Chemical Reactor Design Youn-WLWoo Lee School of Chemical and Biological Engineering Seoul National University 155-741, 599 Gwanangro, Gwanak-gu, Seoul, Korea [email protected] http://sfpl.snu.ac.kr Chapter 4 Isothermal Reactor Design Chemical Reactor Design 化學反應裝置設計 Seoul National University Objectives • Describe th e alihlgorithm thllhhat allows the read er to sol ve ch hilemical reaction engineering problems through logic rather than memorization. • Size batch reactors, semibatch reactors, CSTRs, PFRs, and PBRs for isothermal operation given the rate law and feed conditions. • Studying a liqu id -phase batc h reacto r to determine t he spec ific reaction rate constant needed for the design of a CSTR. • Design of a tubular reactor for a gas -phase pyrolysis reaction . • Account for the effects of pressure drop on conversion in packed bdbed tu blbular reactors and di in pack kdbded bed sph eri cal reactors. Seoul National University Fig. 4-1 Isothermal Reaction Design Algorithm for Conversion Seoul National University Algorithm for isothermal reactor design 1. Mole balance and design equation 2. Rate law 3. Stoichiometry 4. Combine 5. Ev aluate We can solve the equations in the combine step either A. Graphically (Chapter 2) BNB. Numer ica l(Al (Appen diA4)dix A4) C. Analytical (Appendix A1) D. Software packages (polymath) Seoul National University French Menu Analogy Seoul National University French Algorithm for isothermal reactors Menu Analogy Seoul National University 4.2.1 Batch Operation For constant volume batch reactor, themolebalancecanbewritten in terms of concentration dN 1 A 1 dN A 1 dN A dN A /V0 dC A rA rA V dt V dt V0 dt dt dt Generally, when analyzing laboratory experiments, it is best to process the data in terms of the measured variable. Because concentration is the measured variable for most liquid-phase reactions, the general mole balance equation applied to reactions in which there is no volume change becomes dC A r dt A This is the form we will use in analyzing reaction rate data in Chap 5. Seoul National University Reaction time in Batch Operation Algorithm for isothermal reactor design A B 1. Mole balance dX N A0 rAV0 & Design equation dt 2 2. Rate law rA kCA irreversible, 2nd order in A 3. Stoichiometry C A C A0 (1 X ) dX 2 4C4. Com bitibination kCA0 (1 X ) dt 2nd order Isothermal Liquid-phase dX Batch reaction kCA0dt (1 X )2 5. Analytical Evaluation t 1 X dX 1 X dt t 2 0 kCA0 0 (1 X ) kCA0 1 X Seoul National University Reaction time in Batch Operation Typical cycle times for a batch polymerization process tt = tf +t+ te + tR +t+ tc Activity Time (h) 1. Charge feed to the reactor and agitate, tf 1.5-3.0 2. Heat to reaction temperature, te 0.2-2.0 ViVaries 3. Carry out reaction, tR 0.5-1.0 4. Empty and clean reactor, tc Total cycle time excluding reaction 303.0-606.0 Batch polymerization reaction times may vary between 5 and 60 hours. Decreasing the reaction time with a 60-h reaction is a critical problem. As the reaction time is reduced (e.g. 2.5 h for a 2nd-order reaction with X=0.9 and -3 -1 kCA0=10 s ), it becomes important to use large lines and pmpspumps to achieve rapid transfer and to utilize efficient sequencing to minimize the cycle time. Seoul National University Batch Reaction Times A B dX r Mole balance A V dt N A0 First - order Second order Rate law 2 rA kC A rA kCA N A CA CA0 (1 X ) Stoichiometry (V=V0) V0 dX dX 2 Combine k(1 X ) kC A0 (1 X ) dt dt 1 1 X Integration t ln t k 1 X kC A0 (1 X ) Seoul National University Batch Reaction Times -4 1 3 1 1st - order (X 0.9, k 10 s ) 2nd order (X 0.9, kCA0 10 s ) 1 1 X tR ln tR k 1 X kC A0 (1 X ) 1 1 0.9 ln k 1 0.9 kC A0 (1 0.9) 2.3 9 k kC A0 2.3 9 4 1 10 s 103 s 1 23,000 sec 9,000sec 6.4hr 2.5hr Seoul National University Batch Reaction Times Table 4-3 The order of magnitude of time to achieve 90% convers ion For first- and second-order irreversible batch reactions 1st-order 2nd-order Reaction time -1 -1 k (s ) kCA0 (s ) tR 10-4 10-3 Hours 10-2 10-1 Minu tes 1 10 Seconds 1,000 10,000 Milliseconds Seoul National University Design a Reactor to Produce of ethylene glycol Design a CSTR to produce 200 million pounds of ethylene glycol per year by hydrolyzing ethylene oxide. However, before the design can be carried out, it is necessary to perform and analyze a batch reactor experiment to determine the specific reaction rate constant (kA). Since the reaction will be carried out isothermally, kA will need to be determined only at the reaction temperature of the CSTR. At high temperature there is a significant by- product formation, while at temperature below 40oC the reaction does not proceed at a significant rate; consequently, a temperature of 55oChasbeen chosen. Since the water is usually present in excess, its concentration may be considered constant during the course of the reaction. The reaction is first-order in ethylene oxide. OCHO CH2-OH H2SO4 CH2-CH2 + H2O CH2-OH A + B Catalyst C Seoul National University Example 4-1 Determining k from Batch Data In the lab experiment, 500mL of a 2 M solution (2 kmol/m3)ofEOin water was mixed with 500mL of water containing 0.9 wt % sulfuric acid o catalyst. At T=55 C, the CEG was recorded with time. Determine the specific reaction rate at 55oC. Time Concentration of EG EO + H2O → EG (min) (kmol/m3) A + B → C 0.0 0.000 0.5 0.145 1.0 0.270 1.5 0.376 2.0 0.467 3.0 0.610 4.0 0.715 606.0 0. 848 10.0 0.957 Seoul National University Problem Solving Algorithm Example 4-1 Determining k from Batch Data A. Problem statement. Determine the kA D. Assumptions and approximations: B. Sketch Assumptions C. Identify 1. Well mixed C1. Relevant theories A, B, C batch 2. All reactants enter at the same time 3. No side reactions Rate law: rA k AC A 4. Negligible filling and emptying time dN A Mole balance: rAV 5. Isothermal operation C2. Variables dt Apppproximations Dependent: concentrations, Ci 1. Water in excess (CH2O~constant) Independent: time, t CB~CBO C3. Knowns and unknowns E. Specification. The problem is neither Knowns: CEG =f(time) overspecified nor underspecified. Unknowns: 1. CEO =f(time) F. Related material. This problem uses the 2. kA mole balances developed in Chap. 1 3. Reactor volume for a batch reactor and the C4. Inputs and outputs: reactant fed stoichiometry and rate laws developed all at once a bhbatch reactor in Chap. 3. C5. Missing information: None G. Use an Algorithm.(figs 4-1 & 4-2) Seoul National University Problem Solving Algorithm Example 4-1 Determining k from Batch Data 1 dN A 1. MOLE BALANCE r Batch reactor that is well-mixed V dt A Since water is present in such excess, the concentration of water at any time t is virtually the same as the initial concentration and the rate 2RATELAW2. RATE LAW rA kCA law is independent of the concentration of H2O. (CB~CB0) 3. STOICHIOMETRY Species symbol Initial Change Remaining Concentration CH2CH2O A NA0 -NA0XNA=NA0(1-X) CA=CA0(1-X) H2OBO B ΘBNA0 - NA0X NB=NA0(ΘB-X) CB=CA0(ΘB-X) CB~ CA0 ΘB = CB0 (CH2OH)2 C0 NA0XNC =NA0XCC=CA0X NT0 NT =NT0 -NA0X Seoul National University Problem Solving Algorithm Example 4-1 Determining k from Batch Data 1 dN A r V dt A dC A dC A 4. COMBINING rA , r kC kC dt A A dt A Mole balance Rate law 5. EVALUATE For isothermal operation , k is constant: CA dC tt C A kdt k dt ln A0 kt CA0 C A 00 C A kt C A C A0e Seoul National University Problem Solving Algorithm Example 4-1 Determining k from Batch Data The concentration of EG at any time t can be obtained from the reaction stoichiometry A + B C NC N A0 X N A0 N A NC NC kt CC C A0 C A C A0 (1 e ) V V0 kt CC C A0 (1 e ) C C ln A0 C kkt C A0 Seoul National University Example 4-1 Determining k from Batch Data Rearranging and taking the logarithm of both side yields 1 rA (0.311 min )CA C C ln A0 C kt C The rate law can now be used in the design A0 of an industrial CSTR. Note that this rate law was obtained from the lab-scale batch We see that a plot ln[(CA0-CC)/CA0] as a function of t will be a straight line with reactor (1000 mL). a slope –k. 1 ln10 2.3 1 k 0.311 min 0.6 t2 t1 8.95 1.55 Time CA0 CC 0 AA CC (min) C A0 )/ 0.0 1.000 C 0.1 -C 0.5 0.855 A0 0.06 C 101.0 0. 730 (( 1.5 0.624 2.0 0.533 3.0 0.390 0.01 4.0 0.285 024681012 6.0 0.152 1.55 t (min) 8.95 10.0 0.043 Seoul National University 4.3 Design of CSTR Design Equation for a CSTR F X Mole balance V A0 (rA )exit F v C v0CA0 X V C A0 X A0 0 A0 V the space time rA v0 rA For a 1st-order irreversible reaction, the rate law is Rate law rA kCA 1 X CA0 X CbiCombine k 1 X kCA Rearranggging k CSTR relationship X between space time and 1 k conversion for a 1st-order liquid-phase rxn Seoul National University 4.3.1 A single CSTR We could also combine Eq (3-29) and (4-8) to find the exit concenttitration o fACf A, CA: k k X C A C A0 (1 X ) C A0 1 1 k 1 k 1 k k C A0 C A0 1 k 1 k C C A0 A 1 k C exit concentration of A C A0 A 1 k Seoul National University 4.3.2 CSTRs in Series CA1, X1 CA0 v0 CA2, X2 -rA1, V1 -rA2, V2 st For 1 -order irreversible reaction with no volume change (v=v0) is carried out in two CSTRs placed in series.