50
L. Lindmüller et al.
u mf A r (1-ε b ) C d,l
K Q A t dh C d,l
k g a A t dh (C b,l -C d,l )
(1-ε b ) u mf A r (C d,l - C d,l /dh · dh)
(u-u mf ) A r ε b C b,l
ε b (u+du/dh · dh -u mf ) A r (C b,l - C b,l /dh · dh)
r g,l A r (1-ε b ) dh
suspension
bubble
u A r C f,l dh
freeboard
r g,l A r dh
(u+du/dh · dh) A r (C f,l - C f,l /dh · dh)
Fig. 5 Molar balances solved for each discretized height element dh. The suspension and the bubble
phase are connected via diffusive and convective mass transfer (Reprinted with permission from
[8])
f (X ) = 1 − (1 − X )
1/3
(18)
The molar balances of the suspension, bubble and freeboard phase in the
discretized volume elements A r · dh for the gas species are shown in Fig. 5.
Since no homogenous gas reactions occur in the bubble phase, changes in the
molar concentrations happen only due to convective and diffusive gas transfer with
the suspension phase. In the following the concentration changes of all gas species
l at a reactor volume element A r · dh, are shown for the bubble phase b, the dense
suspension phase d and the freeboard f:
bubble phase :
dC b,l
dh
=
˙
J Q,l − k G · a t ·
C b,l − C d,l
− C b,l
du
dh
u − u m f (1 − b )
(19)
dense suspension phase :
dC d,l
dh
=
˙
J Q,l − k G · a t ·
C b,l − C d,l
+ r g,l
u m f (1 − b )
(20)