RECYCLE REACTOR SYSTEM Figure 6.13 shows a PFR where part of the reactor output is recycled to the input. As the recycle ratio increases the reactor behaves more like a MFR!The reactor in the system is still governed by the performance equation for a PFR but we need to account for the fact that the feed to the PFR is not the feed to the system.We can obtain the properties of the feed to the PFR in terms of the properties of the feed to the system by writing mass balances around the mixing point.

Recycle reactor system

Recycle reactor Mass balances around mixing point

So we now have expressions relating the feed to the PFR and the feed to the system as a wholeThe PFR itself had been analyzed previously

Performance equation for plug flow reactor derived earlier:

In our system, we have v0(R+1) entering the reactor instead of v0 and an entering conversion XA1 instead of 0. Thus we get, for the performance equation for the recycle reactor:

Performance equation for the recycle reactor system

This is shown graphically in Fig. 6.14The integral gives the area under the curve between XA1 and XAf . It represents the V/FA0 for the PFR if there was no recycle. If we multiply the average 1/rA in this interval with (R+1) we get the required volume of the reactor with recycle

Fig6_14

Recycle reactor system performanceWe can evaluate the performance of the recycle reactor system at any recycle ratio relative to a straight PFR (recycle ratio of zero) by looking at the space time ratio.

This will need to be done for specific reaction rate expressions, rA

Figure 6.16 looks at 1st order reaction, 6.17 looks at 2nd order. (these are analogous to Fig. 6.5 and 6.6 which looked at the effect of N for MFRs in series).

1st order rxnPFR with recycle

2nd order rxnPFR with recycle

RECYCLE REACTORWe have seen that recycling makes a PFR behave more like a MFR.We have also seen that PFR is the more attractive solution in most cases because it achieves the same conversion with smaller volume.Why then, would we be interested in degrading the performance of a PFR by recycling some of its output to the inlet? An autocatalytic reaction proceeds faster with some product in the feed, or in extreme cases may not proceed at all if there is no product in the feed.

AUTOCATALYTIC REACTIONSone of the products acts as a catalyst:A + M = M + MImportant example:the treatment of biodegradable organic wastes by microorganisms, biodegradation:

biodegradable material + microorganisms + O2 (dissolved oxygen) ------ CO2 + H20 + more microorganisms

The presence of microorganisms is required for the reaction to proceed. The product of the reaction is more microorganisms.

The reaction rate shows some dependence on the initial presence of microorganisms (Fig. 6.18).

Fig6_18

Autocatalytic reactionsSee Chp. 3 for test of reaction rate expression from batch reactor data for the special case:

Autocatalytic reactionsWhat type of reactor is best for these reactions?

PFR with pure A in the feed will not work! We need at least some product in the feed. But how much? If we have too much, that might affect the reaction rate as well. Where do we get the product? One possibility is to use recycle.MFR with pure A feed will work if we get it going initially by having some product in the reactor.We have also seen that a PFR in recycle mode behaves more and more like a MFR as recycle rate increases.So the question is not simply PFR vs MFR, but a PFR with the optimum recycle ratio vs a MFR.

Fig6_19

Autocatalytic reactions MFR vs PFRFigure 6.19 shows that for an autocatalytic reaction MFR is more efficient than PFR at low conversions. At higher conversions they become equivalent, and at even higher conversions, PFR becomes better.

What about a combination of MFR and PFR in series?

Autocatalytic reactions MFR- PFR in seriesSince MFR is better than PFR at low XA it makes sense to use MFR at low XA and then switch to PFR for high XA , Fig. 6.21 (a)

If the product can be separated from the remaining reactant we dont need the PFR, we can simply operate a MFR with a separator, Fig. 6.21 (b)

Note: Fig. 6.21 has been drawn using CA instead of XA. You should be able to go from one to the other with ease.

Fig6_21

Autocatalytic reactions MFR vs PFRWhat is different about these reactions?

i.e. what happened to our analysis resulting in Fig. 6.2 which showed PFR better than MFR?

Compare Fig. 6.18 and 6.19 with Fig. 6.2. It is the minimum in the 1/rA curve ( maximum in rA ) that gives rise to the observation in Fig.6.19

Autocatalytic reactions recycle reactor using a PFRIn Figure 6.20 we can distinguish two systems:1) The actual PFR with feed at XAi and product at XAf 2) The recycle reactor with feed XA0 and product at XAf

The PFRs performance equation says the area under the 1/rA curve from XAi to XAf is V/FAi

We can define an average rate for the PFR by drawing a line that will give us the same area underneath, between XAi to XAf

Autocatalytic reactions recycle reactor using a PFRNow looking at the recycle reactor, the only reaction taking place is in the PFR. So the same reaction rate applies.

The feed to the recycle reactor is at XA0 and its flow is FA0 .

The rectangular area under (1/rA)average from XA0 to XAf is V/FA0This is the actual measure of performance for our system.

If we had no recycle (just the PFR) V/FA0 would be the area under the 1/rA curve from XA0 to XAf

If we had a MFR, V/FA0 would be the rectangular area under the 1/rA (evaluated at Xaf ) line from XA0 to XAf

Autocatalytic reactions optimum recycle ratio in PFRAt high recycle rate (I.e. high XAi, see Fig. 6.14) the recycle reactor resembles a MFR and is clearly inferior to the PFR. As we reduce the recycle rate, the recycle reactors performance improves (V/FA0 is reduced). At even lower recycle rates the performance deteriorates again.

Autocatalytic reactions optimum recycle ratio in PFRRecall the performance equation:

The optimal recycle rate is obtained by taking the derivative of V/FA0 w.r.t. R in the performance equationAnd setting it equal to zero, giving:

The optimum recycle is one that introduces a feed which corresponds to the average reaction rate in the reactor.

Recycle reactor - recaprecycling of reactor output to the input may be done for different reasonsPerformance equation for a PFR with recycle follows from the equation for a PFR but incorporates a mass balance around the mixing point to relate fresh feed, recycle stream, and reactor feedIncreasing the recycle rate makes PFR look more like a MFR

Autocatalytic reactions - recapThese require recycle if a PFR is to be usedMFR superior to PFR at low XA (In contrast to reactions of general order n>0)PFR superior at high XAThere is an optimum recycle rateGood idea to use two reactors in series (MFR first, PFR next)

Example 6.3 Best reactor setup for an autocatalytic reactionDegradation of A in the presence of an enzymeReaction rate data has been obtained in a MFR (Table E6.3) v0=0.1 m3/min with CA0=10 mmol/m3 to be treated to XA=0.9Alternatives considered:(a) PFR with recycle(b) 1 or 2 MFRs in series(c) MFR-PFR in series

Example 6.3 (a) PFR with recycleTrial and error graphical solution: find optimum recycle by adjusting feed to correspond to the average rate of reaction, Fig.E6.3a

CAi=6.6 mmol/m3R=0.607 V=1.08 m3

Example 6.3 (b) 1 or 2 MFRsFor one MFR we can use the reaction rate data directly in the general form of the performance equation.

Two MFRs in series. Possibilities:Equal size Unequal size

How do we determine the size(s)?

For two equal sized MFRs we could use Fig.6.5 if the reaction was 1st order (or Fig.6.6 if the reaction was second order as in Example 6.2) But we do not even have a reaction rate expression, just numerical data.

The graphical method of maximization of rectangles enables us to find the optimum sizes of two unequal MFRs in series (which turns out slightly better than two equal size MFRs) even when we only have reaction rate data but no reaction rate expression.

Example 6.3 (b) 1 MFROne MFR, CA0=10 mmol/m3 ; CAf=1 mmol/m3 (90% conversion)1/rA = 10 m3.min/mmol (from reaction rate data)

Example 6.3 (b) 2 MFRsTwo MFRs in series Fig.E6.3b

Example 6.3 (c) MFR-PFR comboFig.E6.3cMFR:

PFR:

Example 6.3 Summary

CaseVol.1, m3Vol.2, m3Total vol.,m3

Recycle PFR1.081.081 MFR992 MFRs0.591.62.19MFR-PFR0.12 (MFR)0.58 (PFR)0.7

MFRs in series equal or unequal size? Reality check!Example 6.3(b) arrived at V1=0.59 m3, V2=1.6 m3 as optimum for 2 MFRs of unequal size

What would be the volumes if we used 2 equal sized MFRs?If this had been a 1st or 2nd order reaction we could have made use of Fig.6.5 or 6.6 to answer the question.We only have the rate data which we need to use graphically.Find that 2 MFRs of 1.25 m3 will do the job (exercise, see Fig 6.8)

Vtotal=2.2 m3 vs Vtotal=2.5 m3 The operational advantages of 2 identical reactors may outweigh the marginal total volume advantage of 2 unequal reactors.