1. Pulping and Bleaching PSE 476: Lecture 121 Pulping and Bleaching PSE 476/Chem E 471 Lecture #12 The H Factor Lecture #12 The H Factor

2. Pulping and Bleaching PSE 476: Lecture 122 Chemical Pulping Agenda Train question Derivation of “H” factor equation Example “H” factor calulation Validity of “H” factor Train question Derivation of “H” factor equation Example “H” factor calulation Validity of “H” factor

3. Pulping and Bleaching PSE 476: Lecture 123 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. 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.

4. Pulping and Bleaching PSE 476: Lecture 124 Kraft Pulping Kinetics Derivation of “H” Factor (1) 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: Cannot solve equation because k is dependent on temperature dx dt = k f (composition) = rate of lignin removal(1) x(t) = ƒ k dt (2) 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:

5. Pulping and Bleaching PSE 476: Lecture 125 Kraft Pulping Kinetics Derivation of “H” Factor (2) k = A e -E a /RT E a = activation energy(32 kcal/mole (kraft)) T = absolute temperature R = gas constant A = constant Taking the log of both sides: ln k = ln A - (E a /RT) At 100°C, the above equation becomes: ln k 100 = ln A - (E a /R373) (3) (4) (5) Subtracting equation 5 from 4 gives: ln(k/k 100 ) = -(E a /RT) + (E a /373R)

6. Pulping and Bleaching PSE 476: Lecture 126 Kraft Pulping Kinetics Derivation of “H” Factor (3) ln(k/k 100 ) = -(E a /RT) + (E a /373R)(5) ln k r = -(16,113/T) + 43.2 Substituting in the appropriate values k r is called the relative rate constant or a comparison of the rate constant at a temperature to that at 100°C (6) k r = e (43.2-16,113/T) From this equation, it is possible to see that k r is significantly affected by temperature (see figure on page7) (7)

7. Pulping and Bleaching PSE 476: Lecture 127 Kraft Pulping Kinetics Relative Rate Versus Temperature

8. Pulping and Bleaching PSE 476: Lecture 128 Kraft Pulping Kinetics Derivation of “H” Factor (4) Equation 7 can be rewritten k r = e (43.2) e (-16,113/T) Equation 4 becomes: Combining these 2 equations leads to: (8) k = Ae (-16,113/T) (9) k = (p)(k r ) (10) Where p = A/e (43.2)

9. Pulping and Bleaching PSE 476: Lecture 129 Kraft Pulping Kinetics Derivation of “H” Factor (4) Equation 10 can be substituted into equation 2 leaving: ƒ k dt = p ƒ k r dt(p is a constant) The expression ƒ k r dt is referred to as the “H” factor: (11) H = ƒ k r dt (12) 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)

10. Pulping and Bleaching PSE 476: Lecture 1210 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 k r determined. The k r 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,

11. Pulping and Bleaching PSE 476: Lecture 1211 Kraft Pulping Kinetics H Factor/Temperature H factor equal to Area under this Curve

12. Pulping and Bleaching PSE 476: Lecture 1212 Kraft Pulping Kinetics Example H Factor Calculation

13. Pulping and Bleaching PSE 476: Lecture 1213 Kraft Pulping Kinetics H Factor/Temperature

14. Pulping and Bleaching PSE 476: Lecture 1214 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.