An Overview of Chemical Reaction Analysis - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 126

From these two examples, one can observe that the energy balance equation can be further
reduced for a reacting system. Noting that for ideal systems where the enthalpy is only a func-
tion of temperature,

Z

T

H j ¼ DH f j þ C Pj d T (3.136)

T R

and

Z

T

U f j þ

U j ¼ D C Vj d T (3.137)

T R

For ideal gases,

DU f j ¼ DH f j RT R (3.138)

and for liquids,

DU f j zDH f j (3.139)

These equations can be applied to compute the enthalpy and internal energy terms in the
energy balance equations.

3.14. REACTOR MOMENTUM BALANCE

As we have learned in Fluid Mechanics, the flow of a fluid mixture is governed by the
Navier e Stokes equation or the conservation of momentum equations. For a thorough anal-
ysis of a reactor, the solution coupling with the Navier e Stokes equation may be needed.
However, for chemical reactor analysis, we normally simplify the analysis and avoiding
the direct use of the Navier e Stokes equations. For example, in bioprocesses, most of the
time we are dealing with liquid-phase reactions. The concentration of a component in liquid
phase is rarely influenced by the fluid pressure, which is the driving force for flow. Therefore,
the momentum equation is usually neglected in solving reactor problems. Still, in some cases,
the momentum equation can be important, for example, in gas-phase reactions.
The Navier e Stokes equation can be significantly simplified in simple cases, such steady
flow through a straight pipe (tubular reactor), flow through packed beds, and flow through
fluidized beds. For flow through a pipe or column, the momentum equation is reduced to

d P

d z ¼ ru d u

f c D t ru 2

d z þ 2

(3.140)

Where f c is the Fanning friction factor, r is the density of the fluid, D t is the diameter of the
pipe and flow Reynolds number (or velocity, u). For fully turbulent flow, f c is taken as
constant. In laminar flow, however, the friction factor is inversely proportional to the velocity.
When the column is packed with particles of diameter d p , the friction factor is a function of
the particle flow Reynolds number as shown in Fig. 3.9 . When the flow Reynolds number is