Chapter 6 Chemical Reaction Engineering Mutiple Reactions

Objectives  Define different types of selectivity and yield  Choose a reaction system that would maximize the selectivity of the desired product given the rate laws for all the reactions occurring in the system.  Describe the algorithm used to design reactors with multiple reactions.  Size reactors to maximize the selectivity and to determine the species concentrations in a batch reactor, semi-batch reactor, CSTR, PFR, and PBR, systems.

Definition of Multiple Reaction  Parallel rxns (competing rxns) B A C  Series rxns (consecutive rxns) A B C  Complex rxns (Parallel + Series rxns) A + B C + D A + C E  Independent rxns A B + C D E + F k1 k2

Examples of Multiple Reaction  Parallel rxns (competing rxns) 2CO2 + 2H2O CH2=CH2 +O2 CH2-CH2  Series rxns (consecutive rxns) O O CH2-CH2 + NH3 HOCH2CH2NH2 EO EO (HOCH2CH2)2NH2 (HOCH2CH2)3NH2  Complex Rxns (Combination of parallel & series rxns) C2H5OH C2H4 + H2O C2H5OH CH3CHO + H2 C2H4 + CH3CHO C4H6 + H2O  Independent rxns (The cracking of crude oil to form gasoline) C15H32 C12H26 + C3H6 C8H18 C6H14 + C2H4 k1 k2 Monoethanolamine Dinoethanolamine Trinoethanolamine

Desired and Undesired Reaction Parallel Reactions D (Desired Product) A U (Undesired Product) The economic incentive Maximize the formation of D Minimize the formation of U kD kU Competing or side rxn Total cost Reaction cost Separation cost cost Low High A D A, U reaction separation Rxn-separation system producing both D & U Efficiency of a reactor system

Rate selectivity parameter, SDU Rate selectivity parameter, S D (Desired Product) A U (Undesired Product) The rate laws are Rate selectivity parameter = Instantaneous selectivity kD kU We want to maximize SDU Rate of formation of D = Rate of formation of U

Overall Selectivity, SDU ~ Overall Selectivity FD ~ Exit molar flow rate of desired product SDU = = FU Exit molar flow rate of undesired product For Batch Reactor ND ~ SDU = NU

Example 6-1: Comparison between SDU and SDU in a CSTR ~ ~ Mission: Develop a relationship between SDU and SDU in a CSTR Solution rD FD ~ SDU = and SDU = rU FU By the way, FD=rDV and FU=rUV rDV rD FD ~ SDU SDU = = = = FU rUV rU

Instantaneous Yield and Overall Yield Instantaneous Yield (Basis: Reaction Rate) rD YD = -rA Overall Yield (Basis: Molar Flow Rate) ND Mole of desired product formed at the end of reaction ~ YD = = For a batch system: NAo-NA Number of moles of key reactant consumed FD ~ YD = For a flow system: FAo-FA

Overall Selectivity Overall Yield

Note Different definitions for selectivity and yield Check carefully to ascertain the definition intended by the author From an economic standpoint, overall selectivities and yields are important in determining profits The instantaneous selectivities give insights in choosing reactors and reaction schemes that will help maximize the profit

Maximizing SDU in Parallel Reactions  Case 1: a1 > a2 , a = a1- a2 maximize SDU - keeping the concentration of reactant A as high as possible during the rxn - in gas phase rxn, we should run it without inerts and at high pressures to keep CA high - in liquid phase rxn, the use of diluents should be keep to a minimum - use a batch or plug-flow reactor

Maximizing SDU for one reactant  Case 2: a2 > a1 , a = a2- a1 maximize SDU - keeping the concentration of reactant A as low as possible during the rxn - in gas phase rxn, we should run it with inerts and at low pressures to keep CA low - in liquid phase rxn, the use of diluents should be keep to a maximum - use a CSTR or recycle reactor (product stream act as a diluent)

Maximizing SDU for one reactant Whether the reaction should be run at high or low T  Case 3: ED > EU - kD (rD) increases more rapidly with increasing temperature than does the kU. - keeping the temperature as high as possible to maximize SDU.  Case 4: EU > ED - keeping the temperature as low as possible to maximize SDU - not so low that the desired rxn does not proceed to any significant extent.

Example: Minimizing unwanted products (U & Q) for a single reactant A U (2) Q (3) - Pre-exponential factors are comparable - the activation energies of (1) & (2) are much greater than that of (3). at high temperature rQ << rD, rU (4) (5) - From (5), SDU is minimized at low concentration of A 1. High Temperatures (to minimize the formation of Q) 2. Low concentration of A (to minimize the formation of U) - Adding inerts, using low pressures, using CSTR or recycled reactor Textbook Example 6-2: 수업 후 해동에서 꼭 풀어보고 가세요

Reactor Selection and Operating Conditions Rate selectivity parameter, S D (Desired Product) A + B U (Undesired Product) The rate laws are Rate selectivity parameter=Instantaneous selectivity k1 k2

Different reactors and schemes for maximizing the desired product Figure 6-3 Different reactors and schemes for maximizing the desired product A B B A A B A B A B (a) CSTR (b) tubular reactor (c ) batch (d) semi-batch 1 (e) semi-batch 2 A B A B (f) Tubular reactor with side streams (g) Tubular reactor with side streams B A A B (i) Tubular reactor with recycle (h) Series of small CSTRs

Different reactors and schemes for maximizing the desired product Figure 6-3 Different reactors and schemes for maximizing the desired product

Example 6-3: Minimizing unwanted products for two reactants for the parallel reaction D (Desired Product) A + B U (Undesired Product) Case I : a1 > a2, b1 > b2, a = a1-a2 > 0, b = b1-b2 > 0 the rate selectivity parameter k1 k2 To maximize the SDU, maintain the concentration of both A and B as high as possible  a tubular reactor (Figure 6.3 (b))  a batch reactor (Figure 6.3 (c))  high pressures (if gas phase), reduce inert

Example 6-3: Minimizing unwanted products for two reactants for the parallel reaction D (Desired Product) A + B U (Undesired Product) Case II : a1 > a2, b1 < b2, a = a1-a2 > 0, b = b2-b1 > 0 the rate selectivity parameter k1 k2 To maximize the SDU, maintain CA high and CB low.  a semibatch reactor in which B is fed slowly into A. (Figure 6.3(d))  a tubular reactor with side stream of B continually (Figure 6.3(f))  a series of small CSTRs with A fed only to the first reactor (Figure 6.3(h))

Example 6-3: Minimizing unwanted products for two reactants for the parallel reaction D (Desired Product) A + B U (Undesired Product) Case III : a1 < a2, b1 < b2, a = a2-a1 > 0, b = b2-b1 > 0 the rate selectivity parameter k1 k2 To maximize the SDU, maintain the concentration of both A and B as low as possible  a CSTR (Figure 6.3(a))  a tubular reactor in which there is a large recycle ratio (Figure 6.3(i))  a feed diluted with inert material  low pressures (if gas phase)

Example 6-3: Minimizing unwanted products for two reactants for the parallel reaction D (Desired Product) A + B U (Undesired Product) Case IV : a1 < a2, b1 > b2, a = a2-a1 > 0, b = b1-b2 > 0 the rate selectivity parameter k1 k2 To maximize the SDU, maintain the concentration of both A and B as high as possible  a semibatch reactor in which A is slowly fed to B (Figure 6.3(e))  a tubular reactor with side stream of A (Figure 6.3(g))  a series of small CSTRs with fresh B fed to each reactor (Figure 6.3(h))

Maximizing the desired product in series reaction k1 k2 A B C  In parallel rxns, maximize the desired product  by adjusting the reaction conditions  by choosing the proper reactor  In series rxns, maximize the desired product  by adjusting the space-time for a flow reactor  by choosing real-time for a batch reactor

Maximizing the desired product in series reaction k1 k2 A B C Desired Product  If the first reaction is slow and second reaction is fast, it will be extremely difficult to produce species B.  If the first reaction (formation of B) is fast and the reaction to form C is slow, a large yield of B can be achieved.  However, if the reaction is allowed to proceed for a long time in a batch reactor or if the tubular flow reactor is too long, the desired product B will be converted to C.  In no other type reaction is exactness in the calculation of the time needed to carry out the reaction more important than in series reactions.

Example 6-4: Maximizing the yield of the intermediate product The oxidation of ethanol to form acetaldehyde is carried out on a catalyst of 4 wt% Cu-2wt% Cr on Al2O3. Unfortunately, acetaldehyde is also oxidized on this catalyst to form carbon dioxide. The reaction is carried out in a dilute concentrations (ca. 0.1% ethanol, 1% O2, and 98.9% N2). Consequently, the volume change with the reaction can be neglected. Determine the concentration of acetaldehyde as a function of space time. The rxns are irreversible and first-order in ethanol and acetaldehyde, respectively. k1 k2 CH3CH2OH(g) CH3CHO 2CO2

Solution

Reaction paths for different k’s in series reaction A B C k1 k2 For k1/k2>1, a Large quantity of B Can be obtained B For k1/k2<1, a Little quantity of B Can be obtained 1st rxn is slow 2nd rxn is fast A C Long rxn time in batch or long tubular reactor -> B will be converted to C

Algorithm for solution to complex reactions Steps in in Analyzing Multiple Reaction 1. Number each reaction. 2. Mole balance for each species. 3. Determine rij 4. Relate to rate of reaction of each species to the species for which the rate law is given. 5. Determine the net rate of formation of each species 6. Express rate laws as a function of Cj when X<<1. 7. Express rate laws as a function of mole when X>>1. 8. Combine all the above and solve the resulting set of equations Algorithm for solution to complex reactions

1. Mole balances for multiple reactions It is better to solve problems using moles (Nj) or molar flow rates (Fj) rather than conversion Reactor Gas Liquid Batch CSTR PFR/PBR Semibatch

. 2. Net Rates of Reaction Reaction 1: A + B 3C + D Key point: to write the net rate of each species (e.g. A, B, …) Reaction 1: A + B 3C + D Reaction 2: A + 2C 3E Reaction 3: 2B + 3E 4F Reaction q: A + ½C G . k1A k2A K3B kqA Net rates of reaction of A and B:

Total rate of formation of each species from all reaction Number Reaction Stoichiometry q rxns taking place The net rate of rxn for A: species reaction number

. 3. Rate laws rA=r1A+r2A= -k1ACACB-k2ACACC2 Reaction 1: A + B 3C + D Reaction 2: A + 2C 3E Reaction 3: 2B + 3E 4F . k1A k2A k3B 1 1 B rA=r1A+r2A= -k1ACACB-k2ACACC2 We need to determine the rate law for at least one species in each rxn.

4. Stoichiometry: Relative Rates of Reaction Generic reaction: aA + bB cC + dD Relative rate of reactions Multiple rxns: For example, Relative rates of Rxn in reaction i

5. Combining individual rate laws to find net law

6. Stoichiometry: Concentrations as a function of molar flow rate Liquid phase: Ideal Gas: Isothermal gas phase without DP: Net rate of formation

Multiple Reactions in a PFR/PBR (combining mole balance, rate law, and stoichiometry) Mole balance Rate law j Coupled ODEs Isothermal gas phase without DP: .

write the net rates of formation of NO, O2, and N2. Example 6-5: Write the rate law for each species in each reaction and then write the net rates of formation of NO, O2, and N2. Reaction 1: 4NH3 + 6NO  5N2 + 6H2O Reaction 2: 2NO  N2 + O2 Reaction 3: N2 + 2O2  2NO2 Solution

Example 6-6: Write mole balance on a PFR in terms of molar flow rates for each species Reaction 1: 4NH3 + 6NO  5N2 + 6H2O Reaction 2: 2NO  N2 + O2 Reaction 3: N2 + 2O2  2NO2 Solution

Example 6-7: Hydrodealkylation of Mesitylene in a PFR CH3 + H2 + CH4 k1 k2 The hydrodealkylation of mesitylene is to be carried out isothermally at 1500 R and 35 atm in a packed-bed reactor in which the feed is 66.7 mol% hydrogen and 33.3 mol% mesitylene. The volumetric feed rate is 476 ft3/h and the reactor volume (i.e. V=W/rb) is 238 ft3. M=mesitylene, X=xylene, T=toluene, Me=methane, H=hydrogen The bulk density of the catalyst has been included in the specific reaction rate (i.e., k1=k1’ rb) Plot the concentrations of hydrogen, mesitylene, and xylene as a function of space-time. Calculate the space-time where the production of xylene is a maximum (i.e., topt) .

Reaction 1: M + H  X + Me Reaction 2: X + H  T + Me Mole balances: Hydrogen Mesitylene Xylene Toluene Methane 2. Rate laws:

3. Stoichiometry: (no volume change with reaction, v=v0) a. Reaction rates: Reaction 1: -r1H = -r1M = r1X = r1Me Reaction 2: -r2H = -r2X = r2T = r2Me b. Flow rates: Combining and substituting in terms of the space-time ( ) If we know CM, CH, and CX, then CMe and CT can be calculated from the reaction stoichiometry. Consequently, we need only to solve the following three equations:

Ci t (hr) topt Parameter evaluation: We now solve these three equations simultaneously using POLYMATH. 2.0 1.5 1.0 0.5 0.0 t (hr) Ci topt CH CM CX 0.0 0.1 0.2 0.3 0.4 0.5

Multiple reactions in a CSTR For a CSTR, a coupled set of algebraic eqns analogous to PFR differential eqns must be solved. Rearranging yields where After writing a mole balance on each species in the reaction set, we substitute for concentrations in the respective rate laws. If there is no volume change with reaction, we use concentrations, Cj, as variables. If the reactions are gas-phase and there is volume change, we use molar flow rates, Fj as variables. q reactions in gas-phase with N different species to be solved

Example 6-8: Hydrodealkylation of Mesitylene in a CSTR Calculate the conversion of hydrogen and mesitylene along with the exiting concentrations of mesitylene, hydrogen, and xylene in a CSTR. 1. Mole Balances: 3. Stoichiometry: 2. Rate laws: 4. Combining and letting yields:

Example 6-8: Hydrodealkylation of Mesitylene in a CSTR We put these equations in a form such that they can be readily solved using POLYMATH. For t=0.5, the exiting concentrations are CH=0.0089, CM=0.0029 and CX=0.0033. The overall conversion is 2.0 1.5 1.0 0.5 0.0 Ci tCSTR 0.0 1.0 2.0 CH CX CM

Example 6-8: Hydrodealkylation of Mesitylene in a CSTR The moles of hydrogen consumed in reaction 1 are equal to the moles of mesitylene consumed. Therefore, the conversion of hydrogen in reaction 1 is Example 6-8: Hydrodealkylation of Mesitylene in a CSTR The conversion of hydrogen in reaction 2 is The yield of xylene from mesitylene based on molar flow rates exiting the CSTR for t=0.5 is The overall selectivity of xylene relative to toluene is

Selectivity and overall selectivity in a CSTR For a CSTR the instantaneous selectivity and the overall selectivity are the same. For example, the instantaneous selectivity of xylene w.r.t. toluene is The instantaneous selectivity The overall selectivity Mole balances of xylene and toluene yields Substituting in the instantaneous selectivity equation for rX and rT For all ideal CSTR

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