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.
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:
\[ m_{\text{active,extract}} = 90 \text{ kg} \times \frac{0.9}{100} = 0.81 \text{ kg} \]
