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Pulping and Bleaching PSE 476/Chem E 471

Pulping and Bleaching PSE 476/Chem E 471. Lecture #12 The H Factor. Chemical Pulping Agenda. Train question Derivation of “H” factor equation Example “H” factor calulation Validity of “H” factor. Kraft Pulping Kinetics Question about a Train.

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Pulping and Bleaching PSE 476/Chem E 471

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

  2. Chemical PulpingAgenda • Train question • Derivation of “H” factor equation • Example “H” factor calulation • Validity of “H” factor PSE 476: Lecture 12

  3. Kraft Pulping KineticsQuestion 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

  4. (1) dx = k f (composition) = rate of lignin removal dt (2) x(t) = ƒ k dt Kraft Pulping KineticsDerivation 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: 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 PSE 476: Lecture 12

  5. Kraft Pulping KineticsDerivation of “H” Factor (2) Ea = activation energy(32 kcal/mole (kraft)) T = absolute temperature R = gas constant A = constant -Ea/RT (3) k = A e 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

  6. Kraft Pulping KineticsDerivation 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 (43.2-16,113/T) (7) kr = e From this equation, it is possible to see that kr is significantly affected by temperature (see figure on page7) PSE 476: Lecture 12

  7. Kraft Pulping KineticsRelative Rate Versus Temperature PSE 476: Lecture 12

  8. (-16,113/T) (43.2) kr = e e (-16,113/T) k = Ae (43.2) (10) Where p = A/e k = (p)(kr) Kraft Pulping KineticsDerivation of “H” Factor (4) Equation 7 can be rewritten (8) Equation 4 becomes: (9) Combining these 2 equations leads to: PSE 476: Lecture 12

  9. Kraft Pulping KineticsDerivation 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

  10. 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

  11. Kraft Pulping KineticsH Factor/Temperature H factor equal to Area under this Curve PSE 476: Lecture 12

  12. Kraft Pulping KineticsExample H Factor Calculation PSE 476: Lecture 12

  13. Kraft Pulping KineticsH Factor/Temperature PSE 476: Lecture 12

  14. 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

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