RTD studies of plug flow reactor

The Plug Flow Tube Reactor (PFTR) is a model of an ideal reactor characterized by the input of a premixed reaction mixture of reactants and solvents on one side and a removal of the product on the other side. During the flow of the mixture the reactants react with each other. An ideal plug flow is assumed i.e. any flow velocities are constant and no back mixing of components happens.[1]

Real plug flow reactors do not satisfy the idealized flow patterns, back mix flow or plug flow deviation form ideal behavior can be due to channeling of fluid through the vessel, recycling of fluid within the vessel or due to the presence of stagnant region or dead zone of fluid in the vessel.[2] Real plug flow reactors with non ideal behavior have also been modelled.[3]

The residence-time distribution (RTD) of a reactor is a characteristic of the mixing that occurs in the chemical reactor. There is no axial mixing in a plug-flow reactor, and this omission is reflected in the RTD which is exhibited by this class of reactors.[4]

To predict the exact behavior of a vessel as a chemical reactor, RTD or stimulus response technique is used. The tracer technique, the most widely used method for the study of axial dispersion, is usually used in the form of:[5]

• Pulse input
• Step input
• Cyclic input
• Random input

The RTD is determined experimentally by injecting an inert chemical, molecule, or atom, called a tracer, into the reactor at some time t = 0 and then measuring the tracer concentration, C, in the effluent stream as a function of time.[4]

The residence time distribution (RTD) curve of fluid leaving a vessel is called the E-Curve. This curve is normalized in such a way that the area under it is unity:

(1)

${\displaystyle \int E\partial t=1}$

The mean age of the exit stream or mean residence time is:

(2)

${\displaystyle \tau =\int tE\partial t=\sum tE\nabla t}$

When a tracer is injected into a reactor at a location more than two or three particle diameters downstream from the entrance and measured some distance upstream from the exit, the system can be described by the Dispersion model with combinations of open or close boundary conditions.[6] For such a system where there is no discontinuity in type of flow at the point of tracer injection or at the point of tracer measurement, the variance for open-open system is:

(3)

${\displaystyle (\sigma _{\theta })^{2}=(\sigma _{t})^{2}/\tau ^{2}=2/P_{e}+8/(P_{e})^{2}}$

Where,

(4)

${\displaystyle P_{e}=LU/D_{L}}$

which represents the ratio of rate of transport by convection to rate of transport by diffusion or dispersion.

${\displaystyle L}$ = characteristic length (m)

${\displaystyle D_{L}}$ = effective dispersion coefficient ( m²/s)

${\displaystyle U}$ = superficial velocity (m/s) based on empty cross-section

Vessel dispersion number is defined as:

${\displaystyle 1/P_{e}=D_{L}/LU}$

The variance of a continuous distribution measured at a finite number of equidistant locations is given by:

(5)

${\displaystyle (\sigma _{t})^{2}=\sum t_{i}^{2}C_{i}/\sum C_{i}-\sum [t_{i}C_{i}/\sum C_{i}]^{2}}$

Where mean residence time τ is given by:

(6)

${\displaystyle \tau =\sum t_{i}C_{i}/\sum C_{i}}$

(7)

${\displaystyle (\sigma _{\theta })^{2}=(\sigma _{t})^{2}/\tau ^{2}}$

Thus (σ_θ)² can be evaluated from the experimental data on C vs. t and for known values of ${\displaystyle (\sigma _{\theta })^{2}}$, the dispersion number ${\displaystyle (1/P_{e})}$ can be obtained from eq. (3) as:

(8)

${\displaystyle D_{L}/LU={-1+{\sqrt {1+8(\sigma _{\theta })^{2}}} \over 8}}$

Thus axial dispersion coefficient D_L can be estimated (L = packed height)[2]

As mentioned before, there are also other boundary conditions that can be applied to the dispersion model giving different relationships for the dispersion number.[7][8][6]

Advantages

From the safety technical point of view the PFTR has the advantages that [1]

1. It operates in a steady state
2. It is well controllable
3. Large heat transfer areas can be installed

Concerns

The main problems lies in difficult and sometimes critical start-up and shut down operations.[1]

References

1. Plug flow Tube Reactor –S2S (A gate way for the plant and process safety ), Copyright -2003 by PHP –Nuke
2. Levenspiel, Octave (1998). Chemical Reaction Engineering (Third ed.). John Wiley & Sons. pp. 260–265. ISBN 978-0-471-25424-9.CS1 maint: ref=harv (link)
3. Adeniyi, O. D.; Abdulkareem, A. S.; Odigure, Joseph Obofoni; Aweh, E. A.; Nwokoro, U. T. (October 2003). "Mathematical Modeling and Simulation of a Non-Ideal Plug Flow Reactor in a Saponification Pilot Plant". Assumption University Journal of Technology. 7 (2): 65–74.
4. Fogler, H. Scott (2004). Elements of Chemical Reaction Engineering (3rd ed.). New Delhi - 110 001: Prentice Hall of India. p. 812. ISBN 978-81-203-2234-9.CS1 maint: location (link) CS1 maint: ref=harv (link)
5. Coulson, J M; Richardson, J F (1991). "2 - Flow Characteristics of Reactors—Flow Modelling". Chemical Engineering. 3: Chemical and Biochemical Reactors and Process Control (4th ed.). New Delhi: Asian Books Pvt.Lt. pp. 87–92. ISBN 978-0-08-057154-6.CS1 maint: ref=harv (link)
6. Colli, A. N.; Bisang, J. M. (September 2015). "Study of the influence of boundary conditions, non ideal stimulus and dynamics of sensors on the evaluation of residence time distributions". Electrochimica Acta. 176: 463–471. doi:10.1016/j.electacta.2015.07.019.
7. Colli, A. N.; Bisang, J. M. (August 2011). "Evaluation of the hydrodynamic behaviour of turbulence promoters in parallel plate electrochemical reactors by means of the dispersion model". Electrochimica Acta. 56 (21): 7312–7318. doi:10.1016/j.electacta.2011.06.047.
8. Colli, A. N.; Bisang, J. M. (December 2011). "Generalized study of the temporal behaviour in recirculating electrochemical reactor systems". Electrochimica Acta. 58: 406–416. doi:10.1016/j.electacta.2011.09.058.