9814

Estimating Processing Times in a Row of Storage Tanks

The operation of tanks in industrial juice and other beverage processing has four stages: filling, holding, draining, and cleaning, whose durations depend on the particular product, the tanks' sizes, and the input and output flow rates. This Demonstration shows the operation of up to four tanks of equal capacity, where the liquid flow into and from the system is continuous and constant. You select the filling, holding, draining, and cleaning times of the first tank and repeat these parameters in subsequent tanks until each completes its cycle and is ready for reuse. A vertical dashed black line marks the time when the first tank is ready for refill. This determines the minimum number of tanks needed for the chosen cycle. A moving vertical orange line across the normalized volume versus time diagrams controls the appearance of the tanks in the schematic drawing.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Snapshot 1: a filling, holding, draining, and cleaning cycle requiring two tanks
Snapshot 2: a filling, holding, draining, and cleaning cycle requiring three tanks
Snapshot 3: a filling, holding, draining, and cleaning cycle requiring more than four tanks
This Demonstration generates four plots depicting the state of four tanks (a, b, c, d) being filled in succession, as shown in a schematic drawing on the left (valves included but pumps and controls not shown).
In the normalized volume-time plots on the right, diagonal lines represent filling or draining. A horizontal line at level 1.0 stands for a full tank (held for testing and/or contents adjustment). The other horizontal line, at level 0.0, stands for an emptied tank being washed and readied for receiving a new batch of product.
As shown by moving the vertical orange line from left to right with the "process time" slider, the operation starts with filling the first tank (a) at . When the first tank (a) is full, the second tank (b) is being filled and then the third (c) and fourth (d), assuming that the switching time is negligible. The filling, holding, draining, and washing times are chosen with sliders. The time at which the first tank completes its cycle and is ready to receive new product is marked by a vertical black dashed line. If the filling starting point of a tank (c or d) happens to coincide or fall beyond the time the first tank (a) has completed its cycle, the first tank (a) can be reused, that is, a smaller number of tanks would be sufficient for the particular cycle. This number is displayed in red below the four tanks' volume-time diagrams.
Moving the orange solid vertical line with the "process time" slider shows the state of each tank at any given time during the operation. The plotted process duration can also be set with the " axis max." slider.
The main purpose of this Demonstration is to show the role of a tank's cycle in liquid food and beverage processing. Therefore, not all the settings that it allows represent the operation of realistic industrial systems.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+