was blown with air to remove the water residual left from the washout process. At thisstage, the cell along with the rest of the system was ready for any of the next scheduledmeasurements. The hydroxide content of the washout was determined by titration with 0.1 Nstandard hydrochloric acid in the presence of the phenolphthalein indicator. The titrated,equivalent 1 M hydroxide solution volume of the captured washout is the sum of theelectrolyte content of the bed voids and the e\lectrolyte contents of the bottom and the topend-lines extending from distributing volume gaps at each side of the bed to the dead closingends of the valves. Figure C. 1 shows the distribution of the total captured electrolyte.The captured electrolyte consisted of:1- Top and bottom tubing endline volumes, 2.6 mL each, which were measured by fiffing withthe aid of a graduate syringe.2- The 1/8”X118” bore spacings (flow distributing aids), whose precise dimensions are givenin Table A.2.3- The gap spacings at both top and bottom ends of the bed whose sizes were measured on anassembled cell (listed in Table C. 1).1,2 closing 3-way valves3,4 top & bottom gaps5,6 top & bottom endlines7,8 top & bottom bore spaces9 flooded bedFigure C.1: Distribution of the captured electrolyte by quick closing valve method.B- Mathematical method for mass transfer experiments.In this method, the total volume of the packing was calculated based on the geometricaldimensions of the graphite felt packing. Then, the calculated total volume was corrected forthe solid volume of the graphite felt (see Section B.VI) to obtain the net packing void volume.The bed porosity was obtained by dividing of packing void volume to total packing volume.Appendix C. Mathematical Treatment ofData 146The width and length of the packing was known from the time of cutting . The bedthickness was obtained from measurements of the assembled cell..C.1.2. Sample Calculation of the Packed Bed Porosity MeasurementsA- Quick Closing Valve Method, applied in all measurements except mass transfer one.The following is a sample calculation at low porosity for a large cell used for pressuredrop and liquid holdup measurements demonstrates details of the captured electrolytedistribution.The cell was assembled with 11.6 cm length 1/8” Neoprene gasket, and packed with 1/2”Carburundum graphite fiber felt, PL10.6 cm length, PW=5.2953 gr., VS=3.82 cc solidvolume, under 50 kg-cm torque pressure (corresponding to the pressure drop and holdupmeasurements at low porosity):Cell Endline Gaps Dimensions, mm:Bed Thickness Bottom Gap Hei2ht Top Gap Hei2ht Bed Width Bore WidthB=3.2 BH=1 TH=3 BW=48.5 BOW=46Calculation of End Volume Contributions:1-Bottom End: BEL = 2.6 +48.5110*3.2/l0*1/10+(25.418*25.418)*23/1000= 3.1052 mL2- Top End: TEL = 2.6+48.5/10*3.2/10*3/10+(25.4/8*25.418)*23/1000= 3.4156 mL3- Total End Volumes: VLE = 3.1052+3.4156= 6.52 mLFor this analysis two titrations were made with 0.1 N hydrochloric acid in presence ofphenolphthalein indicator; as follows: 1- On the inlet electrolyte itself and 2- On the washoutof the captured electrolyte. The inlet electrolyte titration facilitates calculation of the 1 MNaOH volume ofwashout solution in the absence of the reagent 1 N HC1.1- 5 mL of the inlet electrolyte sample was diluted with 100 mL distilled water, well mixedand V1=10 mL of it was neutralized with V2=4.8 mL HC1 reagent.2- X=10.05 mL of the total Z=568 mL washout solution was neutralized with Y=3.54 mLHC1 solution.Based on the above data the total captured electrolyte in quick closing valve method may becalculated:5YZV1 5*3.54*568*10— X*(l00+5)*V2 — 10.05*105*4.8 —Correcting for end volume contributions, the total bed void volume is:VE = VL - VLE = 19.85-6.52 = 13.33 mLAppendix C. Mathematical Treatment ofData 147Therefore total packed bed volume is:VP=VE+ VS= 13.33+3.82=17.l5mLNow the packed bed porosity is:100VE = 100*13.33=VP 17.73B- Mathematical method for mass transfer experiments.In these experiments the measured dimensions of the packings are given in Tables (D. 13-14). At ZERO level porosity, the following data is at hand:Bed thickness: = 4.02 mmBed width: =29 mmBed length: 4 cmBed solid volume (see Section B.VI): =1.085 cm3Accordingly, the bed porosity is calculated as:60.402*2.9*4_1.085*ioo 759 %0.402*2.9*4Table C. 1 is the listing of the bed porosity values for each case along with the relateddimensional parameters, according to the above sample calculations.Appendix C. Mathematical Treatment ofData 148Table C.1: Measured bed porosities along with contributed endline dimensions, for all cases.procedure 8W B Til 811 BOW BEL TEL VLE Vi V2j VS 6 %pressure drop& liquidholdup:low porosity 48.5 3.2 3 1 46 3.12 3.42 6.52 10 4.8 3.82 77.73zero porosity 48.34 4.2 3.56 1.74 46 3.29 3.66 6.94 10 4.8 3.90 84.23high porosity 47.0 5.12 3.5 2 46 3.42 3.8 7.20 10 4.8 3.90 87.63liquid axialdispersion:low porosity 38 2.95 2.5 1.5 40 3.05 3.16 6.21 10 4.48 1.55 73.40zero porosity 48 4 4 4 46 3.70 3.32 7.02 10 4.42 4.2 84.13high porosity 48 5.5 4 4 46 3.99 3.99 7.98 10 4.78 4.6 86.59flowing foamelectricalconductivity:low porosity 39 2.944 2.5 2.5 -- 2.96 2.96 5.92 10 4.43 1.50 71.01zero porosity 48 4.84 3 3 -- 3.23 3.23 6.69 10 4.77 4.05 84.69high porosity 47 5.54 3.5 3 -- 3.39 3.52 6.91 10 4.82 3.84 87.16overall masstransfercapacity**:zero porosity 29 4.02 -- 1.085 75.9high porosity 29 5.4 -- 1.105 82.36** In this case the bed porosity was obtained by mathematical method, taking into account the total solidvolume of the packed graphite felt.Appendix C. Mathematical Treatment ofData 149C.2 Sample Calculations for Each CaseIn the following sections sample calculations of the mathematical analysis of data obtained infive cases are presented.C.2.1 Calculation of the Flow RatesThe flow of liquid for each run was adjusted by means of rotary dial setting of the Milton Roypump and flow of gas was adjusted using a needle valve and a rotameter. Using the calibrationcorrelations, given in Appendix E for the pump and the rotameter, the volumetric flow rates, Land G were calculated. In this section RUN ID “EML2G111 of pressure drop measurements, ischosen for demonstration purposes. The detailed data at this run is:Cell Configuration Data: Pressure Drop MeasurementsPOROSITY LEVEL GASKET SIZE IN BED POROSITY % BED LENGTH CMLOW 1/8 77.73 10.6BED WEIGHT GR I BED VOID VOL mL I BED SOLID VOL mL mED THICKNESS MMI BED WIDTH MM5.2932 I 13.33 I 3.82 - 3.2 I 48.5 IPressure Drop Data:Press.taplocs,cm: 0.1 10.8Run Pump P P1 P4 Gas RoL P gas T gasID % psig psig psig Reading psig °CEZL2G1I 8.2 I 138 I 132 I 40 I “C” 27 I 195 I 21.6Accordingly the liquid pump is set at PU = 8.2 % and the Cole Parmer rotameter is atGCM = 27 scale reading. The L and G, are calculated as follows:Milton Roy electrolyte supply pumpL=0.1743+ 1.6771 *pTJ000128 *pUA2546E06 *PUA3L0.1743 + 1.6771 * 8.2-.00128 *82A2546E..06* 8.2A3 = 13.8 mL/minCole Parmer rotameter for gas at rotameter conditions, P and TG1=6.5365+0.1872*GCM+0.0021*GCM2= 13.12Gi = 6.5365 + 0.1872 * 27 + 0.0021 * 27 A 2 = 13.12 mL/minFlow rate at STP conditions is calculated from Gi via the transforming equation, utilizing theexpansion factor, EXPF:GG1*EF=G1/TS*PGASV PS*TGASorG = 13.12 1273.15(195 + 14.7) = mL/min STP14.7(21.6 + 273.15)Appendix C. Mathematical Treatment ofData 150The liquid and gas loads, UL and Ug, are calculated from L and G as:U = and Ug=LA AwhereVE+VS 13.33÷3.82 2A= = =1.62 cmFL 10.6henceu 13.33 = 8.6 cm/mm and Ug=21=29.5 cm/mEn atSTPL 1.62 1.62The gas loads at other conditions may be obtained as follows:At entrance conditions:UGIN= * * Ug = 14.7 *(273 15 + 22) * 29.5= 3.20 cm / mmPIN * TS (132 + 14.7) * 273.15At exit conditions:UGOUT=* TOUT*Ug = 14.7 *(273.15+22)*29.5= 8.41 cm! mmPOUT * TS (40+14.7) * 273.15At entrance-exit average conditions:UGIN+UGOUT 8.41+ 320= = 5.8 cm / mm2 2Average foam velocity:UFOAM= UL+UG=8.6+5.8= 14.4 cm/mmFoam volumetric flow rate:QFOAM=UFOAM * A = 14.4 * 1.62 23.33 mL/minThe above numerical results are shown in the following one row table, which is part of thefirst row of the Tables (C. 1,4):The above mathematical routine of the experimental data has been incorporated with maincomputer programs, as a subroutine, to calculate these flow quantities. A listing of thisroutine has been incorporated in Appendix G, Part C.Appendix C. Mathematical Treatment ofData 151C.2.2 Calculation of Liquid Holdup from Washout Solution Obtained in HoldupExperimentsThe liquid holdup of packed cell is the liquid volume fraction in the packed bed under foamflow, condition. The washout solution obtained in this case is being treated in a similar mannerto the porosity case. Except the calculation of the endline electrolyte contributions, due to thepresence of the gas with the liquid. To demonstrate the idea, the data ofRUN ID EML2G1,listed in the following table is analyzed for its holdup value.Cell Configuration Data: Liquid Holdup MeasurementsPOROSITY LEVEL GASKET SIZE IN BED POROSITY % BED LENGTH CMLOW 1/8” 77.73 10.6BED WEIGHT OR BED VOID VOL mL BED SOLID VOLmL BED THICKNESS MM BED WIDTH MM5.2932 13.33 3.82 3.2 48.5Liquid Holdup Data:Run pump P P in P out Gas Rot. P gas T gas X Y ZU) % psig psig psig Reading psig o C ml ml mEML2G1 I 8.2 I 138 I 132 I 40 I “C” 27 195 I 21.6 I 10 2.1 I 250This run corresponds to the cell setup for pressure drop and holdup measurements, at lowlevel porosity and hence has the same total endline volumes, outlined in the porosity samplecalculation of the previous section:End Volume Contributions:1-BottomEnd: BEL=3.11 mL 2-TopEnd: TEL=3.42mL3 - Total End Volumes: VLE = 6.52 mL 4- VS3.82 CC 5- VE = 13.33 mLAs in the previous section, the total liquid content of the entrapped foam in terms ofX, Y andZ, may be obtained as (for the same inlet electrolyte):5YZV1 5*21*250*10VL= = =5.21 mLX*(100+5)*V2 10.05*105*4.8VL value is the sum of entrapped liquids in the top and bottom end lines plus the bed. Withthe assumptions of constant pressure at end volumes, fully gas-liquid concurrent (perfect foamflow) and steady state conditions, the top and bottom end contributing liquid fractions may beestimated as follows:L *3.42L+Ga- At top end section:Appendix C. Mathematical Treatment ofData 152L and GT are the liquid and gas flow rates in the top end. G may be described according tothe outlet temperature and pressure and its value at STP conditions, G:G PS(TOUT+TS)*GT- TS(POUT+PS)From the flow correlations, we obtain the values ofL = 13.8 mL/iriin and G = 47.7 mL/min.Gas flow rate at top end is obtained from the above equation as:GT14.7*(22+273.15) *477 = 13.85 rnL/min273.15 * (40+14.7)Substituting for G value in the top end liquid content contribution to the entrapped foam is13.8 *342=171 mL13.8 + 13.85b- At bottom end section: * 3.11L + GBFollowing a similar path as part (a), the gas flow rate at bottom end conditions isG8= PS(TJN+TS) *G=14.7*(22+273.15)*47.7=5.20 mL/minTS(PIN + PS) 273.15 *(132 + 14.7)and similarly the bottom end liquid content contribution to the entrapped foam is13.8 *311=226 mL13.8 + 5. 20Hence, the total end line liquid contribution is: 1.71 + 2.26 = 3.97 mLTherefore, the bed liquid content is:VL= 5.21 -3.97 1.24 mLNow, holdup can be calculated from, defining formula, as100VL 100*1.24= =7.2%VE+VS 13.33+3.82This result is presented in the first row of the Table D.4.A Basic computer program to analyze the liquid holdup measurements and to calculate theliquid holdup, according to the above routine is listed in Appendix G, Part C.Appendix C. Mathematical Treatment ofData 153C.2.3 Calculation of Liquid Axial Dispersion CoefficientIn measuring the dispersion coefficient of the experimental cell, a conductivity flow cell wasinstalled at the outlet of the cell. The experimental procedures and pertinent concepts areoutlined in chapter of the experimental procedure. In these measurements for each run, a pairof dynamic tracer response data files, one for the overall (the fixed-bed plus the conductivitycell) and the other for the conductivity cell was obtained. In this section, RUN ID “EZL4G3”has been chosen for sample calculation of the dispersion coefficient. The aforementioned pairof response data files associated with this run are EZL4G3 and L4G3. The principle of linearindependent closed vessels in series discussed by Levenspiel, (1972) is utilized, to deconvolutethe overall dispersion coefficient. According to this principle, first the fixed-bed variance iscalculated by subtracting the conductivity cell variance from the overall variance. Thenutilizing the formula relating the dispersion coefficient to the variance, the fixed-bed liquidaxial dispersion coefficient is calculated.Descriptions of each row entries of these two files are given in the chapter ofexperimental procedure and are demonstrated in symbols below. At the end of each run, whenthe tracer viewed in the monitor, showed a prolonged stable zero offset, the logging wasstopped. After completion of each run, the logged file was viewed and the sampling duration,i.e., the best elapsed time which could represent the end of the run was selected. These timevalues were recorded in the last two columns of the experimental design tables to be read bythe computer program which was written and used to analyze the data systematically. In theprogram, 10 % excess on elapsed time was allowed to ensure a complete tracer passout overthe visual judgment of the tracer detected by conductivity sensor.Recorded row entries of the selected two files, at the sampling duration plus 10% confidencetime limits for the logged files, EZL4G3 and L4G3 is:SAMPUNG SIGNAL, [ vdt, f tvdt, f tvdt,FILE DURATION v,ID +1O%,s V V.s V.s2 V.s3EZL4G3 50.30 0.23 7910.83 113054.98 2081091.38L4G3 6.7 0.04 832.46 1795.35 4851.82From the first row of the above table, overall mean residence time and overall variance iscalculated:f tvdt 113054,98= fvdt = 7910.83= 14.29 sf tvdt 2081091.38—1= 1 0288ifvdt 14,292*7910.83 =Appendix C. Mathematical Treatment ofData 154Similarly, from the second row of the table, the mean residence time and the variance of theconductivity cell is calculated:- 1795.35=2.16 sC 832.4602 = 4851.82 —1=0.253C 2.162*832.46On the assumption of the closed vessel, variance of the fixed-bed may be calculated:J2 = cr — = 0.288 — 0.253 = 0.035The applicable characteristic equation, relating dispersion number to the variance in a closedvessel is= 0.035 = 2L)_2(UDL)2(1_e_1)Ignoring the second term on the right hand, one can calculate dispersion number as a firstapproximationD )020.03500175ULL 2 2Calculate the ignored term and correct the approximated value(uL)2(1 _e’L) = (0.0175)(1 — exp(—1 / 0.0175)) = 0. 0003First corrected dispersion number within less than 0.00 1 increaseD)=0.0175+0.00031=0.01781ULLwhich is accepted as the final variance value. The recursive trial and error process may becontinued until the set tolerance level (0.001 in this calculation) is achieved. The axial liquiddispersion coefficient is obtained from its defined relation with dispersion number.D )*U*L=001781*1278*107=0041 cm2/sULLA Basic computer program to analyze the liquid axial dispersion measurements and tocalculate the liquid axial dispersion coefficient, according to the above routine is listed inAppendix G, Part E.Appendix C. Mathematical Treatment ofData 155C.2.4 Calculation of Flooded Bed and Flowing Foam Electrical Conductivitiesa- Flooded Bed Electrical ConductivityThe flowing flooded bed with electrolyte at 80 psig was chosen for this measurement. All theother conditions are the same as explained in the chapter of the experimental procedure. Theonly special treatment in this procedure, worth mentioning is the degassification of the cell,which was tried by strong purges to atmosphere via the 3-way valves #7 & #8, on numerousoccasions, until no tiny bubbles were observed in the purged effluent solution. This treatmentis necessary, ifwe claim a flooded bed is under investigation. After a completely flooded cellwas achieved, 15 mV AC electric potential was applied to it and current measured. Thiscurrent for high level porosity bedof 87.16% isl= 176.4 mA.Rd__Rd-4 WMMM WMWith the assumption of pure Ohmic jnce due resistance due resistance dueresistance in effect, the Ohm’s law to diaphragm to flowing fluid to diaphragmacross the cell and with reference tocircuit ofFigure C.2 may be written Figure C.2: Cell Ohmic resistanceanalogy including diaphragms.R= =2Rd+Rf=[+J(!) (C.1)IReff lcd KSIn the above equation ohmic efficiency of the power supply system, from Appendix E,Re = 0.763; diaphragm thickness, Bd = 0. 1E-3 m; and fiber bed thickness, B = 5.44E-3 m.SuLstituting for known values15 [20.1E35.44E3( 1(C.2)176.4*0.763 lcd K 4.4E—3As can be seen from the above equation the electrical conductivity of the Diaphragm, lcd,must be found and then substituted to obtain the flooded bed electrical conductivity, K. Todo so, another cell was setup, identical but with an extra diaphragm sheet laid in the centerthickness of the packing, i.e., in-between of the halves of the packing ( cut through thecenter). For this cell the passing current was 157,3 mA under the same applied electricpotential. Ohm’s law in this case may be written as:15 301E3544E3 1(C.3)157.3*0.7609 lcd K 4.4E—3Subtracting equation C.2 from equation C.3 reduces the number of unknowns to one, lcdAppendix C. Mathematical Treatment ofData 15615 — 15 — O.1E—3157.3*0.7609 176.4*0.7631(dsolving the last equation for 1(d yields the electrical conductivity of Diaphragm,= 1.659 mho/m. Substituting for ic in equation C.3, the value of the flooded bedelectrical conductivity gave Ic = 14.963 mho/m. Writing Neale & Nader correlation, relatingthe conductivity factor to the electrolyte conductivity, 1(0, and the cell porosity:26K’ = K°3—8Neglecting the presence of the surfactant, 0 may be calculated for the electrolyteK0=10OZ+V÷CA =1O0*1*1*1..E3*158.4=15.84 mho/mSubstituting and s values yields:2*0 8716,c=15.84* = 12.97 mho/m3— 0.8716As can be seen, the measured value deviates from estimated one, ic, by a factor of about+15.34 % higher, which is believed to be due to the surfactant effect. With similarexperiments, flooded bed electrical conductivities of the cells at LOW and ZERO levelporosities were obtained, and are listed in the Table C.2, along with the related parameters.Table C.2: Graphite fiber flooded bed effective electrical conductivity values.Porosity B I V*I R, R5. R S K Dev% mm mA Ohm m mho/m mho/m %87.16 5.544 176.3 2645 85.08 0.762 111.6 4.4E-3 14.963 12.97 15.3484.69 4.844 165.8 2487 90.47 0.762 118.8 3.84E-3 14.435 12.47 15.7671.02 2.944 58.6 879 256 0.746 343.2 1.4E-3 8.1782 9.826 -16.8From the first two rows of the above table, one can judge that the presence of the surfactanthas a positive effect on apparent electrical conductivity of the electrolyte. But, at lowerporosity, other porous structure like partially blocked porous media may be established, whichcould adversely effect the packed cell electrical conductivity. In the above table, columns R prand R are the uncorrected and corrected cell resistances by cell resistance efficiency factor, A’ff.respectively.Appendix C. Mathematical Treatment ofData 157b- Flowing foam electrical conductivityFor the purpose of this sample calculation, the RUN ID EPL2G3” has been chosen. In thisrun, I 127.2 mA with the corresponding resistance efficiency, Reff= 0.77 (see Appendix E).Substituting for I, Reff and for the values B, 1d and S values from Table C.2, in equation C. 115 2*0.1E_3 5.44E—3 1=[ + ]( )127.2*0.77 1.659 lcf 4.4E—3and solving for icr, the electrical conductivity of the flowing foam is calculated as ice- = 6.91mho/m, for EPL2G3 run.A Basic computer routine to analyze the flowing foam electrical conductivitymeasurements and to calculate the Kf, according to the above routine is listed in Appendix G,Part F.Appendix C. Mathematical Treatment ofData 158C.2.5 Calculation of Overall Mass Transfer CapacityThis sample calculation is based on a two-reaction cathodic model (reactions[35,95J C.4 andC.5) in the catholyte compartment, which was proved to be the correct assumption afternumerous chemical and physical experiments were performed on the cell effluent stream. Inthe anode compartment a counter electro-oxidation reaction of hydroxyl ion (reaction 3 )takes place.Cathode:02 + H20 + 2e -> OH + H02 E° -.076 V (SHE) (C.4)2H0 + 2e —* H (gas) + 20H E° = -.80 ( “ ) (C.5)Anode:40W — 2}10 + 02 (gas) + 4e E° = .42 V (SHE) (C.6)The mathematical modeling used in analysis of the data was based on the followingassumptions:1- A cathodically polarized electrode was held for the entire packed bed electrode, forreaction 1.2- A uniform current density prevailed over feeder electrodes.3- Electrochemical reaction 1 is a fast heterogeneous reaction and the process runs at limitingcurrent condition and hence is mass transfer controlled.4- Reactant species, A (oxygen gas molecules), reach the polarized cathode surface and wasreduced to hydrogen peroxide which was released to liquid phase at no difflisionalresistance and with no further homogeneous reaction.5- For oxygen transfer of this process an overall mass transfer capacity, Ka, is defined in termsof its solubiity and perhaps a concentration profile ofFigure C.3.6- The axial dispersion transport effect was considered to be negligible in the species balanceequation. This assumption is fair, because the experimental values of dispersion coefficientsobtaines for foam flow (0.01 to 0.46 cm2.&’, corresponding to Peclet numbers larger than15) would have a small effect on conversion in the cell relative to perfect plug flow.Appendix C. Mathematical Treatment ofData 159Figure C.3: Concentration profile of species A in cathodic reduction.7- Potential drop in solid cathode is negligible compared to the mobile phase and the productconcentration gradient is negligible in packing in any direction.In this way a simple oxygen balance may be written on a differential element of packedelectrode and according to the Figure C.4.Equation C.7 may be written in terms ofoverall mass transfer capacity and theoxygen solubiity at gas-liquid interface,A *(P, T), the Faradaic current density,contribution of reaction 1(C.7)Figure C.4: Peroxide balance for adifferential element of electrode.GRAPHITEFIBER=HALIQUIDFILMBULKLIQUIDLIQUIDSOLIDFILMPA+dPAL([H202]+ d[H201)dytL([ II2 021)Appendix C. Mathematical Treatment ofData 160SKa (A(P, 7)— 0)dy = a = L[H20]I —L[H20]IRearranging and integrating along the bed4= SfKa (A(P, 7)— A,(P, 7))c’ =L[H2O]I—L[H20]I. (C.8)Substituting zero for oxygen concentration at electrode surface and inlet hydrogen peroxideconcentration and solving for mass transfer capacity givesKa= L[H2O] (C.9)sf A*(P,T)dyIn equation C.9, hydrogen peroxide concentration at outlet and the oxygen solubility integralare expressed in terms of the known values as follows:a- Hydrogen peroxide concentration at outlet, H20]In each run a sample of effluent catholyte was taken and 2 mL of it was titrated with VP mLof 0.1 N KMnO4 reagent, according to the standard permanganatometry method. In this wayit may be shown thatH2O]=25E—6VF mole/mL (C.10)Substituting for L = SUL and H20]QUt, from equation C.10 back in equation C.925.E—6VPUL 1Ka= PL s’ (C.11)60*f A(P,T)dyb- Oxygen solubility integral (denominator term of equation C. 11)This integral was evaluated by trapezoidal method along the packing length in 40 incrementmeshes. The oxygen solubility function, A*(,T), is a function of oxygen partial pressure,temperature and sodium hydroxide concentration, and has been evaluated from a series ofcorrelations and conditions [63]. Further details may be viewed in computer routines listed inAppendix G, Part F. In this transfer process, the partial pressure of oxygen (corrected for thewater vapor pressure) and the temperature were assumed to have a linear variation along thebed. Also, water vapor pressure data was calculated from the Antoine[30] equation. Inequation C. 11 liquid load, UL, is known from the data.Appendix C. Mathematical Treatment ofData 161To demonstrate the numerical routine involved in part (b), RUN ID ‘EPL3G2” was chosenwith the following complete raw data along with its other associated cell data values. Startingfrom beginning of the bed (at y=O).Cell Configuration Data: Mass Transfer MeasurementsPOROSITY LEVEL GASKET SIZE IN BED POROSiTY % BED LENGTH CM BED WEIGHT GRHIGH 1/4 82.36 4 1.4807BED VOID VOL rnL BED SOLID VOL mL BED THICKNESS MM BED WIDTH MM CHAR TRX AREA M5.159 1.105 5.4 29Overall Mass Transfer Capacity Data:Run pump E I VP P Pin Pout Tout Gas Rot Pgas TgasU) % volt A mL psig psig psig °C Read. psig °CEPL3G2 111.87 12.2 18 I 6.2 94 82 70 76 “C” 70 I 195 I 22.91- At first mesh point, y=0At the initial point of the bed, oxygen partial pressure and its mole fraction is calculated byPIN=82 + 14.7 96.7 psia: TIN=273 +22 = 295 °kPO2IN=P1N - FNVPW (Tm)FNVPW (T)=10i\(16.373_2818.6/T1.6908*log(T)5.7546E3*T+4.0073E6*T2)* 14.7/760PO2IN= 96.7 - 10”(16.373-28 18.6/295-1 .6908*log(295)5 .7546E-3 *295+4.0073E6*295/2)*14.7/760 94.57 psiaNow the conditions were evaluated while searching for the most suitable solubility flanetionPO2IN=94.57*0.101114.7=0.65 MPaHence, pure water solubility was calculated from the linear combination of the two pressurerangesS3=(P-.i)IO.9 * (S2 - Si) + Si mole/mLFNX1(T)=EXP(3.71814+5596.17/T- 1049668#/T’2)Si = 1 /(FNX1 (T)-1 )118FNX1(T)=EXP(3.71814+5596.17/295 -1049668 /295”2)=41321.48S1= 1 / (41321.48 -1 )/18=i.34E-6 mole/mLS2 = -2.545 + 0.00807# * T - 84.14 * p +O.0002096# * p * TA2 +Appendix C. Mathematical Treatment ofData 16223220 * P/T + i.027*Pf2391.l*P2/TS2 = 2.545 + 0.00807 * 295 - 84.14 * 0.65 +0.0002096#* 0.65* 295 A 2+23220 * 0.65 / 295 + l.027*O.65t.239l.l*0.65t2I295 = 8.02E-6 mole/mLSubstituting for Si and S2 in S3 equationSO = S3 = (0.65-. 1)1.9 * (8.02E-6- 1.34E-6) + 1.34E-65.42E-6 mole/mLNow taking into account for the salting out effect, viaS = SO * A (-FNKS(T))where for 1 M NaOH solution, neglecting surfactant effectFNKS (T)=-0.3076 - 0.00120942# * T+0.00000386# * T A2+ 150.9/TFNKS (295) = -0.3 076 - 0.00 120942* 295+ 0.00000386* 295 A 2+150.9/295 = 0.18Substituting for S3 and salting out parameter, FNKS valueS0 = 5.42E-6 * 10 A (-0.18) 3.56E-6 mole/mL2- at second mesh point y0 + 4/40 = 0.1 cmThe partial pressure of oxygen and temperature along the bed was calculated by a linearvariation assumption, between inlet and outlet values. Hence, knowing the inlet value frompart one, it was necessary to calculate the outlet pressure valuePO2H2OUT= POUT-FNVPW (TOUT)POUT =70 +14.7 = 84.7 psia : TOUT =76 + 273 349 °KPO2H2OUT = 84.7 -1 0’(1 6.373-2818.6/349-1 .6908*log(349)5.7546E3 *3494.0073E6*3492)*14.7/760 = 78.57 psiaTo obtain PO2OUT the gas composition at outlet was needed. This value was calculated fromI and VP values of the data table.Considering reaction 1, oxygen flow rate at the outlet, 02C, was calculated by an oxygenbalance on the bed.02C=G-02D=SUg-02D mL/min (C.12)Where S is the bed cross sectional area: S=(VE+VS)/PL= (5.159+1.105)/41.566 cm2. 02Dwas calculated by employing equation C. 1002D 22400 * 5 UL [H2O2j0= 0.56 * SUVP mL/min (C. 13)Appendix C. Mathematical Treatment ofData 163Similarly, outlet hydrogen effluent rate, H2CH2C=22400*60*12 = 22400*60*(I_Il)= 6.9652*I_02D mL/min (C.14)zF 2*96480Hence, first 02D was calculated from equation C. 1302D=0.56*1.566*12.7*6.2=69.05 mL/minSubstituting back for 02D in equation C. 12 and C. 14 and utilizing Ug generates02C = 1.566*60.3 - 69.05 = 25.38 mL/minH2C = 6.9652* 18 - 69.05 = 56.32 mL/rninHaving 02C and H2C, outlet oxygen partial pressure was calculatedPO2OUT02CPO2H2OUT=25.38 * 78.57 = 24.4 psia(02C +H2C) (25.38 + 56.32)Mole fraction of oxygen at outlet was calculatedYO2OUT=PO2OUT 24.4102882POUT 84.7YO 21N= PO2IN == 0.978PIN 96.7With the assumption of a linear variation for total pressure, temperature and mole fraction ofoxygen along the bed, it can be written that(TOUT_TIN)*Y (349_295)*YTY= +TIN= +295=13.5*Y+295 °KPL 4(YO2OUT_YO2IN)*Y (0.2882_0.978)*YYO2Y— +102J1’J = +0.978= _0.17245*Y+0.978FL 4py(POUT_PIN)*Y+PIN(8.796)*673*y psiaFL 4PO2Y=YO2Y*PY psiaNow it was possible to go back to main stream of calculation of the partial pressure andtemperature at the second mesh point:TY = 13.5*0.1 + 295 = 296.35 °KYO2Y = O.17245*0.1 + 0.978 0.960755py.3*o.1 +96.796.4 psiaAppendix C. Mathematical Treatment ofData 164PO2Y = 96.4*0.960755 = 92.62 psia 92.62*0.101/14.7 = 0.636 MPaHaving TY and PO2Y at y0. 1 cm, it was calculated the pure water solubility, salting outparameter and finally the alkaline solution solubility, Si, from the same equations as for thefirst meshFNX1(296.35)=42289.13 : S1= 1.31E-6 mole/mL : S2=7.75E.-6 mole/mLS0=S3=5.i5E-6 mole/mL : FNKS (296.35)=0.18 :S1=3.39E-6 mole/mLThe solubility integral up to the second mesh point was evaluated by trapezoidal ruleSOLINT= (1+S1)= °°(3.56E—6+3.39E—6)= 0.3475E—6 mole/mLThe procedure performed at second mesh was applied repeatedly to the next mesh points untilall the 40 meshes was covered to obtain the total solubility integral value. A table of thisprocess is listed below:Table C.3: The oxygen solubility integral for RUN U) EPL3G2.Y 02 PRESS BED TEMP SO*1.E6 S*1.E6 SOLUBILITYMM psia oC molelmL molelmL INTEG*1.E60 94.57 22 5.42 3.56 01 92.65 23.35 5.15 3.39 0.352 90.73 24.7 4.89 3.22 0.683 88.82 26.05 4.64 3.06 0.994 86.92 27.4 4.41 2.91 1.295 85.03 28.75 4.18 2.77 1.586 83.15 30.1 3.97 2.63 1.857 81.28 31.45 3.77 2.5 2.18 79.41 32.8 3.57 2.38 2.359 77.56 34.15 3.39 2.26 2.5810 75.71 35.5 3.22 2.15 2.811 73.87 36.85 3.05 2.04 3.0112 72.05 38.2 2.89 1.94 3.2113 70.23 39.55 2.75 1.84 3.3914 68.41 40.9 2.61 1.75 3.5715 66.61 42.25 2.47 1.66 3.7416 64.82 43.6 2.35 1.58 3.9117 63.03 44.95 2.23 1.5 4.0618 61.26 46.3 2.12 1.42 4.2119 59.49 47.65 2.01 1.35 4.3520 57.73 49 1.91 1.29 4.4821 55.98 50.35 1.82 1.23 4.622 54.24 51.7 1.73 1.17 4.7223 52.51 53.05 1.65 1.11 4.8424 50.78 54.4 1.57 1.06 4.9425 49.07 55.75 1.5 1.01 5.050 CDCl)00CDo t.CDoq9 H CD CDCD Cl) —.CD Cl) —. >0 CD — 0 0E. 0 0 ICViCD Cl) 2.*II U’ -c 0 CD C 0 000.rgCl,Cl) m •0Bcn————a r°0,o00000000c,000002.*r°—CI)zo 1r—o0coo—ionO)..-JC.)O))C).CJ1* r m 0)I U’Appendix D. Results Tables & Ffures 166Appendix DExperimental Design Tables and ResultsIn this appendix, the operating data tables and the final objective values are presented alongwith some explanatory plots for the following cases:• Pressure Drop• Liquid Holdup• Dispersion Coefficient• Flowing Phase Electrical Conductivity• Mass Transfer CapacityThe flow pattern was upward and under completely foaming conditions. Inlet temperature setat 22 °C and outlet pressure set at 40 psig, for all runs.m ni -I 0 0 I I.” Q Cl)0 I 0 I I rn 0 -I x C.) z m Cl) Cl) m 0 0 -I 2:mmmmmmmmmmmmmmmmmmmmmmmmiriiøG))G)C)C)0CcOOOC zCD03 3CD CD .4C,CD C,0 -I’CD .4 0 0) .4 0) CD Cn Cl) C -I CD -‘ 0 CD 0) Cl,C CD CD .4 U,C.gQ%J.JF\)r’.)Is)rs.I%J.a...a-a...&....a.a..aC)C)-c°pC)C)C)C)3—CD01C)01C..)CD01(51(51.CD(51rs)(TIIs)CD(5)C)C)CDC)01010C)01.C.)C..)C)(51.(.)C.)Q)01.C..)C..)C)(51.(.)C..)C51.C..)Is)3rn—.zz.c(.)(.)(.)Fs)ts)I’3Is)Is)MC)CD—.0CD4JIs)C)C.)C*)CDTs)C..)C)C)_a01COCD.1.j—.-..-——•t’3.00Ui-..1‘.0.t’.)‘.0C..)-.)‘.0.‘.-.ac.B-0 0 0 Cl)U)Ill -I U) N z w ‘ii 0 •0 0 0 U) w rn 0 ,- ni z -I I C,C,.)C.)C..)C.)I’.)C.)I.) coCD —o)13q9_”C0(CD .4 CD . C 00i Ii IIco —1 C.)0 0)I ot1txi1i1NNNNNNNNNNNNNNNNrrr4r4 -I-i.CCQQCQCC.WUI4W.‘.L’Jt4...UIUIUIUIUI0000000000UIUIUIUIUIO\D\DO-.c0000000000---4-4.3•00••00.-.00ç.00•..00r:i00UI009000UI00-00UI00-00UI0000UI00W-—a—C’I.--4-UI0-4-UI00——-aO O 0 I II I.———--—---————--rUIUIUIUIUI-a—4-ao———————9000u.S.00°0°°———————UI.3.4.I))i3—çj..ppoa-0)CC.)00—00(.)DU00.00c.-4V—.00‘.)I—CQ-004.Ut’.).0-4VL-4000.(‘—‘ICC\C.—.ViD00c.ç-Vi%300‘.0.-4—00-a00=90 I-00 C00Appendix D. Results Tables & Ffures 169Figure D.1: Pressure along the cell, for “ZERO” level porosity bed.1 - First Liquid Level1)3290 0 ØEZL1G1A XEa280 a AE21G370 QEZIiG4C X0 OEZL1G5600 A4,60 ax403020 I I I0 2 4 6 8 12Cell Length, cm2 - Second Liquid Level 3 - Third Liquid Level140k140120QEZL2O1 ZEZ3G1AEZL2G2 •E2L3G2XEZ2G3 XZl3G3DEZL2G4 EZL2G480 OEZL2GS aEZL3G568 80‘IC 6860 C-.. 604040I I I I I I 20 I I I0 2 4 6 8 V 12 0 2 4 6 8 V VCell length, cm Cell Length, cm4 - Fourth Liquid Level S - Fifth Liquid Level$0140kx XEZL4G1 Xl2Ox OEZL4G2 l2OX0 XEZL5G1XEZL4G32 EZL4G4 XEZL5320. V0 X AE21503QEZL4G5C OEZL5G444 80 D 80 QEZL5G584 .4C 44C60 Q. 6040 40 a20 I I I 20 I I I0 2 4 6 8 V 0 2 4 6 8 V12Cell Length, cm Cell Length, cmC)tit1tx1t-rt-C)C)C)t’JI-J1k-rI C)t1tIrx1-rr--.I—C)C)C)C.) O IBeD....l.ctJtJtJ).‘I-I&?‘9’9’P’9’%D%3‘D\QD0000000000‘.0‘.0‘.0‘.0‘00000000000.)-,-.--.‘.)-d)flU100000000000 II I0cjJ0 I.-0000‘.00‘.000000O.wWI-’t’.)‘.)LX.)v1-.Ui,-.I—t%)•I.-.0-bo.0’.o-.•Fr-.-t.)“0—1.C‘.00’,00.I’00.‘.0It’.)-.00..—000’,0’.‘.0..UI-I tV.)00 -J 0 0 00CAppendix D. Results Tables & Ffures 171Figure D.2: Pressure along the cell, for “HIGH” level porosity bed.1 - First Liquid Level 2 - Second Liquid Level140120 OEPL1G1140120AEPL1G2EPL2G1OEPL2G2o XEPLIG3 X XEPL2G3100 OEPL1G4 100 0 AEPL2G4X OEPL1G5 IJEPL2G5080 g8oeqeq 0eq Aa. 0X60 X 60X040 a 4020 I I I I I I 20 I I I I0 2 4 6 8 10 12 0 2 4 6 8 10 12Cell length, cm Cell Length, cm3 - Third Liquid Level 4 - Fourth Lquid Level140 140X XEPL4GI120 - XEPL3G1120 OEPL4G2AEPL4G30 EPL3G2 Cx xXEPL3G3 x XEPL4G4X 100 A CEPL4GS100 0 AEPL3G40CEPL3G5X80 80eqeqeq Cx x60 6040 4020 I I I I I I I I I I0 2 4 6 8 10 12 0 2 4 6 8 10 12Cell Length, cm Cell Length, cmm C) G)(Y1m 0)C)m I- C)C)()m I C) C) tommmI-I-n0)0101C)G)G)—01mmmI-I-n010101C)C)C)()1Oam C)01m C)m I C) (*)m I C) tom I C) -am Ca)C)01m I Ca)C)m I Ca)C)La)mmmI-I-nCa)Ca)toG)G)G)m I- to C,Ca)m I to C,tom I- to C)C 2C,’ 1%)(0 C.)30)0)C)C)C)Ca)Ca)Ca)!ZLz.I.C).—i0).ppoPP9P-io__Cjtototototo———i...a.a....a.aa.a...a..a.a.atototototoC)C)C)C)C)°°Pa)a)a)C)C)C)C)..-U,‘ii m 6) I —I 6) U,m 0 0 I I U,m U) 0 I-I0)C1C5.C) CD C,0 z -h 0 C -I 0, 0 0) 0) I 0 C C.0 C.C CD 0) C -I CD 3 CD CnC C——0Ca)•—.zU,omC)1aCD%JC)1•)Iz(.)O——0 0 U) 6) > U) Co N m z U,m •0 0 0 Cd)U,m m 6) -1 I C)0 U) C.)0 a).E.’-CDCD0S. o — Cs .()0CD OCDCD o0tD SICa)C,)Ca)totototototo01to4rJto.101C)CD010)toC)totoCa)01Ca)toto.a...a...aOO%JCD%JC14.....C)...C)CD._a.%.J4.CI14a%JC)toQ)a0 9 3C -4’0 0) 3U)C,’z m U) U) U, m -I IillmmmnimmiiimniIiiflinimiimnimnini00000000000000000000r11i-I-rr-i-i--i-,-,-I-i-I-rI-i.WC.)C.)C.).)QG)OG)OG)G)G)G)OC)01W3-01.C.)-CJ1C.)Is0iC.)M-Scc m m----C51CO0CCOCY1CY1O110CD$0$0$0(*)C..)(.3(.)Ca)CoCOCoCOO)%J%J%J%JSI-.oLCoO1CoO)01CoCoC7IO)Co01Co(.3Jco<———rMr%)t’3r%)-a-a...a-a.a...a...a....1COCoCo0)C) 3 zCC,CD C,0 -s S -I 0 z cc .4. cc I- 0 C 0. 0 0. C CD 0) ‘I, C -I CD 3 CD .4.0 — 0.0.0 C) 0.N rn 0 C.)0) cc 1%)C.)0-U 0 0 U) C)U)I1 -I Co N ni z cc ni ci 0 0 0 U) cc m ci I ni z C) -I I C.)a%JC1%.I(1-a...a%JC7I%JC511jCOCO.aCOCO..a0))...a-4H-CaCX)O)9....(a).j...a(a)rJ-a....a(.)F.J-a...a(.33..a...a1a-CO)Q.)51.Ca)Ca)N.)4C.)I’.3t.3.P-aCa)r’..r-3-a—0CDCflJCo4F..)I3f’3Ca)CD.-J.)C..3Ca)..a..a....a....a..a...a...a..a...aa...a...a....a.a...aOCo0)C1C)14.0 I I- cc m ci U) 0 ci 0 I 1 cc m ci -4 I C-) z ‘ii Co U) cc m ci ci -I IC.)cc C.)-4zI00LUCoU)LUzI.,NLDLDCDrDcOC)1•—e——————I-———E(00.4-DCEEC)cr%cDco’-’-o)o)cococoNdcocdc.JCDCEEUCV)CDC.1D)cC’1C)C)NCCc—LDC’.J—v-C•.J‘—‘-C’4—-C’JC.)xIzLU-J0LUCO00a-0LULUNU)1•-LUCoCzJ-JLU>LUCo0C.,r-.0,xxII0LU-J-J0>0-J0U)0LU-J-J0>0.00I..004U)4-Ca)EU,(0a)0.0.0-jCO4-(0C04-(0011-C0C.)a)C.)CC.•1r-c-:N00_‘CDCDCDN’CDCDCDCDCDCDSi?.CEC)s_-———U)(0CEC)UCDCDCD(CC‘-‘-e>0LUC,FIC,LU0LUCo)(DCDC’F-C1(DODO)O)o,cor%a)0-C4C)U)‘4-C.CDC’4cOODO0dEJJJJJJJ.Ja-a-a-a-a-a-a-a-a-a,a-a-a.a-a,a-LULUUiLULULUUiLUUiLULUUiLULULULUAppendix D. Results Tables & Fifures 175Dill LiquidAxial DispersionThe following tables are liquid axial dispersion measurements measurements for 1 M NaOHTergitol electrolyte and nitrogen gas foam flow in 1/2” graphite felt bed.Table D.7: Liquid axial dispersion data and results with 5.3-cm Neoprene gasket, for “LOW” levelporosity bed.ULID JcmImin jcmimin I cm/mm_j cm/mm Variance Disp. # cm’.s’_-EML1G1 5.8 24.43 8.58 14.39 0.094 0.049 0.022EML1G2 5.8 32.37 10.33 16.13 0.121 0.065 0.029EML1G32 5.8 40.88 12.57 18.37 0.052 0.027 0.012EML2G1 8.49 24.4 8.9 17.38 0.414 0.286 0.19EML2G2 8.49 32.48 10.3 18.79 0.119 0.064 0.042EML2G3 8.49 40.88 12.17 20.65 0.106 0.056 0.037EML3G1 11.16 24.4 9.21 20.37 0.376 0.248 0.217EML3G22 11.16 32.31 10.58 21.74 0.275 0.164 0.143EML3G3 11.16 40.88 12.73 23.89 0.432 0.305 0.266EML4G1 13.83 24.47 6.61 20.44 0.481 0.365 0.395EML4G2 13.83 33.22 7.94 21.77 0.324 0.202 0.219EML4G3 13.83 40.97 9.38 23.2 0.454 0.33 0.358EML5G1 16.48 24.41 9.24 25.72 0.496 0.385 0.496EML5G2 16.48 33.22 11.97 28.45 0.5 0.39 0.504EML5G3 16.48 40.98 9.73 26.22 0.46 0.338 0.437EML6G1 21.83 24.47 9.31 31.14 0.394 0.265 0.453EML6G2 21.83 33.22 12.04 33.87 0.344 0.219 0.374EML6G3 21.83 40.95 14.31 36.14 0.363 0.236 0.403RUNCell Configuration Data: Axial Liquid Dispersion MeasurementsPOROSiTY LEVEL GASKET SIZE IN BED POROSITY % BED LENGTH CMLOW 1/8 73.40 4.7BED WEIGHT GR BED VOID VOL ML BED SOLID VOL ML BED THICKNESS MM BED WIDTH MM2.1740 4.277 1.55 2.95 38lug (stp) UG Ufoam bisp.Coef.•1 o— C.C.CtCt0 C. I 01 C”tx C)ccccct)x1 C)C)—-t’.t’)t3t•)-I-’I--.R.•-.tJp—C1c-.UI.-.-.:<, —1•I-I-Ift..00.•O C) ii I S.c,‘00000,\0-00“000L’.)0W0’-..ppppppppppppoppppppI-’-‘-‘Q-‘0i-.00-‘•I-‘l••‘—000’V.000’•.-.W‘-00CJ.D0—1.‘0 0.I 0. 0 0.I00 0’. 1 ‘CPPPPPPPPPPPoPPPPooP000000000000000’0D0UiUiI-..00—..Ci0-.aUi-.‘.0UUiUicti)‘-CiUi%0Ui0—.U’.ppppppppppppppppppti)P,-ti).0..•000t’‘0W0UiU)00W’0Ui00C)00...‘0CiCi‘-000—‘‘0VCi00—C”...—.Ci‘0,----------“0’..cJ000q(‘1LUx0IIIILUUi0II0zLU-JUIU,4-C0E0 IU,00)0)0)Loro)ccLOU)LOLOLOLUcOc.)clc.E0.CECOen—0zo—C.)a)—a).C.).oC.)C.)..C.)UE0IpCC.)ha)CONLOC)LOC’440)(OC’JC’)C.,’t.LOLDL)LDLOLOLOLL)LL)LO0)0)NCOCO0)0)0)0)0)0)COCO0)0)0)0)0)0)0)0)0)COCDCOCOCOCOCOCO(O(0(nCl)UI2Em0•1-DCEUC,)C,)0U)NCOCDCOCOCOCOCOCOL0).C0)CO0)COCOC.I..-O)U)0r—C,)0)0)N0).NNN0)OlCDC,lClC,)(D(0C4C,)C’)C,)C’)4-U-eC0C-)CuC)4-C.,a,LII4-CaC04-(a0)C0C.)a,C-)VC,)0000LU2LUNCl)I-LUU)01LU>LU.O)-.9I0EC.,:-.EC’lLOLDNC,r-O)CO!0U)D0Cl)0C1,D-JE0>,DC0c>0LUCO(NC’)U)U)0-JU)U)C’,C0dddoo0)U)COr-_L0LDL0L)oddenU)U)-(N0)LON-(NC’tDCDNCOCC.’)CDCD000000000CDCDCD0CD0CDCD----LULULUUIUILULULUUiLULULULUUIUIUIUILUUILULULI)(0(0(0(0(0CC(00000000—(‘4(N(N(N(‘4(‘4(N(‘4CDCDCDCDLULULULUN0)—(’4C’)000CDCDCDCDCDCDCDCDCDU)LI)LI)(0(0(0CD..JJJ.JJ.IJJ..JUIWWLUWLULIJLULIJLIJUJUIUJWUIU)0(0LUUI0)CD(0-JLU0 B I :1—;-;—;C)C)GOZ-0Occ-asVS—0005Vs.)—00-J0%Vs..J—00..JasVs.)—00—05Vs.)t—005oN‘o-0..a-,a-a-,asasasasoscccccccccccccccc-——------WWccsOccccccoccsocccccc0cc‘0CC00cc0cc‘050cccc0b-.)sososocccc0tCcsocccccc0.-.cc---IsVsOsasaccccoc-0000-cc00Sc50.)s—Scsass-’asccSc00cc5050.Scascc—as.———ccas.‘‘_)t)t)V)I-)t..)t-———————————————--———.t-..0’occ-Iccoccas-—as‘0-VS-0sas—Sc-as—.)occasVs0W‘0—VsU—005.Sc0Vs0500ccocccccc0-——bO I.-asasasas0%OS05050505asosOsasasc-JSccc)wsoccccw-VssjccascboCccc as50 0 Vsas as ScI----------“------0%0%0%‘C%c’Cc%c’C.r0—————j—.‘Cci‘coa—-U%0%0%0%0%%C0%—0%.00‘cW‘00%--------0——————0d’0%Vt)—)—00%0——‘0-00%0‘0‘0‘00%‘0‘0%0‘C.00—0000‘Cr—————————;borcc-00%0%.00000%0%V‘0)000%0%-000%000000000.-—V0%-cccc00;-——a1,.°°.-0%—Os0%0%—0%l%h%d%.....1.—-,-a-.i-—a--a0%-0%0000O 0 1 I-.J--a--a—-J--a--J-—a——a-.-——-a-J----Os0%0%0%0%0%0’00-JL.%J%V%Js‘JsVst-J-J-)t)t-)-))000000—00‘C505050505000Li00 Criiex1r1t1xINNNNNNNNNNNNNNNNCC)C)COQCQQOC)CCCJi.I)(J.))i-(J.w a’ IIc 0 C’.,‘Jt’Ji’.)Jt’.)I-I-—ppppp)ts)S)%)aac.i.p...CDa-‘C.)CD—I\)C.)0)-C.)(TiI%3C.)-C.)CO1%.)00‘.DL’3‘)O00‘D00O0000C’)CV0’.\O00QViI‘—l-——tJ‘1.)—m—.J..)I3tj.)l1bC00ViI.)C000’.c-.)—)—OC’.c3ViWQ0’.00‘.00’.—U’.U’.-.I..)U’..000-.ViWU’.Vi0’.U’.U’.CI..)0’.0’.Vi.0’.U’.U’..0’..‘...-.)ViU’.Vi0’.0’.U’..-Vi-i-‘.0U’.Vi-l--L’.)‘0I..)L’30’.00—)‘0nnn0)OC0)-JCO-0I’.)-.4C.).k(TI(Ti-JC.)C.)CD(31-0)-1)(0.0).CO..w 00 U’‘0C.) C.) 0 0 rgD—.4 U..00D D’ c irr— DCD.Q’c,.CD‘CDCD’cIQI-00 q9.00I-0 0 I cit1ib:1.rC)C)C)C))-‘w-I-IIIIII-P’-oQ)C,eF)coOCDC,)0)-P3C..)—JP3-I0)..-4C)i?-‘000U)“000•...-‘3U).‘.0-.0’.00.1.UIU)UIUI00çQ00000’.Oo.-°°boQI‘.0t3UI•—C’.—)•UIUI0’.00UI-U)‘.0U)0’.UIUIU)-••00Q’.UIU)—U)‘.oU)0’..•‘.0t’3I-000’...0’.U)UIO O ii r I.00 0 00 0‘0 -a00Appendix E. Calibration of the Instruments 183Appeiidix ECalibration of the InstrumentsIn this appendix the results of the calibration of instruments employed in this work arepresented:I - Milton Roy liquid supply pump.II- Cole Parmer and Matheson 602 gas rotameters.ifi- Heath Power supply system (inclusive its associated power amplifier).E.l Calibration of Milton Roy Liquid Supply Pump with IN NaOH Solution of0.1 % v/v Tergitol Surfactant, at 21 °C.The pump flow rate measurements were made at different head pressures and found no effectin the range of the operating pressure of the work.Table E.1: Calibration of Milton Roy (large plunger, 1/4” shaft) Liquid Supply Pump with iN NaOHSolution of 0.1 % v/v Tergitol Surfactant, at 21 °C.PUMP V TIME ITOTAL FLOW% cc mm s mm Imiimi93 93.5 — 39.94 0.6657 140.4685 90 — 41.33 0.6888 130.6675 95 — 49.00 0.8167 116.3365 85.5 — 50.20 0.8367 102.1955 88 1 0.32 1.0053 87.5345 88 1 12.76 1.2127 72.5734.5 43.4 — 46.23 0.7705 56.3330 49 59.53 0.9922 49.3924.2 43 1 4.56 1.0760 39.9620 41 1 14.36 1.2393 33.0815 39.5 1 35.00 1.5833 24.9510 26 1 33.16 1.5527 16.755 14 1 36.96 1.6160 8.662.5 9 2 5.56 2.0927 4.30A correlation was obtained for liquid flow rate, L, in term of the pump discharge setting (%),PU. Polymath software was used for that purpose where the best fit was found to be apolynomial of degree with standard error of 4.41E-2.Calibration equation:CE6,140 j0.108060402000 40 60 80 020rAscharg Setflng, %L = 0.1743 + 1.6771PU -1.28E-3PU -5.46E-6 PU3Appendix E. Calibration of the Instruments 184E.ll Calibration of the Gas Rotameters: Cole Parmer Ser no 015279,tube # 42-15 and Matheson Model No 7630-602.BUBBLE METHODThe rotameters were calibrated by wet bubble - tube method with oxygen and nitrogen gasesindividually. The calibration data is listed in tables below in alphabetical order. In each tablethe first column is the float elevation (at ball center), the second and fourth columns arepressure and temperature of the gas flowing through rotameter, the third column is the gasvolume traveled in bubble tube, the fifth column is the elapsed time of the traveled gas, thesixth column is the gas flow rate at STP, with rotameter conditions, and the last column is thegas flow rate at STP, with STP rotameter conditions. In the following the method forcalculation of the last two columns, evaluated for the first row record of the first table isdemonstrated, in this calculations the temperature of the collected gas was assumed as thefourth column values, but its pressure as barometer pressure, PB.sixth column: (40/61.48)(60*754.3*273)!(273+21)/760 = 35.98 CCIMINseventh column: 35.98*(14.7*(273.15+D40)/(B40+14.7)/273.15y0.5 = 9.90 CC/MENTable E.2: Cole Parmer rotanieter calibration with oxygen at PB =754.3 mm fig and TB=21 °C,Touet=2O.S °C.Table E.3: Matheson‘I,1 oudet”.’3rotameter calibration with oxygen at PB=754.3 mm Hg and TB=21 °C,Rotam. Paas V T2as TIME G 02 G 02Read. psig cc oC s cc/mm STP20 194.50 40 21 61.48 35.98 9.9035 195 40 21.20 45.33 48.76 13.4055 195 40 21.50 30.55 72.28 19.8870 195 40 21.80 23.57 93.59 25.7590 195 40 21.80 17.39 126.85 34.90115 195 40 21.80 12.44 177.32 48.79130 195 40 21.80 10.20 216.26 59.50145 195 40 22 8.61 256.02 70.4670E 60606;’ 40302000 60Ball PositionRotam. Pgas V Tgas TIME G02 G02Read. psig cc o C s cc/mm STP18 195 40 21.80 10.13 217.75 59.9121 195 40 21.80 8.74 252.39 69.4424.50 195 40 21.80 7.51 293.72 80.8135 195 40 21.20 5.24 421.82 115.9445 195 50 21.80 4.99 552.57 152.03I170IlB90 ç.2 E 7060B 25 35 45Ball PositionAppendix E. Calibration of the Instruments 185Table E.4: Cole Parmer rotameter calibration with nitrogen at PB 754.3 mm Hg and T=21 °C,Touet=2O.S °C.Table E.5: Matheson rotameter calibration with nitrogen at P5=754 mm Hg and T=21 °C,= 20.5 CRotani.I Pgas V Tgas TIME G 02 G N2Read. psig CC o C s cc/mm (i STP18 195 50 22 11.29 243.96 67.1521 195 50 22 9.78 281.63 77.5125 196 50 22 8.31 331.45 91.0135 195 50 22 5.90 466.84 128.4945 195.50 50 22 4.50 612.08 168.26The above four sets of experimental data for gas rotameters were utilized and obtained fourcorrelating calibration equation of the gas flow rate in terms of rotameter readings (ballpositions), by Polymath software. The parameters of the polynomial fit along with theirstandard errors are listed in Table E.6.Table E.6: Parameters of the fit of the gas flow rate, G, of Cole Parmer and Matheson rotameters, interm of rotameters reading, GCM, for nitrogen and oxygen gases.model: G = AO + Al*GCM + A2*GCM + A3*GCM + A4*GCMCOEFFICIENT AO Al A2 A3 A4 VALIDVARIANCE RANGECole Parmer:nitrogen: 6.5365 0.1872 2.1OE-3 --- --- 0.1525 15-150oxygen: 6.0104 0.1594 1.50E-3 3.24E-6 --- 6.13E-2 15-150Matheson 602:nitrogen: -55.207 12.903 -0.5334 1.27E-2 -1.06E-4 0 15-50oxygen: 14.937 1.4224 9.O1E-2 -2.O1E-3 1.80E-5 0 15-50Rotam. Pgas V Tgas TIME G 02 G N2Read. psig cc o C s cc/nun (i STP20 195.50 50 22 67.75 40.65 11.1834 195 50 22 50.67 54.36 14.9655 195 50 22 32 86.07 23.6970 195 50 22 25.19 109.34 30.0995 195 50 22 17.68 155.79 42.88115 195 50 22 13.61 202.38 55.70130 195 50 22 11.35 242.67 66.79145 195 50 22 9.74 282.79 77.838070604020o0 50 tOBali Position170EQt . it9°2E 70Lj 5025 35Bail PositionAppendix E. Calibration of the Instrwnents 186EJIl Calibration of Heath Power Supply System (including its associatedpower amplifier)It was explained in chapter of the experimental procedures the necessity and method of thecalibration of the Heath power supply (model EUW - 27) coupled with its amplifier (built inChem. Engr. Dept., Electronic Shop), using standard one Ohm resistance. In the table below,the experimental results in terms of the applied cell potential, V (my), cell through current,I (mA), and resistance efficiency, along with the corresponding figures B. 1 are presented.Table E.7: Calibration data for Heathpower supply and its associated amplifieragainst one Ohm standard resistance.V,mV I,mA VI Reff10 14.4 144 0.69415 20.8 312 0.72120 27.1 542 0.73830 39.9 ‘1197 0.75240 52.8 2112 0.75850 65.4 3270 0.76560 78.2 4692 0.76770 91 6370 0.76980 103.8 8304 0.77190 116.6 10494 0.772100 129.4 12940 0.773110 142.3 15653 0.773120 155.4 18648 0.772129 166.8 21517.2 0.773Figure E.1: Graphical presentation of resistanceefficiency for Heath power supply system.Correlations were obtained for resistance efficiency, R.ff, in term of I*V by two models,depending on best fit to model. The parameters of the correlations along with their statisticalindices are given in Tables (B 8-9).A - ONEOHM RISTANCEVS 1WI.]o 760.74 . r.073 I0.72 . .0.71 ..: ,..0.7 . . ..,..,069 I0.68 ..0 8000 1)000 WOO 20000V.’B- ONEOHM RESISTANCE VS V0.780.770.760.750.740.730.720.710.700.690.680C- ONEOHM RESISTANCEVS I0.780.770.760.750.740.730.720.710.700.690.68T 3020 40 60 80 1)0 0P OTENTIAL, mV50 70 90 11) t30 W 170CURRENT, mAAppendix E. CalibraUon of the Instrumems 187Table E.8: Prameters of the fit for correlation of the resistanceefficiency in term ofV*I with two model.model #1: R=aJ(1+b*xC)Parameter Value StdErr I CV(%) Dependencieia 7.79E-01 9.30E-04 1.19E-01I 0.9076438b 2.23E+00 2.27E-01 1.02E+01I 0.9915004c -5.82E-01 2.09E-02 3.59E÷OOf 0.99412model #2: Rff =a*( I +exp(b*Iog(x)+c*(Iog(x))2))Parameter Value StdErr CV(%) 1 Dependenciesa 0.2556 0.00414 1.62 0.99808b 0.344 0.01 569 4.56 0.99965c -0.042 0.00243 5.776 0.99901To achieve better accuracies, the average of Ri and R2values were utilized at the time of the analysis of data.Table E.9: Comparison of thepredicted and experimentalvalues of resistance efficiencyby models #1 and #2.model model xpeñm#1 #2 ental0.6935 0.6971 0.69440.7223 0.7197 0.72110.7371 0.7338 0.73800.7521 0.7505 0.75180.7595 0.7598 0.75750.7638 0.7653 0.76450.7667 0.7686 0.76720.7687 0.7707 0.76920.7702 0.7719 0.77070.7713 0.7724 0.77180.7722 0.7725 0.77270.7729 0.7723 0.77300.7735 0.7719 0.77220.774 0.7713 0.7733Appendix FMathematical Modeling for Design and Scale-upF.1 GeneralIn modeling of the packed-bed electrochemical processes, one eventually ends up dealingwith solving three simultaneous parametric differential equations of heat, mass, andpotential distributions, in conjunction with a presumed axial velocity profile. A solutionto this system would always be possible either analytically or numerically[93] as longas the parameters are known numerically or are available as correlations in terms ofknown related variables of the prevailing foam flow regime. Figure F.1 represents acathodic packed-bed electrode, through which the electrolyte flows in the y-direction atthe uniform superficial velocity, UL, the bed porosity, , the thickness in the currentdirection, B, and its height in the flow direction, FL. The cathode compartment isseparated from anode with a cationic membrane, which is permeable to the cations andnot to the reacting species (anions in this case).In modeling the performance of such an electrode the following assumptions are madein order to simplify the mathematic treatment.1. Isothermal operation.2. Negligible gas film resistance corresponding to either pure gas phase or small variation of electroactive species A in gas phase along the reactor height, but dispersedplug flow of liquid phase with considerable liquid film resistance.3. A single steady state electrochemical reaction of species A, transferred to electrode188Appendix F. Mathematical Modeling for Design and Scale-up 89ELECTRICCURRENTFLOWPOROUSCATHODEFigure F.1: Coordinates for a three-dimensional flow-by electrode.X = thickness Y = length Z = widthsurface from gas phase via liquid phase, occurs in the cathodic compartment whosestoichiometry is given by:A+ze—B :E°4. Packed bed electrode consists of two pseudo-continuous phases of flowing foam andsolid matrix with effective conductivities of ic and u, respectively.5. A supporting electrolyte is present to suppress the migration phenomenon of reacting species[51,87].FEEDERELECTRODEMEMBRANEI COUNTERECTRODEyCATHOLYTE(F.6)Appendix F. Mathematical Modeling for Design and Scale-up 1906. The PBE is electrochemically active throughout the bed. This condition should beverified using the following equation[37j:EdB(y) = [ jl/2 (F.7)2(1 — E)ZA(y)Fk87. The electrochemical reaction is carried under diffusional mass transfer control, withlocal reaction rate in terms of true mass transfer coefficient and local concentrationby:-=k8A(y) (F.8)8. Electrode matrix is characterized by uniform porosity, E, constant specific surface,a, with wetting efficiency of one and constant effective conductivity o throughoutthe electrode.9. Assuming constant total fluxes in each phase along reactor height.Hence in design of such a reactor one is mainly dealing with two systems of governingequations of: conservation of mass and potential distribution at the working electrode inba1ane with the counter electrode through conservation of charge.Appendix F. Mathematical Modeling for Design and Scale-upF.1.1 Conservation of Mass[66]:—V.N+RA=O (F.9)by assumptions 2 & 5:N = ELDaVA + LILA (F.1O)by assumptions i, 3 & 7:= kLaL(A*— A) —k3a8A (F.ll)= Ag/H (F.12)A pictorial view of the concentration profile is shown in Figure C.3, with adopted filmtheory, at steady state and under general condition of combined mass transfer and kineticcontrol. At the mass transfer control condition of the present work surface concentrationof A is assumed to be zero.To achieve maximum electrode yield, requires a maximum possible value of the meancurrent density. This demand is met if, at each point of the electrode, the full limitingcurrent density corresponding to the local concentration is realized. This condition withsimultaneous assumption of negligible transverse dispersion, would satisfy the constantconcentration across the bed depth, i.e:i[(x, y)] = ie[A(y)j = zFk3(y)A(y) (F.13)Adopting the assumptions and conditions of diffusion limited current density, equationof conservation of mass reduces to one dimensional differential equation:d2A dA6LDa(j) U() + kLaL(A* — A) = ka8A (F.14)The proper boundary conditions are given as[511:— 6LDa() = UL(A — A) at y = 0 (F.15)Appendix F. Mathematical Modeling for Design and Scale-up 192=0 at y=PL (P.16)dyExpressing the above in terms of dimensionless variables:= y/PL, and a = A/A* (F.17)one obtains:1 d2a da+ age(1 — a) = a8 (P.18)with the corresponding dimensionless boundary conditions:at =0,and =0 at =1 (F.19)where the dimensionless parameters, gas-liquid, liquid-solid and Peclet number are:age kLaLPL = ka5PL , Fe=, respectively. An analytical solution forconcentration profile, for special case of constant A* is available[67] as:a = A/A* = cgL +(p 20Pe[crgs/(cgt+ats )—a) (A2e”2 e’1 _AieAl e>’2))?eA1—)2?i and k2 are the roots of the characteristic equation of the differential equation as:= {Pe + [Fe2 + 4Pe(age +at3)]”2} (F.21)= {Pe — [Fe2 + 4Pe(age +a8)]”2} (P.22)In general case, when the A* varies with temperature and pressure, equation will be alinear differential equation with constant coefficient, which must be solved numerically.Appendix F. Mathematical Modeling for Design and Scale-up 193F.1 .2 Conservation of Charge[64]:Potential distribution both in the bed and in the electrolyte is needed for calculating cellvoltage balance, reactor yield, and performance evaluations.The effective conductivitiesof each of the pseudo-continuous phases of solid matrix and electrolyte are o and ,,respectively. The Ohms’ law and laws of conservation of charge are presented as follows:a- Ohms’ law:FCfVE8 = —i3 (F.23)ciVEm m (F.24)b- Conservation of charge:V.js + V.jm = 0 (F.25)= —a5i (F.26)From the above equations come the following differential equations for potential distribution in the solid matrix and electrolyte pseudo-continuous phases:V2ES= 82E+02E5 =(F.27)ax ICfV2Em= 82E+82E =(F.28)ciwhere electrode potential distribution, E = Em — E3, is obtained from:2 82E 2E 1 1V E=—-H--—-=—(—-F—)aze (F.29)8x ãy ciPotential differential equations F.27 and P.28 must be solved either analytically or numerically. Hence, there is always a method of solution available when a set of properboundary conditions are proposed. Boundary conditions are defined mainly based ongeometrical configurations and experimental limitations and conditions. Followings area set of commonly proposed ones[82j.Appendix F. Mathematical Modeling for Design and Scale-up 194a- At the cathode face, inner boundary of the structure, the potentials are constant:I E8 =E,at z=O:0(F.30)1’m Emob- Cathode current collector is insulator to ionic current, assuming whole bed depthto be active:I 0E8/t9x = 0at x=B: (P.31)1 1 fPL[OE/8x]dy ib/cJc- Assuming sufficiently long electrode, as for the case of good design to ensure ahigh conversion factor of the reactive species but avoiding in the same time a too largepotential variation (which can cause a bad process selectivity due to the creation of thesecondary reactions), and with no current flows in the y-direction at the entrance andexit:I 8E/c9y = 0at y = 0, and y = FL : (F.32)t 8Em/8y = 0Introducing the additional dimensionless variables[93j:= x/B, and = zFE/RT0 (F.33)the dimensionless differential equation of potential distribution is:2 B 2OV = + (—) = -Pa (F.34)where the I’ = — (Z) (1 + —)ak3A is dimensionless mass transfer oefficient. The Ais a solubility of A in electrolyte at some standard conditions, and T0 in equation F.23is some standard temperature.Appendix F. Mathematical Modeling for Design and Scale-up 195The corresponding boundary conditions are:a-at e 0: = ZF(Emo —B80)/RT0 (F.35)1 (zFB)iat = 1 : f [84/8]d = — RT0 (36)C-at = 0, and = 1: = 0 (F.37)Equation P.29 is an elliptic PDE with constant coefficients, with strong variation iny direction, but rather smaller variation in x direction. The solution to this equationwhich is the electrode potential distribution along with the concentration profile is usedto identify the electro-active bed depth for the desired reaction and thereto the true masstransfer capacity.Numerical solutions may be obtained for coupled system of differential equations P.19and F.34 (or F.14 and F.29), using the well known finite difference iterative techniques;for example the line-by-line overrelaxation or the Gauss point method1. Finite element orfinite difference direct methods which require more computer memory, are also possiblefor this system.‘Anderson, D. A., Tonnehile, J. C. and Pletcher, R. H., “Computational Fluid Mechanics and HeatTransfer”, Hemispher, N. Y., 1984.Appendix G. The Computer Routines 196Appendix GThe Computer RoutinesThe computer routines and programs which were used to analyze data for each experimentalmeasurement are listed in this appendix. The variables appearing in each section (any programor routine) are classified in two groups. The variable names are either specific to that sectionor belong to the group common to all the programs. Hence, descriptions of the commonvariables are given ahead of all the program listings and the description of the specificvariables are with each program itself.GA Global Variables:A: Bed cross sectional area, perpendicular to foam flow direction, cm2B: Bed packing thickness, mm.BW: Bed packing width, mm.C, M: Rotameter identifier, Cole Parmer or Matheson brand.EXPF: Expansion factor at gas rotameter.GCM: Gas rotameter scale reading (at the center of the floating ball position).GT$: Neoprene gasket nominal thickness, in.L, G: Liquid or gas flow rate at STP, mL/min.LEVEL$: Porosity level of the packed bed, (= LOW, ZERO or HIGH).P: Pressure gauge reading, set before the pre-foamer unit, psig.PGAS,TGAS: Pressure and temperature of the gas at the gas rotameter, psia, °K.PIN,TIN: Cell inflow pressure and temperature, psia, °K.PL: Packing length, cm.POROSITY: Bed porosity value, %.POUT: Cell effluent pressure, psia.PS, TS: Standard pressure and temperature (=14.7 psia, 273.15 OK).PU: Milton Roy liquid supply pump rotary dial setting, %.PW: Graphite fiber bed packing weight, gr.QFOAM: Inlet-outlet average foam flow rate, mL/min.ROTS: Rotameter string variables ( C or M).RUNID$: Run string name.TEXT$: Data file lable heading text strings.UFOAM: Inlet-outlet foam average superficial velocity, cm/mm.Appendix G. The Computer Routines 197UG,TJL: Gas and liquid superficial velocities, at STP, cm/mm.UGAV: Inlet-outlet gas average superficial velocity, cm/mm.UGIN: Inlet gas superficial velocity, cm/mm.UGOUT: Outlet gas superficial velocity, cm/mm.VE: Graphite fiber bed packing void space, mL.VS: Graphite fiber bed packing solid volume, cc.GB Gas and Liquid Flow Rate VariablesSpecific Variables:“PRESSURE.OPR”: Operating input data file.‘PBESSURE.RSL”: Result output file.P1,P2,P3,P4: Pressure tab readings at, inlet, two intermediate locations and outletof the graphite fiber bed packing, psig.10 REM This program reads in operating data file “PRESSURE.OPR”20 REM to analyze for flow rate variables in terms of liquid, gas30 REM and foam fluxes and writes to output file “PRESSURB.RSL”.40:50 PS’= 14.7 : TS = 273.15 : TIN=22+TS60 OPEN “0” #1 “PRESSURE RSL”70 OPEN “I”, #2, “PRESSURE.OPR”80 FORII=1T0290 INPUT #2, TEXT$100 NEXT110 INPUT #2, LEVEL$,GT$,POROSITY,PL,TEXT$,PW,VE,VS,B,BW120 FORII=3T08130 INPUT #2, TEXT$140 NEXT150 GOSUB 500 : REM To write table of results heading160 IF EOF(2) THEN GOTO 280170:180 INPUT #2, RUNTD$, PU, P, P1, P2, P3, P4, POUT, ROTs, GCM, PGAS, TGAS190:200 PIN=P1+PS : POUT=P4+PS : PGAS=PGAS+PS : TGASTGAS+TS210:220 GOSUB 320 : REM To calculate flow rates230 PRINT240:250 PRINT #1,” “;RUNID$;” “;260 PRINT #1, USING” ###.# “; L; G; UL; UG; UGIN; UGAV; UFOAM270 GOTO 160280 CLOSE 1290 CLOSE 2300 END310:Appendix G. The Computer Routines 198320 REM SUBROUTiNE TO CALCULATh GAS & ELECTROLYTh SUPERFICIAL VELOCITffiS33OPRINT340 L = 0.1743 + 1.6771 * PU - 0.00128 * PU A 2 - 5.46E-06 * PU A 3350 IF ROT$ = “M” THEN 380360 G6.5365 +0.1872 * GCM+0.0021 * GCMA2370 GOTO 390380 G = -55.207 + 12.903 * GCM -0.5334 * GCM”2 + 0.0127 * GCM”3 0.00O106#*GCMfs4390 EXPF = SQR(TSIPS* PGAS / TGAS)400 G = G * EXPF410 A=(VE+VS)/PL420UL=L/A:UG=G/A430:440 UGOUT=PS*UG*T1N/POUTrrS : UGIN=PS*UG*T1N/PINIrS450 UGAV = (IJGIN + UGOTJT) /2460 UFOAM = UL + UGAV470 QFOAM = TJFOAM * A480 RETURN490:500 REM SUBROUTINE FORMAKING PRESSURE DROP RESULT TABLE HEADING510 PRINT #1,” Results of pressure drop measurements at “;LEVEL$; “level porosity”520 PRINT #1,” of’; POROSITY; “% with”; GT$; CNR$(34); “- 12 cm Neoprene gasket. The packing”530 PRINT #1,” is 1/2”; CHR$(34); “graphite felt, with”; PL; “cm length,”; PW; “gr. weight”540 PRINT #1,” and “; VS; “cc solid volume, under 50 kg-cm torque setting.”550 PRINT #1,” PRESSURE DROP: :T elect. =22 °C”560 PRINT #1,”570 PRTNT#1,””580 PRINT #1,” RUN ID Q elect. Q gas Ui Ug Ug in Ug av Ufoam590 PRINT #1,” mL/min cc/mm cm.min cm/mm cm/mm cm/mm cm/mm600 PRiNT #1, “ “610 RETURNG.C Liquid HoldupSpecific Variables:“HOLDTJP.OPR’: Operating input data file.“HOLDUP.RSL”: Result output ifie.X: About 10 mL of the washout solution taken to be titrated with Y mL of 0.1 N HC1.Y: Amount of 0.1 N HCI neutralized with X mL ofwashout solution, mL.Z: Total washout solution, mL.HL: Packed bed holdup, %.YLE: Total liquid entrapped in both end lines of the packed bed, mL.VLT: Total liquid entrapped in the cell, by the “quick close valve” action., mL.VL: The amount of liquid entrapped only in the packing, by the “quick closing valve”action, mLBEL: Cell bottom end line volume (numerical values are listed in Table C. 1), mL.Appendix G. The Computer Routines 199TEL: Cell top end line volume (numerical values are listed In Table C. 1), mL.10 REM This program reads in operating data file “HOLDUP.OPR”20 REM to analyze for holdup in terms of liquid, gas and30 REM foam fluxes and writes to output file “HOLDUP.RSL”.40:60 OPEN “0”, #1,”HOLDUP RSL”70 OPEN “I”, #2, ‘HOLDUP.OPR”110 INPUT #2, LEVEL$,GT$,POROSITY,PL,TEXT$,PW,VE,VS,B,BW150 GOSUB 630 : REM To write table of results’ heading160 IF EOF(2) THEN GOTO 290170:180 INPUT #2, RUNID$, PU, P, PIN, POUT, ROT$, GCM, PGAS, TGAS, X, Y, Z200 PIN=PIN+PS-1 : POUT=POUT+PS+1 : PGASPGAS+PS : TGASTGAS+TS210:220 GOSUB 330 : REM To calculate flow rates230 PRINT240 GOSUB 510 : REM To calculate liquid holdup250:260 PRINT #1,” “;RUNID$;” “;270 PRINT #1, USING” #.# “; UL; UG; UGN; UGAV; UFOAM; IlL280 GOTO 160290 CLOSE 1300 CLOSE 23 10 END320:330 REM SUBROUTINE TO CALCULATE GAS & ELECTROLYTE SUPERFICIALVELOCITIES490 RETURN500:510 REM SUBROUTINES TO CALCULATE LIQUID HOLDUP520 D=(TIN)/TS530 E=PS*DJPIN540 F=PS*D/POUT550 E=G*E:FG*F560 E=L+E:F=L+F570 VLE=BEL*LIE+TEL*LfF580 VLT=Y*Z/10.08/X590 VL=VLT-VLENDS600 BL=VL* l00/(VE+VS)610 RETURNAppendix G. The Computer Routines 200620:630 REM SUBROUTINE FORMAKiNG LIQUID HOLDUP RESULT TABLE HEADING640 PRINT #1,” Results of liquid holdup measurements at “; DEGREE$; “level porosity”650 PRINT #1, “ of “; POROSITY; “ % with”; GT$; CI{R$(34); “ - 12 cm Neoprenegasket. The packing”660 PRINT #1, “ is 1/2”; CHR$(34); “graphite felt, with “;PL; cm length,’; PW; “ gr.weight”670 PRINT #1,” and Vs = “; VS; “cc solid volume, under 50 kg-cm torque setting.”680 PRINT #1,” LIQUID HOLDUP T elect =22°C”690 PRINT #1,*****************************************************************‘,700 PRINT #1,710 PRINT #1,” RUN ID UI Ug Ug in Ug av Ufoam HI720 PRINT #1,” cm/mm cm/mm cm/mm cm/mm cm/mm %730 PRINT #1,””740 RETURNG.D Setup of Computer Login Program, “NOTBOOK”, in DispersionMeasurementsSetup procedure involved modification through four setup menus and two setup utilities in the following steps:a- Modification of the setup file from setup menu:-Highlighted SETUP to go into setup menu.-Highlighted CHANNEL and then hit the RETURN key.-Chose NORMAL and then pressed RETURN.-Changed number of channels to 7.At this stage the first two channels have been assigned to the time and the signal (mV) as default, and theremainder of the channels, 3 to 7, were suspended to be assigned to the desired Calculated values of: zeromoment, first moment (signal-time product), second moment (signal-time squared product) for on-lineprocesses, as follows:-Changed current channel to 3.-Changed channel type to CALCULATED by pressing Fl key and moving the cursor to the desired one.-Choosed the channel unit as s*mV.-Changed channel operation by pressing Fl key and choosing the INTEGRAL.-Changed X input channel to the interface channel 2 (signal).using similar route as the last five proceeded steps, the 4 remained calculated channels were setup as of thefollowing poly-sequencial steps:-Changed current channel to 4,5,6,7.-Changed channel type by pressing Fl key and choosin 4 X CALCULATED.-Choosed the channel unit as s*mV, s2.*mV,s2*mV, s- *mV.-Changed channel operation by pressing Fl key and choosing the, X’’Y, INTEGRAL, X”Y, INTEGRAL.-Changed X input channel to the interface channel 2 (signal), 4, 4, 6.Appendix G. The Computer Routines 201At the end when last channel, 7, was setup ESCAPE to SETUP went to FILE, then RETURN to configureoutput ifie:-Changed number of column to 5.-Matched column numbers with channel numbers, as:ColuinnNo: 1 2 3 4 5ChannelNo: 1 2 3 5 7Channel unit: s mV s*mV s2*mV s3*mVDigits allowed: 12 12 12 12 12No. ofFraction: 2 2 2 2 2-Chose data file name and location: a:\OUTPUT.PRNWhen output ifie was setup ESCAPE to SETUP went to DISPLAY/WINDOW, then RETURN to configuremonitor display:-Chose number ofwindow 1.-Chose maximum yvalue 150 mV.-Chose offset 0.-Chose sampling rate 1 (or 5 or 10)When display file was setup ESCAPE to SETUP went to DISPLAY/TRACER, then RETURN to configurenumber of tracers to display:-Chose number of tracer 1.-Chose tracer display [T vs. Y].-Chose y channel No 2.-Chose maximum y value 150 mV.-Escaped to setup menu and used VERIFY command to check the contents of the setup menus listedabove for inconsistent entries in separate menus.-Escaped to setup menu and used SAVE conunand to save the setupconfiguration to TOTAL DISPERSION or CON CELL DISPERSION.-QUIT the NOTEBOOKAt this stage the software with the setup files were ready to log data upon GO command.G.E Dispersion CoefficientSpecific Variables:“DISPERS.OPR”: Operating input data file.“DISPERS.RSL”.: Result output ifie.“RUNID$(1)”, “RUNID$(2)”: Tracer response data files of the fixed-bed plus conductivity cell and theconductivity cell, respectively; logged by “NOTEBOOK”.D: An intermediate dispersion number.DCOEF: Liquid axial dispersion coefficient, cm2/s.DNO: Dispersion number.ET(1), ET(2): Each row first entries of the RIJNID$(l) and RUNII)$(2) files, elapsed logging times, s.SDUR(1), SDUR(2): Sampling duration’s chosen by inspection of the RUNU)$(1), RUNTD$.(2) files, s.SIGINT, SIGTINT, SIGT2INT: Calculated zero, first and second moments of the response signal,respectively, V*s, V*s2 and V*s3.SIGNAL: Tracer response digital signal detected by conductivity cell, logged in RUNII)$(l) file, V.Appendix G. The Computer Routines 202TAU(1), TAU(2), TAU(3): Dynamic mean residence times of fixed-bed plus conductivity cell, conductivitycell, and fixed-bed, respectively, s.VARIN: Variance of the response signal, s2.ZIGM2(l), ZIGM2(2), ZIGM2(3): Dimension less variance of fixed-bed plus conductivity cell, conductivitycell, and fixed-bed; respectively.10 REM This subroutine reads in operating data file “DISPERS.OPR” and two20 REM 5 column sequential data files “RUNID$” produced by “NOTE-BOOK”30 REM to analyze for residence time, variance and dispersion in terms40 REM of the flow rate variables and writes in output file “DISPERS.RSL •50:70 OPEN “I”, #2, “DISPERS.OPR”110 INPUT #2, LEVEL$,GT$,POROSITY,PL,TEXT$,PW,VE,VS,B,BW170 OPEN “0”, #1, “DISPERS.RSL”180 GOSUB 1170 : REM To write output files headings210 IF EOF(2) THEN GOTO 960220 INPUT #2, RUNID$(l), RUNID$(2), PU, P. PIM, POUT, ROT$, (3CM, PGAS, TGAS, SDUR(l), SDUR(2)230:240 P1N=P1N+PS-l : POUT=POUT+PS+1 : PGAS=PGAS+PS : TGAS=TGAS+TS260:270 GOSUB 990 : REM To calculate the gas & liquid flow rates390:400 REM START TO READ THE LOGGED iN TRACER RESPONSE DATA FILES410 FORK= 1 T02420 OPEN “I”, #K, RUNID$K)43OFORI= iTO 14440 INPUT #K, TEXT$450 NEXT460 IF EOF(K) THEN GOTO 530470 INPUT #K, ET(K),SIGNAL,SIGINT,SIGTINT,SIGT2INT480 IF K=2 THEN 510490 IF ET(1) => 1.1*SDUR(1) THEN 530500 GOTO 520510 IF ET(2) => 1.1*SDUR(2) THEN 530520 GOTO 460530 CLOSE K534:535 REM START TO PROCESS DATA FILES TO CALCULATE DYNAMIC PARAMETERS540 TAU(K) = SIGTINT / SIG1NT550 VARIN = SIGT2INT / SIGINT - TAU(K) A 2560 ZIGM2(K) = VARIN / TAU(K) “ 2570 GOTO 600 : PRINT RUNID$(K);580 PRiNT USING” ### ##“ ET(K)590 PRINT USING” ###.###“; TAU(K); ZIGM2(K)600 NEXT K610:620 REM CALCULATE DISPERSION NO BY RECURSIVE TRIAL ERRORMETHOD630 TAU(3) = TAU(1) - TAU(2)640 ZIGM2(3) = ZIGM2(1) - ZIGM2(2)Appendix 0. The Computer Routines 203650 D = ZIGM2(3) /2660 IF D<=0 THENDNO=D : IF D<=0 THEN GOTO 780670 DNO = ZIGM2(3) /2+ D A 2 * (1 - EXP(-1 / D))680 DCOEF=DNO *JJ *)J/()690 IF ABS(D - DNO) <= .001 THEN GOTO 780700D=DNO710 GOTO 67078OPRINT#1,” “;790 PRINT #1, RUNID$(1);800 PRINT #1, USING” ###.##“; UL; UG; UGAV; UFOAM;81OPRINT#1,” H;830 PRINT #1, USING” 114M1##”; ZTGM22(3); DNO; DCOEF840 CLOSE 1950 GOTO 210960 CLOSE 2970 END980:990 REM SUBROUTINE TO CALCULATh GAS & ELECTROLYTE SUPERFICIAL VELOCITIES1150 RETURN1160:1170 REM SUBROUTINE FORMAKING FLOW AND DISPERSION RESULTS TABLES HEADINGS1180J= 11190 PRINT #3,” Results of dispersion measurements at “; LEVEL$; “level porosity”1220 PRINT #3,” of”; POROSiTY; “ % with”; GTS; CHR$(34); “- 11.6 cm Neoprene gasket. The packing”1230 PRINT #3,” is 1/2”; CHR$(34); “graphite felt, with “; PL; “cm length,”; PW; “gr. weight”1240 PRINT #3,” and VS= “;VS; “cc solid volume, under 50 kg-cm torque setting.”1250 PRINT #3,” DISPERSION: T elect. = 22 cC”1260 PRINT #3, “ **********************************************************************“1270 PRINT #3,””1290 PRINT #3,” RUN ID Ul Ug Ug av Ufoam Var. Disp. # Disp. coef.”1300 PRINT #3,” cm/mm cm/mm cm/mm cm/mm cm2/sec.”1350 RETURNG.F Foam Electrical ConductivitySpecial Nomenclature:“CONDUCT.OPR”: Operating input data file.“CONDUCT.RSL”: Result output file.AMP: Electric current through the cell circuit, amp.HL: Predicting liquid holdup.KO: Electric conductivity of iN NaOH solution, mho/m.KDIA: Electric conductivity ofDiaphragm, mho/mKF: Electric conductivity of flowing foam, in graphite fiber bed, mho/m.R: The true resistance, Ohm.Ri: Calculated Ohmic resistance efficiency by correlation model #1.R2: Calculated Ohmic resistance efficiency by correlation model #2.REFF: Ohmic resistance efficiency.Appendix G. The Computer Routines 204S: Electric charge transfer cross sectional area (parallel to foam flow direction), m2.V: Electric potential across the cell or on one Ohm standard resistance, mV.10 REM This subroutine reads in operating data file “CONDUCT.OPR”20 REM to analyze for foam electric conductivity in terms of30 REM liquid, gas and foam fluxes and writes to output ifie40 REM “CONDUCT.RSL”.50 PS=14.7:TS=273.15: TIN=22+TS60 V = 15 : KO = 15.84 : KDIA = 1.65970 OPEN “0” #1 “CONDUCT RSL”80 OPEN “I”, #2, “CONDUCT.OPR”120 iNPUT #2, LEVEL$,GT$,POROSITY,PL,PW,TEXT$,VE,VS,B,BW,S160 GOSUB 670 : REM To write table of results’ heading170 IF EOF(2) THEN GOTO 300180:190 INPUT #2, RUN1DS, PU, AMP, P, PiN, POUT, ROTS, GCM, PGAS, TGAS200:210 PIN=PIN+PS-i : POTJT=POUT+PS+1 : PGAS=PGAS+PS : TGAS=TGAS+TS220:230 GOSUB 340 : REM To calculate flow rates240 PRINT250 GOSUB 520 : REM To calculate foam conductivity and liquid holdup260:270 PRINT #1,” “;RUNID$;” “;280 PRINT #1, USING” ###.# “;UL; UG; UGJN; UGAV; UFOAM, KF, HL290 GOTO 170300 CLOSE 1310 CLOSE 2320 END330340 REM SUBROUTINE TO CALCULATh GAS & ELECTROLYTE SUPERFICIAL VELOCITIES500 RETURN510:520 REM SUBROUTINE TO CALCULATE ThE FOAM CONDUCTIVITY AND LIQUID HOLDUP530 GOSUB 600540 R = WAMP/PEFF550 KF = BD*.00i#/(R*S.000l8#fKDIA)560 KR = KF/K0570 IlL = 300*KR/(2+KR)580 RETURN590:600 REM SUBROUTINE TO CALCULATE THE OHMIC RESISTANCE EFFICIENCY Raft610 X= AMP * v620 A=.779 : B=2.23 : C=-.582 : D=.2556 : E.344 : F-.042630 Ri AJ(1+B*XC) : R2 = D*(1+EXP(E*LOG(X)fLOG(10)+F*(LOG(X)fLOG(10))’V2))640 REFF = (RI+R2)/2650 RETURN660:670 REM SUBROUTINE FOR MAKING FOAM ELECTRIC CONDUCTIVITY RESULT TABLES HEADINGAppendix G. The Computer Routines 205680 PRINT #1,” Results of foam electric conductivity measurements at “; LEVEL$; “level porosity”690 PRINT #1,” of ; POROSiTY; “ % with “; GT$; CHR$(34y, “- 12 cm Neoprene gasket. The packing”700 PRINT #1,” is 1/2”; CHRS(34); “graphite felt, with “; PL; “cm length,”; PW; “gr. weight”710 PRiNT #1,” and VS =“; VS; “cc solid volume, under 50kg-cm torque setting.”720 PRINT #1,” FOAM ELECTRIC CONDUCTIVITY: :T elect. =22°C”730 PRINT #1,740 PRINT #1,750 PRINT #1,” RUN ID UI Ug Ug in Ug av Ufoam Kfoam Ill760 PRINT #1,” cm.min cm/mm cm/mm cm/mm cm/mm mho/m %770 PRINT #1, “ “780 RETURNG.G Mass Transfer CapacityIn the following list, all the flow rates are in SI? conditions.Specific Variables:“MAS-TRX.OPR”: Operating input data file.“MAS-TRX.RSL”: Result output file.FNS3(P,T), FNS4(P,T), FNS5(P,T) : Fractional parts of the solubility function S2.FNX1(T) : An oxygen in water solubility related function.AF : Effluent gas phase hydrogen volume fraction.AREA: Total solubility integral, calculated in related subroutine, (moleJmL)*1.E6.CE : Peroxide production current efficiency, %.E : Electric potential across the cell, volt.H2C : Hydrogen flow rate in effluent stream, inL/min.H2M : Hydrogen flow rate measured at outlet stream, mL/min.11202 : Peroxide concentration at outlet, M.H2O2NET : Net peroxide production rate, mole/mmH2P : Hydrogen production rate generated by any reaction, mL/min.I: Total through current in the cell, DC Ampere.Ii, 12 : Fractional currents in the cell due to reactions 1 and 2, respectively, DC Ampere.KA : Overall mass transfer capacity, s4.02 : mL of oxygen gas content of the effluent stream, detected by Orsat system.02C: Oxygen flow rate in effluent stream, mL/min.02D : Total oxygen demand in electrochemical reduction process to peroxide, mL/min.O2M: Oxygen flow rate measured at outlet stream, rnL/min.02P : Oxygen flow rate produced by reaction, mL/min.OHCROSS : Excess amount of hydroxide in catholyte compartment due to membrane crossing, M.OhM: Measured hydroxide ion in effluent stream, M.O}{P : Produced hydroxide ions, M.OHT : Titrated effluent alkaline content (including perhydroxyl ion), M.PB : Barometer pressure, mm Hg.S1,S2, S3 : Oxygen solubiity functions in pure water, in the specified conditions (P,T), mole/mL.TEF : Effluent fluid temperature, °K.VO : Total effluent gas volume collected by Orsat system in measuring the total cell gas effluent rate, mL.VHCH: Volume of hydrochloric acid used in titration of the 5 rnL of a to 100 mL diluted of 5 mL effluentperoxide solution, to measure total hydroxide ion, including hydroxonium ion, mL.Appendix G. The Computer Routines 206VP : inL of 0.1 N KMnO4 titrated with 2 mL of the cell effluent peroxide solution.10 REM This subroutine reads in operating data file “MAS-TRX.OPR”20 REM to analyze for mass transfer rate coefficient, KA, current30 REM efficiency, CE, and outlet hydrogen peroxide concentration,40 REM H2O2NET in terms of liquid, gas and foam fluxes write to50 REM output files: “MAS-TRX.RSL “.60:70 DY=4/40 : PS= 14.7 : TS = 273.15 : TJN=22+TS : MODEL=180:90 REM Oxygen solubility in pure water m M[63]100:110 REMData from IUPAC Solubiity Data Series Vol. 7, p. 2,3120 REM This equation is effective for T:273 to 423 °K and P:0. 101 MPa125130 DEFFNX1 m=EXP(3.71814+ 5596.17/T- l049668#/T’2)140 REM DEF FNS1(1)= 1 / (FNX1 (T) -1 )/18# : REMMolality, mole/mL150:160 REMData from Svensk paperstid. nr. 17, 1978, p. 541-544170 REM nr. 16, 1979, p. 487-491180 REM This equation is effective for T:323 to 424 °K and P:1 to 5 IviPa, mole/rn3185:190 DEFFNS3 (P = -2.545 + .00807# * T -84.14 * p200 DEFFNS4(P,T)=.0002096#*P*TA2+23220*P/T210 DEFFNS5 (P,T)= 1.027*P239l.1*P/2,T220 REM DEF FNS2(P, = FNS3(P,T)+FNS4(P,T)+FNS5(P,T)230:240 REM Oxygen solubility in iN NaOH solution[511250:260 REM This equation correlates salting-out parameter with NaOH concentration265:270 DEFFNKS (T)= -.3076 - .00120942# * T+ .00000386# * T ‘2 + 150.9/T280290 REM Antoine Eq: Vapor pressure of water, psia, T: °K, St Dev: 0.09[30]295:300 DEFFNVPW310390 OPEN “I”, #2, “MAS-TRX.OPR”430 INPUT #2, LEVEL$,GT$,POROSITY,PL,PW,TEXT$,VE,VS,BD,BW,S480 OPEN “0”, #1, “MAS-TRX.RSL”490 GOSUB 1800 REM To write tables of results headings510 NEXT530 IF EOF(2) THEN GOTO 1160540:550 REM 1- INPUT #2, RUNIDS, PU, I, VP, VU, TEF, PB, VHCL, PIN, TOUT, ROT$, (3CM, PGAS, TGAS, 02590:610 INPUT #2, RUNIDS, PU, B, I, VP, P, PIN, POUT, TOUT, ROTs, GCM, PGAS, TGAS620:620 PIN=PIN+PS-i : POUT=POUT+PS+1 : TOUT=TOUT+TS : PGASPGAS+PS : TGAS=TGAS+TSAppendix G. The Computer Routines 207630:640 REM 1- GO=60*TS*V0*PB/760,TEF/(TS+TGAS) : REM Outlet gas effluent rate cc/mm650 REM 1- AF=1-02/V0 : AF1=1/AF660 REM 1- OIIT=VHCL*1.05/5 : REM Titrated alkalinity, M670 REM 1- ONN = 1+IIL/1.608 : OHMN= (VHCL..1)*1.05/5 : OHCROSS = OIIN-OHMN680:690 GOSUB 1210 : REM To calculate flow rates700 PRINT710:720 H2O2=.025 * VP : REM H202 concentration Mat outlet730 H2O2NET =11202 * L/1000 : REM Net H2O2 production mole/mm740 CE = 8.04 * L*VP/I : REM Current efficiency for 11202 production750 (3OSUB 1340 : REM To calculate model current Distribution.760 GOSUB 1540 : REM To calculate oxygen concentration integral770 KA=02D/22400/AREAJA/60 : REM Overall mass-trx coefficient S1.780 PRiNT940:950 PRINT #1,” “;RUNTD$960 PRINT #1 USING” ### # “ ULUGUGAV UFOAM990 PRiNT #1 USiNG” ## ##“ CE1000 PRINT #1, USING” ##.##“;KA1140 CLOSE 11150 GOTO 5301170 CLOSE 21190 END1200:1210 REM SUBROUTiNE TO CALCULATE GAS & ELECTROLYTE SUPERFICIAL VELOCITIES1320 RETURN13301340 REM SUBROUTINES TO CALCULATE CATHODIC REACTIONS CURRENT DISTRIBUTION1350 REM 2-REACTIONMODEL 1/21360 AF=0 : GO =01370 I1=.0804*L*VP : 12=1-Il1380 H202P = 11/3216 : REM Total H2O2 production mole/mm1390 O2D = H2O2P * 22400 : REM Total oxygen consumption mL/min1400 REM IF O2D > G THEN VP= (G-.005)fL/.56141OREMIFO2D>GGOTO72O1420 ORT = 1+(I1+12)/1.608/L : REM Titrated hydroxyl ion conc. M1430 OFIP = (I1+2*I2)/3.216fL : REM Hydroxide ion produced M1440H2P=6.965174*121450:1460 H2M = AF*GO : O2M = GO-H2M : H2C = H2P-H2D : O2C = G+O2P-02D1470 OHM = 01ff + OHCROSS : OHC = 1+OHP : GOUT = O2C + H2C1480 UGOUT=GOUT/A : UGIN = PS*UG/PIN*TIN/TS /21490 UGAV = (UGIN ÷ PS*UGOUT*TOUT / POUT/TS) /21500 UFOAM = UL + UGAV1510 QFOAM = UFOAM * A1520 RETURN1530Appendix G. The Computer Routines 2081540 REM SUBROUTINE TO CALCULATH THE OXYGEN SOLUBILITY INTEGRAL1550 SOLINT=0 : Y=01560 GOSUB 1710 : REM TO CALCULATE PO2Y AND TY1570 IF Y=>PL THEN GOTO 16901580 T = TY : P = PO2Y I PS “. 1011590 Si = iI(FNX1 (T) - 1)/18# : REM mole/mL1600 S2=(FNS3(P,T)+FNS4(P,T)÷FNS5(P,T))*.000001# : REM mole/inL1610 S3 =(P-.1)/.9 * (S2 - Si) + Si : REM molelmL1620 IF P<=0.1 THEN S0=S1 ELSE IF P=>1 THEN S0=S2 ELSE S0=S31630 S=S0*10A(FNKSm)1640 SOLINT=S+SOLINT1650 IFY=0 THEN SI=S1660 AREA=(SOLINT(SI+S)/2)*DY : IF Y=0 THEN AREA =01670 Y=Y+DY1680 GOTO 15601690 RETURN1700:1710 REM SUBROUTINE TO CALCULATE OXYGEN PARTIAL PRESSURE AND TEMPERATURE PROFILE1720 PO2IN = PIN - FNVPW (TIN) : YO2IN = P02]NIPIN1730 PO2H2OUT = POUT - FNVPW (I’OUI)1740 PO2OUT = O2C * PO2H2OUT /(O2C+H2C) YO2OUT = PO2OUT / POUT1750 YO2Y = YO2IN + (YO2OUT - YO2IN)*Y I PL1760 PY = PIN + (POUT - pll.4)*y / PL : TY= TIN + (TOUTTIN)*Y / PL1770 PO2Y = YO2Y *1780 RETURN1790:1800 REM SUBROUTiNE FOR MAKING FLOW AND MASS TRANSFER RESULT TABLES HEADINGS1810 3=11820 PRINT #3,” Results of mass transfer measurements at “; DEGREE$; “level porosity”1880 PRiNT #J,” of”; POROSITY; “% with”; GT$; CHR$(34); “-4.8 cm Neoprene gasket. The packing”1890 PRINT #3, “ is 1/2”; CHR$(34), “graphite felt, with “; PL; “ cm length,”; PW; “gr. weight and”1900 PRINT #J,” and Vs = “; VS; “cc solid volume, under 50 kg-cm torque setting.”1910 PRiNT #J,” MASS TRANSFER: OPERATING TABLE “OPR” & MODEL # “;MODEL;” :T elect. 22 oC”1920 PRINT #3,”1930 PRINT#3,””1950 PRINT #3,” RUN ID Ui Ug Ug av Ufoam Cu. Effi. Mass-Trx”1960 PRiNT #3,” cm/mm cm/mm cm/mm cm/nun % coef. 1/sec”2040 RETURN


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