Model-based Optimization of a CompactCooking™ G2 Digesting Process Stage

Master’s thesis presentation for the degree of M.Sc. (Tech.) in Process Systems Engineering (Process Automation)

Igor Saavedra

Supervisor: Prof. Sirkka-Liisa Jämsä-JounelaAdvisor: Dr.-Ing. Aldo CiprianoInstructor: D.Sc. Olli Joutsimo

 Tuesday January 26, 2016

IntroductionPulp and Paper

• What is Pulp …• Fibers sources• Lignocellulosic

biomass• Market pulp

• Softwood• Hardwood

• and Paper?• Paper products• Fiber properties

Logs

Woodchips

Pulp

IntroductionKraft Pulp Mill Process

Nueva Aldea Pulp Mill 1500+1500 Adt/d pine & euca, 91% ISO, 460MWth (95 MWe), 1000 L/s water inflow

IntroductionProblem Statement

• Digesting Stage Optimization

• Key area of the Kraft pulp mill transforming woodchips into brownstock and weak black liquor by consuming steam and white liquor

• Given an scenario of operating costs and target production rate: how do we cook pulp optimally?

• CompactCooking G2 (Valmet), digesting system found in the mill, is a highly interacting process that combines liquor recycling and heat integration

IntroductionGoals, Scope and Novelty

• Main Goal• Design a process optimizer able of minimizing cost or maximizing

profit rates of a CompactCooking G2 digesting stage.

• Specific Objectives• Design and validate a dynamic model of the process stage.• Design and perform a steady-state optimization routine based on

the previously validated model.• Assess performance of theoretical optimal set-points versus

current mill set-points.

IntroductionGoals, Scope and Novelty

• Scope• Development of an applied solution for the mill.• Dynamic modeling of KPIs of stage such as

• Kappa number• Production rates • Temperatures and alkali concentrations• Pulp intrinsic viscosity and cellulose DP• “Cooking recipe” values:

• Liquor-to-wood ratios (L/W), • Alkali charges (A/W), • H-factor• Dilution factor (DF) of the wash zone

• Phenomena to be modeled are chip bed compaction, cooking reaction kinetics, and heat-exchanges within cooking liquors.

IntroductionStructure of the Thesis

Chapter 1 IntroductionLITERATURE PART

Chapter 2 The Kraft Pulp MillChapter 3 Pulp Digesting StageChapter 4 Mathematical Models on Pulp Digesters

EXPERIMENTAL PART

Chapter 5 MethodsChapter 6 Process DescriptionChapter 7 Mathematical ModelingChapter 8 Simulator DesignChapter 9 Simulation ResultsChapter 10 Optimizer DesignChapter 11 Optimization ResultsChapter 12 ConclusionsAppendix A Model-based Process Analysis

Literature ReviewMathematical Models on Pulp Digesters

• Review on first-principle modelingVroom (1957) H-Factor concept that describes the extent of delignification based on a

simple kinetic law using temperature and time as parameters

Hatton (1973; 1976) Equations relating cooking yield and kappa number with H-factor and effective alkali for softwood and hardwood species. Later he applies this work to Kraft cooking control.

Smith (1974) First version of the Purdue kinetic model. Wood solid is represented as 5 components, and parallel reaction kinetics are used to describe cooking reactions.

Christensen (1982) Improved Purdue model by search algorithm to adjust kinetics parameters for softwood and hardwood species. Liquor concentrations are also calculated.

Gustafson et al. (1983) First version of the Gustafson kinetic model. Three stages cooking: initial, bulk and residual. Wood solid is represented as 2 components: lignin and carbs

Härkönen (1987) First 2D continuous digester model with emphasis on chips and fluid flow dynamics with a simplified kinetic model. This contributed a framework for bed compaction modeling used in almost all later developments.

Literature ReviewMathematical Models on Pulp Digesters

• Review on first-principle modelingSaltin (1992) A dynamic, continuous digester model using the Purdue kinetics and a

simplified Härkönen bed compaction model. Implemented in GEMS.

Agarwal (1993) A steady-state, continuous digester model using Gustafson kinetics and implemented by the single chip approach. It also incorporated a viscosity model derived from Kubes et al. work and introduced the modelling of diffusion and chip thickness by a sphere-equivalent chip model. Implemented in GEMS.

Michelsen (1995) A dynamic, continuous digester model using a simplified Purdue-like kinetics and a modified Härkönen bed compaction model that involves solving a dynamic momentum balance for the chips phase. First modelling approach of chip level variations. Implemented in MATLAB.

Wisnewski et al. (1997) A dynamic, continuous digester model with improved Purdue kinetics but fixed bed compaction profile. It is also modelled the liquor concentration of dissolved wood substance and the chip internal porosity. Implemented in MATLAB.

He et al. (1999) First 3D model of a continuous digester based on Harkonen and Michelsen fluid dynamics assumptions with a simplified kinetics model. 3D, dyn M&E&P balances

Literature ReviewMathematical Models on Pulp Digesters

• Review on first-principle modelingBhartiya et al. (2001) Continuation of Wisnewski et al. work incorporating advances made by

Michelsen. It also contributed a modelling approach for grade transition. Implemented in MATLAB.

Andersson (2003) New kinetic model that combines Purdue and Gustafson approaches. Wood substance is represented by 5x3 components.

Kayihan et al. (2005) A dynamic, continuous digester model based on Purdue kinetics, modified Härkönen bed compaction, and Agarwal diffusion and chip thickness. It is solved by a novel cinematic approach allowing to model chip level and stochastic changes in chip size distribution. Implemented in MATLAB.

Rantanen (2006) A dynamic, continuous digester model based on Gustafson kinetics, Saltin simplified bed compaction, and Agarwal diffusion and chip thickness. It is applied to describe a LoSolids™ process (two-vessel stage) with grade transition. Implemented in MATLAB.

Nieminen et al. (2014a, 2014b)

New kinetic models of lignin and carbohydrates degradation. Delignification can be described with varying degrees of sophistication (including Donnan equilibrium); and carbs degradation is modelled based on the reaction mechanism of peeling, stopping and alkaline hydrolysis. Reactions dependence on [OH-], [HS-] and [Na+] is considered.

Literature ReviewProcess Control and Optimization

• LP optimization• Objective function as

• Cost or profit rate• Cost or profit per unit of

product or educt• Constraints on

• Flow rates, temperatures, compaction pressures, concentrations, etc.

• Linear input-output models of the process• SP-MV ( u=u(r) )• PV-MV ( y=y(u) )

Process DescriptionCompactCooking G2 System

• Physical input streams:• Woodchips• MP-steam• White liquor• Wash liquor

• Physical output streams:• Cooked pulp

Weak black liquor

Simulator DesignMethodology

• The simulator aims to capture the dynamic behavior of the system with emphasis on interaction effects

• Changes in one input variable affect several outputs in a non-linear form

• Some bias on the output is acceptable, but poor correlation between measured and simulated outputs is not.

• Simulator code builds upon parts of the Pulp Mill Benchmark Model, updating it to represent current cooking technologies

• CompactCooking G2 is a highly interacting process, thus simulation of the whole is a must for a rigorous optimization effort

Start

Process flowsheet abstraction

Conceptual model IO variables

Conceptual model states variables

Data acquisition and conditioning for

testing

Test criteria are met?

Testing runs and parameter adjustment

NO

End

Data acquisition and conditioning for

validation

Validation run

Validation criteria are met?

Validity domain definition

NO

YES

YES

Model implementation

Process historian

P&ID, PFD, DCS visualizations

Literature submodels

Open source models, code

libraries

Validated simulation

model

Process historian

Mod

el V

alid

ation

Mod

el T

estin

g

Castro, J. J., & Doyle, F. J. (2004). A pulp mill benchmark problem for control: problem description. Journal of Process Control, 14(1), 17–29.

Simulator DesignModel structure

• Logical inputs: 16 MVs 14 DVs

• Comparable outputs:

29 PVs

• Total selected outputs:

40 PV

Simulator DesignSimulink model

Simulator DesignSimulink model

Mathematical modelingMain assumptions

• Vessels are tubular moving bed reactors• Fixed levels

• Although levels were tried to be dynamically modeled, computation times increase too much and numerical stability of the model is compromised

• Two-phases reacting system• Concentrations on entrapped liquor are the same as on the free liquor phase,

thus total number of states is lowered• 1D description on the axial direction of bed compaction and reaction

kinetics phenomena• Heat-exchangers are perfectly mixed tanks

• Heat exchange occurs between hot and cold side at a given total heat transfer coefficient UA

• Liquor densities are held constant, although composition is dynamically modeled

• Liquor compositions vary solely due to retention times, no reaction kinetics take place into heat-exchangers

Mathematical modelingMain assumptions

• Woochips are composed of six mass entities• Fast lignin, slow lignin, cellulose, (galacto)glucomanan, (arabino)xylan,

and extractives

• Extractives are represent as instantaneously leached when entering the Impbin

• Liquor is composed of seven mass entities• Sodium hydroxide NaOH(aq), sodium hydrosulfide NaSH(aq), dissolved

lignin, dissolved cellulose and so on

• Consumed NaOH and NaSH are accounted for density calculations in order to keep mass balance consistency

𝜌𝑖 h𝑤 𝑒𝑟𝑒𝑖∈ {𝐿𝑓 ,𝐿𝑠 ,𝐶 ,𝐺𝑀 ,𝑋 ,𝐸 }

𝐶 𝑗 h𝑤 𝑒𝑟𝑒 𝑗∈ {𝑁𝑎𝑂𝐻 ,𝑁𝑎𝑆𝐻 ,𝐷𝐿 ,𝐷𝐶 ,𝐷𝐺𝑀 ,𝐷𝑋 ,𝐷𝐸 }

Mathematical modelingBed Compaction

• Equations based on Härkönen model 𝜌𝑐 ,𝑏=∑

𝑖𝜌𝑖 (𝑧 , 𝑡 )

𝑑𝑃 𝑙

𝑑𝑧 =𝑹𝟏(1−𝜂 )2

𝜂3𝑢𝑙+𝑹𝟐

(1−𝜂 )𝜂3

𝑢𝑙2

𝑑𝑃 𝑐

𝑑𝑧 = (𝜌𝑐 ,𝑤−𝜌𝑙 ) (1−𝜂 )𝑔−𝝁 𝑃𝑐,𝑒𝑥𝑡

𝐷 −𝑑 𝑃 𝑙

𝑑𝑧

𝜂=𝒌𝟎+( 𝑃𝑐 [kPa ]10 )

𝒌𝟏

(−𝒌𝟐+𝒌𝟑 ln (𝜅 ) )

𝜄=(1−𝜂 )(1− 𝜌 𝑐 ,𝑏

𝝆𝒘𝒐𝒐𝒅 )

𝜌𝑙=𝜌𝑤+∑𝑗𝐶 𝑗 (𝑧 , 𝑡 ) 𝜌𝑐 ,𝑤=

𝜌𝑤𝑜𝑜𝑑 (1−𝜂−𝜄 )+𝜌𝑙 𝜄  1−𝜂

𝜂𝜀1−𝜂

1−𝜀

𝑃𝑐 𝑃 𝑙

𝑑𝑉

Volumen fractions free liquor entrapped liquor woodchips solid wood

Härkönen, E. J. (1984). A Mathematical Model for Two-Phase Flow (Doctoral dissertation). Helsinki University of Technology.Härkönen, E. J. (1987). A mathematical model for two-phase flow in a continuous digester. Tappi Journal, 70(12), 122–126.

Mathematical modelingBed Compaction

• Experimental values from literature

Lee, Q. F. (2002). Fluid flow through packed columns of cooked wood chips (Master’s thesis). University of British Columbia.

Mathematical modelingReaction kinetics

• Equations based on Purdue model 𝜌𝑖=𝜌𝑖 (𝑧 , 𝑡 ) 𝑖∈ {𝐿𝑓 (1) ,𝐿𝑠 (2) ,𝐶 (3) ,𝐺(4) ,𝐴(5) ,𝐸 (6 ) }𝐶 𝑗=𝐶 𝑗 (𝑧 , 𝑡 ) 𝑗 ∈ {𝑁𝑎𝑂𝐻 (1 ) ,𝑁𝑎𝑆𝐻 (2 ) ,𝐷𝐿 (3 ) ,𝐷𝐶 (4 ) ,𝐷𝐺 (5 ) ,𝐷𝐴 (6 ) ,𝐷𝐸 (7 ) }

𝑅𝑖=−𝒆𝒇 (𝑘𝑎𝑖𝐶𝑁𝑎𝑂𝐻

12+𝑘𝑏𝑖𝐶𝑁𝑎𝑂𝐻

12𝐶𝑁𝑎𝑆𝐻

12)(𝜌𝑖−𝝆 𝒊

∞ )

𝑘𝑎𝑖=𝑘𝑎0 𝑖 exp(−𝐸𝑎𝑖

𝑅𝑇 ) 𝑘𝑏𝑖=𝑘𝑏0 𝑖exp (−𝐸𝑏𝑖

𝑅𝑇 )𝑅𝑁𝑎𝑂𝐻=1−𝜂𝜂+𝜄 (𝜷𝑬𝑨𝑳∑

𝑖=1

2

𝑅𝑖+𝜷𝑬𝑨𝑪∑𝑖=3

5

𝑅𝑖) 𝑅𝑁𝑎𝑆𝐻=1−𝜂𝜂 𝛽𝐻𝑆𝐿∑𝑖=1

2

𝑅𝑖

𝑅 𝑗=1−𝜂𝜂 𝑅𝑖

Wisnewski, P. A., Doyle, F. J., Kayihan, F. (1997). Fundamental Continuous Pulp-Digester Model for Simulation and Control. AIChE Journal, 43 (12), 3175-3192Christensen, T. (1982,). A Mathematical Model of the Kraft Pulping Process (Doctoral Dissertation). Purdue University.Smith, C. C. & Williams T. J. (1974). Mathematical Modeling, Simulation and Control of the Operation of Kamyr Continuous Digester for Kraft Process,Tech. Rep. 64, PLAIC, Purdue University.

Mathematical modelingReaction kinetics

• Experimental values from literature

Wisnewski, P. A., Doyle, F. J., Kayihan, F. (1997). Fundamental Continuous Pulp-Digester Model for Simulation and Control. AIChE Journal, 43 (12), 3175-3192Christensen, T. (1982). A Mathematical Model of the Kraft Pulping Process (PhD’s thesis). Purdue University.

Mathematical modelingVessel section

• Dynamic mass and energy balances

(𝐴 (1−𝜂 )𝐶𝑃 , 𝑠∑𝑖𝜌𝑖+ 𝐴 (𝜂+𝜄 )(𝐶𝑃 , 𝑠∑

𝑗𝐶 𝑗+𝐶𝑃 ,𝑤 𝜌𝑤 )) 𝜕𝑇𝜕𝑡 =−( 1𝜏𝑐

𝐶𝑃 , 𝑠∑𝑖𝜌𝑖+

1𝜏 𝑙 (𝐶𝑃 , 𝑠∑

𝑗𝐶 𝑗+𝐶𝑃 ,𝑤𝜌𝑤)) 𝜕𝑇𝜕 𝑧 +𝐴𝐻𝑅∑

𝑖𝑅 𝑖

𝜕𝐶 𝑗

𝜕𝑡 =− 1𝜏 𝑙

𝜕𝐶 𝑗

𝜕𝑧 +𝑅 𝑗

𝜕𝜌 𝑖

𝜕𝑡 =− 1𝜏𝑐

𝜕 𝜌𝑖

𝜕 𝑧 +𝑅𝑖1𝜏 𝑙

=𝐹 𝑙

𝐴 (𝜂+𝜄 )𝐹 𝑙

𝐴 =𝑢𝑙

1𝜏𝑐

=𝐹 𝑐

𝐴 (1−𝜂 )𝐹𝑐

𝐴 =𝑢𝑐

𝜂𝜀1−𝜂

1−𝜀

𝐹 𝑐 𝐹 𝑙

𝑑𝑉

Volumen fractions free liquor entrapped liquor woodchips solid wood

• Steady-state momentum balance

Simulation ResultsTesting (Pine)

Laboratory off-line

measure-ments with long delay

Own estimates.

NO SENSOR at the mill

Laboratory off-line

measure-ments with

delay

Manipulated variable (simulated)Disturbance (simulated)Output (simulated)Mill data (measured)

Simulation ResultsTesting (Pine)

DCS estimate.

NO SENSOR at the mill

Cooking and bleaching yield are

actually set point

parameters

Prod. rate is assumed based on yield set points

Manipulated variable (simulated)Disturbance (simulated)Output (simulated)Mill data (measured)

Simulation ResultsValidation (Pine)

Manipulated variable (measured)Disturbance (measured)Output (simulated)Mill data (measured)

Simulation ResultsValidation (Pine)

Output (simulated)Mill data (measured)

Simulation ResultsAssessment

• In general, simulated outputs capture the main dynamic trends with reasonable agreement Model is operationally validated

• Simulated temperature signals show higher variability than measured ones• Improvements in the simulated heat-exchanger networks is required, but

this demands implementing several TI at the mill in order to estimate U coefficients for each heat-exchanger (or to estimate U within the model and to have output signals for comparison)

• Simulated blowline flow rate shows higher variability than measured • This might be generating a bias in the wash zone dilution factor calculation• One way to fix this involves using the signal as a logical input (manipulated

variable) and changing the model structure for bed compaction calculation Long-term effort

Optimizer DesignMethodology

• The routine tries to find a new cooking recipe that optimize process economics by changing following DCS setpoints:

Liquor to wood ratio (L/W) for Impbin (bottom), Digester cook zone 1 and 2

Alkali charge (EA/W) for the whole area, fresh charge to Impbin, and fresh charge to Digester

Alkali splitting as white liquor flow distributionCooking temperature (for H-Factor setpoint)Digester wash zone dilution factor (DF)

• Decision variables are taken as manipulated variables, thus optimization outputs continue to be the same as in the simulation model

• A previously validated model is a critical factor to judge the optimization results

Optimizer DesignObjective Functions

Optimization ResultsRaw Results (Pine)

U0U profit heuopt

U cost heuopt

Chipmeter speed rpm 15.93 15.93 15.93MP steam flow rate kg/s 10.27 7.23 11.05White liquor flow rate l/s 65.05 78.87 43.00Wash liquor flow rate l/s 151.41 116.56 111.18Filter reject flow rate l/s 35.15 96.94 8.78Middle extraction flow rate l/s 35.58 138.33 8.89Transfer liquor flow rate l/s 232.52 58.13 341.89Upper extraction flow rate l/s 114.11 527.65 266.82Lower extraction flow rate l/s 126.10 31.52 45.70White liquor split fraction 1 0.0922 0.2499 0.1068White liquor split fraction 2 0.3995 0.0999 0.0999White liquor split fraction 3 0.0000 0.0000 0.2362Transfer liquor split fraction 1 0.2300 0.0575 0.0575Transfer liquor split fraction 2 0.0223 0.0056 0.1674Upper liquor split fraction 1 0.1397 0.0349 0.0349Upper liquor split fraction 2 0.2406 0.8101 0.8101

Y0Y profit heuopt

Y cost heuopt

Blowline flow rate l/s 148.47 152.10 137.39Top liquor flow rate l/s 151.63 174.80 140.26Bottom liquor flow rate l/s 198.67 276.57 313.93Cooking Kappa 27.87 28.10 28.49Blowline consistency w/v% 11.11 10.89 12.01WBL consistency w/v% 11.06 11.48 12.46Impbin top temp. C 98.93 112.47 106.44Top liquor temp. C 127.74 141.99 140.31Transfer liquor temp. C 119.26 134.58 133.86Digester top temp. C 151.89 148.81 159.51Upper extraction temp. C 157.99 151.62 165.13Lower extraction temp. C 151.11 154.69 159.35Blowline temp. C 100.99 100.70 101.32White liquor hot temp. C 144.49 143.32 148.19Lower extraction cold temp. C 146.08 145.20 150.17Top liquor EA conc. g/l 32.39 28.44 22.37Transfer liquor EA conc. g/l 14.21 15.13 8.77Upper extraction EA conc. g/l 17.10 20.42 9.31Lower extraction EA conc. g/l 10.09 13.32 4.55Cooked pulp prod. rate ADt/d 1582.82 1589.45 1583.77WBL prod. rate tDS/d 2120.25 2337.34 2027.56Cooking yield % 46.37 46.55 46.38Cooking wood sp. cons. m3sub/ADt 5.07 5.05 5.07EA/W total % 22.29 24.66 18.51EA/W impbin fresh % 8.08 5.10 5.64EA/W digester fresh % 12.15 15.34 11.03L/W impbin top m3/BDt 5.60 6.25 5.28L/W impbin bottom m3/BDt 4.60 3.81 4.66L/W digester top m3/BDt 6.09 11.21 7.38L/W digester bottom m3/BDt 2.79 2.06 1.92DF digester wash zone m3/ADt 0.67 0.14 0.45

Impbin max Pc kPa 13.88 14.92 12.99

Digester max Pc kPa 23.37 31.50 23.99Blowline carryover kgDS/BDt 1.96 1.46 2.08WBL heating value HHV MJ/kg dry 15.03 13.66 15.68

Technically feasible?

Digester hang?Lignin precipitation risk?

Optimization ResultsEconomic Assessment

• For each objective function a new cooking recipe has been identified

• But “how much” optimal are these recipes?

Y0Y profit heuopt

Y cost heuopt

Constraint set-points

Bleached pulp prod. rate ADt/d 1535

Cooking kappa κ 28

Computed set-points

EA/W total % 20.05 21.97 18.83

EA/W impbin fresh % 8.02 5.77 6.70

EA/W digester fresh % 12.03 16.20 12.13

L/W impbin top m3/BDt 5.58 5.98 5.18

L/W impbin bottom m3/BDt 4.58 3.44 4.22

L/W digester cook zone 1 m3/BDt 5.89 5.33 6.56

L/W digester cook zone 2 m3/BDt 2.86 3.30 2.62

DF digester wash zone m3/ADt 1.24 0.60 0.99

H-factor H 631.41 714.71 703.77

Simulated variables

Cooking kappa κ 28.66 28.62 28.62

Digester top temp. C 151.63 153.06 152.88

MP steam flow rate kg/s 10.27 8.07 9.40

Cooked pulp prod. rate ADt/d 1663.88 1689.62 1662.80

Cooking yield % 48.74 49.49 48.71

Cooking wood sp. cons. m3sub/ADt 4.82 4.75 4.83

Optimization ResultsEconomic Assessment

Steady-state Optimization

380

400

420

440

460Profit rate

USD

/min

250

260

270

280

290Cost rate

USD

/min

360

370

380

390

400Profit per ADt

USD

/AD

t

225

230

235

240

245Cost per ADt

USD

/AD

t

0 500 1000 1500 200072

74

76

78

80

82Profit per m3sub

USD

/m3 su

b

min0 500 1000 1500 2000

47.5

48

48.5

49

49.5Cost per m3sub

min

USD

/m3 su

b

Profit rate as o.f.Cost rate as o.f.Base case (ss)Base case (dyn)

Optimization ResultsEconomic Assessment

• Process economics can be evaluated from several point of views. This work considers 3 definitions of profit/cost: • per unit of time, • per unit of actual cooked ADt• per unit of actual woodchips m3sub consumed

• Optimized recipe for cost reduction results more attractive economically than the profit recipe• Savings per actual cooked ADt up to 4 USD/ADt• For a line aiming to produce 1500 ADt/d, this represent up to 2.19

MM annual savings

ConclusionsMain Conclusions

• CompactCooking G2 system has been dynamically modeled with fairly good results although high uncertainty on process disturbance signals.

• An LP task can be formulated around an identified mill’s steady state, thus permitting to calculate a new optimized cooking recipe (optimization direction for mill setpoint changes).

• Potential savings based on the model prediction may reach up to 4 USD/ADt, what for a modern mill (1500 – 2000 ADt/d) represent savings in the order of 1 – 3 MM/y.

THANKS FOR YOUR ATTENTION!

Simulated ContributionA novel model-based process analysis technique

Simulated ContributionCase study: CompactCooking G2 analysis

Simulated ContributionCase study: CompactCooking G2 analysis

Simulated ContributionCase study: CompactCooking G2 analysis

… i.e., temperature control scheme must be improved in order to reduce cooking kappa variability