A pulp mill benchmark problem for control: problem description

A pulp mill benchmark problem for control: problem description

J.J. Castroa, F.J. Doyle IIIb,*aChemical Engineering Department, University of Delaware, Newark, DE 19711, USA

bChemical Engineering Department, University of California, Santa Barbara, CA 93106, USA

Abstract

This work introduces a benchmark problem of a pulping process, including both the fiber line and the chemical recovery area.

The complete details of the pulp mill process are presented, including the control objectives, modes of operation, process con-straints, measurements and costs. The dynamic model, including the source/binary code of all the unit operations is made availableto the academic community as a benchmark for use in process system engineering studies.

# 2003 Elsevier Ltd. All rights reserved.

Keywords: Dynamic modeling; Pulp mill process; Process simulation; Process control

1. Introduction

The process control academic community has expres-sed great interest in studying realistic industrial processcontrol problems. In 1986, Shell presented a controlproblem in their process control workshop [16]. TheShell control problem consisted of an oil fractionatorwith seven measured variables, three controlled vari-ables, and two disturbances. The problem generatedtremendous interest in the research community and in1988, the second Shell process control workshop pre-sented 12 papers with solution strategies to the problem[15].The Shell problem was an interesting benchmark for

testing control algorithms but it consisted of a singleunit operation. In 1990, Downs and Vogel [4] presenteda plant-wide industrial process control problem thatbecame known as the Tennessee Eastman challengeproblem. This process consisted of a reactor, condenser,separator, compressor, and stripper with a gas recyclestream. The Tennessee Eastman challenge problem hasbeen studied in detail by several authors including:McAvoy and Ye [13], Lyman and Georgakis [12],Kanadibhotla and Riggs [8], Barnerjee and Arkun [1],McAvoy et al. [14], Ricker [17,18], and others. In 1995,Luyben et al. [11] presented an industrial control prob-

lem that consisted of a process with two reaction steps,three distillation columns and two recycle streams.Several researchers have presented dynamic mathe-

matical models of different unit operations in a pulp andpaper mill. The reader may refer to Kayihan [9] for adetailed review of the work on modeling and control ofpulp and paper processes. The Purdue Laboratory forApplied Industrial Control has published dynamicmodels of the chemical recovery section of a pulp millprocess as well as models of digesters and pulp washers;however the details of the dynamic models as well as thecode are not easily available for distribution [3,5,7].Others have developed commercial proprietary pack-ages of pulp and paper processes, including SIMMONIDEAS1 and CADSIM Plus.2

This work is the first to present a complete bench-mark problem of a pulping process (including both thefiber line and the chemical recovery areas). The com-plete details of the pulp mill process are presented,including the control objectives, modes of operation,process constraints, and process measurements. Inaddition, the details of the mathematical models as wellas the source code for all the unit operations are pro-vided under a license similar to the GPL license used inUnix/Linux systems and available for download fromthe Web.3

0959-1524/03/$ - see front matter # 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/S0959-1524(03)00011-8

Journal of Process Control 14 (2004) 17–29

www.elsevier.com/locate/jprocont

* Corresponding author at present address: Weyerhaeuser Co.,

Vailliant, OK 74764, USA.

E-mail address: [email protected] (F.J Doyle).

1 IDEAS is a trademark of ALEC Technologies Inc.2 CADSIM Plus is a trademark of Aurel Systems Inc.3 Contact F. Doyle for further details.

http://www.elsevier.com/locate/jprocont/a4.3d

mailto:[email protected]

The emergence of such plantwide benchmarks benefitsboth academia and industry. Academic researchers canuse these benchmark problems to test new control tech-nologies, develop plantwide control strategies, andperform optimization studies. Similarly, the industrybenefits from the published control studies of such pro-cesses by implementing new control strategies in theirprocesses. It is the aim of the present authors that thisbenchmark problem may be used as the basis forresearch studies in process modeling, control, optimiza-tion, and fault diagnosis. The application of one plant-wide control design is presented in the second part ofthis article.

2. Process description

The primary goal of a pulp mill is to produce pulp ofa given Kappa no. or brightness while minimizingenergy costs, utilities and chemical make-up streams.Pulp mills can be divided in two major areas: fiber lineand chemical recovery. A typical flowsheet is depicted inFig. 1, which shows the key unit operations: the diges-ter, the brown stock washers, the oxygen reactor, thepre-bleach chest storage tank, the bleach plant (D1ED2),evaporators, recovery boilers, smelt dissolving tank,green liquor clarifiers, mud washers, slaker/classifier,causticizers, white liquor clarifier and the lime kiln.

Fig. 1. Simplified schematic of the pulp mill process.

18 J.J. Castro, F.J. Doyle III / Journal of Process Control 14 (2004) 17–29

The main goal of the fiber line is to remove themajority of the lignin (a ‘‘glue like’’ polymeric substancethat keeps the wood fibers together) from the wood andto achieve a certain brightness coefficient by the end ofbleaching. This is accomplished with such chemicals assodium hydroxide (NaOH), sodium hydro-sulfide(NaSH), oxygen and chlorine dioxide. The chemicalrecovery loop is responsible for regenerating the whiteliquor (solution of sodium hydroxide and sodiumhydrosulfide) from the extracted liquors from the diges-ter and the brown stock sections to make the processeconomically feasible.The fiber line process is primarily sequential from the

digester to brown stock washing, and the bleaching sec-tion. Wood chips enter the digester together with thewhite liquor (mixture of NaOH and NaSH). The mainpurpose of the digester is to delignify the wood so that itcan be blown (separated into fibers). The main variableof interest is the Kappa no., a measure of the amount oflignin remaining in the wood. After the digester, thepulp goes to the brown stock washing section wheredissolved lignin and chemicals are removed and sent tochemical recovery or recycled back to the digester asdilution water. The next sequence of operations takesplace in the bleach plant. The bleaching towers havebeen described using the standard naming conventionsfor bleaching sequences. Specifically, bleach towers arereferenced using letters and subscripts, where the firstcapital letter refers to the oxidizing/reducing chemicalused in the tower and subscripts are used when there ismore than one tower using the same bleaching chemicalto identify such towers in increasing order. Therefore,the bleaching sequence for this process is OD1ED2,which means that the pulp is delignified in an oxygenreactor (O) followed by a chlorine dioxide tower (D1)and then by a sodium hydroxide tower (E). Finally,most of the brightening is accomplished in the secondchlorine dioxide tower (D2). Hence, the most importantvariables in the bleach plant are the Kappa no. and thebrightness. It should be noted that between the O towerand the D1 tower there is an additional storage tank.The chemical recovery loop is necessary to make the

pulping process economically feasible. The main objec-tives of the recovery loop are to regenerate the NaOHand Na2S. Chemical recovery begins with the weakblack liquor (WBL) at 15% solids (organics, sodiumsalts, inerts) coming from the digester extract liquorflows (upper extract from cook zone and lower extractfrom mcc cook zone) and the brown stock washing sys-tem. WBL is concentrated in a multi-effect evaporationsystem to reach a solids content greater than 63%, afterwhich it is considered black liquor (BL) capable of sus-taining combustion. Here the objective is to produce BLwith a solids mass fraction no lower than 60% (toensure combustion of the liquor) and not greater than70% (to avoid excessive scaling in the evaporation sys-

tem). BL is sent to the recovery boiler where the com-bustion of the liquor organics provide the energy toproduce high pressure steam and to carry out thereduction reactions to recover Na2S from Na2SO4 andother sulfur-based salts, and to recover Na2CO3. Themolten smelt (solids from the black liquor) is mixedwith weak wash water in the smelt dissolving tank toproduce green liquor (GL) which is mostly composed ofNa2CO3 and Na2S. GL goes to the green liquor clarifierand the dregs washer where the unburned carbon andother insoluble solids are removed from the liquor.After the clarifier, the GL goes through the slaking/causticizing reactions to produce white liquor (WL).The WL then goes through the while liquor clarifierwhere CaCO3 and other insoluble solids are separatedand the liquor goes to the digester and the oxygen reac-tor. The lime mud from the white liquor clarifier is sentto the lime kiln to recover the lime.The pulp mill process has several recycle streams that

increase process interactions. In the fiber line area, theeffluent from the post-oxygen reactor washer is used aswash liquor in the brown stock washers and for dilutionwater in the digester emcc zone. In addition, the effluentfrom the D2 washer is used as wash liquor for the Ewasher. The chemical recovery area is indeed a largerecycle loop responsible for producing WL from WBL.It also has several internal loops to minimize inorganicchemical losses. The underfiow from the GL clarifier iswashed in a dregs washer with fresh water and theliquor effluent is recycled and mixed with the GL beforeclarification. The lime mud washers effluent is recycledback to the lime mud storage tank or sent to the limekiln loop to recover the CaO from the CaCO3. Finally,some of the condensate from the black liquor evapora-tors is used as shower wash water for pulp washers inthe fiber line area. These recycle streams increase inter-actions in the process as well as the time required toachieve steady-state. The process also exhibits large timedelays and other process nonlinearities that complicatecontroller design and limit the achievable performanceof feedback controllers.The process in operated in six different modes of

operation which result from two different pulp grades(E Kappa no., D2 brightness) and three differentproduction rates (see Table 1).

Table 1

Modes of operation of pulp mill process

Output
Targets
Production ratetons

day

� �
1000, 800, 1200
E Kappa no.
2.50 1.25
D2 Brightness
0.81 0.86
J.J. Castro, F.J. Doyle III / Journal of Process Control 14 (2004) 17–29 19

2.1. Mathematical model

A nonlinear fundamental model of the pulp mill pro-cess has been developed from a flowsheet of an actualpulp mill. For purposes of these modeling studies, thelevel of detail in the dynamic models can by consideredto be of medium complexity. Dynamic mass andenergy balances were used to model all the components(except water) and mechanical energy balances wereneglected.Unit operations were divided into two types: perfectly

mixed vessels and distributed parameter systems (plugflow vessels). The partial differential equations (PDEs)arising from mass and energy balances were solvedusing the method of lines (MOL) [19] or the ‘‘cinematictechnique’’ [10]. Mass and energy balances were com-bined with empirical equations for physical propertiesor thermodynamic information. This level of detail wasnecessary to have a representation of the process thatwas as accurate as possible while still providing a modelthat could be used for real-time open- and closed-loopsimulations.The dynamic model is a collection of modules that

simulate each of the unit operations. The modules arewritten in the C programming language usingMATLAB’s4 s-function format with SIMULINK5 asthe interface to define the millwide process.The complete mathematical model (including the

fiberline and the chemical recovery loop) has approxi-

mately 8200 states, with a total of 142 inputs (82manipulated variables and 60 disturbances) and 114outputs. The number of outputs can be varied toinclude other variables of interest as well as secondarymeasurements for inferential control. The details of thederivation of the mathematical model as well as all thefiles necessary to run the millwide simulations areavailable for download from the Internet.Figs. 2–9 show detailed diagrams of the pulp mill

process with the location of all the outputs andmanipulated variables (MVs). The reader may refer tothe Appendix for a complete list of all the outputs, MVsand disturbances of the millwide model.

2.2. Process measurements and delays

Table 2 shows all the measurement informationavailable for the outputs including the sampling fre-quency of the measurements, and the associated time-delay. The sampling rates and delays are divided intothree categories (slow, nominal, fast). These cate-gories represent the degree of measurement technol-ogy available at the mill. An example of this wouldbe the extracted liquor compositions from the Kamyr

4 MATLAB is a trademark of MathWorks Inc. For more infor-

mation visit the Web-site: http://www.mathworks.com.5 SIMULINK is a trademark of MathWorks Inc. For more infor-

mation visit the Web-site: http://www.mathworks.com.

Fig. 2. Schematic of the digester: square (process outputs), hexagon (process connections), none (manipulated variable).


http://www.mathworks.com

http://www.mathworks.com

digester. If the mill only performs off-line analysis ofthe liquor (which is common in most mills) then thesampling rate will be regarded as slow (i.e. 2 h sam-pling with 2 h delay); however, if the mill hasimplemented on-line analyzers, the sampling rate maybe considered as fast (10 min sampling with 10 mindelay).The measurement delay is assumed to be equal to the

sampling period. For continuous measurements thedelay is zero.

2.3. Control objectives

The control objectives of the process are as follows:

� Maintain process variables at their desired set-points.

� Keep process conditions within their respectiveconstraints (Tables 3 and 4).

� Minimize variability in the production rate andthe quality variables described in Table 1.

Fig. 3. Schematic of the brown-stock: square (process outputs), hexagon (process connections), none (manipulated variable).

Fig. 4. Schematic of the oxygen tower: square (process outputs), hexagon (process connections), none manipulated variable).


Fig. 5. Schematic of the bleach plant: square (process outputs), hexagon (process connections), none (manipulated variable).

Fig. 6. Schematic of the black liquor evaporators: square (process outputs), hexagon (process connections), none (manipulated variable).


� Minimize use of wood chips, utilities and make-up chemicals.

� Reject disturbances as quickly as possible with-out violating constraints on quality variablesduring all the modes of operation.

� Minimize transition time between modes ofoperation without violating process constraints.

2.4. Constraints

Tables 3 and 4 give the constraints on the MVs andoutputs of the process. The MV constraints are hardconstraints and the output constraints are soft con-straints. Most of the MVs are constrained between�1.0 (scaled values). The constraints for the variables

Fig. 7. Schematic of the green liquor section: square (process outputs), hexagon (process connections), none (manipulated variable).

Fig. 8. Schematic of the recausticizing: square (process outputs), hexagon (process connections), none (manipulated variable).


that do not follow such limits are described in Table 3.Table 4 lists the output variables that are constrained.The other outputs are considered to be unconstrained.All the variables have been scaled as follows:

usc ¼u� ussDumax

ð1Þ

ysc ¼y� yssDymax

ð2Þ

where u, uss and umax are the unscaled inputs, nom-inal/steady-state value of inputs, and maximum range ofchange of the inputs, respectively, and y, yss and ymax

are the unscaled outputs, nominal/steady-state value of

outputs, and the maximum range of change of the out-puts, respectively. The nominal values and scaling fac-tors for all outputs, MVs and disturbances are availablefrom the Web.

2.5. Operating costs

Table 5 details the costs that can be used for optimi-zation studies. It is given to facilitate the comparison ofoptimization studies as well as to provide a means toanalyze the economical performance of different controlimplementations.

Fig. 9. Schematic of the lime kiln section: square (process outputs), hexagon (process connections), none (manipulated variable).

Table 2

Process measurements available

Measurement
Sampling period (min)
Temperatures
Continuous
Pressures
Continuous
Liquor compositions
120
BL dissolved solids
5
Dilution factors
5
Wash to liq. ratio
5
Consistency
5
Kappa no.
10
D2 brightness
Continuous
Lime mud composition
120
Vessel volumes
Continuous
Volumetric flows
Continuous
Mass flows
Continuous
Conductivity
Continuous
Table 3

Constraints on manipulated variables of pulp mill model

MV
Low limit High limit MV Low limit High limit
4–8
�1.00 2.00 33 �0.70 0.20
9
�1.00 10.0 34 �0.78 0.22
10
�0.10 0.90 35 �0.40 0.60
11
�0.80 0.19 36 �0.95 1.00
13
�1.00 0.00 39 �0.90 0.10
16
�1.00 0.00 41 �1.00 2.00
17
�1.00 3.00 42–44 �1.00 1.50
20
�1.00 3.00 50 �1.00 2.00
22
�1.00 3.00 51 �0.90 1.00
23
4.00 3.00 52 0.00 1.00
25
�1.00 3.00 54 �0.25 0.00
26
�1.00 3.00 58 �1.00 2.00
29
�0.40 0.40 59 �1.00 3.00
30
�0.90 0.10 65 �0.25 0.70
31
�0.06 0.94 66 �0.9 0.015
32
�0.32 0.68 72 �1.0 10.0

3. Potential applications

The benchmark presented can be used to study anumber of process system engineering topics includingthe following

3.1. Process modeling/estimation

The benchmark model is suitable for fundamentalmodeling studies of pulp and paper processes. Most ofthe unit operations have been modeled using dynamicmass and energy balances. The millwide model can beused as a ‘‘virtual’’ process to test advanced dynamicmodels of particular unit operations which may sub-stitute the ones provided. For example, the mathema-tical model used to describe the digester is based on twophases (chips and free liquor). Such a model can bereplaced by a more detailed three phase model (chips,entrapped liquor and free liquor) and the complete millmodel can be used to generate realistic simulations thatwould show the interactions present in the millwide

process. This is not possible by simply conductingmodeling studies of isolated unit operations.The model may also be used for input/output identi-

fication studies including linear and nonlinear discretemodels. While Jacobian linearization of the process maybe possible, the size and complexity of the model makeit difficult to obtain such continuous linear models.While measurement technologies are constantly evol-

ving, the acceptance of such technologies has been slowand pulp and papers mills currently have low samplingrates for compositions and Kappa no. measurements.Therefore, any control strategy implemented in anactual pulp and paper mill requires estimation techni-ques to improve the performance of control technolo-gies. For this reason, several outputs/secondarymeasurements are included in the process model fortheir utility in state estimation. Liquor density can beused to estimate the Na2CO3 or TTA in the greenliquor that enters the slaker. Conductivity measure-ments are useful to estimate the composition of sodiumhydroxide in white liquor as well as the residual EA inthe digester extracted liquors. The digester blow lineKappa no. can be estimated from the measurements ofthe sodium hydroxide and conductivity and the Kappano. in the bleach plant can be estimated from bright-ness measurements. These secondary outputs are mea-sured at fast sampling times or even continuously,therefore they should be used in combination with theslower, but more reliable measurements to obtain fastand accurate estimates of liquor compositions andKappa no.

3.2. Process control

The benchmark may be used as the basis for multipletypes of control studies. These may range from plant-wide control to the control of particular unit operations.The process may also be tested with a wide range ofcontrol algorithms that may range from classical PIDcontrol to the more advanced model-based controlalgorithms.The benchmark is particularly well suited for plant-

wide control studies as it has several features of interestincluding: lead/lag responses, long time delays, interac-tions from multiple recycle streams, inverse responsesand slow settling times. The process is also rich in thenumber of outputs, manipulated variables and dis-turbances. The second part of this article presents acomparison of decentralized SISO control and MPC ofthe millwide process. The control study is meant toillustrate the application of the benchmark for plant-wide control studies and not to present the best or theonly workable solution to the problem. Plantwide con-trol is an open-ended problem and researchers areencouraged to provide control solutions that performbetter than the ones provided.

Table 4

Soft constraints on output variables

Output
Low limit High limit
3
�1 2
4, 12–14, 19
�1 1
34
�0.1 0.1
35
�1 1
38
0 0.1
39–40, 44
�1 1
60
�3.0 1
62
4 1
76, 78
�1 6
79, 81
�1.5 1
Table 5

Costs and/or selling of chemicals/products and utilities

Specie
Cost ($/kg)a
Wood chips
3.86�10�2
Steam (1 atm)
2.53�10�3
Steam (7.8 atm)
5.18�10�3
Steam (35 atm)
7.94�10�3
Cooling water
5.3�10�5
Process water
1.321�10�5
NaOH
0.20
Oxygen
0.15b
ClO2
1.00b
Na2SO4
0.100
CaO
0.063
Natural gas
0.170
Pulp
0.33c
a Obtained from the ‘‘Chemical Marketing Reporter’’, published by

Schnell Publishing Company, Inc., New York, 1990. Unless otherwise

indicated units are in $/kg.b Obtained from Grace and Malcolm [6].c The pulp market price varies considerably from year to year. This

represents a typical price for bleached pulp.


The process model may also be used for nonlinearcontrol studies; however such studies will be limited toparticular unit operations as the computationalrequirements of nonlinear control increase exponentiallywith the size of the problem (number of inputs, outputs,states and dynamic complexity of the process).

3.3. Process optimization

Steady-state and dynamic optimization studies can bepursued; however dynamic nonlinear optimizations willbe computationally intensive as the model has morethan 8000 states (including both continuous and discretestates). The modes of operation and steady-state condi-tions have not been optimized to minimize operationalcosts. Table 5 provides the costs for all chemicals andutilities so that optimization studies are consistent.

3.4. Fault diagnosis

The model may be used as a ‘‘virtual’’ process toexplore multiple scenarios of fault diagnosis using tech-niques likes expert systems, state estimation and movinghorizon estimation. The model is suitable to exploredifferent types of faults. Faults resulting from processdisturbances are already included in the model; how-ever, other faults like measurement bias or MV bias, arenot included in the model. Researchers are encouragedto modify the model to make it more suitable for faultdiagnosis studies.

3.5. Education

The benchmark can be used in process control coursesto study plantwide control design using classical controlas well as advanced model based control.

4. Conclusion

This article presented an industrial benchmark prob-lem of a pulp mill process (including the fiber-line andthe chemical recovery loop). Complete details of theproblem were presented, including control objectives,modes of operation, process constraints and processmeasurements. Costs of utilities and chemicals, andproduct prices were provided to facilitate a consistentway of comparing control/optimization strategies.The benchmark is based on a nonlinear dynamic

mathematical model with approximately 8200 states anda total of 142 inputs (82 MVs and 60 DVs) and 114outputs (40 in fiberline and 74 in chemical recovery).The number of variables under consideration can bevaried to include other variables of interest like addi-tional disturbances for fault diagnosis or outputs forinferential control. The model is useful for real-time

studies as the simulation time takes 4–6 min per each1000 mins (simulation minutes) in an AMD Athlon 900MHz PC.The complete details on the derivation of the mathe-

matical model as well as the complete code (C source files,MATLAB m-files/mdl-files/mat-files, etc.) are providedto the academic community and available for downloadfrom the Internet. The benchmark is suitable for studiesin several process system engineering topics including:process modeling/identification/estimation, control,optimization, fault diagnosis, and educational purposes.

Acknowledgements

The authors gratefully acknowledge the support ofthe National Science Foundation under Grant CTS9729782, the University of Delaware Process Controland Monitoring Consortium, and the University ofDelaware Presidential Fellowship.

Appendix. Process variables

The process has 82MVs, 58 disturbance variables (DVs)and 114 outputs including the fiberline and chemical

Table A1

Fiberline outputs of pulp mill model. These include CVs, secondary

outputs for inferential control and other miscellaneous outputs

y
Description
1
Digester production rate
2
Storage production rate
3
D2 production rate
4
Digester Kappa no. (fast)
5
Digester Kappa no. (slow)
6
Digester pulp yield (calculated)
7
Bleached pulp yield (calculated)
8
Upper extract EA
9
Lower extract EA
10
Upper extract conductivity
11
Lower extract conductivity
12–14
Cooking T (cook, mcc, emcc)
15
Digester WL T
16
Upper extract T
17–18
Recycle stream no. 1–2
19–20
O Kappa no. and T
21
D1T
22–23
E Kappa no. and T
24
E washer [OH�]
25–26
D2 T and brightness
27–33
Washer no. 1–7 DF
34
Storage V
35
O washer effluent T
36
O washer inlet consistency
37
O P
38
D2V
39
Upper extract EA (estimated)
40
Lower extract EA (estimated)

recovery sections. Table A1 presents all the outputs ofthe fiberline process. Most of the outputs in the fiberlinearea are the same as those presented in a control studyof a fiberline process by Castro and Doyle [2]. The newoutputs in the fiberline model include liquor con-ductivities, estimated EA, oxygen reactor pressure, andD2 tower volume. The conductivity measurements (y10–y11) are useful for state estimation studies when the EAmeasurements are not available at faster (10 min) sam-pling rates. Conductivity was used in combination withslow off-line EA measurements to estimate EA con-tinuously in the digester (outputs 39–40 of fiberline) andthe chemical recovery loop (outputs 66 and 68 of thechemical recovery). The model used by Castro andDoyle [2] to model the oxygen delignification tower didnot include an oxygen balance. The new model con-siders an oxygen mass balance in the oxygen reactor.This is indirectly measured by monitoring the pressurein the tower. Therefore, pressure in the reactor wasadded as an output. Finally, the D2 brightening towerwas considered to have a variable level (not on perfectcontrol), therefore, the D2 volume was included as anoutput of the millwide model.Table A2 presents all the MVs of the fiberline process.

The MVs are the same as those presented previously,except for the WL counter current flow, the oxygen flowto the O tower and the downstream pulp flowrate fromthe D2 tower. The counter-current zone WL flow is thecombined volumetric flowrate of white liquor into themcc and emcc zones of the digester. Given that an oxy-gen balance is performed in the O tower, it was neces-sary to include the flowrate for oxygen to the reactor as

a MV. In the previous model, it was assumed that the Otower was under perfect pressure control, therefore, itwas not necessary to model O2 as a component. Finally,the D2 downstream flowrate was considered a MV. Thesplit fractions are used in the splitter functions of themodel. Split fractions determine how a stream is dividedinto two or tree sub-streams. For example, if a stream of5 m3/min splits into two streams with a split fraction of0.4, one of the exit streams will be of 2 m3/min and theother 3 m3/min. This simplifies the development of themodels without having to include macroscopic momen-tum balances.Table A3 presents all the disturbances included in the

fiberline process. These do not include faults inmeasurement sensors or any other equipment or uncer-tainties in the MVs. In the digester model, the woodchips are divided into five components. The digestermodel uses seven wood components (including watermoisture and wood chips void). All the wood chip den-sities (d2–d8) can vary; however d7 (void density) mustalways be zero at the entrance of the digester.Table A4 presents all the outputs of the chemical

recovery section. The weak black liquor flow (y1) repre-sents the liquor entering the evaporators. It is not con-trolled to a setpoint; however, there is an upper limit onthe flowrate of WBL that the evaporators can manage.In fact, the evaporators are typically production bottle-necks in the recovery loop. The BL solids% (y4) are themass fraction of dissolved solids at the exit of the eva-porators. The smelt dissolving tank (SDT) condensatetemperature (y15) is the temperature of condensate fromthe cooler in the top of the smelt dissolving tank. Theheat released by the smelt causes evaporation of somewater. This goes through a heat exchanger where 5% ofthe vapor is lost to the atmosphere and the rest (95%) iscondensed, cooled and mixed with the green liquor. TheSDT vapor flow (y16) is the flow of vapor evaporatedthat escapes to the atmosphere.The same phenomena may occur in the slaker where

5% of the vapor produced is released to the atmosphere

Table A2

Fiberline manipulated variables of pulp mill model

MV
Description
1
Wood chips flow
2–3
Dig. WL flow (cook/wash zones)
4-8
Dig. steam flows 1–5
9
Mill water flow
10–11
Pulp washing split fraction 1–2
12
O caustic flow
13
Excess WL split fraction
14–15
O steam flow 1–2
16
O split fraction 1
17
O steam flow 3
18
Pulp flow to bleach plant
19–20
D1 water and ClO2 flow
21–22
E1 wash water and steam flow
23–24
E caustic and water flow
25
E steam flow
26–27
D2 ClO2 and caustic flow
28
D2 wash water flow
29
O split fraction 2
30
E split fraction
31–35
Pulp washing split fraction 3–7
36–37
O coolant and oxygen flow
38
Bleached pulp flow
Table A3

Fiberline disturbance variables of pulp mill model

DV
Description
1–8
Wood chips T and densities
9
Mill water T
10–11
O caustic T and concentration
12
D1 mill water T
13–14
D1ClO2 T and concentration
15–16
E caustic T and concentration
17
E water stream T
18–19
D2ClO2 T and concentration
20–21
D2 caustic T and concentration
22
D2 wash water T
Sensor bias or manipulated variable uncertainties are not considered

in the disturbances.


(y24) and the rest is condensed, cooled (y23) and mixedwith the green liquor before entering the first caustici-zer. However, this output is not used in the simulationresults presented in the following sections. Hence thecondensed vapor is not mixed with the green liquor.Several temperatures for the kiln are provided as out-puts. These include: lime exit temperature, front endtemperature (FET), hot gas temperature, and back endtemperature (BET). The hot lime temperature repre-sents the temperature of the lime as it exits the kiln.FET is the hottest temperature of the lime inside thekiln and it is measured using optical devices. The hotgas temperature represents the hottest temperature ofthe combustion gases. BET represents the exhausttemperature of the gases before leaving the kiln. For

purposes of industrial applications, the FET and BETare used for control of the lime kiln. Additionally, twodifferent outputs are given for the CaCO3. One repre-sents the typical 2 h off-line measurement and the otherrepresents a fast measurement (estimated) done every 10min. The control studies presented here are based on theavailability of the slow measurement.The mud flow (y50) and the recycle flows (y54–y60)

represent several recycle streams within the chemicalrecovery loop. A very important step in plantwide con-trol design is to control recycle streams to avoid‘‘snowball effects’’. These streams are included as out-puts because some of them need to be controlled. Thewash to liquor ratio (WLR) is controlled in all the threerotary drum filters (Y51–Y53). It represents the ratio ofwash water/liquor flowrate to lime mud liquor flowrateleaving the filter.Table A5 includes all the MVs in the chemical recov-

ery process. The green liquor clarifier and white liquorclarifier upper zone exit flows (u48, u57) are not used inthe simulations because the models assume perfect levelcontrol and the downstream volumetric flowrates areequal to the upstream volumetric flowrates. This is donebecause the flowrate in the upper zone of the clarifiers isby overflow so the volume is constant. The models used

Table A5

Chemical recovery manipulated variables of pulp mill model

MV
Description
39
Weak BL split fraction 1
40
Evaps. caustic flow 1
41
Evaps. salt-cake flow
42–44
Evaps. effects 1–3 steam flow
45
Sdt scrubber caustic flow
46
Sdt green liquor flow
47–48
Glc dregs/clarified liq. flows
49
Green liquor flow to slaker
50
GL cooler coolant flow
51
Dregs filter wash water flow
52
GL split fraction
53
Fresh lime screw speed
54
Lime feed split fraction
55
WL cooler coolant flow
56
Wlc limemud flow
57
Clarified WL flow
58
Caustic make-up flow
59
O WL flow
60
Limemud mixer exit flow
61
Mud washer filtrate flow
62
Weak wash make-up water flow
63
Limemud flow to filter
64
Limemud dilution water flow
65–66
Limemud split fraction 1–2
67–68
Mud filters wash water flow
69–70
Kiln primary/secondary air flow
71
Kiln fuel flow
72
O wash water flow
73–80
Effect 8–1 exit flow
81–82
Scrubber coolant flows
Table A4

Chemical recovery output variables of pulp mill modela

y
Description
41
WBL flow
42–44
BL T, flow and concentration
45–52
Evaporator no. 1–8 V
53–54
Sdt V, density
55–56
Sdt condensate T and vapor flow
57
Storage tank 1 V
58–59
Glc upper V and lower density
60–61
GL T and Na2CO3 concentration
62–64
Slaker T, condensate/vapor flow
65
Classifier T
66–67
Causticizer no. 1 T and EA
68–69
69–70
71–72
Wlc upper V and lower density
73
Mud mixing tank V
74
Storage tank no. 2 V
75–76
Lime exit T and front end T
77–78
Kiln hot gas T and back end T
79–80
Kiln O2 and CaCO3 mass fraction
81
Kiln CaCO3 (slow)
82–83
WL T and causticity
84–85
WL NaOH concentration and flow
86–87
WL NaSH concentration and flow
88–89
Edt NaSH concentration and flow
90
Mud flow
91–93
Filter 1–3 WLR
94–100
Recycle no. 1–7 flows
101
WL flow
102–103
GL density and solids concentration
104
GL Na2CO3 concentration (estimated)
105
Causticizer 1 conductivity
106
Causticizer 1 EA (estimated)
107
Causticizer 3 conductivity
108
Causticizer 3 EA (estimated)
109
Wlc liquor conductivity
110
Wlc EA (estimated)
111
WL conductivity
112
WL EA (estimated)
113
Mud Ca(OH)2 concentration
114
Mud Ca(OH)2 mass flow
a These include CVs, secondary outputs for inferential control and

other miscellaneous outputs.


in the upper zone of the clarifiers can be used with vari-able level control by modifying a parameter. In this caseu48 and u49 would be used for level (volume) control.Table A6 shows the disturbances in the chemical

recovery section. There are two types of pressure dis-turbances in the evaporator section, effect pressure (d23–d27, d33, d36, d40) and steam pressure (d32, d35, d39). Theeffect pressure is the pressure inside the vapor space andthe steam pressure is the pressure of the steam enteringeffects 1–3. DR represents the displacement ratio of therotary drum filters. The rpm to volumetric flow factor isa constant that converts a flow in revolutions per min-ute to a volumetric flow. It is used in the slaker screwsto calculate the mass of lime fed to the slakers.The rest of the outputs, MVs and disturbances are

typical variables present in all pulp and paper processes.

References

[1] M. Barrette, M. Perrier, Modeling and control of a hypochiorite

bleaching stage for dissolving pulp, in: TAPPI Proc. of the 1995

Process Control Conference, TAPPI Press, Atlanta, 1995, pp. 11–22.

[2] J.J. Castro, F.J. Doyle III, Plantwide control of the fiber line in a

pulp mill, Ind. Eng. Chem. Res. 41 (5) (2002) 1310–1320.

[3] T. Christensen, L.F. Albright, T.J. Williams, A Mathematical

Model of the Kraft Pulping Process, Technical Report 129, Pur-

due Laboratory for Applied Industrial Control, Schools of Engi-

neering, Purdue University, West Lafayette, 1979.

[4] J.J. Downs, E.F. Vogel, A plant-wide industrial process control

problem, Chem. Eng. Sci. 17 (3) (1993) 245–255.

[5] F.L. Galtung, T.J. Williams, A survey of the statues of the

mathematical modeling of the chemical recovery section of a

Kraft paper mill, Technical Report 23, Purdue Laboratory for

Applied Industrial Control, Schools of Engineering, Purdue

University, West Lafayette, 1969.

[6] T.M. Grace, E.W. Malcolm (Eds.), Alkaline Pulping, Pulp and

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Canadian Pulp and Paper Association, 1989.

[7] E.F. Jacobi, T.J. Williams, A dynamic model and advanced direct

digital control system for a Kraft mill liquor preparation system,

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Control, Schools of Engineering, Purdue University, West

Lafayette, 1973.

[8] R.S. Kanadibhotla, J.B. Riggs, Nonlinear model based control of

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[9] F. Kayihan, A review of modeling and control in pulp and paper

industries, in: 5th International Conference on Chemical Process

Control (CPC V), AIChE Symp. Ser., 1997, pp. 117–132.

[10] C.C. Lakshmanan, O.E. Potter, Cinematic modeling of dynamics

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945–956.

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3885–3898.

[12] P.R. Lyman, C. Georgakis, Plant-wide control of the Tennessee

Eastman problem, Comput. Chem. Engng. 19 (3) (1995) 321.

[13] T.J. McAvoy, N. Ye, Base control for the Tennessee Eastman

problem, Comput. Chem. Engng. 18 (5) (1994) 383–413.

[14] T.J. McAvoy, N. Ye, C. Gang, Nonlinear inferential parallel

cascade control, Ind. Eng. Chem. Res. 35 (1) (1996) 130–137.

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Jovanovich, London, 1991.

Table A6

Chemical recovery disturbance variables in pulp mill model

DV
Description
23–27
Effect 8–4 P
28
Evaps. split fraction
29
Evaps. caustic stream T
30
Evaps. salt-cake stream T
31–32
Evaps. effect 1 steam T and P
33
Evaps. effect 1 vapor dome P
34–35
36
37
Evaps. flash tank 1 P
38–39
40
41
Evaps. flash tank 2 P
42
Split fraction 3
43
Sdt scrubber caustic T
44
GL cooler coolant stream T
45
Dregs filter DR
46
Dregs filter water stream T
47
Fresh lime T
48
Ambient T
49
WL cooler coolant stream T
50
Caustic make-up stream T
51
Wash wash make-up water T
52
Limemud dilution water T
53
Mud filter 1 wash water T
54
Mud filter 1 DR
55
Mud filter 2 wash water T
56
Mud filter 2 DR
57
Kiln fuel T
58
Lime screw fill factor
Sensor bias or manipulated variable uncertainties are not considered

in the disturbances.


A pulp mill benchmark problem for control: problem description

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