Reference ID: MET-4048 | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
Recovery yield quantifies the fraction of a target component (here, pigment) that is successfully transferred from the feed stream to the extract stream. It is a key performance indicator in downstream bioprocessing, natural-product extraction, and pigment isolation because it directly links mass‑balance closure to process economics and product quality. Low recovery implies either measurement error, incomplete extraction, or unaccounted losses (e.g., adsorption to equipment, degradation). Typical industrial pigment extractions from sugar‑beet juice operate under ambient pressure and moderate temperature; deviations from the expected 85–95% recovery range flag the need for troubleshooting. The same principles are used to assess citrus juice extractor efficiency in the food‑processing sector.
Methodology & Formulas
Pigment mass in feed
\[ m_{\text{f}} = M_{\text{feed}} \cdot \frac{C_{\text{feed}}}{100} \]
where \( M_{\text{feed}} \) is the total feed mass and \( C_{\text{feed}} \) is the pigment concentration in wt %.
Pigment mass in extract
\[ m_{\text{e}} = M_{\text{extract}} \cdot \frac{C_{\text{extract}}}{100} \]
Recovery yield
\[ \text{Recovery} = \frac{m_{\text{e}}}{\max(m_{\text{f}},\,\epsilon)} \times 100\% \]
with \( \epsilon = 10^{-9} \text{ kg} \) to prevent division by zero.
Loss
\[ \text{Loss} = 100\% - \text{Recovery} \]
Parameter
Typical Range
Units
Remarks
Temperature
20 – 80
°C
Outside range triggers warning
Pressure
1.0 ± 0.1
bar
Deviation > 0.1 bar triggers warning
Recovery
85 – 95
%
Outside range triggers note
Recovery yield (%) = (mass of desired product collected ÷ mass of desired product theoretically produced) × 100.
For continuous systems, use steady-state mass flow rates:
Measure product flow rate (kg h⁻¹) at the outlet.
Measure feed rate of limiting reactant (kg h⁻¹) and convert to theoretical product rate using stoichiometry.
Divide actual product rate by theoretical rate and multiply by 100.
Treat the entire loop as a black box:
Sample the fresh feed entering the loop and the final product leaving the loop.
Ignore internal recycle flows; they cancel out.
Calculate yield on a once-through basis if you need to diagnose catalyst or separator performance separately.
Moisture or solvent left in the product mass reading—always dry to constant weight.
Line losses or hold-up in transfer pipes—flush and weigh catch pots.
Analytical bias in assay values—calibrate instruments daily and run spiked samples.
Use molar yield when:
Multiple products share the same stoichiometric coefficient.
Molecular weights differ significantly between feed and product.
You need to compare catalyst selectivity across different chemistries.
Convert units consistently: moles of product per mole of limiting reactant fed.
Worked Example – Recovery Yield of Active Ingredient from a Batch Extraction
A pharmaceutical plant is extracting an active ingredient from an aqueous feed using a single-stage mixer–settler. After phase separation, the organic extract is analysed to determine how much product has been recovered.
Knowns
Feed mass: 100 kg
Feed concentration: 1.0 wt % active
Extract mass collected: 90 kg
Extract concentration: 0.9 wt % active
Step-by-Step Calculation
Calculate the mass of active in the feed:
\[ m_{\text{active,feed}} = 100 \text{ kg} \times \frac{1.0}{100} = 1.0 \text{ kg} \]
Calculate the mass of active in the extract:
\[ m_{\text{active,extract}} = 90 \text{ kg} \times \frac{0.9}{100} = 0.81 \text{ kg} \]
