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Case study: Method for systematic analysis of paper machine multicylinder drying section
Copyright © IFAC PRP 4 Automation, Ghent, Belgium 1980
CASE STUDY: METHOD FOR SYSTEMATIC ANALYSIS OF PAPER MACHINE MULTICYLINDER DRYING SECTION A. Lemaitre*,
J. Veyre*, B. Lebeau* and C. Foulard**
*Centre Technique du Papier, B.P. 7110, 38020 Grenoble Cedex, France **Laboratoire d'Automatique de Grenoble, B.P. 46, 38042 Saint-Martin-d'Heres, France
Abstract. Drying is a very important phase of papermaking. Both the energy consumption and investment costs required by this process are high. This paper describes a method giving systematic analysis of industrial drying sections during their run and based on a mathematical model of paper cylinder drying. Working on measurements data, it is possible to compute the heat and mass transfer coefficient values to get the complete identification of the considered drying section. Then, it is possible to test by simulation, the effect of new investments (increasing the number of cylinders, moving the size-press location, etc) or of operating point changes (increase of steam-pressure or moisture content at the entrance ... etc) on the machine production and on the steam consumption. This method has been used for an industrial printing paper machine. Computer simulations have allowed to get the optimal size-press location in the drying section and the machine speed variations obtained after the increase of the number of cylinders and this for three different basis weights.
INTRODUCTION Paper drying is a very important phase of the papermaking process. It has a strong influence on the f~nal paper quality but also on the economics of the whole process. As a matter of fact, paper drying is the last part of the water removal phase in which most of its mechanical properties are confered to the paper sheet. Besides both the energy consumption and investment costs required by this process are high. However the design of the drying sections has so far largely been based on empirical rules and the optimum performances as well as the corresponding working conditions are not very well known. Improving the drying sections running conditions is also of very great interest and this subject has been much studied, but very few works have been done to find and to developpe some methods for systematic analysis of paper machine drying sections during their run. The recent process analysis techniques, namely modelling, identification and simulation offer new prospects for such studies, but they have not yet been widely used. The present contribution endeavours to act in this direction. A multicylinder paper machine drying section is made of stea~ heated cylinders on which the sheet is successively applied by clothi ng s ( Fig. 1).
261
rII
_t
h 00 d
~e~~~a~o~~=:t clothing
I
poc k e t
l I I
I I
I
I
\~t!:;i~~r:;J~-sheet
Fig. 1
dryers
hot air blowing roll
A multicylinder drying section
The sheet moisture content at the entrance of the drying section is generally 60 to 70 per cent (water weight/total weight). At the end, the moisture content must be about 5 to 10 per cent. The whole drying section is set in a hood so that the atmosphere in which the evaporation takes place can be controlled by action on the insufflated and extracted air flows. The section is supplied with steam at a pressure of 3 to 10 bars. Since the temperature set-points of the cylinders rise from the beginning to the end of the section,
A. Lemaitre et al.
262
the condensate of every dryer is flashed and the steam, thus produced, is used by the former dryers. When the paper is treated on a size-press, the drying section is divided in two parts : the fore-dryers and the afterdryers, after the size-press. Numerous studies have been carried out concerning the drying section and the theoritical knowledge about the mecanisms that occur is quite large. Many authors have analysed the heat and mass transfer conditions to which the sheet is submitted during its trip in the drying section (1) (2). Very detailed descriptions of the migration of water and vapour inside the sheet have also been proposed (3), (4), (5). However very few authors used these theoritical results to analyse the whole process behaviour (6). Many simplifications must be introduced to obtain what we want, namely, a workable model and to achieve the complete computer simulations from which the relative influence of each design or running parameters can be seen. The elaboration of such a mathematical model (7), (8) is presented here. It is also the basis of a parameter estimation method which has been developped to evaluate the heat and mass transfer coefficients in industrial equipements. An experimental work has been carried out on the pilot paper machine of the CENTRE TECHNIQUE DU PAPIER to test this method. This model has of course been used for simulations, especially to compute the effect of new investments or of operating point changes on the machine production. This paper describes an industrial example on a printing paper machine.
- temperature and moisture content are supposed to be uniform through the web. Only variations in the machine direction (x) are considered - all the internal phenomena (vapour diffusion, capillary transport ... ) are considered only with global relationships - the drying section is in a steady state. At the abscissa x in the machine direction, we consider a sheet element of length dx, width 1 and moving at the speed U (Fig. 3).
x
x
+ dx
u
Fig. 3
Sheet element on the cylinder
1.1. Thermal balance for the sheet element The sheet receives heat from the steam (of course only in the case of web on the cylinder) :
1 • MATHEMATICAL MODEL OF A DRYING SECTION
The main simplifing hypotheses used to construct such a model are as follows : - two typical positions of the paper web are distinguished : web on the cylinder and web in the draw as can be seen from Fig. 2
It exchanges heat with the clothing (web on the cylinder) or with the ambient air (web in the draw)
It also loses some heat because of evaporation of water. Calling B the evaporation rate, and r the latent heat of vaporization, the loss is :
B.r(8 f )·1.dx Then the thermal balance gives
o
(A)
For the two typical positions of the web, we have
+ Dryer i-I
Fig. 2 : The two positions of the paper web
- web on the cylinder : a = afh
heat transfer coefficient between the sheet and the clothing
8 = 8h
temperature of the clothing
- web in the draw :
Method for Systematic Analysis The heat exchange with the ambient air takes place on the two sides of the sheet : heat transfer coefficient between the sheet and the air
a= 2.Cl a f
temperature of the air of course, we have :
Ct
vf
263
of the phenomena which occur in the considered sheet element, we must known the variations of the vapour pressure at the sheet surface. During drying this vapour pressure is not only depending on the temperature 8 f and the moisture content Xf of the sheet, but also on the drying rate. So the paper behaviour during drying is shown on the Fig. 4.
= 0
1.2. Water balance for the sheet element Evaporation rate
B
The water inside the paper is removed by surface evaporation due to the difference of partial pressure of water between the sheet surface and the ambient medium. In the air the evaporation rate B is given by the STEPHAN diffusion law:
_6_ . P. Log
B = -
R.T f
Internal evaporati phase
Surface evaporation phase
(l.:...l:.) P -Pf
vapour pressure in the ambient medium vapour pressure at the sheet surface critical Xcf moisture content
total surrounding pressure
6
mass transfer coefficient between the sheet and the ambient medium
Fig. 4.: Evaporation rate variations during drying
Then the water balance for the sheet element gives : dX+
6
P
P
G.U. --*- = - - - .P.Log (----) dx R. Tf P - Pf
(B)
For the two typical positions of the web, we have
It shows the theoritical variations of the evaporation rate during the drying of an hygroscopic material such as the paper sheet, when this material is dried at constant temperature, with a constant vapour pressure in the surrounding air. Two major phases appear :
6= 2.6 af
p= Pa
6a f : mass transfer coefficient
between the sheet and the air (evaporation from the two sides of the web)
: vapour pressure in the pocket air
We assume that the STEPHAN law is always valid to describe the mass transfer between the web and the clothing. The evaporation still occurs in the ambient air but with a mass transfer coefficient which depends on nature and conditionning of the clothing and which is therefore representative of its efficiency.
6 = Bfh
Xf moisture content
~_~~Ei~~~_~~~E~E~E~~~_E~~~~ When the moisture content of the web is high, the vapour pressure Pf at the surface is equal to the saturated vapour pressure ps(8 f ), at the same temperature. The evaporation takes place like on a free water surface. Then Pf is constant (and also B) even when the moisture content Xf decreases: Pf = Ps(8 f )
When the moisture content Xf becomes lower than the critical moisture content Xcf ' Pf decreases and also B. The sheet surface can no longer be considered as a surface of free water and the vapour comes also from inside the sheet (internal evaporation).
The critical moisture content, corresponding to the transition between the two drying phases, depends on the moisture content gravapour pressure in the air over p = Pa dient inside the sheet, which depends on the clothing the value of the evaporation rate (instantaneous and past). Then the critical moisture 1.3. Paper behaviour during drying content is higher when the evaporation rate is higher. So the paper behaviour during To obtain a complete mathematical representation drying can be represented by a dyn~~c sorption mass transfer coefficient between the sheet and the clothing
A. Lemaitre et aZ.
264
isotherm (8) described by the relationship as follows :
(C)
k f and Xcf not only depend on the evaporation rate but also on the paper characteristics. 1.4. Complete sheet drying model
For the sheet element that we have considered the complete model is constitued by equations' (A) and (B) with the transfer coefficients corresponding to the two web positions (on the cylinder and in the draw). The behaviour of the paper during drying is taken into account by relation (C). The integration of those differential equations on the cylinder and then in the draw is successively done for all the dryers, from the beginning to the end of the drying section. It must, of course take into account the particular value of the parameters for each dryer (as steam temperature, vapour pressure and temperature of the pocket air). This integration, quite easy to perform by means of a digital computer, leads to the complete drying model.
2. PARAMETERS ESTIMATION In this model, the numerical values of many of the parameters are unknown. The estimation of these parameters and of their variations in the drying section is necessary to use the model.
low if we compare it with the heat cam~ng from the steam. Computer simulations show that the value of this coefficient can vary over a wide range and has still a negligible effect on the drying process -Then, the transfer being convective In the draw, it is possib le, in this case, to assume that COLBURN analogy is valid between the heat transfer ~o~fficient aaf and the mass transfer coefflclent Baf. So, we have:
Taking into account these two simplifing hypothesis, only three coefficients have to be estimated : Civf' Bfh and Baf·
2.1. Parameters estimation method From comparison between experimental data and simulations results, it is possible to estimate, cylinder by cylinder, these three coefficients. For that, we need at least three different measures (two temperatures 8 1 and 8 2 , and one moisture content ~) because the evolution of paper drying is given by the temperature and the moisture content of the sheet on each cylinder and draw. Fig. 5 shows the identification algorithm which is quite classical 8f
8 .l
f
i+l
Dryer i of the pilot machine
Xf i
X
i+
In the first phase (cylinder), we need three different parameters Ctvf
heat transfer coefficient between the steam and the sheet
Ci
fh
heat transfer coefficient between the sheet and the clothing
Bfh
mass transfer coefficient between the sheet and the clothing
In the draw, two parameters are required uaf
heat transfer coefficient between the sheet and the air
Baf
mass transfer coefficient between the sheet and the air
Taking into account the possibilities of measurements in a drying section, it is necessary to make different hypothesis in order to simplify the identification : - First, it is possible to ignore the heat transfer coefficient ufh ; indeed the temperatures of the clothlng and of the sheet are almost equal and the heat transfer is
XM (computed)
-.,
18£
i+l
IXf i+l
I
IL-
..JI
Simulated dryer i Fig. 5
Identification algorithm
Method for Systematic Analysis
The criterion J has a quadratic form J
3 L
2
k=l
E k
calling Yk, the measure k, we have : Yk calculated - Yk measured Yk measured The minimisation of the criterion J is carried out by means of a non linear programming method. Many methods have been tested, because some difficulties appeared concerning the algorithm convergence. The equations of the system are coupled and non linear, and it is not possible to get an analytic fOnD of the criterion gradient. We have chosen the M.J.D. POWELL method (8) which allows to resolve this difficulty. This method gives good results and is also very fast. 2.2. Experimental method The experimental work has been carried out on the pilot paper machine of the "CENTRE TECHNIQUE DU PAPIER" Grenoble, France. Measuring the sheet temperature during drying is not an easy task, owing to space restrictions in the pockets. A contact thermometer (SWEMA) is used and two differents measures are taken on each draw. The positions of the two measuring points are not exactly at the beginning and at the end of the draw, but respectively at about one-fifth and fourfifth of its length. The sheet moisture content is determined by means of paper samples taken on each draw at the end of the run. The samples are roughly as long as the draw and therefore, the obtained moisture content is equal to the average value ID the draw. To remove this problem, we developped, in collaboration with the "Institut d'Optique de Paris", an "infrared" moisture meter. This apparatus allows to measure the moisture content in the required place in the draw. The head, which is very small, is mounted on a pipe and is in contact with the sheet during the measurement. This moisture meter must be calibrated by means of samples taken in some draws along the dryer section. Some other measures like the steam pressure are needed ; besides the wet and dry bulb temperature of the air inside each dryer pocket are obtained from a psychrometer mounted on the end of a traversing probe. 3. INDUSTRIAL APPLICATIONS OF THE MODEL The mathematical model and the parameter estimation method have been used to evaluate the heat and mass transfer coefficients on the dryer section of the pilot paper machine of CIP. The variations of these coefficients along the drying section have been studied and also the influence of different running
265
parameters like steam pressure or clothing tension. This parwmeter identification have been also carried out on different industrial paper machines in order to study the influence of the machine speed and to verify some results obtained on the pilot plant (8). Besides computer simulations have been done to find the optimal operating conditions minimizing the energy consumption particularly by adjustment of the ventilation parameters (9). The effect of new clothings has been studied as well as the influence of some design and running parameters on the drying section efficiency (10). But one of the most important use of this model is the developpement of a method for systematic analysis of industrial drying section during their run. This paper describes now a particular example of this method.
3.1. Aim of the work The aim of the work is to compute by means of simulations, the effect of new investments or operating point changes, on the machine production. When a papermaker wants to change his machine production, he has, for instance, to increase the number of cylinders but generally these changes are based on empirical rules. Some mistakes are possible and he does not know exactly the future results of his new investments. Improving the knowledge of his drying section and of its possibi 1 i ties is then of great interest for the papermaker. The main applications are as follows : - to compute the correct number of cylinders for a given increase of production, or the new machine speed corresponding to a higher number of cylinders - to test the effect of the setting up of a new size-press, to optimize his location and to see the influence of this location on the machine drying limitations for different productions - to compute the speed increase for different steam pressures in the cylinders - to check the influence of the removal of a Yankee dryer or of a too large draw length - to compute the machine production variations after the setting up of a hood with a new ventilation system - to give, of course, the influence of changes in running parameters such as the sheet moisture content at the entrance of the dryer section. The approach of such a study, consists then, in identifying the drying section in its present working conditions, to get the values of the heat and mass transfer coefficient, in order to make the desired simulations.
3.2. Paper machine characteristics
A. Lemaitre et al.
266
The chosen example concerns a printing paper machine. This machine is 3,4 m wide. The dryer section consists of 22 fore-dryers and 12 additional dryers after a size-press. The diameter of the cylinders is 1,5 m. The first part of the machine (before the size-press) is divided in three section of 3,7 and 12 cylinders. The steam supply system is a "cascade" type system. The upper and lower after-dryers are separatly supplied. Besides, the dryers are clothed with classical synthetic fabrics, except the first six cylinders which are clothed with a single-felt system. It is then impossible to measure the sheet temperature on these dryers. The pockets are ventilated by hot-air blowing boxes and the air is extracted by a closed hood. The parameter estimation has been carried out for three different basis weights (40, 64 and 80 g/m2). The main operating conditions appear in table 1. In addition to these steam pressure we have measured the sheet temperature in two different places in each draw, the temperature and the moisture content of the air in each pocket, and the sheet moisture content by means of samples. These measurements have been carried out, on the plant, by the 'Technical Assistance Service" of the C.T.P.
Heat transfer coefficient avf(kcal!h.m2.oC)
o~
800
a-d~
600
400
(g/m2)
~ 06_
200
0-
80g/m2
64g/m2 40g/m2
0
:
I
»\\h,Oii \
\
~
0-0- 1
I
AFTER-
I
FORE-DkYING DRYING . .S.;", ; ;E.....Co.;;;;T__I...N~_......L.-.I..&..-......L.I--.::.S=E.::s.T.:.,;I=.:O:.:.N.:...-..L-.-.....LII~
o 5
27 32 3 cylinder number Fig. 6 : Variations of the heat transfer coefficientbe~een the steam and the sheet during drying
10
15
20 22 23
Mass transfer coefficient Sfh(m/h) 300
-6_
80 g/m2 64 g/m2
-0-
40 g/m2
-0-
I I
Cf'0'A /6 ~ \, \ / /'i\
200
Basis weight
:\
.-
3.3. Identifications results The Fig. 6 shows the variations of the heat transfer coefficient a vf between the steam and the sheet during the drying, for the three different basis weights. We observe that this coefficient decreases regularly from the beginning to the end of the drying, as noticed on most of the identified drying sections up to now. The average value is about 500 kcal/h.m2.oC, during the constant evaporation rate period. The Fig. 6 shows also that there is no important difference between the three basis weights concerning the value of this coefficient, because the estimation accuracy is not high enough, to observe such variations. Besides, the average value of this coefficient is quite the same in the fore-drying section and after the size-press.
a
I
I
I
I
I
I
0.... l--~r--\~ /9 o
~ ~c~
o~ ~
o
l
I
5
)0 Fig. 7
)5
I
a-Q
~.~.I e<,~~o
O\~ ,~\;\ \/ /'-\
ORE- DRYING SEcn
I I
::
~a,j\\:"~\ " 0'O~o\h~g> / \
100
I I I I
20
0-
I
./\ [ 6 )yp IAFTER\f :DRYING ECTI N I
'0
6
\ _Q
22 23
27 32 4 cylinder number Variations of the mass transfer coefficient on the cylinder during drying
The Fig. 7 shows the variations of the mass transfer coefficient on the cylinder, for the three considered basis weights.
Steam Machine Machine Dryness Dryness Dryness Dryness Steam Steam Steam Steam after end of pressure pressure pressure pressure pressure Produc- entrance before speed tion of the sizesizethe wet em interm. main lower upper drying press press drying section sectior section cylind. cylind. section A) B2 section C2 A2 A3 (m/mn) (T/j) ( %) (bar) (bar) (bar) (bar) ( %) (%) (bar) (%)
40
601
118
42
96,2
63
94,5
0,2
0,79
1,09
1
0,32
64
498
155
44
96,2
66,7
92,8
1,36
1,87
2,15
1,16
0,52
80
420
165
45
95,6
68,5
94,2
1,36
) ,86
2,13
0,92
Q,40
Table (1)
Operating conditions for the th£ee basis weights
267
Hethod for Systematic Analysis Just as previously, we find again the same results as for the other identified drying sections up to now, namely the regular decrease of this coefficient during the drying. On the other hand, we can observe a difference between the fore-dryers and the afterdryers. The average value of Bfh is higher in the section after the size-press than in the fore-drying section, for the same sheet moisture content. This agre~'with some workers who say that the water removal after the sizepress could be easier than the classical drying, owing to the water pick-up phenomenon However , when we look at the drying curve (Fig. 9), we can see that the evaporation rate is lower after the size-press than in the fore-drying section, for the same sheet moisture content : indeed, this is due to the fact that the steam pressures are lower in the after-dryers (table 1). So the mass transfer coefficient Bfh , which eliminates the influence of the operating conditions gives a good idea of the real drying efficiency (which is better after the size-press than in the foredrying section). The accuracy of these results depends greatly on the measurements accuracy. Assuming the relative error in sheet temperature and moisture content to be 1 %, computer simulations show variations in the three transfer coefficients avf' Bfh and Baf of respectively 15 %, 15 % and 20 %. This unaccuracy is mainly responsible for the serrated shape of the curves (Fig. 6 and 7).
Sheet moisture content (water weight/ fiber weight) 1,2
~
\
\
\
0,9
\
64 g/m2
\
0
\ \
\
0,6
\
\\ \
0,3
~
\
\
\
S.P.
\
5
\
~'o-O
15 20 22
10
b
0
\
0
"'0
23
0
~
32 34
27
cylinder number Fig. 8
Sheet moisture content variations during drying (simulation after identification)
Evaporation rate (kg water/h.m2) 3.4. Simulations results
50
Reference runs : First, computer simulations have been carried out for the three reference runs, keeping constant the heat and mass transfer coefficients as well as all the operating conditions. Fig. 8 shows the evolution of the sheet moisture content along the fore-drying section and after the size-press, for the reference run corresponding to the basis weight of 64 g/m2. For the same reference run, the curves plotted in Fig. 9 show the variations of the evaporation rate in the two parts of the drying section. New runs --------
64 g/m2 40
30
20
/
10
For the three different basis-weights, we want to stUdy the effect of the following changes on the machine production : - increase of the steam pressure from 2 to 3,5 bars
S.P.
After-drying section at t e same moistur content
ORE-DRYING
o
5
10
AFTER-DR ECTION 15
20 22
23 27
NG
32 34
cylinder number
- setting up 10 ne~ dryers in the fore-drying sec t ion (" cas cad e " s y stem, with now 4 sections of 10, 8, 8 and 6 cylinders) - setting up 4 new dryers after the size-press. (Fig. 12).
Fig. 9
Evaporation rate variations during drying (simulation after identification)
A. Lemaitre et al.
268 The main simulations hypothesis are as follows :
- the heat and mass transfer coefficients are assumed to be independent of the steam pressure and of the machine speed - the operating conditions at the entrance of the two sections are kept constant. Besides, the sheet dryness at the end of each sections must be respectively 98,5 % and 94 % - the ventilation conditions are the same as in the reference runs - the differential pressures between the three sections ("cascade" system) of the first part before the size-press take the average values of respectively 0,3, 0,28 and 0,26 bars (for 40, 64 and 80 g/m2) - an average difference of 0,5 bars, between the upper and lower cylinders after the size-press is chosen
When the steam pressure takes the value of 3,5 bars, the machine production increases reach + 59 % (40 g/m2), + 19 % (64 g/m2) and + 21 % (80 g/m2), compared with the reference runs. The variations of the maximum machine speed with the ~eam pressure in the main section (for the fore-dryers) or in the lower cylinders (after the size-press), are plotted in the Fig. 10, where we can see that the foredrying section still limits the production in every case.
The setting up of 10 new cylinders in the fore-drying section lead to an increase of the maximum speed as can be seen from Fig. 11, compared with the reference runs. However the drying balance of the machine has changed and the after-dryers limit now the production.
besides, the starch pick-up and the moisture pick-up in the size-press is assumed to be independent of the machine speed.
Speed (m/min)
-0- 80g/m2 _6_
I
I I
I
/
1
/
:
•
700
64 g/m2
-0-
600
Fig.l0
40
1°
/
0/
°
-I /
I
I
I
1 ;
:1
,I
Il "
I
! I
400
g/~'r/
0_0_
234 main section (bar~) Speed variations for different steam pressures 1n the main section
/
VII
"0
//0
/0
1
I
I
//0'/0
/// 0
/
v{
"
//0
6
~
0/
sect10n (12 cyl.) /"/
6-
/
/6
/
1//
II
// /
/
" //
//~~///
/6
I 11
____ after-drying
-
/
:./
fore-drying sec tion """ (22 cyl.) /// /
80 g/m2
/ / /
I
I !
after-drying (16 cyl)
/~(ection
//
~
Speed (m/ min) 100
-0-
/PI ----
/'/ I
- - fore-drying section (32 cyl)
0
0
I I
800
/
I
I /
90
/
/'
64g/m2 -0-40g/m4' / I
At the present time, the maximum steam pressure is about 2,1 bars and the machine production is limited by the fore-drying section only for the basis weights 64 and 80 g/m2. Simulations show that for 40 g/m2, an increase of the steam pressure from 1,09 (reference run) to 2,1 barsleads to a machine speed of 740 m/min or a production variation of + 24 %. The Fig. 10 shows that this production is still limited by the fore-drying section.
/
2
3
4
Steam pressure in the main section (bars) Fig. 11
Speed variations for different steam pressures in the main section, after the addition of 10 cylinders in the fore-drying section and 4 cylinders after the size-press
When we add 4 new cylinders after the sizepress, the production is limited again by the fore-drying section and the corresponding increases are respectively 41 % (40 g/m2) , 47 % (64 g/rn2) and 47 % (80 g/m2).
Method for Systematic Analysis The Fig. 11 gives also the speed increases obtained with different values of the steam pressure, for this new machine. Then, the curves plotted in the Fig. 10 and 11 allow to compute, for instance, the optimal location of the size-press, for each basis weight and also with different steam pressures. These results have been used by the papermaker and these changes will be soon carried out on this drying section. It will be be then possible to compare these forecasts with the real results on the process.
CONCLUSION A mathematical model of a complete multicylinder drying section has been developped from a theoritical analysis of this process. Some simplifications in the description of the phenomena are introduced, which lead to an overall model, easily workable. But the main elements of the phenomena are preserved so that this model may be useful and particularly so that it can show the relative effect of the running parameters. This model is the basis of a parameter estimation method to evaluate the heat and mass transfer coefficients of industrial processes. This method and particularly the experimental part have been tested on the pilot plant of the CTP and also on different industrial paper machines. Many developpements of this model have been carried out up to now, but one of the most important is the application of the parameter estimation method to analyse industrial drying sections during their run. This method has been used on a printing paper machine to compute the influence of steam pressure increase and of the addition of new cylinders, on the machine speed. So, the machine production variations due to these design or running changes has been obtained and the optimal size-press location has been deduced from them. Improving the knowledge of his drying section and providing him with the real possibilities of his machine is of great interest for the paperrnaker. Especially, he can see very easily and very quickly the effect of new investments before their carrying out. Then, this model takes the place of the old empirical rules, used up to now, and it can become a very interesting and useful tool for the paper machine users.
269
REFERENCES (1) A.H. NISSA~ et W.G. KAYE "An analytical approach to the problem of drying of thin fibrous sheets on multicylinder machines". TAPPI, vol. 38, nO 7 (Juillet 1955) (2) 0.1. LEHTIKOSKI "A mathematical model of the dryer section" Paperi Ja Puu, vol. 52, nO 2 (1970) (3) S.T. RAN "Heat and mass transfer in hot-surface drying of fibre mats" Pulp and Paper Magazine of Canada, vol. 65 nO 12 (1964) ( 4) W. D. BA I NE S
"Analysis of transients effects in drying of paper" Pulp and Paper Magazine of Canada, vol.74 nO 2 (1973) (5) F.T. HARTLEY et R.J. RICHARDS "Hot surface drying of paper. The development of a diffusion model" TAPPI, vol. 57, nO 3 (Mars 1974) (6) R.L. KNIGHT et L.A. KI~K "Simulation of the papermachine drying section" International Water Removal Symposium British Paper and Board Industrie Federation - London (Mars 1975) (7) A. LEMAITRE, M. PERRON, R. CHARUEL '~odelisation et simulation du sechage du papier sur cylindres pour la concep tion de secheries a hautes performances" XVlle EUCEPA Konferenz, Vienne, Autriche, (Octobre 1977) (8) A. LEMAITRE '~odalisation
et identification d'une secherie multicylindrique de machine a papier : optimisation de sa conception et de son fonctionnement" These de Docteur-Ingenieur, Grenoble, France (Septernbre 1978) (9) B. DUFOUR, M. PERRON "Bilan energetique des secheries multicylindriques" 30e Congres A.T.I.P., ArIes (Octobre 1977) (10)A. LEMAITRE, M. PERRON, A. Rfu~Z "Sechage du papier : influence de 1 'habillage et de la ventilation" Symposium O.F.E., Paris (Septembre 1977).
A. Lemaitre et al.
270
NOTATIONS A
coefficient of COLBURN analogy
B
evaporation rate (kg water/h.m2)
ce
specific heat of water (kcal/kg.oC)
cf
specific heat of dry paper (kcal/kg.oC)
G
basis weight (kg/m2)
J
criterion
1
width of the sheet (m)
p
total surrounding pressure
Pa
vapour partial pressure in the ambient air
Pf
vapour partial pressure at the sheet surface
Ps
saturated vapour pressure
r
latent heat of vaporizaticn (kcal/kg)
R
perfect gas constant
u
machine speed (m/min)
S"team
S.P.
~
x
AFTER-DRYING SECTION FORE-DRYING SECTION (22 cylinders) (12 cylinders) (separated supply) ("cascade" system) Steam
AFTER-DRYING SECTION (16 cylinders)
Fig. 12
Xcf
critical moisture content
aaf
heat transfer coefficient between the sheet and the air (kcal/h.m2.oC) heat transfer coefficient between the sheet and the clothing heat transfer coefficient between the steam and the sheet mass transfer coefficient between the air and the sheet (m/h) mass transfer coefficient on the cylinder
8
temperature of the ambient air (OC)
a
temperature of the sheet (absolute temperature : Tf ) 8
temperature of the steam
v
8], 8 , XM : the three measures on the sheet. 2
(32 cylinders)
abcissa in the machine direction sheet moisture content (water weight/ fiber weigh t)
Ctvf
FORE-DRYING SECTION
The drying section before and after the change of the number of cylinders
CASE STUDY: METHOD FOR SYSTEMATIC ANALYSIS OF PAPER MACHINE MULTICYLINDER DRYING SECTION A. Lemaitre*,
J. Veyre*, B. Lebeau* and C. Foulard**
*Centre Technique du Papier, B.P. 7110, 38020 Grenoble Cedex, France **Laboratoire d'Automatique de Grenoble, B.P. 46, 38042 Saint-Martin-d'Heres, France
Abstract. Drying is a very important phase of papermaking. Both the energy consumption and investment costs required by this process are high. This paper describes a method giving systematic analysis of industrial drying sections during their run and based on a mathematical model of paper cylinder drying. Working on measurements data, it is possible to compute the heat and mass transfer coefficient values to get the complete identification of the considered drying section. Then, it is possible to test by simulation, the effect of new investments (increasing the number of cylinders, moving the size-press location, etc) or of operating point changes (increase of steam-pressure or moisture content at the entrance ... etc) on the machine production and on the steam consumption. This method has been used for an industrial printing paper machine. Computer simulations have allowed to get the optimal size-press location in the drying section and the machine speed variations obtained after the increase of the number of cylinders and this for three different basis weights.
INTRODUCTION Paper drying is a very important phase of the papermaking process. It has a strong influence on the f~nal paper quality but also on the economics of the whole process. As a matter of fact, paper drying is the last part of the water removal phase in which most of its mechanical properties are confered to the paper sheet. Besides both the energy consumption and investment costs required by this process are high. However the design of the drying sections has so far largely been based on empirical rules and the optimum performances as well as the corresponding working conditions are not very well known. Improving the drying sections running conditions is also of very great interest and this subject has been much studied, but very few works have been done to find and to developpe some methods for systematic analysis of paper machine drying sections during their run. The recent process analysis techniques, namely modelling, identification and simulation offer new prospects for such studies, but they have not yet been widely used. The present contribution endeavours to act in this direction. A multicylinder paper machine drying section is made of stea~ heated cylinders on which the sheet is successively applied by clothi ng s ( Fig. 1).
261
rII
_t
h 00 d
~e~~~a~o~~=:t clothing
I
poc k e t
l I I
I I
I
I
\~t!:;i~~r:;J~-sheet
Fig. 1
dryers
hot air blowing roll
A multicylinder drying section
The sheet moisture content at the entrance of the drying section is generally 60 to 70 per cent (water weight/total weight). At the end, the moisture content must be about 5 to 10 per cent. The whole drying section is set in a hood so that the atmosphere in which the evaporation takes place can be controlled by action on the insufflated and extracted air flows. The section is supplied with steam at a pressure of 3 to 10 bars. Since the temperature set-points of the cylinders rise from the beginning to the end of the section,
A. Lemaitre et al.
262
the condensate of every dryer is flashed and the steam, thus produced, is used by the former dryers. When the paper is treated on a size-press, the drying section is divided in two parts : the fore-dryers and the afterdryers, after the size-press. Numerous studies have been carried out concerning the drying section and the theoritical knowledge about the mecanisms that occur is quite large. Many authors have analysed the heat and mass transfer conditions to which the sheet is submitted during its trip in the drying section (1) (2). Very detailed descriptions of the migration of water and vapour inside the sheet have also been proposed (3), (4), (5). However very few authors used these theoritical results to analyse the whole process behaviour (6). Many simplifications must be introduced to obtain what we want, namely, a workable model and to achieve the complete computer simulations from which the relative influence of each design or running parameters can be seen. The elaboration of such a mathematical model (7), (8) is presented here. It is also the basis of a parameter estimation method which has been developped to evaluate the heat and mass transfer coefficients in industrial equipements. An experimental work has been carried out on the pilot paper machine of the CENTRE TECHNIQUE DU PAPIER to test this method. This model has of course been used for simulations, especially to compute the effect of new investments or of operating point changes on the machine production. This paper describes an industrial example on a printing paper machine.
- temperature and moisture content are supposed to be uniform through the web. Only variations in the machine direction (x) are considered - all the internal phenomena (vapour diffusion, capillary transport ... ) are considered only with global relationships - the drying section is in a steady state. At the abscissa x in the machine direction, we consider a sheet element of length dx, width 1 and moving at the speed U (Fig. 3).
x
x
+ dx
u
Fig. 3
Sheet element on the cylinder
1.1. Thermal balance for the sheet element The sheet receives heat from the steam (of course only in the case of web on the cylinder) :
1 • MATHEMATICAL MODEL OF A DRYING SECTION
The main simplifing hypotheses used to construct such a model are as follows : - two typical positions of the paper web are distinguished : web on the cylinder and web in the draw as can be seen from Fig. 2
It exchanges heat with the clothing (web on the cylinder) or with the ambient air (web in the draw)
It also loses some heat because of evaporation of water. Calling B the evaporation rate, and r the latent heat of vaporization, the loss is :
B.r(8 f )·1.dx Then the thermal balance gives
o
(A)
For the two typical positions of the web, we have
+ Dryer i-I
Fig. 2 : The two positions of the paper web
- web on the cylinder : a = afh
heat transfer coefficient between the sheet and the clothing
8 = 8h
temperature of the clothing
- web in the draw :
Method for Systematic Analysis The heat exchange with the ambient air takes place on the two sides of the sheet : heat transfer coefficient between the sheet and the air
a= 2.Cl a f
temperature of the air of course, we have :
Ct
vf
263
of the phenomena which occur in the considered sheet element, we must known the variations of the vapour pressure at the sheet surface. During drying this vapour pressure is not only depending on the temperature 8 f and the moisture content Xf of the sheet, but also on the drying rate. So the paper behaviour during drying is shown on the Fig. 4.
= 0
1.2. Water balance for the sheet element Evaporation rate
B
The water inside the paper is removed by surface evaporation due to the difference of partial pressure of water between the sheet surface and the ambient medium. In the air the evaporation rate B is given by the STEPHAN diffusion law:
_6_ . P. Log
B = -
R.T f
Internal evaporati phase
Surface evaporation phase
(l.:...l:.) P -Pf
vapour pressure in the ambient medium vapour pressure at the sheet surface critical Xcf moisture content
total surrounding pressure
6
mass transfer coefficient between the sheet and the ambient medium
Fig. 4.: Evaporation rate variations during drying
Then the water balance for the sheet element gives : dX+
6
P
P
G.U. --*- = - - - .P.Log (----) dx R. Tf P - Pf
(B)
For the two typical positions of the web, we have
It shows the theoritical variations of the evaporation rate during the drying of an hygroscopic material such as the paper sheet, when this material is dried at constant temperature, with a constant vapour pressure in the surrounding air. Two major phases appear :
6= 2.6 af
p= Pa
6a f : mass transfer coefficient
between the sheet and the air (evaporation from the two sides of the web)
: vapour pressure in the pocket air
We assume that the STEPHAN law is always valid to describe the mass transfer between the web and the clothing. The evaporation still occurs in the ambient air but with a mass transfer coefficient which depends on nature and conditionning of the clothing and which is therefore representative of its efficiency.
6 = Bfh
Xf moisture content
~_~~Ei~~~_~~~E~E~E~~~_E~~~~ When the moisture content of the web is high, the vapour pressure Pf at the surface is equal to the saturated vapour pressure ps(8 f ), at the same temperature. The evaporation takes place like on a free water surface. Then Pf is constant (and also B) even when the moisture content Xf decreases: Pf = Ps(8 f )
When the moisture content Xf becomes lower than the critical moisture content Xcf ' Pf decreases and also B. The sheet surface can no longer be considered as a surface of free water and the vapour comes also from inside the sheet (internal evaporation).
The critical moisture content, corresponding to the transition between the two drying phases, depends on the moisture content gravapour pressure in the air over p = Pa dient inside the sheet, which depends on the clothing the value of the evaporation rate (instantaneous and past). Then the critical moisture 1.3. Paper behaviour during drying content is higher when the evaporation rate is higher. So the paper behaviour during To obtain a complete mathematical representation drying can be represented by a dyn~~c sorption mass transfer coefficient between the sheet and the clothing
A. Lemaitre et aZ.
264
isotherm (8) described by the relationship as follows :
(C)
k f and Xcf not only depend on the evaporation rate but also on the paper characteristics. 1.4. Complete sheet drying model
For the sheet element that we have considered the complete model is constitued by equations' (A) and (B) with the transfer coefficients corresponding to the two web positions (on the cylinder and in the draw). The behaviour of the paper during drying is taken into account by relation (C). The integration of those differential equations on the cylinder and then in the draw is successively done for all the dryers, from the beginning to the end of the drying section. It must, of course take into account the particular value of the parameters for each dryer (as steam temperature, vapour pressure and temperature of the pocket air). This integration, quite easy to perform by means of a digital computer, leads to the complete drying model.
2. PARAMETERS ESTIMATION In this model, the numerical values of many of the parameters are unknown. The estimation of these parameters and of their variations in the drying section is necessary to use the model.
low if we compare it with the heat cam~ng from the steam. Computer simulations show that the value of this coefficient can vary over a wide range and has still a negligible effect on the drying process -Then, the transfer being convective In the draw, it is possib le, in this case, to assume that COLBURN analogy is valid between the heat transfer ~o~fficient aaf and the mass transfer coefflclent Baf. So, we have:
Taking into account these two simplifing hypothesis, only three coefficients have to be estimated : Civf' Bfh and Baf·
2.1. Parameters estimation method From comparison between experimental data and simulations results, it is possible to estimate, cylinder by cylinder, these three coefficients. For that, we need at least three different measures (two temperatures 8 1 and 8 2 , and one moisture content ~) because the evolution of paper drying is given by the temperature and the moisture content of the sheet on each cylinder and draw. Fig. 5 shows the identification algorithm which is quite classical 8f
8 .l
f
i+l
Dryer i of the pilot machine
Xf i
X
i+
In the first phase (cylinder), we need three different parameters Ctvf
heat transfer coefficient between the steam and the sheet
Ci
fh
heat transfer coefficient between the sheet and the clothing
Bfh
mass transfer coefficient between the sheet and the clothing
In the draw, two parameters are required uaf
heat transfer coefficient between the sheet and the air
Baf
mass transfer coefficient between the sheet and the air
Taking into account the possibilities of measurements in a drying section, it is necessary to make different hypothesis in order to simplify the identification : - First, it is possible to ignore the heat transfer coefficient ufh ; indeed the temperatures of the clothlng and of the sheet are almost equal and the heat transfer is
XM (computed)
-.,
18£
i+l
IXf i+l
I
IL-
..JI
Simulated dryer i Fig. 5
Identification algorithm
Method for Systematic Analysis
The criterion J has a quadratic form J
3 L
2
k=l
E k
calling Yk, the measure k, we have : Yk calculated - Yk measured Yk measured The minimisation of the criterion J is carried out by means of a non linear programming method. Many methods have been tested, because some difficulties appeared concerning the algorithm convergence. The equations of the system are coupled and non linear, and it is not possible to get an analytic fOnD of the criterion gradient. We have chosen the M.J.D. POWELL method (8) which allows to resolve this difficulty. This method gives good results and is also very fast. 2.2. Experimental method The experimental work has been carried out on the pilot paper machine of the "CENTRE TECHNIQUE DU PAPIER" Grenoble, France. Measuring the sheet temperature during drying is not an easy task, owing to space restrictions in the pockets. A contact thermometer (SWEMA) is used and two differents measures are taken on each draw. The positions of the two measuring points are not exactly at the beginning and at the end of the draw, but respectively at about one-fifth and fourfifth of its length. The sheet moisture content is determined by means of paper samples taken on each draw at the end of the run. The samples are roughly as long as the draw and therefore, the obtained moisture content is equal to the average value ID the draw. To remove this problem, we developped, in collaboration with the "Institut d'Optique de Paris", an "infrared" moisture meter. This apparatus allows to measure the moisture content in the required place in the draw. The head, which is very small, is mounted on a pipe and is in contact with the sheet during the measurement. This moisture meter must be calibrated by means of samples taken in some draws along the dryer section. Some other measures like the steam pressure are needed ; besides the wet and dry bulb temperature of the air inside each dryer pocket are obtained from a psychrometer mounted on the end of a traversing probe. 3. INDUSTRIAL APPLICATIONS OF THE MODEL The mathematical model and the parameter estimation method have been used to evaluate the heat and mass transfer coefficients on the dryer section of the pilot paper machine of CIP. The variations of these coefficients along the drying section have been studied and also the influence of different running
265
parameters like steam pressure or clothing tension. This parwmeter identification have been also carried out on different industrial paper machines in order to study the influence of the machine speed and to verify some results obtained on the pilot plant (8). Besides computer simulations have been done to find the optimal operating conditions minimizing the energy consumption particularly by adjustment of the ventilation parameters (9). The effect of new clothings has been studied as well as the influence of some design and running parameters on the drying section efficiency (10). But one of the most important use of this model is the developpement of a method for systematic analysis of industrial drying section during their run. This paper describes now a particular example of this method.
3.1. Aim of the work The aim of the work is to compute by means of simulations, the effect of new investments or operating point changes, on the machine production. When a papermaker wants to change his machine production, he has, for instance, to increase the number of cylinders but generally these changes are based on empirical rules. Some mistakes are possible and he does not know exactly the future results of his new investments. Improving the knowledge of his drying section and of its possibi 1 i ties is then of great interest for the papermaker. The main applications are as follows : - to compute the correct number of cylinders for a given increase of production, or the new machine speed corresponding to a higher number of cylinders - to test the effect of the setting up of a new size-press, to optimize his location and to see the influence of this location on the machine drying limitations for different productions - to compute the speed increase for different steam pressures in the cylinders - to check the influence of the removal of a Yankee dryer or of a too large draw length - to compute the machine production variations after the setting up of a hood with a new ventilation system - to give, of course, the influence of changes in running parameters such as the sheet moisture content at the entrance of the dryer section. The approach of such a study, consists then, in identifying the drying section in its present working conditions, to get the values of the heat and mass transfer coefficient, in order to make the desired simulations.
3.2. Paper machine characteristics
A. Lemaitre et al.
266
The chosen example concerns a printing paper machine. This machine is 3,4 m wide. The dryer section consists of 22 fore-dryers and 12 additional dryers after a size-press. The diameter of the cylinders is 1,5 m. The first part of the machine (before the size-press) is divided in three section of 3,7 and 12 cylinders. The steam supply system is a "cascade" type system. The upper and lower after-dryers are separatly supplied. Besides, the dryers are clothed with classical synthetic fabrics, except the first six cylinders which are clothed with a single-felt system. It is then impossible to measure the sheet temperature on these dryers. The pockets are ventilated by hot-air blowing boxes and the air is extracted by a closed hood. The parameter estimation has been carried out for three different basis weights (40, 64 and 80 g/m2). The main operating conditions appear in table 1. In addition to these steam pressure we have measured the sheet temperature in two different places in each draw, the temperature and the moisture content of the air in each pocket, and the sheet moisture content by means of samples. These measurements have been carried out, on the plant, by the 'Technical Assistance Service" of the C.T.P.
Heat transfer coefficient avf(kcal!h.m2.oC)
o~
800
a-d~
600
400
(g/m2)
~ 06_
200
0-
80g/m2
64g/m2 40g/m2
0
:
I
»\\h,Oii \
\
~
0-0- 1
I
AFTER-
I
FORE-DkYING DRYING . .S.;", ; ;E.....Co.;;;;T__I...N~_......L.-.I..&..-......L.I--.::.S=E.::s.T.:.,;I=.:O:.:.N.:...-..L-.-.....LII~
o 5
27 32 3 cylinder number Fig. 6 : Variations of the heat transfer coefficientbe~een the steam and the sheet during drying
10
15
20 22 23
Mass transfer coefficient Sfh(m/h) 300
-6_
80 g/m2 64 g/m2
-0-
40 g/m2
-0-
I I
Cf'0'A /6 ~ \, \ / /'i\
200
Basis weight
:\
.-
3.3. Identifications results The Fig. 6 shows the variations of the heat transfer coefficient a vf between the steam and the sheet during the drying, for the three different basis weights. We observe that this coefficient decreases regularly from the beginning to the end of the drying, as noticed on most of the identified drying sections up to now. The average value is about 500 kcal/h.m2.oC, during the constant evaporation rate period. The Fig. 6 shows also that there is no important difference between the three basis weights concerning the value of this coefficient, because the estimation accuracy is not high enough, to observe such variations. Besides, the average value of this coefficient is quite the same in the fore-drying section and after the size-press.
a
I
I
I
I
I
I
0.... l--~r--\~ /9 o
~ ~c~
o~ ~
o
l
I
5
)0 Fig. 7
)5
I
a-Q
~.~.I e<,~~o
O\~ ,~\;\ \/ /'-\
ORE- DRYING SEcn
I I
::
~a,j\\:"~\ " 0'O~o\h~g> / \
100
I I I I
20
0-
I
./\ [ 6 )yp IAFTER\f :DRYING ECTI N I
'0
6
\ _Q
22 23
27 32 4 cylinder number Variations of the mass transfer coefficient on the cylinder during drying
The Fig. 7 shows the variations of the mass transfer coefficient on the cylinder, for the three considered basis weights.
Steam Machine Machine Dryness Dryness Dryness Dryness Steam Steam Steam Steam after end of pressure pressure pressure pressure pressure Produc- entrance before speed tion of the sizesizethe wet em interm. main lower upper drying press press drying section sectior section cylind. cylind. section A) B2 section C2 A2 A3 (m/mn) (T/j) ( %) (bar) (bar) (bar) (bar) ( %) (%) (bar) (%)
40
601
118
42
96,2
63
94,5
0,2
0,79
1,09
1
0,32
64
498
155
44
96,2
66,7
92,8
1,36
1,87
2,15
1,16
0,52
80
420
165
45
95,6
68,5
94,2
1,36
) ,86
2,13
0,92
Q,40
Table (1)
Operating conditions for the th£ee basis weights
267
Hethod for Systematic Analysis Just as previously, we find again the same results as for the other identified drying sections up to now, namely the regular decrease of this coefficient during the drying. On the other hand, we can observe a difference between the fore-dryers and the afterdryers. The average value of Bfh is higher in the section after the size-press than in the fore-drying section, for the same sheet moisture content. This agre~'with some workers who say that the water removal after the sizepress could be easier than the classical drying, owing to the water pick-up phenomenon However , when we look at the drying curve (Fig. 9), we can see that the evaporation rate is lower after the size-press than in the fore-drying section, for the same sheet moisture content : indeed, this is due to the fact that the steam pressures are lower in the after-dryers (table 1). So the mass transfer coefficient Bfh , which eliminates the influence of the operating conditions gives a good idea of the real drying efficiency (which is better after the size-press than in the foredrying section). The accuracy of these results depends greatly on the measurements accuracy. Assuming the relative error in sheet temperature and moisture content to be 1 %, computer simulations show variations in the three transfer coefficients avf' Bfh and Baf of respectively 15 %, 15 % and 20 %. This unaccuracy is mainly responsible for the serrated shape of the curves (Fig. 6 and 7).
Sheet moisture content (water weight/ fiber weight) 1,2
~
\
\
\
0,9
\
64 g/m2
\
0
\ \
\
0,6
\
\\ \
0,3
~
\
\
\
S.P.
\
5
\
~'o-O
15 20 22
10
b
0
\
0
"'0
23
0
~
32 34
27
cylinder number Fig. 8
Sheet moisture content variations during drying (simulation after identification)
Evaporation rate (kg water/h.m2) 3.4. Simulations results
50
Reference runs : First, computer simulations have been carried out for the three reference runs, keeping constant the heat and mass transfer coefficients as well as all the operating conditions. Fig. 8 shows the evolution of the sheet moisture content along the fore-drying section and after the size-press, for the reference run corresponding to the basis weight of 64 g/m2. For the same reference run, the curves plotted in Fig. 9 show the variations of the evaporation rate in the two parts of the drying section. New runs --------
64 g/m2 40
30
20
/
10
For the three different basis-weights, we want to stUdy the effect of the following changes on the machine production : - increase of the steam pressure from 2 to 3,5 bars
S.P.
After-drying section at t e same moistur content
ORE-DRYING
o
5
10
AFTER-DR ECTION 15
20 22
23 27
NG
32 34
cylinder number
- setting up 10 ne~ dryers in the fore-drying sec t ion (" cas cad e " s y stem, with now 4 sections of 10, 8, 8 and 6 cylinders) - setting up 4 new dryers after the size-press. (Fig. 12).
Fig. 9
Evaporation rate variations during drying (simulation after identification)
A. Lemaitre et al.
268 The main simulations hypothesis are as follows :
- the heat and mass transfer coefficients are assumed to be independent of the steam pressure and of the machine speed - the operating conditions at the entrance of the two sections are kept constant. Besides, the sheet dryness at the end of each sections must be respectively 98,5 % and 94 % - the ventilation conditions are the same as in the reference runs - the differential pressures between the three sections ("cascade" system) of the first part before the size-press take the average values of respectively 0,3, 0,28 and 0,26 bars (for 40, 64 and 80 g/m2) - an average difference of 0,5 bars, between the upper and lower cylinders after the size-press is chosen
When the steam pressure takes the value of 3,5 bars, the machine production increases reach + 59 % (40 g/m2), + 19 % (64 g/m2) and + 21 % (80 g/m2), compared with the reference runs. The variations of the maximum machine speed with the ~eam pressure in the main section (for the fore-dryers) or in the lower cylinders (after the size-press), are plotted in the Fig. 10, where we can see that the foredrying section still limits the production in every case.
The setting up of 10 new cylinders in the fore-drying section lead to an increase of the maximum speed as can be seen from Fig. 11, compared with the reference runs. However the drying balance of the machine has changed and the after-dryers limit now the production.
besides, the starch pick-up and the moisture pick-up in the size-press is assumed to be independent of the machine speed.
Speed (m/min)
-0- 80g/m2 _6_
I
I I
I
/
1
/
:
•
700
64 g/m2
-0-
600
Fig.l0
40
1°
/
0/
°
-I /
I
I
I
1 ;
:1
,I
Il "
I
! I
400
g/~'r/
0_0_
234 main section (bar~) Speed variations for different steam pressures 1n the main section
/
VII
"0
//0
/0
1
I
I
//0'/0
/// 0
/
v{
"
//0
6
~
0/
sect10n (12 cyl.) /"/
6-
/
/6
/
1//
II
// /
/
" //
//~~///
/6
I 11
____ after-drying
-
/
:./
fore-drying sec tion """ (22 cyl.) /// /
80 g/m2
/ / /
I
I !
after-drying (16 cyl)
/~(ection
//
~
Speed (m/ min) 100
-0-
/PI ----
/'/ I
- - fore-drying section (32 cyl)
0
0
I I
800
/
I
I /
90
/
/'
64g/m2 -0-40g/m4' / I
At the present time, the maximum steam pressure is about 2,1 bars and the machine production is limited by the fore-drying section only for the basis weights 64 and 80 g/m2. Simulations show that for 40 g/m2, an increase of the steam pressure from 1,09 (reference run) to 2,1 barsleads to a machine speed of 740 m/min or a production variation of + 24 %. The Fig. 10 shows that this production is still limited by the fore-drying section.
/
2
3
4
Steam pressure in the main section (bars) Fig. 11
Speed variations for different steam pressures in the main section, after the addition of 10 cylinders in the fore-drying section and 4 cylinders after the size-press
When we add 4 new cylinders after the sizepress, the production is limited again by the fore-drying section and the corresponding increases are respectively 41 % (40 g/m2) , 47 % (64 g/rn2) and 47 % (80 g/m2).
Method for Systematic Analysis The Fig. 11 gives also the speed increases obtained with different values of the steam pressure, for this new machine. Then, the curves plotted in the Fig. 10 and 11 allow to compute, for instance, the optimal location of the size-press, for each basis weight and also with different steam pressures. These results have been used by the papermaker and these changes will be soon carried out on this drying section. It will be be then possible to compare these forecasts with the real results on the process.
CONCLUSION A mathematical model of a complete multicylinder drying section has been developped from a theoritical analysis of this process. Some simplifications in the description of the phenomena are introduced, which lead to an overall model, easily workable. But the main elements of the phenomena are preserved so that this model may be useful and particularly so that it can show the relative effect of the running parameters. This model is the basis of a parameter estimation method to evaluate the heat and mass transfer coefficients of industrial processes. This method and particularly the experimental part have been tested on the pilot plant of the CTP and also on different industrial paper machines. Many developpements of this model have been carried out up to now, but one of the most important is the application of the parameter estimation method to analyse industrial drying sections during their run. This method has been used on a printing paper machine to compute the influence of steam pressure increase and of the addition of new cylinders, on the machine speed. So, the machine production variations due to these design or running changes has been obtained and the optimal size-press location has been deduced from them. Improving the knowledge of his drying section and providing him with the real possibilities of his machine is of great interest for the paperrnaker. Especially, he can see very easily and very quickly the effect of new investments before their carrying out. Then, this model takes the place of the old empirical rules, used up to now, and it can become a very interesting and useful tool for the paper machine users.
269
REFERENCES (1) A.H. NISSA~ et W.G. KAYE "An analytical approach to the problem of drying of thin fibrous sheets on multicylinder machines". TAPPI, vol. 38, nO 7 (Juillet 1955) (2) 0.1. LEHTIKOSKI "A mathematical model of the dryer section" Paperi Ja Puu, vol. 52, nO 2 (1970) (3) S.T. RAN "Heat and mass transfer in hot-surface drying of fibre mats" Pulp and Paper Magazine of Canada, vol. 65 nO 12 (1964) ( 4) W. D. BA I NE S
"Analysis of transients effects in drying of paper" Pulp and Paper Magazine of Canada, vol.74 nO 2 (1973) (5) F.T. HARTLEY et R.J. RICHARDS "Hot surface drying of paper. The development of a diffusion model" TAPPI, vol. 57, nO 3 (Mars 1974) (6) R.L. KNIGHT et L.A. KI~K "Simulation of the papermachine drying section" International Water Removal Symposium British Paper and Board Industrie Federation - London (Mars 1975) (7) A. LEMAITRE, M. PERRON, R. CHARUEL '~odelisation et simulation du sechage du papier sur cylindres pour la concep tion de secheries a hautes performances" XVlle EUCEPA Konferenz, Vienne, Autriche, (Octobre 1977) (8) A. LEMAITRE '~odalisation
et identification d'une secherie multicylindrique de machine a papier : optimisation de sa conception et de son fonctionnement" These de Docteur-Ingenieur, Grenoble, France (Septernbre 1978) (9) B. DUFOUR, M. PERRON "Bilan energetique des secheries multicylindriques" 30e Congres A.T.I.P., ArIes (Octobre 1977) (10)A. LEMAITRE, M. PERRON, A. Rfu~Z "Sechage du papier : influence de 1 'habillage et de la ventilation" Symposium O.F.E., Paris (Septembre 1977).
A. Lemaitre et al.
270
NOTATIONS A
coefficient of COLBURN analogy
B
evaporation rate (kg water/h.m2)
ce
specific heat of water (kcal/kg.oC)
cf
specific heat of dry paper (kcal/kg.oC)
G
basis weight (kg/m2)
J
criterion
1
width of the sheet (m)
p
total surrounding pressure
Pa
vapour partial pressure in the ambient air
Pf
vapour partial pressure at the sheet surface
Ps
saturated vapour pressure
r
latent heat of vaporizaticn (kcal/kg)
R
perfect gas constant
u
machine speed (m/min)
S"team
S.P.
~
x
AFTER-DRYING SECTION FORE-DRYING SECTION (22 cylinders) (12 cylinders) (separated supply) ("cascade" system) Steam
AFTER-DRYING SECTION (16 cylinders)
Fig. 12
Xcf
critical moisture content
aaf
heat transfer coefficient between the sheet and the air (kcal/h.m2.oC) heat transfer coefficient between the sheet and the clothing heat transfer coefficient between the steam and the sheet mass transfer coefficient between the air and the sheet (m/h) mass transfer coefficient on the cylinder
8
temperature of the ambient air (OC)
a
temperature of the sheet (absolute temperature : Tf ) 8
temperature of the steam
v
8], 8 , XM : the three measures on the sheet. 2
(32 cylinders)
abcissa in the machine direction sheet moisture content (water weight/ fiber weigh t)
Ctvf
FORE-DRYING SECTION
The drying section before and after the change of the number of cylinders