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Applied Reaction Kinetics

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Applied Reaction Kinetics κίνησις "kinesis", movement or to move APPLIED REACTION KINETICS Friday A01 09:00-11:00 (Assoc. prof. Bohumil Bernauer, A27, [email protected], +420220444017 ) Friday BS9 13:00-15:00 (Dr. Milan Bernauer, H08, [email protected], +420220444287) Resources and references • Notes from lectures • Internet web.vscht.cz/bernauem/ • Textbooks Fogler Scott H.: Elements of Chemical Reaction Engineering, 4th Edition, Prentice Hall, 2006. (http://www.engin.umich.edu/~cre/) Missen R.W., Mims C.A., Saville B.A., Introduction to Chemical Reaction Engineering and Kinetics, J. Wiley&Sons, N.Y. 1999. • Journals (on-line) • Software MS Excel, (Matlab, Octave, Athena Visual Studio, FORTRAN, Maple….) Fischer-Tropsch (SASOL, RSA ) WGS (BASF, FRG) N2O decomposition (IPC AS, CZ) Chemical reactor(s) heart of chemical process Methane aromatization (ICTP, CZ) Raw material separation reaction separation product r( composition , T , P ,..., params ) Summary of the 1st lecture • Stoichiometry • Extent of reaction • Fractional conversion of key component • Stoichiometric matrix • Balance of chemical elements • Selectivity, Yield • Reaction rate definition " " the material element (Plato) Stoichiometry " " the count, the quantity 2NO N2 + O2 closed (batch) system t =0 t > 0 Atoms of oxygen nnoo2 nn 2 NOO 2 NOO2 Atoms of nitrogen oo nnNON2 nn 2 2 NON 2 noo22 n n n noo22 n n n NOONOO22NONNON22 n noo 2( n n ) n noo 2( n n ) NONOOO22 NONONN22 o oo nn ()()nOONN n n n NONO 2 2 2 2 2 1 1 -2NO + O2 + N2 = 0 Symbols for species NO = A1 O2 = A2 N2 = A3 Stoichiometric coefficients 1 = -2 2 = 1 3 = 1 i 0 products 3 A 0 0 inerts i i i i 1 i 0 reactants Molar extent of the reaction [ksi:] o oo nn ()()nOONN n n n NON O 2 2 2 2 2 1 1 o ni ni i From the definition of the reaction extent follows: 1. The reaction extent has the dimension of moles (number of molecules) 2. The reaction extent value depends on stoichiometry of reaction 3. The reaction extent is an extensive variable Reaction extent for a single reaction in closed (batch) system t = 0 t > 0 o Closed system n i ni i 0 products N A 0 0 inerts i i i i 1 i 0 reactants nn o ii i o nni i i Example 2NO N2 + O2 AAA1N O , 2 N 2 , 3 O 2 1 2, 2 1, 1 1 A1 T νA 2 1 1 , A 2 A3 Matrix notation A1 T νA 2 1 1A 0 2 A3 Fractional conversion of key component, j X j X j max * o n j n j Number of moles of key max component in limits j (chemical equilibrium or 0) o nnjj n * 0 o XX (0,1) j n i n i ij jjo o n j j n n X i i i j o o max n j i n j o nnjj XX100 (0,100) j jjo n j n o j o i o XXjjmax n n n X i i j j j j Stoichiometric matrix in the case of several reactions N A0 k1, NR ki i i 1 reaction component Stoechimetric matrix has NR rows and N columns 11 12... 1 N A1 21 22... 2 N A νA, 2 . ... A NRNRNRN,1 ,2 , N νA 0 Number of moles of i-th component consumed or created in k-th reaction : o nnki ki nn o Molar extent of k-th reaction : ki ki k ki NR Number of moles of i-th nno components: i i ki k k 1 Matrix notation nnoTνξ n o 11 n1 n n o nn22 ,,o 2 ξ .. .. .. n o NNR n N Problem 1.1 Oxidation of ammonia on Pt-Rh catalyst NH3 + 1.25 O2 NO + 1.5H2O (1) NH3 + O2 0.5 N2O + 1.5H2O (2) NH3 + 0.75O2 0.5 N2 + 1.5H2O (3) Task: To write down the stoichiometric matrix. A1 A2 A3 A4 A5 A6 Reaction NH3 O2 NO N2O N2 H2O (1) -1 -1.25 1 0 0 1.5 (2) -1 -1 0 0.5 0 1.5 (3) -1 -0.75 0 0 0.5 1.5 Molar balance table of component in closed (batch) system Component t = 0 t > 0 o o NH3 n1 nn1 1 () 1 2 3 o o O2 n 2 nn2 2 1.25 1 2 0.75 3 o o NO n 3 nn3 3 1 o o N2O n 4 nn4 40.5 2 o o N2 n 5 nn5 50.5 3 o o H2O n 6 nn6 6 1.5( 1 2 3 ) 6 6 o o n n 0.25 i i 13 i 1 i 1 e.g. molar fraction of NH3 n o () y 1 1 2 3 1 6 n o 0.25 i 13 i 1 Independent reactions Set of NR reactions in reaction network is independent if Rank()=NR or number of independent reactions = Rank() Problem 1.2 NH3 + 1.25 O2 NO + 1.5H2O (1) NH3 + O2 0.5 N2O + 1.5H2O (2) NH3 + 0.75O2 0.5 N2 + 1.5H2O (3) 2NO N2 + O2 (4) Task: To calculate the number of independent reactions. We determine the rank of stoichiometric matrix by Gaussian elimination: 1 1.25 1 0 0 1.5 1 1.25 1 0 0 1.5 1 1 0 0.5 0 1.5 0 0.25 10.5 0 0 1 0.75 0 0 0.51.5 0 0.5 1 0 0.5 0 01 2010 01 2010 1 1.25 1 0 0 1.5 1 1.25 1 0 0 1.5 0 0.25 10.5 0 0 0 0.25 10.5 0 0 0 0 110.50 0 0 1 1 0.5 0 0 0 2 2 1 0 0 0 0 0 0 0 Rank()=3 only 3 reactions are independent Extent of the reaction in a flow system o Fi Fi REACTOR Inlet molar flow rates Outlet molar flow rates [mole of i-th species/s] [mole of i-th species/s] N A0 k1, NR Open (flow) system in a steady state ki i i 1 NR o k FF && i i ki k k k 1 o FFii, -outlet, inlet molar flow rates of i-th species [mole/s] & k extent of k-th reaction per unit of time [m ole/s] mean residence time [s] F o & 1 F1 1 o T & F F o & F = F + νξ FF2 ,,o 2 ξ& 2 .. .. .. F o & N FN NR A reaction is at steady-state if the concentration of all species in each element of the reaction space (i.e. volume in the case of homogeneous reaction or surface of catalyst in the case of catalytic heterogeneous reaction) does not change in time. Balance of chemical elements o j j REACTOR N A0 k1, NR Open (flow) system at steady state ki i i 1 o jj o j ,j -outlet, inlet molar flows of j-th chemical element [mole/s] o Φ = Φ o 1 1 o ΦΦ2 , o 2 NEL - Number of .. .. chemical elements o NEL NEL Formula matrix E NEL elements NEL=3 N components N H O N=6 Formula vector of NH NH3 1 3 0 3 O2 0 0 2 NO 1 0 1 N2O 2 0 1 N2 2 0 0 H2O 0 2 1 There are no creation or annihilation of chemical elements in chemical reactions: 11 12... 1NNEL EEE 11 12 ... 1, 0 0 ... 0 21 22... 2NNELEE 21 ... ... 2 , 0 0 ... 0 NR νE = 0 .. . ... EEE ... NRNRNRNNNNNEL,1 ,2 , ,1 ,2 , 0 0 ... 0 NEL Molar* weight (relative molecular mass) of i-th species: NEL M E m i ij j j 1 M = E m Atomic weights (relative atomic mass) of j-th element Mm11 Mm Mm22 , .. .. MmNNEL and we have for molar weights of species νM = νE m 0 because νE 0 *The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. Avogadro constant = 6.022 141 29(27) × 1023 mol−1 (http://www.nist.gov) Balances of atoms in batch and flow systems Closed (batch) system: n = no + νξT T ETTTTTT n = E no + E ν ξ E n o + νE ξ E n o Open (flow) system at steady state: F = Fo + νξT & T ETTTTTT F = E Fo + E ν ξ&& E F o + νE ξ E F o because νE 0 Finally TToo These equations are used E n n E n n 0 in data reconciliation tasks around chemical reactors. ETT F Foo = E F F 0 The last equation (flow system) is valid only at steady state. Problem 1.3 Steady state, Selective reduction of NOx by C3H8 unknown o stoichiometry Fi Fi of reactions NO NO2 CO C3H8 CO2 H2O O2 N2 o Fi [ mole / min] 4.563 0.1845 0 2.943 0 0 90 0 Fi [ m ole / m in] 2.2905 2.3355 0 2.898 x x x x Calculate the missing outlet molar flow rates ET F o - F = E T F 0 F1 1-NO 2-NO2 3-CO 4-C3H8 5-CO2 6-H2O 7-O2 8-N2 known N 1 1 0 0 0 0 0 2 F2 O 1 2 1 0 2 1 2 0 C 0 0 1 3 1 0 0 0 F 3 H 0 0 0 8 0 2 0 0 F T 4 E T E 1 2 F TT 5 E12 FKNOWNUNKNOWN E F 0 F6 TT EFEF21UNKNOWNKNOWN unknown F7 11 TTTT F FEEFQFQEE i UNKNOWNKNOWNKNOWN 2 1 2 1 F8 We obtain using Excel (homework 1) 0 0 1 3 0 0 0 4 Q o 0.5 1 0.5 5 Fi [ mole / min] F[ m ole / m in] i 0.5 0.5 0 0 1 TT and taking FEEFQF 2 2 1 1 1 we have NO NO2 CO C3H8 CO2 H2O O2 N2 4.563 0.1845 0 2.943 0 0 90 0 2.2905 2.3355 0 2.898 0.135 0.18 88.76 0.061 Selectivity Moles of a particular product generated per mole of key reactant consumed o Yield n1 Moles of a particular product generated per one initial mole of key reactant n o o 2 nn2 2 1.25 1 2 0.75 3 o n 3 Ammonia oxidation o o n 4 nn4 40.5 2 o o Component t = 0 t >n 50 nn5 50.5 3 o NH3 nn1o 1 () 1 2 3 o n 6 nn6 6 1.5( 1 2 3 ) O2 o NO nn3 3 1 N2O N2 H2O n o S 31 1 NONH 3 ()()1 2 3 1 2 3 n o 0 n o 3 Y 31 1 NONH 3 oo nn11 Reaction rate (IUPAC Gold Book = rate of conversion ) d 1 dn m ax r i m ole.s 1 d Closed system of uniform dt dt dt i pressure, temperature and d k composition.
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