Reactor Design Final Project Memo
This project aims to discuss the differences in plug flow reactors (PFRs), packed bed
reactors (PBRs), and how these reactors are affected by including a membrane to add or remove
a species. A PFR, a PBR, and a membrane PFR were modeled in polymath for the reversible
reaction:
A↔B+C
The same conditions were used for all of the reactors: KC = 0.05 mol/L, FA0 = 10
mol/min, CA0 = 0.2 mol/L, kF = 0.7 min-1, and the reactor volume is 500 L. For the PBR, some
additional conditions are required; ⍺ = 0.001 kg-1 is used to calculate the pressure drop term and
⍴b = 1058 kg/m3 is used to convert reactor volume to catalyst weight. The molar flow rate of C
(FC) is not shown on plots where FB = FC.
Figure 1. Molar flow rate vs reactor volume for a PFR.
For the PFR, plotted in Figure 1, it can be seen that equilibrium for the reaction is
reached around 150-200 liters, far less than the 500 liter reactor volume. This means that the
remaining ~300 liters are not necessary to reach maximum conversion of about 0.45.
Figure 2. Molar flow rate vs reactor volume of a membrane PFR
The PFR in Figure 2 includes a membrane to remove species B from the reactor. Since
species B is a product, removing it from the reactor pushes the reaction further toward the
products, increasing the conversion. This can be seen by comparing figures 1 and 2; Figure 2
shows that the final conversion of the membrane reactor is about 0.6, which is a 25% increase in
conversion vs the PFR with no membrane. One benefit of membrane reactors is that they can
produce much higher conversions for reversible reactions, and can theoretically reach 100%
conversion since either a product is being removed or a reactant is being added. This means that
higher conversions can easily be achieved by simply increasing the volume of the reactor.
However, if a very high conversion is desired, the reactor will be large and expensive.
Figure 3. Molar flow rate and conversion vs catalyst weight for a 500 liter PBR with bulk
catalyst density of 1058 kg/m3.
It can be seen in Figure 3 that the final conversion for a PBR with 529 kg of catalyst is
about 0.55, which is higher than the normal PFR, but still lower than the membrane PFR. Figure
3 also shows that the reaction does not reach equilibrium in this reactor. Additional catalyst can
be added to the PBR to determine the equilibrium conversion for this reactor; this is plotted
below in Figure 4.
Figure 4. Molar flow rate and conversion vs catalyst weight for additional catalyst (700 kg of
catalyst).
Figure 4 shows that equilibrium for this PBR is reached just before 700 kg of catalyst and
the final conversion is about 0.6, slightly higher than the PBR with 529 kg of catalyst. Although
the conversion is higher, with the same bulk catalyst density, a reactor volume of around 660 L is
required for this increase in conversion. Increasing the size of the reactor this much is likely not
justifiable for this small conversion increase, as it would significantly increase the cost of the
reactor. This conversion could also be reached by increasing the bulk catalyst density, which
could be achieved by either increasing the weight of the catalyst held by the pellets or reducing
the pellet size. The latter reduces the void fraction, effectively increasing the bulk catalyst
density. This is a better option than increasing the reactor size, but if a higher conversion is
required, implementing a membrane is an even better choice, as a much higher conversion could
be achieved for the same reactor volume and bulk catalyst density.
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While the most basic PFR designs are the cheapest option of the reactors mentioned, it
can be seen by comparing Figures 1 and 3 that reactions often happen much more quickly in
PFRs than PBRs. Because of this, heat is generated (for exothermic reactions) or consumed (for
endothermic reactions) more quickly in PFRs, so more advanced heat transfer mechanisms are
required, increasing their cost significantly.
PFRs often have lower conversions than PBRs or membrane reactors, but because the
reaction reaches equilibrium quickly, they do not require nearly as large of a volume as the other
reactor types. This makes PFRs a good choice if high conversion is not necessary, a high reaction
speed is required, or if the reactor has a size restriction. PBRs do not require as advanced heat
transfer methods as PFRs, which results in cheaper manufacturing and operating costs. PBRs are
a good choice if a higher conversion is desired but cost is also an important factor. Membrane
reactors (both PBRs and PFRs) are the most expensive, but they can also produce much higher
conversions than the other reactor types. Including a membrane in a reactor is a good choice if a
very high conversion is desired or if high cost is not an issue.