Mt: Diffusion With A Heterogeneous Chemical Reaction

MT: Diffusion with a heterogeneous chemical reaction Instructor Date

:Dr. Nurul Hasan :13/04/09

Universiti Teknologi PETRONAS

What we will learn today? ♦ Shell balance of mass transfer ♦ Application of Fick’s Law ♦ Assumption of the stagnant gas-film ♦ Reaction Model for mass transfer

Conservation of mass in the shell  Rate of   Rate of   rate of mass    −   +    mass in   mass out   production  = ( Accumalation )

SN Az | z − SN Az | z + ∆z = 0

Divide/ Taking Limit Divide by

S∆z and taking the limit of ∆z → 0 dN Az − =0 dz

dN Az =0 dz

Apply Fick’s Law Molar flux to the concentration gradient

N Az = −cDAB

∂x A + x A ( N Az + N Bz ) ∂z

Rearranging the above eqn

N Az

cDAB dx A =− 1 1− x A dz 2

Apply Fick’s Law (cont..) Molar flux to the concentration gradient

d  cDAB dx A    = 0 dz  1 − 1 / 2 x A dz  Rearranging the above eqn

d  1 dx A    = 0 dz  1 − 1 / 2 x A dz 

Taking Integration Taking integration

 1  − 2 ln1 − x A  = C1 z + C2 = −( 2 ln K1 ) z − ( 2 ln K 2 )  2  The BCs are:

at , z = 0, x A = x A0 at , z = δ , x A = 0

Apply B.C., concentration Using the BC: 1−( z δ )

 1   1  1 − X A  = 1 − X A 0   2   2 

Application of Concentration Molar flux at the interface:

N Az

2cDAB = δ

    1  ln  1 − 1 x  A0  2 

What we learnt today •Shell balance of mass transfer •Application of Fick’s Law •Assumption of the stagnant gas-film •Reaction Model for mass transfer