Model-based Optimization of a CompactCooking G2 Digesting Process Stage
1. 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-Jounela
Advisor: Dr.-Ing. Aldo Cipriano
Instructor: D.Sc. Olli Joutsimo
Tuesday January 26, 2016
2.
3. Introduction
Pulp and Paper
• What is Pulp …
• Fibers sources
• Lignocellulosic
biomass
• Market pulp
• Softwood
• Hardwood
• and Paper?
• Paper products
• Fiber properties
Logs
Woodchips
Pulp
4. Introduction
Kraft Pulp Mill Process
Nueva Aldea Pulp Mill 1500+1500 Adt/d pine & euca, 91% ISO, 460MWth (95 MWe), 1000 L/s water inflow
5. Introduction
Problem 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
6. Introduction
Goals, 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.
7. Introduction
Goals, 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.
8. Introduction
Structure of the Thesis
Chapter 1 Introduction
LITERATURE PART
Chapter 2 The Kraft Pulp Mill
Chapter 3 Pulp Digesting Stage
Chapter 4 Mathematical Models on Pulp Digesters
EXPERIMENTAL PART
Chapter 5 Methods
Chapter 6 Process Description
Chapter 7 Mathematical Modeling
Chapter 8 Simulator Design
Chapter 9 Simulation Results
Chapter 10 Optimizer Design
Chapter 11 Optimization Results
Chapter 12 Conclusions
Appendix A Model-based Process Analysis
9. Literature Review
Mathematical Models on Pulp Digesters
• Review on first-principle modeling
Vroom (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.
10. Literature Review
Mathematical Models on Pulp Digesters
• Review on first-principle modeling
Saltin (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
11. Literature Review
Mathematical Models on Pulp Digesters
• Review on first-principle modeling
Bhartiya 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.
12. Literature Review
Process 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) )
13. Process Description
CompactCooking G2 System
• Physical input
streams:
• Woodchips
• MP-steam
• White liquor
• Wash liquor
• Physical output
streams:
• Cooked pulp
Weak black
liquor
14. Simulator Design
Methodology
• 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
ModelValidationModelTesting
Castro, J. J., & Doyle, F. J. (2004). A pulp mill benchmark problem for control: problem description.
Journal of Process Control, 14(1), 17–29.
18. Mathematical modeling
Main 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
19. Mathematical modeling
Main 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 𝑤ℎ𝑒𝑟𝑒 𝑖 ∈ 𝐿 𝑓, 𝐿 𝑠, 𝐶, 𝐺𝑀, 𝑋, 𝐸
𝐶𝑗 𝑤ℎ𝑒𝑟𝑒 𝑗 ∈ 𝑁𝑎𝑂𝐻, 𝑁𝑎𝑆𝐻, 𝐷𝐿, 𝐷𝐶, 𝐷𝐺𝑀, 𝐷𝑋, 𝐷𝐸
20. Mathematical modeling
Bed Compaction
• Equations based on Härkönen model
𝜌 𝑐,𝑏 =
𝑖
𝜌𝑖 𝑧, 𝑡
𝑑𝑃𝑙
𝑑𝑧
= 𝑹 𝟏
1 − 𝜂 2
𝜂3 𝑢𝑙 + 𝑹 𝟐
1 − 𝜂
𝜂3 𝑢𝑙
2
𝑑𝑃𝑐
𝑑𝑧
= 𝜌𝑐,𝑤 − 𝜌𝑙 1 − 𝜂 𝑔 − 𝝁
𝑃𝑐,𝑒𝑥𝑡
𝐷
−
𝑑𝑃𝑙
𝑑𝑧
𝜂 = 𝒌 𝟎 +
𝑃𝑐 kPa
10
𝒌 𝟏
−𝒌 𝟐 + 𝒌 𝟑ln 𝜅
𝜄 = 1 − 𝜂 1 −
𝜌 𝑐,𝑏
𝝆 𝒘𝒐𝒐𝒅
𝜌𝑙 = 𝜌 𝑤 +
𝑗
𝐶𝑗 𝑧, 𝑡 𝜌𝑐,𝑤 =
𝜌 𝑤𝑜𝑜𝑑 1 − 𝜂 − 𝜄 + 𝜌𝑙 𝜄
1 − 𝜂
𝜂
𝜀
1 − 𝜂
1 − 𝜀
𝑃𝑐 𝑃𝑙
𝑑𝑉
Volumen fractions
𝜂 free liquor
𝜀 entrapped liquor
1 − 𝜂 woodchips
(1 − 𝜂)(1 − 𝜀) 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.
21. Mathematical modeling
Bed 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.
22. Mathematical modeling
Reaction kinetics
• Equations based on Purdue model
𝜌𝑖 = 𝜌𝑖 𝑧, 𝑡 𝑖 ∈ 𝐿 𝑓(1), 𝐿 𝑠(2), 𝐶(3), 𝐺(4), 𝐴(5), 𝐸 6
𝐶𝑗 = 𝐶𝑗 𝑧, 𝑡 𝑗 ∈ 𝑁𝑎𝑂𝐻 1 , 𝑁𝑎𝑆𝐻 2 , 𝐷𝐿 3 , 𝐷𝐶 4 , 𝐷𝐺 5 , 𝐷𝐴 6 , 𝐷𝐸 7
𝑅𝑖 = −𝒆 𝒇 𝑘 𝑎𝑖 𝐶 𝑁𝑎𝑂𝐻
1
2 + 𝑘 𝑏𝑖 𝐶 𝑁𝑎𝑂𝐻
1
2 𝐶 𝑁𝑎𝑆𝐻
1
2 𝜌𝑖 − 𝝆𝒊
∞
𝑘 𝑎𝑖 = 𝑘 𝑎0𝑖exp
−𝐸 𝑎𝑖
𝑅𝑇
𝑘 𝑏𝑖 = 𝑘 𝑏0𝑖exp
−𝐸 𝑏𝑖
𝑅𝑇
𝑅 𝑁𝑎𝑂𝐻 =
1 − 𝜂
𝜂 + 𝜄
𝜷 𝑬𝑨𝑳
𝑖=1
2
𝑅𝑖 + 𝜷 𝑬𝑨𝑪
𝑖=3
5
𝑅𝑖
𝑅 𝑁𝑎𝑆𝐻 =
1 − 𝜂
𝜂
𝛽 𝐻𝑆𝐿
𝑖=1
2
𝑅𝑖
𝑅𝑗 =
1 − 𝜂
𝜂
𝑅𝑖
Wisnewski, P. A., Doyle, F. J., Kayihan, F. (1997). Fundamental Continuous Pulp-Digester Model for Simulation and Control. AIChE Journal, 43 (12), 3175-3192
Christensen, 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.
23. Mathematical modeling
Reaction 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), 3175-3192
Christensen, T. (1982). A Mathematical Model of the Kraft Pulping Process (PhD’s thesis). Purdue University.
26. Simulation Results
Testing (Pine)
DCS
estimate.
NO
SENSOR
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)
29. Simulation Results
Assessment
• 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
30. Optimizer Design
Methodology
• 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 distribution
Cooking 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
32. Optimization Results
Raw Results (Pine)
U0
U profit
heuopt
U cost
heuopt
Chipmeter speed rpm 15.93 15.93 15.93
MP steam flow rate kg/s 10.27 7.23 11.05
White liquor flow rate l/s 65.05 78.87 43.00
Wash liquor flow rate l/s 151.41 116.56 111.18
Filter reject flow rate l/s 35.15 96.94 8.78
Middle extraction flow rate l/s 35.58 138.33 8.89
Transfer liquor flow rate l/s 232.52 58.13 341.89
Upper extraction flow rate l/s 114.11 527.65 266.82
Lower extraction flow rate l/s 126.10 31.52 45.70
White liquor split fraction 1 0.0922 0.2499 0.1068
White liquor split fraction 2 0.3995 0.0999 0.0999
White liquor split fraction 3 0.0000 0.0000 0.2362
Transfer liquor split fraction 1 0.2300 0.0575 0.0575
Transfer liquor split fraction 2 0.0223 0.0056 0.1674
Upper liquor split fraction 1 0.1397 0.0349 0.0349
Upper liquor split fraction 2 0.2406 0.8101 0.8101
Y0
Y profit
heuopt
Y cost
heuopt
Blowline flow rate l/s 148.47 152.10 137.39
Top liquor flow rate l/s 151.63 174.80 140.26
Bottom liquor flow rate l/s 198.67 276.57 313.93
Cooking Kappa 27.87 28.10 28.49
Blowline consistency w/v% 11.11 10.89 12.01
WBL consistency w/v% 11.06 11.48 12.46
Impbin top temp. C 98.93 112.47 106.44
Top liquor temp. C 127.74 141.99 140.31
Transfer liquor temp. C 119.26 134.58 133.86
Digester top temp. C 151.89 148.81 159.51
Upper extraction temp. C 157.99 151.62 165.13
Lower extraction temp. C 151.11 154.69 159.35
Blowline temp. C 100.99 100.70 101.32
White liquor hot temp. C 144.49 143.32 148.19
Lower extraction cold temp. C 146.08 145.20 150.17
Top liquor EA conc. g/l 32.39 28.44 22.37
Transfer liquor EA conc. g/l 14.21 15.13 8.77
Upper extraction EA conc. g/l 17.10 20.42 9.31
Lower extraction EA conc. g/l 10.09 13.32 4.55
Cooked pulp prod. rate ADt/d 1582.82 1589.45 1583.77
WBL prod. rate tDS/d 2120.25 2337.34 2027.56
Cooking yield % 46.37 46.55 46.38
Cooking wood sp. cons. m3sub/ADt 5.07 5.05 5.07
EA/W total % 22.29 24.66 18.51
EA/W impbin fresh % 8.08 5.10 5.64
EA/W digester fresh % 12.15 15.34 11.03
L/W impbin top m3/BDt 5.60 6.25 5.28
L/W impbin bottom m3/BDt 4.60 3.81 4.66
L/W digester top m3/BDt 6.09 11.21 7.38
L/W digester bottom m3/BDt 2.79 2.06 1.92
DF 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 23.99
Blowline carryover kgDS/BDt 1.96 1.46 2.08
WBL heating value HHV MJ/kg dry 15.03 13.66 15.68
Technically feasible?
Digester hang?
Lignin precipitation risk?
33. Optimization Results
EconomicAssessment
• For each objective
function a new cooking
recipe has been
identified
• But “how much”
optimal are these
recipes?
Y0
Y 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
34. Optimization Results
EconomicAssessment
Steady-state Optimization
380
400
420
440
460
Profit rate
USD/min
250
260
270
280
290
Cost rate
USD/min
360
370
380
390
400
Profit per ADt
USD/ADt
225
230
235
240
245
Cost per ADt
USD/ADt
0 500 1000 1500 2000
72
74
76
78
80
82
Profit per m3
sub
USD/m
3
sub
min
0 500 1000 1500 2000
47.5
48
48.5
49
49.5
Cost per m3
sub
min
USD/m
3
sub
Profit rate as o.f.
Cost rate as o.f.
Base case (ss)
Base case (dyn)
35. Optimization Results
EconomicAssessment
• 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
36. Conclusions
Main 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.
41. Simulated Contribution
Case study: CompactCooking G2 analysis
… i.e., temperature control scheme must be
improved in order to reduce cooking kappa
variability
Hinweis der Redaktion
First of all, I would like to start this presentation from a reflection that motivates the subject of the thesis. It is about the forest industry, our consumption habits, and the role of the engineers. We are probably producing much more paper products than what we really need, and this is putting a huge burden on our natural resources. As engineers, we are far from being to able to solve this problem, but we can do our best with the aim of optimizing our production processes. In this sense, we should minimize the consumption of energy, water, and chemicals, as well as the generation of environmental emissions. This is certainly not an easy task. However, today we have amazing tools in the field of process modeling & simulation that must leveraged if we really want to arrive to better solutions for the pulp & paper industry.
OK. But, what is pulp and paper?
Types of fiber sources: primary and secondary
Lignocellulosic biomass: softwood and hardwood
Fiber properties: tensile, tear, burst indices among several others (density, opacity, brightness, etc)
Fiberization and lignin fraction -> kappa number
White liquor: sodium hydroxide and sodium sulphide (Na2S) turn into effective alkali and sodium hydrosulphide (NaHS)
Kraft cooking, white liquor composition, temperature and residence time –> H-factor
Blue plots: MV
Green plots: DV
Black plots: estimated signal e.g. woodchips flow is estimated from chip meter rpm and woodchip bulk density as seen by DCS (not shown)
In a rigorous model structure, flow rate of the cooked pulp stream should be a logical input for the model, and vessel levels would be outputs instead. However, due to the difficulty of modeling vessel levels, these are fixed and cooked pulp stream is seen as an output signal.
Original DCS visualization has an error as it doesn’t show one more black liquor split point, for this reason one circle seems to be pointing to no-split.
Except for 3 signals (Temp Woodchips, Temp MP-Steam, and Pressure MP-Steam) all the rest are highly uncertain since there is no online instrument available.
Instrumentation could be installed demanding low capital investment for measuring several of these signals.
Grey signals are covered by simulated signals, i.e., the model takes input signals identical to actual mill as measured data (except for noise filtering)
Blue plots: Inputs – Manipulated Variables
Green plots: Inputs - Disturbances
Red plots: Outputs
Grey plots: Mill data
Blue plots: Inputs – Manipulated Variables
Green plots: Inputs - Disturbances
Red plots: Outputs
Gray plots: Mill data
Grey signals are covered by simulated signals, i.e., the model takes input signals identical to actual mill as measured data (except for noise filtering)
Blue plots: MV
Green plots: DV
Black plots: estimated signal e.g. woodchips flow is estimated from chip meter rpm and woodchip bulk density as seen by DCS (not shown)
Blue plots: MV
Green plots: DV
Black plots: estimated signal e.g. woodchips flow is estimated from chip meter rpm and woodchip bulk density as seen by DCS (not shown)
Blue plots: MV
Green plots: DV
Black plots: estimated signal e.g. woodchips flow is estimated from chip meter rpm and woodchip bulk density as seen by DCS (not shown)
Blue plots: MV
Green plots: DV
Black plots: estimated signal e.g. woodchips flow is estimated from chip meter rpm and woodchip bulk density as seen by DCS (not shown)
Blue plots: MV
Green plots: DV
Black plots: estimated signal e.g. woodchips flow is estimated from chip meter rpm and woodchip bulk density as seen by DCS (not shown)
Blue plots: MV
Green plots: DV
Black plots: estimated signal e.g. woodchips flow is estimated from chip meter rpm and woodchip bulk density as seen by DCS (not shown)