Name: Kevin Adrián Rodríguez Ruiz Professor: José Herney Ramírez Subject: Chemical Reaction Engineering Universidad Nacional de Colombia, April 02 of 2013
Code: 244693
Reactors in Parallel To understand the possibilities in a continuous reactive process with CSTRs and PFRs placed in parallel, we can consider a process in which the feed is distributed among reactors in parallel to achieve a specific total conversion at the exit:
a.
b.
Figure 1. (a) CSTRs in parallel and (b) PFRs in parallel, left and right respectively.
Conversion of reactors The total conversion conversion of an arrangement in parallel is given by:
∑ =
To know how to get the best conversion distribution, consider two reactors in parallel (any type):
+2 2 + (1 − ) 2
/
(1− ) /
Where and 2 Deriving at conditions of maximum conversion:
− 2 0
As c an conclude that the maximum conversion conversion is achieved when the conversion conversion in all reactors 2, we can is the same, not only in two reactors arrangements but also in any arrangement, arrangement, , as long as there is only one feed stream. If there is more than one reactor in each branch, the reactors can have different conversions, conversions, but the conversion conversion in each branch must be the th e same and equal to the total conversion.
⋯ ⋯
CSTRs in parallel From a single CSTR
Figure 2. Single CSTR
Considering isothermal operation, steady state and perfect mixture:
− + 0
−X V F A −rA X FA −rA
Reordering:
, hence the
Accordingly, in a parallel arrangement, as the conversion in each reactor is the same, reaction rate, , the right term of this equation is constant for all CSTRs:
− − ( )
V FAi
Besides, from this relationship we can say that when the conversion is the same, the size of a CSTR is proportional to the inlet stream of reactive, i.e., if we divide the feed of a single CSTR and bring it into several CSTRs placed in parallel, to get the same conversion of the single CSTR, the total size of the parallel CSTRs would be equal to the single reactor. PFRs in parallel From a single PFR
Figure 3. Single PFR
Considering isothermal operation, steady state, pressure drop negligible and no radial gradients of concentration or velocity:
− Reordering and integrating from 0 and 0 − ∫ −
As with CSTR, in a parallel arrangement of PFRs the right term of this equation is constant for all PFR, due to the conversion in each reactor is the same, hence the reaction rate, and the integral term, this is:
, V FAi
− − ( )
Then, we can conclude the same of the CSTRs in parallel: if the conversion is the same, the size of a PFR is proportional to the inlet stream of reactive, and if the feed of a single PFR is divided and brought it into several PFRs placed in parallel, to get the same conversion of the single PFR, the total size of the parallel PFRs would be equal to the single reactor. About pressure drop Considering that CSTRs and PFRs are widely employed for liquid phase and gas phase reactions, respectively, is important to keep in mind: o Even with large pressure drops, the effect of this variable on the velocity rate is negligible in liquid phase reactions. o In gas phase, the concentration of a substance is proportional to the pressure, so if the pressure drop is meaningful across a gas phase reactor, the design task must consider it. Usually the pressure drop reduces the conversion inside a reactor. Now, like pressure drop inside tubular reactors (PFR and PBR) depends of the reactor dimensions, while larger is the reactor larger is the pressure drop, then, if we divide the feed of a tubular reactor and bring it into several reactors, as these reactors individually are smaller than the single one, the pressure drop across the reactors in parallel would be lower than the drop across the single reactor, thus the conversion would be different between a single tu bular reactor and tubular reactors in parallel with a total size equal to the size of the single reactor.
Bibliography Fogler H. Scott. Elements of chemical reactions engineering. Third Edition. Upper Saddle River, New Jersey. Prentice Hall. 1999 O. Levenspiel. Ingeniería de las Reacciones Químicas. Second Edition. Barcelona, Spain. Reverté. 1986 Asociación de reactores en paralelo: reactores de flujo pistón y de mezcla perfecta. [Online]. Consulted March 31, 2013. Available in http://www.sc.ehu.es/iawfemaf/archivos/materia/00632.htm