1 carbohydrate loss models modeling yield prediction – a very difficult modeling problem
Post on 21-Dec-2015
233 views
TRANSCRIPT
1
Carbohydrate Loss Models
Modeling yield prediction – A Very Difficult Modeling ProblemModeling yield prediction – A Very Difficult Modeling Problem
2
Gustafson Model
• Two methods have been tested, but since both have the same accuracy, the simplest has been retained.
• Two methods have been tested, but since both have the same accuracy, the simplest has been retained.
3
Gustafson: Model I
Initial k=2.5*[OH-]0.1
Bulk k=0.47
Residual k=2.19
Basic Structure: dc/dt=k*dL/dt
Some physical justification for this is given by carbohydrate-lignin linkages.
Carbohydrates lumped into a single group.
4
Gustafson: Model I
• Carbohydrate/lignin relation is assumed to be stable and not a strong function of pulping conditions.
• Selectivity of reactions assumed to be slightly dependent on OH- but independent of temperature.
• Yield/kappa relationship can be improved by using both lower pulping temperature and less alkali.
• Carbohydrate/lignin relation is assumed to be stable and not a strong function of pulping conditions.
• Selectivity of reactions assumed to be slightly dependent on OH- but independent of temperature.
• Yield/kappa relationship can be improved by using both lower pulping temperature and less alkali.
5
Gustafson: Model II
• Divide the carbohydrates into cellulose and hemicellulose.
• For each of those divide the pulping into initial and bulk pulping.
• The transitions are defined by the lignin content.
• Divide the carbohydrates into cellulose and hemicellulose.
• For each of those divide the pulping into initial and bulk pulping.
• The transitions are defined by the lignin content.
6
Gustafson: Model II- Initial Phase
dH/dt=k1*[OH-]1.5(H-5)
dC/dt=k2*[OH-]1.5(C-32)
High reaction orders came from data generated by Genco
E ≈ 8,300 cal/mole
7
Gustafson: Model II- Bulk Phase
dH/dt=k3*[OH-] (H-5.0) E ≈ 22,000 cal/mole
dC/dt=k4*[OH-](C-32) E ≈ 36,000 cal/mole
8
Gustafson: Model II Application
• Applied the model to predict pulping behavior of RDH and SuperBatch (displacement batch) digesters.
• Model could predict, but was unstable at extremes, especially high alkaline conditions.
• Applied the model to predict pulping behavior of RDH and SuperBatch (displacement batch) digesters.
• Model could predict, but was unstable at extremes, especially high alkaline conditions.
9
Purdue Model
• Carbohydrates divided into cellulose, xylans and glucomannan
• All components use the form:
» dCn/dt=(k1[OH-]+k2[OH-]1/2[HS-]1/2)(Cn-Cnf)
• Carbohydrates divided into cellulose, xylans and glucomannan
• All components use the form:
» dCn/dt=(k1[OH-]+k2[OH-]1/2[HS-]1/2)(Cn-Cnf)
10
Purdue Model
• Assumed to have fast and slow reaction components much like lignin
• Assumed to have fast and slow reaction components much like lignin
Cellulose/Xylan E ≈ 9000 cal/mole
Glucomannan (fast) E ≈ 17,000 cal/mole
Glucomannan (slow) E ≈ 40,000 cal/mole
11
Andersson Model
• Carbohydrates split into:» Cellulose
» Glucomannan
» Xylan
• Fast, medium and slow components are assumed for each carbohydrate phase.
• Carbohydrates split into:» Cellulose
» Glucomannan
» Xylan
• Fast, medium and slow components are assumed for each carbohydrate phase.
12
Andersson Model
• General Kinetics:• General Kinetics:
CkOHkdt
dC a *)][( 21
In practice, all carbohydrates are lumped together into CH.
13
Andersson Model
• Complex model to estimate relative amount of medium and slow carbohydrate
• Complex model to estimate relative amount of medium and slow carbohydrate
CH* ≡ Carbohydrate content where CH2 & CH3 are equal
≡ 42.3 + 3.65 ( [OH-] + 0.05 )-0.54
14
Andersson Model
• Activation Energies:• Activation Energies:
Fast E ≈ 12,000 cal/mole
Medium E ≈ 35,000 cal/mole
15
Model PerformanceGustafson model
Virkola data on mill chips
16
Model PerformanceAndersson model
Prediction of cellulose and glucomannans
17
Model PerformanceAndersson model
Prediction of xylans
18
Model PerformanceAndersson model
Prediction of total carbohydrates as function of [OH-]
19
Model PerformanceAndersson model
Prediction of total carbohydrates as function of temperature
20
Prediction of pulp viscosity
Dependence of viscosity on pulping conditions was modeled
»Viscosity is a measure of degradation of cellulose chains
»Effect of temperature, alkalinity, initial DP, and time on viscosity is modeled
»Model is compared with experimental data from two sources
21
Prediction of pulp viscosity
dDPdt
k OH e DP
KDP
C C
n E RTn
cell na
pulp cell non cell
02
1
[ ]
[ ]
[ ] [ ] ( )[ ]
/
[ ] - Intrinsic viscosity
C - Cellulose fraction in pulp
- Degree of polymerization for celluloseDPn
22
Gullichsen’s viscosity data
23
Virkola’s viscosity data
24
Virkola’s viscosity data
H-factor
IntrinsicViscositydm3/ kg
600
700
800
900
1000
1100
1200
0 1000 2000 3000 4000
19% E.A.22% E.A.
25% E.A.
25
[OH-] & [HS-] Predictions
• Calculated by stoichiometry in all models as follows:• Calculated by stoichiometry in all models as follows:
)/,/(][
dtdCdtdLfdt
OHd
0][
dt
HSd
)/,/(][
dtdCdtdLfdt
OHd
)/(][
dtdLfdt
HSd
Gustafson
Purdue
Andersson - Stoichiometry
26
Model PerformanceGustafson model
Gullichsen data on mill chips