Plate Gap Estimation based on Physical Refining Measurements

Anders Karlström 1

David Sikter 2

Mattias Gustavsson 1

1) Chalmers Industriteknik Foundation

2) Holmen Paper AB

ABSTRACT

To estimate the plate gap in refiners, reliable process measurements besides good physical models are required. The

model used in this study is developed to cover estimations of the thermodynamic work as well as the refining work

simultaneously. The model has been applied to a full-scale industrial first stage refiner and various operating

conditions have been studied to verify its robustness. According to the model the estimated plate gap as well as the

spatial refining work varies significantly, also during time sequences where the motor load is almost the same. The

fiber concentration in the refining zone varies with different operating points as well. Moreover, the fluctuations in

the fiber concentration are related to the local pressure gradients which are derived from temperature measurements

inside the refining zone. These disturbances affect the radial steam velocity and thereby the fiber velocity

substantially. This means that the commonly used control concept of keeping constant specific energy should be

reconsidered since the residence time in different parts of the refining zone can vary over time and thereby influence

the pulp quality.

INTRODUCTION

Modern mills have focused increasingly on raising capacity, while reducing operating costs and obtaining improved

uniform product quality. Significant improvements have been made and many research projects aim to improve the

energy efficiency in Thermo Mechanical Pulp (TMP) plants. However, reducing electricity consumption in TMP is

difficult, as pulp quality is often affected negatively and this also leads to an increase in fuel consumption in the

power plant. Instead, the key question is whether or not a smaller operating window, in which pulp that is "good

enough" is produced with optimal steam production, can be targeted.

To meet the demand, i.e. good enough pulp quality and optimal steam production, new control strategies for refiners

have been proposed and it has long been requested to find appropriate control variables to characterize the refining

process [1] and produce a well-controlled operating window [2,14].

New refiner control strategies have therefore focused on new measurement techniques to keep the quality as

consistent as possible [3,4,5,6,7,14]. Novel modeling techniques covering material and energy balances for the

refining process have been proposed as a complement to different measurement technologies [8].

Industrial process computer systems provide information from thousands of ordinary sensors and the use of these

sensors naturally offers great potential for improved control. However, when designing complex real-time systems

for sensor-rich controllers based on special algorithms for soft sensor information, i.e. information based on

estimated process states that cannot be measured using standard hardware devices, substantial computational power

is sometimes required. Information on ways of implementing the energy balances in process computers is sparse in

the literature, even though on-line deterministic models for estimating consistency have been proposed.

To meet such future challenges combined skills in both sensor development and software, that are not as yet

widespread in industry, are required.

In this paper a sensor-rich system is considered as well as software in terms of a non-linear model originally used for

estimation of thermodynamic and refining work [13]. This entropy model, described in the first section, has been

further developed in order to estimate the plate gap, i.e. the distance between the rotor and stator segments. Besides

the plate gap estimation, the model provides other soft sensors, such as the distributed consistency and the fiber

distribution inside the refining zone. The model requires information from robust sensor arrays for temperature

measurements inside the refining zone besides process variables such as the motor load, production, dilution water

feed rate, inlet and blow line pressure/temperature. Other parameters, such as the segment taper and the segment

specific area besides the sensor positions in the refining zone, heat capacity for the chips and pulp and other material

constants are required as well.

The next section is focused on results from test series where hydraulic pressure, dilution water feed rate and

production have been changed to cover the main dynamics in the system. This section also includes a discussion of

the results where strengths and weaknesses are pointed out. Finally a section including conclusions is given.

THE MODEL

It is assumed that three distinct phases exist inside the refining zone – The chips/fiber (oven-dry) material, water

which is assumed to be bound in the fibers and the steam. The indices 1, 2 and 3 used below denote the fibers, water

and steam respectively.

The material balances for the refining process can be written as

( )( )outout

out

out

outinin

in

in

mmCm

mmmCm

211

1211

+=

=+=

The superscripts, { }outin, , are flow directions with respect to the refiner. The variables inC and

outC are the

consistencies in the refiner inlet and outlet respectively.

As it is assumed that no energy is accumulated, the energy balance see Fig. 1, becomes

( )∑=

+−=3

1j

loss

in

j

in

j

out

j

out

jR QmhmhW

where }{ 3,2,1, ∈jhj are the enthalpies given by the steam temperature assuming saturated conditions.

Figure 1: Approximate energy balance for a hypothetical refiner.

The variable lossQ is, from a thermodynamic perspective, the energy loss in the refining processes i.e.

xrefloss QWQ += .

Normally, lossQ is assumed to include only losses due to heat radiation and motor losses,

xQ . However, from an

energy perspective with the steam balance in focus the work of refining pulp, refW is also a loss and must be

included in this term1.

The system is considered as adiabatic and that the transport of heat and material is only radially dependent. The

electricity consumption in the refiners, LW which is easy to measure, can be expressed as

1 In this paper, the refining work includes the work related to the breaking and separation of fibers from each other,

as well as the fibrillation work which is more closely associated with the process which makes the fibers soft and

flexible.

Refiner

ininhm 11

ininhm 22

ininhm 33

outouthm 11

outouthm 22

outouthm 33

RW

lossQ

( )∫=+==out

in

r

r

RlossthRL rdrrwQWWW π2

where inr and outr are the inlet and outlet radius, ( ) ( ) ( ) ( )rqrwrwrw xrefthR ++= the work per unit area. The

variables RW and

thW relate to the estimated total work and the thermodynamic work, respectively.

In the case of large refiners, it is known that an even energy distribution over the refining zone cannot be assumed

[15]. Instead, the total work per unit area is dependent on plate gap, the shear force et cetera. In the absence of a

better model for the work, it is assumed that

( ) ( ) ωξ rrrwR =

where ω is the angular speed of the disc and that the shear force can be modeled as

( ) ( ) ( ) ( )( )r

rrrrr

∆=≈

ωµαξξ 111

Knowing the taper, the plate gap ∆ can be set as radius dependent and recent research [16] has shown that this is a

useful approximation to obtain a better estimate of the shear force. However, several other parameters such as the

mass flows must be derived as well which requires some other assumptions to be applicable, namely that the pulp

can be regarded as fluidized and obeying Stoke's viscosity relationships [9] and that the flow profile in the rotational

direction is approximately laminar.2 Moreover, the viscosity

1µ is most definitely a variable, since the temperature in

the refining zone varies considerably along the radius. To get a good estimate of the fiber concentration, ( )r1α ,

several assumptions must be made. One such assumption is that the concentration is primarily a function of the fiber

distribution, see below.

The mass flow is assumed to be described as

( ) ( ) ( ) ( )rvrArrmjjjj

ρ= where }{ 3,2,1∈j for details see attached variable list below.

In its simplest form, Darcy´s law is assumed to be valid for the steam phase, i.e.

( ) ( )( ) r

P

r

rrv

∂

∂−=

3

3µ

κ

where the permeability κ is assumed to be expressed as ( ) ( ) ( )( )2

21/ rrcr αακ += i.e. ( ) ( ) ( )( )2

1/ rrCcr ακ = .

The total area can be expressed as ( ) ( )rArrA pp+∆= π2 where ( )rApp is the plate pattern specific area.

Assuming the water to be bounded to the fibers, i.e. ( ) ( )rvrv 21 = , the fiber concentration ( )r1α can be found from

the equation

( ) ( )( ) 0/1/11

2

1 =−++ aab KKKrr αα

where

( ) ( )( ) ( ) ( )

( ) ( )( ) ( )

=

∂∂−=

rrm

rrmK

rPrCrcrA

rmrK

b

a

21

12

2

3

33

/

ρ

ρ

ρ

µ

From the equations above the radially dependent average pulp velocity ( )rv1 can be found. The total residence time

of pulp in the refining zone can thereafter then be estimated as

( )( ) ( )

( )dr

rm

rrdr

rv

outr

inr

outr

inr

∫∫ ==1

11

1

1 αρτ

The entropy generation in an infinitesimal control volume is assumed to be given by the expression for the viscous

dissipation δ [12]

( ) ( )( )

( ) rdrrrT

rrdS π

δ2∆=

2 This is most likely not true but can be used as an assumption to obtain the best possible estimate. However, this

was considered by Frazier [10] and Radoslavova et al [11] and partly validated by Backlund [15].

where

( )( )

( )( )r

rw

r

rr R

∆=

∆=

2

ωµδ

If the temperature profile is measured in the refining zone, together with the temperature or the pressure of the inlet

mass flows in addition to the pressure in the blow line, it is possible to estimate all enthalpies and entropies. Given

the mass flow of dry wood as well as the total water input to the refiner3, the entropy balance

( ) ( ) ( ) ( ) ( ) ( )( )∑=

−+++

+=

3

2

1 lnj

jjjjp rsrmdrrsdrrmT

drrTcmrdS

can be used to derive the mass flow of water and steam.

From the assumptions follows that the thermodynamic work per unit area is given by the enthalpy relationship

( ) ( ) ( )( ) ( ) ( ) ( ) ( )( )∑=

−+++−+=3

2

12j

jjjjpth rhrmdrrhdrrmrTdrrTcmrdrrw π

If the mass flows are known besides ( )rwR and ( )rwth

, an estimate for the irreversible work ( )rwref or

refW can be

obtained from the material balances described above if inm1 and inm2

are known.

The amount of steam is unknown4 and so is the true plate gap. Consequently, two more assumptions are required to

solve the set of equations.

The peak position ( )( )rTrmax, is commonly assumed to coincide with the steam turning point ( ) 03 =rm

r , see Fig. 2 and

the computed refiner work must equal the measured value. These two assumptions allow the mass flow of steam and

the gap to be computed by minimizing the differences

( )( ) ( ) 03max =−

rmrTrr and RL

WW − , respectively.

Figure 2: Temperature, plate gap and steam mass flow profiles for a hypothetical refiner.

3 The consistency of wood chips,

inC , normally displays small variations over time if the feed stock is not changed

significantly [13]. 4 This is a consequence of the fact that the mass flow of steam is not measured in that position.

( )rm3 ( )r∆Temp

inr ( )( ) ( ) 03mmax ==

rrr

rT

maxT

outr

min∆

;

max3m

DISCUSSION OF RESULTS

In this paper an Andritz RTS 68” single disc refiner has been studied, see Fig. 3. In the primary refiner a sensor

array of eight temperature sensors has been mounted between two stator plates in order to cover the energy balance

required in the entropy model. In order to simplify the analysis only the primary refiner is considered in the

discussion below.

Figure 3: The refiner line studied.

The extended entropy model described above has been applied on process data where step changes in hydraulic

pressure, dilution water feed rate and production were performed, see Fig. 4.

Figure 4: Step changes performed in the Andritz RTS 68” single disc refiner.

To understand a refiner response to such step changes, given in Fig. 4, a survey of the forces acting on the plates5

can be performed. By plotting the closing force applied on the plates versus the forces generated inside the refining

5 That is, the integral of forces acting on the surfaces (rotor and stator) from the inner part to the periphery of the

segments.

preheating screw

1 st stage refiner Andritz RTS, SD 68”

2 nd stage refiner SD 65”

cyclone cyclone pulper

refining zone temperature sensors

consistency sensor on - line pulp analyzer

tap steam

preheating screw

1 st stage refiner Andritz RTS, SD 68”

2 nd stage refiner SD 65”

cyclone cyclone pulper

refining zone temperature sensors

consistency sensor on - line pulp analyzer

tap steam

zone, i.e. the steam force, derived from the temperature measurements, the refiner’s controllability aspects can be

discussed.

Figure 5: Closing force versus Steam force for different step changes in the input signals (legends correspond to

time when the step responses (high, medium, low) where performed according to Fig. 4).

As seen in Fig. 5, with regards to the temperature inside the refining zone, the refiner in this study is primarily

controllable by using the hydraulic pressure as an input signal. This does not necessary means that the other two

input signals, i.e. the dilution water feed rate and production, cause controllability problems in the refiner which will

be discussed later in this section6. However, one reason to the limited response in Fsteam is probably that the refiner,

during the test period, runs on lower consistency. A higher consistency in the refiner would probably result in a

better spread of the relations between the closing and steam forces when performing the step responses in dilution

water feed rate and production rate. This is indicated by the entropy model see Fig. 6, which estimates the

consistency to be about 5% lower compared with the measured consistency.

Figure 6: Measured and estimated consistencies in the refiner blow-line.

Similar information as given in Fig. 5 and Fig. 6 can be extracted from the time series by comparing the correlation

coefficients between the specific energy7 and other parameters when changing the hydraulic pressure, dilution water

feed rate and production rate, see appendix 1. The correlation coefficients in the first columns in each matrix show

clearly that the best correlation occurs when changing the hydraulic pressure. It is interesting to see that the

correlation between specific energy and the temperature is lower in some positions than others, especially in

positions near the maximum temperatures (denoted T3 and T4 in appendix 1). This statement does not coincide with

the arguments [5] that the local temperature measurements and specific energy contains similar information.

In the periphery, good correlation between the specific energy and the temperature (denoted T6) is obtained. This is

not necessary true when studying disturbances instead responses due to step changes [14].

6 Within the typical operating window of the refiner studied, the hydraulic pressure is the input variable to an open

system which has the clearly strongest effect on the temperature levels and Fsteam [14]. 7 The integral of the ratio between the energy distribution ( )rkwR

and mass flow ( )rm1, where k is a conversion

factor, is certainly process and plate specific.

( )kNsteamF ( )kNsteamF ( )kNsteamF

Fcl

osi

ng(k

N)

Hydraulic pressure Dilution water Production

Hence, the temperature measurements inside the refining zone contain additional information which the specific

energy does not cover [14,16].

It is important to repeat that the specific energy is influenced by all three input parameters, which is shown in Fig. 7.

Therefore, overconfidence in traditional control concepts, such as using specific energy as a target value, can result

in pulp quality variations due to process disturbances.

Figure 7: Specific energy as a function of time according to the step changes given in Fig. 4.

This is clearly indicated in Fig 8 where the force acting on the pulp has been derived from the difference between

the closing force and the steam force.

Figure 8: Force acting on the pulp as a function of time according to the step changes given in Fig. 4.

This is a quite simple way to describe the force acting on the pulp inside the refining zone as it should be divided

into different forces acting in radial as well as the tangential direction. Nevertheless, it gives a glimpse of the

variations in the forces acting on the pulp and it is interesting to see that the impact on the fibers to step responses in

hydraulic pressure is not as dominant as expected according to Fig. 5 while the changes in production rate affect the

forces more distinct.

Even though several papers indicate the usefulness of temperature profile measurements [3,4,5,6,7,13,14,15,16],

questions can be raised about the added value of measuring the temperature inside the refining zone. Some attempts

have been made to control the temperature profile [4,5,7,13] and thereby the pulp quality but until recently, the

results have been sparse [14]. However, one thing can be stated: Without the temperature profile measurement

neither the thermo-dynamical work related to the steam generation nor the shape of the profile or the position where

the temperature reaches its maximum can be estimated. Moreover, internal states in future control concepts would

not be possible to derive without refining zone measurements. Such control parameters have not been used in any

control concepts so far but a closer look on the temperature profiles in Fig. 9, shows that the profiles give interesting

indirect information related to the internal states like for instance the fiber pad distribution.

As concluded in Fig. 5, the major impact on the process in terms of a temperature profile change, will occur when

changing the hydraulic pressure which is also seen in Fig. 9.

Sp

ec. E

ner

gy

(kW

h/A

DM

T)

Change in

Hydraulic pressure

Change in Dilution

Water feed rate

Change in

Production

Change in

Hydraulic pressure

Change in Dilution

Water feed rate

Change in

Production

Fpulp

(kN

)

An increased hydraulic pressure will influence the temperature profile over the entire radius and thereby increase the

fiber pad friction on the plates. This makes it more difficult for the steam to evacuate from the refining zone and

hence result in an increased temperature.

It is noteworthy that an increased hydraulic pressure should result in a reduced plate gap implying an increased Fpulp

but the force acting on the pulp seems to be almost unchanged, see Fig. 8. This phenomenon is probably due to

changes in the fiber pad distribution between the plates.

Figure 9: Temperature profiles related to the step responses in hydraulic pressure, dilution water and production.

Another thing to consider in general is that the inner temperature changes a lot when performing all step responses.

Studying the temperature profiles when for instance the production is increased, it is logical to expect the

concentration of the fiber pad to increase, especially in the feeding zone, and thereby force steam to flow forward

instead of backwards in the refining zone to a larger extent. When increasing the dilution water feed rate, the fiber

pad will be cooler in the inner part of the refiner which in total will result in more steam flowing forward in the

refining zone and result in a temperature increase near the rim of the plates. According to Fig. 9, the position for the

maximum temperature will also be shifted when performing the step changes and this appears to have a major

influence on the pulp quality as shown by Sikter et al[14].

How the changes in the temperature profile affect the fiber pad distribution are difficult to predict on beforehand but

recent research [14] shows that a controlled temperature profile appears to be useful for suppressing quality

variations. However, so far no one has controlled the entire temperature profile. Instead, the focus has been on the

control of the maximum temperature or the radius where the maximum temperature appears. Control concepts

including the maximum temperature as well as the maximum position will probably be studied in the future [14].

We can conclude from the discussion above that the numbers of parameters which are necessary to cope with form a

complex challenge especially when it comes to the analysis of the distributed refiner work ( )rwRand plate gap

behavior.

As the motor load is a consequence of what actually happens inside the refining zone, the distributed work along the

radius can give additional information.

Several attempts to measure the shear forces inside larger refiners [15] show that the major part of the load is

distributed over the plate after the temperature peak. From a phenomenological perspective such assumptions

influence the modeled parameters significantly.

To illustrate this, a traditional way to analyze the measured motor load, LW and the estimated energy loss

lossQ , see

Fig 10, is given below.

Tem

per

atu

re(C

)

radius(m) radius(m) radius(m)

Hydraulic pressure Dilution water Production

Figure 10: Motor load and estimated energy loss for the complete time series studied.

As seen in Fig. 10 the estimated losslossQ , which is the integral of the distributed loss, is following the motor load as

expected even though some variations occur, see Fig. 11.

The heat radiation and motor loss xQ is assumed to be about 3% of the motor load. The computed refiner

work ( )rwref varies around 4%.

However, the crucial question to answer is if the energy distribution over the plates has to show the same behavior.

To answer this question, it is important to bear in mind that the distribution of fibers over the plates is not

homogeneous which has been known for a long time [17].

Figure 11: Ratio between the estimated energy loss and the motor load for the complete time series studied.

The entropy model described above covers such phenomena and uses the measurements of temperature as input

signals in order to get proper estimates of the local pressure gradients in the refining zone which will affect the fiber

concentration ( )r1α in the refining zone.

Whether or not this is an adequate description, the temperature fluctuations will cause, via the steam generation, an

inhomogeneous distribution of steam and fibers inside the refining zone. This is illustrated in Fig. 12 where the fiber

concentration is visualized at three radii in the refining zone.

time(min)

Qlo

ss/W

L(%

)W

L(M

W)

Qlo

ss(M

W)

time(min)

Figure 12: Fiber concentration as a function of time at three different radii.

This inhomogeneous distribution will of course affect the energy distribution inside the refining zone, see Fig. 13.

If this represents the process behavior to any appreciable account, the refining intensity and thereby the fiber

residence time will vary in different parts of the refining zone and hence affect the final pulp quality out from the

refiner.

Figure 13: Ratios between the distributed energy loss and motor load as a function of time at three different radii.

As the spatial fiber distribution is not homogeneous as a function of time, the expected plate gap will certainly vary

when changing the hydraulic pressure, dilution water feed rate and the production rate. As a consequence of that, the

ratio between the energy loss lossQ and the motor load

LW , given in Fig. 11, must not necessary follow the plate gap,

see Fig. 14.

Figure 14: Plate gap estimation for the complete time series studied.

It is worth mentioning that the estimation of the fiber concentration, shown in Fig. 12, is closely related to residence

time as well, see Fig. 15 and the equations above. This estimated residence time is hard to rely on as an absolute

qlo

ss/w

r(%

)

1α

[mm]∆

value. However, different models for the permeabilityκ have been applied8 and all simulations show that the

dynamic part of the estimation will not be affected significantly.

Figure 15: Total estimated fiber residence time as a function of time.

Since the absolute value of the residence time is hard to estimate, the ratio between the residence time before the

radius where the maximum temperature appears and the total residence time can be valuable to study, see Fig. 16.

It is interesting to see that the ratio is affected by the hydraulic pressure and the production changes but not the step

changes in dilution water feed rate. This is primarily a consequence of the shift in the position of the maximum

temperature, see Fig 9.

Another observation, similar to the one related to the forces acting on the pulp in Fig. 8, is that the ratio does not

change as one might expect when changing the hydraulic pressure. The variations in the ratio caused by the

production level changes are probably due to a rearrangement of the fiber pad distribution in the refining zone.

Figure 16: The ratio between the residence time before maxT and the total residence time as a function of time.

As the pressure gradient is possible to derive from the temperature profile, a large variation in the local temperature

over the time will cause a variation in the steam velocity. Since all parameters are linked to each other the spatial

fiber concentration varies and consequently the pulp quality due to variable residence time in the refining zone. The

magnitude of such changes is not clear but using the entropy model described above a glimpse of a possible scenario

can be obtained, see Fig 17.

As seen in Fig. 17, the scatter in temperature for each step change in hydraulic pressure, dilution water feed rate and

production rate visualized in Fig.4 are largest in the inner part of the refining zone which is also indicated in Fig. 9

and will therefore affect the steam clearance considerably.

Additional information to this section can be found in appendix 1 where special attention should be put on the

correlation between the residence time (Rtot in Appendix 1) and other parameters.

8 One such example is that the permeability follows a linear approximation which is not dependent on the

consistency. Future research will cover tests of different hypothesis regarding the permeability description according

to planned fiber packing degree measurements.

[ ]sectotτ

[ ]%max

tot

rr T

τ

τ ≤

Figure 17: Intervals in estimated steam velocity and temperature measurements when changing the hydraulic

pressure, dilution water feed rate and production rate according to Fig. 4.

CONCLUSIONS

The results presented in this paper are based on a non-linear entropy model applied on data obtained from an Andritz

RTS 68¨ single disc refiner. The model has been used to estimate refiner variables, such as consistency, residence

time, refining work and plate gap, using temperature profile measurements in the refining zones.

The model provides a method to divide the total work carried out in the refining zone, i.e. the work associated with

the motor load, into spatial thermodynamic and refining work.

Moreover, it is emphasized that the calculated spatial refining work can vary significantly, also during time

sequences where the motor load is almost the same. This could be a consequence of the variable fiber concentration,

i.e. a redistribution of the fiber pad, inside the refining zone due to process disturbances and changes in operating

points.

By using the measurement of the temperature profile in the refining zone, the local pressure gradients can be derived

and together with the model give indirect information about the fiber distribution and thereby the radial steam

velocity.

Even though the model accuracy can be questioned, the temperature fluctuations in the refining zone should be

reduced as it will influence the residence time and thereby the pulp quality. Therefore, a production with a stable

temperature profile by means of small variations in time can be expected to produce a more stable pulp quality. This

means that the commonly used control concept of keeping constant specific energy should be reconsidered since the

residence time in different parts of the refining zone can vary over time and thereby influence the pulp quality.

Finally, it is stated that the position along the radius where the temperature profile reaches a maximum value

depends on where in the operating window the refiner is positioned. This implies that both the maximum

temperature and its radial position should be interesting to consider when designing new pulp quality control

concepts.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge funding by the Swedish Energy Agency and all those who have not been

mentioned in the reference list.

High

Medium

Low

Changes in production

rate

High

Medium

Low

Changes in dil water

feed rate

High

Medium

Low

[m/s] 3

v

[C] T

Changes in hydraulic

pressure

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Appendix 1

Sp. En.

Sp. En. 1 Wtot

Wtot 0,998 1 Wref

Wref 0,905 0,906 1 Wref/Wtot

Wref/Wtot 0,762 0,763 0,965 1 Rtot

Rtot 0,415 0,409 0,388 0,341 1 R<Tm

R<Tm 0,068 0,064 0,273 0,378 -0,209 1 R>Tm

R>Tm 0,225 0,223 0,131 0,063 0,684 -0,499 1 R<Tm/Rtot

R<Tm/Rtot -0,122 -0,125 0,084 0,206 -0,384 0,957 -0,588 1 M Cons

M Cons 0,602 0,602 0,682 0,669 0,471 0,319 0,162 0,112 1 E Cons

E Cons 0,909 0,910 0,838 0,716 0,600 -0,089 0,393 -0,325 0,701 1 Gap

Gap -0,906 -0,911 -0,891 -0,795 -0,161 -0,307 0,018 -0,145 -0,590 -0,760 1 Pout

Pout 0,428 0,438 0,304 0,191 -0,140 -0,220 0,003 -0,229 -0,060 0,267 -0,542 1 Pin

Pin 0,243 0,252 0,142 0,058 -0,105 -0,337 0,062 -0,310 -0,092 0,154 -0,297 0,594 1 T1

T1 0,474 0,474 0,494 0,462 0,496 0,369 0,158 0,162 0,759 0,592 -0,436 -0,209 -0,081 1 T2

T2 0,442 0,442 0,539 0,550 0,360 0,179 0,146 0,047 0,622 0,596 -0,438 -0,094 0,094 0,683 1 T3

T3 0,755 0,752 0,766 0,704 0,608 -0,066 0,390 -0,284 0,629 0,862 -0,637 0,195 -0,029 0,407 0,411 1 T4

T4 0,065 0,064 0,269 0,370 -0,216 0,802 -0,428 0,786 0,215 -0,096 -0,353 -0,039 -0,278 0,040 -0,058 0,055 1 T5

T5 0,857 0,859 0,811 0,705 0,471 0,066 0,256 -0,155 0,713 0,881 -0,795 0,302 0,301 0,687 0,579 0,688 -0,059 1 T6

T6 0,860 0,865 0,868 0,789 0,321 0,146 0,139 -0,043 0,542 0,772 -0,900 0,557 0,267 0,357 0,294 0,709 0,256 0,801 1 Fclos

Fclos 0,912 0,914 0,879 0,776 0,441 0,170 0,200 -0,052 0,742 0,890 -0,894 0,382 0,220 0,638 0,518 0,773 0,135 0,922 0,881 1 Fst

Fst 0,797 0,798 0,864 0,824 0,486 0,325 0,169 0,098 0,824 0,852 -0,823 0,169 0,124 0,786 0,770 0,742 0,229 0,873 0,765 0,900 1 Fpulp

Fpulp 0,568 0,568 0,368 0,207 0,086 -0,225 0,136 -0,304 0,131 0,413 -0,479 0,548 0,265 -0,034 -0,276 0,357 -0,126 0,447 0,557 0,572 0,158 1

corrBB=Dilution water changes

Sp. En.

Sp. En. 1 Wtot

Wtot 0,997 1 Wref

Wref 0,855 0,860 1 Wref/Wtot

Wref/Wtot 0,707 0,713 0,971 1 Rtot

Rtot -0,636 -0,635 -0,739 -0,718 1 R<Tm

R<Tm -0,627 -0,629 -0,521 -0,420 0,702 1 R>Tm

R>Tm -0,436 -0,434 -0,580 -0,594 0,790 0,381 1 R<Tm/Rtot

R<Tm/Rtot -0,267 -0,271 -0,039 0,074 0,132 0,766 -0,122 1 M Cons

M Cons -0,720 -0,717 -0,751 -0,695 0,929 0,829 0,670 0,313 1 E Cons

E Cons -0,613 -0,609 -0,683 -0,653 0,956 0,768 0,719 0,202 0,960 1 Gap

Gap -0,854 -0,852 -0,873 -0,800 0,916 0,755 0,682 0,217 0,947 0,919 1 Pout

Pout 0,765 0,768 0,681 0,575 -0,353 -0,383 -0,226 -0,183 -0,452 -0,343 -0,600 1 Pin

Pin 0,456 0,460 0,531 0,515 -0,856 -0,753 -0,621 -0,275 -0,858 -0,872 -0,746 0,195 1 T1

T1 -0,699 -0,704 -0,752 -0,704 0,812 0,750 0,578 0,286 0,833 0,804 0,821 -0,507 -0,831 1 T2

T2 -0,304 -0,305 -0,187 -0,114 0,441 0,368 0,328 0,194 0,407 0,456 0,362 -0,281 -0,390 0,461 1 T3

T3 -0,381 -0,379 -0,415 -0,392 0,817 0,658 0,616 0,176 0,788 0,857 0,681 -0,072 -0,875 0,687 0,452 1 T4

T4 -0,309 -0,311 -0,144 -0,052 0,504 0,845 0,233 0,742 0,617 0,591 0,452 -0,076 -0,682 0,499 0,404 0,692 1 T5

T5 0,789 0,793 0,734 0,637 -0,772 -0,795 -0,522 -0,394 -0,853 -0,801 -0,885 0,518 0,676 -0,736 -0,314 -0,642 -0,573 1 T6

T6 0,840 0,847 0,923 0,872 -0,734 -0,620 -0,539 -0,178 -0,790 -0,716 -0,883 0,736 0,568 -0,790 -0,286 -0,458 -0,261 0,802 1 Fclos

Fclos 0,366 0,367 0,251 0,173 0,257 0,174 0,209 0,042 0,167 0,271 -0,038 0,743 -0,493 0,122 0,031 0,518 0,399 0,006 0,272 1 Fst

Fst -0,119 -0,117 -0,026 0,020 0,502 0,523 0,340 0,322 0,467 0,545 0,305 0,062 -0,647 0,541 0,783 0,732 0,700 -0,280 -0,087 0,507 1 Fpulp

Fpulp 0,459 0,458 0,254 0,134 -0,314 -0,411 -0,181 -0,312 -0,357 -0,348 -0,366 0,603 0,258 -0,478 -0,823 -0,328 -0,401 0,309 0,340 0,351 -0,629 1

Sp. En.

Sp. En. 1 Wtot

Wtot -0,725 1 Wref

Wref -0,697 0,879 1 Wref/Wtot

Wref/Wtot -0,601 0,704 0,957 1 Rtot

Rtot 0,908 -0,802 -0,835 -0,759 1 R<Tm

R<Tm 0,359 -0,314 -0,052 0,112 0,081 1 R>Tm

R>Tm 0,695 -0,614 -0,708 -0,682 0,848 -0,182 1 R<Tm/Rtot

R<Tm/Rtot -0,422 0,379 0,595 0,656 -0,666 0,670 -0,745 1 M Cons

M Cons 0,545 -0,432 -0,448 -0,405 0,498 0,210 0,378 -0,214 1 E Cons

E Cons -0,373 0,669 0,412 0,209 -0,255 -0,708 -0,041 -0,321 -0,242 1 Gap

Gap -0,067 -0,512 -0,512 -0,450 0,213 -0,229 0,243 -0,320 0,055 -0,336 1 Pout

Pout -0,439 0,715 0,518 0,338 -0,429 -0,437 -0,261 0,005 -0,345 0,678 -0,557 1 Pin

Pin 0,104 -0,326 -0,169 -0,052 0,172 0,018 0,145 -0,127 -0,057 -0,346 0,472 -0,344 1 T1

T1 0,836 -0,831 -0,852 -0,767 0,866 0,306 0,672 -0,433 0,464 -0,365 0,151 -0,490 0,008 1 T2

T2 0,531 -0,521 -0,436 -0,335 0,594 0,101 0,491 -0,353 0,268 0,010 -0,033 -0,318 0,002 0,664 1 T3

T3 -0,320 0,465 0,258 0,103 -0,202 -0,499 -0,048 -0,208 -0,038 0,701 -0,302 0,656 -0,503 -0,236 -0,128 1 T4

T4 -0,637 0,673 0,829 0,826 -0,817 0,318 -0,784 0,858 -0,355 0,089 -0,488 0,339 -0,320 -0,656 -0,404 0,184 1 T5

T5 0,010 0,215 0,072 -0,022 -0,016 -0,317 0,064 -0,228 -0,073 0,288 -0,240 0,371 -0,152 -0,180 -0,150 0,150 -0,121 1 T6

T6 -0,761 0,848 0,856 0,762 -0,800 -0,279 -0,621 0,388 -0,536 0,490 -0,419 0,717 -0,222 -0,818 -0,550 0,438 0,696 0,199 1 Fclos

Fclos -0,415 0,718 0,512 0,326 -0,436 -0,365 -0,287 0,067 -0,264 0,676 -0,621 0,931 -0,626 -0,433 -0,284 0,703 0,409 0,373 0,679 1 Fst

Fst 0,391 -0,262 -0,233 -0,191 0,422 0,093 0,344 -0,238 0,166 0,219 -0,372 0,079 -0,304 0,581 0,820 0,290 -0,132 -0,053 -0,202 0,142 1 Fpulp

Fpulp -0,615 0,753 0,572 0,397 -0,655 -0,352 -0,481 0,231 -0,330 0,358 -0,200 0,661 -0,256 -0,773 -0,838 0,326 0,416 0,329 0,677 0,666 -0,643 1

Correlation coefficients

when changing the Hydraulic pressure

Correlation coefficients

when changing the Dilution water feed rate

Correlation coefficients

when changing the Production rate