Compounding Math

How to Calculate Batch Blend Time, Pigment Loading, and Resin Yield in Compounding

Work through the core compounding math: blend time, pigment loading percent, resin yield loss, and cleaning solvent volume, with real inputs and units.

Blend time is the anchor calculation for any compounding cell. The working relation is t = k x (V / (N x D^3)), where V is batch volume in liters, N is impeller speed in rev per second, D is impeller diameter in meters, and k is a rig-specific constant you back out from historical batches. For a 4,000 L reactor with a 0.9 m Cowles disperser at 12 rev per second, a well-dispersed carbon black tint typically resolves in 35 to 55 minutes to reach a Hegman reading of 7. Pull the k value from three past batches of the same viscosity class rather than guessing, then feed V, N, and D into the Batch Blend Time calculator to confirm.

Pigment loading is a mass fraction, not a volume guess. Pigment weight percent equals pigment mass divided by total wet batch mass, times 100. A batch with 620 kg of TiO2 in a 4,000 kg letdown runs 15.5 percent by weight. Watch the difference between pigment volume concentration (PVC) and weight percent: PVC uses densities, so 15.5 percent TiO2 by weight at a resin density of 1.05 and pigment density of 4.1 converts to roughly 4.5 percent by volume. Quoting the wrong basis is the single most common spec error, so the Pigment Loading Cost calculator keeps both bases visible on one screen.

Resin yield loss captures what never makes it into a sellable drum. Yield loss percent equals (charged mass minus net good output) divided by charged mass, times 100. Charge 4,000 kg, ship 3,830 kg, and you lost 170 kg, or 4.25 percent. That loss splits into cling (film left on vessel walls and the disperser shaft), transfer line holdup, filter cake, and off-spec purge. On a 400 gallon steel kettle, wall cling alone commonly holds 8 to 20 kg per batch. Run the numbers per batch, not per month, so a single bad cleanout does not hide in the average. The Resin Yield Loss calculator itemizes each loss stream.

Cleaning solvent volume follows the surface area you must wet, not the batch size. A workable estimate is solvent liters equals wetted internal area in square meters times a coverage factor of 0.4 to 0.8 L per square meter per rinse, times the number of rinses. A 4,000 L vessel with roughly 22 square meters of wetted steel at 0.6 L per square meter over two rinses needs about 26 L per color change, before you add line flush. Cut rinse count by staging light to dark and you drop solvent draw directly. The Cleaning Solvent Usage calculator ties rinses to area and color sequence.

Color match rework is a probability-weighted loop, not a fixed adder. Expected rework mass equals first-pass fail rate times average correction mass per fail. If 18 percent of batches miss dE 1.0 on the first shot and each correction adds 22 kg of tint plus 12 kg of clear, budget 0.18 times 34, or about 6.1 kg of extra material per batch across the run. Each correction also adds a blend and sample cycle. Track the fail rate by colorant family, because organic reds and phthalo blues drift far more than inorganic earth tones. The Color Match Rework calculator carries the loop cost.

Mixer utilization is straight time accounting: utilization equals productive blend hours divided by scheduled hours, times 100. A disperser scheduled 20 hours per day that runs actual product for 13.2 hours sits at 66 percent, with the other 6.8 hours split across cleaning, charging, waiting on QC, and changeover. Separate loading and unloading from true idle, because those are necessary and cleaning is partly recoverable. Feed the split into the Mixer Utilization calculator to see where the missing hours live before you chase a throughput number that the schedule cannot support.

Fill throughput closes the loop from bulk batch to shipped containers. Containers per hour equals 3,600 divided by (fill time plus indexing time plus cap and label time) in seconds per unit. A tote line filling 1,000 L IBCs at 180 seconds fill, 25 seconds index, and 40 seconds cap runs 3,600 divided by 245, or about 14.7 totes per hour. Convert a 3,830 kg good batch at 1.08 kg per L to about 3,546 L, which is roughly 3.5 totes, so that batch clears the fill head in under 15 minutes. The Drum/tote Fill Throughput calculator links fill rate to net batch volume.

Chain the calculations in the order product moves: blend time sets cycle length, pigment loading sets the recipe, yield loss corrects charged mass to shipped mass, solvent and rework add the hidden mass and time, utilization sets how many cycles fit the day, and fill throughput turns liters into containers. Keep every input in one unit system per batch sheet, either metric or US, and convert once at the boundary. A single kg versus lb slip on a 4,000 kg charge is a 2.2x error that no downstream calculation will catch for you.

Published 2026-07-01.