ITK-330Chemical Reaction Engineering Multiple Reactions Dicky Dermawan www.dickydermawan.net78.net
[email protected] Significance SELDOM is the reaction of interest the only ONE that occurs in a chemical Reactor Some reactions are Desired (D), some are Undesired (U) Goal: Maximize D, minimize U SELDOM ONE Paralel reactions Series or consecutive reactions Mixed series – paralel reactions Classification A + B A + C C + D E A B C k 1 k 2 A B C k 1 k 2 Industrially Significant Examples CH 2 CH 2 O NH 3 HOCH 2 CH 2 NH 2 CH 2 CH 2 O (HOCH 2 CH 2 ) 2 NH (HOCH 2 CH 2 ) 3 N CH 2 CH 2 O CH 2 =CH 2 + O 2 2 CO 2 + H 2 O CH 2 CH 2 O C 2 H 5 OH C 2 H 4 + H 2 O C 2 H 5 OH CH 3 CHO + H 2 C 2 H 4 + CH 3 CHO C 2 H 6 + H 2 O Selectivity Selectivity: 2 1 o o ÷ = = A U D U D DU C k k r r S A D Desired A U Undesired k D k U 1 o A D D C k r = 2 o A U U C k r = Desired vs Undesired Maximizing Selectivity o 1 ÷ o 2 + - C A Keep it High Keep it Low Inerts No Yes Diluents No Yes Recommended Reactor Batch, Plug Flow CSTR 2 1 o o ÷ = = A U D U D DU C k k r r S + - Recommendations Other Definitions for selectivy Overall Selectivity, DU S ~ ) 12 6 ( ~ ÷ = = U of rate Flow Molar Exit D of rate Flow Molar Exit F F S U D DU Untuk reaktor Batch: U D DU N N S = ~ Yield A A D D N N N Y ÷ = 0 ~ Instantaneous Yield at a point: Overall Yield: Batch System: Flow System: A D D r r Y ÷ = A A D D F F F Y ÷ = 0 ~ Parallel Reactions – Simple Example Senyawa A terdekomposisi menurut persamaan: 2 A ÷ R r R = 0.7. C A 2 A ÷ S r S = 0,1.C A Suatu larutan yang mengandung A dengan konsentrasi 2 mol/L diumpankan ke dalam reaktor pipa dengan waktu tinggal 36 menit. Tentukan konsentrasi A, R, dan S pada aliran yang meninggalkan reaktor. Simple Paralel Reactions: Hand Calculation Solvable min 3 . 0 min 06 . 0 min 002 . 0 3 3 2 3 1 2 2 3 1 1 · = = ÷ = = ÷ · = = ÷ ÷ mol dm k C k r Y A k C k r B A dm mol k k r X A A Y A B x P6-6 A Consider the following system of gas-phase reactions: min 3 . 0 min 06 . 0 min 002 . 0 3 3 2 3 1 2 2 3 1 1 · = = ÷ = = ÷ · = = ÷ ÷ mol dm k C k r Y A k C k r B A dm mol k k r X A A Y A B x B is the desired product, and X and Y are foul pollutants that are expensive to get rid of. The specific reaction rates are at 27°C. The reaction system is to be operated at 27°C and 4 atm. Pure A enters the system at a volumetric flow rate of 10 dm 3 /min. a. Sketch the instantaneous selectivities (S BX , S BY , and S B/XY = r B /(r x + r y ) ) as a function of . the concentration of C A . b. Consider series of reactors. What should be the volume of the first reactor? c. What are the effluent concentrations of A, B, X, and Y from the first reactor? d. What is the conversion of A in the first reactor? e. If 90% conversion of A is desired, what reaction scheme and reactor sizes should you use? f. Suppose that E 1 = 10,000 cal/mol, E 2 = 20,000 cal/mol, and E 3 = 30,000 cal/mol. What temperature would you recommend for a single CSTR with a space-time of 10 min . and an entering concentration of A of 0.1 mol/dm 3 ? Paralel Reactions – Economic Tradeoff Series Reactions: Hand Calculation Solvable P6-7 B Pharmacokinetics concerns the ingestion, distribution, reaction, and elimination reactions of drugs in the body. Consider the application of pharmacokinetics to one of the major problems we have in the united states, drinking and driving. Here we shall model how long one must wait to drive after having a tall martini. In most states the legal intoxication limit is 1.0 g of ethanol per liter of body fluid. (In Sweden it is 0.5 g/L, and in Eastern Europe and Russia it is any value above 0.0 g/L.) The ingestion of ethanol into the bloodstream and subsequent elimination can be modeled as a series reaction. The rate of absorption from the gastrointestinal tract into the bloodstream and body is a first-order reaction with a specific rate constant of 10 h -1 . The rate at which ethanol is broken down in the bloodstream is limited by regeneration of a coenzyme. Consequently, the process may be modeled as a zero order reaction with a specific rate of 0.192 g/h.L of body fluid. How long would a person have to wait (a) in the united states; (b) in Sweden; and (c) in Russia if they drank two tall martinis immediately after arriving at a party? How would your answer change if (d) the drinks were taken hour apart; (e) the two drinks were consumed at a uniform rate during the first hour? (f) Suppose that one went to a party, had one and a half tall martinis right away, and then received a phone call saying an emergency had come up and they needed to drive home immediately. How many minutes would they have to reach home before he/she became legally intoxicated, assuming that the person had nothing further to drink? (g) How would your answers be different for a thin person? A heavy person? For each case make a plot of concentration as a function of time.(Hint: Base all ethanol in the blood as a function of time.) What generalizations can you make? What is the point of this problem? Additional Information: Ethanol in a tall martini: 40 g Volume of a body fluid: 40 L 2 1 Series Reactions: Hand Calculation Solvable The elementary liquid phase series reaction: is carried out in a 500 dm 3 batch reactor. The initial concentration of A is 1.6 mol/dm 3 . The desired product is B and separation of the undesired product C is very difficult and costly. Because the reaction is carried out at a relatively high temperature, the reaction is easily quenched. Additional information: Cost of pure reactant A = $10/mol A Selling Price of Pure B = $50/molB Separation cost of A from B = $50/mol A Separation cost of C from B = $30 (e 0.5Cc – 1 ) k 1 = 0.4 hr -1 , k 2 = 0.01 hr -1 @ 100°C C B A k k ÷÷ ÷ ÷÷ ÷ 2 1 P6-9 B Series Reactions: Hand Calculation Solvable (lanjutan) a) Assuming that each reaction is reversible, plot the concentrations of A, B, and C as a function of time b) Calculate the time the reaction should be quenched to achieve maximum profit c) For a CSTR space-time of 0.5 h, what temperature would you recommend to maximize B? (E 1 = 10000 cal/mol, E 2 = 20000 cal/mol) d) Assume that the firs reaction is reversible with k -1 = 0.3 h -1 . Plot the concentration of A, B, and C as a function of time e) Plot the concentrations of A, B, and C as a function of time for the case where both reactions are reversible with k -2 = 0.005 h -1 f) Vary k 1 , k 2 , k -1 , and k -2 . Explain the consequence of k 1 > 100 and k 2 <0.1 with k -1 = k -2 = 0 Systematic Approach to handle Multiple Reaction Problems Mole Balances for Multiple Reactions Use moles N j or molar flow rates F j rather than Conversion X. Use differential form rather than integral form Metode Penyelesaian Untuk Reaksi Jamak: Lanjutan • Net Rates of Reaction for N Reactions Taking Place • Hukum Laju (Rate Law) untuk tiap reaksi dinyatakan dalam konsentrasi tiap spesi yang bereaksi. • Stoichiometry: Relative Rates of Reaction eg: a A + b B c C + d D (reaction i) d r c r b r a r iD iC iB iA = = ÷ = ÷ ¿ = = N i ij j r r 1 species Reaction number Reactants Metode Penyelesaian Untuk Reaksi Jamak: Lanjutan Stoichiometry: Concentrations Liquid Phase, 0 u j j F C = T T P P F F C T j j 0 0 | | . | \ | = For Ideal Gasses: Dengan: 0 0 u T F 0 T C ¿ = = n j j T F F 1 0 0 0 RT P C T = dan For | | . | \ | = T j T j F F C C 0 0 P P T T 0 Isothermal System. NO Pressure Drop, Metode Penyelesaian Untuk Reaksi Jamak: Lanjutan Combining Step: Example for gas reaction in PFR | | . | \ | = = = | | . | \ | = = = ¿ ¿ = = T j T T T j q i ij j j T j T T T q i i F F C F F C fn r r dV dF F F C F F C fn r r dV dF 0 1 0 1 0 1 0 1 1 1 1 1 ..., , . . . ..., , Review on the Role of CSTR & Net Rate of Reaction Principles ¿ = = N i ij j r r 1 CSTR Design for Multiple Reactions ¿ = = N i ij j r r 1 Mole Balances 0 V r F F r F F V A A 0 A A A 0 A = · + ÷ ¬ ÷ ÷ = 0 r C C A A 0 A 0 = t · + ÷ ¬ u = u All liquid reactions & gas with all c = 0 Kinetic expression Write down for ALL species Stoichiometry d r c r b r a r iD iC iB iA = = ÷ = ÷ Auxiliary expressions: ¿ = = n j j T F F 1 0 0 0 RT P C T = | | . | \ | = T j T j F F C C 0 0 P P T T 0 Combining equations form n nonlinear equation with n variables, i.e. F A , F B , F C ,… or CA , C B , C C ,…. n = number of species involved The following liquid phase reactions are carried out isothermally in a 50 L PFR: A + 2 B ÷ C + D r D1 = k D1 . C A . C B 2 2 D + 3 A ÷ C + E r E2 = k E2 . C A . C D B + 2 C ÷ D + F r E3 = k E3 . C B . C C 2 P6-13 B Maximizing Selectivity: Semibatch Reactor A + B ÷ D A + B ÷ U B 2 A 1 D C C k r · · = 2 B A 2 D C C k r · · = B A 2 1 U D U / D C C k k r r S · = = Keep C A high, C B low A B Semibatch Reactor Design A B B A For the case P6-13B, which one is better to maximize the production of D? A + 2 B ÷ C + D r D1 = k D1 . C A . C B 2 2 D + 3 A ÷ C + E r E2 = k E2 . C A . C D B + 2 C ÷ D + F r E3 = k E3 . C B . C C 2 Semibatch Reactor for Multiple Reaction ¿ = = N i ij j r r 1 Laju masuk – laju keluar + laju pembentukan = laju akumulasi Misalnya reaktor mula-mula hanya berisi A dengan volume V 0 dt dN V r 0 0 A A = · + ÷ B dialirkan ke reaktor dengan laju konstan u o dt dN V r 0 F B B 0 B = · + ÷ C,D,E,F mula-mula tidak ada; tidak dialirkan dt dN V r 0 0 C C = · + ÷ dt dN V r 0 0 D D = · + ÷ dt dN V r 0 0 E E = · + ÷ dt dN V r 0 0 F F = · + ÷ t u V V 0 0 · + = Auxiliary equations: 0 B o 0 B C u F · = V C N j j · = Kinetics: Stoichiometry: d r c r b r a r iD iC iB iA = = ÷ = ÷ Performance equations: Packed Bed Reactor Design for Multiple Reactions ¿ = = N i ij j r r 1 d r c r b r a r iD iC iB iA = = ÷ = ÷ Mole Balances All liquid reactions follows exactly the same rule as PFR Design Kinetic expression Write down for ALL species Stoichiometry Auxiliary expressions: ¿ = = n j j T F F 1 0 0 0 RT P C T = T T 0 Combining equations form (n+1) ordinary differential equations with (n+1) variables, i.e. F A , F B , F C ,… or CA , C B , C C ,…. AND P n = number of species involved j j ' r dW dF = 0 u = u 0 T j 0 T j P P F F C C · | | . | \ | = Pressure drop 0 T T 0 0 0 F F P / P P T T 2 dW dP · · · o ÷ = Packed Bed Reactor Design for Multiple Reactions P6-16C The following hydrodealkylation reactions occur . over a Houdry Detol catalyst near 800 K and 3500 kPa: (1) H 2 + C 6 H(CH 3 ) 5 ÷ C 6 H 2 (CH 3 ) 4 + CH 4 r 1 = k 1 .C H2 ½ .C 11 (2) H 2 + C 6 H 2 (CH 3 ) 4 ÷ C 6 H 3 (CH 3 ) 3 + CH 4 r 2 = k 2 .C H2 ½ .C 10 (3) H 2 + C 6 H 3 (CH 3 ) 3 ÷ C 6 H 4 (CH 3 ) 2 + CH 4 r 3 = k 3 .C H2 ½ .C 9 (4) H 2 + C 6 H 4 (CH 3 ) 2 ÷ C 6 H 5 (CH 3 ) + CH 4 r 4 = k 4 .C H2 ½ .C 8 (5) H 2 + C 6 H 5 (CH 3 ) ÷ C 6 H 6 + CH 4 r 5 = k 5 .C H2 ½ .C 7 k 5 = 2,1 (mol/L) -½ .s -1 k 1 /k 5 = 17.6 k 2 /k 5 = 10 k 3 /k 5 =4.4 k 4 /k 5 = 2.7 6 , 17 5 1 k k = 10 5 2 k k = 4 , 4 5 3 k k = 7 , 2 5 4 k k = The feed is equimolar in hydrogen and pentamethylbenzene. (a) For an entering volumetric flowrate of 1 m 3 /s, what ratio of hydrogen to pentamethylbenzene and what PFR reactor volume would you recommend to maximize the formation of C 6 H 4 (CH 3 ) 2 ? . [Hint: Plot the overall selectivity as a function of reactor volume] P6-24C Methanol Synthesis A new catalyst has been proposed for the synthesis of methanol from carbon monoxide and hydrogen gas. This catalist is reasonably active between temperatures of 330 K to about 430 K. The isothermal reactions involved in the synthesis include: CO + 2 H 2 CH 3 OH CO + H 2 O CO 2 + H 2 CH 3 OH CH 2 O + H 2 The reactions are elementary and take place in the gas phase. The reaction is to be carried out isothermally and as a first approximating pressure drop will be neglected. The feed consists of 7/15 hydrogen gas, 1/5 carbon monoxide, 1/5 carbon dioxide, and 2/15 steam. The total molar flow rate is 300 mol/s. The entering pressure may be varied between 1 atm and 160 atm and the entering temperature between 300 K and 400 K. Tubular (PFR) reactor volumes between 0.1 m3 and 2 m3 are available for use. a. Determine the entering conditions of temperature and pressure and reactor volume that will optimize the production of methanol. (Hint: first try T 0 = 330 K at P 0 = 40 atm, then try T 0 = 380 K and P 0 = 1 atm) b. Vary the ratios of the entering reactant to CO 2 (i.e. thetaH 2 and thetaH 2 O) to maximize methanol production. How do your results compare with those in part (a)? Describe what you find. Methanol Synthesis ( ) 2 3 2 1 001987 . 0 298 1 1 620 , 30 exp 667 . 131 | | . | \ | ( ¸ ( ¸ | . | \ | ÷ ÷ = mol dm T T R K ( ¸ ( ¸ | . | \ | ÷ ÷ = 298 1 1 834 , 9 exp 943 , 103 2 T R K CO + 2 H 2 CH 3 OH CO + H 2 O CO 2 + H 2 CH 3 OH CH 2 O + H 2 P6-24 C K mol cal R K T dm V 987 . 1 , ] [ , 40 3 = = = Data: 1 2 3 1 1 330 1 400 , 31 5 . 2 exp 933 . 0 ÷ | | . | \ | ( ¸ ( ¸ | | . | \ | | . | \ | ÷ · · = s mol dm T R k s mol dm T R k · ( ¸ ( ¸ | . | \ | ÷ · = 3 2 1 300 1 000 , 18 exp 636 . 0 1 3 1 325 1 956 , 28 5 . 1 exp 244 . 0 ÷ ( ¸ ( ¸ | | . | \ | | . | \ | ÷ · · = s T R k Series Reactions The elementary liquid phase series reaction: is carried out in a 500 dm 3 batch reactor. The initial concentration of A is 1.6 mol/dm 3 . The desired product is B and separation of the undesired product C is very difficult and costly. Because the reaction is carried out at a relatively high temperature, the reaction is easily quenched. Additional information: Cost of pure reactant A = $10/mol A Selling Price of Pure B = $50/molB Separation cost of A from B = $50/mol A Separation cost of C from B = $30 (e 0.5Cc – 1 ) k 1 = 0.4 hr -1 , k 2 = 0.01 hr -1 @ 100°C C B A 2 1 k k ÷ ÷÷ ÷ ÷÷ ÷ (b) Calculate the time the reaction should be quenched to achieve the maximum profit.