Polymer Drying Hopper Volume, Dew Point & Heater Duty

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. The 9 inputs are read from the form on every keystroke: Polymer Throughput, Required Residence Time, Chip Bulk Density, Incoming Chip Moisture, Target Moisture at the Extruder, Process Air Dew Point, Drying Temperature, Return Air Temperature and Process Air Ratio.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves Required Hopper Volume together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Chip Held in the Hopper, Water Removed, Absolute Humidity at the Dew Point, Process Air Flow, Process Heater Duty, Specific Drying Energy, Moisture Reduction Factor and Air Mass per Unit Water Removed — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

Substituting

The air-to-water ratio of 808 is the number that explains the whole machine: 808 kg of air is circulated for every kilogram of water removed. Drying is not a heat problem, it is a mass-transfer problem being solved by brute-force air circulation, which is why dew point rather than temperature is the specification.

How to use it

1. Work through the input groups in order — Throughput & Hopper and Moisture & Air. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read Required Hopper Volume in the dark results panel — that is the headline figure, expressed in m3.
4. Check the supporting rows underneath (Chip Held in the Hopper, Water Removed, Absolute Humidity at the Dew Point, Process Air Flow, Process Heater Duty, Specific Drying Energy, Moisture Reduction Factor and Air Mass per Unit Water Removed) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Process planning — establishing Required Hopper Volume before a trial is booked, so machine time and material in Polymer Rheology & Synthetic Extrusion are committed against a calculated figure rather than an estimate.
• Costing and quotation — Required Hopper Volume is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Polymer Throughput) shows how much of the gap in Required Hopper Volume each variable explains.
• Teaching and study — the accepted ranges bracket normal Polymer Rheology & Synthetic Extrusion practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Reading the result

Typical bands and what each one is telling you.

Assumptions and limits

• The hopper volume is the working volume for chip and takes no account of freeboard, cone geometry or the distribution cone, so a real vessel will be larger. Residence time assumes plug flow; a hopper with poor mass flow will channel and give some of the chip far less than the nominal time while the rest sits, which is a common cause of intermittent IV variation with no process change to point at. Heater duty is sensible heat on the process air only and excludes desiccant regeneration, which on a twin-tower system can be comparable in size, and excludes losses through the vessel wall. Air density is taken at the metering condition rather than at temperature; blowers are normally rated volumetrically at inlet, which is the convention followed here. The moisture figures are mass ppm as determined by Karl Fischer or equivalent, not the volumetric ppm sometimes quoted for gases.
• Every input is bounded to the range normal practice occupies (Polymer Throughput 1 to 10000 kg/h, Required Residence Time 0.5 to 24 h and Chip Bulk Density 300 to 1400 kg/m3, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Standards and further reading

• ISO 15512 - Plastics, Determination of water content, the reference method for the ppm figures used here.
• ASTM D6869 - Coulometric and Volumetric Determination of Moisture in Plastics using Karl Fischer reaction.
• ASTM D4603 - Inherent viscosity of PET, the measurement that shows whether drying succeeded.
• Magnus-Tetens coefficients over ice as given by Sonntag (1990) for the dew point conversion.

Questions people ask