1. Field of Invention
The present invention relates to a method and a system for controlling a paper machine, wherein a dryer is controlled by predicting the moisture percentage of a web at a dryer part inlet and also predicting the dryer's steam pressure according to the predicted moisture percentage.
2. Description of Prior Art
FIG. 1 is a schematic view showing the configuration of a typical paper machine. In the figure, raw pulp is discharged from a stock inlet 81 to a wire part 82. The wire part 82 is moved in the direction of arrow A by means of rotating rolls 821. The raw pulp discharged onto the wire part 82 is subjected to drainage so as to form a web (that is paper). The web thus formed is transferred to a press part 83 for further water drainage.
The web subjected to water drainage at the press part 83 is transferred to a pre-dryer 84. A multitude of steam drums 841 are disposed in the pre-dryer 84 and heated by steam introduced thereinto. The web is wound around the steam drums as it is moved forward, so that the web is drived until a given moisture percentage is reached.
The dried web is subjected to a sizing process, such as application of a sizing agent (coating agent) at a size press 85; is further dried by an after-dryer 86; and is then take up as a product indicated by numeral 87. It should be noted that the after-dryer 86 is configured in the same way as the pre-dryer 84.
Numerals 88 and 89 denote BM systems, both of which detect the basis weight, moisture percentage, and other data items of the web as it comes out of the pre-dryer 84 and after-dryer 86, respectively. The values of data items thus detected are input to a control apparatus not shown in the figure. The control apparatus controls the amount of raw pulp discharged onto the wire part 82 or the amount of steam introduced into the steam drums of the pre-dryer 84 and after-dryer 86, as well as the machine speed and other parameters, so that the product in question complies with predetermined specifications. Grade change control whereby different types of product are produced is also practiced commonly.
In grade change control, any product obtained during the time of grade change, wherein a switch is made to another type of product, will be treated as broke, i.e., non-standard paper. Therefore, the duration of grade change must be minimized in order to increase operation efficiency. To solve this problem, an invention of a method of predicting a steam pressure setpoint after grade change by simulation is described in the specification of U.S. Pat. No. 3,094,798.
Now, the aforementioned invention is described briefly.
The invention described in the specification of U.S. Pat. No. 3,094,798 uses an iron model wherein the steam drums of the pre-dryer 84 and after-dryer 86 are simplified into a planar form. In the model, the state of contact among the steam drum, web, and canvas wound continuously round the steam drums is classified into five patterns. Then, the heat-transfer differential equation of each pattern is derived and converted to a difference equation, so that a steam pressure setpoint after grade change is predicted by solving the difference equation.
For convenience, the numbering of the equations in this specification are 5-13 and 18-23. The numbers 1-4 and 14-17 have been omitted.
The heat-transfer differential equations of a pattern wherein the steam drum, web and canvas are in contact with each other in this order are represented as equations 5 to 7 below.                                                         L              D                        ·                          ρ              D                        ·                          C              D                                ⁢                                    ⅆ                                                T                  1                                ⁡                                  (                  t                  )                                                                    ⅆ              t                                      =                                            h              S                        ·                          (                                                                    T                    S                                    ⁡                                      (                    t                    )                                                  -                                                      T                    1                                    ⁡                                      (                    t                    )                                                              )                                -                                    h              DW                        ·                          (                                                                    T                    1                                    ⁡                                      (                    t                    )                                                  -                                                      T                    2                                    ⁡                                      (                    t                    )                                                              )                                                          (        5        )                                                                                                                          L                    W                                    ·                                      ρ                    W                                    ·                                      C                    W                                                  ⁢                                                      ⅆ                                                                  T                        2                                            ⁡                                              (                        t                        )                                                                                                  ⅆ                    t                                                              =                            ⁢                                                                    h                    DW                                    ·                                      (                                                                                            T                          1                                                ⁡                                                  (                          t                          )                                                                    -                                                                        T                          2                                                ⁡                                                  (                          t                          )                                                                                      )                                                  -                                                                                                      ⁢                                                                    -                                          h                      WC                                                        ·                                      (                                                                                            T                          2                                                ⁡                                                  (                          t                          )                                                                    -                                                                        T                          3                                                ⁡                                                  (                          t                          )                                                                                      )                                                  ⁢                                  Evapo                  ⁡                                      (                                                                  T                        2                                            ,                                              T                        W                                                              )                                                                                                          (        6        )                                                                    L              C                        ·                          ρ              C                        ·                          C              C                                ⁢                                    ⅆ                                                T                  3                                ⁡                                  (                  t                  )                                                                    ⅆ              t                                      =                                            h              WC                        ·                          (                                                                    T                    2                                    ⁡                                      (                    t                    )                                                  -                                                      T                    3                                    ⁡                                      (                    t                    )                                                              )                                -                                    h              a                        ·                          (                                                                    T                    3                                    ⁡                                      (                    t                    )                                                  -                                                      T                    a                                    ⁡                                      (                    t                    )                                                              )                                                          (        7        )            
The meanings of the parameters included in equations 5 to 7 are as follows.
LD:Drum thickness (m)LW:Web thickness (m)LC:Canvas thickness (m)Ts:Steam temperature within drum (° C.)T1:Drum's surface temperature (° C.)T2:Web (paper) temperature (° C.)T3:Canvas temperature (° C.)Ta:Dry-bulb temperature of air within hood (° C.)CD:Drum's specific heat (kJ/(kg · ° C.))CW:Web's (paper's) specific heat (kJ/(kg · ° C.))CC:Canvas' specific heat (kJ/(kg · ° C.))ρD:Drum's density (kg/m3)ρW:Web's (paper's) density (kg/m3)ρC:Canvas' density (kg/m3)hS:Coefficient of heat transfer between steam within drum and drumsurface (kJ/(m2 · sec · ° C.))hDW:Coefficient of heat transfer between drum surface and web(kJ/(m2 · sec · ° C.))hWC:Coefficient of heat transfer between web surface and canvas(kJ/(m2 · sec · ° C.))ha:Coefficient of heat transfer between canvas and air within hood(kJ/(m · sec · ° C.))
FIG. 2 is a table that summarizes the above-listed parameters.
The term Evapo(T2, TW) in equation 6 is a function representing the amount of heat of evaporation removed from the web as the result of moisture evaporation, and is given by equation 8 below.
 Evapo(T2, Tw)=V(MPABS)·K·(P(T2)−P(Tw))·SB(T2)(kJ/(m2·sec))  (8)
where
    P(T)=Saturation vapor pressure (kPa) at temperature T (° C.)    SB(T)=Heat of evaporation (kJ/H2Okg) at temperature T (° C.)    TW=Wet-bulb temperature of air within hood (° C.)    V(MPABS)=Function representing moisture evaporation intensity at absolute moisture percentage MPABS, where 0.0≦V(MPABS)≦1.0 (dimensionless)    K=Drying rate coefficient (H2Okg/(m2·sec·kPa)).
Although heat-transfer differential equations for patterns of contact other than those mentioned above are also given by the invention described in the specification of U.S. Pat. No. 3,094,798, these equations are omitted here to avoid complication.
In differential equations 5 to 7 discussed earlier, a length of time is segmented into time intervals Δt, which is determined by the machine speed, circumference of a steam drum, and other data items, so that a difference equation is derived and the numeric solution thereof is obtained. Since the web moves from the upstream side to the downstream side of the paper machine as time elapses, it is possible to calculate the web temperature at the steam drum by numerically solving the difference equation.
From equation 8, EvapoMP(T2, TW)(H2Okg/(m2·sec)), which is the amount of moisture evaporated from the web per unit area and unit time, can be represented by equation 9 below.EvapoMP(T2, TW)=V(MPABS)·K·(P(T2)−P(Tw))(H2Okg/(m2·sec))  (9)
By using this equation, it is possible to calculate the absolute moisture percentage MPABS(j) (j=1, . . . , N) of the web after the lapse of the incremental time interval Δt as shown in equation 10 below.                                           MP            ABS                    ⁡                      (                          j              +              1                        )                          =                                            MP              ABS                        ⁡                          (              j              )                                -                                                                      10                  3                                ·                                  EvapoMP                  ⁡                                      (                                                                  T                        2                                            ,                                              T                        W                                                              )                                                  ·                Δ                            ⁢                                                           ⁢              t                        BD                                              (        10        )            where    BD=Bone-dry basis weight(g/m2)    Δt=Incremental time interval (sec)    MPABS(j) (j=1, . . . , N)=Absolute moisture percentage (%) at mesh division j
From this absolute moisture percentage, it is possible to calculate the (relative) moisture percentage MP(j) (j=1, . . . , N) ( %) as shown in equation 11 below.                               MP          ⁡                      (            j            )                          =                              100            ·                                                            MP                  ABS                                ⁡                                  (                  j                  )                                                            1                +                                                      MP                    ABS                                    ⁡                                      (                    j                    )                                                                                ⁢                                           ⁢                      (            %            )                                              (        11        )            where    MP(j) (j=1, . . . , N)=Relative moisture percentage (%) at mesh division j
FIG. 3 is a flowchart representing the algorithm of a steady-state simulation using equations 5 to 11. In the first step, the current operation status data, such as the current machine speed (m/min), basis weight setpoint (g/m2), and moisture percentage setpoint (%), are acquired. In the second step, the incremental time interval Δt for differential calculations is determined from the machine speed, drum's circumference, and other data items. In the third step, the steam temperature Ts(j) (j=1, . . . , N) within the drum is calculated from the current dryer steam pressure setpoint by using a saturation vapor pressure curve. Note that N is the number of mesh divisions.
In a further step, equations 5 to 11 and the difference equations derived therefrom are used to calculate the drum temperature T1(j) (j=1, . . . , N), web temperature T2(j) (j=1, . . . , N), canvas temperature T3(j) (j=1, . . . , N), and web's final moisture percentage MP(j) (j=1, . . . , N). In yet a further step, a judgment is made on convergence between the web's relative moisture percentage MP(N) and actual measured value MPMEASURE provided by a moisture sensor at a final cylinder. Convergence has been reached if the absolute value of the difference between MP(N) and MPMEASURE is smaller than the given value EP.
If convergence has not yet been reached, the drying rate coefficient K is corrected by ΔK to calculate the drum temperature, web temperature, canvas temperature, and web's relative moisture percentage once again. When convergence has been reached, the drying rate coefficient K, drum temperature T1(j), web temperature T2(j), canvas temperature T3(j), and web's moisture percentage MP(j) are fixed to their values at that moment, and the steady-state simulation ends.
For a dryer part consisting of pre-dryer and after-dryer parts, it is also acceptable to calculate the moisture percentage at an after-dryer outlet as the final moisture percentage. Alternatively, moisture percentages at the pre-dryer and after-dryer outlets may be defined as the final moisture percentages. In the latter case, a convergence calculation should be made for each of the dryer parts.
In the steady-state simulation heretofore discussed, the drying rate coefficient K is adjusted so that the absolute moisture percentage at the final cylinder is approximated to the actual measured value. Next, a simulation of steam pressure prediction is carried out, in order to predict the optimum steam pressure setpoint in an operation status after grade change. The simulation of steam pressure prediction is explained by referring to FIG. 4.
In the first step in FIG. 4, operation status data after grade change, i.e., the machine speed (m/min), basis weight setpoint (g/m2), and moisture percentage setpoint (%), are acquired. In the second step, the incremental time interval Δt for differential calculations is determined from the machine speed, drum's circumference, and other data items. In the third step, the steam temperature Ts(j) (j=1, . . . , N) within the drum is calculated from the current dryer steam pressure setpoint P (kPa) by using a saturation vapor pressure curve. Note that N is the number of mesh divisions.
In a further step, the value of the drying rate coefficient K determined in the steady-state simulation, as well as the value before grade change used in the steady-state simulation, for example, as the pre-dryer part inlet moisture percentage, is used to find the numerical solutions of equations 5 to 11 and their difference equations, thereby calculating the drum temperature T1(j) (j=1, . . . , N), web temperature T2(j) (j=1, . . . , N), canvas temperature T3(j) (j=1, . . . , N), and web's moisture percentage MP(j) (j=1, . . . , N) as the initial values for the difference equations.
In yet a further step, the value of the web's moisture percentage MP(N) at the final cylinder and the moisture percentage setpoint after grade change are compared, in order to judge convergence in the same way as in the case of the steady-state simulation. If convergence has not yet been reached, the dryer steam pressure setpoint is corrected by the given value Δt, and the drum temperature, web temperature, canvas temperature, and web's relative moisture percentage are calculated once again. When convergence has been reached, the values of these data items at that moment are fixed and the simulation of steam pressure prediction ends.
In such a paper machine as discussed above, controlling the process of drying a product is an important factor in order to produce products of consistent quality. Drying at the after-dryer 86 is particularly important since the drying process directly affects product quality. For this reason, it is necessary to precisely know the moisture percentage of a product at the dryer inlet.
Traditionally, the moisture percentage of a product at the inlet of the after-dryer 86 has been calculated by using a measured value provided by the BM system 88 installed before the size press 85 and then applying, for example, equation 12 shown below. It should be noted that the absolute moisture percentage in the equation means the ratio of moisture weight to the bone-dry weight of a web which is a product.                               absMP          AFTIN                =                                                            BD                PRE                            ×                              absMP                PREEND                                      +                          CW              ·                                                100                  -                  S                                S                                                          BD            AFT                                              (        12        )            where    absMPAFTIN=Absolute moisture percentage (0.0 to 1.0) at after-dryer 86 inlet    absMPPREEND=Absolute moisture percentage (0.0 to 1.0) at pre-dryer 84 outlet (calculated by simulation)    BDPRE=Bone-dry basis weight (g/m2) at pre-dryer 84 outlet (measured with BM system)    BDAFT=Bone-dry basis weight (g/m2) at after-dryer 86 outlet (measured with BM system)    CW=Size's bone-dry coated weight (g/m2)    S=Moving average of size's (coating agent's) concentration (%).
The pre-dryer 84 outlet absolute moisture percentage absMPPREEND is evaluated as a solution given by simulating the steady state formed in the pre-dryer 84. However, a size with a concentration of 5 to 10% is coated at the size press 85 and therefore, the moisture percentage must be corrected by the amount of moisture produced by such coating.
More specifically, the first term BDPRE×absMPPREEND of the numerator on the right-hand side of equation 12 denotes a moisture weight (g/m2) per unit area at the outlet of the pre-dryer 84, whereas the second term CW·(100−S)/S denotes a moisture weight (g/m2) contained in the coated size per unit area. Since the sum of these two terms is the amount of moisture contained per unit area of a product at the inlet of the after-dryer 86, it is clear that the absolute moisture percentage is evaluated by dividing this amount by the bone-dry basis weight BDAFT measured with the BM system 89.
It should be noted that as the size's bone-dry coated weight CW, equation 12 uses the value calculated by equation 13 below, which is the difference between the bone-dry basis weights measured with the BM systems 88 and 89.CW=BDAFT−BDPRE  (13)