Modelling and simulation of the thernomechanical pulping process

Copyright

© IFAC PRP 4 Automation, Ghent, Belgium 1980

MODELLING AND SIMULATION OF THE THERMOMECHANICAL PULPING PROCESS I. Aarni* and

J. Virkkunen

Helsinki University of Technology, Control EngineenOng Laboratory, SF-02150 Espoo 15, Finland *Present address: Helsinki Telephone Company, PL 238, Helsinki 10, Finland

Abstract. The Thermomechanical Pulping Process consists of a preheater, which heats the wood chips, and a pressurized doublecisc refiner, which produces the pulp. This paper develops a dynamical model of the process. The models of the refiner and the preheater are mixed distributed and lumped parameter models. A modified Lax-Wendroff type method was used to solve the equations of the fourth-order hyperbolic partial differentia~ equation system describing the refiner. The simulated results were comDared with experimental results measured on an industrial-scale refiner. The results were used to optimize the static operating point of the refiner and to study the effects of the control variables on operation. The effects of several disturbances were also simulated. The shape of the optimal plate gap is also a feature included in the st~dy. Keywords. Pulping industry; thermomechanical pulping; system analysis; simulation; partial differential equations. INTRODUCTION The thermomechanical pulping process has been in industrial use for only 2 short time. The process is capable of producing high-grade pulp at the expense of high energy demand. Several industrial units are still beeing developed and only some of the information about the physical details is exact. More detailed information is especially needed to design efficient computer control systems to improve the quality of the pulp and the economics at the same time, as the present study suggests. This work was started early in 1976 as a joint project by Enso-Gutzeit, Finland, and the Control Engineering Laboratory of the University of Technology. The co~pany was res~onsible for the Drocess studies and the knowledge and the group at t~e University concentrated o~ ~odelling and simulation. This latter aSDe~t is briefly reviewed in this reDort. lhis work has previously been-reported in Finnish only (Aar~~ 1977 a, Aarni and Kuikka 1978) with the exce~tion of a report by Aarni (1977 b). ~ The modelling and simulation project concentrated on studyin~ the two main 219

units in the thermomechanical pulping plant, the preheater and the refiner. The model of the preheater is only briefly reported in this paper and the main item is the refiner, which is a much more difficult and inadequately known process unit. The dynamical models are based on the laws of physics, on mass, energy and impulse balances. The resulting equations are inevitably rather complex partial and ordinary differential equations. The integration of the equations also necessitated some research in the numerical integration of first order hyberbolic partial differential equations (Aarni 1977 b). The simulated results were compared with eXDerimental results and operational experience of the refiner at the Summa Mllls, Finland. Major difficulties do, however, arise in collecting exact and rich information from an industrial plant of this kind. A lot of imDortant information was thus taken from eXDerimental results reDorted in the literature and some pa;ameters were only estiwated on the basis of co~mon sense and scientific training. ODerational experience has shown that the results fo~nd in the study are reliable and the models

I. Aarni and J. Virkkunen

220

the chips (by conduction and as the latent heat of the condensing steam), i is the enthalpy of the water and the w symbols i ' i are short-hand wT dT notations

represent the physical reality adequately. PHYSICAL MODELS The preheater The preheater is a horizontal vessel of cylindrical cross-section. The chips are transported through the vessel in two minutes by a screw. The chips are heated by saturated steam, which is fed under the layer of chips in the input end of the preheater. The heated chips are fed into the refiner. The material flow in the preheater is formed by two phases, the wet chips and the steam. The flow of chips is modelled as a flow of dry wood (mass flow rate m ) and a flow of water (flow d rate m ) moving on with the same veloci¥y v . Standard mass balancing techniquesrgive the e~uation ~ ( md ) + amd = 0 (1) ~t v dX r

where id is the enthalpy of dry wood. The steam volume V is filled by saturated steam, the DroDerties of which depend only on temperature. The steam volume is taken as a homogeneous phase without any dependence on the xcoordinate. The mass balance is simply - _, f

md dv -r v dt ·

(2)

r

.

w~ ex

(6)

where m is the steam flow to the hy volume V and the integral gives the amount of steam condensing per unit time. The density of steam is Ph. From this we get

representing the differential balance of the chips. The physical meaning of the term md/v r is mass of chips/unit length. The velocity v is a function of time but not of the ~oordinate x, so that Eq. (1) can be transformed into the final form

l

(7)

The three partial differential equations (2), (4) and (5) and the ordinary differential equation (7) are the state equations of the preheater.

The material balance of the water is The Refiner ( 3)

where wl is the mass of water consending from the steam phase per unit length and time. As before the final form is found to be

am w at

+ v

a;;: --.-!!. 2a x

( 4)

Two more Dartial differential eouations can be fo~nd by considering ene;gy balances of the chiDs and of the steam phase. Straightforward but lengthy calculation gives the heat balance of the chips: - - ~\/".]

u - - ( -=- - -=- ....;. ) /:.~ ~ .-

-----v

: .. ~:-:'.• ,+~.---:"""'~-= ''w,....

....;,.

"-/\/

...........

--

(5)

r

_.....

T .is the temperature of the chips,r

3

is the thermal resistance Der unit length from the preheater to the external environment (temperature T ), u

q is the heat flow from the steam to

The design of the refiner is represented in Fig. 1. Typical operational parameters for the refiner studied are given in Table I. The discs rotate at the same sDeed in oPDosite directions. The chins are fed i~to the center of the reflner. The rotating center throws the chips into the gap between the discs and the chiDs then move as pulp into the refiner- chamber at a great velocity. Water is added to the center. This water and that absorbed by the chips is partly evaporated in the gaD. Some of the stea8 flows back into~the center anc is removed. In the gap the steam is approximately saturated (AtacK, Stationwala). The therrrodynamic state of the steam deter~ines the physical conditions in the gap. The center, the gap and the chamber were cescribed by separate models. The model of the gaD is a distributed narameter model, the other two concentrated Darameter models. There is also a distributed model describing

Hodelling and Simulation The mass balance of the steam

the pulping energy of the wood and a lumped model describing the axial motion of the other disc, which is used to control the gap width.

4nrm

('

V

plate

~ at

Scheme of the refiner.

1.

+

~ or

+

where TABLE I Main characteristic of the refiner pressure at the inlet 260 pressure at the outlet 240 water flow at the inlet 1.840 wood flow at the inlet 0.6944 consistency at the inlet 27.4 % 0.5 440 660

peripheral gap inlet radius outlet radius plate taper 440
kPa kPa kg/s kg/s mm mm mm

0.0450 0.0000 157 . 1 3000

rad/s kw

It is supposed that there are no dry wood losses. The gap is taken as a flow channel with variable cross sectio where the wood flows in Dlug-flow manner, flow rate m . The same is d applicable to the flow m with the w

additional feature that the amount m s is evaporated Der unit disc area and unit time. The material balances give

am

d

alTI

d

(8)

-!..;.nrm v

(10 )

s

( 9)

S

where v is the common linear velocity of the chips and water and r is the radial distance from the center-line.

P

P-p P

D

au

3r

+

1. (2 p

p

r

+

2 ~s) s or

+

2 £ ~a ~ p

p

_

Tn s

at - p s '

p

is an abbreviation for dp/dp.

The impulse balance gives one more equation for the variables D and U. The forces included in the balance are: the centrifugal force, frictional force between the steam and the discs frictional force between the st~am and the pulp-water mixture in the gap, net-force of the pressure gradient. The tangential velocity is supposed to have a linear velocity distribution between the Dlates. The frictional force betwee~ the steam and the pulp is proportional to the mass of water and pulD in the gap and to the squared relative velocity. Lengthy calculations yield (Aarni 1977 a):

au

at +

at+var--=O,

lS

where m is the steam flow and U the h velocity of the steam. The steam flow is m = 4ns'pU, where s' is half the h gap width and p is the density of saturated steam, p=p(p). The ga~ wid t his wr i t ten 2· s' (r, t) = 2[ s (r) + a (t)] where a (t) is the extraDolated gap width at the center. The density p of the saturated steam is a function of pressure only. Changing the dependent variable from p to p, making substitutions and some arrangements, yields the dynamic equations for the steam flow: ( 11 )

feediTiP~

of

Fig

221

+ U~ p

~ at

_u da _ kfU s dt 2s

- k

+ 2U 3U +J (p Ul +J )dp ar p p d1'"'

u2 +~12Y'2 ') ,. v'u2+(1-K)~D/rL

= _(2~ cJ~;)U2 r s elr'

+ .}. kL;»-r

'1

(m +m ) 'I signCU-v) ~CU-v)-

3

~-

1

(12)

v VV 47H'S where k is the friction coefficient between the steam and the disc, k is the slip coefficient of the tangential motion and k is the friction v

coefficient between the steam and the pulp. W lS the angular velocity of the discs. The other symbols were defined above. The energy balance in the refiner gaD is needed to calculate the quantity m s the amount of water evaDorated Der unit area and unit time. Le~~th calculations yield

I. Aarni and J. Virkkunen

222

14( i 1Tr

m

wp w

+

i, m.) (2 ~?.r +?1.:) 1 ap d

V

dt

C1

~1t.

3)

where e is the effect transported from the discs per unit area, the second term of the sum is the energy of the steam and the third term the energy of the pulp-water mixture. The enthalpy is i for water, id for dry wood, i h w for steam, i , i d ' and i h are wp p p derivates with respect to pressure p. The expression (12) is substituted in Equations (9) and (11). Together with Equations (8) and (12) we thus obtain four partial differential equations describing the physics of the materials inside the refiner. The other disc is movable and can be used to control the process. The equation of motion is simply 2

Md a + Bda = F -F dt2 dt 1 s where F

Operational parameters. The most important operational parameter is the pressure in the chamber of the refiner, by which the temperature is also fixed. In the refiner studied here the speed of rotation is constant. The gap between the discs and the power generation at the surfaces of the discs cannot be measured during operation. These important parameters were estimated on the basis of measured mass flows.

( 14 )

is the force generated by the

s hydraulic cylinder and F

of the refiner and especially the form of the gap can be found from the cons~ruction data. The frictional coefficient between the steam flow and the surface of the disc (k ), f likewise the slip coefficient k, are dependent on the construction of the disc surface (the grooves). Sensitivity analysis sho~ed that the model is insensitive to the exact values and approximate values found from the literature were used (kf=O.OOS ... 0.01). A change in the slip coefficient from k=O to k=1 changes the steam generation by e.g. 3 %.

1

is the

opposing force generated by the pressure distribution inside the refiner:

F__ I

M is the mass of the disc, B a frictional coefficient, P1 the pressure in the center, P2 the pressure in the chamber, r

and r the rajii of the 1 2 pulping zone in the refiner.

Finding relevant model parameters was one of the most difficult aspects of this modelling. The main data sources were industrial experiments and (Atack, and Stationwala 1975). The validity of the total model was checked against different experimental runs and common operational experience. The simulated values do not always reproduce exactly the measured values for the refiner in question. However, the qualitative agreement is very good and the quantitative agreement reasonable, so that the authors rely on the conclusions to be drawn from the simulations. THE INTEGRATION METHOD

Parameters and validity of the model The model contains a number of parameters that can be divided several groups. Tabulated physical parameters. The density and enthalpY~f St92~.'1 '....ater=:: wood and relation of pressure and temperature for saturated steam were transformed into approximate equations.

The partial differential e~uations derived above are hyperbolic in the t-direction and can be brought to the so-called normal form dX

dX

at+ACr,t,x)ar+B(r,t,x)=O

(16)

-4

The coefficient of friction k gives the dependence between the re¥istance force and the flow of steam through the pulp. The parameter was estimated from steam flow measurements. Mathematical sensitivity analysis showed that the model is sensitive to the exact value of the parameter k v and a feasible ~

value was hard to find. Construction parameters.

The dimensiors

where x is a vector representing the state of the system, and A and Bare square matrices, the elements of which depend on the sLate, tiDe and radius. The numerical sol11tion of Lhe hyperbolic parLial differential e~~~tion systems can be obtained by the f~:lowing twostep Lax-":Jencroff t:ype !T.e' :hoG presented by Aarni (1977 a). First subscript i refers to the radius and tte second j to the ti~e. Tne first step gives the mid-points used by the second step

223

Modelling and Simulation

The effect of the pressure difference was studied by varying it from -50 kPa to +200 kPa and keeping the average pressure level constant. Fig. 3 shows the decrease in the steam flow from the plate gap to the cent er when the pressure difference is increasing. This shows clearly how the back-flow effect can be compensated by pressure difference.

( 1 7~)

_24 66t[ r

CA.

l+

1

--4 ~t(B. l

+

1

1

.+/\ . . )(x. '1 .-x . . )] 1,J ;+.,J :,j

,]

.+B.

,J

~).

l ,...;

Here 6r = r i + 1 -r i and 6t=t i + 1 -t i . The second step gives the new state

2.0

total s team flow

s~the inlet

at

(18 ) -100 -50

0 50

'0)

150 200

(kPa:

Fig. 3

+1.0

o

-0.5

plate gap(mm)

Fig. 4

2.0

This modified Lax-Wendorff method is second-order accurate. The method was programmed in FORTRAN and the program was run on the UNlVAC 1108 computer. Further details are given by Aarni (1977 a).

+0.5

2.0

total steam flow

total steam flow

~ 1.0

team flow at the inlet

~ conslstency (%' 0

SlMULATlONS

25

27.5

I

30-4

2.5

3.0

The effects of the control variables

Fig. 5

on the steady state

The distance between the plates was changed ± 1 mm by keeping the pressures at the inlet and at the outlet at their reference values. A reduction of one millimeter in the plate gap increased the pressure maximum by 12 kPa. Also the steam production increased and the relative shore of the inlet steam flow increased. Figure 4 shows the steam flows from the plate gap as functions of the plate gap.

The main control variables of the refiner are the distance between the plates, the pressure difference between the outlet and the inlet of the plate gap, the wood flow and the water flow at the inlet. The reference data for the simulation runs were chosen according to production runs made at the refinering of the Summa mills in spring 1977 and are given in Table I. 40.0

Varying the feed consistency had only a minor effect on the steam production. The consistency at the inlet was varied from 24.9 % to 31.6 & and the effects on the steam flows are shown in Fig.5. The pressure distributions were almost insensitive to changes in consistency.

m/ s veloci ty

20.0

The production or the wood flow was varied from 0.55 kg/s (2.0 tons/h to 0.83 kg/s (3.0 tons/h) keeping the consistency and the distance between the discs constant. Figure 6 shows the effect on the steam flows.

2JO"--'--..............................-..................~

u..o

radi us flow

1.0

660

~o kg/s flow

1.0

radius

Fig.

Fig. 6

2

Stationary distributions of pressure, velocity of steam, water flow, wood flow.

660

The steady state simulations propose that the main control variables are the pressure difference and the distance between the refining plates. The effect of ~~e consistency is insignificant and the production is usually kept as high as possible. The steam flow to the center of the discs leaves the center partly through the feeding channels.

I. Aarni and J. Virkkunen

224

This effect may cause interruptions in the feed which can be fatal for the refining plates. The effects of the dilution water added to the center are mostly in condensing the steam from the plate gap. The effect of the shape and length of the refining zone The length of the refining zone was increased by keeping the outer diameter distance between the plates and the slopes of the plates constant. The length was varied from 100 mm to 340 mm. This caused the total steam flow to increase from 0.8 kg/s to 1.7 kg/s and the energy consumption increased 113 %. Figure 7 shows the total steam flow and the steam flow to the center as functions of the length of the refining zone. The increased steam flows mainly to the center of the discs. 2.0 total steam flow

width (mm) 150

Fig.

7

200

250

300

350

Steam flow as functions of the length of the refining zone.

The effect of the changing point of the slope or the taperness of the plates was studied. It was found that increasing the length of the outer refining zone moved the pressure maximum closer to the center and the steam flow to the center increased. The slope of the inner zone had almost no effect on the steam flows, but increasing the slope or the taperness of the outer refining zone moved the pressure maximum away from the center closer to the outer diameter and also increased the maximum. Hoglund, Sohlin and Tistad (1975) and Becker, Hoglund and Tistad (1977) suggest that the fibrillisation result is best when the Droduct of the torsional modulus- and the internal =riction of the wood has its maximum. 'l'his maximum is a function of the temperature and frequency of mechanical touches caused by the edges of ~he grcoves in the refining plates. As the frequency increases the temperature must also be increased ~o obtain optimum refining couditions. Usu~lly the amount of grooves on the reflner

plate increases with radiL~ and therefore the temperature should also increase with radius. The temperature is a function of the Dressure of saturated steam and therefore the shape of the plates should be constructed so that the Dressure maximum is very close to the· outer diameter of the refining zone. This can be achieved by a continuously tapered plate gap. Another way to achieve an increasing temperature distribution is to use a negative pressure difference, which means that the pressure outside the discs is higher than at the center of the discs. The amount of grocves and the shape of the profile of the plates can De optimized to give the best pulp. Simulated properties of the preheater Experimental tests have shown that the moisture of chips fed into the preheater oscillates. This is caused by the screw feeder and the chip washer. The situation was simulated by letting the chip moisture oscillate at a frequency of 0.0025 Hz and amplitude 5 %. The moisture at the other and of the preheater started oscillating after a delay of 122.5 s damped to 4.3 %. The temperature oscillated at an amplitude of 7.1 0 • The chips are usually stored outdoors and in winter some chips may be very cold and wet or icy. Similarly in summer some of the chips may be very dry and hot. Such changes damp for instance, in the chip washer but some changes can also occur at the preheater input. These situations were simulated first by raising the moisture of the chiDs from 45 % to 60 % and 18wering the • temperature from 55 0 C to 30 C for one second; secondly, by l~wering the moisture from 45 % to 33 % and raising the temperature from 55°C to 62°C. The temperature change -22 0 was 0 amplified to -40 and the moisture change decreased from 15 % to 14 %. The second situation was handled better by the preheater because the 10 o change increased to 14 0 and the moisture change decreased from 12 % to 11.6 %.

°

Simulation of

dyna~ic

effects

The dynamic effect of pressure changes at the center of the discs was simulated by decreasing The pressure a~ the inlet from 260 kPa to 245 kPa. The mass flows were keet constant. As the pressure decreased he-steaD flow to the center increased 32 % ~~ 30 mic~oseco~ds. Gradually t began TO rise towards the new steady state value, which was

225

Modelling and Simulation

reached in 5 ms. The steam flow at the outlet began to change after a 0.95 ms delay. The effect on the steam flow at the outlet depended on the shape of the pressure distribution. A high pressure maximum caused damping in the changes in the flow and a lower pressure maximum let changes through easily. Figure 8 shows the pressure distributions as a function of time and Fig. 9 shows corresponding changes at the velocity distribution of the steam flow. Figure 10 shows the velocity of the steam flow at the inlet. 0.27

The flow to the center increased after a 1 ms delay by 85.7 % and also reached the new steady state value after 5 ms. In this case too a higher pressure maximum caused greater damping in pressure disturbances. When the refiner is running the rotating discs bend a little at their axes and this causes oscillations in the distance between the refining plates. There are two main components in these oscillations, the first with a frequency equal to the rotational speed and the second with a frequency three times higher.

pressure

30

[MPa]

Velocity [m/s]

440

[mm]

Time [ms]

Fig.8 Development of the pressure distribution in Ex.1

Fig.9 Development of the velocity of the steam flow in Ex. 1

o or----...._-.;O',.;;.2_ _~O...... L -__---:.O~.6-_~O~.8-__---:.1.~O__

time (ms) -10

outlet steam flow inlet steam flow to

-20 -30

0.5

-La

time (ms) 01

15

01

time (ms) 15

-50

Fig. 11 Steam flows at the outlet aild inlet.

-60

-70

velocity (m/s)

Fig. 10 inlet.

Velocity of steam at the

A stepwise change in the pressure at the outlet of the plate gap was also simulated. The pressure was raised from 250 kPa to 255 kPa. The steam flow to the cent er of the discs and the flow leaving the plate gap are shown in Fig. 11 as functions of time. The pressure step occured at instant t=1 ms. The outgoing flow immediately decreased 37.5 % and after 5 ms it had reached the new steady state value. I.A.A.-Q

This situatioil was si~ulated by varying the distance between the plates at frequencies 25 H= and 73 Ez, and the amplitude was 0.5 mm. ~his amolitude wa~ 8.9 % of the dista~ce at the beginning of the refining zone and 25 % at the end. The effect of oscillation was that the steam flow leaving the plate gap oscillated aT the same frequency and the aplitude was 12.8 ~ of the mean value. Correspo~dingly the flow to the center of the discs oscillated with a~ amplitude of 46.1 % of the mean value. The result was the same with both frequencies, which is natural because ~he response times

I. Aarni and J. Virkkunen

226

of the refiner are of the order of 1 to 5 ms and the corresponding frequencies are of the order of 200 Hz to 1000 Hz. The distance between the plates is controlled by a hydraulic cylinder which causes a force acting on the moving disc. This force was five times larger than the normal force and the distance was decreased 10 % in 10 ms. This gives some idea of the difficulty of controlling the changes in steam flows and pressures by such equipment.

The pressure difference and the plate gap can be chosen so that the temperature distribution is close to optimal as regard fibrillisation. Fightening the plate gap from this increases the energy consumption and steam production, but the pulp quality decreases. Thus maximum energy consumption does not necessarily mean maximum pulp quality. The dilution water fed into the center of the discs condenses some of the steam from the plate gap, but has little or almost no effect on steam flows or pressure distribution.

DISCUSSION The simulations show that the fastest response times of the refiner are of the order of 30 microseconds and the time that a disturbance takes to travel through the refiner is one millisecond. New steady state conditions can be achieved in 5 ms. Controlling such rapid disturbances by changing the distance between the refining plates requires very great forces, because heavy masses must be moved. This is not sensible and not always even possible, so that the refiner should be made indifferent to disturbances in steam flows and pressure. Especially the steam flow to the cent er of the discs is very sensitive to disturbances and therefore the center should be constructed so that the feeding of chips is not disturbed by the steam flow and so that the steam flow easily passes through the center. The shape of the profile of the plate gap and the number of grooves on the refining plate can be constructed so that the radial temperature distriliutiGn provides the best conditions for fibrillisation. For instance, if the number of grooves increases with the radius, the shape of the profile should be such that the temperature rises with the radius as far as possible. This means that the pressure and the temperature maximum are as close to the outer diameter of the discs as possible.

The amount of steam flowing to the center of the discs can be reduced by enlarging the distance between the plates or by enlararging the pressure difference. However, both these actions decrease the quality of the pulp. If the center does not block the steam flow the pressure difference can be kept as small as possible or negative. A negative pressure difference causes a rising temperature distribution, which is favourable to the pulp quality.

Acknowledgement. The work has been supported financially by the w. Ahlstrom foundation. REFERENCES Aarni, I. (1977a): Kuumahierreprosessin dynaaminen malli (Dynamical model of the thermomechanical pulping process), Helsinki University of Technology, Control Engineering Laboratory, Reports No 9, (58 p) (in Finnish). Aarni, I. (1977b): On numerical methods for solving first order hyperbolic partial differential equation systems, Helsinki Univ. of Tech., Control Engn. Lab., Report s No 13, (28 p). Aarni, I., Kuikka, S. (1978): Kuumahierreprosessin simuloinnista ja toiminnan optimoinnista (Simulation and optimization of the thermomechanical pulping process), Automation Days -78, The Finnish Society of Automatic Control, (20 p), (in Finnish). Atack, D., Stationwala, H.I. (1975): On the measurement of temperature and pressure in the refining zone of an open discharge refiner. Proceedings of the TAPPI 5th International Mechanical Pulping Conference, pp. 1 35 -1 41 . Becker, H., Hoglund, H., Tistad, G. (1977): Frequency and temperature in chip refining. Paperi ja Puu 59, pp. 123-130. -Hoglund ,H., Sohlin, U., Tistad ,G. (1975) : The effect of physical Droperties of the wood on chip refining. Pro~. of the TAPPI 5th Int. Mech. Pulp. Conf., pp 77-85. Mi 1 e s, K. B., Ma y, \\.J. D (1 9 7 7 ): Dy n a mic disc misalignment in a chip refiner. I MP C 1 9 7 7, Pr 0 c., vol. I I I .