2-D plug flow Reactor.pdf

2 - Dimensions plug flow reactor,
Calculation
Derivations
Reactor design
Description

1. TWO-DIMENSIONAL TUBULAR
(PLUG FLOW) REACTOR

Consider a reaction A — products in a tubular reactor with heat
exchanged between the reactor and the surroundings. If the reaction
is exothermic and heat is removed at the walls, a radial temperature
gradient occurs because the temperature at this point is greater than
at any other radial position. Reactants are readily consumed at the
center resulting in a steep transverse concentration gradient. The
reactant diffuses toward the tube axis with a corresponding outward
flow ofthe products. The concentration and radial temperature
ents in this system now make the one tubular (plug flow)
reactor inadequate. It is necessary to consider both the mass and
energy balance equations for the two dimensions 1 and r. With refer-
ence to Figure 6-15, consider the effect of longitudinal dispersion and
heat conduction. The following develops both material and energy

lance equations for component A in an elementary annulus radius
ör and length öl. It is also assumed that equimolecular counter diffu-
sion occurs. Other assumptions are:

G
Mass enters clement
€) Redal
(2) Longitudinally

=a

Figure 6-15. Differential section of two-dimensional tubular reactor

2. Non-Isothermal Reactors 493

+ Laminar flow

+ Constant dispersion and thermal conductivity coefficients

+ Instantaneous heat transfer between solid catalyst and the reacting,
ideal gas mixture

+ Neglect potential energy

+ The reaction rate is independent of total pressure

‘The component mass balance of species A entering the element
longitudinally and radially per unit time is

Mass entering by longitudinal bulk flow

nr8rG(N,), (6-98)
Dan) em

Mass entering by longitudinal diffusion

an,
PSE À
¡2 ) (6-100)
Mass leaving by longitudinal bulk flow
= zmrc[n, a) (6-101)
A ha
Mass leaving radially by diffusion
an, ¿EN
=D, 2ne(e+ 598 Na ¿PNa 6.102)
2 sani NaN «| (6-102)
Mass leaving by longitudinal diffusion
an, BN
0208 Na + Pa gy 6
rita + BN 3) (6-103)

Mass of component produced by chemical reaction
EN) (6-104)

where Dj = ax
D, = ra

diffusivity
al diffusivity

3. 494 Modeling of Chemical Kinetics and Reactor Design

In assuming a steady state, the algebraic sum of the components
of mass entering (Equations 6-98, 6-99, and 6-100) and leaving (Equa-
tions 6-101, 6-102, 6-103, and 6-104) the element are zero. Expanding
the terms evaluated at (1 + Öl) and (r + 8) in Taylor seri
points Hand r, and neglecting the second order differences,

where ky = axial thermal conductivity
k, = radial thermal conductivity

If the reaction rate is a function of pressure, then the momentum
balance is considered along with the mass and energy balance equa-
tions. Both Equations 6-105 and 6-106 are coupled and highly non-
linear because of the effect of temperature on the reaction rate
Numerical methods of solution involving the use of finite difference
are generally adopted. A review of the partial differential equation
employing the finite diffe ethod is illustrated in Appendix D,
Figures 6-16 and 6-17, respectively, show typical profiles of an exo-
thermic catalytic reaction,

Figures 6-16 and 6-17, respectively, show the conversion is higher
along the tube axis than at other radial positions and extremely higl
temperatures can be reached at the tube axis. These temperatures can
be sufficiently high to damage the catalyst by overheating. A maximum
temperature is also obtained along the reactor length, and the location
of this hot spot can alter with changes in catalyst activity