n n. y i, 1 Composition (mole fraction) t i Time (s) N2 H2 NH3

Transcription

1 Ammoia sthesis via Haber-Bosch process Istructor: Nam Su Wag ammoiarxseideraspemcd Ammoia sthesis 5 N H 2 NH 3 Reactio stoichiometr ( ) ( 2 ) ( 5 5 ) R 834 J/(mole K)=kJ/(kmole K) Reactio rate, i kmol N 2 /(m 3 cat s), p i atm, i K; from Eq 278 of Seider r(, p ) 4 9 exp 5 p 5 p 3 4 exp Reactio rate, i mol NH 3 /(m 3 cat s), iput p i bar, i K p r(, p ) r, 3 2 Batch Reactor Operatig coditio temperature, pressure, iitial volume, catalst loadig of equal volume of catalst ad iitial reactat charge, where iitial charge iit is 5 mole of N 2 ad 5 mole of H 2 6 K P bar V V = m 3 /mole=/desit P 5 iit ( 5 5 ) iit = 2 start with 2 moles of reactats: cat iit V catalst volume, i m 3 cat = catalst volume, i m ODE for batch reactio: d/dt ddt( t, ) cat r, 3 P cat wt cat 2 cat wt = 97 kg Call a routie to itegrate from t= to t=t f i steps t f 2 step i step t rkfixed iit,, t f, step, ddt < > t t submatrix( t,, step,, 3) mole fractio p < > i 2 Batch Reactor Compositio Batch Reactor Compositio Compositio (moles) i, i, i, Compositio (mole fractio) 5 step, = 2 2 t i t i ime (s) ime (s) 398 fial coversio i mole his is also the fractioal coversio, s ice the complete (%) stoichiometric ield is mole of NH 3 Implemet reccle to covert more uused reactats

2 2 ammoiarxseideraspemcd Plug Flow Reactor (PFR) -- /w residece time as idepedet variable (quick & dirt) Equal volume of vapor ad catalst (ie, vapor void fractio=5) 5 V V vapor V cat F dv dt dv vapor dt dv cat dt Volumetric vapor flow rate (i m 3 /s) t=residece time Whe the batch reactor has alread bee simulated (as doe i the last sectio), a eas wa to covert the batch results to PFR is simpl to keep the residece time t as the idepedet variable ad itegrate the additioal ODE dv/dt to fid V versus t (ie, to relate PFR volume V to residece time t) Below, we umericall itegrate dv/dt with Euler's method is molar flow rate i mole/s, P i bar, m 3 dv dt P t V V f i P 5 step V step = 69m 3 2 PFR Compositio PFR Compositio Compositio (moles) i, i, i, Compositio (mole fractio) 5 Because there is a chage i the total umber of moles upo reactio, the PFR volume versus residece time is ot exactl liear PFR Volume vs Residece ime 2 2 t i Residece ime (s)

3 3 ammoiarxseideraspemcd Plug Flow Reactor (PFR) -- Rigorous /w V as idepedet variable ODE for PFR is d/dv, which describes how the molar flow rates of the various chemical species chage with reactor volume V (aalogous to d/dt i batch that describes how # moles chage with time) Note that i the batch case, the variable stads for # moles; whereas i the PFR case, the depedet variable is the molar flow rate (# moles/time) From the above batch case, reactio rate, i mol NH 3 /(m 3 cat s), iput p i bar, i K ddv( V, ) r, P dt P dv F dtdv( V, ) almost o chage from the batch case, except for the amout of catalst P 5 where is molar flow rate i mole/s, P i bar, m 3 Combie the above two ODEs ito oe vector fuctio Likewise, combie two depedet variable & t ito oe vector t t dtdv ddv dtdv dtdt( V, t) stack( ddv( V, ), dtdv( V, ) ) dtdv( V, t) stack ddv( V, submatrix( t,, 2,, ) ), ( ) t iit stack iit, ( ) dtdv( V, submatrix( t,, 2,, ) ) Call a routie to itegrate from V= to V=V f i steps V f 7 m 3 step i step Vt rkfixed t iit,, V f, step, dtdv < > V Vt submatrix( Vt,, step,, 3) t < > Vt 4 mole fractio < > i less covoluted i v4 2 PFR Compositio PFR Compositio Compositio (moles) i, i, i, Compositio (mole fractio) 5 V f residece time t step = 2 sec PFR volume (vapor+catalst packig) = 34 m 3 o duplicate the compositio versus volume plot, we adjust the PFR vapor volume V f so that the residece time is 2 sec step, = 393 fial coversio i mole his is also the fractioal coversio his should be theoreticall idetical to the batch case for the same residece time, but umericall ver slightl differet

4 4 ammoiarxseideraspemcd Aspe Implemet the same kietics i Aspe he idepedet variable time t i a batch reactor is equivalet to residece time, which i tur is related to reactor volume a plug flow reactor (PFR) I a batch reactor, the reactio rate r is expressed as moles of reactio (ie, extet of reactio) per uit of catalst per uit time; whereas i a plug flow reactor, the reactio rate is expressed as moles/s of reactio per uit weight or uit volume of catalst I Aspe, we break the reversible ammoia sthesis ito 2 separate reactios: forward ad reverse: forward: 5 N H 2 NH 3 reverse: NH 3 5 N H 2 Reactio rate, i kmol N 2 /(m 3 s), p i atm, i K; from Eq 278 of Seider r r forward r reverse exp p p 3 4 exp We break the above rate expressio ito 2 separate reactios: forward ad reverse r forward exp p p 5 r reverse 3 4 exp I Aspe, we eter reactio rate costat (ie, pre-expoetial factor) based o SI uits, regardless of how the phsical uits are specified elsewhere! the followig coverts reactio rate to kmol NH 3 /(kg cat s), iput p i Pa (ie, SI uit), i K Note that the uit coversio factor for the forward reactio is differet from that for the reverse reactio, because of the differet partial pressure expoets Assume the catalst has a specific gravit of 2 (ie, desit=2 kg/m 3 ) r forward 4 mole mole atm 2 m3cat 9 5 exp p m3cat s atm 2 5 mole 3 5 Pa 2 2 kgcat p p p 5 r forward exp p p pre-expoetial factor=624e-9 & E=9 kj/mole r mole mole atm m3cat 4 reverse 3 exp p m3cat s atm 5 mole 3 5 Pa 2 kgcat r 4 reverse 2389 exp p pre-expoetial factor=2389 & E=4 kj/mole I Aspe, Simulatio Reactios RXN-HB Iput Stoichiometr, specif the stoichiometr for the forward reactio

5 5 ammoiarxseideraspemcd I Aspe, Simulatio Reactios RXN-HB Iput Stoichiometr, specif the stoichiometr for the reverse reactio I Aspe, Simulatio Reactios RXN-HB Iput Kietic, specif the reactio rate costat for the forward reactio

6 6 ammoiarxseideraspemcd I Aspe, Simulatio Reactios RXN-HB Iput Kietic, specif the reactio rate costat for the reverse reactio

7 7 ammoiarxseideraspemcd I Aspe, Blocks HB Setup Catalst, eter 24kg for "Catalst loadig" (correspodig to 2kg for V=m 3 i batch, or a similar loadig of ~24kg for V=~2m 3 ) ad 5 for "Bed voidage" (correspodig to equal volume of solid catalst ad vapor phase)

8 8 ammoiarxseideraspemcd After ruig with 5 mole of N 2 5 mole of H 2 i the feed stream at =6K ad P=bar, Simulatio Blocks HB Profiles View Molar Compositio Plot ields the followig plot of mole fractio versus PFR legth he PFR dimesio is such that the residece time is 2 sec (per Simulatio Blocks HB Results ), which turs out to be 35 m 3 at a void fractio of 5 (or ~75 m 3 of void space) for a iitial flow of 2 mole/s Had there bee o shrikage of volume upo reactio, the void volume correspodig to a residece time of 2 sec would be 2 m 3 at a flow rate of 2 mole/s (or m 3 /sec) he followig plot earl duplicates that of a batch reactor from page of this Mathcad worksheet Simulatio Blocks HB Stream Results shows that the fial NH 3 cocetratio is 398 mole, or equivaletl a ield of 398, which agrees with that of "b-had" batch simulatio

9 9 ammoiarxseideraspemcd I Aspe, there are ma was to specif the same reactio he followig describe 3 alterative was: RXN-HB2, RXN-HBEQ, RXN-HBE2 Reactio "RXN-HB2" is based o "LHHW" rate expressio; broke ito 2 reactios; the forward & reverse reactio expoets are specified i the respective "Drivig Force" tabs Reactio "RXN-HBEQ" is based o "GENERAL" rate expressio; reactio class "LHHW"; check "Active"; check "Reversible" Ol oe reactio stoichiometr (ie, ot broke ito forward & reverse reactios) r exp 5 5 p p exp p r exp p 5 5 p exp 4 R 9 R p r exp Keq p p 5 p 5 p 5 5 p exp 49 p exp 49 l K eq l R 2564 Simulatio Reactios RXN-HBEQ Iput Kietic Drivig force, i the "Drivig Force Expressio widow, check "Compute reverse rate usig microscopic reversibilit", ad must specif the reactat expoets (5 for, 5 for ) but must leave the product expoets or blak ( or blak for, ot what the equilibrium expressio idicates!); i the "Equilibrium" tab, eter A=-2564 ad B=5894 r exp l( cost) l p 5 5 p exp Reactio "RXN-HBE2" is also based o "GENERAL" rate expressio Simulatio Reactios RXN-HBE2 Iput Kietic Drivig force, check "Specif rate cost ad coc expoets for forward ad reverse reactios" I the "Drivig Force Expressio" tab, for "forward reactio", eter A=B=C=D= For "reverse reactio", eter A=2564 ad B=-5894 Note the sigs for A ad B are the opposite of RXN-HBEQ, ad the "Equilibrium" tab is uavailable Reactio "RXN-HBE3" is also based o "GENERAL" rate expressio Simulatio Reactios RXN-HBE3 Iput Kietic Drivig force, check "Specif rate cost ad coc expoets for forward ad reverse reactios" I the "Drivig Force Expressio" tab, for "forward reactio", eter A=B=C=D= For "reverse reactio", eter A=2564 ad B=-5894 Note the sigs for A ad B are the opposite of RXN-HBEQ, ad the "Equilibrium" tab is uavailable p