10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. William H. Green
Lecture 1: Preliminaries & Remembrance of Things Past
This lecture covers: reaction stoichiometry, lumped stoichiometries in complex
systems such as bioconversions and cell growth (yields), extent of reaction,
independence of reactions, measures of concentrations, single reactions and reaction
networks, and bioreaction pathways.
Fo
FA
Figure 1. A schematic of a control volume with inflow of Fo and outflow of species A,
FA.
F = total molar flow rate (moles/sec)
Fo = total molar flow rate entering control volume
FA = molar flow rate of species A
FAo = molar flow rate of species A entering control volume
NA = Moles of species A
Mass balance: (change in “A” inside control volume)= (amount of “A” that entered)(amount of “A” that exited) + (amount of “A” created inside the control volume) –
(amount of “A” destroyed inside the control volume)
dN A
= FAo − FA + GA
dt
moles
GA [ = ]
sec
If homogeneous, GA = rAV
else, GA = ∫ rA dV
where V is volume and rA is the rate of A created or destroyed (moles/sec/volume).
The mass balance can also be written as:
diffusion
convection
d ρA P
2
= v∇ρ A + D∇ ρ A + rA
dt
where v is velocity, D is the diffusion coefficient, and ρA is the molar density of A
(moles/volume).
Example:
Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering,
Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
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A+B→C+D
rA = − k [ A][ B ] , rC = + k [ A][ B ] ,
[ A][ = ]
mole A
liter
where k is a measurable rate constant that changes with respect to T and P but
remains constant with respect to changing concentrations.
r1 = k [ A][ B ] , then
=−1
P
rA = ν A,1 r1
If
ν A,1 is the stoichiometric coefficient for species A in reaction 1.
=+1
P
rC = ν C ,1 r1
where
Likewise,
If there are n reactions involving species “A” then
n
rA = ∑ν A,i ri
i =1
GA (t ) = ∫∫∫
rA ( x, y, z, t )
dxdydz
Vol . - k (T ( x , y , z ,t )) A( x , y , z ,t ) B ( x , y , z ,t )
[
][
]
P
d [ A]
NA V
= − k [ A][ B ] → *only true if there are no flows!
dt
dN A
= ∫ rA dV ≈ rAV , assume rA is true throughout volume
dt
If the system is homogeneous and there are no flows:
dN A
= rAV
dt
Therefore:
d ⎛ NA ⎞
⎜
⎟ = rA iff homogeneous, no flow, constant V
dt ⎝ V ⎠
Extent of Reaction
ξ [ =] moles, extent of rxn.
moles
, rate of extent of rxn.
sec
A+ B → C + D
ξ [ = ]
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. William H. Green
Lecture 1
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N A = N A,initially − ξ , if there is one reaction involving A
N A = N A,initially − ∑ν A,nξ n , if there are several reactions
n
ξn = ∫ rn dV , n is the reaction number
GA = ∫ rA dV , A is the species
Conversion
A+ B → C + D
N
− NA
(dimensionless)
X A = A,initial
N A,initial
NC
( ≈ 1 since rxn is 1:1)
XC =
N A,initial
⎛ A+ B → C + D⎞
⎟ Selectivity is good if A → C , bad if A → U .
⎜
A →U
⎝
⎠
*May worsen as rxn. goes on ( A → C slows, A → U keeps going)
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. William H. Green
Lecture 1
Page 3 of 3
Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering,
Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].