Transcript No Slide Title

Pulping
and
Bleaching
Pulping and Bleaching
PSE 476/Chem E 471
Lecture #12
The H Factor
PSE 476: Lecture 12
1
Pulping
and
Bleaching
•
•
•
•
Chemical Pulping
Agenda
Train question
Derivation of “H” factor equation
Example “H” factor calulation
Validity of “H” factor
PSE 476: Lecture 12
2
Pulping
and
Bleaching
Kraft Pulping Kinetics
Question about a Train
• Consider you are the engineer on this train. Your
windows are painted shut and you need to travel
from Seattle to exactly the station in Portland.
How do you do it????????
• If all you have is your speedometer and your
trusty watch, you could record your speed at
specified time intervals and plot your progress.
This is basically what is done in a pulp mill to
determine when to stop the pulping reaction.
This is accomplished through the use of the “H”
factor.
PSE 476: Lecture 12
3
Pulping
and
Bleaching
Kraft Pulping Kinetics
Derivation of “H” Factor (1)
In order to determine when to stop a kraft cook, it is necessary
to know the extent of the reaction which is based on the rate of
lignin removal. This can be expressed as:
(1) dx = k f (composition) = rate of lignin removal
dt
f (composition) = [lignin]a[OH-]b[HS-]c[phase of the moon]d
Within a given cook, there is assumed to be a unique
relationship between the extent of the reaction and the
composition so the top relationship can be integrated to give:
(2)
x(t) = ƒ k dt
Cannot solve equation because k is
dependent on temperature
PSE 476: Lecture 12
4
Pulping
and
Bleaching
(3)
Kraft Pulping Kinetics
Derivation of “H” Factor (2)
k =Ae
-Ea/RT
Ea = activation energy(32 kcal/mole (kraft))
T = absolute temperature
R = gas constant
A = constant
Taking the log of both sides:
(4)
ln k = ln A - (Ea/RT)
At 100°C, the above equation becomes:
(5)
ln k100 = ln A - (Ea/R373)
Subtracting equation 5 from 4 gives:
ln(k/k100) = -(Ea/RT) + (Ea/373R)
PSE 476: Lecture 12
5
Pulping
and
Bleaching
Kraft Pulping Kinetics
Derivation of “H” Factor (3)
(5) ln(k/k100) = -(Ea/RT) + (Ea/373R)
Substituting in the appropriate values
(6) ln kr = -(16,113/T) + 43.2
kr is called the relative rate constant or a comparison of the
rate constant at a temperature to that at 100°C
(7) kr = e (43.2-16,113/T)
From this equation, it is possible to see that kr is significantly
affected by temperature (see figure on page7)
PSE 476: Lecture 12
6
Relative Rate Constant
Pulping
and
Bleaching
Kraft Pulping Kinetics
Relative Rate Versus Temperature
10000
8000
6000
4000
2000
0
100
120
140
160
180
200
220
Temperature (°C)
PSE 476: Lecture 12
7
Pulping
and
Bleaching
Kraft Pulping Kinetics
Derivation of “H” Factor (4)
Equation 7 can be rewritten
(-16,113/T)
(43.2)
(8) kr = e
e
Equation 4 becomes:
(9) k = Ae
(-16,113/T)
Combining these 2 equations leads to:
(43.2)
(10) k = (p)(kr)
Where p = A/e
PSE 476: Lecture 12
8
Pulping
and
Bleaching
Kraft Pulping Kinetics
Derivation of “H” Factor (4)
Equation 10 can be substituted into equation 2 leaving:
(11) ƒ k dt = p ƒ kr dt (p is a constant)
The expression ƒ kr dt is referred to as the “H” factor:
(12) H = ƒ kr dt
By combining equations 2, 11, and 12, it can be seen that the
extent to which a pulping reaction has proceeded is a function
of the H factor.
x(t) = (p)(H) or x = f(H)
PSE 476: Lecture 12
9
Pulping
and
Bleaching
Kraft Pulping Kinetics
“H” Factor Information
In order to solve for the factor, temperature readings are
taken every 0.25 hours (or sooner - every minute) of the cook
and relative rate constants kr determined. The kr is plotted
versus time. The area under the curve is equivalent to the H
factor (Figure slide 11). Sample calculations for the
determination of the H factor can be found in slide 12. The
accuracy of this method can be seen in slide 13 for the
determination of endpoint at 3 different temperatures. It
needs to be stressed that this equation only estimates the
effects of time and temperature and assumes constant
effective alkali, sulfidity, liquor/wood, wood species, etc. All
these factors and more can change the rate,
PSE 476: Lecture 12
10
Kraft Pulping Kinetics
H Factor/Temperature
Pulping
and
Bleaching
Relative Rate
1000
800
H factor equal to
Area under this
Curve
600
400
200
0
0
20
40
60
80
100 120 140 160 180
Time (min)
PSE 476: Lecture 12
11
Pulping
and
Bleaching
Kraft Pulping Kinetics
Example H Factor Calculation
PSE 476: Lecture 12
12
Kraft Pulping Kinetics
H Factor/Temperature
Pulping
and
Bleaching
Lignin (% of Pulp)
30
25
20
150°C
160°C
15
170°C
10
5
0
0
500
1000
1500
2000
2500
H Factor
PSE 476: Lecture 12
13
Pulping
and
Bleaching
H Factor Versus Kappa Number
As mentioned previously, H
factor is used to determine
the time required at a given
EA and sulfidity to reach a
desired kappa. This figure
shows the effect that
changing the active alkali
has on the H factor required
to reach a kappa.
PSE 476: Lecture 12
14