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									                        BSE 422 Midterm, 4 November, 2010
                 Take Home – Due Tuesday, 9 November; 4:00 PM PST

This midterm is to be worked on by yourself with no assistance from anyone.
Failure to do so will be met with severe consequences.

This exam looks at lime mud filters used in the recovery area of a pulp mill. The model
presented here comes from "The Modeling Of Rotary Lime Mud Filters", by Kent R. Davey,
George Vachtsevanos, and Jim C. Cheng, Tappi Journal, Vol. 72, No.8, pp 150-156, August
1989.

Lime mud consists of CaCO3 and residual alkali from the causticizing process. The lime kiln
converts CaCO3 to CaO to be reused in the causticizing reaction to regenerate the kraft cooking
liquor. Before the lime mud can be ran through the lime kiln two things need to be done. The
lime mud is fed to the filter as slurry at an average solids content of 35%. The solids content
must be increased to around 70% prior to the kiln (30% moisture). The alkali concentration in the
mud also needs to be controlled. Too high an alkali concentration causes the drying lime to stick
together and form large balls. Too low and it won’t stick together at all and high dusting losses
occur. The job of the lime mud filter is to increase the solids and regulate the alkali concentration
of the lime mud going to the lime kiln. A diagram of a drum filter is shown in Figure 1.

Lime mud enters the vat and builds up on the vacuum drum. Wash water is applied to the
lime mud cake to reduce the alkali concentration. This also has the effect of increasing
the moisture content of the lime mud. A higher drum speed will give a lower moisture
content and lower alkali concentration. For the problems presented here the production
rate will be treated as a disturbance.


                        Lime Mud
                          Cake
                                                                      Wash
                                                                     Shower
                Scraper
                 Blade



                                             Vacuum
                                              Drum
                                                                     Vat
                                              Slurry
               Mud
             Conveyor


Figure 1. Drum mud filter.



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Table I lists the nominal operating conditions for the mud filter.

Table I. Nominal operating conditions for lime mud filter.
Mud moisture content (%)              30
Alkali concentration (%)              1.5
Blade position (cm)                   3.5
Drum vacuum (relative)                  1
Wash shower flow (L/s)                  3
Drum speed (rpm)                        5
Production rate (m3/s)                  1

Figures 2 and 3 represent block diagrams of the lime mud process.

                               W              P


                                9            36


     S           -8                                          M


Figure 2. Lime mud filter process model; drum speed (S), wash flow (W), production (P), moisture
content (M).


                                S             P


                              -0.2            2

   W          -0.125                                         A


Figure 3. Lime mud filter process model; wash flow (W), drum speed (S), production (P), alkali
concentration (A).




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Problem 1 (25 points)

The blade position (B) and the drum vacuum (V) affect the lime mud moisture content
(M) and alkali concentration (A). The data in table I show operational data for the mud
filter for these two variables. Note that the first row is the nominal operating point.


                            Table 1. Lime mud filter operational data.
          Blade Position, cm (B)   Vacuum, rel (V)   Moisture, % (M)     Alkali, % (A)
                   3.5                   1                 30                 1.5
                   3.0                   1                 26                 1.4
                   3.5                  1.25               27                 1.3



Derive a linear incremental model where the blade position (B) is the manipulated
variable, drum vacuum (V) is a disturbance, and the mud moisture (M) is the output.
Draw a block diagram for the model.




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Problem 2 (25 points)

Design a feed forward control strategy (using the block diagrams and process data from
page 2) for the alkali concentration (A) that would result in perfect control. Use the wash
water (W) as the manipulated variable. The drum speed (S) and production rate (P) are
the disturbance variables. The solution should include a block diagram of the process
with the control strategy. Show the numerical values of the feed forward controller gains
in the block diagram. Calculate the change in alkali concentration (A) and the wash
water (W) when the alkali concentration setpoint is increased to 1.7% and the drum
speed is increased by 0.5 rpm.




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Problem 3 (25 points)

Design a feedback control strategy (using the block diagrams and process data from page
2) for the mud moisture content (M) using the drum speed (S) as the manipulated
variable. The wash water (W) and production rate (P) are the disturbance variables. Use
a loop gain of 4 for the controller. The solution should include a block diagram of the
process with the controller. Calculate the change in mud moisture content (M) and the
drum speed (S) when the mud moisture content setpoint is reduced to 25%.




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Problem 4 (25 points)

The mud moisture needs to remain in the range of ± 5%, but the wash flow varies by ± 2
L/s. For the feedback only control strategy in Problem 3, determine the minimum
controller gain required to keep the mud moisture content in the specified range. What is
the loop gain for this situation?




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                      BSE 422 Midterm, 4 November, 2010
               Take Home – Due Tuesday, 9 November; 4:00 PM PST

This midterm is to be worked on by yourself with no assistance from anyone.
Failure to do so will be met with severe consequences.

Take Home Problem 1 – (50 points)


The following block diagram is a decoupled control system that uses the drum speed to
control the mud moisture content and the wash flow to control the alkali concentration.
The decouplers remove the influence of the drum speed controller output (SCO) on the
alkali concentration (A) and the wash flow controller output (WCO) on the mud moisture
content (M). The control engineer retuned the control system during a shutdown on a
Friday afternoon right before he was leaving on vacation for a remote island in the
Federated States of Micronesia. After the start up the system is very unstable and the
operators have to run the process in manual control. You get called in at midnight that
night to fix the problem. There appears to be some problems with the controller gains.
What changes would you make, if any, to the feedback controller gains (KCM and KCA)
and the decoupler gains (KDM and KDA) to make the process stable? For feedback control
you can consider a loop gain of 4 to be reasonable. Note that the 4 gains on the right are
the process gains and SCO and WCO are the feedback controller outputs for the drum speed
and wash flow, respectively.


           -                 SCO                       S
MSP                 -5.7                                         -7                          M
                    KCM                 KDA

                                       -2.14                     7


                                        -10                    -0.3
                    KCA                 KDM
ASP                 28.6                                       -0.14                         A
                             WCO                       W
           -
                 Feedback           Decouplers               Process




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Take Home Problem 2 – (50 points)

WinGems problem

The cost of wash water is actually born by the cost of producing steam for the multiple
effect evaporators. In this problem we will look at the combined operating and capital
costs associated with washing and evaporation.

Modify your three washer simulation such that the weak liquor from the wash train
(stream without the pulp) enters into an Evaps block where the liquor will be evaporated
to 65% solids. (An Evaps block splits the weak black liquor into one stream containing
the dissolved solids – called the strong black liquor – and a condensate stream. The
condensate stream contains all the water that was evaporated in the evaporator). You can
assume the strong black liquor and condensate exit the evaporators at 200oF. Assume the
consistency exiting each of the three washers is 10%. You can also assume Norden
efficiency of each washer is identical.

It has been determined that the optimal operating condition is when the total capital cost
of the washers equals the annual operating costs of the evaporators. The capital cost of
the washers is equal to $1 million per over all Norden number (i.e. if you have three
washers with En = 5 each the capital cost would be $15 million). The operating cost of
the evaporators is equal to $15 per ton of steam. The evaporators have an economy of
five, which means it takes one ton of steam to evaporate 5 tons of water.

Find the dilution factor and overall Norden number such that the total capital cost of the
washers equals the annual operating costs of the evaporators. The dissolved solids exiting
with the pulp is 0.25% or 2.5kg/metric ton liquor. The dissolved solids of the thick black
liquor exiting the evaporators needs to be 65%. The feed to washer is the same as in the
HW: Production rate: 900 odst pulp/day, Consistency as blown: 12.5%, Temperature as
blown: 221°F, Dissolved solids as blown: 21.4% mass of liquor

Set up a simulation such that all the input parameters come from Excel, and the financial
calculations are done in Excel using data imported from the WinGems simulation. Turn
in a short write up with your solution and email me the WinGems and Excel files.




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