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The continuous-flow, well-stirred tank reactor or CSTR finds wide application in the chemical industry from pilot plant to full-scale production operation. The basic arrangement, sketched below, comprises a tank thermostated at some surrounding temperature Ta into which one or more reactant feed streams flow at some controlled rate. The contents react in the tank and are stirred either mechanically or as a consequence of the flow characteristics, and there is an outflow.
The various control parameters include:
· the inflow concentrations ci,0 of the different reactants;
· the total volumetric flow rate v through the reactor;
· the ambient temperature or the temperature of any cooling jacket Ta
· the inflow temperature T0 (which may be different from Ta)
whilst other features, such as reactor shape and size might be of interest at the design stage.
The response variables are the concentrations ci and the temperature T within the reactor.
The product/reactant mix flows out with concentrations ci and temperature T equal to the values in the reactor.
The continuous inflow of fresh reactants (and matching volumetric outflow of reactant and-product mixture) provides a thermodynamically open system, in which true steady state behaviour can be sustained 'indefinitely'.
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The reason that a PFR requires less volume than a CSTR is the difference in residence time distribution between the reactors. Residence time is the amount of time molecules spend in the reactor which equal to v/vo (v=volume of the reactor and v0 is volumetric flow rate). Let us assume that we design a PFR and CSTR that have similar residence time i.e. ratio of volume v and v0 is the same and we are pumping about 100 molecule per minute to each reactor. In the case of PFR, all the 100 molecules will spend exactly the same time inside the reactor (v/v0). In the case of CSTR, things are little more complicated, once the 100 molecule hit the CSTR, they mixted instantaneously and thus some of these 100 molecules will leave from the reactor exit stream very early i.e. will spend much less time inside the reactor (less the v/v0) and of course some these 100 molecule will spend more time making the average residence time the same as the PFR. Therefore, with the chance that molecules will spend shorter time in CSTR, we try to compensate for that effect by making bigger reactors so the ratio of these molecules spending short period of time inside the reactor less and thus its performance is comparable to the PFR. Very logical and easy to understand explanation. But how to prove series of CSTR equals to one PFR which is having a volume of sum of all CSTRs?
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The reason that a PFR requires less volume than a CSTR is the difference in residence time distribution between the reactors. Residence time is the amount of time molecules spend in the reactor which equal to v/vo (v=volume of the reactor and v0 is volumetric flow rate). Let us assume that we design a PFR and CSTR that have similar residence time i.e. ratio of volume v and v0 is the same and we are pumping about 100 molecule per minute to each reactor. In the case of PFR, all the 100 molecules will spend exactly the same time inside the reactor (v/v0). In the case of CSTR, things are little more complicated, once the 100 molecule hit the CSTR, they mixted instantaneously and thus some of these 100 molecules will leave from the reactor exit stream very early i.e. will spend much less time inside the reactor (less the v/v0) and of course some these 100 molecule will spend more time making the average residence time the same as the PFR. Therefore, with the chance that molecules will spend shorter time in CSTR, we try to compensate for that effect by making bigger reactors so the ratio of these molecules spending short period of time inside the reactor less and thus its performance is comparable to the PFR. Very logical and easy to understand explanation. But how to prove series of CSTR equals to one PFR which is having a volume of sum of all CSTRs?
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. The transformation of glucose into fructose by the enzyme glucose isomerase, was carried out in two different types suspended-enzyme bioreactors: 1) CSTR, and 2) plug flow reactor. The process obeys Michaelis-Menten kinetics. The following parameters and kinetic constants were kept the same in both bioreactors: $ So (input substrate concentration) = 1.0 mMol/L; $ F (volumetric flow rate) = 1.0 m3/h; $ Km = 7x10-4 Mol/L; $ Vmax = 0.2 mMol/(L.h) Determine: $ Volume of CSTR for 50% conversion of glucose; $ Volume of PFR for 50% conversion of glucose; $ Volumes of CSTR and PFR in series (assume that the volumes are equal) in two cases: $ first CSTR $ first PFR 2. Calculate the volume of a stirred tank bioreactor containing the same enzyme, but immobilized on the surface of a flat-geometry support. The value of the mass-transfer coefficient is 0.6 h-1. The values of the rest of process parameters are the same as above.
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