"Applied Science, Faculty of"@en . "Chemical and Biological Engineering, Department of"@en . "DSpace"@en . "UBCV"@en . "Netprasat, Vorapoj"@en . "2009-12-21T20:56:59Z"@en . "2004"@en . "Master of Applied Science - MASc"@en . "University of British Columbia"@en . "The objectives of the present study were to compare the adsorption isotherms of various gases on various adsorbents using gravimetric, volumetric, and chromatographic methods: to determine whether the Langmuir isotherm model is appropriate for the N\u00E2\u0082\u0082 adsorption isotherms up to 300 kPa on zeolite NaX and zeolite LiX; to identify the dominant dynamic behaviour through a laminate bed of these and other adsorbents and to determine the effect of flowrate on the magnitude of the axial dispersion or mass transfer resistance within the laminated bed of adsorbent.\r\n\r\nThe gas adsorption isotherms of CO, and CO\u00E2\u0082\u0082 on zeolite 13X were obtained using the volumetric, gravimetric, and chromatographic methods. The isotherms obtained from the volumetric and gravimetric methods showed good agreement. The gravimetric method was used to measure adsorption isotherms of N\u00E2\u0082\u0082 up to 300 kPa for N\u00E2\u0082\u0082 on zeolite LiX relevant in the air separation industry. The N\u00E2\u0082\u0082 adsorption capacity of zeolite LiX, obtained in the present study, was higher than the N2 adsorption capacity of NaX or 13X used traditionally for air seperation.\r\n\r\nThe chromatographic method was used to determine the dispersion and mass transfer coefficients in a laminated bed of adsorbent. The results suggested that at low interstitial velocities, \u00CF\u0085 < 1.7 cm/sec, dispersion dominated, while at high interstitial velocities, \u00CF\u0085 \u00C2\u00BB 1.7 cm/sec, macropore and micropore mass transfer resistance dominated. Estimated dispersion and external fluid film mass transfer resistances were consistent with literature values. However, the micropore diffusivity obtained was lower than that reported in available literature data. The difference was most likely due to the inaccuracy in the results obtained using only two particle sizes. Furthermore, from the mass transfer resistances obtained for PSA with short cycle times using laminate beds, fast PSA with cycle time of 0.6 to 3 seconds is possible."@en . "https://circle.library.ubc.ca/rest/handle/2429/16970?expand=metadata"@en . "BREAKTHROUGH ANALYSIS OF A STRUCTURED ADSORBENT BED by VORAPOJ NETPRASAT B .A .Sc , The University of British Columbia, 2000 A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF M A S T E R OF APPLIED SCIENCE in THE F A C U L T Y OF G R A D U A T E STUDIES (DEPARTMENT OF C H E M I C A L A N D BIOLOGICAL ENGINEERING) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A April, 2004 \u00C2\u00A9 Vorapoj Netprasat, 2004 Library Authorization In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Name of Author (please print) Date (dd/mm/yyyy) Title of Thesis: A Y T H jgQ \)G Y) A N A i - V l i - f oF A ^Trgv/CTt/f\u00C3\u00A9fJP fir \u00C3\u008E) ..Co BENT QBD : Degree: /I/). A- $c- Y e a r : 0,00^ Department of C U g / U l I \u00C3\u0087 A \u00C3\u00A7 /tfJti fop? LP 6\u00C2\u00A3 \u00C2\u00A3 / H N I f ' E&lNG The University of British Columbia Vancouver, BC Canada Abstract The objectives of the present study were to compare the adsorption isotherms of various gases on various adsorbents using gravimetric, volumetric, and chromatographic methods: to determine whether the Langmuir isotherm model is appropriate for the N2 adsorption isotherms up to 300 kPa on zeolite NaX and zeolite L i X ; to identify the dominant dynamic behaviour through a laminate bed of these and other adsorbents and to determine the effect of flowrate on the magnitude of the axial dispersion or mass transfer resistance within the laminated bed of adsorbent. The gas adsorption isotherms of CO, and CO2 on zeolite 13X were obtained using the volumetric, gravimetric, and chromatographic methods. The isotherms obtained from the volumetric and gravimetric methods showed good agreement. The gravimetric method was used to measure adsorption isotherms of N2 up to 300 kPa for N2 on zeolite L i X relevant in the air separation industry. The N2 adsorption capacity of zeolite L i X , obtained in the present study, was higher than the N2 adsorption capacity of NaX or 13X used traditionally for air seperation. The chromatographic method was used to determine the dispersion and mass transfer coefficients in a laminated bed of adsorbent. The results suggested that at low interstitial velocities, u < 1.7 cm/sec, dispersion dominated, while at high interstitial velocities, u \u00C2\u00BB 1.7 cm/sec, macropore and micropore mass transfer resistance dominated. Estimated dispersion and external fluid film mass transfer resistances were consistent with literature values. However, the micropore diffusivity obtained was lower than that reported in available literature data. The difference was most likely due to the inaccuracy in the results obtained using only two particle sizes. Furthermore, from the mass transfer resistances obtained for PSA with short cycle times using laminate beds, fast PSA with cycle time of 0.6 to 3 seconds is possible. Table of Content Abstract i i List of Tables viii List of Figures x Nomenclature xiv Acknowledgement xx Chapter 1 : Introduction 1 1.1 Background 1 1.2 Motivation for the Study 5 1.3 Objectives 8 Chapter 2: Literature Review 9 2.1 Adsorption 10 2.1.1 Pressure Swing Adsorption 12 2.2.2 PSA with Short Cycle Time 15 2.2.3 Adsorbent Development in Air Separation 20 2.2 Gas Adsorption Isotherms 23 2.2.1 Background 23 2.2.1.1 Henry's Law 24 2.2.1.2 The Langmuir Isotherm 25 2.2.1.3 Freundlich and Langmuir Isotherms 26 2.2.2 Isotherm Measurement Methods 27 2.2.2.1 Volumetric Method 27 2.2.2.2 Gravimetric Analysis 28 2.2.2.3 Breakthrough Analysis 28 2.2.2.4 Comparison Between Isotherm Measurement Methods 32 2.3 Bed Configurations 33 2.3.1 Packed Bed .....33 2.3.2 Monolithic Bed 35 2.4 Experimental Methods in Measuring Gas Adsorption Dynamics 38 2.4.1 Zero Length Column 40 2.4.2 Permeation 40 2.4.3 Frequency Response Method 41 2.4.4 Chromatography method 42 Chapter 3: Experimental 50 3.1 Procedure and Apparatus 50 3.1.1 Gas isotherm measurement 50 3.1.1.1 Gravimetric Analysis 50 3.1.1.2 High Pressure Gravimetric Measurement 54 3.1.1.3 Volumetric Adsorption Isotherm Measurement 56 3.1.1.4 Breakthrough Analysis 58 3.1.2 Chromatographic Method 59 3.1.3 Pressure Drop Through Structured Adsorbent Bed 61 3.2 Materials 62 3.2.1 Adsorption Isotherm 62 3.2.2 Kinetic Parameters 63 Chapter4: Adsorption Isotherm Measurements 65 4.1 Introduction 65 4.2 CO and C O 2 adsorption isotherms 65 4.3 N2 Adsorption Isotherms 77 4.4 Heats of Adsorption 90 Chapter 5 : Dispersion and Mass Transfer in Structure Adsorbent Bed 94 5.1 Introduction 94 5.2 Henry's Constant Estimates 96 5.3 Dispersion and Mass Transfer Estimates 101 5.4 Macropore and Micropore Mass Transfer 109 5.6 Parametric Study 121 Chapter 6: Conclusions and Recommendations for Future Work 127 6.1 Conclusions 127 6.2 Recommendations for Future Work 128 Reference: 129 Appendix 1 : Isotherm Measurements Data 135 Appendix 2: Summary of Breakthrough Data 145 Appendix 3: Breakthrough Curves for Breakthrough Experiments 149 Appendix 4: Mass Transfer Resistance Comparison 154 Appendix 5: Calculation of Mass Transfer Resistance 155 Appendix 6: Pressure Drop Through the Structured Adsorbent Bed 157 Appendix 7: Detailed Experimental Procedures 159 Low pressure (atmospheric) gravimetric method 159 High pressure (up to 3 bar) gravimetric method 159 Volumetric method 160 Programming a sample file 160 Desorption breakthrough experiment 161 Running breakthrough measurements 161 Breakthrough method used to estimate dispersion and mass transfer coefficients 163 Appendix 8: F test 165 Appendix 9: Heat Adsorption Calculations 174 Appendix 10: Matlab\u00E2\u0084\u00A2 Program 178 List of Tables Table 1.1 Usage of hydrogen, nitrogen, and oxygen Table 2.1 Advantages and disadvantages in adsorption dynamics measurement method Table 3.1 Adsorbents used in the present study ( Table 4.1 Comparison of Langmuir adsorption constants at 30 \u00C2\u00B0C determined using the volumetric gravimetric, and desorption breakthrough methods on zeolite NaX Table 4.2 F-test comparison between volumetric and gravimetric data for CO and CO2 adsorption on zeolite NaX at 30 \u00C2\u00B0C Table 4.3 F-test comparison of N2 adsorption on zeolite NaX by volumetric and gravimetric methods Table 4.4 Langmuir constants for N2 on zeolite L i X Table 4.5 Langmuir constants for high and low pressure data for N2 on QP Table 4.6 F-test comparison for significant difference between low and high pressure N2 adsorption isotherms on QP vs. both sets of data Table 5.1 Summary of Adsorption structure dimensions 1 Table 5.2 Henry constants and their 95% confidence intervals 1 Table 5.3 Comparison of gas adsorbed at 101 kPa and 24 \u00C2\u00B0C between gravimetric and chromatographic method 1 Table 5.4 Dispersion coefficients estimated for structured adsorbent beds 1 Table 5.5 Lumped mass transfer resistances estimated using HETP/2u vs. I/o at low flow rate 1 Table 5.6 Lumped mass transfer rates estimated using Plate theory at high flow rate and their 95% confidence intervals 1 Table 5.7 Individual mass transfer coefficients 112 Table 5.8 Fluid film mass transfer coefficient 113 Table 5.9 Fluid film mass transfer coefficient compared with literature value 114 Table 5.10 SSE and F-values from the F-test for predicted data from Matlab\u00E2\u0084\u00A2 program and measured data 121 List of Figures Figure 2.1 Skarstrom cycle ..: 14 Figure 2.2 PSA with short cycle Process (source: Sircar & Hartley, 1995) 16 Figure 2.3 Brunauer classification of isotherms 24 Figure 2.4 General equilibrium relationship 29 Figure 3.1 Flowsheet of gravimetric apparatus used for adsorption isotherm measurement 51 Figure 3.2 Schematic of the gravimetric analyzer unit 52 Figure 3.3 Graphical representation of high pressure TGA 55 Figure 3.4 Schematic diagram of ASAP 2010 57 Figure 3.5 Breakthrough experiment for mass-spectrometer system 58 Figure 3.6 Breakthrough experimental set up with TCD for low flow rate experiments 60 Figure 3.7 Breakthrough experiment set up with TCD for high flow rate experiments 61 Figure 3.8 Graphical representation of the structured adsorbent 64 Figure 4.1 CO and CO2 adsorption isotherms on zeolite NaX at 30 \u00C2\u00B0C obtained by the volumetric and gravimetric methods 66 Figure 4.2 Measured and fitted adsorption isotherms for CO at 30 \u00C2\u00B0C on zeolite NaX 68 Figure 4.3 Measured and fitted adsorption isotherms for CO2 at 30 \u00C2\u00B0C on zeolite NaX 69 Figure 4.4 Comparison of the CO adsorption isotherms for zeolite NaX based on Langmuir parameters obtained from volumetric, gravimetric, and desorption breakthrough method at 30 \u00C2\u00B0C 70 Figure 4.5 Comparison of the CO2 adsorption isotherms at 30 \u00C2\u00B0C for zeolite NaX based on Langmuir parameters obtained from volumetric, gravimetric, and desorption breakthrough method 71 Figure 4.6 ( q * - q ' 0 ) / ( q o - q ' o ) vs. (c-c'0)/(c0-c'o) for CO 75 Figure 4.7 (q* -q 'o ) / (qo-q 'o ) vs. (c-c'0)/(c0-c'0) for C 0 2 76 Figure 4.8 C/Co vs. 1/Jut-z plot for CO at 30 \u00C2\u00B0C 77 Figure 4.9 Measured N2 adsorption isotherms on zeolite NaX obtained by the volumetric and gravimetric methods 79 Figure 4.10 N2 adsorption isotherms for zeolite L i X obtained by the gravimetric method 81 Figure 4.11 ln K vs. 1/T for the extrapolation of Henry's constant of N 2 isotherm on zeolite NaX 83 Figure 4.12 ln b vs. 1/T for the extrapolation of Langmuir constant, b of N2 isotherm on zeolite L i X 84 Figure 4.13 N2 adsorption isotherm on NaX at 25 \u00C2\u00B0C 85 Figure 4.14 N2 adsorption isotherm on L i X at 25 \u00C2\u00B0C 86 Figure 4.15 Comparison of extrapoled high pressure isotherm data with measured high pressure data for N2 on QP 88 Figure 4.16 ln K vs. 1000/T used to determined heat of adsorption of N 2 , CO, and C 0 2 on QA2 adsorbent from the data measured volumetrically 91 Figure 4.17 ln K vs. 1000/T used to determined heat of adsorption of N2 on zeolite NaX adsorbent from the data measured gravimetrically 92 Figure 4.18 ln b vs. 1000/T used to determined heat of adsorption of N2 on zeolite L i X adsorbent using Langmuir parameter, b 93 Figure 5.1 u, vs. 1/F for high X-sectional area structure for N2 at 24 \u00C2\u00B0C and 101 kPa 97 Figure 5.2 p. vs. 1/F for mid X-sectional area structure for N2 at 24 \u00C2\u00B0C and 101 kPa 97 Figure 5.3 p vs. 1/F for low X-sectional area structure for N 2 at 24 \u00C2\u00B0C and 101 kPa 98 Figure 5.4 u. vs. 1/F for high voidage structure for N2 at 24 \u00C2\u00B0C and 101 kPa 98 Figure 5.5 p. vs. 1/F for thick adsorbent sheets structure for N2 at 24 \u00C2\u00B0C and 101 kPa 99 Figure 5.6 HETP/2u vs. I/o 2 for high X-sectional area structure for N2 at 24 \u00C2\u00B0C and 101 kPa 102 Figure 5.7 HETP/2u vs. 1/u2 for mid X-sectional area structure for N2 at 24 \u00C2\u00B0C and 101 kPa : 102 Figure 5.8 HETP/2u vs. 1/u2 for low X-sectional area structure for N 2 at 24 \u00C2\u00B0C and 101 kPa 103 Figure 5.9 HETP/2u vs. 1/u2 for non adsorbing structure for N 2 at 24 \u00C2\u00B0C and 101 kPa 103 Figure 5.10 HETP/2u vs. 1/u2 for high voidage structure for N 2 at 24 \u00C2\u00B0C and 101 kPa 104 Figure 5.11 HETP/2u vs. 1/u2 for thick adsorbent sheets structure for N2 at 24 \u00C2\u00B0C and 101 kPa 104 Figure 5.12 HETP vs. interstitial velocity plot used to determine the lumped mass transfer coefficient for v > 7 cm/s 108 1 2 Figure 5.13 \u00E2\u0080\u0094 vs. (aR p) used to determine macropore and micropore mass transfer JcK coefficients 110 1 2 Figure 5.14 \u00E2\u0080\u0094 vs. (aR p) used to determine macropore and micropore mass transfer JcK. coefficients 112 Figure 5.15 Predicted breakthrough curve and raw data for high X-sectional area structure with flow = 100 S C C M 115 Figure 5.16 Predicted breakthrough curve and raw data for mid X-sectional area structure with flow = 100 S C C M 116 Figure 5.17 Predicted breakthrough curve and raw data for non-adsorbing structure with flow = 100 S C C M 117 Figure 5.18 Predicted breakthrough curve and raw data for low X-sectional area structure with flow = 100 S C C M 118 Figure 5.19 Predicted breakthrough curve and raw data for high voidage structure with flow = 100 S C C M 119 Figure 5.20 Predicted breakthrough curve and raw data for thick adsorbent sheets structure with flow = 100 S C C M : 120 Figure 5.21 Predicted breakthrough curve for change in external fluid film coefficient, k f : 122 Figure 5.22 Predicted breakthrough curve for change in macropore mass transfer coefficient, D P 123 Figure 5.23 Predicted breakthrough curve for change in micropore mass transfer coefficient, D C 124 Figure 5.24 Predicted breakthrough curve for change in dispersion coefficient, DL 125 Nomenclature Units a = Langmuir constant mmol g\"1 kPa' A = Percent open frontal area of a monolith % A w = Wall correction term for Equation [2.28] A i = Molecular diffusion term in Equation [2.53] cm A2 = Eddy diffusion term in Equation [2.53] cm A 3 = Mass transfer resistances term in Equation [2.53] cm b = Langmuir constant kPa\"1 B = Monolith channel cross section constant B w = Wall correction term for Equation [2.28] c = Concentration mol/L c'o,c0 = Initial (t < 0) and final (t > 0) steady state values of c CMS = Carbon Molecular Sieve d = Diameter um or m dCh = Monolith channel diameter cm dh = Hydraulic diameter cm dp = Particle diameter pm or m D/dp = Tube to particle diameter ratio \u00E2\u0080\u00A2y D c = Micropore diffusivity cm /sec D L = Axial dispersion coefficient cm /sec \u00E2\u0080\u00A2y D m = Molecular dispersion coefficient cm /sec -y Dp = Macropore diffusivity cm /sec d.f. = Degree of freedom erfc = Error function E = Electric field / = Friction factor Fstats = F factor defined as F1/F2 or volumetric flow rate F = Volumetric flow rate cm3/sec F factor = F s t a ts obtained from Statistical F-test F, = SSE/d.f. of data set 1 F 2 = SSE/d.f. of data set 2 Fb = Buoyancy force N FCritica],(x=o.05 = F values from F distribution table at 95% confidence interval FR = Frequency Response g 0 = Gravitational constant m/sec2 HETP = Height Equivalent Theoretical Plate cm or m k = Mass transfer coefficient sec\"1 kf = External fluid film mass transfer coefficient cm/sec ki = Coefficient of wall effect correction term k 2 = Coefficient of wall effect correction term K = Henry constant (expressed on a particle volume basis) K ' = Henry constant K c = Dimensionless equilibrium constant, expressed on a solid volume basis K 0 = Pre-exponential factors in K = K 0exp(-AU/RT) and K ' = K' 0exp(-AH/RT) K i = Coefficient of pressure correlation m = Initial mass of the sample kg or g L = Length cm or m L i , M e 2 + X = Zeolite X with L i and metal ion with 2+ charge L i , M e 3 + X = Zeolite X with L i and metal ion with 3+ charge N = Amount of gas adsorbed mmol/g M e 2 + = Metal cation with 2+ charge p = Pressure kPa PSA = Pressure Swing Adsorption q = Amount of gas adsorbed or sorbate concentration mmol/g q = Equilibrium value of q mmol/g q' 0 , q 0, q' = Initial, final, and surface value of q mmol/g q', = Surface value of gas adsorbed mol/L q s = Amount of gas adsorbed at saturation mmol/g qL - Value of gas adsorbed over crystal particle mol/L r = Radius pm or m r c = Radius of a zeolite crystal pm or m R = Universal gas constant kPa*m3/(mol*K) R p = Particle radius pm or m Re = Reynolds number s = Second sec Se = Schmidt number S C C M = Standard cubic centimeter per minute cm3/min Sh = Sherwood number SSE = Sum of square of errors defined as [Y(predicted) - Y(average)]2 T = Temperature K or \u00C2\u00B0C t = Time sec TGA = Thermo gravimetric analyzer v = Interstitial velocity cm/sec V f = Volume of fluid cm 3 V s = Volume of sorbate cm 3 w( c) = Concentration profile velocity ' cm/sec W = Mass flow rate g/sec Wfiow - Weight of sample with He flow g Wstatic = Weight of sample without He flow g W t = Sample weight after adsorption g Ug = Kinetic energy of sorbate in the bulk phase kJ U s = Kinetic energy of sorbate in the adsorbed phase kJ z = Length of the adsorption column cm or m ZLC = Zero Length Chromatography G R E E K L E T T E R S P = Dimensionless variable defined as 1 \u00E2\u0080\u00A2\u00E2\u0080\u0094\u00E2\u0080\u0094 D = Energy due to Dispersion kJ Q = Energy due to Quadruple force kJ ) of adsorption comprises van der Waals forces (dispersion (attraction) -repulsion) and electrostatic interactions (polarization, dipole, and quadrupole interactions). For an ionic adsorbent such as zeolite (cationic adsorbent), the overall potential is given by the sum of the six terms $ = ,-,+ R + (/>,, +min \u00C2\u00AB ' 1 and Equation [2.6] reduces to Henry's law where qsb = K. At high pressure, (1+bp) -> bp and hence q q s. The model parameters (b and qs) can be determined from the slope and intercept of a plot of (1/q) vs. (1/p) or by curve fitting the q vs. qsbp/(l+bp) curve with a parameter estimation algorithm. At low sorbate pressure, the temperature dependence of the Henry's constant follows the van't Hoff equation. AH 1 AS v \u00E2\u0080\u009E ( AH H ^ . m m \nK = + \u00E2\u0080\u0094 or K = Kn exp Equation [2.7] R T R \ R TJ where K 0 = The van't Hoff relation (Equation [2.7]) can be obtained from the following Gibbs free energy equations. AG = AH - TAS Equation [2.8a] AG = -RTlnK Equation [2.8b] The enthalpy change during adsorption can be determined by plotting ln K versus (1/T). From Equation [2.6] and Equation [2.7], q s is independent of temperature and the change in enthalpy is independent of concentration. Rege and Yang (1997) reported the heat of adsorption of N 2 on L i X and NaX to be 23.4 kJ/mol and 18.0 kJ/mol, respectively. The ideal Langmuir isotherm has two advantages: it makes a good approximation of many adsorption systems and it reduces to Henry's law in the low concentration limit, which is a requirement for thermodynamic consistency in any physical adsorption system. For these reasons, Langmuir isotherms are widely used in PSA systems for qualitative and semiquantitative purposes. Furthermore, Langmuir isotherm in the form of a generalized Langmuir isotherm can be extend to include the adsorption on heterogeneous system. f be\" \ + bcn Equation [2.9] 2.2.1.3 Freundlich and Langmuir Isotherms. The Type I isotherm can also be modeled by the Freundlich equation: q = bc 1 / n , n>1.0 Equation [2.10] where b and n= Freudlich constants The Freudlich isotherm is based on a distribution of affinities among the surface adsorption sites, but it is probably better regarded as an empirical expression. 2.2.2 Isotherm Measurement Methods In order to select appropriate adsorbents to be used in pressure swing adsorption, adsorption isotherms must be measured. There are many experimental techniques which can be used to obtain these isotherms. In the present study, gravimetric and volumetric adsorption methods as well as desorption breakthrough (or the chromatographic method) have been used to determine the adsorption isotherm. 2.2.2.1 Volumetric Method The volumetric method of determining an adsorption isotherm generally involves measuring the volume adsorbed by monitoring change in fluid phase concentration or bulk concentration. In a gaseous system, the fluid phase concentration is measured by monitoring the change in pressure. For a gas adsorption isotherm, the known amount of adsorbate is introduced into the adsorbent chamber of known volume to pressurize the chamber at a fixed pressure and a fixed temperature followed by equilibration of gas between the bulk and the adsorbed phase. After the system is allowed to come to equilibrium, the pressure is measured and compared to the original pressure. If the pressure decreases, a known amount of adsorbate is added to obtain the original pressure. On the other hand, if there is no change in pressure, then the bulk gas is assumed to be in equilibrium with the adsorbed gas at that pressure and temperature. The entire adsorption isotherm can be obtained by measuring the adsorbed volume at other pressures. To account for the volume in of gas in the bulk phase, a blank sample tube can be run at the same conditions as the isotherm measurement and this volume can be subtracted from the total volume in the bulk phase and adsorbed phase to obtain the volume of gas adsorbed by the adsorbents. 2.2.2.2 Gravimetric Analysis The gravimetric method measures the weight change of a sample when exposed to different pressures of adsorbate at a fixed temperature. The amount adsorbed can be calculated by W - F N = \u00E2\u0080\u0094 1 L Equation [2.11] m x Mw where W t is the sample weight after adsorption, M w is the gas molecular weight, m is the initial mass of the sample, and Fb is the total buoyancy force. In a typical thermogravimetric apparatus, the buoyancy force can be obtained by monitoring the weight change in the sample with and without He flow, assuming that helium does not adsorb onto the sample. F b = Wfiow - WstatiC Equation [2.12] where W f l O W = weight of sample with He flow Wstatic = weight of sample without He flow 2.2.2.3 Breakthrough Analysis Unlike the gravimetric or volumetric methods, breakthrough analysis does not generate experimental isotherms which can be fitted with Langmuir or other isotherm models. However, by measuring the desorption dynamics of a pre-adsorbed adsorbate from a bed of adsorbent, the adsorbate concentration profile through the bed can be determined. The concentration profile along the length of the bed yields Langmuir isotherm parameters, a and b where a = qsb. (Ruthven, 1984) The general nature of a concentration front or mass transfer zone traveling down the length of a packed column is entirely dependent on the equilibrium isotherm. However, the shape of the concentration front is dictated by kinetic effects and dispersion. Usually, an equilibrium relationship over the concentration range under consideration can be classified as linear, favourable, and unfavourable. These three forms of equilibrium relationship arise from plotting a dimensionless adsorbed phase versus fluid phase concentration, (q*-q 0 ) / ( q o - q o) and (c c o)/(c0-c o) as illustrated in Figure 2.4. Figure 2.4 General equilibrium relationship The three general equilibrium relationships in Figure 2.4 correspond to: 29 Favourable Qo . c - cc > Qo lo co cc Linear q -q0 _ c-cc Qo Qo co cc Unfavourable < C-Cr q0-q0 c, o Usually, the adsorption isotherm is favourable, therefore, the desorption isotherm will be unfavourable. In desorption, the mass transfer zone is therefore dispersive meaning that the concentration profile spreads and becomes more dispersed as it travels down the length of the bed. Since the profile spreads in direct proportion to the distance traveled, this is referred to as \"proportionate pattern\" behaviour. Assuming that the column is long enough so that equilibrium is reached at the end of the packed column, it is possible to extract adsorption isotherm parameters for a given system. For isothermal plug flow of a trace component in an inert carrier system used in packed bed configuration, the material balance is de dc (l-e^ v\u00E2\u0080\u0094 + \u00E2\u0080\u0094 + dz dt \ s ) dt o Equation [2.14] and assuming mass transfer equilibrium: dt v J (dqj^ V & J dq*i fdc^ dc Equation [2.15] with a Langmuir adsorption model, whose derivative with respect to concentration is dq L bqs de (l + be)2 Substituting Equation [2.15] and Equation [2.16] into Equation [2.14] yields the concentration profile velocity propagating down the length of the column: w(c) = (dc/dt)z (dc/dz), v 1 + dc -e v \u00C2\u00A3 J J _ Equation [2.17] By substituting Equation [2.15] into Equation [2.17], followed by integration, the concentration profile down the length of the bed can be determined: \u00C2\u00B1>i\u00C2\u00BB where the dimensionless variables are defined as c/c0 = concentration/initial concentration 0 = i-*e- = (i+bcoy q. and T (ot - Z) \ \u00C2\u00A3 J Equation [2.18] or f 1 ^ \bcOJ vt-z V \u00C3\u00A0 J -1 Equation [2.19] The plot of c/c0 versus \/yjut-z yields the Langmuir isotherm parameters (b,qs) from the intercept and the slope, provided s is known. 2.2.2.4 Comparison Between Isotherm Measurement Methods Adsorption isotherms are normally obtained by either volumetric or gravimetric measurement. Both methods are time consuming since they require several points to directly and adequately define the adsorption isotherm. Physical adsorption isotherms are often rectangular or Langmuir (Type 1) and more data points are needed so that the curvature of the isotherm can be accurately defined. Furthermore, some isotherms have a steep slope in the linear region, hence, if an inadequate number of data points are taken, the curved region of the isotherm might only be represented by one data point or even worse no data point. Depending on what type of adsorbents and/or gas is used, either volumetric or gravimetric methods might be more advantageous. For adsorption of small molecules such as hydrogen, the volumetric measurement might be more advantageous since buoyancy force correction is important in gravimetric methods. If the mass of adsorbed gas is comparable to the buoyancy force exerted on the sample, accurate results may not be obtained (Robens et al., 1999). In the volumetric measurement, the system free space (dead volume) must be determined and this is usually done with He at 77 K or ambient temperature, under the assumption that that the adsorbent does not adsorb He. However, a small error in the dead volume measurement may introduce significant errors in the isotherm measurement. Analysis of the desorption of pre-adsorbed adsorbent can also be used to determine the adsorption isotherm. However, this method does not generate the adsorption isotherm directly. Rather parameters of the Langmuir isotherm are extracted from the desorption profile and this could be quite cumbersome and inaccurate since the method requires large quantities of data to be collected and the desorption curve must be carefully generated. Also, the adsorbent used in the breakthrough experiment must be bound into larger particles to avoid significant pressure drop through the system. Inert materials are used as binders during pelletization introducing errors into the adsorption isotherm obtained. 2.3 Bed Configurations Traditionally, absorbents in most adsorption processes are contacted by the fluid phase in a packed bed, resulting in significant pressure drop at high flow rate. From a process economic point of view, high pressure drops result in higher pumping cost. Alternatively, reducing flow rate to reduce pressure drop results in longer residence time and less productivity. If high flow rate is maintained, then large particles must be used due to a significant increase in pressure drop, which results in an increase in mass transfer resistance. An alternative approach to a packed bed of adsorbent particles is to use adsorbent placed in a structured monolith. The monolith reduces pressure drop, and hence, higher flow rate can be used without significantly increasing particle size or mass transfer resistance. 2.3.1 Packed Bed Pressure drop in flow through a packed bed has been investigated by several investigators, some of which include Chilton and Colburn (1931) and Ergun (1952). Usually, a dimensionless friction factor (f) is used to correlate pressure drop to particle size and flow rate. ' 2 0 J A p Equation [2.20] pf{svf where Ap is the pressure drop, pf = fluid density, and su is the superficial fluid velocity. Two commonly used correlations for the friction factor are: Chilton-Colburn(1931) Re<40 Re>40 f=38/Re' 0.15 Ergun(1952) / = + 1.75 Equation [2.22] V A Re where Re (Reynolds number) = vd pp/p where v = velocity, d p = particle diameter, p = density, and p = viscosity As can be seen from Equation [2.20] and [2.22], pressure drop is a function of both velocity and Reynolds number, i.e., particle size. The smaller the particle size and the higher the velocity, the higher the pressure drop, especially for the velocity since it shows a square relationship with the pressure drop. Hence, increasing velocity (flowrate) will increase the pressure drop significantly. Furthermore, in order to keep the pressure drop low, catalyst particles will have to be larger, resulting in higher mass transfer resistance. Eisfeld and Schnitzlein (2001) reported recently on the influence of walls on pressure drop in packed beds. Among 24 correlations they attempted to fit to 2300 data points, the Reichelt (1972) correlation (Equation [2.23]), which is based on the Ergun equation, yielded the best fit. Furthermore, they showed that for tube-to-particle diameter ratios (D/dp) of less than 10, the Ergun equation normally over predicts the pressure drop whereas, the pressure drop predicted by the Reichelt equation is lower than the Ergun equation and it also shows good agreement with experimental data. Eisfeld and Schnitzlein (2001) reported that the Reichelt equation can be used to calculate pressure drop in the following ranges: 0.01 < Re <17635, 1.624 < D/d p <250, and 0.330 a=o.o5 H i : \ if Fstats > F c ritical,a=0.05 where cr,2 and o\ are the variance of the two data sets from the two adsorption methods Fstats = F factor defined as F1/F2 Fi =SSE/d.f. of data set 1 F 2 = SSE/d.f. of data set 2 SSE = sum of square of errors defined as [Y(measured) - Y(average)]2 d.f. = degree of freedom Fcriticai,a=o.o5 = F values from F distribution table at 95% confidence interval The F factors and F-critical values for CO and C 0 2 data are summarized in Table 4.2. Table 4.2 F-test comparison between volumetric and gravimetric data for CO and C 0 2 adsorption on zeolite NaX at 30 \u00C2\u00B0C. Gas Fstats - F ] / F 2 Fcritical.a =0.05 for M1/M2 CO 1.46 1.96 C 0 2 0.94 1.96 Fi = F factor for adsorption isotherm obtained from volumetric measurement F 2 = F factor for adsorption isotherm obtained from gravimetric measurement M i = Data obtained from volumetric method M2 = Data obtained from gravimetric method From Table 4.2, we concluded that the fit to the isotherm data for CO and CO2 obtained from the volumetric and gravimetric methods was not significantly different since the F factors are less than the F-critical values. Adsorption isotherms derived from Langmuir parameters extracted from the desorption breakthrough curves were much higher than those obtained from the volumetric and gravimetric data, as can been seen in Figure 4.4 and Figure 4.5. Possible explanations for this discrepancy are as follows: 1. Sample differences: The sample used for the desorption breakthrough method was not in powder form, as was the case for the other two methods. The sample had been pelletized and contained approximately 20 percent \"inert\" binding materials. 2. The assumptions made for desorption breakthrough analysis may not all be valid. These assumptions include plug flow, negligible mass transfer resistance, and a favourable adsorption isotherm. The first two assumptions are more likely to introduce error in the Langmuir adsorption constants extracted. Axial dispersion is fairly significant in any packed bed system. According to Ruthven and Karger (1992), for W r f e in 4A zeolite, the axial dispersion, D L , is 0.7 cm2/sec at 35 \u00C2\u00B0 C . Mass transfer resistance may not be negligible as assumed since the particle diameter was quite large (approximately 2 mm), which results in significant macropore mass transfer resistance. The last assumption of a favorable isotherm is often valid since adsorption processes that can be fitted with Langmuir isotherm models should be favourable. Figure 4.6 and 4.7 confirms that both * \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 Q \u00E2\u0080\u0094 Q C \u00E2\u0080\u0094 C C O and CO2 adsorption isotherms are indeed favourable. If \u00E2\u0080\u0094 > %-, i.e., Qo co co q -q0 q0 - q0 vs. c, c-c, o -c, o 0 graph is above the diagonal or 45\u00C2\u00B0 line, then the isotherm is said to be favourable. (OC'o^Cb-C'o) \u00E2\u0080\u00A2 CO at 30 C \u00E2\u0080\u0094 L i near (45 degree line) Figure 4.6 (q*-q'o)/(q0-q'o) vs. (c-c'0)/(c0-c'0) for CO. 0 0.2 0.4 0.6 0.8 1 (c-c'o)/(c0-c'o) \u00E2\u0080\u00A2 C02 at 30 C \u00E2\u0080\u0094 Linear (45 degree line) Figure 4.7 ( q * - q ' 0 ) / ( q o - q ' o ) vs. (c-c'0)/(c0-c'0) for C 0 2 . 3. Estimation of the Langmuir parameters is based on the slope and intercept of the c/c0 versus 1/ Vvr-z plot, which may not be accurately extracted as shown in Figure 4.8. The 95% confidence intervals for the slope and the intercept were determined to be \u00C2\u00B1 5 % and \u00C2\u00B1 3 0 %, respectively The results from the present study suggests that Desorption breakthrough method is not a suitable method in obtaining gas adsorption isotherms for the system under study. o o o 0.2 0.4 0.6 1/(vt-z) 0.8 0.5 1.2 Figure 4.8 C/Co vs. VJut-z plot for CO at 30 \u00C2\u00B0C. 4.3 N2 Adsorption Isotherms N 2 adsorption isotherms on zeolite NaX were also obtained at 30 \u00C2\u00B0C and 50 \u00C2\u00B0C, as shown in Figure 4.9. These adsorption isotherms were fitted by the linear Henry's law equation. F tests were also performed for these data sets. The F s t a t s values, summarized in Table 4.3, indicate that no significant difference existed between measured and fitted data for both sets of data obtained by the volumetric and gravimetric methods. Table 4.3 also lists the Henry's constants for N 2 adsorption isotherms on zeolite NaX at 30 \u00C2\u00B0C and 50 \u00C2\u00B0C. As can be seen in Figure 4.9, the adsorption process is temperature dependence as the process is exothermic. If follows that the adsorption decreases with increasing temperature. Table 4.3 F-test comparison of N 2 adsorption on zeolite NaX by volumetric and gravimetric methods. Temperature (\u00C2\u00B0C) Method Henry's constant (mmol g'1 kPa\"1) Fstats F, /F 2 F C r i t ica1,a =0.05 For M1/M2 30 Volumetric 0.004460+0.000048 1.91 1.96 Gravimetric 0.004279+0.000208 50 Volumetric 0.002617\u00C2\u00B10.000023 0.78 1.96 Gravimetric 0.00291810.000075 Fi = F factor for adsorption isotherm obtained from volumetric measurement F 2 = F factor for adsorption isotherm obtained from gravimetric measurement M i = Data obtained from volumetric method M 2 = Data obtained from gravimetric method 0.6 0.5 O\u00C3\u0099 7? 0.4 -T3 \u00C2\u00A3 0.3 \u00E2\u0080\u0094 o \u00E2\u0080\u0094 c 0.2 o S < 0.1 0.0 30\u00C2\u00B0C \u00E2\u0080\u00A2 \ \u00E2\u0080\u00A2 \ II \u00E2\u0080\u00A2 \" \ \ \u00E2\u0080\u00A2 \ 1 \u00E2\u0080\u00A2 - - - - - - - A \u00E2\u0080\u00A2 -A \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 A 4 \u00E2\u0080\u00A2 _ \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \" \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 A \u00E2\u0080\u00A2 , , 50\u00C2\u00B0C 1 1 ! 0 20 40 60 80 100 120 Pressure (kPa) \u00E2\u0080\u00A2 Volumetric at 50 C \u00E2\u0080\u00A2 Volumetric at 30 C A gravimetric at 50 C M gravimetric at 30 C Figure 4.9 Measured N 2 adsorption isotherms on zeolite NaX obtained by the volumetric and gravimetric methods. Furthermore, N 2 adsorption isotherms were obtained at various temperatures for zeolite L i X adsorbent using the gravimetric method, as shown in Figure 4.10. The Langmuir parameters for the N 2 isotherm on zeolite L i X are listed in Table 4.4. When comparing the N 2 adsorption capacity of zeolite NaX and zeolite L i X adsorbents at 30 \u00C2\u00B0C and 50 \u00C2\u00B0C, the affinity for N 2 on zeolite L i X was approximately 3 times higher than that on zeolite NaX. This is consistent with literature reports. Zeolite L i X has been reported to give 3-4 times higher adsorption capacity than zeolite NaX (Mullhaupt and Stephenson, 1995). Also, N 2 adsorbs more strongly on zeolite 79 than zeolite NaX (Mullhaupt and Stephenson, 1995). Also, N 2 adsorbs more strongly on zeolite L i X since L i + has the smallest ionic radius and hence the shortest distance between the nucleus of L i and the N 2 molecule (Yang et al., 1996). Table 4.4 Langmuir constants for N 2 on zeolite L i X Temperature (\u00C2\u00B0C) Langmuir Constant, a (mmol g\"1 kPa\"1) Langmuir Constant, b (kPa 1) 30 0.02461\u00C2\u00B1 0.00182 0.00775\u00C2\u00B1 0.00151 40 0.01700\u00C2\u00B1 0.00097 0.00576+0.00100 50 0.00938\u00C2\u00B1 0.00065 0.00343\u00C2\u00B1 0.00102 60 0.00652\u00C2\u00B1 0.00069 0.00176\u00C2\u00B1 0.00144 80 0.00437\u00C2\u00B1 0.00071 0.00041\u00C2\u00B1 0.00193 0 20 40 60 80 100 120 Pressure (kPa) \u00E2\u0080\u00A2 T = 3 0 C H T= 40 C * T = 5 0 C * T= 60 C x T= 80 C Figure 4.10 N 2 adsorption isotherms for zeolite L i X obtained by the gravimetric method. After having determined N 2 adsorption isotherms on zeolite NaX and zeolite L i X , it is desirable to compare these isotherms to the reported literature values. However, since N 2 adsorption isotherms on NaX and L i X reported in the literature were obtained at 25 \u00C2\u00B0C, the experimental N 2 adsorption isotherms on these adsorbents were extrapolated to give the isotherms at the same temperature. The extrapolation to determine the Henry's constant for the N 2 adsorption isotherm on zeolite NaX was done by plotting the ln K vs. 1000/T using the experimental data and extrapolating this plot to 25 \u00C2\u00B0C using the slope and the intercept as shown in Figure 4.11. The extrapolation for the Langmuir constant, b of N 2 adsorption isotherm on zeolite L i X was done using the plot of In b vs. 1000/T as shown in Figure 4.12 while the Langmuir constant, a was calculated by determining the amount adsorbed at saturation, q s at the temperatures listed in Table 4.4. Since q s is independent of temperature, it should remain constant for all temperatures, however, q s value for N 2 isotherm on zeolite L i X at 80 \u00C2\u00B0C was approximately 3 times larger than at other temperatures. This is due to the large error associated with the Langmuir constant, b at this temperature. Since the 95% confidence interval of the Langmuir constant is higher than the Langmuir constant, b at 80 \u00C2\u00B0C, this data point was discarded. As a result, q s was determined to be the average q s of the N 2 isotherm data at 30 \u00C2\u00B0C, 40 \u00C2\u00B0C, 50 \u00C2\u00B0C, and 60 \u00C2\u00B0C. After having determined b and q s, the Langmuir constant, a can easily be determined since a = qs*b. N 2 adsorption isotherms on zeolite NaX and zeolite L i X at 25 \u00C2\u00B0C were then compared with the literature values in Figure 4.13 and 4.14. As can be seen in Figure 4.13, the experimental and literature adsorption isotherms (both obtained from N 2 on zeolite NaX in powder form (binderless)) agree within 12 percent. Again, an F test was performed at 95 percent confidence interval for these two sets of data. The F factor was determined to be 0.78, which is less than the F-critical value of 2.18. Hence, it can be concluded that there is no statistically significant difference between the two data sets. Figure 4.14 compares the experimental results with two literature values for N 2 adsorption isotherms on L i X . N 2 adsorption isotherm on L i X reported by Rege and Yang (1997) is comparable with the experimental results of the present study. The F factor and F-critical value were determined to be 1.10 and 2.18, respectively, indicating that these two sets of isotherms are not significantly different. However, Yang et al. (1996) reported a much lower N 2 adsorption capacity than that of Rege and Yang (1997) and the experimental results. This is due to the L i content present in zeolite X . Zeolilte L i X used in both Rege and Yang (1997) and this study contained 100 percent L i on zeolite X whereas Zeolilte L i X used in Yang et al. (1996) had L i content of 85 percent. Gaffney (1996) reported that N 2 capacity on L i X increased sharply as L i content was increased from 85 to 100 percent. Kimer (1993) reported N 2 capacity on L i X with 85 percent L i content as 0.85 mmol/g, which was slightly higher than 0.73 mmol/g of Yang et al. (1996). By comparing experimental results with the literature values, N 2 adsorption capacity increases with increasing L i content when L i content is 85% or higher. -5.4 i 1 1 1 1 1 \u00E2\u0080\u0094 i 3.1 3.1 3.2 3.2 3.3 3.3 3.4 10007T(K\"1) Figure 4.11 ln K vs. 1/T for the extrapolation of Henry's constant of N 2 isotherm on zeolite NaX. Figure 4.12 ln b vs. 1/T for the extrapolation of Langmuir constant, b of N 2 isotherm on zeolite L i X . 0.55 0 20 40 60 Pressure (kPa) 80 100 (Yang et al., 1996) \u00E2\u0080\u0094 Experimental results Figure 4.13 N 2 adsorption isotherm on NaX at 25 \u00C2\u00B0C. 0 20 40 60 80 100 Pressure (kPa) Figure 4.14 N 2 adsorption isotherm on L i X at 25 \u00C2\u00B0C. Having generated adsorption isotherms at low pressure and determined the Langmuir adsorption constants from these data, adsorption capacities at higher pressure were calculated using the Langmuir constants. However, in order to confirm that these extrapolated Langmuir adsorption capacities were valid, adsorption isotherms up to 300 kPa were measured using the gravimetric method in the high pressure gravimetric analyzer. Low pressure adsorption isotherms (0-101 kPa) measured using the volumetric method for QuestAir proprietary adsorbent (QP) were provided by Questair Technologies Inc. The extrapolation from low pressure data are compared with low pressure and high pressure data in Figure 4.15 for N 2 on QP. Table 4.5 summarizes the Langmuir constants for QP. Table 4.5 Langmuir constants for high and low pressure data for N 2 on QP Temperature C O Langmuir Constant, a (mmol g\"1 kPa') Langmuir Constant, b (kPa 1) Low pressure 60 0.0144\u00C2\u00B1 0.0001 0.0079\u00C2\u00B1 0.0001 80 0.0086+0.0001 0.0046\u00C2\u00B1 0.0002 100 0.0056\u00C2\u00B1 0.0001 0.0033\u00C2\u00B1 0.0002 High pressure 60 0.0127\u00C2\u00B1 0.0025 0.0063\u00C2\u00B1 0.0011 80 0.0080\u00C2\u00B1 0.0029 0.0039\u00C2\u00B1 0.0015 100 0.0056\u00C2\u00B1 0.0011 0.0031\u00C2\u00B1 0.0015 0.0 - F 1 1 1 , 1 , 1 0 50 100 150 200 250 300 350 Pressure (kPa) \u00E2\u0080\u00A2 Questairat60 C s Questairat80 C A Questairat 100 C H 60 C x 80 C \u00C2\u00A9 100 C Extrap 60 C Extrap 80 C Extrap 100 C Figure 4.15 Comparison of extrapoled high pressure isotherm data with measured high pressure data for N 2 on QP. Figure 4.15 shows that the Langmuir adsorption uptakes, calculated from low pressure adsorption isotherms can be extrapolated to higher pressure without significant errors. F tests similar to those described earlier were also performed on the data of Figure 4.15. The F factors, which are summarized in Table 4.6, were all less than the F-critical, and hence, there was no significant difference between fitted and measured data at low and high pressure. Table 4.6 F-test comparison for significant difference between low and high pressure N 2 adsorption isotherms on QP vs. both sets of data. Gas Temperature (\u00C2\u00B0C) F1/F3 F 2 /F 3 Fcritical.a =0.05 For M , / M 3 Fcritical.a =0.05 For M 2 / M 3 N 2 60 1.05 1.00 1.95 2.36 80 0.93 1.41 1.95 2.36 100 0.84 1.68 1.95 2.36 Fi = F factor for adsorption isotherm obtained from low pressure measurement F 2 = F factor for adsorption isotherm obtained from high pressure measurement F3 = F factor for adsorption isotherm obtained from both the low and high pressure measurement M i = Data obtained from low pressure method M 2 = Data obtained from high pressure method M 3 = Data obtained from both the low and high pressure method The results suggest that the CO and C 0 2 adsorption on zeolite NaX, N 2 adsorption on zeolite L i X and QP follow a simple Langmuir adsorption model while the N 2 adsorption on zeolite NaX follows Henry's law. Furthermore, the adsorption isotherm seems to fall into type I isotherm according to the Brunauer classification, indicating that the adsorption process follows a chemical adsorption on microporous adsorbent where the saturation point is limited by the monolayer coverage of adsorbed gas on the adsorbent surface. 4.4 Heats of Adsorption. Heats of adsorption were also calculated from the measured adsorption data for N 2 , CO, and C 0 2 on zeolite NaX; and for N 2 on zeolite L i X . The slope of the plot ln (K) vs. 1000/T where K is the Langmuir constant b for the Langmuir model and K is Henry's constant for Henry's law, was used to calculate the apparent heat of adsorption according to equation [2.07] and are shown in Appendix 9. The heats of adsorption for N 2 on zeolite NaX adsorbent determined using gravimetric and volumetric methods are 19.2\u00C2\u00B10.6 kJ/mol and 21.6\u00C2\u00B10.8 kJ/mol, respectively, which show consistency between volumetric and gravimetric values. There is only 11.5 percent error between the two values. According to Ruthven (1984) the heat of adsorption for N 2 on zeolite NaX is approximately 5 kcal/mol or 20.9 kJ/mol, which is in very good agreement with the heat of adsorption obtained from the present study. For CO and C 0 2 on zeolite NaX, the heat of adsorption was obtained using the volumetric data since these sets of data have more data points. The heats of adsorption for CO and C 0 2 on zeolite NaX measured volumetrically are 12.0\u00C2\u00B15.2 kJ/mol and 22.2\u00C2\u00B123.3 kJ/mol, respectively. However, when compared to the literature value, the heat of adsorption for C 0 2 obtained from the volumetric method (22.2 kJ/mol) is much lower than the literature value (10 kcal/mol or 41.9 kJ/mol) (Ruthven, 1984). The difference is due to the errors in the Langmuir parameter b even though it was shown previously that data obtained from both the volumetric and gravimetric method were in good agreement. A slight change in the value of the initial slope in the linear region of the CO and C 0 2 adsorption isotherm will not change the overall trend of the isotherm by much, but, this slight change in the initial slope or the Langmuir constant, b could affect the heats of adsorption's calculations considering that only two temperatures were used in these calculations. When considering the large error associated with the heats of adsorption for C 0 2 on zeolite NaX adsorbent, the heats of adsorption obtained is not accurate. When comparing the heat of adsorption of N 2 on zeolite NaX and zeolite L i X , the heat of adsorption for zeolite L i X (41.4 \u00C2\u00B1 24.8 kJ/mol) is higher than that of zeolite NaX (19.2 kJ/mol determined by the gravimetric method and 21.6 kJ/mol by the volumetric method). The higher heat of adsorption of N 2 on zeolite L i X is due to a stronger adsorption between the adsorbate and adsorbent surface. The heat of adsorption for N 2 on zeolite L i X of (41.4 \u00C2\u00B1 24.8 kJ/mol) obtained in the study is comparable to the value of 23.5 kJ/mol reported by Rege and Yang (1997) when considering its 95% confidence interval. Figure 4.16 to Figure 4.18 show ln k vs. 1000/T plots used to determine the heat of adsorption. Q -i 1 1 1 1 , . _ 7 J _ _ _ 1 3.05 3.1 3.15 3.2 3.25 3.3 3.35 1000/T (K\"1) Figure 4.16 In K vs. 1000/T used to determined heat of adsorption of N 2 , CO, and C 0 2 on zeolite NaX adsorbent from the data measured volumetrically. Figure 4.17 ln K vs. 1000/T used to determined heat of adsorption of N 2 on zeolite NaX adsorbent from the data measured gravimetrically. Figure 4.18 ln b vs. 1000/T used to determined heat of adsorption of N 2 on zeolite L i X adsorbent using Langmuir parameter, b. Chapter 5: Dispersion and Mass Transfer in Structured Adsorbent Bed 5.1 Introduction The dynamic response of an adsorbent structure is determined by such parameters as the gas dispersion and mass transfer resistances within the adsorbent structure. The value of these parameters can be estimated by measuring the dynamic response to a step change in inlet adsorbate concentration as a function of the particle size (particle diameter), the interstitial gas velocity, and by replacing the adsorbent of interest with inert particles. For a given adsorbent structure, two parameters can be determined: the axial dispersion coefficient and the lumped mass transfer coefficient. Sometimes, the dispersion can mask the significance of mass transfer resistances. In order to separate the two effects, experiments must be done using two identical adsorbent structures, except that one structure is filled with non-adsorbing particles while the other is filled with the adsorbent of interest. The dynamic response to the non-adsorbing particles will directly give the dispersion since there is no micropore or macropore mass transfer resistance in this case. In addition, the magnitude of the dispersion coefficient of a non-adsorbing structure and other adsorbent structure can be compared to confirm if the values determined are correct. Furthermore, the external fluid film coefficient, which contributes to the lumped mass transfer coefficient, can also be estimated from the non-adsorbing structure dynamic response data. The contributions to the lumped mass transfer coefficient can be accounted for from three individual mass transfer coefficients: external fluid film resistance, macropore mass transfer resistance, and micropore mass transfer resistance. In order to determine these individual mass transfer coefficients, particle size and interstitial velocities were varied. If \u00E2\u0080\u0094!\u00E2\u0080\u0094 for two or more kK different particle sizes are known, then the plot of \u00E2\u0080\u0094 vs. R p 2 can be used to determine the kK individual mass transfer coefficients (Equation [2.40]). In order to determine the dispersion coefficient and the individual mass transfer coefficient, several adsorbent structures were studied. Table 5.1 lists the dimensions of the structures and the characteristics of these adsorbent structures were as follows: 1. High X-sectional area structure contained zeolite L i X adsorbent dispersed on a substrate with cross sectional area of 12.41 cm 2. 2. Mid X-sectional area structure contained zeolite L i X adsorbent dispersed on a substrate with cross sectional area of 6.29 cm 2. The cross sectional area of the mid X-sectional area structure is approximately half that of the high X-sectional area structure. 3. Low X-sectional area structure contained zeolite L i X adsorbent dispersed on a substrate with cross sectional area of 3.70 cm 2. The cross sectional area of the low X-se\u00C3\u00A7tional area structure was approximately one quarter of the high X-sectional area structure. 4. Non-adsorbing structure contained non-adsorbing solid dispersed on a substrate with cross sectional area of 6.14 cm 2. 5. High Voidage adsorbent structure contained zeolite L i X adsorbent dispersed on a substrate with cross sectional area of 6.22 cm . The high voidage adsorbent structure had similar cross-sectional area as the mid X-sectional area structure. However, the spacing between each adsorbent sheets, i.e. the spacer height used in this pack was approximately 40 percent less than that of the mid X-sectional area structure. 6. Thick adsorbent sheets structure contained zeolite L i X adsorbent dispersed on a substrate with cross sectional area of 6.22 cm 2. The thick adsorbent sheets structure had similar cross sectional area as the mid X-sectional area structure. However, the adsorbent sheets thickness of this pack was twice that of the mid X-sectional area structure. Note: X-sectional area refers to cross sectional area Table 5.1 Summary of Adsorption structure dimensions. Structure 1 2 3 4 5 6 Width (cm) 6.25 3.18 1.87 3.10 3.10 3.10 Height (cm) 1.99 1.98 1.98 1.98 2.01 2.01 Length (cm) 20.32 20.32 20.32 20.32 20.32 20.32 Spacer Tortuosity High X Low X X X X X Voidage Ratio High X Low X X X X X Cross Sectional High X Area Mid Low X X X X X Absorbent Sheet Thick X Thin X X X X X N 2 Adsorbing Yes No X X X X X X 5.2 Henry's Constant Estimates In order to determine the dispersion and mass transfer resistances of an adsorbent structure, the gas adsorption constant or Henry's constant must first be determined since the model equations used to extract dispersion and mass transfer resistances are dependent on the amount of gas adsorbed or the Henry's constant, K. The Henry's constants and their 95 percent confidence intervals were obtained from the slope of the plot u. vs. 1/F using a curve fitting algorithm, and the values are summarized in Table 5.2. Figure 5.1 to Figure 5.5 shows the JLI vs. 1/F plots used to obtain the Henry's constant reported in Table 5.2; in all cases two sets of data were obtained. 1800 1600 1400 1200 1000 * 800 600 400 200 0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 1/F (s/cm3) Figure 5.1 p vs. 1/F for high X-sectional area structure for N 2 at 24 \u00C2\u00B0C and 101 kPa. 1400 0.00 0.20 0.40 0.60 1/F (s/cm3) 0.80 1.00 1.20 Figure 5.2 p vs. 1/F for mid X-sectional area structure for N 2 at 24 \u00C2\u00B0C and 101 kPa. il) 800 700 600 500 400 300 200 100 0 0.00 0.20 0.40 0.60 1/F (s/cm3) 0.80 1.00 1.20 Figure 5.3 u. vs. 1/F for low X-sectional area structure for N 2 at 24 \u00C2\u00B0C and 101 kPa. 1800 600 400 0.00 0.20 0.40 0.60 1/F (s/cm3) 0.80 1.00 1.20 Figure 5.4 LI vs. 1/F for high voidage structure for N 2 at 24 \u00C2\u00B0C and 101 kPa. 0.00 0.20 0.40 0.60 1/F (s/cm3) 0.80 1.00 1.20 Figure 5.5 a. vs. 1/F for thick adsorbent sheets structure for N 2 at 24 \u00C2\u00B0C and 101 kPa. Table 5.2 Henry constants and their 95% confidence intervais. Pack High X - Mid X - Low X - High Thick sectional sectional sectional Voidage Adsorbent Area Area Area Sheets Henry's constant 17.81\u00C2\u00B10.30 14.81\u00C2\u00B10.25 13.83\u00C2\u00B10.42 17.48\u00C2\u00B10.28 15.88+0.25 Henry's constants were calculated based on a volume per volume basis (volume adsorbed per volume of adsorbent). Henry's constants expressed in terms of volume, cannot be directly compared with other literature values or experimental values, since the amount of gas adsorbed is most often expressed in mmol/g. Hence, the amount of gas adsorbed at 101 kPa was calculated using Henry's law and the results are listed in mmol/g in Table 5.3. Table 5.3 below compares the amount of gas adsorbed from the gravimetric method (Chapter 4) to the values calculated from the Henry constants determined from the dynamic response measurement. Table 5.3 Comparison of gas adsorbed at 101 kPa and 24 \u00C2\u00B0C between gravimetric and chromatographic method N 2 Adsorbed at 101 kPa and 24 \u00C2\u00B0C (mmol/g) Gravimetric Method (extrapolated to 24 \u00C2\u00B0C from experimental data) 1.856 High X-sectional Area 1.834+0.031 Mid X-sectional Area 1.212\u00C2\u00B10.020 Low X-sectional Area 1.134+0.034 High Voidage 1.188+0.019 Thick Adsorbent sheets 1.615+0.025 From Table 5.3 the adsorbent uptake estimated from the chromatographic and gravimetric methods are comparable for the high X-sectional area structure. The thick adsorbent sheets structure had a 15% lower value than the gravimetric value. The amount of gas adsorbed for other adsorbent structures is significantly lower than that determined from the gravimetric method. The most likely explanation for this difference is that errors exist in the calculation of the adsorbent sheet thickness as well as the quantity of adsorbent contained within these prototype adsorbent structures. Furthermore, it might be possible that moisture exists within some of the adsorbent structures prior to the experiment because the adsorbent structures did not undergo thermal desorption treatment prior to each experiment. As a result, some of the adsorption sites might have been occupied by water molecules which could have led to lower adsorption data seen in some of the adsorbent structures. 5.3 Dispersion and Mass Transfer Estimates Having estimated the Henry's constants, the 1st and 2nd moments were determined and used to calculate the dispersion and lumped mass transfer resistances from the plot HETP/2u or 2 2 2 (a l\i )L/2u vs. 1/u (as per Equation [2.40]). The dispersions and their 95 % confidence intervals are summarized in Table 5.4. Figure 5.6 to Figure 5.11 show the HETP/2u or (a2/u.2)L/2u vs. 1/u2 plot (using two sets of data) used to calculate the dispersion and lumped mass transfer coefficients. 7.00 -i 6.00 -5.00 -> 4.00 -ro a. 3.00 -2.00 -1.00 -0.00 -0.0 2.0 4.0 6.0 l / v ^ / c m 2 ) 8.0 10.0 Figure 5.6 HETP/2u vs. 1/u for high X-section area structure for N 2 at 24 \u00C2\u00B0C and 101 kPa. 0.00 0.50 1.00 1.50 (s2/cm2) 2.00 2.50 Figure 5.7 HETP/2u vs. 1/u for mid X-sectional area structure for N 2 at 24 \u00C2\u00B0C and 101 kPa. 2.50 -t 2.00 -> 1.50 -0.50 0.00 0.00 0.50 1.00 1.50 2.00 2.50 1/v2 (s2/cm2) Figure 5.8 HETP/2u vs. 1/u2 for low X-sectional area structure for N 2 at 24 \u00C2\u00B0C and 101 kPa. 6.00 5.00 4.oo > CNJ 3.00 ^ 2.00 1.00 0.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 l / v ^ / c m 2 ) Figure 5.9 HETP/2u vs. I/o 2 for non adsorbing structure for N 2 at 24 \u00C2\u00B0C and 101 kPa. Figure 5.10 HETP/2o vs. I/o 2 for high voidage adsorbent structure for N 2 at 24 \u00C2\u00B0C and 101 kPa. Table 5.4 Dispersion coefficients estimated for structured adsorbent beds. Pack Dispersion Coefficient (cm2/s) High X-sectional Area 0.635 \u00C2\u00B1 0.034 Mid X-sectional Area 0.894 \u00C2\u00B1 0.074 Low X-sectional Area 0.897 \u00C2\u00B1 0.037 Non-adsorbing 0.844 \u00C2\u00B1 0.133 High Voidage 0.896 \u00C2\u00B1 0.137 Thick Adsorbent Sheets 0.970 \u00C2\u00B1 0.295 The dispersion coefficients obtained from the mid X-sectional area, low X-sectional area, non adsorbing, and high voidage adsorbent structure show very good agreement. They are within 6 percent of each other. The thickness of adsorbent sheets and cross-sectional area are approximately equal for these four adsorbent structures (mid X-sectional area, non adsorbing, and high voidage adsorbent structur) except for the low X-sectional area structure where the cross-sectional area is half of the other three packs. The dispersion coefficient for the thick adsorbent sheets structure is slightly higher than the other adsorbent structures, but is still within the same range when considering the 95 % confidence interval of the estimated dispersion coefficient of these adsorbent structures. For the high X-sectional area structure, the dispersion 2 2 coefficient was significantly lower at 0.635 cm /sec compared to about 0.90 cm /sec for the other packs. One possible explanation for the difference in dispersion coefficient is that the substrate of the high X-sectional Area structure was made up of different materials from other adsorbent structures. The difference in the substrates may contribute to the higher dispersion observed in the mid X-sectional Area, low X-sectional Area, non-adsorbing, high voidage, and thick adsorbent sheets structure compared to the high X-sectional area structure. The different in the substrates could contribute to more mixing between channels which should be reflected in a higher dispersion coefficient. The dispersion coefficients obtained were also compared with literature values by estimating the molecular dispersion, D M from the dispersion coefficient. According to Kovacevic (2000), for N 2 /He, the molecular dispersion was estimated as 0.86 cm2/sec at 35 \u00C2\u00B0C from dispersion coefficients obtained from a 13 X packed bed. This value is of the same magnitude as the D M = 0.91 cm /sec estimated from the high X-sectional area structure dispersion of the present study, calculated from the equation D L = 0.7D M. Also, Satterfield (1970) reported the molecular dispersion of N 2 in He to be 0.69 cm2/sec. The molecular dispersions estimated in the present study are within 25% of literature values. The mass transfer resistances were also determined from the plot of HETP/2o vs. I/o 2 at low flow rates (o < 1.7 cm/s), and the values are summarized in Table 5.5. Table 5.5 Lumped mass transfer resistances estimated using HETP/2o vs. I/o 2 at low flow rate. Pack High X - Mid X - Low X - Non- High Thick sectional sectional sectional adsorbing Voidage Adsorbent Area Area Area Sheets 1/kK (sec) 0.411 + 0.282\u00C2\u00B1 0.268\u00C2\u00B1 0.292+ 0.842\u00C2\u00B1 0.538\u00C2\u00B1 0.268 0.160 0.081 2.000 0.243 1.307 k(sec') 0.137 0.239 0.270 N / A 0.068 0.117 Alternatively, chromatographic plate theory can be used to determine the lumped mass transfer rates at high velocities, o > 7 cm/s where mass transfer resistances dominate over the dispersion. According to Equation [2.48], the slope of the van Deemter plot equals A 3 \u00C2\u00AB 2[e/(l-s)]/kK, from which the lump mass transfer resistance can be calculated knowing s. The mass transfer rates for high X-sectional area, high voidage, and thick adsorbent sheets structures were determined from the slope of Figure 5.12 and are summarized in Table 5.6. The lumped mass transfer resistance (1/kK) of the adsorbent structure ranges from 0.28 to 0.84 sec suggesting that short cycle PSA with cycle times 0.6 to 3 seconds is possible. The mass transfer resistance can be further reduced by reducing the size of the adsorbent structure, as seen from the values of 1/kK for the mid X-sectional area structure, to further decrease the cycle time needed for the short cycle PSA. Although the cycle time can be decreased by reducing the adsorbent structure size, N 2 adsorption capacity is reduced since less adsorbent is available for adsorption. A reduction in the adsorbent sheets thickness can also reduce 1/kK as shown in Table 5.5. However, by reducing the adsorbent sheets thickness, there will be less adsorbent present, i.e., less N 2 adsorption capacity as shown in the data of Table 5.3. The amount of gas adsorbed at 101 kPa and 24 \u00C2\u00B0C for the thick adsorbent sheets structure and the mid X-sectional area structure were determined to be 1.615 \u00C2\u00B1 0.025 mmol/g and 1.212 \u00C2\u00B1 0.020 mmol/g, respectively. 1/kK values cannot be compared directly to reported values since the lumped mass transfer resistances on L i X adsorbent are not available. However, 1/kK can be compared with reported values for N 2 on other zeolite X such as 13X. Kovacevic (2000) reported 1/kK for N 2 on 13X 8/12 mesh and 16/40 mesh for the interstitial velocity of 0.8 to 3.5 cm/sec as 0.09 and 0.02 second, respectively. 1/kK reported by Kavocevic (2000) was obtained from similar experimental conditions as those used in the present study except that the adsorbent structures used by Kavocevic (2000) was a packed bed of adsorbent beads. 1/kK values obtained in this study are 2 to 8 times higher than those reported by Kovacevic (2000), suggesting that the structured adsorbent bed configuration does not reduce the mass transfer resistance. However, the dispersion coefficient in the structured adsorbent bed is usually higher than in the packed bed, which can mask the mass transfer resistance, i.e., resulting in higher mass transfer resistance. Furthermore, since the adsorbents used in the present study and literature are not the same, the comparison should only be considered qualitatively. 3.00 0.00 5.00 10.00 15.00 Interstitial Velocity (cm/s) 20.00 25.00 \u00E2\u0080\u00A2 Mid X-sectional area \u00E2\u0080\u00A2 High voidage A Thick adsorbent sheets Figure 5.12 HETP vs. interstitial velocity plot used to determine the lumped mass transfer coefficient for v > 7 cm/s. Table 5.6 Lumped mass transfer rates estimated using Plate theory at high flow rate and their 95% confidence intervals. Pack Mid X-Sectional Area High Voidage Thick Adsorbent Sheet k (sec1) 0.402 \u00C2\u00B10.174 0.328 \u00C2\u00B10.176 0.422\u00C2\u00B10.105 The lumped mass transfer rates obtained from both methods, as summarized in Table 5.5 and 5.6 show similar magnitude. The discrepancies between the two methods are most likely a result of both the scatter in data at high flow rates. At high flow rates, it becomes increasingly more difficult to correct for the mean and the variance of the dead volume in the system, the errors in the dead volume mean and variance ranges from 30-50% of the measured mean and variance. If comparison between the k values of the Mid X-sectional area at low and high velocity (Table 5.5 and 5.6) is made, the difference is approximately 68%. Since the errors associated with the measurement itself and the dead volume in the system can be up to 50%, there is no significant difference between the k values at low and high velocity given the large errors in the estimate of k at high velocity. The measurement is limited when the mean and variance of the dead volume approaches that of the measured mean and variance. Furthermore, at high velocity, the film layer thickness will decrease, which in turn increases film mass transfer rate. This may also contribute to high values of k. 5.4 Macropore and Micropore Mass Transfer The mass transfer resistances listed in Table 5.5 are the lumped mass transfer resistances in the system, which consist of external fluid film mass transfer resistance, macropore mass transfer resistance, and micropore mass transfer resistance. From the slope and intercept of the plot of 1 2 1 \u00E2\u0080\u0094 vs. R p , these individual mass transfer resistances can be separated when \u00E2\u0080\u0094 are known for kK kK two or more particle sizes, according to Equation [2.40]. Figure 5.13 shows the plot of \u00E2\u0080\u0094^\u00E2\u0080\u0094 vs. kK (aR p) where a is an arbitrary constant used to conceal the actual particle size due to non-disclosure agreement. The intercept gives the micropore mass transfer coefficient and the slope gives a combination of external fluid film and macropore mass transfer coefficients. Calculation of the molecular diffusivity from any standard gas diffusion equation such as Equation [5.1] can _ 0.001858r 3 / 2[(M, + M 2 ) / M , M 2 ] 1 / 2 determine the external fluid film. D, PcTz2nD Equation [5.1] Where T = temperature in K, M i , M 2 are the molecular weight of the two species, P is the total pressure (atm), Qp is the \"collision integral,\" a function of kT/si 2 , e,a are the force constants in the Lennard-Jones potential function, and k is the Boltzmann constant. 0.60 0.50 0.40 * 0.30 0.20 0.10 0.00 0 1/kKvs . ( a rV y=0.1931x+0.193 R 2=1 0.5 (aRp)2(cm2) 1.5 1 2 Figure 5.13 \u00E2\u0080\u0094 vs. (aR p) used to determine macropore and micropore mass transfer kK coefficients. Macropore and micropore diffusivities obtained from Figure 5.13 are summarized in Table 5.7. Karger et al. (1997) reported micropore diffusivity of N 2 in zeolites NaX as 3 X 10\"5 cm2/sec (using the pulsed field gradient n.m.r. method), which is 4 orders of magnitude different from the diffusivity found in this study. The difference could be due to the different methodology used and the difference in adsorbent (LiX in this study vs. NaX reported). However, micropore diffusivity of N 2 in zeolite L i X was determined from the intercept of Figure 5.13. The intercept is very sensitive to the error in \u00E2\u0080\u00945\u00E2\u0080\u0094. Suppose, if the \u00E2\u0080\u0094 v a l u e for the kK kK smaller particle size adsorbent structure were to be decreased by 33 percent and \u00E2\u0080\u0094^\u00E2\u0080\u0094 value for kK the larger particle size adsorbent structure were to be increased by 36 percent. The intercept will change dramatically as shown in Figure 5.14, resulting in the micropore diffusivity of 2.5 X 10\"5 cm2/sec, which is almost the same as the micropore diffusivity obtained by Karger et al (1997). The error associated with the micropore diffusivity measurement is most likely due to the variability in the adsorbent sheet thickness or the particle size within the adsorbent structure. If three or more particle sizes were used instead of two, a more accurate micropore diffusivity could be determined. Only two adsorbent sheets thickness (particle sizes) were used because manufacturing adsorbent structures at different adsorbent sheets thickness were difficult and not feasible at the time of the present study. I l l Table 5.7 Individual mass transfer coefficients. _ Macropore Diffusivity, D p (cm /sec) 1.93 X 10\"4 Micropore Diffusivity, D c (cm2/sec) 5.25 X 10\"1U To determine the external fluid film mass transfer coefficient, the Sh s 2kfR p/Dm \u00C2\u00AB 2 approximation at low Reynolds is used. Hence, kf = D m / R p where D m can taken as 0.7DL at these low flow rates and D L was listed in Table 5.4. As a result k f values are specific for each adsorbent structure and are listed in Table 5.8. Table 5.8 Fluid film mass transfer coefficient. Pack High X -sectional Area Mid X -sectional Area Low X -sectional Area Non-adsorbing High Voidage Thick Adsorbent Sheet Fluid Film Mass Transfer coefficient (cm/sec) 84.1 125.8 126.1 128.1 138.3 69.5 The k f values in Table 5.8 were then compared with k f values calculated from the correlations listed in section 2.3.2. Table 5.9 lists the k f obtained from various correlations and the percent difference between the experimental values and the values obtained from these correlations. As can be seen from Table 5.9, among all the correlations used, the fluid film mass transfer coefficient calculated from Ranz and Marshall (1952) seems to give the best agreement with the results of the present study. The difference between k f obtained from Ranz and Marshall (1952) and the experimental values are within 10%. Furthermore, in order to calculate k f , the Sherwood number must first be calculated. From Equation [2.27] to Equation [2.29], at low Reynolds number, the Sherwood number, Sh approaches the limiting value of 2.98, 2.69, and 3.53, respectively. These limiting values all correspond to the square monolith. However, the adsorbent structure used in this study contains plane monolith, i.e., each adsorbent sheet is separated by an empty space and there is no adsorbent material on the side wall of the adsorbent structure. As a result, the limiting values in Equation [2.27] to Equation [2.29] should be closer to 2.0 as in Ranz and Marshall (1952) correlation for the monolith geometry used in this study. Table 5.9 Fluid film mass transfer coefficient compared with literature value. Correlation High X -sectional Area High X -sectional Area High X -sectional Area Non-adsorbing High Voidage Thick Adsorbent Sheet kf kf kf kf kf kf (cm/s) (cm/s) (cm/s) (cm/s) (cm/s) (cm/s) Ranz and Marshall (1952) 91 136 138 139 149 76 Percent difference (%) 8 \u00E2\u0080\u00A2 8 10 .8 7 9 Hawthorn (1974) 125 187 188 191 206 104 Percent difference (%) 49 49 \"49 49 49 49 Uberoi and Pereira (1996) 113 169 170 173 186 94 Percent difference (%) 35 35 35 35 35 35 Holmgren and Andersson (1998) 148 222 223 226 244 123 Percent difference (%) 76 76 77 77 76 76 Experimental 84 126 126 128 138 70 After having estimated the dynamics of the system: the dispersion and individual mass transfer coefficients, the relative magnitude of these resistances at different flow rates can be ^2 determined. From Equation [2.36], mass transfer will dominate when \u00C2\u00BB 1 because as the kKDL interstitial velocity increases, D L /u will decrease. This occurs at u \u00C2\u00BB 1.7 cm/sec. At lower interstitial velocities, axial dispersion dominates. Moreover, as velocity increases, the relative magnitude of the various dynamic parameters shows that the macropore and micropore mass transfer resistances will dominate. Physically, at high gas velocity, the adsorption process may be limited due to the diffusion rate within the marcropores and micropores since the gas retention time will significantly be decreased. As a result, some of the gas will not have sufficient time for adsorption since the gas have to diffuse through the macropores and micropores prior to adsorption. The calculations are shown in Appendix 4. Furthermore, with the dispersion and the individual mass transfer coefficients identified, a simple linear rate model can be used to predict the breakthrough curves, according to Equation [2.51] with the effective rate coefficient being Equation [2.49]. Figure 5.15 to Figure 5.20 compares the predicted breakthrough curves with measured data at 100 S C C M for all adsorbent structures with the kf value from Table 5.4, D L value from Table 5.7, Dp=0.000193 cm2/s, Dc=5.25 X 10\"10 cm2/s, and rc=1.50 X 10\"4 cm. 0.8 0.6 o O O 0.4 0.2 M e a s u r e d \ / P r e d i c t e d I I I 10 15 2 0 D i m e n s i o n l e s s T i m e , T a u 2 5 3 0 Figure 5.15 Predicted breakthrough curve and raw data for high X-sectiona area structure with flow = 100 S C C M . Figure 5.16 Predicted breakthrough curve and raw data for mid X-sectional area structure with flow = 100 S C C M . 0.8 0.6 o O \u00C3\u00B4 0.4 0.2 0 Predicted 0 JJ W U Measured 10 20 30 40 Dimensionless Time, Tau 50 ?ure 5.17 Predicted breakthrough curve and raw data for non-adsorbing structure with flow 100 S C C M . 0.8 0.6 0.4 0.2 Measured c^Cfl ' V I M Y A / Predicted , m ni 0 10 20 30 40 50 60 70 Dimensionless Time, Tau Figure 5.18 Predicted breakthrough curve and raw data for low X-sectional area structure with flow = 100 S C C M . Figure 5.19 Predicted breakthrough curve and raw data for high voidage structure with flow 100 S C C M . 0 10 20 30 40 50 60 Dimensionless Time, Tau Figure 5.20 Predicted breakthrough curve and raw data for thick adsorbent sheets structure with flow= 100 S C C M . Figures 5.15 to Figure 5.20 show that the first-order adsorption rate model can adequately described the measured breakthrough data for all adsorbent structures in this study. The sum of squares of errors (SSE) between the predicted data and measured data were calculated for Figure 5.15 to 5.20 and the values are summarized in Table 5.10. F-tests were also performed on these sets of data and are listed in Table 5.10. Small values of SSE and the F s tats less than that of the F-critical values in Table 5.10 from 280 data points for non-adsorbing structure to 2500 data points for high X-sectional area structure suggest that the first-order adsorption rate model can describe the measured breakthrough data in this study. Table 5.10 SSE and F s t a t s from the F-test for predicted data from Matlab\u00E2\u0084\u00A2 program and measured data Pack SSE Fstats F-critical, a =0.05 High X-sectional Area 2.425 0.913 1.062 Mid X-sectional Area 0.536 0.952 1.084 Low X-sectional Area 0.605 0.966 1.086 Non-adsorbing 0.596 0.972 1.183 High Voidage 0.827 0.909 1.084 Thick Adsorbent Sheets 0.583 0.947 1.084 5.6 Parametric Study A Matlab\u00E2\u0084\u00A2 program was developed to investigate the effects of increasing and decreasing mass transfer coefficients and dispersion to assess the sensitivity of the adsorbent structures to these parameters at a fixed flow rate of 4000 S C C M or 13 cm/s for the full-size pack. The effects of increasing and decreasing mass transfer coefficients and dispersion are shown in Figure 5.21 to 5.24 where standard conditions refer to the following values for mass transfer coefficients and dispersion: D L = 0.64 cm2/sec, kf = 84.7 cm/sec, Dp = 1.93 XlO\" 4 \u00E2\u0080\u00A2y 10 9 cm /sec, and Dc = 5.25 X 10\" cm /sec. \u00C2\u00A3, and Tau in Figure 5.21 to 5.24 refer to dimensionless bed length and dimensionless time, respectively (Equation [2.49]). Tau Figure 5.21 Predicted breakthrough curve for change in external fluid film coefficient, kf. Tau Figure 5.24 Predicted breakthrough curve for change in dispersion coefficient, D L -Figure 5.21 and 5.24 show that reducing the dispersion and fluid film mass transfer coefficient has little effect on the breakthrough since at the interstitial velocity used, the mass transfer dominates; moreover, the fluid film mass transfer coefficient does not contribute much to the overall mass transfer resistances as shown in Appendix 4. Significant increase in the magnitude of the dispersion will have a severe effect on the breakthrough. Figure 5.21 and 5.24 indicate that increasing the dispersion by two orders of magnitude or decreasing the fluid film mass transfer coefficient by several orders of magnitude will greatly shift the dimensionless time of the breakthrough curve, resulting in less adsorption. Figure 5.22 and 5.23 shows that increasing both D p and D c , the rates of macropore and micropore diffusion by an order of magnitude or two will largely shift the breakthrough curve to the right, hence, improving the breakthrough characteristics. Hence, in order to improve the performance of the packs used in the present study, an increase in D p and D c by orders of magnitude must be achieved. 0 4 Chapter 6: Conclusions and Recommendations for Future Work 6.1 Conclusions Accurate gas adsorption isotherms up to atmospheric pressure can be obtained gravimetrically or volumetrically. There was no significant difference between the measured data obtained using either method. However, gas adsorption isotherms generated using breakthrough analysis, which utilizes the desorption of gas in the non-linear region of the isotherm, appears to give much higher uptakes than those from either the gravimetric or volumetric method. Buoyancy effects limit the accuracy of gravimetric adsorption isotherm measurements whereas the measurement of free space or dead volume limits the accuracy of measurements by the volumetric method. Nitrogen adsorption capacity of L i X is far superior to that of NaX zeolite, the capacity of L i X being three times larger than that of NaX, is consistent with the literature reports. The chromatographic method can be used to obtain estimates of dispersion and mass transfer coefficients present in a structured adsorbent bed. At low interstitial velocities, o < 1.7 cm/sec, dispersion dominates while at high interstitial velocities, u \u00C2\u00BB 1.7 cm/sec, macropore and micropore mass transfer resistance dominates. Estimated values of the dispersion and external fluid film mass transfer resistance were consistent with literature values. However, the estimated micropore diffusivity was much lower than the literature value and this difference is most likely due to the inaccuracy of the results obtained in the present study that were based on only two particle sizes. Furthermore, from the mass transfer resistances obtained for PSA with short cycle time using structured adsorbent beds, fast PSA with cycle time of 0.6 to 3 seconds are possible. The simple linear rate model can be used to predict breakthrough curves at different flow rates. Dispersion and fluid film mass transfer coefficients do not affect breakthrough response at high flow rate used while increasing the macropore and micropore mass transfer coefficients by an order of magnitude will significantly improve the adsorption rate. 6.2 Recommendations for Future Work \u00E2\u0080\u00A2 Adsorption of gas mixtures on inert porous solids like zeolites provide the basis for a variety of gas separation processes including the separation of air into nitrogen and oxygen enriched streams at ambient temperature. Pure component isotherms were measured in the present study; however, gas separation applications almost always involve multicomponent mixtures. Even though there exist several models that can predict multicomponent adsorption isotherms, the accuracy of the prediction is often less than desirable. As a result, there is a need for direct measurement of multicomponent isotherms. There are accurate models that can predict multicomponent isotherms once the binary component data are available. Hence, one of the recommendations for future work is to obtain binary gas adsorption isotherms at high pressure using the gravimetric method. \u00E2\u0080\u00A2 The micropore and macropore mass transfer resistances measured in the present study had large errors associated with them since only two particle sizes (adsorbent sheets thickness) were used in the estimation of these values. Hence, it is recommended that further study should be done on measuring these mass transfer resistances using 3 or more particle sizes. If more accurate mass transfer resistances are obtained, they can be use to predict breakthrough curves and consequently optimize the PSA cycle. 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APPENDIX Appendix 1 :Isotherm Measurements Data Table A. 1.1 Nitrogen Isotherm data on NaX at 50 \u00C2\u00B0C Temperature Volumetric TGA Pressure Amount Pressure Amount (\u00C2\u00B0C) (kPa) (mmol adsorbed/g) (kPa) (mmol adsorbed/g) 50 0.7 0.002 3 0.013 1.4 0.004 10 0.037 2.1 0.007 31 0.090 4.2 0.012 51 0.149 6.9 0.020 77 0.220 13.8 0.039 103 0.302 20.4 0.057 27.1 0.074 33.8 0.092 40.4 0.110 47.1 0.127 53.8 0.145 60.4 0.162 67.1 0.178 73.8 0.195 80.4 0.211 87.1 0.228 93.8 0.244 100.4 0.260 107.1 0.276 113.8 0.291 Temperature Volumetric TGA Pressure Amount Pressure Amount (\u00C2\u00B0C) (kPa) (mmol adsorbed/g) (kPa) (mmol adsorbed/g) 30 0.6 0.003 3 0.022 1.4 0.007 10 0.055 2.1 0.011 30 0.146 4.1 0.021 51 0.229 6.9 0.034 77 0.327 13.7 0.066 103 0.429 20.3 0.098 27.0 0.129 33.7 0.159 40.4 0.189 47.0 0.219 53.7 0.248 60.4 0.276 67.0 0.305 73.7 0.333 80.4 0.361 t|J\u00C3\u00AFK|F\":-: li\u00C3\u00AF^ O\u00C3\u00AF ; \"111 87.1 0.388 93.7 0.415 100.4 0.442 107.1 0.469 113.7 0.494 Temperature Volumetric TGA Pressure Amount Pressure Amount (\u00C2\u00B0C) (kPa) (mmol adsorbed/g) (kPa) (mmol adsorbed/g) 50 0.7 0.010 3 0.043 1.3 0.018 10 0.100 2.0 0.027 30 0.277 4.0 0.049 50 0.433 6.8 0.064 76 0.625 12.7 0.169 101 0.817 19.8 0.243 26.5 0.313 33.2 0.376 39.9 0.437 46.6 0.497 53.3 0.553 60.0 0.606 66.7 0.656 73.4 0.704 80.1 0.752 86.7 0.801 93.4 0.846 100.1 0.891 106.8 0.931 113.5 0.972 Temperature Volumetric TGA Pressure Amount Pressure Amount (\u00C2\u00B0C) (kPa) (mmol adsorbed/g) (kPa) (mmol adsorbed/g) 30 0.7 0.014 3 0.055 1.3 0.025 10 0.184 2.0 0.039 31 0.482 4.1 0.079 51 0.714 6.4 0.120 76 0.965 13.7 0.240 102 1.179 19.4 0.327 27.1 0.436 32.9 0.511 39.5 0.592 46.2 0.669 52.9 0.741 59.6 0.810 66.3 0.874 73.0 0.936 79.8 0.994 86.5 1.049 93.2 1.101 99.9 1.151 106.5 1.200 113.2 1.247 Temperature Volumetric TGA Pressure Amount Pressure Amount CC) (kPa) (mmol adsorbed/g) (kPa) (mmol adsorbed/g) 50 0.6 1.148 3 1.880 1.3 1.552 10 2.940 1.9 1.826 30 4.029 3.8 2.344 51 4.523 6.5 2.779 76 4.953 13.0 3.437 103 5.252 20.0 3.869 26.7 4.153 32.8 4.357 39.6 4.540 46.5 4.692 53.5 4.821 60.4 4.932 66.2 5.008 72.8 5.091 79.5 5.167 86.3 5.235 93.1 5.296 99.8 5.354 106.5 5.406 113.2 5.455 ilIlil\u00C3\u00AFBl^B\u00C3\u00AE Temperature Volumetric TGA Pressure Amount Pressure Amount (\u00C2\u00B0C) (kPa) (mmol adsorbed/g) (kPa) (mmol adsorbed/g) 30 0.6 1.768 4 2.038 1.3 2.230 10 3.903 1.9 2.525 31 4.918 3.8 3.098 51 5.319 6.5 3.597 76 5.605 12.9 4.275 102 5.778 20.0 4.705 26.8 4.971 32.9 5.150 39.8 5.310 46.7 5.444 53.8 5.554 59.5 5.631 66.1 5.712 72.9 5.783 79.6 5.849 86.5 5.904 93.1 5.959 99.9 6.008 106.6 6.053 113.3 6.093 N2 Amount Temperature pressure adsorbed (\u00C2\u00B0C) (kPa) (mmol/g) 30 3.38 0.079 10.46 0.247 30.67 0.616 50.31 0.891 76.85 1.166 102.46 1.419 40 3.19 0.061 10.71 0.188 31.31 0.460 51.39 0.707 76.62 0.943 102.98 1.141 50 3.06 0.039 10.42 0.106 30.99 0.275 50.90 0.430 76.46 0.594 102.56 0.753 60 3.07 0.023 10.24 0.075 29.92 0.191 49.71 0.295 75.13 0.424 102.50 0.571 80 3.25 0.025 10.14 0.054 28.90 0.130 49.59 0.216 75.24 0.316 101.37 0.435 Low Pressure H igh Pressure Measured Measured Pressure Amount Pressure Amount (kPa) (mmol adsorbed/g) (kPa) (mmol adsorbed/g) 0.7 0.011 56 0.495 1.3 0.020 83 0.680 2.0 0.030 112 0.859 3.3 0.047 155 1.005 6.4 0.089 209 1.135 12.8 0.168 252 1.230 19.7 0.247 302 1.308 26.5 0.316 33.2 0.379 39.9 0.436 46.6 0.489 53.2 0.538 59.9 0.583 66.6 0.625 73.3 0.665 79.9 0.702 86.6 0.739 93.3 0.772 99.9 0.805 106.6 0.835 113.3 0.862 Low Pressure H igh Pressure Measured Measured Pressure Amount Pressure Amount (kPa) (mmol adsorbed/g) (kPa) (mmol adsorbed/g) 0.7 0.007 56 0.336 1.4 0.013 83 0.477 2.0 0.018 111 0.624 3.3 0.029 153 0.805 6.5 0.056 204 0.942 13.1 0.108 251 1.011 19.9 0.158 302 1.079 26.6 0.203 33.3 0.245 39.9 0.290 46.6 0.331 53.3 0.368 59.9 0.405 66.6 0.441 73.3 0.472 79.9 0.504 86.6 0.535 93.3 0.565 100.1 0.586 107.2 0.615 113.3 0.643 Low Pressure H igh Pressure Measured Measured Pressure Amount Pressure Amount (kPa) (mmol adsorbed/g) (kPa) (mmol adsorbed/g) 0.6 0.004 54 0.230 1.4 0.008 84 0.344 2.0 0.012 111 0.476 3.4 0.019 153 0.613 6.6 0.036 203 0.716 13.2 0.070 251 0.784 20.0 0.103 302 0.853 26.6 0.136 33.3 0.167 40.0 0.199 46.7 0.227 53.4 0.252 60.0 0.279 66.7 0.305 73.4 0.330 80.0 0.354 86.7 0.378 93.3 0.400 100.0 0.425 106.8 0.443 114.1 0.458 Appendix 2: Summary of Breakthrough Data Table A.2.1 Summary of breakthrough data for high X-section area adsorbent structure Bed voidage 0.413 Length (L) 20.32cm X Sect Area 12.41cm2 Volumetric Flow Rate (cc/min) Interstitial Velocity (cm/s) (s) a 2 (s2) HETP ( a V ) L (cm) HETP/2v (o-V)L/2v (s) 1/F (s/cm3) 1/v2 (s2/cm2) Temp\u00C3\u00A9r\u00C3\u00A2t ure (\u00C2\u00B0C) 60 0.19 2437 1453762 4.97 12.76 1.00 26.3 23.2 100 0.32 1624 531337 4.09 6.30 0.60 9.5 21.5 140 0.45 1189 201472 2.90 3.18 0.43 4.8 22.7 180 0.58 890 97456 2.50 2.14 0.33 2.9 22.7 220 0.71 749 66173 2 39 1.67 0.27 2.0 23.2 230 0.84 631 36737 1.87 1.11 0.23 1.4 23.2 60 0.19 2437 1453762 4.97 12.76 1.00 26.3 23.2 100 0.32 1653 543372 4.04 6.22 0.60 9.5 22.7 140 0.45 1157 216707 3.29 3.62 0.43 4.8 22.7 180 0.58 971 111072 2.39 2.04 0.33 2.9 22.3 220 0.71 727 52593 2.02 1.41 0.27 2.0 23.2 260 0.84 640 38230 1.90 1.12 0.23 1.4 23.2 Table A.2.2 Summary of breakthrough data for mid X-section area adsorbent structure Bed voidage 0.380 Length (L) 20.32cm X Sect Area 6.29cm2 Volumetric Flow Rate (cc/min) Interstitial Velocity (cm/s) (s) a 2 (s2) HETP ( a V )L (cm) HETP/2v (aV)L/2v (s) 1/F (s/cm3) 1/v2 (s2/cm2) Temp\u00C3\u00A9r\u00C3\u00A2t ure (\u00C2\u00B0C) 60 0.42 1212 292217 4.04 4.83 1.00 5.72 23.8 100 0.70 740 76692 2.84 2.04 0.60 2.06 23.8 140 0.98 544 31099 2.13 1.09 0.43 1.05 23.7 180 1.25 425 17859 2.01 0.80 0.33 0.64 23.5 220 1.53 343 10629 1.84 0.60 0.27 0.43 23.5 260 1.81 287 6322 1.56 0.43 0.23 0.30 24.0 60 0.42 1185 302798 4.38 5.24 1.00 5.72 23.3 100 0.70 743 74792 2.75 1.98 0.60 2.06 23.7 140 0.98 537 29710 2.09 1.07 0.43 1.05 23.7 180 1.25 416 14272 1.67 0.67 0.33 0.64 23.5 220 1.53 353 9292 1.51 0.49 0.27 0.43 23.6 260 1.81 288 5647 1.38 0.38 0.23 0.30 23.3 Bed voidage 0.380 Length (L) 20.32cm X Sect Area 3.70cm2 Volumetric Flow Rate (cc/min) Interstitial Velocity (cm/s) (s) a 2 (s2) HETP (o-V)L (cm) HETP/2v (o-V)L/2v (s) 1/F (s/cm3) 1/v2 (s2/cm2) Temperature (\u00C2\u00B0C) 60 0.71 686 63384 2.74 1.93 1.00 1.98 21.0 100 1.18 427 17248 1.92 0.81 0.60 0.71 21.0 140 1.66 308 7550 1.62 0.49 0.43 0.36 21.0 180 2.13 236 2651 0.96 0.23 0.33 0 22 21 0 220 2.61 196 2128 1.13 0.22 0.27 0.15 21.0 260 3.08 165 1046 0.78 0.13 0.23 0.11 21.0 60 0.71 637 61229 3.06 2.15 1.00 1.98 22.3 '100 1.18 390 13344 1.78 0.75 0.60 0.71 22.5 140 1.66 282 6174 1.58 0.48 0.43 0.36 22.5 180 2.13 224 2418 0.98 0.23 0.33 0.22 22.6 220 2.61 184 1942 1.16 0.22 0.27 0.15 22.4 260 3.08 157 1361 1.13 0.18 0.23 0.11 22.5 Table A.2.4 Summary of breakthrough data for non-adsorbing structure Bed voidage 0.399 Length (L) 20.32cm X Sect Area 6.14cm2 Volumetric Flow Rate (cc/min) Interstitial Velocity (cm/s) (^ (s) a 2 (s2) HETP (o - V ) L (cm) HETP/2v (GV)L/2V (s) 1/F (s/cm3) 1/v2 (s2/cm2) Temperature (\u00C2\u00B0C) 60 0.41 125 3182 4.13 5.07 1.000 6.01 100 0.68 79 732 2.35 1.73 0.600 2.16 140 0.95 55 298 1.97 1.04 0.429 1.10 180 1.22 46 135 1.32 0.54 0.333 0.67 220 1.50 38 66 0.94 0.31 0.273 0.45 260 1.77 28 87 2.34 0.66 0.231 0.32 60 0.41 126 3373 4 34 5.32 1.000 6.01 100 0.68 77 644 2.21 1.62 0.600 2.16 140 0.95 56 395 2.52 1.32 0.429 1.10 180 1.22 45 115 1.15 0.47 0.333 0.67 220 1.50 38 74 1.07 0.36 0.273 0.45 260 1.77 28 56 1.49 0.42 0.231 0.32 Bed voidage 0.289 Length (L) 20.32cm X Sect Area 6.22cm2 Volumetric Flow Rate (cc/min) Interstitial Velocity (cm/s) (s) o 2 (s2) HETP (o-V)L (cm) HETP/2V (oV)L/2v (s) 1/F (s/cm3) 1/v2 (s2/cm2) Temperature (\u00C2\u00B0C) 60 0.56 1581 465762 3.79 3.40 1.00 3.23 24.5 100 0.93 .925 103361 2.46 1 32] 0.60 1 16 24.5 140 1.30 686 58358 2.52 0.97 0.43 0.59 N/A 180 1 67 ; 559 32128 2.09 ' 0.63 0.33 ;o.36 24.5 220 2.04 445 20100 2.06 0.50 0.27 0.24 N/A 260 2.41 373 13793 2.01 0.42 0.23 0.17 N/A 60 0.56 1616 432265 3 37 3.02 1.00 3.23 22.7 100 0.93 977 120747 2.57 1.39 0.60 1.16 22.7 140 1.30 721 54099 2.11 0.81 0.43 0.59 22.7 180 1.67 534 30821 2.19 0.66 0.33 0.36 N/A 220 2.04 463 23521 2.23 0.55 0.27 0.24 22.6 26,0 , 2.41 : 394 13680 1.79 0.37 0.23 0.17 22.7 Table A.2.6 Summary of breakthrough data for thick adsorbent sheets structure Bed voidage 0.230 Length (L) 20.32cm X Sect Area 6.22cm2 Volumetric Flow Rate (cc/min) Interstitial Velocity (cm/s) (s) a2 (s2) HETP (aV)L (cm) HETP/2v (o-2/u.2)L/2v (s) 1/F (s/cm3) 1/v2 (s2/cm2) Temperature (\u00C2\u00B0C) 60 0.70 1546 308771 2.63 1.87 1.00 2.04 23.9 100 1.17 976 95879 2.05 0.88 0.60 0.73 23.8 140 1.63 689 38736 1.66 0.51 0.43 0.37 23.9 180 2.10 - 540 21914 1.53 0.36 0.33 0.23 24.1 220 2.57 444 12353 1.27 0.25 0.27 0.15 24.2 260 3.03 380 7661 1.08 0 18 0.23 0.11 24.0 60 0.70 1545 389469 3.31 2.37 1.00 2.04 23.8 100 1.17 943 99552 2.27 0.97 0.60 0.73 23 9 140 1.63 693 33761 1.43 0.44 0.43 0.37 23.6 180 2.10 544 18803 1.29 0 31 0.33 0.23 23.7 220 2.57 446 10409 1.06 0.21 0.27 0.15 23.7 260 * 3.03 ... , * > 3 7 2 7471 1.10 \"0.18 0.23 ^'0.11 24.0 Pack FlowRate Interstitial Residence Variance HETP Velocity Time (SCCM) (cm/s) (s) (cm) mid X-section area 1200 8.37 114 321 0.50 adsorbent structure 1500 10.46 89 452 1.17 1700 11.85 84 358 1.03 2000 13.95 76 520 1.85 2200 15.34 72 455 1.78 High voidage 1200 11.13 136 1372 1.51 1500 13.91 104 1003 1.88 1700 15.77 97 693 1.49 2000 18.55 87 932 2.52 2200 20.40 81 883 2.73 Thick adsorbent 1200 13.98 138 621 0.66 sheets 1500 17.48 107 542 0.97 1700 19.81 97 510 1.10 2000 23.31 87 556 1.48 Appendix 3: Breakthrough Curves for Breakthrough Experiments 1 0.8 o 0.6 O Figure A.3. ^ p ^ y ! \u00E2\u0080\u0094 ^ \u00E2\u0080\u0094 - ^ \u00E2\u0080\u0094 ^ ' // / ^y~^ Flow rate increases 0 i i i i i 1000 2000 3000 4000 5000 Time (s) 60 SCCM 100 SCCM 140 S C C M -180 SCCM 220 SCCM 260 S C C M l Breakthrough curves for high X-sectional area structure 0 1000 2000 3000 Time (s) 60 SCCM - 100 SCCM 140 S C C M 180 SCCM 220 SCCM \u00E2\u0080\u0094 260 S C C M Figure A.3.2 Breakthrough curves for mid X-sectional area structure Time (s) 60 SCCM \u00E2\u0080\u0094 100 SCCM 140 S C C M 180 SCCM 220 SCCM \u00E2\u0080\u0094 260 S C C M Figure A.3.3 Breakthrough curves for low X-sectional area structure 400 Time (s) 60 SCCM 100 SCCM 140 SCCM 180 SCCM 220 SCCM \u00E2\u0080\u0094 260 SCCM Figure A.3.4 Breakthrough curves for non-adsorbing structure Time (s) 60 SCCM -\u00E2\u0080\u0094 100 SCCM 140 S C C M \u00E2\u0080\u0094 180 SCCM -\u00E2\u0080\u0094 220 SCCM -\u00E2\u0080\u0094 260 S C C M Figure A.3.5 Breakthrough curves for high voidage adsorbent structure 1 0.8 o 0.6 O O 0.4 0.2 0 Flow rate increases 0 1000 I 2000 3000 Time (s) 60 SCCM -100 SCCM 140 S C C M \u00E2\u0080\u0094 1 8 0 SCCM -\u00E2\u0080\u0094 220 SCCM -\u00E2\u0080\u0094 260 S C C M Figure A.3.6 Breakthrough curves for thick adsorbent sheets structure 0 Flow rate increases 0 1 100 i 200 300 Time (s) 1200 SCCM 1500 SCCM 1700 S C C M 2000 SCCM -\u00E2\u0080\u0094 2200 SCCM 400 Figure A.3.7 Breakthrough curves for mid X-sectional area structure at high flow rates 0 100 200 Time (s) 300 400 1200 SCCM 1500 SCCM 1700 S C C M 2000 SCCM \u00E2\u0080\u0094 2200 SCCM Figure A.3.8 Breakthrough curves for high voidage structure at high flow rates Figure A.3.9 Breakthrough curves for thick adsorbent sheets structure at high flow rates Appendix 4: Mass Transfer Resistance Comparison Particle voidage 0.398 Dm 1.229 Length 20.32 Pack voidage Dp Dc 1.93E-04 5.25E-10 DLA/2 DL 0.38e/(1-e) 0.613 (1+e/1-e)/K) 1.04 Film K Macro 14.81 Micro L/v DL/v2 1/kK HETP/2V 1/v2 cm/sec sec 0.1 86.0 0.860 1 58E-05 0.2117 0.1090 203.2 86.03 0.5675 86.5976 100.00 0.2 21.5 0.860 1 58E-05 0.2117 0.1090 101.6 21.51 0.5675 22.0751 25.00 0.3 9.6 0.860 1 58E-05 0.2117 0.1090 67.7 9.56 0.5675 10.1264 11.11 0.5 3.4 0.860 1 58E-05 0.2117 0.1090 40.6 3.44 0.5675 4.0088 4.00 0.75 1.5 0.860 1 58E-05 0.2117 0.1090 27.1 1.53 0.5675 2.0970 1.78 1 0.9 0.860 1 58E-05 0.2117 0.1090 20.3 0.86 0.5675 1.4279 1.00 1.25 0.6 0.860 1 58E-05 0.2117 0.1090 16.3 0.55 0.5675 1.1181 0.64 2 0.2 0.860 1 58E-05 0.2117 0.1090 10.2 0.22 0.5675 0.7826 0.25 2.5 0.1 0.860 1 58E-05 0.2117 0.1090 8.1 0.14 0.5675 0.7052 0.16 3 0.1 0.860 1 58E-05 0.2117 0.1090 6.8 0.10 0.5675 0.6631 0.11 3.5 0.1 0.861 1 58E-05 0.2117 0.1090 5.8 0.07 0.5675 0.6378 0.08 4 0.1 0.861 1 58E-05 0.2117 0.1090 5.1 0.05 0.5675 0.6213 0.06 4.5 0.0 0.861 1 58E-05 0.2117 0.1090 4.5 0.04 0.5675 0.6100 0.05 5 0.0 0.861 1 58E-05 0.2117 0.1090 4.1 0.03 0.5675 0.6020 0.04 5.5 0.0 0.861 1 58E-05 0.2117 0.1090 3.7 0.03 0.5675 0.5960 0.03 6 0.0 0.861 1 58E-05 0.2117 0.1090 3.4 0.02 0.5675 0.5915 0.03 6.5 0.0 0.861 1 58E-05 0.2117 0.1090 3.1 0.02 0.5675 0.5879 0.02 7 0.0 0.861 1 58E-05 0.2117 0.1090 2.9 0.02 0.5675 0.5851 0.02 7.5 0.0 0.861 1 58E-05 0.2117 0.1090 2.7 0.02 0.5675 0.5829 0.02 8 0.0 0.861 1 58E-05 0.2117 0.1090 2.5 0.01 0.5675 0.5810 0.02 8.5 0.0 0.861 1 58E-05 0.2117 0.1090 2.4 0.01 0.5675 0.5795 0.01 9 0.0 0.862 1 58E-05 0.2117 0.1090 2.3 0.01 0.5675 0.5782 0.01 9.5 0.0 0.862 1 .58E-05 0.2117 0.1090 2.1 0.01 0.5675 0.5771 0.01 10 0.0 0.862 1 58E-05 0.2117 0.1090 2.0 0.01 0.5675 0.5762 0.01 12 0.0 0.863 1 58E-05 0.2117 0.1090 1.7 0.01 0.5675 0.5735 0.01 15 0.0 0.864 1 .58E-05 0.2117 0.1090 1.4 0.00 0.5675 0.5714 0.00 18 0.0 0.866 1 .58E-05 0.2117 0.1090 1.1 0.00 0.5675 0.5702 0.00 20 0.0 0.867 1 .58E-05 0.2117 0.1090 1.0 0.00 0.5675 0.5697 0.00 25 0.0 0.870 1 .58E-05 0.2117 0.1090 0.8 0.00 0.5675 0.5689 0.00 V2/DlkK 0.007 0.026 0.059 0.165 0.371 0.66 1.031 2.639 4.123 5.936 8.079 10.55 13.35 16.48 19.94 23.73 27.85 32.29 37.07 42.17 47.6 53.35 59.44 65.84 94.74 147.8 212.4 261.9 407.5 Appendix 5: Calculation of Mass Transfer Resistance laminate thickness, (aRp) 0.0068m mid X-sectional area structure 0.013 4m Thick adsorbent sheets structure 1/kK 0.2825s mid X-sectional area structure 0.5376s Thick adsorbent sheets structure (aRp) 2 4.634E-05m mid X-sectional area structure 1.785E-04m2 Thick adsorbent sheets structure (aRp)2 0.4634cm mid X-sectional area structure 1.7847cm2 Thick adsorbent sheets structure L.50E-04cm From the 1/kK vs. (aRp) plot slope 0.1931 intercept 0.193 laminate voidage 0.398 Dm 1.278cm2/s 8P is 0.398 . \" <==laminate voidage Dp=l/(slope-0.33Dm)/15/D 0.000193cm2/s D c / r c 2 =1/(15K(intercept)) D c 0.0233s\" 5.25E-10cm7s by using correlations to estimate Dm micropore Appendix 6: Pressure Drop Through the Structure Adsorbent Bed Table A.6.1 Sample Pressure drop for high flow breakthrough experiments HighFlow After breakthrough Pack Flow rate Inlet Outlet Ap H E T P HETP Description Pressure Pressure (Po/P L ) -1 correction correction (SCCM) (psi) (psi) (psi) (approximate) High X- 1200 28.9 28.4 0.5 0.036 1.018 1.009 Sectional 1500 42.9 42.1 0.8 0.038 1.019 1.010 Area 2000 76.5 75.2 1.3 0.035 1.017 1.009 2500 114.5 112.7 1.8 0.032 1.016 1.008 3000 160.5 158.3 2.2 0.028 1.014 1.007 Mid X - 1200 28.2 Sectional 1500 40.7 Area 2000 69.3 2500 107.2 3000 154.4 Low X- 1200 29.2 28.7 0.5 0.035 1.018 1.009 Sectional 1500 42.7 42 0.7 0.034 1.017 1.008 Area 2000 73.8 72.5 1.3 0.036 1.018 1.009 Non-adsorb 1200 29.1 28.6 0.5 0.035 1.018 1.009 1500 42.1 41.4 0.7 0.034 1.017 1.008 2000 73.8 72.7 1.1 0.030 1.015 1.008 2500 112.7 111.1 1.6 0.029 1.015 1.007 3000 161 159 2 0.025 1.013 1.006 bypass 1200 29.4 28.5 0.9 0.064 1.032 1.016 1500 43.3 41.8 1.5 0.073 1.037 1.018 2000 75.1 72.7 2.4 0.067 1.034 1.017 2500 114.4 111.2 3.2 0.058 1.029 1.014 3000 160.8 156.6 4.2 0.054 1.027 1.013 Pack Description New Data High flow Flow rate (SCCM) After breakthrough Inlet Pressure (psi) Outlet Pressure (psi) Ap (psi) (Po/P L) 2-1 H E T P correction (approximate) HETP correction Mid X- 1200 26 25.6 0.4 0.031 1.016 1.008 Sectional 1500 40 39.3 0.7 0.036 1.018 1.009 Area 2000 49.8 49.1 0.7 0.029 1.014 1.007 2500 70.3 69.2 1.1 0.032 1.016 1.008 3000 86.1 84.9 1.2 0.028 1.014 1.007 High voidage 1200 25.8 25.3 0.5 0.040 1.020 1.010 1500 39.6 38.8 0.8 0.042 1.021 1.010 2000 49.6 48.5 1.1 0.046 1.023 1.011 2500 69.7 68.3 1.4 0.041 1.021 1.010 3000 84.9 83.3 1.6 0.039 1.019 1.010 Thick adsorbent 1200 25.8 25.3 0.5 0.040 1.020 1.010 sheets 1500 39.8 39.1 0.7 0.036 1.018 1.009 2000 49.4 48.6 0.8 0.033 1.017 1.008 2500 70.5 69.3 1.2 0.035 1.017 1.009 3000 85.6 84.3 1.3 0.031 1.016 1.008 Bypass 1200 28.6 27.6 1 0.074 1.037 1.018 1500 45.7 44.2 1.5 0.069 1.035 1.017 2000 56.9 55 1.9 0.070 1.035 1.017 2500 78.5 76 2.5 0.067 1.033 1.017 3000 95.6 92.8 2.8 0.061 1.031 1.015 Table A.6.3 Sample Pressure drop for low flow breakthrough experiments Pack Flow rate Inlet Outlet Ap \u00C3\u008F H E T P H E T P Description Pressure Pressure (Po/P L) 2-1 correction correction (SCCM) (psi) (psi) (psi) (approximate) all packs 260 10.1 10 0.1 0.020 1.010 1.005 all packs 260 10 | 10 0 0.000 N/A N/A Appendix 7: Detailed Experimental Procedures Low pressure (atmospheric) gravimetric method 1. Clean the sample pan from previous run 2. Put approximately 20-25 mg of sample in the pan 3. Load the sample in the T G A 4. Measure the weight of the sample (wet mass) on bypass 5. Establish He flow of 400 mL/min through the unit overnight 6. Program the T G A to heat up the sample to 450 \u00C2\u00B0C at 10 \u00C2\u00B0C/min 7. Hold the temperature at 450 \u00C2\u00B0C for 4 hours 8. Cool down to measurement temperature, e.g., 30 \u00C2\u00B0C 9. Wait until the weight signal is stable 10. Measure the weight of the sample on both bypass and with gas going through (dry mass) 11. Introduce a mixture of test gas in He with a flow rate of 400 mL/min into the TGA 12. Open the program to record the weight changes of the sample 13. Wait until the weight signal is stable, then record the weight of the sample 14. Repeat steps 11-13 for other compositions of gas until the entire isotherm is obtained (up to 1 atmospheric pressure) High pressure (up to 3 bar) gravimetric method 1. Clean the sample pan from previous run 2. Put approximately 20-25 mg of sample in the pan 3. Load the sample in the T G A 4. Measure the weight of the sample (wet mass) on bypass 5. Establish He flow of 400 mL/min through the unit 6. Program the T G A to heat up the sample to 450 \u00C2\u00B0C at 10 \u00C2\u00B0C/min 7. Hold the temperature at 450 \u00C2\u00B0C for 3 hours 8. Cool down to measurement temperature, e.g., 60 \u00C2\u00B0C 9. Wait until the weight signal is table 10. Record sample weight on bypass and while gas going through the unit 11. Establish a mixture of test gas and He at 400 mL/min through the unit 12. Open a file to record weight changes of the sample 13. When the weight signal is stable, record the sample weight Repeat steps 11-13 for other compositions of gas up to the pressure of 3 bars Volumetric method A detailed experimental procedure including programming a sample file for volumetric measurement is as follows: 1. Obtain a clean sample tube and put quartz/glass wool in the tube to support the sample. 2. Degas the empty tube at 150 \u00C2\u00B0C under vacuum for 2 hrs to drive off the moisture in the tube. 3. After the empty tube is degassed, weigh the empty tube, then, put approximately 350 mg of sample into the tube. 4. Degas the sample tube with the sample at 350 \u00C2\u00B0C under vacuum for 14 hrs. 5. Weigh the sample tube again (the difference between the empty tube weight and the tube with sample yields the dry sample weight) 6. Load sample tube onto the chemisorption port. 7. Connect the two ends of the sample tube to the chemisorption unit. 8. Bring up the furnace and insulate the top of the furnace with glass wool to keep constant temperature in the furnace. 9. Turn on the fan to help cool down and stabilize the temperature at lower experimental temperature. (30 \u00C2\u00B0C) 10. Program a sample file to set up the pre-treatment and experiment conditions. 11. Start the program. Programming a sample file The following gives a rough description of a typical pre-treatment and experiment conditions to be programmed into a sample file. 1. Evacuate the sample tube for about 30 minutes to establish vacuum, (test if the o-rings seal at both end of the sample tube) 2. Heat up the sample tube from 30 \u00C2\u00B0C under vacuum to 450 \u00C2\u00B0C under vacuum to drive off moisture when loading up the sample tube. 3. Hold the temperature at 450 \u00C2\u00B0C under vacuum for 3 Vi hrs. 4. Cool down the sample to the experimental temperature (either 30 or 50 \u00C2\u00B0C) under vacuum. 5. Continue evacuation for 30 minutes. 6. Test for leak to see if 5 urn Hg can be reached. 7. Continue evacuation for 30 minutes. 8. Begin collecting the adsorption isotherm. 9. Backfill the sample tube with He. Desorption breakthrough experiment A detailed experimental procedure for the desorption (breakthrough) experiment is as follows: Loading up the laminate bed into the column 1. Uncap the black rubber cap on one end of the bed. 2. Quickly put on the adaptor and cap the end of the adaptor with the 1/8-inch cap. 3. Follow step 1-2 to put on the adaptor on the other end of the bed. 4. Bring the bed to the experimental equipment set up. 5. Uncap one end of the bed, then, quickly connect it to the 1/8-inch tube. 6. Uncap the other end of the bed, then, connect it to the 1/8-inch tube. 7. Immediately flow 30 cc/min of He through the system (i.e., through the bed) to keep moisture from getting into the adsorbent in the bed. Running breakthrough measurements Note: Before beginning an experiment, a flow of 30 cc/min He was established through the system after the laminate bed was attached. 1. Open the adsorbent gas cylinder. 2. Set V I to vent. 3. Set absorbent gas flow to 50 cc/min to flush the line. 4. Turn on the mass spectrometer. 5. Turn on the protect feature in the mass spectrometer, (to automatically turn off the filament if the pressure exceeds 5E-5 torr) 6. Turn on the filament. 7. Enable total pressure detector on mass spectrometer. 8. View bar graph on the mass spectrometer. 9. Wait for about 30 minutes for the pressure in the chamber of the mass spectrometer to reduce and stabilize. 10. Open the black valve to let gas from the system enters the mass spec chamber. 11. Go to the peak selection mode in the mass spectrometer. 12. Disable all peak selections except for channel two. 13. Adjust the scanning mass to an appropriate value depending on the adsorbate gas (e.g., 28 for N 2 ) 14. Wait until the display pressure value on channel 2 stabilizes. 15. Turn on the computer. 16. Enter Labtech notebook program. 17. Set an appropriate sampling time by adjusting the data logging frequency. 18. Set total flow rate to be tested with 5% adsorbate gas in He, for example, for the total flow rate of 100 S C C M , set absorbate flow rate to 5 S C C M and He flow rate to 95 SCCM. 19. Wait until the flow rates stabilize. 20. Start the data logging program. 21. After having collected 25 data points, switch valve V I from vent to the system. 22. Wait until the pressure increases until breakthrough occurs. 23. After breakthrough is reached, i.e., when the pressure does not change anymore, stop the data logging. 24. Switch valve V I to vent. 25. Set He flow rate to 500 S C C M to flush the absorbate gas from the laminate bed. 26. Wait until the absorbate has been flushed out, i.e., the pressure returns to roughly the same value as before the experiment. 27. Change the total flow rate of the gas for the 5% absorbent in He mixture. 28. Repeat step 19 to 26. Shutting down 1. Adjust the He flow rate to 30 SCCM. 2. Turn off the computer. 3. Close the black valve connecting the system to the mass spectrometer. 4. Switch valve V I to vent. 5. Turn off adsorbate gas flow. 6. Turn off the mass spectrometer's filament. 7. Turn off the mass spectrometer. Breakthrough method used to estimate dispersion and mass transfer coefficients A detailed experimental procedure for the breakthrough experiment is as follows: Loading up the laminate bed (adsorbent pack) into the column and running the experiment 1. Uncap the cap on one end of the pack 2. Bring the bed to the experimental equipment set up 3. Uncap one end of the bed, then, quickly connect it to the 1/8-inch tube 4. Uncap the other end of the bed, then, connect it to the 1/8-inch tube 5. Immediately flow 100 cc/min of He through the system (i.e., through the bed) to keep moisture from getting into the adsorbent in the bed 6. Open the adsorbate (N 2) cylinder 7. Set vent valve to vent 8. Flush the line with adsorbate gas 9. Turn on the GC and set up the data logging program. 10. Set an appropriate sampling time by adjusting the data logging frequency. 11. Set total flow rate to be tested with 5% adsorbate gas in He, for example, for the total flow rate of 1000 S C C M , set absorbate flow rate to 50 S C C M and He flow rate to 950 SCCM. Note: For high flow rate system: Set the reference gas (MFC2) flow rate to 30 S C C M , then set MFC3 flow rate to 30 S C C M 163 For low flow rate system: Set the reference gas to as close to the flow rate of the total test gas (carrier + sorbate) 12. Wait until the flow rates stabilize 13. Start the data logging program 14. After 25 seconds, switch vent valve from vent to the system 15. Wait until the TCD signal increases until breakthrough occurs 16. After breakthrough is reached, i.e., when the TCD signal does not change anymore, stop the data logging 17. Switch vent valve to vent 18. Set He flow rate to 500 S C C M to flush the absorbate gas from the laminate bed 19. Wait until the absorbate has been flushed out, i.e., the TCD signal returns to roughly the same value as before the experiment 20. Change the total flow rate of the gas for the 5% absorbent in He mixture 21. Repeat step 11 to 20 to perform experiment at different flow rate. Shutting down 1. Turn computer off 2. Turn off the TCD 3. Take out the adsorbent pack 4. Turn off all flows and turn off the mass flow controller box 5. Close all the gas cylinders Appendix 8: F test Volumetric T G A [Y(measured) -Y(average)]2 Measured Measured Volumetric TGA Pressure (kPa) Amount (mmol adsorbed/g) Pressure (kPa) Amount (mmol adsorbed/g) 0.6 0.003 3 0.022 4.79E-02 3.22E-02 1.4 0.007 10 0.055 4.61E-02 2.14E-02 2.1 0.011 30 0.146 4.46E-02 3.04E-03 4.1 0.021 51 0.229 4.05E-02 7.63E-04 6.9 0.034 77 0.327 3.53E-02 1.57E-02 13.7 0.066 103 0.429 2.43E-02 5.18E-02 20.3 0.098 1.55E-02 27.0 0.129 8.79E-03 33.7 0.159 4.02E-03 40.4 0.189 1.10E-03 47.0 0.219 1.25E-05 53.7 0.248 6.53E-04 60.4 0.276 2.90E-03 67.0 0.305 6.79E-03 73.7 0.333 1.23E-02 80.4 0.361 1.92E-02 87.1 0.388 2.76E-02 93.7 0.415 3.72E-02 100.4 0.442 4.82E-02 107.1 0.469 6.07E-02 113.7 0.494 7.41E-02 average 0.222 average 0.202SSE 5.58E-01 7.30E-02 ratio of SSE/(d.F.) 2.79E-02 1.46E-02 SSE/d.f. vol/TGA F-critical,a =0.05 1.91 1.96 Volumetric TGA [Y(predicted) -Y(average)]2 Measured Measured Volumetric TGA Pressure Amount Pressure Amount (kPa) (mmol adsorbed/g) (kPa) (mmol adsorbed/g) 0.7 0.002 3 0.013 1.64E-02 1.50E-02 1.4 0.004 10 0.037 1.58E-02 9.62E-03 2.1 0.007 31 0.090 1.53E-02 2.02E-03 4.2 0.012 51 0.149 1.39E-02 1.94E-04 6.9 0.020 77 0.220 1.21E-02 7.16E-03 13.8 0.039 103 0.302 8.38E-03 2.79E-02 20.4 0.057 5.41E-03 27.1 0.074 3.14E-03 33.8 0.092 1.45E-03 40.4 0.110 4.14E-04 47.1 0.127 7.75E-06 53.8 0.145 2.06E-04 60.4 0.162 9.82E-04 67.1 0.178 2.31E-03 73.8 0.195 4.13E-03 80.4 0.211 6.55E-03 87.1 0.228 9.57E-03 93.8 0.244 1.31E-02 100.4 0.260 1.70E-02 107.1 0.276 2.12E-02 113.8 0.291 2.60E-02 average 0.130 average 0.135SSE 1.93E-01 6.19E-02 SSE/(d.F.) 9.66E-03 1.24E-02 ratio of SSE/d.f. vol/both F-critical,a =0.05 0.78 1.96 Volumetric TGA [Y(measured) -Y(average)]2 Measured Measured Volumetric TGA Pressure Amount Pressure Amount (kPa) (mmol adsorbed/g) (kPa) (mmol adsorbed/g) 0.7 0.014 3 0.055 3.75E-01 2.94E-01 1.3 0.025 10 0.184 3.61E-01 1.70E-01 2.0 0.039 31 0.482 3.45E-01 1.31E-02 4.1 0.079 51 0.714 3.00E-01 1.39E-02 6.4 0.120 76 0.965 2.56E-01 1.35E-01 13.7 0.240 102 1.179 1.49E-01 3.40E-01 19.4 0.327 8.99E-02 27.1 0.436 3.64E-02 32.9 0.511 1.32E-02 39.5 0.592 1.18E-03 46.2 0.669 1.79E-03 52.9 0.741 1.32E-02 59.6 0.810 3.36E-02 66.3 0.874 6.12E-02 73.0 0.936 9.57E-02 79.8 0.994 1.35E-01 86.5 1.049 1.79E-01 93.2 1.101 2.26E-01 99.9 1.151 2.76E-01 106.5 1.200 3.29E-01 113.2 1.247 3.85E-01 average 0.626 average 0.596SSE . 3.66E+00 6.26E-01 SSE/(d.F.) 1.83E-01 1.25E-01 ratio of SSE/d.f. vol/TGA F-critical,a =0.05 1.46 1.96 Volumetric TGA [Y(predicted) -Y(average)]2 Measured Measured Volumetric TGA Pressure Amount Pressure Amount (kPa) (mmol adsorbed/g) (kPa) (mmol adsorbed/g) 0.6 1.768 4 2.038 9.43E+00 6.53E+00 1.3 2.230 10 3.903 6.81E+00 4.77E-01 1.9 2.525 31 4.918 5.35E+00 1.05E-01 3.8 3.098 51 5.319 3.03E+00 5.27E-01 6.5 3.597 76 5.605 1.54E+00 1.02E+00 12.9 4.275 102 5.778 3.18E-01 1.40E+00 20.0 4.705 1.81E-02 26.8 4.971 1.75E-02 32.9 5.150 9.68E-02 39.8 5.310 2.22E-01 46.7 5.444 3.66E-01 53.8 5.554 5.11E-01 59.5 5.631 6.28E-01 66.1 5.712 7.62E-01 72.9 5.783 8.90E-01 79.6 5.849 1.02E+00 86.5 5.904 1.13E+00 93.1 5.959 1.25E+00 99.9 6.008 1.37E+00 106.6 6.053 1.47E+00 113.3 6.093 1.57E+00 average 4.839 average 4.594SSE 3.78E+01 l.OlE+01 SSE/(d.F.) 1.89E+00 2.01E+00 ratio of SSE/d.f. vol/both F-critical,a =0.05 0.94 1.96 Low Pressure High Pressure [Y(measured) -Y(predicted)]2 [Y(predicted) -Y(average)]2 Measured Predicted Measured Predicted Low High Low High Pressure Amount Amount Pressure Amount Amount Pressure Pressure Pressure Pressure (kPa) (mmol/g) (mmol/g) (kPa) (mmol/g) (mmol/g) 0.7 0.011 0.010 56 0.495 0.523 5.85E-07 8.00E-04 1.90E-01 1.90E-01 1.3 0.020 0.019 83 0.680 0.688 1.32E-06 6.36E-05 1.82E-01 7.33E-02 2.0 0.030 0.028 112 0.859 0.829 1.92E-06 8.94E-04 1.74E-01 1.69E-02 3.3 0.047 0.046 155 1.005 0.991 3.13E-06 1.81E-04 1.60E-01 1.06E-03 6.4 0.089 0.087 209 1.135 1.140 3.95E-06 3.02E-05 1.29E-01 3.30E-02 12.8 0.168 0.167 252 1.230 1.232 1.36E-06 1.34E-06 7.76E-02 7.44E-02 19.7 0.247 0.245 302 1.308 1.316 3.50E-06 5.93E-05 4.02E-02 1.27E-01 26.5 0.316 0.315 1.34E-06 1.71E-02 33.2 0.379 0.378 1.75E-06 4.58E-03 39.9 0.436 0.436 3.27E-07 9.60E-05 46.6 0.489 0.489 3.02E-08 1.90E-03 53.2 0.538 0.539 4.68E-07 8.67E-03 59.9 0.583 0.585 3.32E-06 1.93E-02 66.6 0.625 0.627 5.37E-06 3.30E-02 73.3 0.665 0.667 5.49E-06 4.91E-02 79.9 0.702 0.705 5.65E-06 6.70E-02 86.6 0.739 0.739 2.83E-08 8.63E-02 93.3 0.772 0.773 5.12E-07 1.07E-01 99.9 0.805 0.803 1.99E-06 1.28E-01 106.6 0.835 0.833 6.79E-06 1.50E-01 113.3 0.862 0.860 2.38E-06 1.72E-01 average 0.446 average 0.959SSE 5.12E-05 2.03E-03 1.80 0.52 SSE/(d.F.) 2.56E-06 3.38E-04 0.09 0.09 ratio of ratio of SSE/d.f. SSE/d.f. both high and low P low P/both High P/both SSE 2.31 SSE/(d.F.) 0.09 1.05 1.00 Low Pressure High Pressure [Y(measured) -Y(predicted)]2 [Y(predicted) -Y(average)]2 Measured Predicted Measured Predicted Low High Low High Pressure Amount Amount Pressure Amount Amount Pressure Pressure Pressure Pressure (kPa) (mmol/g) (mmol/g) (kPa) (mmol/g) (mmol/g) 0.7 0.007 0.006 56 0.336 0.366 2.47E-07 9.10E-04 9.48E-02 1.50E-01 1.4 0.013 0.012 83 0.477 0.505 6.24E-07 7.71E-04 9.12E-02 6.18E-02 2.0 0.018 0.017 111 0.624 0.621 9.67E-07 1.01E-05 8.80E-02 1.76E-02 3.3 0.029 0.028 153 0.805 0.767 9.78E-07 1.46E-03 8.17E-02 1.77E-04 6.5 0.056 0.055 204 0.942 0.909 2.21E-06 1.13E-03 6.72E-02 2.40E-02 13.1 0.108 0.106 251 1.011 1.015 4.64E-06 2.00E-05 4.31E-02 6.85E-02 19.9 0.158 0.157 302 1.079 1.108 1.58E-07 8.46E-04 2.46E-02 1.26E-01 26.6 0.203 0.204 1.71E-06 1.20E-02 33.3 0.245 0.249 1.32E-05 4.25E-03 39.9 0.290 0.290 1.87E-07 5.57E-04 46.6 0.331 0.331 1.25E-08 2.86E-04 53.3 0.368 0.369 1.88E-07 3.00E-03 59.9 0.405 0.405 6.30E-11 8.26E-03 66.6 0.441 0.439 5.66E-06 1.57E-02 73.3 0.472 0.472 2.51E-08 2.51E-02 79.9 0.504 0.503 1.16E-06 3.58E-02 86.6 0.535 0.533 3.52E-06 4.82E-02 93.3 0.565 0.562 7.51E-06 6.16E-02 100.1 0.586 0.590 1.74E-05 7.62E-02 107.2 0.615 0.618 8.99E-06 9.24E-02 113.3 0.643 0.641 4.22E-06 1.07E-01 average 0.314 average 0.753SSE SSE / (d.F.) ratio of SSE/d.f. SSE SSE/(d.F.) both high and low P 1.43 0.05 7.36E-05 3.68E-06 ratio of SSE/d.f. High 5.15E-03 8.59E-04 0.98 0.05 low P/both P/both 0.93 1.41 0.45 0.07 Low Pressure High Pressure [Y(measured) -Y(predicted)]2 [Y(predicted) -Y(average)]2 Measured Predicted Measured Predicted Low High Low High Pressure Amount Amount Pressure Amount Amount Pressure Pressure Pressure Pressure (kPa) (mmol/g) (mmol/g) (kPa) (mmol/g) (mmol/g) 0.6 0.004 0.004 54 0.230 0.261 7.88E-08 9.43E-04 4.66E-02 9.79E-02 1.4 0.008 0.008 84 0.344 0.373 1.79E-07 8.27E-04 4.48E-02 4.04E-02 2.0 0.012 0.011 111 0.476 0.462 2.70E-07 1.96E-04 4.33E-02 1.25E-02 3.4 0.019 0.019 153 0.613 0.581 2.77E-07 1.06E-03 4.03E-02 4.59E-05 6.6 0.036 0.036 203 0.716 0.696 8.39E-09 3.97E-04 3.36E-02 1.49E-02 13.2 0.070 0.071 251 0.784 0.790 4.98E-07 2.84E-05 2.20E-02 4.66E-02 20.0 0.103 0.105 302 0.853 0.872 1.72E-06 3.49E-04 1.32E-02 8.87E-02 26.6 0.136 0.137 3.32E-07 6.81 E-03 33.3 0.167 0.168 3.02E-07 2.65E-03 40.0 0.199 0.197 1.48E-06 4.82E-04 46.7 0.227 0.226 9.55E-07 4.58E-05 53.4 0.252 0.254 2.50E-06 1.18E-03 60.0 0.279 0.280 9.33E-07 3.67E-03 66.7 0.305 0.306 1.08E-07 7.44E-03 73.4 0.330 0.330 7.02E-09 1.23E-02 80.0 0.354 0.354 1.02E-08 1.81E-02 86.7 0.378 0.377 6.66E-07 2.48E-02 93.3 0.400 0.399 6.65E-07 3.23E-02 100.0 0.425 0.421 2.19E-05 4.04E-02 106.8 0.443 0.442 1.53E-06 4.94E-02 114.1 0.458 0.464 2.93E-05 5.97E-02 average 0.219 average 0.574SSE 6.38E-05 3.80E-03 0.50 0.30 SSE/(d.F.) 3.19E-06 6.33E-04 0.03 0.05 ratio of ratio of SSE/d.f. SSE/d.f. High both high and low P low P/both P/both SSE 0.80 SSE/(d.F.) 0.03 0.84 1.68 Table A.8.8 F test for N2 on NaX at 25 \u00C2\u00B0C between literature and experimental results. [Y(experiment) - [Y(predicted) -Y(literature)]2 Y(average)]2 Amount Adsorbed (mmol/g) Low Hi gh Pressur (Rege and Yang, e 1997) Experimental Pressure Pressure (kPa) 2.0 0.009 0.010 1.28E-06 3.57E-02 4.58E-02 5.0 0.021 i 0.024 7.99E-06 3.10E-02 3.98E-02 10.0 0.043 0.048 3.20E-05 2.40E-02 3.08E-02 20.0 0.085 0.096 1.28E-04 1.26E-02 1.62E-02 30.0 0.128 0.145 2.88E-04 4.88E-03 6.26E-03 40.0 0.170 0.19^ 5.11E-04 7.45E-04 9.56E-04 50.0 0.213 0.241 7.99E-04 2.32E-04 2.98E-04 60.0 0.255 0 28') 1.15E-03 3.34E-03 4.28E-03 70.0 0.298 0.^37 1.57E-03 1.01E-02 1.29E-02 80.0 0.340 2.05E-03 2.04E-02 2.62E-02 90.0 0.383 O 434 2.59E-03 3.44E-02 4.41E-02 100.0 0.425 0 182 3.20E-03 5.19E-02 6.67E-02 average .. 0.197 0.224SSE 1.23E-02 ().22lJ3 0.29.13 SSE/(d.F.) I.I2I\".-(H O.O2085 0.02676 F factor 0.78 F-critical,a =0.05 2.18 [Y(measured) -Y(predicted)]2 [Y(predicted) - Y(average)] Amount Adsorbed (mmol/g) Low H i | (Rege and Yang, Pressure 1997) Experimental Pressure Pressure (kPa) 2.0 0.053 0.071 3.38E-04 7.71E-01 8.25E-01 5.0 0.130 0.173 1.78E-03 6.41E-01 6.51E-01 10.0 0.255 0.328 5.34E-03 4.57E-01 4.25E-01 20.0 0.486 0.595 1.19E-02 1.98E-01 1.48E-01 30.0 0.698 0.817 1.43E-02 5.44E-02 2.63E-02 40.0 0.891 1.005 1.29E-02 1.57E-03 6.37E-04 50.0 1.069 1.165 9.20E-03 1.92E-02 3.45E-02 60.0 1.234 1.304 4.95E-03 9.18E-02 1.05E-01 70.0 1.386 1.425 1.56E-03 2.07E-01 1.99E-01 80.0 1.527 1.532 2.53E-05 3.56E-01 3.05E-01 90.0 1.659 1.627 9.99E-04 5.30E-01 4.19E-01 100.0 1.782 1.712 4.83E-03 7.24E-01 5.36E-01 average 0.931 0.980SSE 6.81E-02 4.0496 3.6756 SSE / (d.F.) 6.I9E-03 0.36815 0.33415 F factor 1.10 F-criticaJ,a =0.05 2.18 Appendix 9: Heat Adsorption Calculations Table A.9.1 Adsorption Isotherm parameters for NaX Method Linear Isotherm Langmuir Isotherm q=KP q=aP/(l+bP) K, mmol/(g-kPa) a, mmol/(g-kPa) b,kPa-l QA2 adsorbent Gravimetric N 2 at 30\u00C2\u00B0C 0.00422 Gravimetric N 2 at 50\u00C2\u00B0C 0.00264 Volumetric N 2 at 30\u00C2\u00B0C 0.00446 Volumetric N 2 at 50\u00C2\u00B0C 0.00262 Volumetric CO at 30\u00C2\u00B0C 0.01866 0.00620 Volumetric CO at 50\u00C2\u00B0C 0.01249 0.00462 Volumetric C 0 2 at 30\u00C2\u00B0C 1.88840 0.31916 Volumetric C 0 2 at 50\u00C2\u00B0C 0.99910 0.18508 Henry constant Method Gas Temperature or Langmuir 1000/T (K\"1)ln b (K) constant, b Gravimetric N2 303 0.00422 3.30 -5.468 323 0.00264 3.10 -5.939 Volumetric N 2 303 0.00446 3.30 -5.413 323 0.00262 3.10 -5.945 Volumetric CO 303 0.00620 3.30 -5.083 323 0.00462 3.10 -5.377 Volumetric C O 2 303 0.31916 3.30 -1.142 323 0.18508 3.10 -1.687 Langmuir using b Method Gas From graph, slope = Gravimetric N2 2.3046AH = 19.2kJ/mol Volumetric N 2 2.6032AH = 21.6kJ/mol Volumetric CO 1.4394AH = 12.0kJ/mol Volumetric C 0 2 2.6665AH = 22.2kJ/mol -5.400 3.35 3.10 3.15 3.20 3.25 330 3.35 -5.500 -5.600 --5.700 -5.800 -5.900 -6.000 y = 2.3046X- 13.074 R 2 = 1 1000/T (K-1) Figure A . 9 . IN2 on NaX:ln(K) vs. 1000/T measured gravimetrically. -5.300 -5.400w -5.500 -5.600 - -5.700 -5.800 -5.900 -6.000 3.35 3.10 3.15 3.20 3.25 3.30 3.35 R 2=1 1000/T (K-1) Figure A.9.2 N 2 on NaX:ln(K) vs. 1000/T measured volumetrically -5.050 -5.100 -5.150 2- -5.200 - -5.250 -5.300 -5.350 -5.400 .3.05 3.10 3.15 3.20 3.25 3/60 3.35 y = 1.4394x-9.8338 R^ -1 -1000/T(K-1) Figure A.9.3 CO on NaX:ln(b) vs. 1000/T measured volumetrically 0.000 -0.2003^5 3J-0 3J-5 3,20 3,25 3.30 3,{35 -0.400 -0.600 S -0.800 y =2.6665x-9.9423 1000fi~(K-1) Figure A.9.4 C O 2 on NaX:ln(b) vs. 1000/T measured volumetrically Table A.9.2 Adsorption Isotherm parameters for L i X Langmuir Isotherm q=aP/(] 1+bP) a, mmol/(g-kPa) b,kPa-l Q A N2 adsorbent N 2 at 30\u00C2\u00B0C 0.02461 0.00775 N 2 at 40\u00C2\u00B0C 0.01700 0.00576 N 2 a t50\u00C2\u00B0C 0.00983 0.00343 N 2 at 60\u00C2\u00B0C 0.00652 0.00176 N 2 at 80\u00C2\u00B0C 0.00437 0.00041 Temperature Langmuir 1000/T (K\"1) In b constant, b 303 0.00775 3.30 -4.861 313 0.00576 3.19 -5.158 323 0.00343 3.10 -5.676 333 0.00176 3.00 -6.342 353 0.00041 2.83 -7.790 Langmuir using b From graph, slope = 4.9814 AH = 41.4kJ/mol 0.000 -1.0002\u00C2\u00A30 -2.000 g -3.000 -j -= -4.000 -5.000 -6.000 -7.000 -3.00- -3J-0- -3,2-0-y = 4.9814x-21.193 FT = 0.9629 1000/T (K-1) -3,30- -3,40 Figure A.9.5 N 2 on LiX:ln(b) vs. 1000/T measured gravimetrically Appendix 10: Matlab Program Comparison of predicted and measured C/Co clear; clear all; clc; tic; %bks3_model3TaueditJunel4_03.m is a m-file that predicts breakthrough curve based on extracted values %and compare it with raw data at flow rates where raw data is available. %Parameters extracted used here are derived based on using the bed voidage without the laminate voidage %defining some values %Length of adsorption pack (in cm) z = 20.32; %Laminate voidage ep = 0.398; %Mass transfer resistances %kf (in cm/s) Dp (in cm2/s) Dc (in cm2/s) rc (cm) %Dm = 0.64/0.7; %cm2/s %Rpfull = 0.02159/2; %cm %Sh = 2 * k f Rp/Dm = 2, kf = Dm/Rp; %kf = Dm/Rpfull; %kf =0.0107; Dc = 5.25e-10; rc = 1.5e-4; Number = input('Please enter the number of times you want to run the program \n'); for c=l:Number totaltime = input('Please enter the total time for breakthrough (sec) \n'); iftotaltime> 20000 fprintf('Maximum Simulation time exceeded'); break elseif totaltime <= 0 fprintf('Simulation time can not be less than or equal to zero'); break end Q = input('Please enter the volumetric flowrate of gas (SCCM) \n'); if Q > 10000 fprintf('Maximum Simulation flowrate exceeded'); break elseif Q <= 0 fprintf('Simulation flowrate can not be less than or equal to zero'); break end pack = input(' Please enter which pack you want to run the simulation for\n 1 = Full-size pack (A244)\n 2 = Half-size pack (A267)\n 3 = Quarter-size pack\n 4 = non-adsorbing pack\n 5 = space-height pack\n 6 = laminate-thickness pack\n'); %cross-sectional area of different packs (in cm2) cross = [12.41 6.29 3.70 6.14 6.22 6.22]; %including laminate voidage of different packs voidage =[0.413 0.380 0.380 0.399 0.289 0.230]; lam_thick(l,l :6) = lam_thick/2; %Henry constant (vol/vol) for (including laminate voidage in calculating interstitial velocity) Henry = [17.81 14.81 13.83 1.04 17.48 15.88]; %Dispersion coefficient (cm2/sec) (including laminate voidage in calculating interstitial velocity) Disperse = [0.64 0.89 0.90 0.84 0.90 0.97]; for n = 1:6 if pack == n xsect = cross(n); void = voidage(n); Rp = lam_thick(n); K = Henry (n); DL = Disperse(n); end end v = Q/(xsect*void*60); Dm = DL/0.7; % 1/Kk' mass_x_fer = (DL/v A2)*((l-void)/void)+((Rp/(3*kf))+(RpA2/(15*ep*Dp))+(rcA2/(15*K*Dc)))^ %k' kprime = l/(mass_x_fer*K); %Calculating X i (the dimensionless bed length X i = (kprime*K*z/v)*((l-void)/void); %Calculating the predicted C/Co for t = b: 1 : totaltime if t < z/v b=t+l; else Tau(t) = kprime *(t-z/v); X = sqrt(Xi)-sqrt(Tau(t)); storetime(t)=t; conc3(t) = (l/2)*erfc(X); end end %Initializing adsorption time vector Time 1=0; %Initializing Total time to read the raw data (number of data required) for comparison totaltimeraw = totaltime; %Reading raw data for adsorption time from 0 to saturation and concentration up to saturation and/or %reading adsorption time and concentration (C/Co) up to the time inputted by user to run the simulation if pack == 1 ifQ==60 totaltimeraw=totaltime/2 ; [Time 1 ,concraw]=textread('FullA244_C_over_Co_60.txtV%d %f,totaltimeraw); elseifQ==100 totaltimeraw^totaltime/2 ; [Timel,concraw]=textread(TullA244_C_over_Co_100.txt','%d%f, totaltimeraw); elseif Q== 140 totaltimeraw=totaltime/2 ; [Time 1 ,concraw]=textread('FullA244_C_over_Co_l40.txt','%d %f,totaltimeraw); elseif Q== 180 totaltimeraw=totaltime/2; [Timel ,concraw]=textread('FullA244_C_over_Co_l 80.txt','%d %f,totaltimeraw); elseif Q==220 totaltimeraw=totaltime/2 ; [Time 1 ,concraw]=textread('FullA244_C_over_Co_220.txt','%d % f ,totaltimeraw); elseif Q==260 totaltimeraw=totaltime/2 ; [Time 1 ,concraw]=textread('FullA244_C_over_Co_260.txt','%d %f,totaltimeraw); end end if pack == 2 ifQ==60 totaltimeraw=totaltime/2 ; [Time 1 ,concraw]=textread('Half_C_over_Co_60.txt','%d %f,totaltimeraw); elseif Q== 100 totaltimeraw=totaltime/2 ; [Time 1 ,concraw]=textread('Half_C_over_Co_l 00.txt','%d %f,totaltimeraw); elseif Q== 140 totaltimeraw=totaltime/2 ; [Time 1 ,concraw]=textread('Half_C_over_Co_l40.txt','%d %f,totaltimeraw); elseif Q==l 80 totaltimeraw=total time/2 ; [Timel,concraw]=textread('Half_C_over_Co_l80.txt','%d %f,totaltimeraw); elseif Q==220 totaltimeraw=totaltime/2 ; [Time 1 ,concraw]=textread('Half_C_over_Co_220.txt','%d %f,totaltimeraw); elseif Q==260 totaltimeraw=totaltime/2 ; [Timel,concraw]=textread('Half_C_over_Co_260.txt','%d %f,totaltimeraw); elseif Q== 1200 totaltimeraw=total time/0.5 ; [Timel ,concraw]=textread('Half_C_over_Co_1200to2200.txt','%f % f % * f % * f % * f % * f,totaltimeraw) ; elseif Q==l 500 totaltimeraw=totaltime/0.5; [Timel ,concraw]=textread('Half_C_over_Co_1200to2200.txt','%f % * f % f % * f % * f %* f, totaltimeraw) ; elseif Q== 1700 totaltimer aw=totaltime/0.5; [Timel ,concraw]=textread('Half_C_over_Co_1200to2200.txt';%f % * f % * f % f % * f % * f ,totaltimeraw) ; elseif Q==2000 totaltimeraw=totaltime/0.5; [Timel ,concraw]=textread('Half_C_over_Co_l 200to2200.txt,,\"%f %* f % * f % * f % f %*f,totaltimeraw); elseif Q==2200 totaltimeraw=total time/0.5 ; [Timel ,concraw]=textread('Half_C_over_Co_l 200to2200.txt',*%f % * f % * f % * f % * f %f,totaltimeraw); end end if pack == 3 ifQ==60 totaltimeraw=totaltime; [Time 1 ,concraw]=textread('Quarter_C_over_Co_60.txtV%d %f,totaltimeraw); elseif Q== 100 total timeraw=total time ; [Time 1 ,concraw]=textread('Quarter_C_over_Co_l 00.txt','%d % f ,totaltimeraw); elseif Q== 140 totaltimeraw=totaltime ; [Time 1 ,concraw]=textread('Quarter_C_over_Co_l40.txt','%d % f , total timeraw); elseif Q==180 totaltimeraw=totaltime ; [Time 1 ,concraw]=textread('Quarter_C_over_Co_l 80to260.txt','%d % f % * f % * f ,totaltimeraw) ; elseif Q==220 total timeraw=totaltime ; [Time 1 ,concraw]=textread('Quarter_C_over_Co_l 80to260.txt','%d % * f % f %* f ,totaltimeraw); elseif Q==260 totaltimeraw=totaltime; [Timel ,concraw]=textread('Quarter_C_over_Co_l80to260.txt','%d % * f % * f %f,totaltimeraw); end end if pack == 4 if Q==60 totaltimeraw=totaltime/0.5 ; [Timel,concraw]=textread('nonadsorb_C_over_Co_60.txt','%f%f,totaltimeraw); elseif Q==l 00 total timeraw=totaltime/0.5; [Time 1 ,concraw]=textread('nonadsorb_C_over_Co_l 00to260.txt','%f % f % * f % * f % * f % * f ,totaltimeraw) ; elseif Q== 140 to taltimeraw=total time/0.5 ; [Timel,concraw]=textread('nonadsorb_C_over_Co_100to260.txt','o/of%*fo/of%*f0/o*f % * f ,totaltimeraw) ; elseif Q== 180 totaltimeraw=totaltime/0.5; [Timel ,concraw]=textread('nonadsorb_C_over_Co_l 00to260.txt','%f % * f % * f % f % * f % * f ,totaltimer aw) ; elseif Q==220 totaltimeraw=totaltime/0.5 ; [Timel ,concraw]=textread('nonadsorb_C_over_Co_l 00to260.txt','%f % * f % * f % * f % f % * f, totaltimeraw) ; elseif Q==260 total timeraw=total time/0.5 ; [Time 1 ,concraw]=textread('nonadsorb_C_over_Co_l 00to260.txt','%f % * f % * f % * f % * f %f,total timeraw) ; end if pack == 5 ifQ==60 totaltimeraw=totaltime/2 ; [Timel,concraw]=textread('spaceheight_C_over_Co_60.txt','%d %f,totaltimeraw); elseif Q = l 00 totaltimeraw=totaltime/2 ; [Time 1 ,concraw]=textread('spaceheight_C_over_Co_l 00.txt','%d %f,totaltimeraw); elseif Q== 140 total timer aw=total time/2 ; [Time 1 ,concraw]=textread('spaceheight_C_over_Co_l40.txt','%d %f,totaltimeraw); elseif Q==l 80 totaltimeraw=totaltime/2 ; [Timel ,concraw]=textread('spaceheight_C_over_Co_l 80.txt','%d %f,total timeraw); elseif Q==220 totaltimeraw=totaltime/2 ; [Time 1 ,concraw]=textread('spaceheight_C_over_Co_220.txt','%d %f,total timeraw); elseif Q==260 totaltimeraw=totaltime/2 ; [Time 1 ,concraw]=textread('spaceheight_C_over_Co_260.txt','%d %f,totaltimeraw); elseif Q==l 200 totaltimer aw=totaltime/0.5; [Timel ,concraw]=textread('spaceheight_C_over_Co_l 200to2200.txt','%f % f % * f % * f % * f % * f ,totaltimeraw) ; elseif Q = 1500 totaltimeraw=totaltime/0.5; [Time 1 ,concraw]=textread('spaceheight_C_over_Co_l 200to2200.txt','%f % * f % f % * f % * f % * f ,totaltimeraw) ; elseif Q = l 700 totaltimeraw=totaltime/0.5; [Time 1 ,concraw]=textread('spaceheight_C_over_Co_l 200to2200.txt',*%f % * f % * f % f % * f % * f, total timer aw) ; elseif Q==2000 totaltimeraw=totaltime/0.5; [Timel ,concraw]=textread('spaceheight_C_over_Co_l 200to2200.txt','%f % * f % * f % * f % f % * f ,totaltimeraw) ; elseif Q==2200 [Timel,concraw]=textread('spaceheight_C_over_Co_1200to2200.txtV%f % * f % * f % * f % * f %f,totaltimeraw); end end if pack == 6 ifQ==60 totaltimeraw=totaltime/2 ; [Time 1 ,concraw]=textread('thickness_C_over_Co_60.txt','%d %f,totaltimeraw); elseif Q==l 00 totaltimeraw=totaltime/2 ; [Timel,concraw]=textread('thickness_C_over_Co_l00.txt','%d %f,totaltimeraw); elseif Q = 140 totaltimeraw=totaltime/2 ; [Timel,concraw]=textread('thickness_C_over_Co_140.txtV%d %f,totaltimeraw); elseif Q==l 80 totaltimeraw=totaltime/2 ; [Timel ,concraw]=textread('thickness_C_over_Co_l 80.txt' ,'%d %f,totaltimeraw); elseif Q==220 totaltimeraw=totaltime/2 ; [Time 1 ,concraw]=textread('thickness_C_over_Co_220.txt','%d %f,totaltimeraw); elseif Q==260 total timera w=totaltime/2 ; [Time 1 ,concraw]=textread('thickness_C_over_Co_260.txt','%d %f,totaltimeraw); elseif Q==l 200 totaltimeraw=totaltime/0.5; [Timel,concraw]=textread('thickness_C_over_Co_1200to2200.txt','%f%f % * f % * f % * f %*f,totaltimeraw); elseif Q = l 500 totaltimeraw=totaltime/0.5; [Timel ,concraw]=textread('thickness_C_over_Co_l 200to2200.txt','%f % * f % f % * f % * f % * f ,totaltimeraw) ; elseif Q==l 700 totaltimera w=totaltime/0.5; [Timel ,concraw]=textread('thickness_C_over_Co_l 200to2200.txt','%f % * f % * f % f % * f %*f,totaltimeraw); elseif Q==2000 totaltimera w=totaltime/0.5; [Time 1 ,concraw]=textread('thickness_C_over_Co_l 200to2200.txt','%f % * f % * f % * f % f %* f,total timeraw) ; elseif Q==2200 totaltimeraw=totaltime/0.5; [Timel ,concraw]=textread('thickness_C_over_Co_l 200to2200.txt','%f % * f % * f % * f % * f %f,totaltimeraw); end end %inputting flow rates that raw data are available for comparison for each pack if pack == 1 flowmat = [60 100 140 180 220 260]; elseif pack == 2 flowmat = [60 100 140 180 220 260 1200 1500 1700 2000 2200]; elseif pack == 3 flowmat = [60 100 140 180 220 260]; elseif pack == 4 flowmat = [60 100 140 180 220 260]; elseif pack == 5 flowmat = [60 100 140 180 220 260 1200 1500 1700 2000 2200]; elseif pack == 6 flowmat = [60 100 140 180 220 260 1200 1500 1700 2000 2200]; end %Initializing variables required to plot model in case the inputted flow rates does not match %raw data flow rates realtimeraw = 0; d = l ; for e = 1 :length(flowmat) if Q == flowmat(e) for d=2:length(Timel) ifTimel(d) length(Timel) realtimeraw = length(Timel); end h = realtimeraw; bb=0; for g=l:h Tau2(g) = kprime*(Timel(g)-z/v); end p=b; %Plotting the predicted C/Co and raw data to compare if totaltime < b fprintf('Insufficient totaltime specified'); break end rawda = 0; if length(flowmat)> 1 for f = 1 :length(flowmat) if Q = flowmat(f) figure(c) plot(Tau(b:t),conc3(b:t),'bA',Tau2(b:realtimeraw),concraw(b:realtimeraw),' xlabel(Tau'); ylabel('C/Co'); title('C/Co vs. Tau'); legend('model3','raw'); rawda = 1 ; end end if rawda ~=1 figure(c) plot(Tau(b:t),conc3(b:f),'bA'); xlabel('Tau'); ylabel('C/Co'); title('C/Co vs. Time'); legend('model3'); end X i end toe Tau2temp:=Tau2' ; conc3temp=conc3'; Tautemp=Tau'; concrawtemp=concraw' ; for o=l :length(conc3temp) p=2*o; if p>length(conc3temp) break end conc3temp2(o) = conc3temp(p); end %writing the results to text file to be used to plot the C/Co vs. Tau for predicted and measured values %in Microsolf Excel y = [Timel ;concraw;storetimetemp;conc3temp2]; fid = fopen(Thickness 100 June 14.txt','wt'); fprintf(fid,'%6.4f\n',y); fclose(fid); Comparison of the effects of changing dispersion, film mass transfer coefficient, macropore mass transfer coefficient, and micropore mass transfer coefficient clear; clear all; clc; tic; %bk_para_mod_Decl2Tauedit.m is a m-file that predicts breakthrough curve based on extracted values and compare it with %raw data at flow rates where raw data is available. %Parameters extracted used here are derived based on using the bed voidage without the laminate voidage %Testing for changing in packing %defining some values %Length of adsorption pack (in cm) z = 20.32; %Laminate voidage ep = 0.398; %Mass transfer resistances %kf (in cm/s) Dp (in cm2/s) Dc (in cm2/s) rc (cm) Dp(l) = 0.000193; %Dp(l) = 0.000775; Dc(l) = 5.25e-10; rc(l)= 1.5e-4; Number = input('Please enter the number of times you want to run the program \n'); for c=l:Number totaltime = input('Please enter the total time for breakthrough (sec) \n'); if totaltime > 20000 fprintf('Maximum Simulation time exceeded'); break elseif totaltime <= 0 fprintf('Simulation time can not be less than or equal to zero'); break end Q = input('Please enter the volumetric flowrate of gas (SCCM) \n'); if Q > 10000 fprintf('Maximum Simulation flowrate exceeded'); break elseif Q <= 0 fprintf('Simulation flowrate can not be less than or equal to zero'); break end pack = input(' Please enter which pack you want to run the simulation for\n 1 = Full-size pack (A244)\n 2 = Half-size pack (A267)\n 3 = Quarter-size pack\n 4 = non-adsorbing packVn 5 = space-height pack\n 6 = laminate-thickness pack\n'); if pack > 6 nottrue = 1 ; elseif pack < 1 nottrue = 1 ; else nottrue = 0; end if nottrue ==1 fprintf('Must select the number from 1 to 6'); break end %cross-sectional area of different packs (in cm2) cross =[12.41 6.29 3.70 6.14 6.22 6.22]; %including laminate voidage of different packs voidage(l,l:6) = [0.413 0.380 0.380 0.399 0.289 0.230]; lam_thick(l,l:6) = lam_thick/2; %Henry constant (vol/vol) for (including laminate voidage in calculating interstitial velocity) Henry = [17.81 14.81 13.83 1.04 17.48 15.88]; %Dispersion coefficient (cm2/sec) (including laminate voidage in calculating interstitial velocity) Disperse = [0.64 0.89 0.90 0.84 0.90 0.97]; for n = 1:6 if pack == n xsect = cross(n); void(l) = voidage(l,n); Rp(l) = lam_thick(l,n); K = Henry (n); DL = Disperse(n); end end Dm = DL/0.7; kf(l) = Dm/Rp(l); per_lam = input('Please enter the percentage that the laminate thickness changes by \n positive number = increase in laminate thickness \n negative number = decrease in laminate thickness \n'); i f per_lam ~= 0 perc = l+per_lam/100; elseif per_lam = 0 perc = 1 ; end ifper_lam<=-100 fprintf('changed in laminate thickness can not exceed -100%'); break end per_spac = input('Please enter the percentage that the space height changes by \n positive number = increase in space height \n negative number = decrease in space height \n'); if per_spac ~= 0 perc2 = l+per_spac/100; elseif per_spac == 0 perc2 = 1 ; end if per_spac <= -100 fprintf('changed in space height can not exceed -100%'); break end Rp(2) = perc*Rp(l); %Pack dimension (m) width = [6.248e-2 3.175e-2 1.867e-2 3.099e-2 3.099e-2 3.099e-2]; height = [1.986e-2 1.981e-2 1.981e-2 1.981e-2 2.007e-2 2.007e-2]; % New(changed) space height newspacer = perc2*spacer(l,pack); %Defining total volume of laminate (m3) vollam(l,l:6) = [1.480e-4 7.341e-5 4.317e-5 8.059e-5 8.861e-5 1.004e-4]; totallhtemp = totallh(pack)-Rp(2)/100; %thickness or height of one laminate sheet and one spacer (m) onelayer = Rp(2)/100+newspacer; %changed(new) number of spacers and sheets numspac = totallh(pack)/onelayer; numlam = numspac + 1 ; %changed(new) volume of spacers and sheets newvollam = width(pack)*height(pack)*(Rp(2)/100)* numlam; newvolspac = width(pack)*height(pack)*newspacer*numspac; %changed(new) total volume (spacers + laminates)(m3) newtotvol = newvollam+newvolspac; %void(2) = 1 - newvollam/newtotvol; void(2) = void(l); per_kf = input('Please enter the percentage that the external fluid film changes by \n positive number = increase in parameter value \n negative number = decrease in parameter value \n'); perDp = input('Please enter the percentage that the macropore diffusivity changes by \n positive number = increase in parameter value \n negative number = decrease in parameter value \n'); per_Dc = input('Please enter the percentage that the micropore diffusivity changes by \n positive number = increase in parameter value \n negative number = decrease in parameter value \n'); per_rc = input('Please enter the percentage that the zeolite crystal diameter changes by \n positive number = increase in diameter \n negative number = decrease in diameter \n'); per_DL = input('Please enter the percentage that the dispersion changes by \n positive number = increase in dispersion number \n negative number = decrease in dispersion number \n'); if per_kf ~= 0 perc_kf = l+per_kf/100; elseif per_kf == 0 perc_kf = 1; end ifper_kf<=-100 fprintf('changed in laminate thickness can not exceed -100%'); break end if per_Dp ~= 0 perc_Dp= l+per_Dp/100; elseif per_Dp == 0 perc_Dp = 1 ; end ifper_Dp <=-100 fprintf('changed in laminate thickness can not exceed -100%'); break end if per_Dc ~= 0 perc_Dc = l+per_Dc/100; elseif per_Dc == 0 perc_Dc = 1 ; end ifper_Dc<=-100 fprintf('changed in laminate thickness can not exceed -100%'); break end if per_rc ~= 0 perc_rc = l+per_rc/100; elseif per_rc == 0 perc_rc = 1 ; end ifperjc <= -100 fprintf('changed in laminate thickness can not exceed -100%'); break end ifper_DL ~= 0 perc_DL = l+per_DL/100; elseif per_DL == 0 perc_DL = 1 ; end ifper_DL<=-100 fprintf('changed in laminate thickness can not exceed -100%)'); break end kf(2) = perc_kf*kf(l); Dp(2) = perc_Dp*Dp(l); Dc(2) = perc_Dc*Dc(l); rc(2) = perc_rc*rc(l); DL(2) = perc_DL*DL(l); for d= 1:2 v(d) = Q/(xsect*void(d)*60); % 1/Kk' mass_x_fer = (DL(d)/v(d)A2)*((l-void(d))/void(d))+((Rp(d)/(3*kf(d)))+(Rp(d)A2/(15*ep*Dp(d)))+(rc(d)A2/(15*K*Dc(d)))); %k' kprime(d) = l/(mass_x_fer*K); %Calculating X i (the dimensionless bed length) Xi(d) = (kprime(d)*K*z/v(d))*((l-void(d))/void(d)); fort = b:l:totaltime if t < z/v(d) b=t+l; else Tau(d,t) = kprime(d)*(t-z/v(d)); X = sqrt(Xi(d))-sqrt(Tau(d,t)); stor\u00C3\u00A8time(f)=t; conc3(d,t) = (l/2)*erfc(X); end end end %Plotting the predicted C/Co and raw data to compare if totaltime < b fprintf('Insufficient totaltime specified1); break end figure(c) plot(Tau(l,b:t),conc3(l,b:t),,bA',Tau(2,b:t),conc3(2,b:t);go'); xlabel('Tau'); ylabel('C/Co'); title('C/Co vs. Tau'); legend('model3_standard','model3_changed'); X i end toe Tautemp=Tau'; Tautemp 1 =Tautemp( 1 : length(storetime), 1 ) ; Tautemp2=Tautemp( 1 : length(storetime),2) ; conc3 stand=conc3 (1,1 :length(storetime))'; conc3chang=conc3(2,1 :length(storetime))'; %writing the results to a text file to be used in Excel to plot C/Co vs. Tau graphs y = [Tautempl;conc3stand;Tautemp2;conc3chang]; fid = fopen('disper99.99neg.txt','wt'); fprintf(fid,'%6.4f\n',y); fclose(fid); "@en . "Thesis/Dissertation"@en . "2004-05"@en . "10.14288/1.0058946"@en . "eng"@en . "Chemical and Biological Engineering"@en . "Vancouver : University of British Columbia Library"@en . "University of British Columbia"@en . "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en . "Graduate"@en . "Breakthrough analysis of a structured adsorbent bed"@en . "Text"@en . "http://hdl.handle.net/2429/16970"@en .