ChE 512: Topic 1 Reactions at a fluid non-porous solid interface. P.A. Ramachandran

Transcription

1 he 512: Topc 1 Reactons at a flud non-porous sold nterface P.. Ramachandran rama@wustl.edu

2 OUTLIE External Transport: Flm oncept Mass transfer coeffcents Effect of transport on reacton multaneous heat and mass transfer Multcomponent dffuson omputer smulaton Examples:

3 Flm oncept ear a old ear the gas-sold nterface, there exts a regon of relatvely slow movng gas. Gas velocty becomes zero at the sold surface (o slp condton) Hydrodynamc boundary layer If the sold surface s at a dfferent concentraton then a concentraton boundary layer exsts. Dffuson-convecton transport n ths boundary layer s Represented by a stagnant regon near the sold flm.

4 Flm Model: chematcs Gas old tagnant flm G δ Flm thcness oncentraton Profle Flm Representaton Dffusve Flux to urface D δ ( ) ( ) G m G m mass transfer coeffcent D δ

5 Effect of Reacton: Frst Order H 4 δ G substrate H + 4 2H 2 ( ) Rate of transport to surface ( J ) m G Rate of reacton at surface ( R ) s ( R ) s mole/m 2 s. urface area s used as a measure.

6 Rate of reacton: Frst Order t steady state, speces produced at the surface (per unt area) must balance the flux from the surface. R J m ( ) m G + G m ( ) m R G + m

7 Effectveness factor (on-porous) R + m ηext G m actual rate rate at bul condtons R b m For frst order reacton 1 resstance due to surface reacton 1 resstance due to mass transfer lso η ext Da Da m m FIRT ORDER mass transfer ress tan ce netc ress tan ce

8 Effect of Reacton: econd Order The physcal pcture stll holds but Let 1 Da a m ( ) 2 R 2 ( ) 2 G G and ( ) 2 1 a a ηext ηda + η 1 0 Da 2 2 G m Resstances n seres do not hold.

9 Effect of product counterdffuson H 4 H 2 H + H 4( g ) ( s) 2 2( g ) 2 moles dffusve n opposte drecton for every one mole. et velocty s non-zero. V r Fcs law: Movng reference tatonary frame eed to add convectve transport

10 Molar Flux: tatonary Frame r + ( n + 1)B r J + dy dz r V D + y t ( n + ) 1 B H + 4 2H 2 1 D ny dy ( + ) dz t t V t y t + B n

11 Effect of counterdffuson: frst order reacton y B Bul z y 0 δ Flm thcness 1 D + ny dy dz y B.. at z 0 0 R B.. at z δ y y B η ext y B D ηy δ 1+ ηyb ln 1+ ηy η B B ext

12 on-porous system: effect of heat transfer T α T s α T b and T b T s b b s s 0 δ x chematc representaton of the temperature and reactant concentraton profles for Exothermc reacton Endothermc reacton 0 δ x

13 on-porous system: effect of heat transfer ( ' ) E RT n R e ( 2 mol m s) m ( ) E RTs n e b s s h ( ) ( ) E RTs n T T Δ H e s b r s olve for both s and T s. ( ' ) E RTs n E RTb n R e η e actual can be rearranged to a non-lnear equaton for s ηext b

14 Multcomponent ystems Transport s descrbed by tefan-maxwell Equatons y n j1 1 cd j ( y y ) where D j are the bnary par dffusvty for -j par D j can be calculated for nstance by hapman-ensog equaton j j ote D j D j If n3, then we need three bnary par dffusvtes D 12, D 13 and D 23

15 Boundary ondtons t t z z 0, R f ( cy1, cy2 etc.) δ, y y ( Bul values) δ R Rate of nr productonby chemcal reacton ν rrr r where, 1 ν r stochometrc coeffcent of speces th nthe r reacton th r rate functon for the r reacton r umercal soluton s usually requred (Treat y and both as varables) For a smpler problem see BL, Example 18.5

16 Pseudo-Bnary Dffusvty Ths s defned as though Fc s law holds: cd 1 m y + y j 1 D m Pseudo-bnary dffusvty of n the mxture Rearrangng tefan-maxwell equaton we fnd: 1 cd m n 1 cd j ( y y ) In general D m are dependent on postons. n average value or a constant value can be used as an approxmaton. j y n j 1 j j j

17 ystem Invarants Example: team Reformng of Methane H 4 +H 2 O 3H 2 +O H 4 +2H 2 O 4H 2 +O 2 ystem nvarants can be found usng MTLB. hoosng methane and water as the ey components: nu Use functon rref to reduce t to an echelon form: rref (nu) ans The nvarants are the column vectors for each speces H 2 O O2 2 2 H 4 H 4 H 4 + H 2O H 2O H 2O Only two molar fluxes are ndependent and the rest are ted to these by the relatons shown above

18 Examples hemcal Vapor deposton Reacton on non-porous surfaces