ChE laboratory
CONTINUOUS AND BATCH DISTILLATION IN AN OLDERSHAW TRAY COLUMN
Carlos M. Silva, Raquel V. Vaz, Ana S. Santiago, and Patrícia F. Lito Universidade de Aveiro, Campus de Santiago • 3810-193 Aveiro, PORTUGAL istillation is by far the most frequently used industrial calculations, mostly using Excel, Matlab, Hysys, and Math- separation process. Although not energy-efficient, it ematica software.[4-6] Moreover, virtual laboratories involving has a simple flowsheet and is a low-risk process. It distillation units have been developed in order to enhance the Dis indeed the benchmark with which all newer competitive understanding of the process units and to improve the teaching processes must be compared. Following Null,[1] distillation effectiveness.[7, 8] Nonetheless, students are usually uninter- should be selected if the relative volatility is greater than 1.05, ested in a problem unless they can visualize it in practice, so [2] [3] whereas Nath and Motard and Douglas indicate α12 greater experiments in the lab should never be totally replaced by than 1.10, a more conservative critical value for the relative simulated experiments on a computer, notwithstanding its volatility. Generally, design heuristics point out that processes ease and less time-consuming approach. using energy separation agents should be favored. In this work, experiments are performed in an Oldershaw For the reasons outlined above, distillation experiments column with five sieve trays to separate cyclohexane/n-hep- are included in the Chemical Engineering Integrated Master tane under different modes of operation. These modes include curriculum of the Department of Chemistry at University of total reflux, continuous rectification with partial reflux, and Aveiro (DCUA). Students start receiving lectures on distil- lation as part of the Separation Processes I course, which is Carlos M. Silva is a professor of chemical engineering at the Depart- ment of Chemistry, University of Aveiro, Portugal. He received his B.S. essentially devoted to equilibrium-staged unit operations. and Ph.D. degrees at the School of Engineering, University of Porto, Afterwards, experiments are carried out in Laboratórios EQ Portugal. His research interests are transport phenomena, membranes, (Chemical Engineering Laboratory), a weekly six-hour lab ion exchange, and supercritical fluid separation processes. course intended to provide hands-on experience on separa- Raquel V. Vaz is a Ph.D. student at the Department of Chemistry, tions, reaction, and control. Each experiment lasts two weeks: University of Aveiro, Portugal. She received her Master’s degree in chemical engineering from the University of Aveiro. Her main research in the first week students—divided into groups of three—carry interest focuses on molecular dynamics simulation and modeling of out the lab exercise and some calculations, and in the sec- diffusion coefficients of nonpolar and polar systems. ond week students do numerical calculations and computer Ana S. Santiago is a post-Ph.D. student in the Department of Chemistry, simulations, which require computational support. Student University of Aveiro, Portugal. She received her B.S. degree in chemi- cal engineering from the University of Coimbra and Ph.D. in chemical assessment is based on a very short individual oral quiz and engineering from the University of Aveiro. Her main research interest a report prepared by the student groups. focuses on bio-refinery and membrane separation processes. In this paper a lab exercise on continuous and batch Patrícia F. Lito is a post-Ph.D. student in the Department of Chemistry, University of Aveiro, Portugal. She received her B.S. and Ph.D. degrees rectification developed at DCUA is presented. Papers with in chemical engineering from the University of Aveiro. Her main research experimental work in the distillation field are scarce and ac- interest focuses on mass transfer, membrane separation processes, ion exchange, and molecular dynamics simulation and modeling of cordingly this communication intends to fill this gap. There are diffusion coefficients of nonpolar and polar systems. a number of educational publications concerning distillation
© Copyright ChE Division of ASEE 2011
106 Chemical Engineering Education batch rectification with constant reflux. An Oldershaw tray ture sensors immersed in the reboiler and located in the top column is a laboratory-scale column equipped with perforated condenser allowing the determination of the bottom and head trays. Of special importance is the fact that it exhibits a sepa- compositions, respectively. The column is used to separate ration capacity close to that of large industrial columns.[9] In c.a. 800 mL of a cyclohexane (Lab-Scan, 99%) / n-heptane fact, experimental results show that commercial towers will (Lab-Scan, 99%) mixture with 30% (mol) of cyclohexane. require a similar number of stages to reach the same separa- The calibration curve—measured in this work—to deter- tion level obtained in the Oldershaw unit.[10] mine the cyclohexane mole fraction (x1) in a cyclohexane–n- With this work students practice relevant concepts in- heptane mixture at 30 ˚C as function of refractive index (RI), 2 troduced earlier in their curriculum, namely vapor-liquid is given by x1=-309.95 RI + 895.15 RI – 645.15. equilibrium, continuous vs. batch operation, McCabe-Thiele Experiments at Total Reflux, R = ∞ graphical method, column efficiency, and application of the generalized Rayleigh equation. Moreover, students use in- Rectifications at total reflux were performed at two distinct dustrial simulation software (Aspen) to predict experimental effective reboiler powers (P = 75 and 125 W) to evaluate results, giving them the opportunity to improve their skills in the effect of the internal molar flow upon separation and this field, too. By examining experimental results and compar- column efficiency. The invariance of the top and bottom (TD ing them with those obtained from simulations, students gain and TB) temperatures was used to detect the steady state. Ad- insight to this unit operation. ditionally, they were utilized to determine the corresponding cyclohexane molar compositions, xD and xB, by vapor-liquid LABORATORY DESCRIPTION equilibrium calculations assuming that the column is kept at atmospheric pressure (pressure drop along the column is Experimental Setup considered negligible). Experiments are performed in an Oldershaw tray column instrumented and equipped with a control system supplied Continuous Rectification at Partial Reflux by Normschliff Gerätebau (similar equipment is available This Oldershaw tray column is extremely versatile. It can from Normag GmbH Imenau). Other commercial teaching be operated continuously under partial reflux. With simple equipment for continuous distillation is offered, for example, modifications, the distillate may be directly fed to the reboiler by Armfield, Ltd. (
Vol. 45, No. 2, Spring 2011 107 DATA ANALYSIS subtracting one stage (corresponding to reboiler) from the Vapor-Liquid Equilibrium total number of equilibrium stages. At low pressure, vapor-liquid equilibrium of a component Overall Efficiencies i may be represented by: The experimental overall efficiency is given by: yP = xxγ PTσ ()1 it ii()i () Nideal Eov ()%(=×100 4) Nreal where yi and xi are the vapor and liquid molar fractions, σ respectively, Pi is its vapor pressure, γ is its activity coef- i where Nideal is the ideal number of equilibrium stages and Nreal Pσ ficient, and Pt is total pressure. i is computed by the Antoine is the actual number of trays (in this case Nreal = 5). equation and γi by Margules equations, whose constants may The overall efficiency can be estimated by empirical be found in the literature. correlations, namely, those by Drickamer and Bradford[12] == [13] [12] Since ∑∑xyii1, the liquid molar fraction may be and O’Connell. Drickamer and Bradford correlate Eov determined for any temperature by the relation: with the feed viscosity, μ, at the average temperature of the σσcolumn: Pxt = 11γγ()xP11()Tx+−()1222()xP()T () Ecov ()%.=−13 3668.logµ()P ()5 where x denotes the liquid composition vector. The vapor molar fraction can be then determined by Eq. (1). O’Connell used a viscosity and relative volatility, α12, depen- Number of Equilibrium Stages dence. His graphical result can be fit with −0.226 The number of equilibrium stages is obtained by the well- Ec%.=×50 36αµP () ov () 12 () known McCabe-Thiele method.[11] In this work the column has a rectifying section only, hence the operating line is: where α12 is the geometric average of the bottom and top R 1 values. y = x + x (33) nn+1 D R +1 R +1 Generalized Rayleigh Equation
The moles of liquid in the reboiler are related to its residue where yn+1 and xn are the cyclohexane vapor and liquid frac- composition by the Generalized Rayleigh equation: tions of trays n+1 and n, respectively. At total reflux (R = ∞) the operating line coincides with the diagonal line. The num- xBf, inal B dx ber of equilibrium stages is given by the number of outlined ln = B ()7 F ∫ xx− steps between x and x . The number of trays is obtained by DB D B xB,0
TABLE 1 where F and B are the initial and final Experimental Conditions and Results for the Experiments at Total Reflux moles of mixture in the reboiler, respec- tively. Knowing experimental pairs of Eov(%) P(W) T (˚C) T (˚C) x x D B D B data (x , x ), B/F fraction may be ob- Exp. Eq. 5 Eq. 6 D B tained by numerical integration. 75 83.9 92.6 0.878 0.281 95.1 53.1 64.8 125 84.2 92.7 0.864 0.273 92.1 53.2 64.9 Results and Discussion
1.0 1.0 In Table 1 the re- P = 125 W P = 125 W sults obtained at total 0.9 2a 0.9 2b R = ∞ R = 6 reflux at 75 and 125 0.8 0.8 W are presented. For 0.7 0.7 illustration, the Mc- 0.6 0.6 Cabe-Thiele diagram Operating line y y 0.5 0.5 for 125 W is plotted in
0.4 0.4 Figure 2. 0.3 0.3 McCabe-Thiele 0.2 0.2 diagram for a) total 0.1 0.1 reflux distillation x = x B x = x D x = x B x = x D 0.0 0.0 and b) continuous 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 rectification at par- x x tial reflux.
108 Chemical Engineering Education
Figure 2a. The minimum number of equilibrium stages was 0.7 4.76 and 4.61 for P = 75 and 125 W, respectively, giving rise to overall efficiencies of 95.1% and 92.1%. These results indicate 0.6 the column is more efficient when operated at 75 W, which is usually unexpected for the students. Actually, higher reboiler 0.5 powers generate higher internal flows. Although such effect Distillate may lead to a foreseen increase of mass transfer coefficients, 0.4 it also decreases the mean residence times of both phases 0.3 in each tray, which has a larger overall impact. Students are Composition frequently aware of the first effect, since they associate large 0.2 Residue Reynolds numbers to large Sherwood values, but neglect the second and more dominant effect in this case. 0.1
The experimental and predicted overall efficiencies are 0.0 listed in Table 1, and show that both correlations under- 0 5 10 15 20 25 30 35 40 45 50 55 estimate Eov. Students frequently get disappointed with such time (min) diverging results. Instructors notice that students almost Figure 3. Distillate and residue compositions during the always doubt their own experimental results, tending to ac- cept without hesitation model predictions. At this point it is batch rectification at P = 125 W and R = 6. essential to keep in mind that the overall column efficiency is a complex function of system properties, operating conditions, 5.0 y = -12137x4 + 4060.2x3 - 320.08x2 - 22.27x + 5.2365 and column geometric variables, and that common empirical R2 = 0.977 correlations take only some system properties into account, as 4.0 is the case of Eqs. (5) and (6) adopted here. Students should be encouraged to search data for similar systems to see that )
B 3.0
data are frequently 10 to 20% higher than O’Connell’s pre- x -
[11] D
dictions. x
The results obtained for the continuous rectification at 1/( 2.0 partial reflux (P = 125 W and R = 6) are given in Table 2 and Figure 2b. As may be observed, the overall efficiency 1.0 achieved is about the same of that obtained at total reflux for the same power (92.0% vs. 92.1%). Furthermore, the separa- 0.0 → tion achieved now (0.234 0.685) is inferior to that obtained 0.00 0.05 0.10 0.15 0.20 → at R = ∞ (0.273 0.864; see Table 1), which is the expected x B result for all students. Figure 3 shows the evolution of both distillate and residue Figure 4. Numerical data used for the integration of molar compositions during the batch rectification (P = 125 Rayleigh equation. W and R = 6). As expected, the cyclohexane content of the residue approaches zero since it is the lighter component. using a polynomial fitted to experimental data (see Figure 4). The fraction of undistilled liquid in the flask, B/F, was de- Many times students are not aware of the impact that the fitted termined by numerical integration of the Rayleigh equation, equation has upon the numerical solution. For instance, some groups try to integrate by the trapezoid rule, which gives rise TABLE 2 to scattered positive and negative data. Results for Continuous Rectification Experiment Students calculate B/F also by mass balance using the initial at P = 125 W and R = 6 (xB,0) and final (xB,final) residue compositions, and the average T (˚C) T (˚C) x x E (%) D B D B ov composition of distillate determined by refractive index. The 87.8 93.5 0.685 0.234 92.0 results found are frequently very similar. In this run (see Table 3) they found B/F = 0.696 and 0.667 using the Rayleigh TABLE 3 and mass balance approaches, respectively. B/F Fraction Obtained by Rayleigh Equation and Mass Balance Results for Experiment at P =125 W and R-6 ASPEN SIMULATIONS
xD B/F B/F Distillations at total reflux and partial reflux (P = (RI) (Rayleigh Eq.) (mass balance) 125 W) may be simulated using BatchSep 2006.5 by 0.410 0.696 0.667 Aspentech, Inc., a simulator frequently used in industry.
Vol. 45, No. 2, Spring 2011 109 This software allows the simulation of distillation ing a predetermined time to charge the tower with the same number columns under different operating conditions and of moles that our Oldershaw column contains initially. Subsequently, modes of operation. The embedded VLE calculations a null distillate flow must be imposed to reach total reflux condition were based on the RK-SOAVE method. (see Figure 5). The simulation is carried out in two consecutive steps: Total Reflux Simulation i) column charge and ii) distillation at total reflux. Table 5 compiles the pertinent data and options selection for the total reflux calcula- The total reflux simulation is carried out using tions, in order to help students to reproduce our results. the input specifications and additional information shown in Table 4. For this case, the column is as- Simulation of Continuous Rectification at Partial Reflux sumed to be initially filled with nitrogen, therefore a The continuous rectification at partial reflux (R = 6) is computed partial condenser has to be selected in order to purge with the input specifications and additional information compiled in it from the system. A feed stream was imposed dur- Table 6 ( page 112). For this simulation, the column has to be initially at total reflux and only then submitted to R = 6. Students should TABLE 4 realize this approach is in accordance with industrial columns start- Information for Aspen Simulation at Total Reflux up: distillation towers are frequently started up at total reflux, after an initial charge of feed, and this condition runs until both distillate Input Specifications and bottom compositions reach the desired project specifications; - Column initially empty (initially filled with N ) [14] 2 only then is the finite reflux ratio implemented. In our case, R = - Partial condenser 6, the column holdups and pressure drop values are those obtained - Feed stream to introduce the initial charge of mixture previously from the total reflux simulation, and the feed stream is the - Null distillate flow to get ∞ = R distillate recycled to column (see Figure 6, page 112). Table 7 (page Additional Information 113) compiles data and options for the continuous rectification at partial reflux calculations. - Column configuration number( of stages, including reboiler and condenser) Simulation Results - Reboiler geometry (dimensions and jacket type) The simulation results, presented in Table 8 (page 113) for both total - Power (P = 125 W) and partial reflux, are in good agreement with the measured values; the
- Condenser specifications pressure,( type, area, con- relative deviations found lie between 1.0 and 19.3%, being higher for R densing coefficient, coolant inlet temperature, coolant = 6. The calculated separation for R = ∞ (xD – xB = 0.584) is very near the mass flow, and coolant heat capacity) experimental one (xD – xB = 0.591) whereas it diverges for R = 6 (0.484 - Tray specifications and dimensions against 0.451, respectively). It is curious to notice that students usually
Operation Steps doubt their experimental observations against the simulated results, sug- gesting possible experimental errors for the deviations found for R = 6. - i) Column charge - ii) Distillation at ∞=R Nonetheless, in this case such large error may be attributed to the fact that some operating parameters, including pressure drop and holdups, were Results calculated at R = ∞ and assumed to be the same in the continuous partial - Column holdups reflux simulation. On the whole, students and instructors are amazed
- Pressure drop with simulation results due to the large number of input parameters and - Composition profile specifications, particularly those for geometrical variables.
- Temperature profile CONCLUSIONS This work describes an experiment in which students have the op- portunity to study dis- tillation, using an Old- ershaw tray column, under three different modes of operation: total reflux, continuous partial reflux, and batch with constant reflux. The effect of the internal Figure 5. Detail of an Aspen BatchSep 2006.5 window for the total reflux simulation. molar flows on column
110 Chemical Engineering Education TABLE 5 Specification and Options Selection for the Total Reflux Simulation Carried Out With Aspen Batchsep 2006.5 Window Tab Specifications/Selections Number of stages: 7 Configuration Valid phases: Vapor-Liquid Pot orientation: vertical Pot head type: Pot Geometry Top Hemispherical, bottom Hemispherical Diameter: 0.18m Height: 0.18m Jacket: Heating, Jacket covers head Pot Heat Transfer Setup Top height: 0.08m Condenser type: Partial Partial condenser spec: Coolant temperature Condensing coefficient: 100 cal/hr/m2 Condenser Area: 0.15 m2 Coolant inlet temperature: 18 ˚C Coolant mass flow: 100 kg/hr Coolant heat capacity: 4.18 kJ/kg/K Reflux Distillate mass flow rate: 0 kg/hr Heating option: Specified duty Jacket Heating Jacket Heating Duty: 0.125 kW Pressure/Holdups Pressure Pressure profile and holdups: Calculated Section: Start stage: 2 End stage: 6
Tray Specifications: Diameter: 0.03m Internal 1 Specification Spacing: 0.025m Weir height: 0.005m Lw/D: 0.83 % Active area: 90 % Hole area: 15 Discharge coefficient: 0.8 Initial condition: Empty Initial Conditions Main Initial temperature: 20 ˚C Initial pressure: 1.01325 bar Charge stage: 7 Valid phases: Liquid-Only Feed convention: On-stage Type: Fresh feed Flow rate basis: Mole
Conditions: Charge Stream Feed Main Temperature: 20 ˚C Pressure: 1.01325 bar
Composition: Composition basis: Mole-Frac CYCLO-01: 0.3 N-HEP-01: 0.7 N2: 0 Location: Charge stream/Feed Charge stream/Feed/Mole flow rate: 0.75 mol/min Changed Parameters Jacket/Heating/Duty: 0 kW Operating Step Charge Condenser/Coolant mass flow: 0 kg/hr Step end condition: Elapsed time End Conditions Duration: 10 min Location: Charge stream/Feed Charge stream/Feed/Mole flow rate: 0 mol/min Operating Step Distill Changed Parameters Jacket/Heating/Duty: 0.125 kW Condenser/Coolant mass flow: 100 kg/hr
Vol. 45, No. 2, Spring 2011 111 performance was investigated at total reflux by changing well as data analysis with the generalized Rayleigh equation. reboiler power. Furthermore, they are introduced to the use of simulation Results show that the efficiency decreases slightly with software, an important tool for their chemical engineering increasing flows. Moreover, column efficiency measured at instruction. partial reflux is analogous to that obtained at total reflux. For batch distillation, the application of the generalized Rayleigh ACKNOWLEDGMENTS equation provides good results. The results at infinite reflux Patrícia F. Lito and Ana Santiago wish to express their and for the continuous rectification at partial reflux were com- gratitude to Fundação para a Ciência e Tecnologia (Portugal) pared with those obtained by Aspen BatchSep simulations, for the grants provided (SFRH/BD/25580/2005 and SFRH/ giving rise to relative deviations between 1.0 and 19.3%. BPD/48258/2008), and to B.R. Figueiredo and Professor F. With this work students practice relevant concepts, includ- A. Da Silva for Aspen simulations and pictures support. ing vapor-liquid equilibrium, continuous vs. batch operation, McCabe-Thiele graphical method, and column efficiency as NOMENCLATURE B Final number of moles of liquid in the reboiler, mol
TABLE 6 Eov Overall efficiency, % Information for Aspen Simulation of the Continuous Rectification F Initial number of moles of liquid in the reboiler, mol
at Partial Reflux Nreal Number of real trays Input Specifications Nideal Ideal number of equilibrium stages P Reboiler power, W - Column initially at total reflux Pt Total pressure, atm - Total condenser Pσ Vapor pressure, atm - Total initial charge and composition R Reflux ratio RI Refractive index - Distillate flow to get R = 6 T Temperature, ˚C Additional Information x Molar fraction of liquid phase - Column configuration (number of stages, including reboiler and condenser ) y Molar fraction of vapor phase - Reboiler geometry (dimensions and jacket type) Greek letters α Relative volatility - Power (P = 125 W) 12 γ Activity coefficient - Column pressure drop and tray holdups μ Molar average liquid viscosity, cP - Distillate charge stream (charge stage, type, temperature, pressure) Subscripts Operating Steps B Bottom D Top - Distillation at R = 6 final Final condition Results i Component i - Composition profile 0 Initial condition - Temperature profile
Figure 6. Continuous partial reflux simulation flowsheet.
112 Chemical Engineering Education REFERENCES TABLE 7 1. Null, H.R., “Selection of a Specification and Options Selection for the Continuous Rectification Separation Process,” in Hand- at Partial Reflux Simulation Carried Out With Aspen Batchsep 2006.5 book of Separation Process Technology, Rousseau, R.W., Window Tab Specifications/Selections Ed., Wiley-Interscience, New Number of stages: 7 Configuration York (1987) Valid phases: Vapor-Liquid 2. Nath, R., and R.L. Motard, “Evolutionary Synthesis of Pot orientation: vertical Separation Processes,” AIChE Pot head type: J., 27, 578-587 (1981) Pot Geometry 3. Douglas, J.M., Conceptual Top Hemispherical, bottom Hemispherical Design of Chemical Process- Setup Diameter: 0.18m es, McGraw-Hill, New York Height: 0.18m (1988) Jacket: Heating, Jacket covers head Pot Heat Transfer 4. van der Lee, J.H., D.G. Olsen, Top height: 0.08m B.R. Young, and W.Y. Svrcek, “An Integrated, Real-Time Condenser Condenser type: Total Computing Environment for Reflux Reflux ratio: 6 Advanced Process Control Heating option: Specified duty Development,” Chem. Eng. Jacket Heating Jacket Heating Duty: 0.125 kW Ed., 35(3) 172 (2001) 5. Binous, H., “Equilibrium Holdup basis: Mole Staged Separations Using Mat- Pressure/Holdups Holdups Start Stage: 2 lab and Mathematica,” Chem. Stage Holdup: 5E-5 kmol Eng. Ed., 42(2) 69 (2008) Initial condition: Total reflux 6. Nasri, Z., and H. Binous, “Ap- Initial drum liquid volume fraction: 0.5 plications of the Peng-Robin- Main Initial temperature: 20 ˚C son Equation of State Using Initial pressure: 1.01325 bar Matlab,” Chem. Eng. Ed., 43(2) Initial Conditions 115 (2009) Composition basis: Mole-frac Total initial charge: 0.0075 kmol 7. Santoro, M., and M. Mazzotti, Initial Charge “HYPER-TVT: Development CYCLO-01: 0.3 and Implementation of an Inter- N-HEP-01: 0.7 active Learning Environment Charge stage: 7 for Students of Chemical and Valid phases: Liquid-Only Process Engineering,” Chem. Feed convention: On-stage Eng. Ed., 43(2) 175 (2009) Type: Distillate receiver recycle 8. Fleming, P.J., and M.E. Paulai- Charge Stream Flow rate basis: Mole Main tis, “A Virtual Unit Operations Distillate Laboratory,” Chem. Eng. Ed., Conditions: Temperature: 80 ˚C 36(2) 166 (2002) Pressure: 1.01325 bar 9. Fair, J.R., H.R. Null, and W.L. Bolles, “Scale-up of Plate Distillate receiver: 1 Efficiency From Laboratory Oldershaw Data,” Ind. Eng. Location: Charge stream/Distillate Charge stream/Distillate/Mole flow rate: 0.1 mol/s Chem. Process Des. Dev., 22, Operating Step Changed Parameters Liquid distillate receiver: 1 53-58 (1983) Rpartial 10. Humphrey, J.L., and G.E. Condenser pressure: 1.01325 Keller, Separation Process Jacket/Heating/Duty: 0.125 kW Technology, McGraw-Hill, New York (1997) 11. Seader, J.D., and E.J. Henley, Separation Process TABLE 8 Principles, 2nd Ed., John Wiley & Sons, New York Total Reflux and Continuous Rectification Simulations Results (2006) Bracketed values are relative deviations to the experimental ones. 12. Drickamer, H.G., and J.R. Bradford, Transactions T (˚C) T (˚C) x x AIChE, 39, 319-360 (1943) D B D B 42 Total reflux 13. O’Connell, H.E., Transactions AIChE, , 741-755 83.8 92.1 0.873 (1.0%) 0.289 (5.9%) (1946) (R = ∞) 14. Foust, A.S., L.A. Wenzel, C.W. Clump, L. Maus, and Cont. rectification 85.6 92.4 0.774 (13.0%) 0.290 (19.3%) L.B. Andersen, Principles of Unit Operations, 2nd (R = 6) Ed., John Wiley & Sons, New York (1980) p
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