Supplementary Information
for
Material Properties and Operating Configurations of Membrane
Reactors for Propane Dehydrogenation
Seung-Won Choi, Christopher W. Jones, Sankar Nair*, and David S. Sholl*
School of Chemical & Biomolecular Engineering, Georgia Institute of Technology,
Atlanta, GA 30332-0100
Jason S. Moore, Yujun Liu, Ravindra S. Dixit, and John G. Pendergast
Engineering & Process Sciences, The Dow Chemical Company, Freeport, TX 77541
*Corresponding authors: sankar.nair@chbe.gatech, david.sholl@chbe.gatech.edu
S1
Dimensionless Energy Balance Equations and Boundary Conditions
 
dT
=
dz
 Peheat
B.C.
  L   1 d  dT
  
r
R
r
dr


 dr


2

z = 0 ,

r = 0 ,


    d 2T 
 -H  -r

+
 A

  2  + Da

C pT0

 Peheat   dz 
(Tube)
d T

=0

dz

dT
d T
hR
=0, r =1,
=
 M - T 
dr
dr
keff

(S1)
0 = 1 , z = 1 ,

keff
,
  heat =
C p

Peheat =
(S2)
 heat 

uL 
(S3)
Here  represents dimensionless temperature which is defined by temperature divided by inlet
temperature (T0). The governing equations include thermal diffusivity (heat) and Péclet number
for heat transfer as generally defined above. The keff is effective thermal diffusivity and and Cp
denote average density and heat capacity respectively. The u is linear velocity along the axial
direction and h is heat transfer coefficient. The Da and dimensionless reaction term in Equation
S1 are the same as what we use in the mass transfer equation. For the membrane side, we
consider heat conduction across the support as follows:
1 d  d m 
r
= 0
r dr  dr 
(Membrane support)
(S4)
S2

r = 0 ,


r = 1 ,

B.C.
h
d M

= m  M - T  
dr
keff


h m
d M
=
 S -  M  
dr
keff

(S5)
We also set up a heat transfer equation for the shell side as follows:
2
   L   1 d  d s  
d s
=
  
r

dz
 Peheat   S   r dr  dr  
B.C.

r = 0 ,


r = 1 ,

(Shell)
(S6)
d s
h
= S  s -  m  , r = 1 ,
dr
k gas
d s

= 0 (adiatatic) 
dr


d s
h S
Tw
=
(non - adiatatic) 
 w -  s  ,  w =
dr
k gas
Ts

(S7)
The subscripts t. m and s denote the tube, membrane and shell sides. For each side, the
characteristic length in radial direction is the radial distance between its radial boundaries. For
example, for the shell side the characteristic length (s) is from the boundary between membrane
support and the shell side to the outer wall of the reactor. We assume constant wall heat flux with
fixed heat transfer coefficient, which is estimated based on Nusselt number in plug flow. The
average heat capacity and conductivity for the gas mixture are estimated by extrapolating gas
property data provided by NIST to 600°C, and are assumed to be constant throughout the reactor.
The gas density is calculated from equation of state at 1 atm and 600°C. The heat transfer
equation parameters are summarized in Table S1.
S3
Table S1. Parameter values for heat transfer equation.
Parameter
Value
H, J.mol-1
125,000
h, W.m-2.K
59.2
kgas, W.m-1.K
0.04
Cp, J.g-1.K
4.1
kg.m-3 (inlet)
0.614
Notation
H : Heat of reaction (J.mol-1)
Cp : Average heat capacity (J.g-1.K)
h : Heat transfer coefficient (W.m-2.K)
heat : thermal diffusivity (m2.s-1)
gas : Average density of gas component (g.m-3)
keff : Effective thermal conductivity (W.m-1.K)
 : Dimensionless temperature
S4