GL&V Inc.
For our contextual and teaching and learning portion, I
decided that my dadŐs workplace would be a great place to find math in the real
world. GL&V is a company that has three different divisions: the pulp and
paper group, the water treatment group, and manufacturing. My dad is
specifically involved in the pulp and paper group, so I decided I would narrow
down my findings of math used at GL&V to the pulp and paper area. While my
dad does not deal directly with math, he was able to put me in contact with a Process
& Service Manager who deals with math every single day!
Math is used in math different ways, from basic conversions
to calculation flow rates and making calculations in order to create parts for
different functions. Some simple math that is used daily are conversions. For
convenience, a spread sheet was created with some conversions that are used day
to day. These conversion are not difficult, but can be time consuming when you
are dealing with large numbers, and the calculations have to be done many times a day. These conversions consist
of changing feet to meters, psi (pounds per square inch) to kPa, which is a
kilopascal (unit that measures pressure). Then the kPa can be converted into
meters, and then feet. The conversions get a little more complex, in which the
spreadsheet comes in handy. Sometimes, it is necessary to change gallons/minute
to liters/minute and then liters/second. Another conversion on this spreadsheet
that deals with calculating the amount of to be pretty vital takes liters/second,
converts it to kg/minute, and then tons/day. The tons/day is then used to
calculate the Bone Dry Short Tons Per Day, or BDSTPD. This is the amount of
pulp that is pumped from the pulp and water mixture in tons per day. A spread
sheet with these calculations and formulas is attached as an excel spreadsheet.
Another set of calculations that are important to maintain a
profitable company involve calculating
the power consumption in a pump and the cost savings that can come with using
more efficient equipment requiring less pressure. The following chart shows how
the feed pressure of a pump will essentially change how much it costs to run
the pump. We can see just from this chart that conversions that were mentioned
earlier are extremely necessary in this process, as well as the mathematics
behind developing the formulas that will provide you with your desired end
result. One must also take accurate and precise measurements in order for the
formulas to provide the correct cost difference.
|
Feed Flow (gpm): |
9900 |
9900 |
|
Feed Flow (lpm): |
37472 |
37472 |
|
Feed pressure (psi) = pressure needed up by equipment: |
65 |
31 |
|
Feed Pressure (kPa): |
464 |
221 |
|
Height from pump to cleaner
header (feet): |
20 |
20 |
|
Pump efficiency (if no info.
86% set as default): |
86 |
86 |
|
Motor efficiency (92-96%) |
95 |
95 |
|
Pump energy required (kW): |
382 |
206 |
|
|
|
|
|
Energy cost per kWh: |
$0.07 |
$0.07 |
|
|
|
|
|
Days of operation: |
320 |
320 |
|
|
|
|
|
Energy cost per year: |
$205,126 |
$110,676 |
So we see that when the feed pressure is decreased from 65psi
to 31psi, the difference in cost is $94,450! After the mathematics is used to
calculate these numbers, someone else must come along and use more mathematics
to design a part that will operate under 31psi, rather than 65psi.
Here is another example of how math is used in the pulp and
paper group:
Parts are designed in order to meet a certain need of the
company. In one instance, a stand pipe is needed in order for the pulp slurry
(mixture of pulp and water) to travel through. So, the diameter of the pipe
will need to be constructed so that the pulp-slurry will be traveling through
the pipe at a certain velocity. So, say the desired velocity of flow is
0.5ft/sec. Then the formula used to help determine the diameter of the pipe is
as follows:
Diameter=sqrt ((0.41*flow)/(ft./sec.))
Our desired flow is
0.5ft/sec, so ,sqrt((0.41*0.5)/(ft./sec.)=0.452769 feet. So the diameter of the pipe necessary
to pump pulp-slurry at a rate of .5ft/sec is .452769 feet. The diagram below
shows a stand pipe in which the pulp-slurry is pumped through. A picture of the
stand pipe mentioned here is attached as a pdf.
Another fairly simple
way math is used every day at GL&V is used to calculate the flow of pulp
stock coming out from a pipe.
They use a 5 gallon
bucket, and it takes 23 seconds to fill it up. So using some basic math, we know
can show that it takes .38333 minutes to fill up 5 gallons. So, we can
calculate the flow in gallons per minute by dividing 5 gallons by .38333
minutes. Hence, the flow is 13.043 gallons/minute.
Using this
calculation, it is now possible to determine how much pulp-slurry will be
needed to obtain a desired amount of pulp using this flow above. So, for
example, say GL&V needs 100 grams of pulp. The pulp-slurry available has a
concentration of .55%. We can convert the .55grams/deciliter to grams/liter by
multiplying .55 by 10 (simple conversion facts!) So, the concentration of the
pulp-slurry is 5.5grams/liter. Since we need 100 grams of pulp, we take
100grams/5.5(grams/liter) gives us 18.18 liters.
These are just a few
ways in which math is used every day at GL&V. It is very interesting to see
how involved math truly is in the world around us. It is important for students
to be able to see the connection between math and the world around them, as
this could not only drive interest in the subject but also motivate students to
do well in the classroom. I found this exploration particularly intriguing, and
I think high school math students would greatly benefit from a similar
experience.
All information, examples, and diagrams provided by: Ann-Christine Eriksson Patey, Process and Service Manager, GL&V USA Inc.
GL&V Website: www.glv.com
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