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Heuristic Algorithm for Production Control of an Integrated Pulp and Paper Mill
HEURISTIC ALGORITHM FOR PRODUCTION CONTROL OF AN INTEGRATED PULP AND PAPER MILL K. Leiviska*, H. Komokallio*, H. Aurasmaa** and P. Uronen*** *Unz"verS'ity of Oulu, Department of Process Engz"neenOng, Oulu, Fz"nland **Altim Control Ky, Varkaus, Finland ***Unz"versz"ty of Oulu and IIASA, Vz"enna, Austn'a
Abstract. The work reported here is a part of a larger development project going on in the Division of Control Engineering, University of Oulu in cooperation with some Finnish pulp and paper industry. In this project the development of the hierarchical dynamic proquction control system for an integrated pulp and paper mill is studied. The whole system will include a paper mi 11, pulp lines of the mill, a chemical recovery cycle and the whole energy system of the mi 11. Based on the mathematical models a general simulation program package for the production control was developed. The scheduling is based on repeated simulations and on some simple logical rules for the calculation of the production schedules. The scheduling proceeds iteratively from a given production schedule to a production schedule that satisfies the system contstraints. Keywords. Production control; simulation; heuristic programming; hierarchical systems; pulp and paper mill. INTRODUCTION This study aims to develop a simulation model and a heuristic control strategy that can be used to control the production system of the complex integrated pulp and paper mill. The production schedules are determined for the period of 2... 3 days. The- energy control consideres the balancing of both consumption and the generation of steam and the consumption and the generation of the electric power. In the control of the electric power both the power generated in the power plant of the mi 11 and that to be bought is taken into account.
To use the intermediary storages in order to compensate disturbances and to store energy indirectly ~o that the storages are never empty or flow over.
3.
To assure the required levels of the storages at the end of the scheduling peri od.
4.
To take both the planned shut-downs and the random disturbances into account in advance.
5.
To minimize the costs of energy by an efficient coordination system.
The system must also give following information:
The production control system must provide the operational staff with the production schedules calculated for the scheduling period of 2... 3 days. These production schedules must assure the most economical production taking the capacity of the processes and the constraining storage capacity into account. If the integrated pulp and paper mill system shOWn in Fig. 1 is considered, following targets for the production control system can be given: 1.
2.
1.
What effects the deviations from the optimal production schedules have on the operation?
2.
What is the most advantageous state in the case of random disturbances?
3.
How the planned shut-downs are included in the production schedules?
The overall target of the production control is to maximize the net profit. This can be done either by selecting the net profit function as a performance function (Golemanov, 1972, Golemanov and Koivula, 1973, Tinnis, 1974) or by minimizing the number of production rate changes (Petterson, 1969, 1970, Leiviska and Uronen, 1979 a).
To determine the production schedules in optimal way so that the required produc~ ion schedules of pulp and paper are fulfi lled.
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SIMULATION IN PRODUCTION CONTROL
PROCESS DESCRIPTION
When simulation methods are used in production control the greatest difficulty is in obtaining adequate a priori information so that the best possible production schedule can be obtained. Of course, one can start with an arbitrary production schedule. If all the constraints are fulfilled a feasible production schedule is obtained. If not, another schedule is applied, unti 1 a feasible solution is obtained. This approach has following features:
Let us consider once again the integrated pulp and paper mill presented in Fig. 1. It shows the paper mill with three paper machines, a mechanical pulp mi 11 consisting of a groundwood mill and a refiner pulp mil1,and the sulphate pulp mill. Also a sawmill is considered. Table 1 shows the summary of the process departments and Table 2 the corresponding summary of the intermediary storages. The notations needed in the modelling are also shown in Fig. 1.
1.
A feasible production schedule can easily be obtained, if the user is experienced in the production control of the mill in question.
2.
The solution is, in no way, optimal, only feasible.
3.
I. f there are many a 1ternat i ves to be simulated, the amount of manual work increases very much.
This integrated mill produces both mechanical and chemical pulp. The chemical pulp is produced in the digesting house from the wood chips using white liquor (mainly NaOH and Na2S) as a digesting chemical. Pulp is washed and screened and further bleached in the conventional bleaching plant. The bleac~ ed pulp is used either by the paper machines or by the drying machine. The used chemicals are washed from the pulp in the washing. This solution called weak black liquor is first evaporated to higher solids content and after that burned in the recovery boi1e~ The smelt from the recovery boi ler i~ diI uted to form green liquor (most I y Na2C03). This reacts with ca1siumhydroxide in the causticization plant to sodium hydroxide, white liquor. The chemical losses in the recovery cycle are replaced by make-up chemicals. The recovery boiler produces also considerable amounts of steam.
If a logical, heuristic algorithm is used instead of manual methods, the efficiency of the pure simulation approach is improved. Of course, a lot of experience is required in order to develop this kind of algorithm, too. As for the control strategy especially the bottleneck processes (this means, the processes which are the most critical for the realization of the production schedule) must be taken into account. In order to handle with the random disturbances in this connection, following questions can arise (see a I so Fig. 2): 1.
What is the best target level of the intermediary storage, when the disturbance occurs?
2.
How broad is the available region of the storage level?
3.
How this region is reached, if the level goes outside of it?
The answers might be: 1.
The high target level before the bottleneck process and correspondingly the low target level after it maximize its production.
2.
Random disturbances can be taken into account by selecting suitable available region of the storage level. The safety margins outside this region must be capable to compensate the dominating disturbances. There is, of course, an optimum between the cost of the storage size and the cost of the production rate changes caused by too small storages.
3.
The bottleneck process must not be used to control the storage levels.
The production of mechanical pulp is much simpler as a process. The integrated pulp and paper mi 11 uses a considerable amount of energy. The steam energy consumed in the pulp mill is mostly (80 ... 90 %) produced by the recovery boi 1er. The rest is generated by the auxiliary boiler. The electric power consumed in the pulp mill is produced as a counter pressure power with the turbines using the high pressure steam produced by the recovery boiler. The steam and electric power for the paper mill is produced by the oil burning boilers (primary boilers). Because the groundwood mill and the refinerpu1p mill do not use any steam, enough counter pressure power is not avai 1ab1e, but part of the electric power must be bought. Tables 3, 4 and 5 show the energy balance data of the mill. MATHEMATICAL MODEL It has been shown in Leiviska and Uronen (1979 b), how the system consisting of processes and intermediary storages can be modelled in the state space form
x = B~
+
Cv.
( 1)
Here the control variable u denotes the prod~ction rates of the process departments and x the amount of material in the storage The required production schedules of pulp
Heuristic Algorithm for Production Control
and paper are denoted by the deterministic disturbance variable ~. Now both the states and controls are constrained (2)
(3)
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implemented in a heuristic algorithm which is used in connection with a simulation model and a program that generates production schedules. If the simulations show that the suggested production schedule cannot be achieved without violating the constraints, the algorithm calculates, how the schedule must be changed. The upper level priority rules can, for example, be formulated as follows:
The steam balance can be presented as
s = D~
PRIORITY V:
+ E~
Storage levels must lie in the region
(4)
;Min(t) < ;(t) < ;Max(t)
and correspondingly the power balance as F~ + G~.
P
The upper capacity constraints can never be exceeded
Here S denotes the total steam consumption and P correspondingly the total power consumption.
~(t) : ~Max(t)
S. (t) : S.Max(t)
The variables describing the generation of energy are constrained as
p i Mi n ( t)
I
~ SjMaX(t)
(6)
~ P i (t) ~ P i Max ( t)
(7)
SiMin(t) < Si (t)
The index i denotes the boiler that generates the energy or the amount of power that must be bought. The matrices B, C, D, E, F and G are shown in Appendix 1 together with the values of different constraints. Now we must have
f Si (t)
S (t)
LP. (t)
p(t)
i
I
I
I
P. (t) < P. Max (t) . I
PRIORITY IV: Shut-downs of the processes must be avoided
~(t) ~ ~Min(t) S.(t) ~ S.Min(t) I > I Mi n P. (t) - P. I
I
(t).
PRIORITY I I I: The required levels of the storages at the end of the scheduling period must be reached. PRIORITY I I: Production rate changes must be avoided.
STATEMENT OF THE PROBLEM Priority rules In Introduction some general targets of the production control were presented. It can be seen very easily that the targets do not represent the equal value as for the mill operations. This means that if some of these targets are not fulfilled, severe disturbances occur, for instance, loss of production, loss of energy etc. Some of the targets can, however, be missed without considerable extra costs. These targets can, however, be given a certain order that describes their importance for the mill operations. This order is presented now as a set of priority rules. Upper level priority rules and lower level control strategies are discussed. Upper level priority rules consist of the capactty constraints and the targets presented before. The use of lower level control strategies leads to process coordination. This is described in more detail in the sequel. The priority rules and control strategies are L.S.S.-T*
PRIORITY I: The levels of the intermediary storages must follow some prescribed trajectory. This order of priority must be understood so that the formulated control strategy for a priority never violates any higher priority under normal operation conditions. The upper level priority rules determine also the order of actions followed in order to reach a feasible control strategy. If a feasible control strategy cannot be reached for a priority, say PRIORITY I, in the next phase the production rate changes are allowed, and so on. Control strategy The production rate scheduling and the energy management must be carried out at the same time. The most difficult problem is the production control of the pulp mill, because there the production rate scheduling has a considerable effect on the control of consumption and generation of energy. The recovery boiler must be considered mainly as a
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part of the chemical recovery cycle, and a proper chemical balance must be provided. Because most of the energy used in the pulp mill is produced by the recovery boiler also the energy balance must be kept in mind. The control properties of the recovery boiler as for the compensation of short-term disturbances in the consumption of energy are not adequate. The production rate changes in the recovery boiler have an unfavourable effect on chemical balance, too. Therefore other processes must be preferred for this task. The auxiliary boilers can be used to compensate peak consumptions. During the shut-downs of energy consuming processes, excess steam is available, which cannot be stored directly. The steam can, however, be stored indirectly by producing some steam consuming product (thick liquor, bleached pulp) in excess amounts. This must be done according to the corresponding storage situation. In order to diminish the number of alternatives to respond to different disturbances (so to minimize the computer load) and to obtain a straightforward control, a lower level control strategy is fixed. The purpose of this strategy is to determine the best possible production schedule. In order to get this the following stages are used: 1.
For the determination of a production schedule the order of calculation is chosen, according to which the production schedules of the processes are calculated one by one.
2.
The initial production schedules are calculated based on a priori data.
3.
Simulations are carried out. If the constraints are not violated, the initial production schedule is also an optimal one.
4.
If the initial production schedules are not feasible, these schedules are changed. The priority rules provide the order of actions followed. The rules must be therefore written in mathematical form. This means that if, for example, a storage level restriction is violated, it must be possible to calculate the necessary production rate change to keep the storage level inside the available region.
The production schedules are calculated starting from the bleach plant. Then the calculation proceeds to the digester house and via the evaporator plant to the causticization plant. Finally the production schedules of the groundwood and refiner mechanical pulp mills are calculated. The initial production schedules are based on the average pulp and paper production. The time delays are taken into account. A shut-down decreases the total production of a process during the whole scheduling period. Thus the loss of production during a shut-down must be compensated by
increased production during the intervals, where no disturbances occur. In order to obtain efficient coordination it is of importance to formulate the control strategy in the form of distinct 'control loops'. Figure 1 shows clearly that all storages can be controlled by two production rates. Taking the storage of washed pulp, x , as an example, it can be controlled by 2 the production rate of the washing plant, u , or by the production rate of the bleach ptant, u1. Now, the only possibil ity to control the bleached pulp storage, xl' is to util ize the production rate of the bleach plant. Therefore, in order to avoid conflict situations, the production rate of the washing plant must be selected to control the washed pulp storage. The whole control strategy formulated in this manner is shown in Table 6. In some situations, however, this simple strategy does not succeed in getting feasible production schedules. This is the case when shut-downs or capacity restrictions become c,r it i ca 1. In these si tuat ions it must be possi~le to change the control strategy. The changing of the strategy is also included in the logical, heuristic algorithm. Therefore the solution is found in an iterative way according to the order of calculations, utilizing the priority rules and control strategies. The energy coordination is faci1 itated by determining a production schedule that is as smooth as possible. Thus smooth energy generation is possible too. Because of several alternatives to generate energy in the example mill the optimal energy coordination is obtained using logical rules and the knowledge of how the steam boilers must be operated. The aim is to minimize the energy generation costs. THE PROGRAM PACKAGE Functions of the programs The program package was formulated hierarchically according to Fig. 3. The hierarchical structure was selected in order to describe clearly the information flow inside the simulation system and to diminish the need of changing information between different programs. The program package includes the following options (Komokall io, 1979): 1.
Reading and handling of input data and the overall coordination - coordinator: PCSUPR
2.
Calculation of the production schedule - coordinator: PCPROD
3.
Calculation of the energy generation - coordinator: PCENER
4.
Report i n9 - PCTRAJ, PCTEXT
Heuristic Algorithm for Production Control
The functions of different programs are:
2.
Let us assume a shut-down on the bleach plant, u1. Further let us assume that the shut-down is compensated during the other intervals so that the final state of the storage Xl is reached and the shut-down leads to a violation of the upper 'constraint, x2 Max during interval k. Now, PCPROD makes a decision to change the production rate of the washing plant, u2' during intervals k l ,k 2 •.•
3.
If it is not possible to carry out the production rate change of the washing plant, the storage x2 is tried to be controlled by the control variable with the next highest priority, in this case by the production rate of the bleach plant, ul. Same procedure for ul as described for u2 is carried out during intervals k 1 ,k2, ...k. If all the priority rules (tested automatically in PCPROD) have been examined and there is no other alternative than a shut-down of a process, in this case u2' this is carried out in PCSTOP.
PCSUPR PCPROD
The main program The subroutine. The coordination program for production rate calculations PCMODU The subroutine. Determines the production schedule of a certain process department according to the constraints set by a certain intermediary storage PCSIMl The subroutine. Calculates the levels of the intermediary storages and shows the possible breaking-up of the constraints PCFRCE The subroutine. Checks the production rates PCSTOP The subroutine. Carries out the shut-down of a certain process PCSCHl The subroutine. Determines the initial production schedules based on the required production schedules of pulp and paper PCSIM2 The subroutine. Calculates the total need of energy for the whole mill and the corresponding generation of the electric power The subroutine. The coordination PCENER program for the energy balance calculations PCUNO 1.•. Subroutines. Calculate the generation of PCUN04 energy by the recovery boiler, the auxiliary boiler, the power boiler and the amount of energy to be bought The subroutine. Finds out a nonPCNOZE zero element from the matrix B PCTEXT The subroutine. Print-out as tables PCTRAJ The subroutine. Print-out the trajectories of all variables to be considered PCTtTL The subroutine. Finds out the titles for different print-out options PCZERO The subroutine. Sets the elements of a certain vector to zero The subroutine. Finds out the PCMAXI greatest element of a given vector The most important programs are PCPROD and PCMODU. PCPROD forms the decision to change the production rate of a certain process department. Correspondingly, this new production rate is calculated in PCMODU. Let us take a simple example that describes the control of the washed pulp storage, x2. The production rate of the washing plant, uZ' is chosen as a control variable (Table 6). The scheduling proceeds as follows: 1.
The initial schedules for all the process departments are calculated in PCSCHl based on the average pulp and paper production. This initial schedule includes no production rate changes. It can thus be said to represent PRIORITY I.
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4.
After each calculated production schedule, for one process at a time, algorithm in PCPROD checks if the production schedules so far calculated are acceptable. If they are not, the production schedules are corrected. If there exists no solution to the production scheduling problem, it is informed by PCPROD. All the knowledge concerning the priority rules and the order of calculation together with the weighting factors of the final states of the storages are transferred by a priority matrix. The mechanical pulp mills or the pulp mill can be omitted in the simulation using this priority matrix. Part of the algorithm inp1emented in PCMODU is shown in Appendix 2. The main program PCSUPR acts as the overall coordinator of the mill's operation. After the calculations of the production schedules and the consumption and generation of the steam and power these calculations are checked in PCSUPR. If some inba1ance is found in the energy balance, a decision is made to change the production rates of the process departments. The steam balance in the pulp mill is corrected changing the
K. Leiviska et al.
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production rate of some process department or the rate of the recovery boiler and/or auxiliary boiler. The power balance is controlled by the purchased power or by changing the production rates of the mechanical pulp mills. Proceeding of the simulation Proceeding of the simulation is carried out according to the following sequence: 1.
Read the starting date of the production scheduling. Read the input data and modify them to fit the process mode 1 (PCSUPR).
2.
Calculate the production schedules for the processes (PCPROD, PCMODU ... ).
3.
Calculate the energy demand of the whole mill and the corresponding back pressure power generation (PCSIM2).
4.
Calculate the energy generation of the different steam boilers and the amount of purchased power required (PCENER, PCUNO 1, ..• ,PCUN04) .
5.
If on 1y pu 1p mill i s con side red go to step 7. If only the groundwood and/or mechanical pulp mill (s) are considered, go to step 9. Otherwise go to step 6.
6.
Disconnect the mechanical pulp mills apart from the simulation in order to decrease the computation load using the priority matrix.
7.
Test whether the coordination of the pulp mill and the recovery boiler and t he a ux i 1ia r y bo i 1er s i s good. Ifit i s not acceptable, go to step 8, otherwise to step 9.
8.
Recalculate the production schedule of the pulp mill in order to get the energy consumption and generation in balance. Do stages 3 and 4 and go to step 7.
9.
If on 1y the pu 1p mill i s con side red, go to step 11. Otherwise test whether the coordination of the mechanical pulp mills is acceptable? If it is not, go to step 10, otherwise go to step 11.
10.
Recalculate the production schedule(s) of the groundwood and/or refiner mechanical pulp mill (s) in order to keep the amount of purchased power under the contracted upper limit.
11.
Print out the simulation results. Stop.
SIMULATION EXAMPLE As an simulation example the following problem is examined and solved by the simulation program package. The planned pulp and paper production is presented in Table 7. The planned shut-downs are carried out on the PM 1 and PM 2. Both shut-downs are planned
to last 8 h. There exists also a short repair shut-down of 4 hours on the groundwood pulp mill. In the mechanical pulp mills the target levels of the mechanical pulp storages depend on the time of the day. This is to increase the production rate of the mechanical pulp mills in the night, when more cheap purchased power is available (sawmill is in operation only in the day time). The target level for all the storages at the end of the simulation period (48 h) is 50 %. Simulation interval is 4 h. The results of the simulation are presented in Fig. 4. When examining the simulation results it can be observed that the pulp mill is able to run smoothly. One production rate change on the bleach plant is due to the planned shutdown of the paper machine 1 and the capacity restriction of the storage 1. Production rate changes on the mechanical pulp mills are due to the target levels and the planned shut-down of the groundwood pulp mill. All the target levels at the end of the simulation period are exactly reached. The excess steam generation of the recovery boiler is used in the paper mill. The auxiliary boiler is operated at it's maximum bark burning capacity, so to decrease the need of oil burning in the oil boiler. The changes in the generation of energy are due to the planned shut-downs. There is a considerable need of purchased power during the whole simulation period. Purchased power is available in excess amount in the day time because of the high production rates of the mechanical pulp mills in the night time. The amount of the contracted power could slightly be decreased. Table 8 shows the corresponding computer time and the use of the core memory. Several other simulation runs have been carried out both with the integrated mill and with the pulp mill. Using the example mill described in Leiviska and Uronen (1979 b) the optimal schedules have been achieved. The computer times comparable to those given in Leiviska and Uronen (1979 b) have been achieved, too. CONCLUSION When compared with the optimization methods, the simulation approach has some advantages, namely 1.
It is possible to deal with much more detailed subjects; no limitations because of solution methods.
2.
Random disturbances can be taken into account in a much easier way.
Also some limitations exists:
Heuristic Algorithm for Production Control
1.
The development work of the simulation approach is much more time consuming, than the development work of the optimal control approach.
2.
The amount of a priori process data is considerable. The same is true, however, as for the application of the optimal control approach.
The possibilities of the use of the simulation approach have generally been considered inconvenient because of the non optimal solution and the 1aborous work for getting a feasible solution. The simulation results obtained using the heuristic simulation algorithm described in this paper have, however, shown to be optimal in regarding to the product ion schedu 1es. It is the authors I opinion that the simulation approach can be used as well as an optimal control approach. Comparing with the results gained using a hierarchical algorithm (Leiviska and Uronen 1979 b), it can be said that both approaches show qual itative1y nearly equal performance. The simulation approach gives more versatile possibilities, if the energy management is considered. The computer resources are used in nearly equal amounts and the computer time needed for the simulation is no longer for the simulation approach than for the optimal control approaches (Leiviska and Uronen 1979 b). "The results of this research are very encouraging. Besides the production and energy control of pulp and paper mills there exist adaption possibilities for the simulation approach both in the chemical and petrochemical fields. There is, however, much development work left for the program package for the production and energy control of pulp and paper mills e.g. management of much more comp1 icated stream connections, extending the energy generation, improving the overall coordination, management of very unfavourable bottleneck situations, management of random disturbances, determination of the optimal shut-dewn times, timing of grade changes and maximizing the production of the end products.
Leiviska K., Uronen P., (1979 a). Dynamic optimization of a sulphate mill pulp line. Preprints of IFAC/IFORS Symposium Comparison of Automatic Control and Operational Research Techniques App1 ied to Large Systems Analysis and Control, Toulouse, March 6-8. Leiviska K., Uronen P., (1979 b). Hierarchical control of an integrated pulp and paper mill - principles and examples. PLAIC Report 113. Purdue University, West Lafayette. Petterson B., (1969). Production control of a complex integrated pulp and paper mill. Tappi ~, 11,2155 ... 2159. Petterson B., (1970). Opt i ma 1 product i on schemes coordinating subprocesses in a complex integrated pulp and paper mill. Pulp and Paper Magazine of Canada 71, 5 59 ... 63. Tinnis v., (1974). An optimum production control system. Pulp and Paper Magazine of Canada 12, 7, 84 ... 88. Table 1. Description of the processes in Fig.l. DEPARTMENT
SYMBOL
BLEACH PLANT
u
WASHING PLANT
u
DIGESTER HOUSE
u
2
TYPE
CAP/\C ITY
C/D-E/D/E/D
700 TN BP/D
4 STAGES
630 TN/D
8 DIGESTERS
630 TN/D
5 STAGES
210 TN WATER/H
610 MJ/TN WATER RECOVERY BOILER
u
1100 TN SOLIDS
5
117 MW STEAM CAUSTICIZATION
u
24 MW POWER 80 M3/H WHITE
6
PLANT
LIQUOR
REFINER PULP MILL u GROUNDWOOD MILL PAPER MACHINE PAPER MACHINE 2
Go1emanov L.A., (1972). Systems theoretical approach in the projecting and control of industrial production systems. EKONO Publication 133. Helsinki.
PAPER MACHINE 3 OIL BOILER
Golemanov L.A., Koivu1a E., (1973). Optimal production control and mathematical programming. Paperi ja Puu 12, 2, 53 ... 67.
AUXILIARY BOILER
Komokall io H., (1979). Thesis for M.Sc. (Eng.). University of Oulu, Department of Process Engineering, Finland.
1
3 EVAPORATION PLANT u 4
DRYING MACHINE LITERATURE
557
300 TN/D
7
Ug
400 TN/D
v4 v1 v2
400 TN/D
v
3
FINE PAPER
500 TN/D
PRINTING
200 TN/D
NEWSPAPER
300 TN/D 330 MW STEAM 60 MW POWER 40 MW STEAM 8 MW POWER
80UGHT ELECTRIC POWER ACCORDING TO THE CONTRACT
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K. Leiviska et al..
Table 2. Description of the intermediary storages
Table 6. The control strategy to control the intermediary storages. The symbols refer to Tables 1 and 2.
Storage
Controlled variable
Symbol Capacity Delay with the maximum m3 production rate
Bleached pulp Screened pulp Blow tank Weak black 1 i quor Thick black 1 i quor Green liquor Whi te 1 i quor Groundwood pulp Re fine r pu 1p
xl x 2 x x3 4
1600 2000 600 2000
10.2 10 3.3 9.7
x
600
13.6
700 2000 3000 2000
9.6 30.6
5
x 6 x x7 8 x 9
7.8
Table 7
1T. 7
Table 3. The consumption of energy in the mill using the maximum capacity. All pulp is assumed to be used in the paper machines.
Control variable
The required production schedules of different products for the simulation example.
~-;r;;'c-"::~~;-rr~-F-'aPt-~-DaDe~Der Drying Mach i ne Mach i ne Mach i nt' 1
-~--~C1:--~lOo--'-10-0---TOO----O
Department
Power
2
Steam
3 4
5
MW
6
7
Pulp mi 11 Groundwood mi 11 Refi ner DU 1D mi 11 Paper mi 11 Sawmi 11
16.6 11.2 14.4
99.0 1.5 1.3
32.2 4.4
95.0
7.4 mY
~
Table 4. The generation of energy using the maximum capacity of the mi 11 as a reference. The recovery boiler produces 12.6 MW more than is consumed in the pulp mill. This energy is consumed by the other mills.
Sawmi 11
8
9 10 11 12
,,,,\() 15-22 Mc 22 - 02 Tu 02-06 Tu 06-10 Tu 10-14 Tu 14-18 Tu 18-22 Tu 22-02 We 02-06 We 06-10 We 10-14
100 0 0 100 100 100 100 100 100 100 100
100 100 100 0 0 100 100 100 100 100 100
100 100 100 100 100 1'10 100 100 100 100 100
0 0 0 C 0 0 0 0 0 0 0
100 100 0 0 100 100 100 100 0 0 100 100
Table 8. Computer time and core memory used in the simulation example Core Memory
CODE 11911 words DATA 15576 words Computer Time Calculations 9 secs Tables 1.9 secs Trajectories 29 secs
Steam
Power MW Re cove ry bo i 1er Oi 1 boi 1ers Aux i 1i a ry bo i 1er Bought energy
111.6 70.6 22.0
17. 7 14.3
4.5 42.4
7S":9 Table 5. The maximum capacities of the energy producing. departments.
SAFETY liARGINS
-
TARGET LEVEL
AVAILABLE REGION
Steam
Power MW Recove ry bo i 1er 24 Oil boilers 60 Auxiliary boiler * 8 * Uses bark, wood and oil
117 330
40
Fig. 2. Some notations concerning the control of intermediary storages.
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Heuristic Algorithm for Production Control
PAPER
WOOD
C
V
13 3
HANDLING
IUWMILL
h PROCESS DEPARTMENT
--+
STEAM
AN D
o
POWER
Fig. 1. The simplified flow sheet of the integratEd pulp and paper mill.
Fig. 3. The hierarchical formulation of the programs in the simu12tion program package.
STORAGE TANK
K. Lei viska et al.
560
j (m 3/h)
APPENDIX 1. Definition of matrices B, C, D, E, F and G for the simulation example presented in the text. 0.722 0 0 0 0 0 -1 1.089 0 0 0 0 -1 0 1 0 Q 0 0 1.124 0 -1 0 0 B= 0 0 0 0.213 -1 0 0 0 0 0 1.662 -1 0 0 -0.356 0 0 0.893 0 0 0 0 0 0 0 0 0 0 0 0
C=
-6.509 -1.302 -0.65~ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -30.6 0 -20.5 0
-6.509 0 0 lJ
0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
D=[0.303
0
E=[9.128
8.130
7.383
4.619
1.416]
F=[0.082 0.108
0.076 0.024 0.257]
0.007
0
G=[3
2.6
2.24
APPENDIX 2.
Comment
0.651
0.573
0.61
0
0 0 0 0 0 0 0 0 1
0.087
Umax,j maximum value of the product~on rate of the process k=l
Comment
The algorithm can be used to control the flow of the process j into the tank or out of the tank. Inflow or outflow needs certain sign options. However, these options are not marked when controlling the outflow.
Comment
The first part of the algorithm Calculating of the feasible production schema.
Comment
Storing of u. into auxiliary var i ab 1e u 1 +- 1 un t i 1 n do (1) +-a~~ (1) u aux J k +1
k~ -<-k
k f +k -k +1-9 3 2 j k f is the number of thosQ intervals on which k. is tried to be changed J
Comment
0]
1£ kf
~~.!~.!!!. PCPROD. Not possible to control the tank i by process j
Calculate ~x., the difference between the act~al value of xi (k +1) . or x . 3. and x. . or x mIn, I f In, I ma x, I depending on k
0.023
0.07]
The functioning of subprogram PCMODU. The subprogram PCMODU calculates the production rate of process j according to the storage i..
Let the following indexes be given by th~ production coordination program PCPROD: storage tank process department j total number of time intern vals x . maximum permitted value of max, I the leve1 0f the storage tank i (m 3 ) minimum permitted value of X. • rnl n, I the level of the storage tank i (m 3 ) final state of the level of the storage tank i. This is the state to which ~e want to run the 1eve 1 (m J ) time interval for which k x. (k+l»x . or x.(k+l)< Xl. • i fm~~ri Ior x. ~k+l)~ ml n, I . f kI x fi n, i I -n control matrix B the length of the time inT terval (h) 9. time delay as intervals of J the process department j u. . minimum value of the producmln,J tion rate of the process
is the first time interval
k
1
0
(m /h)-
j
Comment
Comment
for k +-1 .-until k -8 j do uj (k 1) + 1 3 u. (k 1) - ~x. (k +1)/(S . . ·kf·T) J J 3 I ,J ~j(k3+1) is divided equally on ea r 1i e r in te rva 1s
2 Comment
liu. +0 J
summing variable to test the values of u. J
for 1+k
do
until k -9 j 2 3 calculate the number of those time intervals kl 1 on which u.(l»u ma j x, (1) or u. (1)
if liu.=O then go to 3
-
else
if
J
-
for 1+k 2 un t i 1 k -9. -- 3 J do calculate the number of those time intervals k1 2 on which Umin,j< u. (1)
-
for 1+k
until k -9 2 3 j sum liu. equally to u.(l) on those k1 'ftee ' time intetvals 2
Heuristic Algorithm for Production Control
3
561
Calculate the new storage tank levels using u.1s obtained
Comment A feasible scheme has now been calculated
for k
Comment The second part of the algorithm. Decreasing the number of production rate changes. Method: Total sum of the material flow of the process j is kept constant. So we do not change the final state obtained in the first part of the algorithm. Because of somewhat lenghty formulation this part of the algorithm is omitted.
J
+- 1 unt i 1 n do 3 wh i 1ex.I (k 3+ 1) >xmax,1. 0 r x.I (k 3+ 1) < ----X. when mln,1. - k
we accept the schema on intervals 1..• k -1
4
STEA~1
BACl' PREssrRE POl.:Ei\ r,E~ERAT]O~ Ot THE RECOVERY B01LER
r,E~ERAT10t\
OF THE RECOVERY BOILER ) r..l/h
1)1)
r,. TI h
- - -- - - -
0-----------'" o 4'3 GJ /h
r,J/~--------
, ()()~ r - - - - - - - - - -
r_--------
~--------.
o--------~
o
h
48 h
BACK PRESSURE POWER r.ENERATION OF THE AUXIL. BOILER
STEAM GENERATIO~ or THE AUXIL. BOILER
r----------
30 GJ /~-------'{f)
1 Qfj%
r---------
1 no7.
~ - - - - - - - -__-
'\
I
r----------~r---------
~--------.l
r.J / ~
o
r)----------J n----------J
t------------I
o
49 h
4R h
BACK PRESSURE POWER GENERATIOK or THE OIL BOILER
STEAM GENERATION OF THE OIL BOILER (;J/h
XB
L'1
------- r----------
1f)() r . . T / r . - - - - - - - - - -
f)
r,.T/h 0
4S h
0
£";.1
1007.
()
48 h
PL'RCHASED POWER
111
If)
r.J
SOLD POWER
It.
()
lOO:
0
l'5
L'h
U7
\'1
-
~~
\'5
0 Cl
4'3 h
A.
Q
4P h
1')(/::
JL
~
\'1
1 0n! ~---------
_ - - - - - - - - l ------.......- - - - - -
.:.8
48 0
l)
B. Fig. 4. A sample of simulation results. A. Steam and power generation schedules. B. Storage level trajectories and the production rate schedules.
Abstract. The work reported here is a part of a larger development project going on in the Division of Control Engineering, University of Oulu in cooperation with some Finnish pulp and paper industry. In this project the development of the hierarchical dynamic proquction control system for an integrated pulp and paper mill is studied. The whole system will include a paper mi 11, pulp lines of the mill, a chemical recovery cycle and the whole energy system of the mi 11. Based on the mathematical models a general simulation program package for the production control was developed. The scheduling is based on repeated simulations and on some simple logical rules for the calculation of the production schedules. The scheduling proceeds iteratively from a given production schedule to a production schedule that satisfies the system contstraints. Keywords. Production control; simulation; heuristic programming; hierarchical systems; pulp and paper mill. INTRODUCTION This study aims to develop a simulation model and a heuristic control strategy that can be used to control the production system of the complex integrated pulp and paper mill. The production schedules are determined for the period of 2... 3 days. The- energy control consideres the balancing of both consumption and the generation of steam and the consumption and the generation of the electric power. In the control of the electric power both the power generated in the power plant of the mi 11 and that to be bought is taken into account.
To use the intermediary storages in order to compensate disturbances and to store energy indirectly ~o that the storages are never empty or flow over.
3.
To assure the required levels of the storages at the end of the scheduling peri od.
4.
To take both the planned shut-downs and the random disturbances into account in advance.
5.
To minimize the costs of energy by an efficient coordination system.
The system must also give following information:
The production control system must provide the operational staff with the production schedules calculated for the scheduling period of 2... 3 days. These production schedules must assure the most economical production taking the capacity of the processes and the constraining storage capacity into account. If the integrated pulp and paper mill system shOWn in Fig. 1 is considered, following targets for the production control system can be given: 1.
2.
1.
What effects the deviations from the optimal production schedules have on the operation?
2.
What is the most advantageous state in the case of random disturbances?
3.
How the planned shut-downs are included in the production schedules?
The overall target of the production control is to maximize the net profit. This can be done either by selecting the net profit function as a performance function (Golemanov, 1972, Golemanov and Koivula, 1973, Tinnis, 1974) or by minimizing the number of production rate changes (Petterson, 1969, 1970, Leiviska and Uronen, 1979 a).
To determine the production schedules in optimal way so that the required produc~ ion schedules of pulp and paper are fulfi lled.
551
K. Leiviska et al.
552
SIMULATION IN PRODUCTION CONTROL
PROCESS DESCRIPTION
When simulation methods are used in production control the greatest difficulty is in obtaining adequate a priori information so that the best possible production schedule can be obtained. Of course, one can start with an arbitrary production schedule. If all the constraints are fulfilled a feasible production schedule is obtained. If not, another schedule is applied, unti 1 a feasible solution is obtained. This approach has following features:
Let us consider once again the integrated pulp and paper mill presented in Fig. 1. It shows the paper mill with three paper machines, a mechanical pulp mi 11 consisting of a groundwood mill and a refiner pulp mil1,and the sulphate pulp mill. Also a sawmill is considered. Table 1 shows the summary of the process departments and Table 2 the corresponding summary of the intermediary storages. The notations needed in the modelling are also shown in Fig. 1.
1.
A feasible production schedule can easily be obtained, if the user is experienced in the production control of the mill in question.
2.
The solution is, in no way, optimal, only feasible.
3.
I. f there are many a 1ternat i ves to be simulated, the amount of manual work increases very much.
This integrated mill produces both mechanical and chemical pulp. The chemical pulp is produced in the digesting house from the wood chips using white liquor (mainly NaOH and Na2S) as a digesting chemical. Pulp is washed and screened and further bleached in the conventional bleaching plant. The bleac~ ed pulp is used either by the paper machines or by the drying machine. The used chemicals are washed from the pulp in the washing. This solution called weak black liquor is first evaporated to higher solids content and after that burned in the recovery boi1e~ The smelt from the recovery boi ler i~ diI uted to form green liquor (most I y Na2C03). This reacts with ca1siumhydroxide in the causticization plant to sodium hydroxide, white liquor. The chemical losses in the recovery cycle are replaced by make-up chemicals. The recovery boiler produces also considerable amounts of steam.
If a logical, heuristic algorithm is used instead of manual methods, the efficiency of the pure simulation approach is improved. Of course, a lot of experience is required in order to develop this kind of algorithm, too. As for the control strategy especially the bottleneck processes (this means, the processes which are the most critical for the realization of the production schedule) must be taken into account. In order to handle with the random disturbances in this connection, following questions can arise (see a I so Fig. 2): 1.
What is the best target level of the intermediary storage, when the disturbance occurs?
2.
How broad is the available region of the storage level?
3.
How this region is reached, if the level goes outside of it?
The answers might be: 1.
The high target level before the bottleneck process and correspondingly the low target level after it maximize its production.
2.
Random disturbances can be taken into account by selecting suitable available region of the storage level. The safety margins outside this region must be capable to compensate the dominating disturbances. There is, of course, an optimum between the cost of the storage size and the cost of the production rate changes caused by too small storages.
3.
The bottleneck process must not be used to control the storage levels.
The production of mechanical pulp is much simpler as a process. The integrated pulp and paper mi 11 uses a considerable amount of energy. The steam energy consumed in the pulp mill is mostly (80 ... 90 %) produced by the recovery boi 1er. The rest is generated by the auxiliary boiler. The electric power consumed in the pulp mill is produced as a counter pressure power with the turbines using the high pressure steam produced by the recovery boiler. The steam and electric power for the paper mill is produced by the oil burning boilers (primary boilers). Because the groundwood mill and the refinerpu1p mill do not use any steam, enough counter pressure power is not avai 1ab1e, but part of the electric power must be bought. Tables 3, 4 and 5 show the energy balance data of the mill. MATHEMATICAL MODEL It has been shown in Leiviska and Uronen (1979 b), how the system consisting of processes and intermediary storages can be modelled in the state space form
x = B~
+
Cv.
( 1)
Here the control variable u denotes the prod~ction rates of the process departments and x the amount of material in the storage The required production schedules of pulp
Heuristic Algorithm for Production Control
and paper are denoted by the deterministic disturbance variable ~. Now both the states and controls are constrained (2)
(3)
553
implemented in a heuristic algorithm which is used in connection with a simulation model and a program that generates production schedules. If the simulations show that the suggested production schedule cannot be achieved without violating the constraints, the algorithm calculates, how the schedule must be changed. The upper level priority rules can, for example, be formulated as follows:
The steam balance can be presented as
s = D~
PRIORITY V:
+ E~
Storage levels must lie in the region
(4)
;Min(t) < ;(t) < ;Max(t)
and correspondingly the power balance as F~ + G~.
P
The upper capacity constraints can never be exceeded
Here S denotes the total steam consumption and P correspondingly the total power consumption.
~(t) : ~Max(t)
S. (t) : S.Max(t)
The variables describing the generation of energy are constrained as
p i Mi n ( t)
I
~ SjMaX(t)
(6)
~ P i (t) ~ P i Max ( t)
(7)
SiMin(t) < Si (t)
The index i denotes the boiler that generates the energy or the amount of power that must be bought. The matrices B, C, D, E, F and G are shown in Appendix 1 together with the values of different constraints. Now we must have
f Si (t)
S (t)
LP. (t)
p(t)
i
I
I
I
P. (t) < P. Max (t) . I
PRIORITY IV: Shut-downs of the processes must be avoided
~(t) ~ ~Min(t) S.(t) ~ S.Min(t) I > I Mi n P. (t) - P. I
I
(t).
PRIORITY I I I: The required levels of the storages at the end of the scheduling period must be reached. PRIORITY I I: Production rate changes must be avoided.
STATEMENT OF THE PROBLEM Priority rules In Introduction some general targets of the production control were presented. It can be seen very easily that the targets do not represent the equal value as for the mill operations. This means that if some of these targets are not fulfilled, severe disturbances occur, for instance, loss of production, loss of energy etc. Some of the targets can, however, be missed without considerable extra costs. These targets can, however, be given a certain order that describes their importance for the mill operations. This order is presented now as a set of priority rules. Upper level priority rules and lower level control strategies are discussed. Upper level priority rules consist of the capactty constraints and the targets presented before. The use of lower level control strategies leads to process coordination. This is described in more detail in the sequel. The priority rules and control strategies are L.S.S.-T*
PRIORITY I: The levels of the intermediary storages must follow some prescribed trajectory. This order of priority must be understood so that the formulated control strategy for a priority never violates any higher priority under normal operation conditions. The upper level priority rules determine also the order of actions followed in order to reach a feasible control strategy. If a feasible control strategy cannot be reached for a priority, say PRIORITY I, in the next phase the production rate changes are allowed, and so on. Control strategy The production rate scheduling and the energy management must be carried out at the same time. The most difficult problem is the production control of the pulp mill, because there the production rate scheduling has a considerable effect on the control of consumption and generation of energy. The recovery boiler must be considered mainly as a
554
K. Leiviska et al.
part of the chemical recovery cycle, and a proper chemical balance must be provided. Because most of the energy used in the pulp mill is produced by the recovery boiler also the energy balance must be kept in mind. The control properties of the recovery boiler as for the compensation of short-term disturbances in the consumption of energy are not adequate. The production rate changes in the recovery boiler have an unfavourable effect on chemical balance, too. Therefore other processes must be preferred for this task. The auxiliary boilers can be used to compensate peak consumptions. During the shut-downs of energy consuming processes, excess steam is available, which cannot be stored directly. The steam can, however, be stored indirectly by producing some steam consuming product (thick liquor, bleached pulp) in excess amounts. This must be done according to the corresponding storage situation. In order to diminish the number of alternatives to respond to different disturbances (so to minimize the computer load) and to obtain a straightforward control, a lower level control strategy is fixed. The purpose of this strategy is to determine the best possible production schedule. In order to get this the following stages are used: 1.
For the determination of a production schedule the order of calculation is chosen, according to which the production schedules of the processes are calculated one by one.
2.
The initial production schedules are calculated based on a priori data.
3.
Simulations are carried out. If the constraints are not violated, the initial production schedule is also an optimal one.
4.
If the initial production schedules are not feasible, these schedules are changed. The priority rules provide the order of actions followed. The rules must be therefore written in mathematical form. This means that if, for example, a storage level restriction is violated, it must be possible to calculate the necessary production rate change to keep the storage level inside the available region.
The production schedules are calculated starting from the bleach plant. Then the calculation proceeds to the digester house and via the evaporator plant to the causticization plant. Finally the production schedules of the groundwood and refiner mechanical pulp mills are calculated. The initial production schedules are based on the average pulp and paper production. The time delays are taken into account. A shut-down decreases the total production of a process during the whole scheduling period. Thus the loss of production during a shut-down must be compensated by
increased production during the intervals, where no disturbances occur. In order to obtain efficient coordination it is of importance to formulate the control strategy in the form of distinct 'control loops'. Figure 1 shows clearly that all storages can be controlled by two production rates. Taking the storage of washed pulp, x , as an example, it can be controlled by 2 the production rate of the washing plant, u , or by the production rate of the bleach ptant, u1. Now, the only possibil ity to control the bleached pulp storage, xl' is to util ize the production rate of the bleach plant. Therefore, in order to avoid conflict situations, the production rate of the washing plant must be selected to control the washed pulp storage. The whole control strategy formulated in this manner is shown in Table 6. In some situations, however, this simple strategy does not succeed in getting feasible production schedules. This is the case when shut-downs or capacity restrictions become c,r it i ca 1. In these si tuat ions it must be possi~le to change the control strategy. The changing of the strategy is also included in the logical, heuristic algorithm. Therefore the solution is found in an iterative way according to the order of calculations, utilizing the priority rules and control strategies. The energy coordination is faci1 itated by determining a production schedule that is as smooth as possible. Thus smooth energy generation is possible too. Because of several alternatives to generate energy in the example mill the optimal energy coordination is obtained using logical rules and the knowledge of how the steam boilers must be operated. The aim is to minimize the energy generation costs. THE PROGRAM PACKAGE Functions of the programs The program package was formulated hierarchically according to Fig. 3. The hierarchical structure was selected in order to describe clearly the information flow inside the simulation system and to diminish the need of changing information between different programs. The program package includes the following options (Komokall io, 1979): 1.
Reading and handling of input data and the overall coordination - coordinator: PCSUPR
2.
Calculation of the production schedule - coordinator: PCPROD
3.
Calculation of the energy generation - coordinator: PCENER
4.
Report i n9 - PCTRAJ, PCTEXT
Heuristic Algorithm for Production Control
The functions of different programs are:
2.
Let us assume a shut-down on the bleach plant, u1. Further let us assume that the shut-down is compensated during the other intervals so that the final state of the storage Xl is reached and the shut-down leads to a violation of the upper 'constraint, x2 Max during interval k. Now, PCPROD makes a decision to change the production rate of the washing plant, u2' during intervals k l ,k 2 •.•
3.
If it is not possible to carry out the production rate change of the washing plant, the storage x2 is tried to be controlled by the control variable with the next highest priority, in this case by the production rate of the bleach plant, ul. Same procedure for ul as described for u2 is carried out during intervals k 1 ,k2, ...
PCSUPR PCPROD
The main program The subroutine. The coordination program for production rate calculations PCMODU The subroutine. Determines the production schedule of a certain process department according to the constraints set by a certain intermediary storage PCSIMl The subroutine. Calculates the levels of the intermediary storages and shows the possible breaking-up of the constraints PCFRCE The subroutine. Checks the production rates PCSTOP The subroutine. Carries out the shut-down of a certain process PCSCHl The subroutine. Determines the initial production schedules based on the required production schedules of pulp and paper PCSIM2 The subroutine. Calculates the total need of energy for the whole mill and the corresponding generation of the electric power The subroutine. The coordination PCENER program for the energy balance calculations PCUNO 1.•. Subroutines. Calculate the generation of PCUN04 energy by the recovery boiler, the auxiliary boiler, the power boiler and the amount of energy to be bought The subroutine. Finds out a nonPCNOZE zero element from the matrix B PCTEXT The subroutine. Print-out as tables PCTRAJ The subroutine. Print-out the trajectories of all variables to be considered PCTtTL The subroutine. Finds out the titles for different print-out options PCZERO The subroutine. Sets the elements of a certain vector to zero The subroutine. Finds out the PCMAXI greatest element of a given vector The most important programs are PCPROD and PCMODU. PCPROD forms the decision to change the production rate of a certain process department. Correspondingly, this new production rate is calculated in PCMODU. Let us take a simple example that describes the control of the washed pulp storage, x2. The production rate of the washing plant, uZ' is chosen as a control variable (Table 6). The scheduling proceeds as follows: 1.
The initial schedules for all the process departments are calculated in PCSCHl based on the average pulp and paper production. This initial schedule includes no production rate changes. It can thus be said to represent PRIORITY I.
555
4.
After each calculated production schedule, for one process at a time, algorithm in PCPROD checks if the production schedules so far calculated are acceptable. If they are not, the production schedules are corrected. If there exists no solution to the production scheduling problem, it is informed by PCPROD. All the knowledge concerning the priority rules and the order of calculation together with the weighting factors of the final states of the storages are transferred by a priority matrix. The mechanical pulp mills or the pulp mill can be omitted in the simulation using this priority matrix. Part of the algorithm inp1emented in PCMODU is shown in Appendix 2. The main program PCSUPR acts as the overall coordinator of the mill's operation. After the calculations of the production schedules and the consumption and generation of the steam and power these calculations are checked in PCSUPR. If some inba1ance is found in the energy balance, a decision is made to change the production rates of the process departments. The steam balance in the pulp mill is corrected changing the
K. Leiviska et al.
556
production rate of some process department or the rate of the recovery boiler and/or auxiliary boiler. The power balance is controlled by the purchased power or by changing the production rates of the mechanical pulp mills. Proceeding of the simulation Proceeding of the simulation is carried out according to the following sequence: 1.
Read the starting date of the production scheduling. Read the input data and modify them to fit the process mode 1 (PCSUPR).
2.
Calculate the production schedules for the processes (PCPROD, PCMODU ... ).
3.
Calculate the energy demand of the whole mill and the corresponding back pressure power generation (PCSIM2).
4.
Calculate the energy generation of the different steam boilers and the amount of purchased power required (PCENER, PCUNO 1, ..• ,PCUN04) .
5.
If on 1y pu 1p mill i s con side red go to step 7. If only the groundwood and/or mechanical pulp mill (s) are considered, go to step 9. Otherwise go to step 6.
6.
Disconnect the mechanical pulp mills apart from the simulation in order to decrease the computation load using the priority matrix.
7.
Test whether the coordination of the pulp mill and the recovery boiler and t he a ux i 1ia r y bo i 1er s i s good. Ifit i s not acceptable, go to step 8, otherwise to step 9.
8.
Recalculate the production schedule of the pulp mill in order to get the energy consumption and generation in balance. Do stages 3 and 4 and go to step 7.
9.
If on 1y the pu 1p mill i s con side red, go to step 11. Otherwise test whether the coordination of the mechanical pulp mills is acceptable? If it is not, go to step 10, otherwise go to step 11.
10.
Recalculate the production schedule(s) of the groundwood and/or refiner mechanical pulp mill (s) in order to keep the amount of purchased power under the contracted upper limit.
11.
Print out the simulation results. Stop.
SIMULATION EXAMPLE As an simulation example the following problem is examined and solved by the simulation program package. The planned pulp and paper production is presented in Table 7. The planned shut-downs are carried out on the PM 1 and PM 2. Both shut-downs are planned
to last 8 h. There exists also a short repair shut-down of 4 hours on the groundwood pulp mill. In the mechanical pulp mills the target levels of the mechanical pulp storages depend on the time of the day. This is to increase the production rate of the mechanical pulp mills in the night, when more cheap purchased power is available (sawmill is in operation only in the day time). The target level for all the storages at the end of the simulation period (48 h) is 50 %. Simulation interval is 4 h. The results of the simulation are presented in Fig. 4. When examining the simulation results it can be observed that the pulp mill is able to run smoothly. One production rate change on the bleach plant is due to the planned shutdown of the paper machine 1 and the capacity restriction of the storage 1. Production rate changes on the mechanical pulp mills are due to the target levels and the planned shut-down of the groundwood pulp mill. All the target levels at the end of the simulation period are exactly reached. The excess steam generation of the recovery boiler is used in the paper mill. The auxiliary boiler is operated at it's maximum bark burning capacity, so to decrease the need of oil burning in the oil boiler. The changes in the generation of energy are due to the planned shut-downs. There is a considerable need of purchased power during the whole simulation period. Purchased power is available in excess amount in the day time because of the high production rates of the mechanical pulp mills in the night time. The amount of the contracted power could slightly be decreased. Table 8 shows the corresponding computer time and the use of the core memory. Several other simulation runs have been carried out both with the integrated mill and with the pulp mill. Using the example mill described in Leiviska and Uronen (1979 b) the optimal schedules have been achieved. The computer times comparable to those given in Leiviska and Uronen (1979 b) have been achieved, too. CONCLUSION When compared with the optimization methods, the simulation approach has some advantages, namely 1.
It is possible to deal with much more detailed subjects; no limitations because of solution methods.
2.
Random disturbances can be taken into account in a much easier way.
Also some limitations exists:
Heuristic Algorithm for Production Control
1.
The development work of the simulation approach is much more time consuming, than the development work of the optimal control approach.
2.
The amount of a priori process data is considerable. The same is true, however, as for the application of the optimal control approach.
The possibilities of the use of the simulation approach have generally been considered inconvenient because of the non optimal solution and the 1aborous work for getting a feasible solution. The simulation results obtained using the heuristic simulation algorithm described in this paper have, however, shown to be optimal in regarding to the product ion schedu 1es. It is the authors I opinion that the simulation approach can be used as well as an optimal control approach. Comparing with the results gained using a hierarchical algorithm (Leiviska and Uronen 1979 b), it can be said that both approaches show qual itative1y nearly equal performance. The simulation approach gives more versatile possibilities, if the energy management is considered. The computer resources are used in nearly equal amounts and the computer time needed for the simulation is no longer for the simulation approach than for the optimal control approaches (Leiviska and Uronen 1979 b). "The results of this research are very encouraging. Besides the production and energy control of pulp and paper mills there exist adaption possibilities for the simulation approach both in the chemical and petrochemical fields. There is, however, much development work left for the program package for the production and energy control of pulp and paper mills e.g. management of much more comp1 icated stream connections, extending the energy generation, improving the overall coordination, management of very unfavourable bottleneck situations, management of random disturbances, determination of the optimal shut-dewn times, timing of grade changes and maximizing the production of the end products.
Leiviska K., Uronen P., (1979 a). Dynamic optimization of a sulphate mill pulp line. Preprints of IFAC/IFORS Symposium Comparison of Automatic Control and Operational Research Techniques App1 ied to Large Systems Analysis and Control, Toulouse, March 6-8. Leiviska K., Uronen P., (1979 b). Hierarchical control of an integrated pulp and paper mill - principles and examples. PLAIC Report 113. Purdue University, West Lafayette. Petterson B., (1969). Production control of a complex integrated pulp and paper mill. Tappi ~, 11,2155 ... 2159. Petterson B., (1970). Opt i ma 1 product i on schemes coordinating subprocesses in a complex integrated pulp and paper mill. Pulp and Paper Magazine of Canada 71, 5 59 ... 63. Tinnis v., (1974). An optimum production control system. Pulp and Paper Magazine of Canada 12, 7, 84 ... 88. Table 1. Description of the processes in Fig.l. DEPARTMENT
SYMBOL
BLEACH PLANT
u
WASHING PLANT
u
DIGESTER HOUSE
u
2
TYPE
CAP/\C ITY
C/D-E/D/E/D
700 TN BP/D
4 STAGES
630 TN/D
8 DIGESTERS
630 TN/D
5 STAGES
210 TN WATER/H
610 MJ/TN WATER RECOVERY BOILER
u
1100 TN SOLIDS
5
117 MW STEAM CAUSTICIZATION
u
24 MW POWER 80 M3/H WHITE
6
PLANT
LIQUOR
REFINER PULP MILL u GROUNDWOOD MILL PAPER MACHINE PAPER MACHINE 2
Go1emanov L.A., (1972). Systems theoretical approach in the projecting and control of industrial production systems. EKONO Publication 133. Helsinki.
PAPER MACHINE 3 OIL BOILER
Golemanov L.A., Koivu1a E., (1973). Optimal production control and mathematical programming. Paperi ja Puu 12, 2, 53 ... 67.
AUXILIARY BOILER
Komokall io H., (1979). Thesis for M.Sc. (Eng.). University of Oulu, Department of Process Engineering, Finland.
1
3 EVAPORATION PLANT u 4
DRYING MACHINE LITERATURE
557
300 TN/D
7
Ug
400 TN/D
v4 v1 v2
400 TN/D
v
3
FINE PAPER
500 TN/D
PRINTING
200 TN/D
NEWSPAPER
300 TN/D 330 MW STEAM 60 MW POWER 40 MW STEAM 8 MW POWER
80UGHT ELECTRIC POWER ACCORDING TO THE CONTRACT
558
K. Leiviska et al..
Table 2. Description of the intermediary storages
Table 6. The control strategy to control the intermediary storages. The symbols refer to Tables 1 and 2.
Storage
Controlled variable
Symbol Capacity Delay with the maximum m3 production rate
Bleached pulp Screened pulp Blow tank Weak black 1 i quor Thick black 1 i quor Green liquor Whi te 1 i quor Groundwood pulp Re fine r pu 1p
xl x 2 x x3 4
1600 2000 600 2000
10.2 10 3.3 9.7
x
600
13.6
700 2000 3000 2000
9.6 30.6
5
x 6 x x7 8 x 9
7.8
Table 7
1T. 7
Table 3. The consumption of energy in the mill using the maximum capacity. All pulp is assumed to be used in the paper machines.
Control variable
The required production schedules of different products for the simulation example.
~-;r;;'c-"::~~;-rr~-F-'aPt-~-DaDe~Der Drying Mach i ne Mach i ne Mach i nt' 1
-~--~C1:--~lOo--'-10-0---TOO----O
Department
Power
2
Steam
3 4
5
MW
6
7
Pulp mi 11 Groundwood mi 11 Refi ner DU 1D mi 11 Paper mi 11 Sawmi 11
16.6 11.2 14.4
99.0 1.5 1.3
32.2 4.4
95.0
7.4 mY
~
Table 4. The generation of energy using the maximum capacity of the mi 11 as a reference. The recovery boiler produces 12.6 MW more than is consumed in the pulp mill. This energy is consumed by the other mills.
Sawmi 11
8
9 10 11 12
,,,,\() 15-22 Mc 22 - 02 Tu 02-06 Tu 06-10 Tu 10-14 Tu 14-18 Tu 18-22 Tu 22-02 We 02-06 We 06-10 We 10-14
100 0 0 100 100 100 100 100 100 100 100
100 100 100 0 0 100 100 100 100 100 100
100 100 100 100 100 1'10 100 100 100 100 100
0 0 0 C 0 0 0 0 0 0 0
100 100 0 0 100 100 100 100 0 0 100 100
Table 8. Computer time and core memory used in the simulation example Core Memory
CODE 11911 words DATA 15576 words Computer Time Calculations 9 secs Tables 1.9 secs Trajectories 29 secs
Steam
Power MW Re cove ry bo i 1er Oi 1 boi 1ers Aux i 1i a ry bo i 1er Bought energy
111.6 70.6 22.0
17. 7 14.3
4.5 42.4
7S":9 Table 5. The maximum capacities of the energy producing. departments.
SAFETY liARGINS
-
TARGET LEVEL
AVAILABLE REGION
Steam
Power MW Recove ry bo i 1er 24 Oil boilers 60 Auxiliary boiler * 8 * Uses bark, wood and oil
117 330
40
Fig. 2. Some notations concerning the control of intermediary storages.
559
Heuristic Algorithm for Production Control
PAPER
WOOD
C
V
13 3
HANDLING
IUWMILL
h PROCESS DEPARTMENT
--+
STEAM
AN D
o
POWER
Fig. 1. The simplified flow sheet of the integratEd pulp and paper mill.
Fig. 3. The hierarchical formulation of the programs in the simu12tion program package.
STORAGE TANK
K. Lei viska et al.
560
j (m 3/h)
APPENDIX 1. Definition of matrices B, C, D, E, F and G for the simulation example presented in the text. 0.722 0 0 0 0 0 -1 1.089 0 0 0 0 -1 0 1 0 Q 0 0 1.124 0 -1 0 0 B= 0 0 0 0.213 -1 0 0 0 0 0 1.662 -1 0 0 -0.356 0 0 0.893 0 0 0 0 0 0 0 0 0 0 0 0
C=
-6.509 -1.302 -0.65~ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -30.6 0 -20.5 0
-6.509 0 0 lJ
0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
D=[0.303
0
E=[9.128
8.130
7.383
4.619
1.416]
F=[0.082 0.108
0.076 0.024 0.257]
0.007
0
G=[3
2.6
2.24
APPENDIX 2.
Comment
0.651
0.573
0.61
0
0 0 0 0 0 0 0 0 1
0.087
Umax,j maximum value of the product~on rate of the process k=l
Comment
The algorithm can be used to control the flow of the process j into the tank or out of the tank. Inflow or outflow needs certain sign options. However, these options are not marked when controlling the outflow.
Comment
The first part of the algorithm Calculating of the feasible production schema.
Comment
Storing of u. into auxiliary var i ab 1e u 1 +- 1 un t i 1 n do (1) +-a~~ (1) u aux J k +1
k~ -<-k
k f +k -k +1-9 3 2 j k f is the number of thosQ intervals on which k. is tried to be changed J
Comment
0]
1£ kf
~~.!~.!!!. PCPROD. Not possible to control the tank i by process j
Calculate ~x., the difference between the act~al value of xi (k +1) . or x . 3. and x. . or x mIn, I f In, I ma x, I depending on k
0.023
0.07]
The functioning of subprogram PCMODU. The subprogram PCMODU calculates the production rate of process j according to the storage i..
Let the following indexes be given by th~ production coordination program PCPROD: storage tank process department j total number of time intern vals x . maximum permitted value of max, I the leve1 0f the storage tank i (m 3 ) minimum permitted value of X. • rnl n, I the level of the storage tank i (m 3 ) final state of the level of the storage tank i. This is the state to which ~e want to run the 1eve 1 (m J ) time interval for which k x. (k+l»x . or x.(k+l)< Xl. • i fm~~ri Ior x. ~k+l)~ ml n, I . f kI x fi n, i I -n control matrix B the length of the time inT terval (h) 9. time delay as intervals of J the process department j u. . minimum value of the producmln,J tion rate of the process
is the first time interval
k
1
0
(m /h)-
j
Comment
Comment
for k +-1 .-until k -8 j do uj (k 1) + 1 3 u. (k 1) - ~x. (k +1)/(S . . ·kf·T) J J 3 I ,J ~j(k3+1) is divided equally on ea r 1i e r in te rva 1s
2 Comment
liu. +0 J
summing variable to test the values of u. J
for 1+k
do
until k -9 j 2 3 calculate the number of those time intervals kl 1 on which u.(l»u ma j x, (1) or u. (1)
if liu.=O then go to 3
-
else
if
J
-
for 1+k 2 un t i 1 k -9. -- 3 J do calculate the number of those time intervals k1 2 on which Umin,j< u. (1)
-
for 1+k
until k -9 2 3 j sum liu. equally to u.(l) on those k1 'ftee ' time intetvals 2
Heuristic Algorithm for Production Control
3
561
Calculate the new storage tank levels using u.1s obtained
Comment A feasible scheme has now been calculated
for k
Comment The second part of the algorithm. Decreasing the number of production rate changes. Method: Total sum of the material flow of the process j is kept constant. So we do not change the final state obtained in the first part of the algorithm. Because of somewhat lenghty formulation this part of the algorithm is omitted.
J
+- 1 unt i 1 n do 3 wh i 1ex.I (k 3+ 1) >xmax,1. 0 r x.I (k 3+ 1) < ----X. when mln,1. - k
we accept the schema on intervals 1..• k -1
4
STEA~1
BACl' PREssrRE POl.:Ei\ r,E~ERAT]O~ Ot THE RECOVERY B01LER
r,E~ERAT10t\
OF THE RECOVERY BOILER ) r..l/h
1)1)
r,. TI h
- - -- - - -
0-----------'" o 4'3 GJ /h
r,J/~--------
, ()()~ r - - - - - - - - - -
r_--------
~--------.
o--------~
o
h
48 h
BACK PRESSURE POWER r.ENERATION OF THE AUXIL. BOILER
STEAM GENERATIO~ or THE AUXIL. BOILER
r----------
30 GJ /~-------'{f)
1 Qfj%
r---------
1 no7.
~ - - - - - - - -__-
'\
I
r----------~r---------
~--------.l
r.J / ~
o
r)----------J n----------J
t------------I
o
49 h
4R h
BACK PRESSURE POWER GENERATIOK or THE OIL BOILER
STEAM GENERATION OF THE OIL BOILER (;J/h
XB
L'1
------- r----------
1f)() r . . T / r . - - - - - - - - - -
f)
r,.T/h 0
4S h
0
£";.1
1007.
()
48 h
PL'RCHASED POWER
111
If)
r.J
SOLD POWER
It.
()
lOO:
0
l'5
L'h
U7
\'1
-
~~
\'5
0 Cl
4'3 h
A.
Q
4P h
1')(/::
JL
~
\'1
1 0n! ~---------
_ - - - - - - - - l ------.......- - - - - -
.:.8
48 0
l)
B. Fig. 4. A sample of simulation results. A. Steam and power generation schedules. B. Storage level trajectories and the production rate schedules.