Simulation of the dynamics of the wet end of a board machine

Transcription

1 DEGREE PROJECT IN CHEMICAL SCIENCE AND ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2018 Simulation of the dynamics of the wet end of a board machine EUGENIO CIUCANI KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES IN CHEMISTRY, BIOTECHNOLOGY AND HEALTH

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3 To Roberto, Maria Paola, Maria Chiara and Alessandro 1

4 The Buddha, the Godhead, resides quite as comfortably in the circuits of a digital computer or the gears of a cycle transmission as he does at the top of the mountain, or in the petals of a flower. To think otherwise is to demean the Buddha - which is to demean oneself. (Robert M. Pirsig) 2

5 Abstract The wet-end of the centre ply of the paperboard machine n 2 ( Kartongmaskin 2 or KM2) in Iggesund was simulated to obtain both qualitative and quantitative results on its start-up dynamics and its variation damping capacity. The accuracy of the model was controlled by comparing the simulation results with data from the real production process. Furthermore, alternative strategies with the objective of reducing the time needed for start-ups and grade changes were evaluated. The modeling was done using the Paperfront simulation software. Variables such as layout for the mixing system, retention level and amplitude and period of inlet concentration were used as parameters. As alternative operation strategies for start-up and grade change, increased flowrate in the early phase of a start-up and the temporary overdosing during the beginning of a stock change were evaluated. The results indicate a strong control of the mixing system over the short circulation both in dynamics at start-up and in general operation with a time constant for the machine close to 35 minutes. In addition, variations in consistency are more easily controlled by a double-chest mixing system and, in general, variations are more easily damped the higher the active volume in the mixing system. Finally, times needed for start-up and composition changes could be reduced by as much as 50% by using a more proactive approach. 3

6 Table of contents 1. Introduction and background Papermaking process General description of relevant processes and equipment Dynamics of mixing and approach flow systems Step-change and mixing models Stability evaluation Retention and short circulation dynamics Previous work Objectives of the thesis Modeling Model description Description of the modeling software Assumptions Test procedure Parameters Process layout Variation characteristics Process conditions Operation strategies Process data for verification Results and discussion General behavior Influence of process layout Influence of production characteristics Fitting of process data Advanced dosage strategy for startup and grade change Effect of process control Conclusions Dynamics Mill implications References Appendix Figures Acknowledgments

7 1. Introduction and background 1.1 Papermaking process General description of relevant processes and equipment The production process of paper and paperboard rests on three main objectives: to prepare a suspension of fibers, form a sheet of interlocked fibers and depriving it of water [1]. The suspension is prepared by blending different pulps, which can be the result of chemical and/or mechanical pulping as well as broke [2], water and chemicals [1,3]. The forming and part of the dewatering are performed by spreading the fiber suspension on a woven permeable wire[4], pressing water out of the fibre network in press nips, and removing most of the remaining water using steam-heated cylinders. [5]. A CAD model of a three-ply paperboard machine in the Iggesund mill (KM2) is shown in Figure 1. Figure 1: Sketch of one of the two paperboard machines in Iggesund[6]. At the lower-left corner of the picture there is the forming section of the machine with three headboxes and three wire sections. The suspensions flowing out of each headbox is spread with a concentration of less than 1% fibres. The resulting three webs are couched together and the resulting web exits this section at a consistency of roughly 15%. At this stage, the dewatering happens both via filtration and suction [7,8]. The following section is the press section where the fibre mat is dewatered to a consistency of approximately 40%. The final dewatering is performed thermally with the use of steamheated cylinders [6,9,10]. At the end of the machine, on the upper-right corner, the coating, calendaring and reeling processes take place [6]. The give the product a smoother surface, resulting in a much better printability. The focus of this project has been directed at the approach flow system and at the wire. The approach flow system comprehends the processes and equipment from the chests where the fibers are mixed with chemicals and other additives up to the headbox [2]. The diagram in Figure 2 represents a sketch of the approach flow system of one of the three plies of the KM2 paperboard machine in the Iggesund mill. 5

8 Mixing system Short circulation Figure 2: Sketch of both the mixing and the short circulation systems. The incoming fibers (virgin and broke, if used) are mixed with chemicals, retention aids and sizing agents (the mixture is referred to as thick stock [11]) in the mixing chest at the left-hand side of Figure 2. The mixing chest has both the task of obtaining uniformity between the various components of the stock (blending) and a thorough agitation of the stock (mixing) [2]. The consistency of the stock is kept at a value between 3% and 4% [12]. Between the mixing and machine chests the consistency is usually decreased to further reduce variations and obtain a constant thick stock flow to the dosing valve [13]. Both mixing and machine chests have stirrers to ensure an ideal mixing of the flow, however, as shown by Ein-Mozaffari et al., most chests can show non-ideal behavior under normal operating conditions, for example due to a non-sufficient power of the stirrers [14]. The stock is dosed by the thick stock valve and diluted at the wire pit. The dilution results in a suspension of a consistency between 0.1% and 1.5% [15] (the normal operating consistency at the Iggesund mill is 0.8% [6]). The dilution is done with the water from the dewatering of the fiber mat at the wire. The suspension is pumped to the headbox and the fiber-mat is formed on the wire, which is a belt of woven plastic or metal fabric [16,17]. The fiber web proceeds to further sections of the board machine while the water is reused. The processes and equipment after the thick stock valve (left half of the sketch in Figure 2) in which the water from the wire is recirculated comprise the short circulation of the board machine [2]. 6

9 1.2 Dynamics of mixing and approach flow systems Mixing is an important aspect of the board-making process [17]. It ensures that all the components are homogeneously blended together so that no time-dependent variation of any given property is present in the final product. In addition, mixing is used to control the consistency of the stock and to even out variations in the stock coming from upstream [18]. An example of this effect is given in Figure 3. As it can be seen, the pulp incoming to the first chest on the left presents an oscillation around the middle value of 4% consistency. The consistency is lowered by the use of whitewater while the variation amplitude diminishes after each chest to be almost completely evened out by the outlet of the machine chest [19]. Figure 3: Effect of a series of chests on consistency variations[19] Step-change and mixing models Two models were considered to describe the behavior of the flow through the mixing section of the board machine. The flow through the chests could either be plug flow or perfectly mixed [20]. The difference between the two models is illustrated in Figure 4. Figure 4: Different response (as function of time) to a step input by a plug flow and a well-mixed model [21]. As it can be seen in the illustration in Figure 4, both volumes are subjected to the same input. The difference between the two volumes is extent of mixing, which is absent in the first and maximum in the second. As such, the first volume behaves similarily to the flow in a pipe and the concentration over the characteristic dimension of the volume varies only as a function of the space coordinate [22]. In the second case the mixing is thorough and the flow is always blended with the material still in the chest. The stock composition is identical in any part of the volume[20]. The input fed to both the systems in Figure 4 is referred to as step-input; the description of the input has been provided by many authors and is shown in Equation (1.1) [23] 7

10 c ii (t) = 0 ii t < t 0 M ii t t 0 (1.1) The left-hand side of equation (1.1) is the inlet concentration as a function of time, which corresponds either to 0 if the time is less than the starting time t 0, or has a amplitude equal to M for all times greater than the starting time t 0. The response of a chest with plug flow behavior is shown in Equation (1.2) [23] 0 ii t < τ c ooo (t) = M ii t τ (1.2) Where τ = V cheee [min] is the average residence time of the chest [24]. The system modeled as a Thrrrrhppp plug flow has no transient, and a sketch of three different systems with varying residence times is given in Figure 5. Amplitude [-] 1 0,8 0,6 0,4 0, Time [min] Input Residence time = 10 minutes Residence time = 5 min Residence time = 15 minutes Figure 5: Input and output of three different plug-flow chests. As it can be seen in Figure 5, the step input happens at t 0 =0 minutes, the three systems have a residence time of respectively 5, 10 and 15 minutes. As expected from the relations in equations (1.1) and (1.2), the outlet concentration has the same amplitude of the inlet instantaneously after the residence time. The chest modeled as a plug does not exhibit a transient phase. The perfectly mixed chest, referred to also as first order system [25] has a different behavior. The description of the response of a system to a step-change is shown in equation (1.3) [23]. c ooo (t) = M 1 exp t (1.3) τ The equation shows how the concentration at the outlet is time-dependent with an exponential curve. M is the amplitude of the step, while τ [min] is the ratio of chest volume and material throughput (i.e. the average residence time). Finally, t is the absolute time. It can be seen from equation (1.3) how different residence times will lead to different transient periods. A sketch of three chests with different residence times is provided in Figure 6. 8

11 Amplitude [-] 1 0,8 0,6 0,4 0, Time [min] Input Residence time = 10 min Residence time = 5 min Residence time = 15 min Figure 6: Input and output of three different perfectly mixed chests. The three chests evaluated in Figure 6 have a residence time of 5, 10 and 15 minutes, respectively. The systems are slower to reach equilibrium the longer their residence time. In addition, it can be noted how the perfectly mixed chests reach roughly 63% of the step-change for a time corresponding to their residence time and need roughly three times their residence time to reach a threshold of 95% the step-change [20]. Comparing the graph with the one in Figure 5 it is evident how the plug flow model would result in faster systems. It should be noted, however, that both plug flow and perfect mixing are ideal approximations. In reality the behavior of the chest is too complicated to be described solely by these two models and more realistic models should be taken in consideration [14,26]. Due to the use of both virgin fibers and broke in the stock for the centerply of the boards produced by KM2, two chests are operated in series, the first chests blends the stock components and the second provides a stable outflow to the approach flow system. Two chests can be modeled, assuming perfect mixing approximation, as shown in Equation (1.4) [27]. c ooo (t) = M 1 τ 1 exp t τ1 τ 2 exp t τ2 τ 1 τ 2 (1.4) The parameters in the model described by Equation (1.4) are τ 1 and τ 2 [min], which represent the residence times of the different units, t as absolute time, and M as the amplitude of the step-change. A comparison of two chests in series, one with a residence time of 5 minutes and the other of 10 minutes, and a single chest with a residence time of 15 minutes is given in Figure 7. 9

12 Amplitude [-] 1 0,8 0,6 0,4 0, Time [min] Input single perfectly mixed chest two perfectly mixed chests two plug flow chests Figure 7: Comparison of the transient time of two chests in series to a single chest. As it can be seen, the double-chest arrangement with a plug flow model is the simplest. As the residence time of the resulting system is the sum of the residence times of the single chests [24], the result, according to equation (1.2) is a plug flow system with a residence time of 15 minutes. Concerning the perfectly mixed chests, two chests in series have a different behavior than a single chest. As it can be seen the single chest is faster in the beginning but the double chest arrangement is faster after a time slightly bigger than the average residence time. In addition, the behavior of the system tends to approximate the output of a plug flow system the bigger the number of chests in series [20]. Finally, in this work the effect of flow in the pipes was not considered as, due to the high flows involved, the residence times of the piping system would be negligible compared to that of the chests [20]. As such, the delay effect of the pipes was neglected in the results Stability evaluation To fully understand the dynamics of the mixing and approach flow systems a description of the possible variations with a periodic nature which can be encountered and the ability of the machine to even them out will be will be given. It is important to understand which parts of the process have the most effect in avoiding product variations at the reel. A mathematical description of sinusoidal oscillations is provided by Marlin et al. and is given in Equation (1.5) [25]. c ii (t) = A sss(ωω) (1.5) In Equation (1.5) A is the amplitude of the variation, ω the frequency and t the absolute time while c in (t) is the variation of the inlet consistency. The response of a single chest is, after using Laplace transforms, composed by a sum of addends, as explained by Seborg et al. [23] AAA c ooo (t) = exp t + ω 2 τ 2 +1 τ A ω 2 τ 2 +1 sin(ωω + φ) (1.6) The parameters present in Equation (1.6) are A as the amplitude of the inlet variation, τ as the residence time of the chests, ω as the frequency, φ = arctan( ωω) as the phase shift of the resulting oscillation [28]. The graph in Figure 8 shows the graphical interpretation of Equations (1.5) and (1.6) [28] 10

13 Figure 8: Response of a chest to a periodic variation. Both the decaying exponential and the oscillatory response are visible. [29] In the graph in Figure 8, the abscissa is normalized time (i.e. the ratio of time over average residence time) and the y-axis is the amplitude of both input and outlet. The signal at the outlet of the chest is both smaller and shifted compared to the signal at the inlet. Moreover, all the components of the outlet signal (the thick line) are present and the exponential term becomes negligible already at twice the residence time of the chest after the onset of the variation. The exponential term is as such neglected for long-term and steady-state variations [23,30]. The resulting equation for the steady state outlet oscillation is described by Seborg et al [23]. A c ooo (t) = sin(ωω + φ) = ω 2 τ 2 +1 A sin (ωω + φ) (1.7) The term A in Equation (1.7) is the amplitude of the outlet variation. Similarly to the step-change, the equation for a double-chest system is given by Johnston [28] c ooo (t) = A ω 2 τ ω 2 τ sin (ωω + φ) (1.8) The parameter τ i in equation (1.8) is the residence time of each chest. The ratio AA = A A is called amplitude ratio [31] and quantifies the effective damping of the system. Together with the phase shift φ the amplitude ratio is plotted as function of frequency to obtain a Bode plot [32]. An example of Bode plot is given in Figure 9. The upper graph in Figure 9 shows how the amplitude ratio changes as a function of the frequency of the inlet variation, while the lower graph shows the phase shift (which describes how the periodicity is shifted) It should be noted how the output signal will always be shifted with a negative angle (i.e. will be delayed in time). Both graphs have logarithmic scales for the x-axis. The amplitude ratio plot has also a logarithmic y-axis whereas the phase shift diagram has a linear y-axis [23]. 11

14 Figure 9: Example of Bode plot. The graphs show both amplitude ratio and phase shift as function of frequency. The Bode diagram is a powerful tool to understand not only how much of the amplitude will be reduced with relation to the inlet variation, but also how much of the signal will be shifted with time. This information helps when looking for the source of a variation by interpreting the data upstream. The spectrum of periodic variations that could be encountered in the approach flow system varies from low frequency noise coming from variations in the pulping sections to faster high frequency oscillation caused by the equipment, as shown in Figure 10 [2]. Figure 10: Possible oscillations present in the approach flow system.[2] Barasch et al. showed how most of the high frequency noise comes from the last parts of the approach flow system such as fan pumps, pressure screens and headbox recirculation (namely points 3, 4, 5, 6 in Figure 10) or by parallel operation of similar equipment [33] while most of the low-frequency oscillations, not easily evened out in the mixing system as pointed out by Wilson et al., come from the previous stages in the process [34]. 12

15 1.2.3 Retention and short circulation dynamics A sketch relating volumetric flow rates, mass flow rates, and concentrations in the short circulation can be found in the Ljungberg compendium [36]. Q HB, c HB (t) Figure 11: Sketch of the short circulation. [15,36] The thick stock is fed from the left side of Figure 11 with a flow Q 0 at a concentration c 0, mixed with whitewhitewater from the wire pit (Q 2, c 2 (t)) resulting in the headbox feed with flow Q HB and c HB (t). The retention in the short circulation, R S, providing all the flows are known and the system is at steady state (i.e. c i are not a function of time), can be determined according to Equation (1.9) [2,37] R S = Q 0c 3 Q HH c HH = Q 1c 1 Q 2 c 2 Q HH c HH = 1 Q 2c 2 Q HH c HH (1.9) The retention is the ratio between the solids remaining on the wire to the total amount ejected onto the wire by the headbox. An illustration of the situation at the wire, which shows what happens to the components of the thick stock, is given in Figure 12 [35]. Figure 12: Different retention of the furnish components. Smaller fractions are more likely to pass through the mesh.[35] 13

16 In the beginning of the dewatering process, long fibers are unable to pass through the wire mesh and are retained. Shorter fibers, fines (<0,1 mm) and fillers pass through the wire mesh more easily. [35]. However, retention is not a constant, single value for a given stock. The dominant dewatering mechanism on standard formers is by filtration and results from a constantly decreasing layer of liquid suspension above the forming fiber mat [4]. The longer fibers stack up, resulting in a successively higher retention of the smaller fractions. Figure 13 shows an example of the increasingly denser fiber mat as the grammage on the wire increases [38]. Figure 13: Fiber mat increasing in thickness over the length of the wire (left-to-right). [38] The retention value has also an effect on both the dynamics of the formation and the short circulation. The following relation regarding the effect of retention on the time-dependent concentration of the stock on the wire is stated in the Ljungberg compendium [36] c 3 (t) c 0 = 1 (1 R) exp ( R t τ ) (1.10) In equation (1.10) c 0 represents the stock concentration, as seen in Figure 11 and c 3 is the concentration on the wire, while R is the retention value and τ = V/Q 2 is the average residence time in the wire pit. An immediate implication of equation (1.10) is that whenever retention drops, or the material flow in the short circulation diminishes, the system is slower to reach equilibrium, and the volume of the wire pit will be exchanged many times [36]. Examples for the effect of a variation in retention between 10% and 80% on the time-depended change of the concentration are shown in Figure

17 Figure 14: Time needed to reach equilibrium for various levels of wire retention. [36] 15

18 1.3 Previous work Previous work has been directed at the characterization of the dynamics in the wet-end. Ein-Mozaffari, Bennington and Dumont showed how the effective mixing hypothesis is valid only at significantly high stirrer speeds and that relevant non-ideal behavior (channeling and short circuiting) limits the damping effect of the chests [14]. Furthermore, it was shown by Ein-Mozaffari et al. how the yield stress of the pulp suspension affects the mixing of the chests and how a decrease of yield stress allowed for better performances of the mixing system [39]. Wilson proposed a different approach to study the disturbance propagation in the wet-end including the effect of the piping network and concluded that the effect of the wire pit volume is not as relevant as previously estimated in damping vibrations in the short circulation and that instead the effect of the piping system should be more investigated [34]. Cutts proposed an alternative, more compact wet-end for the paper machines which resulted in time savings for grade changes and improvements in the overall energy efficiency for the machine [40]. Savolainen used the APROS Paper software to study the behavior of two paper machines and showed how a system with lower retention has a marginally better damping efficiency than a system with higher retention[41]. Lappalainen proposed a new model for automatic grade change based on simulation and validation of a paper machine model again using APROS paper [42] and showed how automatic control in the short circulation can help reduce both transient times and product quality variation. Jagebäck used FlowMac and characterized the behavior of the FEX pilot paper machine at STFI (now RISE) over retention and other parameters [43]. Kokko et al. used adaptive process control and discovered how better results can be obtained in controlling consistency variation with multivariate control than with using normal feedback loops [44]. 16

19 1.4 Objectives of the thesis The objective of this work is to obtain an understanding and quantify the dynamics and of the material flows in the wet end of the Paperboard machine N o 2 (Kartongmaskin 2 or KM2) in the Iggesund mill. The process is simulated in a dynamic process simulation in the PaperFront software. The effect of varying the dimensions or process layout of the mixing system on startup times and damping of variation will be quantified. In addition, the effect of the variation of the retention in the whitewater system will be analyzed. An evaluation of the accuracy of the dynamic model will be performed by comparing model predictions with historical data from the quality control system of the mill. Finally, several suggestions regarding a modified process operation in order to reduce the start-up time will be evaluated. 17

20 2 Modeling 2.1 Model description Figure 15: Overview of the general model with its two submodels, the mixing system and the short circulation. With reference to Figure 15, the approach flow system of the center-ply of KM2 was divided into two main areas of interest: mixing system and short circulation. The mixing system receives the thick stock and ensures that the variations in concentration are reduced significantly. The stabilized thick stock is dosed into the short circulation via a dosing valve. In the short circulation the stock is diluted with whitewater in the wire pit. The fiber suspension is pumped to the headbox and ejected onto the wire. The dewatered product exits the boundaries while the water is recirculated. Figure 16: The two alternatives for the mixing system that were investigated. Figure 16 shows two possible layouts for the mixing system. Above is a single chest while and below a coupling in series of two chests. For a simple step-increase of the pulp concentration the relations describing the response of each of the two layouts are described in equations (2.1) and (2.2): 18

21 ssssss cheee: c ooo (t) = 1 e t τ (2.1) dddddd cheee c ooo (t) = 1 τ 1e t τ1 τ 2 e t τ2 (2.2) τ 1 τ 2 τ is the average residence time of each chest and t is the time. Figure 17: Retention as a function of fibre length for average retention values of 80%, 90% and 95% The dynamic behavior of the short circulation is defined both by the retention at the wire and by the dynamic model of the wire pit. Figure 17 shows three selective retention curves for average retention levels of 80%, 90%, and 95%, respectively. As it can be seen, lower average retention values were modeled by decreasing the retention of shorter fibres/fibre fragments. The wire pit, depending on the modeled retention, will be then more or less charged with smaller material and that, as explained in the previous chapter, will determine how fast the system will arrive to equilibrium. In Figure 18 there is the complete selective retention graph for an average wire retention of 95%, it was decided to use a retention value of 50% for both fines and fillers. 19

22 100% 90% 80% 70% Retention [-] 60% 50% 40% 30% 20% 10% 0% filler fines 0.1 mm0.2 mm0.3 mm0.4 mm0.6 mm0.8 mm1.0 mm1.5 mm2.0 mm3.0 mm Figure 18: Retention values for an average wire retention of 95% including fines and filler material for a typical hardwood or softwood chemical pulp. 20

23 2.2 Description of the modeling software The software used in the simulation is PaperFront, developed by FrontWay AB ( Based on ExtendSim, PaperFront is a process design simulation software strongly focused on unit-operation and the pulp and paper industry. It is characterized by an open workspace graphical user interface (GUI) [45] where pre-compiled units (blocks) can be placed and connected with each other. Figure 19: Example of a Simple PaperFront model. The process units are placed in the workspace and connected to each other. The simulation can be controlled upstream or downstream by using either a push-operated or demandoperated block: in the first case the user will define the flow upstream and the units will transmit a signal with equal value downstream, in the second case the user defines a value on a selected block which will transmit a request to the unit immediately upstream. An example of push and demand units is shown in Figure 19: the unit upstream of the pump is operated in demand-mode while the one downstream is a push-block. In this case the flow is defined at the pump itself, which acts as a mixed control unit and will demand the amount of flow from the supplier which will push to downstream units. Push-mode enables direct actions on the flows through the units at the expense of flexibility (the user will have to modify each stream according to ach possibility). Demand mode has the opposite effect: simulations in pure demand mode do not allow the user to directly define the magnitude of the input/output flows but are more easily tuned to varying process conditions. Each unit is customizable. As an example, a chest block is shown in Figure 20. Characteristics as chest volume, operation mode, filling degree and start concentration can be modified by the user. Unit-specific material and energy balances can also be controlled. Another feature of the software is its ability to execute a list of user-defined operations in sequence at a certain time. This scenario-handling option enables the user to simulate more possible processes and productions during a single simulation. 21

24 Figure 20: Chest block, icon (left) and control panel (right). The model of the mixing system with two chests is shown in Figure 21. On the left side of the workspace there is the feed section which, in this model, is composed by two inlet lines (one pulp and the other water). The feed is defined in the feed pump and the flow is directed to the two chests composing the mixing system (mixing chest and machine chest). The chests are push-operated and kept at a constant level (further models were set in demand mode and required level control, which had an effect on startup dynamics). The outlet from the machine chest is pumped to the short circulation. Figure 21: Feeders and mixing system without the broke circuit. 22

25 The material flow from the machine chest is pumped to the wire pit, which was modeled as a perfectly mixed chest. In this unit the stock is diluted to a concentration of 4 g/l with white water from the wire, as it can be seen in Figure 22. Characteristics of the headbox such as shower flow, recirculation, speed and lip opening are user-definable. In the wire unit, retention can be either defined as a mean value or computed by assigning a selective retention value to each component. The production can be registered in various measurement units and the product grammage can be controlled via a specific basis weight controller. Figure 22: Wire pit and wire. The enhanced feed and mixing systems are shown in Figure 23 and Figure 24. The main difference between the feed lines in Figure 23 and the feed line in Figure 20 is in the use of three different feeds: virgin fibers, coated broke and uncoated broke. The modification was made to obtain a system as adherent to the real machine as possible. Like its real counterpart, the broke line has a small mixing chest of 25 m3. The dilution of the incoming lines with whitewater from the overflow of the wire pit was also implemented. Level control was used to keep the level constant in the chests. The share of coated and uncoated broke, as well as the fraction of virgin fibers, were decided in two mixing points on solids basis. The dilution point after the broke mixing chest and the one between mixing and machine chests had a concentration-control purpose. In the mixing system in Figure 24 the difference with the older model is in the use of two demand-operated level controlled chests. The two valves before the chests are used to control the level in the units while the last valve doses the thick stock to the white water system. 23

26 Figure 23: Feeders for the model with the broke circuit. Figure 24: Mixing system for the second model. 24

27 2.3 Assumptions Some assumptions were made to make the modeling feasible while maintaining a certain level of validity for the obtained results. An important approximation was to consider all the chests in the wet-end to be perfectly mixed vessels. This choice was dictated both by observation of their real counterparts (both mixing and machine chests in the center-ply production line have impellers) and by the absence of any other usable mixing model in the simulation software. This assumption may implicate a slower dynamic response of the model compared to the real machine. On a more practical level, the incoming flows of broke and virgin fibers were considered constant and not depending on the two broke storage towers. In the real machine, the broke feed is dependent both on the production and on the level of the broke storage. This way, the control of the simulation was more dependent on the situation at the wire. In a similar fashion, in the first part of the simulations only the short circulation was considered: as a result the effect of the white water recycling on the mixing system was, in a first approximation, neglected. This meant that the flow incoming to the mixing chest could be defined as a single entity. After the recycle of the wire pit overflow in the model, the assumption fell, the incoming flow was modeled as the mixing of both coated/uncoated broke and virgin fibers and both lines were diluted with whitewater from the forming section, as in the real machine. It was chosen not to implement the disc filters due to the increased complexity of the model (which simulates only the center-ply while the screens process the whitewater from all three plies indistinctively) in spite of the actual small improvement in the obtainable results. Furthermore, the screens placed on the fiber-line were not implemented. Lastly, the effect of retention aids was not modeled other that by assuming a size-dependent retention value. 2.4 Test procedure The test procedure was divided into a startup phase and an oscillatory phase: the machine begun with its tanks filled only with water. At first the system was subjected to a step increase of the feed concentration from 0 to 40 g/l. After the step input the concentration in the inlet feed would start to oscillate. Figure 25 shows the procedure in graphic form: the start-up phase lasted 240 step (each step corresponding to a minute). Oscillation began at the 240 th step and the first 60 steps were characterized by growing oscillation prior to steady state oscillations. The variation is described by equation (2.3) with the attached conditions in equation (2.4). y(t) = A sin 2π b t (2.3) Where 0.25 g/l A = 0.5 g/l 1.0 g/l and 10 mmm b = 30 mmm 60 mmm (2.4) To implement the oscillating function in the PaperFront model, blocks native to ExtendSim were used. The blocks on the left in Figure 26 were used to define amplitude and average, the sine block included the definition for the period. The independent value was the simulation step. The result from 25

28 the sine block was used to oscillate the fiber feeder, while the remaining share was used to vary the water feeder. Concentration [g/l] Time [min] Feed Figure 25: Feed profile for the simulation. A step-increase startup followed by an oscillation in the feed concentration. sine Set 0,5 ### hold Amplitude 13. Mixe r Flow share ### hold 100 constant ### 4 hold Average 3, Set 13. Mixe r Flow share 2 Figure 26: Logic blocks for the oscillating variation. 26

29 2.5 Parameters The dynamics of the simulated wet end of the board machine were analyzed with a parametric study. Different process layouts and process conditions were simulated and the response of the system subjected to a step-change in concentration and a dynamic perturbation was evaluated Process layout The mixing system in the center-ply is a second order system composed by two first-order systems (mixing chest and machine chest). As a comparison, it was decided to analyze the dynamic performance both in terms of start-up from 0 g/l concentration and rejection of noise once at steady state with a comparable first order system (i.e. a single chest whose volume, and consequently residence time, would be equal to those in the total double-chest mixing system, as seen in Table 2). In the real machine, the center-ply employs two chests in its thick stock preparation, the outer plies only have a machine chest, both lacking a mixing chest. Figure 27 shows how the two systems looked like on GUI of PaperFront. Figure 27: Comparison between single- and double-chest mixing systems. The active volume in the chest plays also a very important role in defining its dynamic characteristics. This option was developed in both a design approach and an operation approach. In the first case a choice was made between possible chest volumes. In the second case, the normal chest volume was used and various filling levels were tested. For both cases, the varying volume was that of the mixing chest, being it the bigger unit and, as such, the one with the bigger effect on the dynamic behavior of the process [31]. The various volumes and levels are shown in Table 3. With reference to Figure 23 and Figure 24 the level of the chests varied in the enhanced model. The mixing chest level was raised in April to solve head problems in the machine pump. All the chest levels in the enhanced model are listed in Table 4. 27

30 2.5.2 Variation characteristics The amplitude of the oscillation in the pulp feed was kept in consideration. Three sinusoidal waves with a period of 60 minutes and different amplitudes of 6.25%, 12.5% and 25% were tested. The effects of the perturbation were observed for three levels of the mixing chest (10%, 70%, 100%). The other evaluated variation characteristic was the effect of a variation in the period of the oscillation. Three main scenarios with a fixed amplitude of 12.5% and a varying period were modeled. The first wave was set to have a 10 min oscillation period, the second 30 min and the third 60 min. Figure 28 shows a comparison between the oscillations with a period of 10 minutes and 60 minutes. It can be noted on the 10-minute wave how the top and bottom peaks become more jagged. This is due to the plotting step being bigger than the simulation step. This did not influence the accuracy of the simulation. 15% Variation [%] 5% -5% -15% Time [min] 15% Variation [%] 5% -5% -15% Time [min] Feed Figure 28: Examples of varying oscillations, 60 minutes [top] and 10 minutes [bottom]. 28

31 2.5.3 Process conditions The standard operating conditions are listed in Table 1. The average residence time in the mixing chest is 10 minutes, 4 minutes in the machine chest and 30 seconds owing to the much higher material flow. The first two chests are kept at 70% level while the latter is filled to 100%. For most products the machine speed is between 400 and 500 m/min (some productions are both at higher and lower speeds) and production for the center-ply is normally up to 18 BDton/hr. The headbox jets are normally kept at 50 mm. Table 1: Standard process condition for the simulated model Mixing system White water system Flow ~7500 LPM Flow ~90000 LPM Concentration 40 g/l Chest volumes Wire speed m/min Mixing chest 100 m3 Jets opening 50 mm Machine chest 43 m3 Web width 4900 mm Wire pit 40 m3 Production BDton/hr The data presented in Table 2 is referred to the tested different layouts for the mixing system and it is referred to a feedstock flow of 7560 LPM. As it can be seen, the single-chest system was designed so that the residence time in the single mixing chest was equal total residence time of the double-chest layout. Both systems were compared at 70% of their total volume. Table 3 presents the data regarding the variation of the mixing chest. 2 scenarios were proposed with ±50 m3 to the standard 100 m3 mixing chest. Furthermore, for all volumes three levels (10%, 70%, 100%) representing empty chest, normal operation and full level were tested. Table 2: Specifications for single- and double- chest layout Mixing chest Machine chest Volume 2-chest layout Operating volume Level 100 m3 70 m3 70% 43 m3 30,1 m3 70% Avg. residence time 9,26 min 3,98 min Mixing chest Volume 143 m3 1-chest layout Filled volume 100,1 m3 Level 70% Avg. residence time 13,24 min Table 3: Chests volumes, chest levels and average residence times. Running conditions Flow 7560 LPM Volume Filled volume Level Avg. residence time Mixing chest 100 m3 70 m3 70% 9,26 min Machine chest 43 m3 30,1 m3 70% 3,98 min Wire pit 40 m3 40 m3 100% 30,0 sec Volume variation (mixing chest) Standard Increased volume Decreased volume Chest Filled Chest Filled Chest Filled Level Level volume volume volume volume volume volume Level 100 m3 70 m3 70% 150 m3 105 m3 70% 50 m3 35 m3 70% 29

32 100 m3 100 m3 100% 150 m3 150 m3 100% 50 m3 50 m3 100% 100 m3 10 m3 10% 150 m3 15 m3 10% 50 m3 5 m3 10% Holdup time Holdup time Avg. residence time Level Level Level 70% 9,3 min 70% 13,9 min 70% 4,6 min 100% 13,2 min 100% 19,8 min 100% 6,6 min 10% 1,3 min 10% 2,0 min 10% 40,0 sec In later models, the machine chest level was raised to 75% to keep the same level of its real counterpart. Regarding the mixing chest no change was made. The levels are listed on Table 4. Table 4: Chest volumes and chest levels for the later studies. Volume Filled volume Level Broke mixing chest 25 m3 16,25 m3 65% Mixing chest 100 m3 70 m3 70% Machine chest 43 m3 32,25 m3 75% The assumed pulp fiber length distribution used in the simulations is shown in Figure 29. It corresponds to that of a typical softwood pulp and the predominant fibers are between 0.8 and 2.0 mm long. Figure 29 shows the average selective retention for each component. The average retention on the wire is 95% in total. Simulations both with varying average and selective retention of fillers and fines were run in both an uncontrolled and controlled system. Table 5 shows the various retention values used in the simulations fines 0.1 mm 0.2 mm 0.3 mm 0.4 mm 0.6 mm 0.8 mm 1.0 mm 1.5 mm 2.0 mm 3.0 mm Figure 29: Pulp feed fiber length distribution used in the simulation. 30

33 Table 5: Retention variation for various simulations. Controlled system Uncontrolled system Retention values Retention values Average 90% 95% 99% 10% 50% 90% 95% 99% Fillers 50% 70% 90% / / / / / Fines / / / 10% 30% 50% 80% 100% The dynamics of the simulated machine at steady state were also studied as a function of basis weight. Damping performance for a range of products from 180 to 300 g/m2 was evaluated. There are two main domains in the production: for heavier grammages the production rate is constant due to the drying section of the machine which acts as a bottleneck. For lighter productions Operation strategies To reduce the time needed from the system to reach equilibrium different startup strategies were tested. One of them is presented in Figure 30. Instead of using a normal step change, startup was performed more aggressively by using an increased flow in the first ten minutes. The startup procedure was also employed with the help of the process controllers in later models. The same idea was used in the simulation of a change in the share of the fibers. In that case, an overdosage in the fiber-share was performed instead of an increase in the volumetric flow. Rate of change [-] 130% 120% 110% 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Time [min] standard feed step increase feed increase with overdosage Figure 30: Standard step and overshoot startup procedures. 2.6 Process data for verification No laboratory analysis was performed in this work and it was decided to use process data from the digital control system and see how well the model, with its assumptions, would fit the process data. The scenario of interest was a sharp variation in the broke composition but production stoppages and normal operation were also considered. During normal operation the information system at Iggesund 31

34 has a threshold variation value. Events which fail to have an effect bigger than the threshold would not be stored. This meant that only equilibrium stages were traceable in the beginning. In April a new ashmetering device was put online both in the headbox and in the short circulation. This proved extremely useful as it could give an online and minute-scale reading of the filler concentration. 32

35 3 Results and discussion This chapter shows the findings of the simulations and highlights their implications in both the dynamic performance of the board machine and in possible improvement to its operation. The variables at play have been both process conditions and process layouts. Improvements for the normal operation strategies have also been propose in forms of more proactive process control. In addition, the simulated machine results were used to describe and fit actual process data to show how the system could as well be used as a suitable prediction tool both qualitatively and quantitatively. 3.1 General behavior The startup procedure was common to all layouts in all models. Figure 31 shows a typical example of the change in concentration in the modeled mixing system of the center-ply of the board machine starting from chests filled only with water. The violet line represent the step-increase from 0 to 40 g/l while the cyan and red lines are the responses of the first and second-order system, respectively. The models reach a value correspondent to 95% of the steady state concentration after around 40 minutes from the startup. Normalized concentration [-] 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Time [min] Feed Single chest layout Double chest layout Figure 31 : Example of startup behavior for the models after a step-increase. A sketch of the start-up behavior of the short circulation system is given in Figure 32, where the evolution of the consistency in the wire pit (in red) is plotted as a function of time; the dotted black line represents the analytical model for a single perfectly mixed chest of the same volume. 33

36 Rate of change [-] 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Time [s] Simulation Analytical model Figure 32: Start-up behavior for the short circulation. As it can be seen from Figure 34 the short circulation system reaches equilibrium in about 120 seconds, which is an order of magnitude faster than the mixing systems shown in Figure 33. Thus, the mixing system is the system with the highest inertia, defining the total time to equilibrium. Figure 33 shows the results from the standard mixing system to a sinusoidal variation of pulp concentration with a 60-minutes period and a variation of 12.5% from the steady state. The blue line is the feed concentration variation and the red line is the signal at the outlet of the machine chest. As it can be seen, the outlet of the mixing system is an oscillation with both reduced amplitude and a delayed phase from the incoming variation. The system used to obtain the graph in Figure 33 was composed by two chests in series. 34

37 15% 10% Amplitude difference Variation [-] 5% 0% -5% -10% -15% Phase shift Time [min] Feed oscillation Machine chest output Figure 33: Example of the effect of thick stock oscillations in a 2-chest mixing system as function of amplitude variation with a standard layout and 70% level. The mixing chest was filled for 70% of its volume. The effect of a difference in the amplitude of the variation were then observed. Three different runs (plus six more, three for a level of 100% and three for a level of 10%) per each amplitude were performed. Table 1 shows the results. As it can be seen, the ratio of outlet signal to inlet signal and the phase delay is the same for all the amplitudes (per level). A better dampening performance is obtained with higher chest level. The reason, remembering the equations for the amplitude ratio in Chapter 1, is in the longer residence time of the machine chest. Table 6: results from varying the variation amplitude Amplitude Level 10% 70% 100% 6,25% Ratio 0,9 Ratio 0,66 Ratio 0,54 Delay 5 min Delay 11 min Delay 13 min 12,5% Ratio 0,9 Ratio 0,66 Ratio 0,54 Delay 5 min Delay 11 min Delay 13 min 25% Ratio 0,9 Ratio 0,66 Ratio 0,54 Delay 5 min Delay 11 min Delay 13 min The other parameter of the variation which was observed was the oscillation period. Figure 34 represents the response of the mixing system to a perturbation with a period of 60 minutes, without going yet into the quantitative point of view, it can be easily seen how the damping happens predominantly in the larger mixing chest and, to a lesser extent, in the smaller machine chest. 35

38 15% 10% Variation [%] 5% 0% -5% -10% -15% Time [min] Feed Mixing chest outlet Machine chest outlet Wire pit outlet Production Figure 34: Example of output of the standard double-chest mixing system subjected to a oscillating variation in the pulp concentration. As shown in Chapter 1, the Bode plot is a very useful representation to have a quick insight in the frequency response of a system. This graph will be the main tool in showing the effect of all the parameters at play in the simulated board machine. The graph in Figure 35 is the Bode plot for the standard mixing system used in the machine. The chests both had a level of 70% of their maximum volume. To better use the diagram for the purpose of the work, the x-axis is set for wave period rather than frequency, due to the use of perturbations of the same timescale of the residence time of the chests. The dimensionless amplitude ratio is plotted on the vertical axis of the first graph. On the second graph the phase shift is plotted as a function of wave period. It would normally be plotted in units of degrees, but again due to the timescale of the variation, it was decided to plot it in minutes. Analyzing the second graph in Figure 35, it can be seen how the outlet oscillation of the mixing system will be more shifted to the right (delayed) the longer the variation period and vice-versa. 36

39 100,0% Amplitude ratio [-] 10,0% 1,0% 0,1% 0,0% Variation period [min] Phase shift [min] Variation period [min] 10 1 Figure 35: Bode plot for the double-chest layout filled at 70% for a combined average residence time of 14 minutes. The lower part of the graph represents the delay of the signal out of the machine chest. 37

40 3.2 Influence of process layout A very important question was how the mixing system would perform if the layout presented either a double-chest arrangement or a single-chest process layout. In KM 2 both system layouts are present. The top and bottom plies employ a single chest layout while the center ply uses both a machine and a mixing chest placed in series. Both startup and noise rejection abilities were tested for both layouts. Figure 36 and Figure 37 show the different start-up performances. Start-up, and composition changes in general were considered complete when 95% of the final value was reached. Variation [-] 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Time [min] Feed Mixing chest outlet Machine chest outlet wire pit outlet Production Figure 36: Startup of double-chest mixing system, 95% of the final concentration is reached within 37 min. The double-chest layout in Figure 36 reaches 95% of the steady state within 37 minutes. Looking more at the graph in the figure it can be seen how the first unit in the system, i.e. the mixing chest, reaches the 95%-value for the concentration about 6 minutes in advance. The dynamics of the doublechest system are defined very early in the process due to the difference in residence time between the mixing and machine chest (roughly twice the average residence time in the first unit). As a result, the remaining units reach steady state relatively at the same time. The initial delay in the graph is due to the system being set in demand mode. As it was explained in Chapter 2, the first 3 steps of the simulation were used by the software to request the starting value. Figure 37, on the other hand, shows a different story; the threshold value is reached in about 43 minutes. The difference with the previous graphs lies in the different volume of the mixing chest, and consequently a difference in average residence time. The single-chest mixing system was designed, for comparison reasons, to have the same total volume as the combined two-chest solution. As such, the dynamics of the setup would have to be necessarily slower (as seen in Chapter 1 and Chapter 2). However, in this case there is hardly any lag between the mixing stage and the short circulation, as all the units reached 95% of the steady state at relatively the same time. 38