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The hydrogenation of an unsaturated organic is to be carried out in
a trickle bed reactor packed with 0.20-cm-diameter spherical catalyst particles.
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The reaction in the pellet is first-order in both hydrogen and the
organic. Hydrogen and nitrogen are fed in equimolar portions at a total pressure
of 20 atm and a total molar rate of 10 mol/s. The reactor diameter is to be 1.0
m. The superficial liquid mass velocity is 5.0 kg/m 2 s. The corresponding pressure
gradient through the bed is 25 kPa/m.
As a first approximation, assume that the concentration of organic is constant and
the pseudo-first-order specific reaction rate is 3 x 10 -5
m 3 / kg cat.s at 400 K.
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(a) For each transport step, determine its fraction of the
total resistance to mass transport and reaction.
(b) Calculate the catalyst weight necessary to achieve 55% conversion of the
hydrogen.
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Additional information:
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(a) Let A = H 2
, B = unsaturated organic, and C = saturated organic:
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1.Mole balance on H
2
(A):
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(CDE12-1.1)
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2. Rate law.Assuming a constant liquid reactant concentration
for low conversion of B,
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(CDE12-1.2)
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with
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(CDE12-1.3)
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3 .Stoichiometry. The isothermal gas-phase
concentration is
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(CDE12-1.4)
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4. Pressure drop:
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(CDE12-1.5)
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5. Combining yields
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(CDE12-1.6)
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Integrating gives us
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(CDE12-1.7)
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6. Evaluating the parameters:
A.Solubility
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(CDE12-1.8)
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B. Internal diffusion and reaction
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(CDE12-1.9)
(CDE12-1.10)
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For large values of the Thiele modulus,
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(CDE12-1.11)
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C. Gas absorption
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(CDE12-1.12)
(TCD12-1A)
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D. Transport from gas-liquid interface to bulk liquid
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(CDE12-1.13)
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From the correlation for organic liquids,
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(CDE12-1.14)
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It has been noted 5
that this correlation gives a mass transfer coefficient that is too low
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E. Resistance from bulk liquid to catalyst
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(CDE12-1.15)
(TCD12-IF)
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F. Total and percentage resistances
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R T =
R c + R l
+ R g + R R
=
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(CDE12-1.16)
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Individual resistances:
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(b) Calculate catalyst weight
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(CDE12-1.7)
(CDE12-1.17)
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Substitution yields
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Solving, for W, we obtain
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W = 34,500 kg
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The reactor volume corresponding to this catalyst weight is
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The total height of the reactor
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Four 1-m-diameter towers each 12.2 m in height connected in series
will be sufficient.
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Checking assumption of constant C B
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Consequently, our assumption that the concentration of organic is
essentially constant was valid.
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