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3.7 Three-Phase Fixed Beds: Trickle-Bed and Ped Bubble-Bed Reactors ack 173

required. Smith (1981) states that the concentration is constant when pure A is used in reac-
tions of the form a A (gas) + B (liquid) → products. In this case, there is no resistance in the
gas film, and thus K L ≅ k fg and in turn C G,i = C G and C L = C G,i / H = C G / H . Hoif the er , we v
expansion factor is not zero, eq. (3.365) is not applicable, since it does not include this
effect. Smith’s approach of constant gas concentration is valid in the following situations:

• The expansion factor is zero. This means that there are gas products and the stoichio-
f metric coeficients can result in = 0. In this case, we can work with eq. (3.365), the
underlying fact being that the concentration of A in the gas phase cannot be constant
since the gas phase is a mixture due to gas products (the feed is pure not the reac- A,
tion mixture). However, the gas-phase concentration of A could be practically constant
if it is in great excess and/or the concentration of B is so low that the consumption of
A is in turn low enough and the concentration of the gas products is also very lo . In w
this case, the deri ati v e in eq. (3.365) is practically zero and the equation is not needed. v
• If all products are liquids and the gas phase constitutes only one compound A, irre-
spective of whether it is the limiting reactant or not, its gas-phase concentration is con-
xpansion f actor is –1, stant (see Examples 4 and 5). However, in this case, the eand thus
we cannot use eq. (3.365) to draw conclusions unless the con . ery lo w v ersion of A is v
• If ≠ 0 and thus ≠ 0, and if A is the limiting reactant,
R

x )
F F A,i (1 A (1 x )
C A C A (3.372)
A (1 A,i (1
Q Q x ) x )
G G,i R A RA
Then, if x A → 0, or in other w if the conthe concentra- ords, , A is e xtremely lo w ersion of v
tion of A remains practically unchanged. So, eq. (3.359) is not applicable since

d F d x
AG F A 0 (3.373)
d V A,i d V

(b) The liquid feed is saturated in A throughout the r eactor: The liquid phase mass bal-
ance (3.367) is eliminated. In this case, C = C =C / H = constant, whereas for a pure
L,i L G,i
compound A in the gas phase, C = C / H = C / H .
L G,i G
Furthermore, the trickle-bed model eqs. (3.365), (3.367), and (3.368) hold for the general
case, where more than one reactant is present in the gas and liquid phase. Specif , ically

• The gas-phase mass balance (3.365) is used for reactants that are present in both the
gas and the liquid phase.
• The liquid-phase mass balance (3.367) is used for v olatile reactants being originally in
the liquid phase and for reactants that are in the gas phase and are dissolved in the liq-
uid phase. This mass balance is also called “volatile liquid-phase mass balance”
(Hopper et al. , 2001).
• The liquid-phase mass balance (3.368) is used for non-volatile reactants that are pres-
ent in the liquid-phase. This mass balance is called “non-volatile liquid-phase mass bal-
ance” (Hopper et al ., 2001).