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Unformatted text preview: An Calculator NF ORMA T I ON SHEET PROVIDE D A18436 . Graph paper available Calculators may be used in this examination but must not be used to store text. Calculators with the ability to store text should have their memories deleted prior to the start of the examination. THE UNIVERSITY OF BIRMINGHAM Level C School of Engineering Department of Chemical Engineering. First Examination. CHEMICAL ENGINEERING 04 17043 (ChE 1CBP) Chemical and Biochemical Processes Time Allowed: Two Hours May/June, 2005 Answer ALL questions in Section A. To record your answers to section A, use the separate sheet provided and submit it at the end of the examination. BE CAREFUL NOT TO FOLD OR CREASE THE ANSWER SHEET. Answer T W0 questions chosen from Section B and record each of your answers in separate answer books. The figures in brackets at the end of each question or part of a question are an indication of the marks available. Sections A and B each count 50% of the total marks for this paper PLEASE TURN OVER... Page 1 of 9 A18436 An Calculator NF ORMA T I 0N SHEET PROVIDE D SECTION A: Answer ALL questions on the grid provided. Each question carries the same mark. The total of the marks for this section is 50. A reaction 2A —> B is to be scaled up for industrial production. Lab tests have shown that the conversion obtained in a batch reactor is 80 % afier 2 hours. Assuming the same behaviour at full scale, how many moles of A need to be supplied to the reactor to produce 88 moles B in 2 hours? a 55 moles b 88 moles c 110 moles d 176 moles e 220 moles At 25°C a rate constant has a value of 2 x 10'3 s". The activation energy is 50 kJ mol". What is the value of the rate constant for the same reaction at 85 °C? b 0.059s‘l c 5.9x 10‘3s" a2x10‘3s" d 4><10_3 s" e 0.059 m3mol" s" For a second order reaction 2A —> Products, the rate constant is to be deduced from a set of reaction kinetics data. A table of values of conversion versus time is available and all initial conditions in the reactor, such as compositions, are known. What variables should be plotted to give a graph with a slope equal to the rate constant, k? a -1n(1-X)vst b lanst c In M—X vs(M-1)CA0t M(1-X) Note M: Cgo/CAO d ( M—X ) vst X 1" e vsC t M(1—X) 1_X A0 Note [kl= Cgo/CAO A CSTR reactor of volume 2 m3 is fed with A at a rate of 3 x 10'3 m3s". If the conversion at the reactor outlet is 60 %, calculate the first order rate constant. a 2.25 x 10'3 s'1 b 1.25 x 10'2s'1 c 1.25 x 10%" d 5 ><10'3s‘l e 3 x10'3s'] PLEASE TURN OVER Page 2 of 9 An Calculator FORMATION SHEET PROVIDE D _~_—_—_,___T_____ 5. A plug flow reactor has a volume of 4 m and operates with a volumetric flow rate of 0.5 m3 min'l. The rate constant for the reaction A ——> B, which is carried out in the PFR is 0.05 min". Calculate the conversion, assuming a liquid phase reaction without volume change. a 0.2 b 0.330 c 0.419 d 0.5 e 0.735 6. A 3 batch reactor has a volume of 1 In and can be filled at a rate of 0.1 m3 min'1 and emptied at a rate of 0.05 m3 min'l. The rate constant is 0.02 min'1 and the conversion of the only reactant is 70%. 1 hour is allowed for cleaning. What is the batch cycle time? a 1.33 hours b 147 min c 2.5 hours d 134.6 min e 45 min Three CSTRs are to be operated in series. The reactors have a volumetric throughput of 0.5 m3 s'1 and a rate constant of 0.1 s'1 in each reactor. The overall conversion after the third tank is 85 %. Assuming the tanks to be of equal volume, calculate the volume of one tank. a 16.7 m3 b 25 m3 c 4.41m3 d 0.176 m3 e 12 m3 A gas phase reaction A + B a P is to be operated in a PFR without inerts. In the feed 1 mol A is added for every 1 mol B. What is the value of the expansion coefficient? Assume all of A reacts. a -0.5 b -0.25 c 1 d 4 e 2 A yeast, Pichia pastoris, is widely forecast to be a useful future expression system for the production of recombinant protein products. In earlier experiments the value for the maximum specific growth rate umax for this culture has been found to be 0.5 h'1 and the saturation constant Ks value for glucose was 2 kg m'3. It is proposed to use a 1 m3 bioreactor with a continuous feed containing glucose as the limiting substrate at a concentration of 40 kg m‘3 at a flow rate of 0.3 m3 h". The glucose concentration in the outlet would be: a 1kgm'3 b 2kgm'3 c 3kgm'3 d 4kgm'3 e 5kg1n'3 ___——______—_1___ I 10. A18436 Page 3 of 9 f the Yield Constant Yx/S in the last question is 0.55 kg cells (kg g1ucose)’ , the cell concentration in the reactor outflow would be: a 35 kgm'3 b 16.25 kgm'3 c 18.5 kgm‘3 d 20.35 kgm'3 e 12.15 kgm'3 PLEASE TURN OVER An Calculator NF ORMA T I 0N SHEET PR 0 VIDE I Figure 1 below is the pressure-temperature diagram for a pure substance. Refer to Figure 1 to answer questions 11 and 12: Figure l. 11. a. b. c. d. e. 12. a. b. c. d. e. 13. a. b. c. d. e. A18436 Page 4 of 9 Line AB Pressure Temperature Regions A, B and C represent the following: A = solid, B = liquid, C = vapour. A = solid, B = vapour, C = liquid. A = vapour, B = liquid, C = solid. A = solid-vapour mixture, B = liquid-vapour mixture, C = solid-liquid mixture. A = boiling region, B = melting region, C = sublimation region. Lines AB, BC and AC represent the following: AB = boiling points line, BC = melting points line, AC = sublimation line. AB = melting points line, BC = sublimation line, AC = boiling point line. AB = triple points line, BC = boiling points line, AC = critical line. AB = melting points line, BC = boiling points line, AC = sublimation line. AB = evaporation line, BC = critical points line, AC = triple points line. In the design of a fractionation column, if the slope of the top operating line (TOL) is at maximum (i.e. coincides with the 45° line), the column is then operating under Minimum reflux conditions. Total reflux conditions. Very low pressure. Very high vapour and liquid flow rates. The column is shut down. PLEASE TURN OVER An Calculator NF ORMA T 1 ON SHEET PRO VIDE D 14. On each tray of the distillation column, the statements below describe what takes place. Which of these statements is FALSE? :1. The vapour stream rises and mixes thoroughly with the falling liquid stream. b. Some of the more volatile component evaporates to join the rising vapour, and some of the less volatile component condenses to join the falling liquid. c. The vapour stream becomes richer in the less volatile component, and the liquid stream becomes richer in the more volatile component. d. Concentration of the more volatile component reaches maximum at the top tray. e. Concentration of the more volatile component is minimum at the bottom tray. 15. Below is the feed-line equation, whose slope describes the condition of the feed: q xF — - — x + — yq 1- q q 1-q where yq and xq are the mole fractions of the more volatile component (MVC) in the vapour and liquid at the feed plate, respectively, and xp is the mole fraction of the MVC at the feed. In which way does the value of the slope of the q- line describe the feed condition? a. Liquid at b.p = negative, partially vapour = O, totally vapour = 00. b. Liquid at b.p = positive, partially vapour = 00, totally vapour = 0. c. Liquid at b.p = 0, partially vapour = 1, totally vapour = 00. (1. Liquid at b.p = 1, partially vapour = 0, totally vapour = positive. e. Liquid at b.p = 00, partially vapour = negative, totally vapour = 0. A18436 PLEASE TURN OVER Page 5 of 9 An Calculator NF ORMA T ION SHEET PROVIDE D SECTION B: Answer TWO questions. All questions carry equal marks. 1. The reaction A + B —> C + D has been investigated experimentally in a batch reactor, to determine the reaction kinetics. Values of the concentration of A, CA, at various times, t, are available below for a temperature of 25 °C. I. 3000 4000 00213 By making the appropriate graphical plot, show that the reaction is second order and determine the rate constant, k. Note that C130 = 0.1449 mol dm'3. [25 marks] 2. In this question, constant density conditions can be assumed and the reactions are first order: the moles reacted per unit time in unit volume, -r = kC, where k is the rate constant and C is the concentration of substance which reacts. (a) A plug flow reactor of volume 1 m3 is being used for the first order reaction of substance A. The feed rate of A to the reactor is 0.2 kmol s'1 and the concentration of A in the feed is 3 kmol m'3. The conversion of A is 70 %. Calculate a value for the rate constant, k. [8 marks] (b) For the reaction in part (a), the frequency factor in the Arrhenius equation is 1.4 x 107 s'1 and the energy of activation is 50,000 J mol". At what temperature must the reactor be operated to achieve the rate constant calculated in part (a)? [7 marks] (c) A CSTR of volume 1 m3 is to be added after the PFR, to which it is connected in series. What is the reactant concentration after the CSTR, assuming operation of the CSTR at 50 °C? [10 marks] A18436 PLEASE TURN OVER Page 6 of 9 An Calculator NF ORMA T I 0N SHEET PR 0 VIDE I 3. (a) Bacteria, mammalian cells and whole plants each have characteristics that make them suitable for bioproduct manufacture. List the principal advantages of each and indicate in each case some typical products in current or projected manufacture. [7 marks] (b) There is more to a bioreactor than just a ‘stirred tank chemical reactor’. In what ways (e. g. process inputs and outputs, control loops, etc) is a bioreactor different? [8 marks] (c) The simplest model for the dependency of microbial specific growth rate u on the concentration of a limiting substrate S is given by Monod as: What is the significance of umax and Ks, and how may these parameters be determined using a continuous completely-mixed stirred tank bioreactor? Derive any relationships required in answering the question. [10 marks] 4. The feed to a fractionating column operating at atmospheric pressure contains 55 mole per cent of hexane and 45 mole per cent of toluene (methylbenzene). It is 65 mole per cent vapour. The top product (distillate) contains 90 mole per cent of hexane. (a) If the minimum number of theoretical stages is three, show on the vapour-liquid equilibrium diagram on either page 8 or 9 how the composition of the bottom product is found. What is that composition? [4 marks] (b) Determine the minimum reflux ratio, Rm, using the vapour-liquid equilibrium diagram on either page 8 or 9. [4 marks] (c) The column is to be operated with a reflux ratio of 1.5 to obtain a top product containing 90 mole per cent of hexane and a bottom product containing 10 mole per cent of hexane (this is not the answer to (a) l). The top product is produced at a rate of 45 kmol h'l. (i) Determine the feed rate and rate of production of the bottom product. [4 marks] (ii) Determine the number of theoretical stages required to obtain the desired products. [10 marks] (iii) Which is the feed stage? [3 marks] VAPOUR—LIQUID EQUILIBRIUM DATA FOR HEXANE-TOLUENE ARE ON PAGES 8 AND 9 (THE SAME ON EACH). It these diagrams are used gut your registration number on them and attach them to your answer book. A18436 PLEASE TURN OVER Page 7 of 9 An Calculator FORMA T I 0N SHEET PROVIDE I If this diagram is used for the calculations, But your registration number in the sgace below and attach it to {our answer book. Candidate' Number VAPOUR - LIQUID EQUIUBRIUM DATA FOR HEXANE - TOLUENE AT ATMOSPHERIC PRESSURE 1.013 BAR 1 .0 _ l—ll'l III'I I—- l m ,4. finnflngfiafiw "" =:..:= .. .a:::=§§qmnm"m::fi=.2-F_?:' Mfi—gfifiéfififiiififii'mififififififimfififiéw 0 9 ' Wflfigfiwfiaflh“fifi=nfififg _ '5" .. mfiafié—gfigfifiwmnfifiqm-y 4:"... 9&flw. Eiwafimi‘zfifl" 08 mfifiw ymgwgfimwfifi fiwfi%=:::a—-'m -wfifimmfi :.'§£§:E$E=fl “mm =. II- . I-IIII-l -mm-me$a.fl%==mfifiiamfi=fla= mem -.=-'-._:--'"- :ma .0 \l 9 .p. Mole Fraction of Hexane in the Vapour Phase .0 m .0 m Mole Fraction of Hexane in the Liquid Phase (The smallest scale division is a mole fraction of 0.01) A18436 PLEASE TURN OVER Page 8 of 9 An Calculator F ORMA T ION SHEET PROVIDE D If this diagram is used for the calculations, gut [our registration number in the sgace below and attach it to your answer book. Candidate' Number VAPOUR — LIQUID EQUIUBRIUM DATA FOR HEXANE - TOLUENE AT ATMOSPHERIC PRESSURE {1.013 BAR) III- I. ml!- Inm .1. --.... -:::-- -::a:::::.:.-.:..:a:=. ..:-.=:%5::-":..=---: firm-fl I... nfl- II- II I: .- .........._=_§-“§=.........:..:. =::§E..::fi_igfifi:fii_=_fi§==fiirnfl§fifi§v .3. 03 gammaaafifigm” hag? ....:.'.!'.:*'.:::§§gang?":g mnlnllmmm-nuumlnmnlunlull-mill- ‘I Inwln- M mfifififim" -==-'='-'==w-=.a§==- “:4:- m ' m-Eam.-w = m II II... .‘lllI—I- Ill :9 I...- n-n-m:. .' J. = V Ill-llI—Illlll—llI-lllllll II?- . fl III III’I _ umunmlnnmmflglnwmlm lm=Imm=§nm=l$ELmafi WME—IIIII“ Ell-"IIIIIIl-Ilfll'laa— =I mam III-III...”- Iulnllnflllum==gfifififii:a 0.7 .0 m .0 .p. Mole Fraction of Hexane in the Vapour Phase .0 m .0 N Mole Fraction of Hexane in the Liquid Phase (The smallest scale division is a mole fraction of 0.01) A18436 END Page 9 of9 PTO. A18436 Page 1 of 2 CHEMICAL ENGINEERING 04 17043 (1 CBP) INFORMATION SHEET FOR REACTION ENGINEERING (Dr J Wood) NOTATION . . . Glossary of Terms and Definitions L Rm.“ W W) or (m . _ _ _ _ (—rA) indicates that reactant A being used-up (r3) indicates that B is the product 2. The rate of reaction is expressed as rate-of change of me] A with respect to unit volume or some other appropriate property of the system. a) Reaction volume (V) . 8.314 J mol‘ K' (_ _ i «INA moi m—s (-1 V dt In a constant volume system, NA = CA V dNA = d(CA V) Fractional convetsron of species 1 l d(CA V) d(CA ) -3 -1 . , _ =___.__-_~__._mol ‘t x' “3 X" (es Species A) — ( r") V dt d m NB. For liquid phase reactors V at V9, the reactor .volume but for gases V = Vi-since all of the reactor is occupied by reacting phase. we mm A _ V, Volume of reaction system (eg. P V’ = N.R'I') Total mols in a system N mols of species i M 01 ‘ (eg. species A) b) 2-Phase Reactor The reaction occurs at the interphase between two phases - ldNA -2 -1 _r _-_ molm t ( A)- S dt S = interfacial area c) Heterogeneous Catalytic Reaction _ There are two possible ways of expressing rate (_ Q): _ 1 “NA mol m'2 t“ .._____ S dt , . ii . as a function of catal st mass _ ) y (w) 1 dN -l -l . . . . . . (—r )=—__—A mol(gcat) t — A w at x mole extent of reaction (eg. CMXA = Amotmt of product formed) Oi Page 2 of 2 3. Order of Reaction 4. 5. The rate of reaction is a function of reactant (and sometimes product) concentration. (—rA)=kf(CA,CB,Cc.....) = kc; ,C3 ,C2 where a, b, c are the respective orders of reaction with respect to CA , CB , Cc . . . . andn = a+b+c+. . . .. = Overallreactionorder Thus if, (—rA) = k CA reaction is FIRST ORDER (4,.) = k C1 reaction is SECOND ORDER (—rA) = k CA CB reaction is SECOND ORDER (ie. First order in cA and First order in CB) NOTE: a) Reaction order must be detemiined experimentally but most simple reactions ' are ZERO, FIRST or SECOND order. b) Complex reactions can have. simple kinetics (eg chain reactions or heterogeneous reactions) and cases of their kinetics can lead to 0, V2, 1%, 2 order reactions but in the case of very complex kinetics, for example: (_r )= k cA cB A (1+irA cA + chB)2 an overall reaction order cannot be stated The above equation is an example of heterogeneous kinetics. Arrhenius equation: [Sr] k = (frequency factor) e- Variable Volume Batch Reactors These are, in a sense, similar to plug flow reactors because the volume changes to maintain constant pressure. Thus for a nth order reaction, , N n (" 1'A) = k where, NA = number of moles of A V = Volume of the system NA = NAo (1 — XA) XA = fractional conversion of A __ NA0 — NA Initial mols — Final mols X __ —— = " NM Initial mols and V= V0 (1 + sXA) A18436 6. The volume of a system is a linear function of the number of moles and hence the conversion. Thus, 6 _ Final mols — initial mols _ Initial mols dXA _ k 05;“)(1—XA)“ . dt (1 + .9 X A )" “ When a = 0 (liquid phase, and gas phase where there is no mole change) (if: = k Caro—l) (1 _ XA)D FIRST ORDER (n= 1) dX . A = k(1 — XA) dXA =kdt =>=> —ln(1—XA)=kt (1 — XA) SECOND ORDER (n= 2) dX th = k CA0(1_ XA)2 IfCAo =Cno: dXA X ———=kC dt =>=> 4=kcot (l—XA)2 AD- (l—XA) A If CM ¢ Cg. (ie. when Cr;o = M CM) 1,, _M_'_X_A__ =k(M-1)th MO—XQ Design Equations X A dX a) Batch t =CA0 I A 0 (— rA) XA b) Pl g Flow (PFR) V' dXA U = FAo o (— I.A) ) CSTR V' X“ c -— = FAo (- 1'A) \l ...
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This note was uploaded on 06/06/2011 for the course CHEM 3040 taught by Professor Reddy during the Spring '10 term at Taylor's.

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exam pap-1 - An Calculator NF ORMA T I ON SHEET PROVIDE D...

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