Heat and Mass Transfer Flashcards
When does internal or intraphase transport occur?
The reactant diffuses into the pores of the
particle.
Where does external or interphase transport occur?
The reactant diffuses through the stagnant boundary layer surrounding the particle.
Fick’s first law equation
N(a)=-D(ab) ∇Ca
Molar flux of ‘A’ through the film (external mass transport)
Na=Kc( C(ab)-C(as) )
Present the rate equation for a 1st order reaction in terms of measurable quantities
r=C(ab)/(1/Kc +1/Ks)
Observable rate constant
1/Kobs = 1/Kc +1/Ks
What is the Sherwood number definition
The Sherwood number relates the mass transfer coefficient of a species A to its diffusivity and the radius of a catalyst particle, Rp
Sherwood number equation
Sh=Kc2Rp/D(AB)
Sherwood number for flow around spherical particles
Sh=2+0.6(Re^0.5)(Sc^1/3)
Reynolds number
Re= (velocitydensitydiameter)/viscosity
Schmidt number
Sc=viscosity/(density*diffusivity)
Heat transfer equation
q=h( T(b)-T(s) )
When will the max temperature change occur
C(as)=0
This is when the max observable rate occurs
What is molecular diffusion?
This occurs in external mass transfer.
Occurs in macropores (>50nm)
Collisions with other molecules are more frequent than with the wall.
What is Knudsen diffusion?
Occurs in internal mass transfer.
Occurs in mesopores (2-50nm)
Molecule-wall collisions are dominant.
Diffusivity decreases with pore size.
What is single file diffusion?
Occurs in micropores (<2nm).
Pores are too small to allow molecules to pass each other.
Transition diffusivity
Bosanquet equation
1/D(ta)= 1/D(ab) + 1/D(ka)
Knudsen diffusivity equation
D(ka)=(9.710^3)Rpore*(T/Ma)^0.5
Thiele modulus equation
Φ=L (k/D(ta))^0.5
Small Φ
The diffusional resistance is insufficient to
limit the rate of reaction
Big Φ
A significant diffusional resistance
prevents a constant concentration profile
Porosity definition
The ratio of void volume within the pellet to the total pellet volume
Tortuosity definition
Accounts for the deviations in the path length of the pores.
Effective Knudsen or molecular diffusivity
De = (porosity/tortuosity)*D
Effectiveness factor general
η=robs / rmax
Effectiveness factor sphere
η= 3/Φ [1/tanh(Φ) - 1/Φ]
Effectiveness factor for a slab
η= tanh(Φ)/Φ
Length parameter
L(p) =V(p)/S(p)
What is the observed order of reaction in terms of true order ‘n’, under severe diffusional limitations?
=(n+1)/2
What is the observed activation energy in terms of actual activation energy Ea?
=Ea/2
How does temperature affect diffusional resistances and then rate?
At low temperatures, the reaction
rate is not limited by diffusional
resistances.
At high temperatures, the reaction
rate is inhibited by diffusional
resistances. The observed activation
energy is half the true value.
Prater number
β= (-ΔHrDeC(as) )/ (lambda*Ts)
Prater relationship for temperature and concentration.
T= T(s)+ β( C(as)-C(a) )
Max temperature rise in catalyst pellet
(Tmax-Ts)/Ts=β
Damkohler number
Da=ks/kc
What does the Damkohler number indicate?
The Damkohler number indicates which characteristic first order process is faster: external diffusion or reaction.
For large values of Da the surface concentration of reactant approaches zero.
For small values of Da the surface concentration approaches the bulk fluid concentration.
Biot number for mass
Bi=x(p)*kc/De
Biot number for heat
Bi=x(p)*h(t)/Lambda
Overall effectiveness factor
η=η(interphase)*η(intraphase)
