EUTECNIQ Sciences

See every page on one mapArrow keys move through results · Enter opens · Esc closes

Process engineering & scale-up Textbook equations Educational simulations Planned pilot train

An extract becomes a reproducible ingredient when heat, mass and momentum transfer are controlled, from flask to plant

How a laboratory extraction changes at plant scale: balances, transport physics, process safety and quality by design. Scale-up rules and technology transfer are on the scale-up page.

Status. EUTECNIQ owns no pilot plant and has run no batches; pilot extraction, solvent recovery and drying are planned for Phase II (facility plan, October 2026). Calculators are educational simulations, not designs.

Related: scale-up and tech transfer · Ostwald ripening simulation

11 °Cwhere ethanol's saturated vapor reaches its lower flammable limit, 3.3% in air
78 → 42 °Cethanol's boiling point at 1 atm and under a 20 kPa vacuum
120.2 °Ccondensing temperature of saturated steam at 200 kPa absolute
7dimensionless numbers that carry a laboratory result to plant scale

Reference equations of state via CoolProp (agree with the NIST WebBook); NIOSH Pocket Guide, ethanol; Bird, Stewart and Lightfoot, Transport Phenomena, 2nd ed. (2002).

What this page answers

Most scale-up failures come from physics that the laboratory hides: slower heating, coarser particles, longer mixing and the cost of recovering solvent

Process engineering predicts these differences, designs around them and proves the result in pilot runs.

Moving one recipe from a 1 L flask to a 4 m³ vessel slows heating and diffusion about sixteenfold, while mixing stays in secondsModel output, default inputs
Four effects the flask hides, at the scale calculator's default settings: slower heating, longer diffusion, longer but still short mixing, and the heat cost of solvent1Heating slowsτ = Mcp​ / UA ∝ V1/3​1 L4 m³heat-up, 20 to 60 °CflaskHeating slows, flask: 69 s69 splantHeating slows, plant: 19 min19 minJacket area per volume falls from 46to 2.9 m²/m³2Diffusion lengthenstD​ = R2​ / Deff​0.5 mm2 mmdiffusion time at Deff​ = 10−11​ m²/sflaskDiffusion lengthens, flask: 1.7 h1.7 hplantDiffusion lengthens, plant: 28 h28 hParticle diameter 0.5 → 2 mm; time ∝R², so 16 times longer3Mixing slows, but stays shortθ95​ = 5.2 (T/D)2​ / (N Po1/3​)blend time θ95​ at constant P/VflaskMixing slows, but stays short, flask: 4.2 s4.2 splantMixing slows, but stays short, plant: 26 s26 sImpeller 400 → 63 rpm; secondsagainst hours of diffusion4Solvent costs heatQ = S · Δhvap​condenselatent heat to recover, per kg herbflaskSolvent costs heat, flask: 28 MJ28 MJplantSolvent costs heat, plant: 11 MJ11 MJ20 → 8 kg solvent per kg herb;one-stage equilibrium limit 96% →90%Four effects the flask hides, at the scale calculator's default settings: slower heating, longer diffusion, longer but still short mixing, and the heat cost of solvent1Heating slowsτ = Mcp​ / UA ∝ V1/3​1 L4 m³heat-up, 20 to 60 °CflaskHeating slows, flask: 69 s69 splantHeating slows, plant: 19 min19 minJacket area per volume falls from 46 to 2.9 m²/m³2Diffusion lengthenstD​ = R2​ / Deff​0.5 mm2 mmdiffusion time at Deff​ = 10−11​ m²/sflaskDiffusion lengthens, flask: 1.7 h1.7 hplantDiffusion lengthens, plant: 28 h28 hParticle diameter 0.5 → 2 mm; time ∝ R², so 16 timeslonger3Mixing slows, but stays shortθ95​ = 5.2 (T/D)2​ / (N Po1/3​)blend time θ95​ at constant P/VflaskMixing slows, but stays short, flask: 4.2 s4.2 splantMixing slows, but stays short, plant: 26 s26 sImpeller 400 → 63 rpm; seconds against hours ofdiffusion4Solvent costs heatQ = S · Δhvap​condenselatent heat to recover, per kg herbflaskSolvent costs heat, flask: 28 MJ28 MJplantSolvent costs heat, plant: 11 MJ11 MJ20 → 8 kg solvent per kg herb; one-stage equilibriumlimit 96% → 90%
Computed with the equations and default inputs of the scale-up calculator below: extraction at 60 °C, steam at 120 °C, U = 500 W/(m²·K), vessel height equal to diameter with jacket area 1.25πT², 60% w/w ethanol, Deff = 10⁻¹¹ m²/s, Rushton turbine (Po = 5, D/T = 0.33) at 400 rpm in the flask and constant power per volume at scale. Bergman et al. 2011; Crank 1975; Grenville and Nienow 2003; latent heats 837 and 2,257 kJ/kg (NIST). Illustrative inputs, not plant data.
Text version of the four effects
  • Heating slows. The time constant Mcp/UA grows with the cube root of volume. Jacket area per volume falls from 46 m²/m³ (1 L) to 2.9 m²/m³ (4 m³), and heat-up from 20 to 60 °C takes about 69 s in the flask and 19 min in the vessel.
  • Diffusion lengthens. The diffusion time R²/Deff rises with the square of particle size: 0.5 mm particles give 1.7 h, the plant's 2 mm particles 28 h, sixteen times longer.
  • Mixing slows, but stays short. At constant power per volume the impeller slows from 400 to 63 rpm and the blend time θ95 rises from 4.2 s to 26 s, still seconds against hours of diffusion.
  • Solvent costs heat. A flask can use 20 kg of solvent per kg of herb; the plant uses 8. Recovering it takes 28 MJ and 11 MJ of latent heat per kg of herb, while the one-stage equilibrium limit falls from 96% to 90%.
Explanation, details and sources
EUTECNIQ would
  • Close mass and energy balances
  • Measure scale-dependent parameters in pilot runs
  • Write transfer packages: ranges, controls, records
  • Lead hazard analyses with qualified engineers
Proposed
Qualified partners would
  • Provide pilot or commercial capacity first
  • Do detailed engineering, fire-code and electrical classification
  • Fabricate and qualify equipment
External partner
EUTECNIQ does not claim
  • Equipment, batches, yields or process data
  • That any calculator here is a validated design
  • Regulatory approval of any process
Limits
Founder background

Process engineering is the founder's own discipline

A doctorate in computer-aided molecular and process design, early papers on solvent extraction in rotating-disk contactors, pilot scale-up and process modeling at Yazaki, and, as reported by the founder, leadership of plant process engineering for a $140M cGMP expansion at MilliporeSigma. These are prior-employer roles, not EUTECNIQ results (founder page).

Founder-reported Publications verified
  • An educational simulation≠a validated industrial design
  • A laboratory yield≠a plant yield
  • A P&ID-style schematic≠an engineered, code-reviewed design
  • Laboratory feasibility≠commercial demonstration
From laboratory to plant

The same recipe gives a lower yield and more degradation at plant scale, unless the process is redesigned around heat transfer, particle size and solvent recovery

Governing relationsheat-up: th = McpUA lnTs − T0Ts − T
extraction: F(τ*), sphere
 in a limited bath
τ* = ∫D(T)dt / R²
mixing: θ95 = 5.2 (T/D)²
 / (N Po1/3)
Batch temperature and extraction progress, flask versus plantEducational simulation
Laboratory flask versus plant vessel for the same recipe
Quantity1 L flaskPlantWhat drives the difference
Working volumeScale
Particle diameterPlants mill coarser so the marc can be filtered
Solvent per kg herbEvery kilogram of solvent has to be evaporated again
Heat-up to extraction temperatureJacket area per volume falls as V−1/3
Cool-down to 35 °CSame physics, in reverse
Mixing time θ95 at constant power per volumeSlower impeller at scale; still short against diffusion
Equilibrium limit of one stageSolvent ratio: less solvent leaves more solute behind
Extracted at the end of the batchParticle size (diffusion time ∝ R²) and the equilibrium limit
Heat-labile marker degradedLonger time near temperature during heating and cooling
Solvent to recover per kg extractSolvent ratio divided by yield
Latent heat to recover it, per kg extractThe largest energy cost of a solvent process
Heat to warm the batch, per kg extractThermal mass of solvent and herb

Lower bound of the mass-transfer Biot number, Bi = kfR/Deff ≥ DL/Deff = 100 with no convection at all (Sh = 2). Because Bi ≫ 1, diffusion inside the particles, not agitation, limits extraction at both scales.

Sphere in a well-stirred solution of limited volume: Crank J. The Mathematics of Diffusion. 2nd ed. Oxford: Clarendon Press; 1975, eq. 6.30. Batch heating: Bergman et al. 2011. Blend time: Grenville RK, Nienow AW, in Paul EL, et al., eds. Handbook of Industrial Mixing. Wiley; 2003:507–542. Ethanol latent heat 38.56 kJ/mol at 351.5 K: NIST Chemistry WebBook. All inputs and fixed constants are illustrative.
A falling-film evaporator runs the extract down heated tubes as a thin film and works under vacuum, so the solvent is recovered at a lower boiling temperatureSchematic · computed boiling points
Isometric cutaway of a generic falling-film evaporator. Feed enters the top head and a distributor spreads it over the inside of vertical tubes, where it flows down as a thin film heated by steam condensing outside the tubes. Vapor and concentrate leave the bottom into a separator; the vapor goes to a condenser and a receiver for recovered solvent, and a vacuum pump keeps the pressure low so the solvent boils at a lower temperature. An enlarged section shows steam, tube wall, liquid film and vapor core, and a note gives computed boiling points of ethanol and water.
Principle: Minton PE. Handbook of Evaporation Technology. Noyes; 1986; McCabe WL, Smith JC, Harriott P. Unit Operations of Chemical Engineering, 7th ed. 2005. Boiling points computed with CoolProp. Generated illustration, EUTECNIQ; generic, no vendor design. Full-size SVG
Method, assumptions and limits
What it calculates
For one recipe at two scales: the batch temperature history, the fraction of extractable solids in solution, the loss of a heat-labile marker, the mixing time, and energy per kilogram of extract for heating and for solvent recovery.
Equations
Vessel: cylinder with liquid height equal to diameter, jacket on wall and flat bottom, A = 1.25πT². Heating with steam at 120 °C from 20 °C, then a hold, then cooling with 20 °C water to 35 °C, each segment exponential with time constant Mcp/UA. Extraction: F = (α/(1+α))·[1 − Σ 6α(1+α) e−qn²τ*/(9 + 9α + qn²α²)], with tan qn = 3qn/(3 + αqn²) and α = solvent-to-particle volume ratio; τ* = ∫D(T)dt/R², exact for a diffusivity that changes in time but not in space. D(T) and the degradation rate k(T) follow Arrhenius laws. Blend time: Grenville and Nienow correlation, impeller speed scaled at constant power per volume.
Variables and units
Solvent 60% w/w ethanol, 900 kg/m³, cp 3.4 kJ/(kg·K); herb cp 1.5 kJ/(kg·K), particle density 1,000 kg/m³, extractable solids 18% of herb; U = 500 W/(m²·K); diffusion activation energy 20 kJ/mol; marker degradation 0.2% per minute at 60 °C with 80 kJ/mol activation energy; liquid diffusivity 10⁻⁹ m²/s; Rushton turbine, Po = 5, D/T = 0.33, 400 rpm in the flask. Latent heats 837 kJ/kg (ethanol) and 2,257 kJ/kg (water), mass-weighted.
Assumptions
One well-mixed stage; partition coefficient 1; uniform spherical particles; no washing of the marc; extract solution not cooled before filtration beyond the stated cool-down; heat of mixing and sensible heat of evaporation ignored.
Valid range
Plant 0.1–10 m³; particles 0.5–5 mm; 4–20 kg solvent per kg herb; 40–80 °C; 15–240 min hold; diffusivity 10⁻¹² to 10⁻¹⁰ m²/s at 60 °C. Very short times use the short-time limit of the series.
What it does not establish
It does not predict a yield for any real botanical. Plants recover yield with countercurrent stages (see the Kremser calculator) and recover energy with multiple-effect or vapor-recompression evaporation; neither is modeled here. Real particles are not spheres, and real constituents degrade by several routes.
Verification
An independent Python reference in tests/numerics/ref/technologies-process-engineering.py solves the diffusion equation in the sphere and bath numerically in real time (method of lines, scipy), without the series or the transformed time, and is checked against the page.
Explanation, details and sources

One recipe runs in a 1 L flask (fine grind, generous solvent) and in a plant vessel with the coarser grind and leaner solvent ratio that filtration and energy cost force. Change the plant settings to see which effect dominates.

Flow diagram and balances

One planned pilot train, its mass and energy balances, and the utilities it would draw on

Nineteen numbered streams: solvent outweighs herb eight to one, and the dried extract is 1% of the mass that movesIllustrative example
Process flow diagram of the planned pilot train with 19 numbered streams and a stream table for an illustrative 1,000 kg dry-herb batchExtraction and solvent recoveryPurification and dryingDry herbM-101M12Makeup solventR-101P-1014F-1015steamE-101Marc desolventizing610Spent marcSolvent recoverychilled waterE-102V-1028VP-10119Vent lossP-1033Recycled solvent to R-1019C-101711Wash water12Eluent, 70% ethanol13WastewaterE-1031415Recovered eluentP-104D-10116H-101Ambient airCY-10117Extract powderBF-101FinesK-10118Exhaust airStream12345678910111213141516171819Total, kgStream 1: Milled dry herb to extractor R-1011,000Stream 2: Makeup solvent to R-101750Stream 3: Recycled solvent from V-102 to R-1017,250Stream 4: Slurry, R-101 to filter F-1019,000Stream 5: Filtrate to evaporator E-1016,980Stream 6: Wet marc to desolventizing2,020Stream 7: Aqueous concentrate to resin column C-101780Stream 8: Solvent vapor from E-101 to recovery6,200Stream 9: Solvent vapor from marc desolventizing to recovery1,080Stream 10: Spent marc940Stream 11: Wash water to C-101400Stream 12: Eluent, 70% ethanol, to C-101500Stream 13: Wastewater from C-1011,084Stream 14: Eluate to concentrator E-103596Stream 15: Recovered eluent from E-103356Stream 16: Dryer feed, E-103 to spray dryer D-101240Stream 17: Extract powder100Stream 18: Water vapor leaving with the dryer exhaust air140Stream 19: Vent loss from solvent recovery30SolidsStream 1: Milled dry herb to extractor R-1011,000Stream 2: Makeup solvent to R-1010Stream 3: Recycled solvent from V-102 to R-1010Stream 4: Slurry, R-101 to filter F-1011,000Stream 5: Filtrate to evaporator E-101180Stream 6: Wet marc to desolventizing820Stream 7: Aqueous concentrate to resin column C-101180Stream 8: Solvent vapor from E-101 to recovery0Stream 9: Solvent vapor from marc desolventizing to recovery0Stream 10: Spent marc820Stream 11: Wash water to C-1010Stream 12: Eluent, 70% ethanol, to C-1010Stream 13: Wastewater from C-10184Stream 14: Eluate to concentrator E-10396Stream 15: Recovered eluent from E-1030Stream 16: Dryer feed, E-103 to spray dryer D-10196Stream 17: Extract powder96Stream 18: Water vapor leaving with the dryer exhaust air0Stream 19: Vent loss from solvent recovery0EthanolStream 1: Milled dry herb to extractor R-1010Stream 2: Makeup solvent to R-10130Stream 3: Recycled solvent from V-102 to R-1014,770Stream 4: Slurry, R-101 to filter F-1014,800Stream 5: Filtrate to evaporator E-1014,080Stream 6: Wet marc to desolventizing720Stream 7: Aqueous concentrate to resin column C-1010Stream 8: Solvent vapor from E-101 to recovery4,080Stream 9: Solvent vapor from marc desolventizing to recovery720Stream 10: Spent marc0Stream 11: Wash water to C-1010Stream 12: Eluent, 70% ethanol, to C-101350Stream 13: Wastewater from C-1010Stream 14: Eluate to concentrator E-103350Stream 15: Recovered eluent from E-103350Stream 16: Dryer feed, E-103 to spray dryer D-1010Stream 17: Extract powder0Stream 18: Water vapor leaving with the dryer exhaust air0Stream 19: Vent loss from solvent recovery30WaterStream 1: Milled dry herb to extractor R-1010Stream 2: Makeup solvent to R-101720Stream 3: Recycled solvent from V-102 to R-1012,480Stream 4: Slurry, R-101 to filter F-1013,200Stream 5: Filtrate to evaporator E-1012,720Stream 6: Wet marc to desolventizing480Stream 7: Aqueous concentrate to resin column C-101600Stream 8: Solvent vapor from E-101 to recovery2,120Stream 9: Solvent vapor from marc desolventizing to recovery360Stream 10: Spent marc120Stream 11: Wash water to C-101400Stream 12: Eluent, 70% ethanol, to C-101150Stream 13: Wastewater from C-1011,000Stream 14: Eluate to concentrator E-103150Stream 15: Recovered eluent from E-1036Stream 16: Dryer feed, E-103 to spray dryer D-101144Stream 17: Extract powder4Stream 18: Water vapor leaving with the dryer exhaust air140Stream 19: Vent loss from solvent recovery0Basis: 1,000 kg dry herb; 60% w/w ethanol at 8 kg per kg herb. Every unit closes in total mass, solids, ethanol and water; stream 3 closes the solvent loop.10.0%powder yield on dry herb (stream 17 ÷stream 1)99.4%of the 4,800 kg ethanol chargerecovered; 30 kg lost at the vent90.6%of the 8,000 kg solvent chargereturned as stream 31.0%of the 9,900 kg moving through thetrain leaves as product
Process flow diagram drawn after ISO 10628 conventions; equipment classes and tags as in the pilot-train schematic below; no sizes are specified and nothing has been purchased. Assumptions: 60% w/w ethanol at 8 : 1 solvent to herb; 18% of herb mass extractable; the marc retains 1,200 kg of solvent, of which ethanol is fully and water partly recovered; 30 kg ethanol lost at vents; the resin binds 96 of 180 kg extracted solids; powder leaves at 4.0% moisture. Every unit balances in total mass, solids, ethanol and water; the figure's generator checks this at build time.
In the proposed pilot train, extract moves from extraction through filtration, evaporation and spray drying to packed powder, and the evaporator returns solvent for reuseProposed design · schematic
Isometric drawing of the proposed pilot train: a jacketed, agitated extraction vessel; a cartridge filter; a falling-film evaporator and separator whose vapor is condensed and returned as recovered solvent; a spray dryer with a rotary atomizer fed with hot air; a cyclone that separates the powder from the air; and a powder drum. Teal lines carry the product, dashed teal the recovered solvent; instrument bubbles use ISA-5.1 tags.
Generated isometric drawing, EUTECNIQ. Unit operations in their usual order; instrument tags per ISA-5.1. Proposed design for illustration; no equipment has been selected and proportions are not to scale. Full-size SVG
Stream table as text (kg per 1,000 kg dry-herb batch)
StreamTotal (kg)SolidsEthanolWater
1 · Milled dry herb, M-101 → extractor R-1011,0001,00000
2 · Makeup solvent → R-101750030720
3 · Recycled solvent, solvent recovery (V-102) → R-1017,25004,7702,480
4 · Slurry, R-101 → filter F-1019,0001,0004,8003,200
5 · Filtrate, F-101 → evaporator E-1016,9801804,0802,720
6 · Wet marc, F-101 → marc desolventizing2,020820720480
7 · Aqueous concentrate, E-101 → resin column C-1017801800600
8 · Solvent vapor, E-101 → solvent recovery6,20004,0802,120
9 · Solvent vapor, marc desolventizing → solvent recovery1,0800720360
10 · Spent marc9408200120
11 · Wash water → C-10140000400
12 · Eluent, 70% ethanol → C-1015000350150
13 · Wastewater, C-101 →1,0848401,000
14 · Eluate, C-101 → concentrator E-10359696350150
15 · Recovered eluent, E-103 →35603506
16 · Dryer feed, E-103 → spray dryer D-101240960144
17 · Extract powder, D-101 →1009604
18 · Water vapor to exhaust, D-101 →14000140
19 · Vent loss, solvent recovery →300300

Powder yield 10.0% on dry herb (100 kg per 1,000 kg); 99.4% of the 4,800 kg ethanol charge recovered, 30 kg lost at vents; 90.6% of the 8,000 kg solvent charge returned from recovery; 1.0% of the 9,900 kg that moves through the train leaves as product.

Recovering solvent takes about 31 times the latent heat the spray dryer needs, and water carries most of itIllustrative example
Latent heat per illustrative batch: solvent recovery needs about 9,921 MJ, roughly 31 times the 316 MJ the spray dryer needs; water carries 57% of the recovery dutyLatent heat per batch, MJ03,0006,0009,000Evaporator E-101stream 8Evaporator E-101: ethanol 4,080 kg × 0.837 MJ/kg = 3,415 MJEvaporator E-101: water 2,120 kg × 2.257 MJ/kg = 4,785 MJ8,200 MJMarc desolventizingstream 9Marc desolventizing: ethanol 720 kg × 0.837 MJ/kg = 603 MJMarc desolventizing: water 360 kg × 2.257 MJ/kg = 813 MJ1,415 MJEluate concentrator E-103stream 15Eluate concentrator E-103: ethanol 350 kg × 0.837 MJ/kg = 293 MJEluate concentrator E-103: water 6 kg × 2.257 MJ/kg = 14 MJ306 MJSpray dryer D-101stream 18, for comparisonSpray dryer D-101: water 140 kg × 2.257 MJ/kg = 316 MJ316 MJethanolwater, solvent recoverywater, spray dryer9,921 MJto recover solvent from one batch99 MJper kg of extract powder31 ×the spray dryer's 316 MJ; water is57% of the recovery dutyMasses from the PFD stream table; heat of mixing and sensible heat ignored. Ethanol 837 kJ/kg (38.56 kJ/mol at 351.5 K); water 2,257 kJ/kg at 100 °C.Latent heat per illustrative batch: solvent recovery needs about 9,921 MJ, roughly 31 times the 316 MJ the spray dryer needsEvaporator E-101 · stream 8Evaporator E-101: ethanol 3,415 MJEvaporator E-101: water 4,785 MJ8,200 MJMarc desolventizing · stream 9Marc desolventizing: ethanol 603 MJMarc desolventizing: water 813 MJ1,415 MJEluate concentrator E-103 · stream 15Eluate concentrator E-103: ethanol 293 MJEluate concentrator E-103: water 14 MJ306 MJSpray dryer D-101 · stream 18, for comparisonSpray dryer D-101: water 316 MJ316 MJethanolwater9,921 MJto recover solvent from one batch99 MJper kg of extract powder31 ×the spray dryer's 316 MJ; water is 57%of the recovery dutyEthanol 837 kJ/kg; water 2,257 kJ/kg; heat of mixing andsensible heat ignored.
Masses from the illustrative stream table. Ethanol 38.56 kJ/mol at 351.5 K (Majer and Svoboda, via NIST Chemistry WebBook) = 837 kJ/kg; water 2,257 kJ/kg at 100 °C. Heat of mixing and sensible heat are ignored. Multiple-effect evaporation or vapor recompression would cut the steam needed for this duty.
Text version: latent heat by recovery step
Latent heat to recover solvent per illustrative batch
Recovery step (per 1,000 kg herb batch)Ethanol (kg)Water (kg)Latent heat (MJ)
Evaporator E-101 (extract)4,0802,1208,200
Marc desolventizing7203601,415
Eluate concentrator E-1033506306
Total solvent recovery5,1502,4869,921
For comparison: water removed in the spray dryer0140316

About 99 MJ of latent heat per kilogram of powder goes into solvent recovery in this example, roughly thirty times the latent heat the spray dryer needs. Table regenerated by src/modules/process/compute/static_tables.py.

Eight unit operations, with a control loop on each variable that sets product quality

Hover or tab to a unit for its operating principle; the descriptions are also listed below.

Planned pilot train: milling, extraction, filtration, evaporation with solvent recovery, resin purification and spray dryingIllustrative schematic
Drawn to ANSI/ISA-5.1 conventions: a circle is a field instrument, a circle in a square a control-system function, a dashed line a signal. Tags follow the ISA letter code (first letter = measured variable: T temperature, P pressure, L level, F flow, A analysis; following letters = function: I indicate, C control, T transmit, D differential). Equipment classes, tags and loop numbers are illustrative; no sizes are specified and nothing has been purchased. Source: ANSI/ISA-5.1-2024, Instrumentation and Control Symbols and Identification.
Show unit descriptions
  • M-101 Hammer mill. Size reduction. Particle size sets the diffusion path, and the time to a given extraction yield scales with the radius squared (see Science lab). Design variables: screen size, rotor speed, feed rate. Too fine a grind slows filtration and heats the material.
  • R-101 Jacketed, agitated extractor. Solvent dissolves the soluble constituents; temperature, time, solvent ratio and agitation set yield and composition. Nitrogen blanket for the flammable solvent. Design variables: working volume, jacket area, impeller type and speed, temperature range.
  • F-101 Filter. Separates spent plant material (marc) from the extract. Pressure drop rises as the cake builds (PDI-102). Filter area and media are sized from pilot filtration tests.
  • E-101 Falling-film evaporator. Liquid runs down heated tubes as a thin film: short residence time and, under vacuum, a low boiling temperature, which suits heat-sensitive extracts. Steam condenses on the shell side. Design variables: area, wetting rate, pressure, steam temperature.
  • V-101 Vapor–liquid separator. Disengages solvent vapor from the concentrate leaving the evaporator.
  • E-102 Condenser. Chilled water condenses the solvent vapor so ethanol can be recovered and reused. Duty is set by the vapor rate and its latent heat.
  • V-102 Solvent receiver. Holds recovered solvent under nitrogen; its ethanol content is checked before it returns to extraction.
  • VP-101 Vacuum pump. Holds the evaporator and condenser under vacuum (PIC-103); lower pressure lowers the boiling temperature.
  • C-101 Adsorption-resin column. A macroporous resin binds target constituents from the aqueous concentrate; sugars and salts pass to waste; ethanol elutes the enriched fraction, cut by UV absorbance (AT-105). Design variables: resin, bed volume, loading, flow in bed volumes per hour, eluent strength.
  • E-103 Eluate concentrator. Removes eluent ethanol and water to reach the dryer's target feed solids.
  • H-101 Air heater. A steam coil heats filtered ambient air to the dryer inlet temperature (TIC-106).
  • D-101 Spray dryer. An atomizer makes droplets that dry in the hot air; while water evaporates, evaporative cooling holds each droplet near the wet-bulb temperature. Outlet temperature tracks residual moisture (TIC-107 trims the feed rate). Design variables: inlet and outlet temperature, feed solids, atomization, residence time.
  • CY-101 Cyclone. Separates powder from the exhaust air by centrifugal force; product leaves through a rotary valve.
  • BF-101 Bag filter. Captures fines the cyclone misses before the air is exhausted (PDI-108).
  • K-101 Exhaust fan. Draws air through the dryer train, holding the chamber slightly below atmospheric pressure.
At loop level, the dryer's quality-setting variables each close through a transmitter, a control-system function and a final elementIllustrative schematic
P&ID fragment of the planned spray-drying section showing three control loops: inlet-air temperature TIC-106 on the heater steam valve, outlet-air temperature TIC-107 on the feed-pump speed, and bag-filter pressure drop PDI-10816Feed fromE-103MP-104D-101H-101Ambient airSteamTV-106TcondensateTT106CY-101TT10717Extract powderrotary valveBF-101FinesK-10118ExhaustPDT108TIC106sets the drying driving forceTIC107speedholds the outlet temperature, which tracks residual moisture, by trimming the feed ratePDI108pulse cleaningand alarmTTfield instrument (circle)TICcontrol-system function,operator-accessibleelectrical signalutility
P&ID fragment of the drying section to ANSI/ISA-5.1-2024 conventions. TV-106 is the steam control valve of loop 106; T marks the steam trap. Stream numbers match the process flow diagram above. Not to scale; no vendor design implied.
Text version: the eight control loops of the pilot train
LoopMeasuresActs onWhy it matters for the product
TIC-101Extractor temperatureSteam valve on the jacketExtraction rate rises with temperature; so does degradation of heat-labile constituents
PDI-102Pressure drop across the filterOperator alarmA rising drop signals cake build-up or blinding before the filter fails
PIC-103Evaporator pressure (vacuum)Vacuum pump speedLower pressure lowers the boiling point and the thermal load on the extract
LIC-104Solvent receiver levelRecycle pumpHolds the recovered-solvent inventory that is returned to extraction
AT-105UV absorbance at the column outletThree-way valve: waste or eluateCuts the enriched fraction reproducibly instead of by elapsed time
TIC-106Dryer inlet-air temperatureSteam valve on the air heaterSets the drying driving force
TIC-107Dryer outlet-air temperatureFeed-pump speedOutlet temperature tracks residual moisture, so feed rate is trimmed to hold it
PDI-108Pressure drop across the bag filterPulse cleaning and alarmKeeps fines capture and exhaust flow stable

Drawn as flows, the solvent loop dominates: recycled solvent is 7,250 of the 9,000 kg in the extractor

Mass balance per batch (kg), basis 1,000 kg herb, dry basisIllustrative example
Recycled solvent is drawn as its own source on the left and as a return on the right, joined by the dashed loop; a Sankey diagram cannot draw a cycle directly. Assumptions: 60% w/w ethanol at 8:1 solvent to herb; 18% of herb mass extractable; the marc retains 1,200 kg of solvent, of which ethanol is fully and water partly recovered; 30 kg ethanol lost at vents; the resin binds 96 of 180 kg extracted solids; powder leaves at 4.0% moisture. Every node balances in total mass, solids, ethanol and water (a check runs when the page loads).

Spray drying spends roughly half its heat on evaporation; most of the rest leaves in the exhaust air

How it works

The air rate follows from an energy balance on the chamber. A hotter inlet or cooler outlet cuts the air needed per kilogram of water; the outlet temperature also governs residual moisture and heat exposure. The default feed is stream 16 processed over two hours.

Chamber energy balance (reference: ambient air and liquid water at T₀; ΔT = T − T₀)G cH[(1 − f)ΔTin − ΔTout]
= E(λ0 + cvΔTout) + P cpΔTout
Water evaporated
Powder made
Dry air required
Inlet air volume
Heater duty
Heat per kg water
Overall thermal efficiency (Masters)
Exhaust dew point (margin)

Where the heater duty goes (kW)Model output
Heat per kilogram of water versus inlet temperatureModel output
ASHRAE Handbook—Fundamentals (2017), ch. 1 Psychrometrics; Masters K. Spray Drying Handbook, 4th ed. (1985), overall thermal efficiency η = (Tin − Tout)/(Tin − T0); NIST Chemistry WebBook (water, 20 °C, 101.325 kPa); Murphy DM, Koop T. Q J R Meteorol Soc. 2005;131:1539–1565.
Method, assumptions and limits
What it calculates
Water evaporated, powder made, dry-air rate, inlet air volume, heater duty and its split, heat per kilogram of water, thermal efficiency and the exhaust dew point.
Equations
Solids balance P = Fxs/(1 − xp); water E = F(1 − xs) − Pxp; the chamber balance above solved for G; heater duty Q = GcHΔTin; humid heat cH = 1.006 + 1.86W0; λ0 = 2,501 − (4.184 − 1.86)T0; exhaust humidity W1 = W0 + E/G; dew point where the Murphy–Koop liquid vapor pressure equals pW1/(0.621945 + W1).
Variables and units
Flows in kg/h; heats in kJ/kg and kJ/(kg·K); duty in kW (kJ/h ÷ 3,600); air volume from the moist-air specific volume 287.05(T + 273.15)(1 + 1.6078W)/101,325 m³ per kg dry air. Each term of the balance is kg/h × kJ/kg = kJ/h.
Assumptions
Steady state; feed enters at ambient temperature; powder leaves at the outlet-air temperature with dry-solids cp 1.5 kJ/(kg·K) (illustrative); wall loss a fixed fraction of heater duty; atmospheric pressure.
Valid range
A solution exists only when (1 − f)ΔTin exceeds ΔTout; otherwise the readouts say "no solution" and a warning explains why.
What it does not establish
Stickiness, glass transition, volatile losses, particle size and residence time, which set the real operating window, are outside the balance.
Verification
Independent Python reference using CoolProp humid-air properties for the dew point, in tests/numerics/ref/technologies-process-engineering.py.

Solvent recovery is the largest energy demand of an ethanol extraction train, so utilities are sized from the mass balance

Each utility is sized from a balance and carries its own safety and quality requirements.

Pressure sets the boiling and condensing temperatures of the solvent recovery loopReference equations of state
Vapor pressure of water and ethanol from 0 to 130 degrees C on a log scale: at 20 kPa ethanol boils at about 42 degrees C and water at 60; steam at 200 kPa condenses at 120.2 degrees C0.5125102050100200020406080100120temperature, °CkPaWaterEthanol1 atm (101.3 kPa)20 kPa vacuumethanol 42 °Cethanol 42 °Cwater 60 °Cwater 60 °CsteamsteamWhat the curves setEvaporating under 20 kPa lets ethanol boilnear 42 °C instead of 78 °C, so the extractspends its concentration step cooler.A jacket fed with saturated steam at 200 kPaabsolute holds 120.2 °C; pressure sets theheating temperature.The same vacuum lowers the condensingtemperature, so the condenser needs coldercoolant to recover the vapor.
Vapor pressures from CoolProp (IAPWS-95 for water; reference equation for ethanol), computed October 24, 2026; 200 kPa steam at 120.2 °C agrees with NIST.
Show the table (7 rows)
UtilityUsed bySized fromRequirement to resolve in design
Steam and condensateExtractor jacket, evaporators, dryer air heaterEvaporation duty and heat-up ratePressure rating; condensate return
Chilled and cooling waterSolvent condensers, batch cool-down, homogenizer coolersCondenser duty at the vapor rateTemperature low enough to hold vent losses down
VacuumEvaporatorsNon-condensable gas load and leak ratePump exhaust routed away from ignition sources
NitrogenBlanketing of solvent vessels; inerting a closed-cycle dryerVessel volumes and purge ratesOxygen monitoring; asphyxiation risk in enclosed spaces
Compressed airInstruments, bag-filter pulse cleaningConsumers and duty cyclesOil-free and dry where it touches product
Process waterExtraction, washing, cleaningRecipe and cleaning volumesQuality set by specification for each use
Dust collection and ventilationMilling, powder handling, the dryer exhaustCapture velocities and air changesDust hazard analysis (see process safety below)
Five process solvents against water at 25 °C: ethanol needs 38% of water's latent heat but conducts heat at a quarter of its rateReference equations of state
CoolProp reference equations (IAPWS-95 water; ethanol, methanol, n-hexane, n-heptane), 25 °C and 101.325 kPa; cells are ratios to water. ρ density, μ viscosity, cp heat capacity, k thermal conductivity, ΔHv latent heat at the normal boiling point, pv vapor pressure at 25 °C. Acetone is omitted because CoolProp has no viscosity model for it. Click a column to sort.
Data table (absolute values)
SolventDensity, kg/m³Viscosity, mPa·scp, kJ/(kg·K)k, W/(m·K)Latent heat, MJ/kgVapor pressure 25 °C, kPaBoiling point, °C
Water997.00.8904.1810.6072.2573.1799.97
Ethanol785.11.0822.4350.1640.8507.8978.42
Methanol786.30.5442.5350.2001.10116.9864.48
n-Hexane654.90.2982.2730.1200.33520.1668.72
n-Heptane679.60.3902.2410.1220.3176.0998.38

Latent heats in this table come from the reference equations of state in CoolProp; for ethanol that gives 0.850 MJ/kg, while the solvent-recovery figures above use the measured 38.56 kJ/mol (NIST WebBook), 0.837 MJ/kg. The 1.5% difference changes no conclusion.

Explanation, details and sources

A balance that closes is the first deliverable of a pilot campaign; without it, yield, solvent-loss and residual-solvent claims cannot be trusted. The example is invented but closes on every component.

Transport phenomena

Seven dimensionless numbers decide whether a laboratory observation carries over to the plant

Each number is a ratio of two competing effects; when one changes between scales, the controlling mechanism can changeTextbook definitions
Seven dimensionless numbers, each the ratio of two competing effects: Reynolds, Prandtl, Schmidt, Nusselt, Sherwood, Péclet and the mass-transfer Biot number, with the place each matters in extraction and dryingReReynoldsρvL / μinertia ÷ viscous forceslaminar or turbulent; stirred-tankregimePrPrandtlcp​μ / kmomentum ÷ thermal diffusivityjacket and exchanger correlationsScSchmidtμ / (ρD)momentum ÷ mass diffusivityabout 103​ for small molecules inwaterNuNusselthL / kconvective ÷ conductive heattransferfilm coefficients inside UShSherwoodkf​L / Dconvective ÷ diffusive masstransferSh = 2 for a sphere in still liquidPePécletvL / Dadvection ÷ diffusionaxial dispersion; solute crowding ina drying dropletBiBiot (mass)kf​R / Deff​external ÷ internal conductanceBi ≫ 1: stirring harder does not helpWhen a number changes betweenscales, the controlling mechanismcan change, and so can the result.

Bird RB, Stewart WE, Lightfoot EN. Transport Phenomena. 2nd ed. Wiley; 2002; Bergman TL, et al. Fundamentals of Heat and Mass Transfer. 7th ed. Wiley; 2011.

Counterflow recovers more heat than parallel flow from the same exchanger, and the gap widens as the exchanger grows

How it works

The effectiveness–NTU method gives outlet temperatures from the conductance UA and the two heat-capacity rates. Here water cools a hot process stream.

Effectiveness–NTU (counterflow) · log-mean temperature differenceε = 1 − e−NTU(1−Cr)1 − Cr e−NTU(1−Cr)
NTU = UACmin
Q = ε Cmin(Th,in − Tc,in) = UA ΔTlm
Heat duty
Hot outlet
Water outlet
Effectiveness ε
NTU · Cr
ΔTlm (check UA·ΔTlm)
Same UA, other arrangement
Temperature along the exchanger (fraction of heat-transfer area)Model output
Effectiveness versus NTU at the current heat-capacity ratioModel output
Bergman TL, Lavine AS, Incropera FP, DeWitt DP. Fundamentals of Heat and Mass Transfer, 7th ed. Wiley; 2011 (ch. 11, effectiveness–NTU relations). Profiles are integrated from the local energy balances dTh/dx = −(UA/Ch)(Th − Tc) and dTc/dx = ∓(UA/Cc)(Th − Tc).
Method, assumptions and limits
What it calculates
Heat duty, outlet temperatures, effectiveness and the log-mean temperature difference of a two-stream exchanger in counterflow or parallel flow, and the same duty for the other arrangement.
Equations
Counterflow ε = (1 − e−NTU(1−Cr))/(1 − Cre−NTU(1−Cr)), and NTU/(1 + NTU) when Cr = 1; parallel ε = (1 − e−NTU(1+Cr))/(1 + Cr); Q = εCmin(Th,in − Tc,in); the profiles integrate the local balances with a fourth-order Runge–Kutta step.
Variables and units
Flows in kg/h (÷ 3,600 to kg/s); heat capacities in kJ/(kg·K); C = ṁcp in kW/K; UA in kW/K on a logarithmic slider from 0.2 to 20; temperatures in °C; duty in kW.
Assumptions
Constant U and heat capacities; no phase change; no heat loss; water cp 4.18 kJ/(kg·K); the process-stream heat capacity is an illustrative input (ethanol–water mixtures lie below water). Fouling would lower U over a campaign; design adds a fouling resistance.
Valid range
Single-phase liquids within the slider ranges. The UA·ΔTlm check equals the duty to rounding.
What it does not establish
Exchanger area, pressure drop, fouling margin or mechanical design.
Verification
An independent Python reference integrates the two differential energy balances numerically (scipy) and compares outlet temperatures with the page, in tests/numerics/ref/technologies-process-engineering.py.

A 2,000 L batch takes about thirteen times as long to heat as 1 L, because jacket area per liter falls as volume rises

How it works

With condensing steam in the jacket, a well-mixed batch approaches the steam temperature exponentially, with a time constant M cp/UA that grows with the cube root of volume for similar vessels.

Batch heating with an isothermal heating mediumT(t) = Ts − (Ts − T0)
 × exp(−UA tM cp)
1 L to target
100 L to target
2,000 L to target
Jacket area per liter, 1 L → 2,000 L
Batch temperature versus time at three scalesModel output
Time to target versus batch volume (log–log): slope one-thirdModel output
Bergman et al. 2011, lumped-capacitance energy balance; Perry's Chemical Engineers' Handbook, 9th ed. (2018), batch heating of agitated vessels; NIST Chemistry WebBook, saturation properties of water.
Method, assumptions and limits
What it calculates
The time for a well-mixed batch to heat from its starting temperature to a target with condensing steam in the jacket, at 1 L, 100 L and 2,000 L.
Equations
T(t) = Ts − (Ts − T0)e−t/τ, τ = Mcp/(UA); time to target t = τ ln[(Ts − T0)/(Ts − T)]; vessel diameter T = (4V/π)1/3, jacket area 1.25πT².
Variables and units
U in W/(m²·K); M = 998V kg; cp = 4,184 J/(kg·K); A in m²; τ in s.
Assumptions
Cylindrical vessels with liquid height equal to diameter, jacket on the wetted wall and a flat bottom, geometrically similar across scales; constant U (an illustrative input); water-like contents (998 kg/m³, 4.18 kJ/(kg·K)), well mixed; no heat loss. Saturated steam at 200 kPa absolute condenses at 120.2 °C (NIST).
Valid range
Target temperature below the steam temperature (the target is held at least 0.5 K below it).
What it does not establish
Real U depends on agitation, fouling and the jacket side; internal coils change the area-to-volume ratio.
Verification
Independent Python reference in tests/numerics/ref/technologies-process-engineering.py.
Time to target across batch volume and overall coefficient UModel output

Volume and time are on logarithmic axes. Amber marks heat-up within 60 minutes. Points mark 1 L, 100 L and 2,000 L at the U set above; the steam, starting and target temperatures follow the sliders.

Show data (minutes to target)
VolumeU = 1002505001,0001,500 W/m²·K
The table fills in when the page's scripts run; the equation above gives every value.
Same equation and assumptions as the calculator above: geometric similarity, liquid height equal to diameter, jacket on the wetted wall and bottom, water-like contents, constant U. Heat-up time scales as V1/3/U, so a tenfold larger U offsets a thousandfold larger volume.

Three ideal countercurrent stages at a solvent ratio of 1.5 recover 88% of the solute, and each added stage buys less

How it works

Fresh solvent meets the most exhausted material, so every stage keeps a concentration difference. The Kremser equation gives the fraction left after N ideal stages; the solvent ratio S also sets the evaporation load downstream.

Kremser equation, countercurrent washing (stripping form)φ = S − 1SN+1 − 1 recovery = 1 − φ
S = VL
Solute recovered
Left in the marc
Stages for 99% at this S
Adding one more stage
Solute recovered versus number of ideal stagesModel output
Ideal stages needed versus solvent ratio: solvent and stages trade against each otherModel output
Kremser A. Theoretical analysis of absorption process. National Petroleum News. 1930; Seader JD, Henley EJ, Roper DK. Separation Process Principles, 3rd ed. Wiley; 2011 (Kremser method; leaching and washing).
Method, assumptions and limits
What it calculates
The fraction of solute recovered after N ideal countercurrent washing stages at solvent ratio S, the stages needed for 99% and the gain from one more stage.
Equations
Fraction left in the marc φ = (S − 1)/(SN+1 − 1), and 1/(N + 1) when S = 1; recovery = 1 − φ.
Variables and units
S = fresh solvent flow ÷ retained solution flow (dimensionless); N whole number.
Assumptions
Ideal stages (overflow and retained solution leave at the same concentration); constant underflow (retained solution per kg of solids); solute already dissolved; solute-free fresh solvent.
Valid range
S 0.5–4, N 1–10; with S < 1 recovery approaches S and 99% may be unreachable, which the readout states.
What it does not establish
Diffusion out of particles makes real stages less than ideal; stage efficiency is measured in pilot runs.
Verification
An independent Python reference solves the stage-by-stage solute balances as a linear system (numpy) instead of using the closed form, in tests/numerics/ref/technologies-process-engineering.py.

In drying, heat supply to the surface limits the constant-rate period and moisture moving out of the solid limits the falling-rate period

How it works

Above the critical moisture content the surface stays wet and dries at a rate set by the air. Below it, internal transport limits the rate, so the last few percent of moisture take most of the time.

Drying time, constant rate then linear falling ratetc = Ls(X0 − Xc)A Nc
tf = Ls(Xc − Xe)A Nc lnXc − XeX − Xe
Constant-rate period
Falling-rate period
Total to target

Drying-rate curve and moisture versus timeModel output
Total drying time versus target moisture: the last few percent cost the mostModel output
Geankoplis CJ. Transport Processes and Separation Process Principles, 4th ed. Prentice Hall; 2003 (drying of process materials); Perry's Chemical Engineers' Handbook, 9th ed. (2018), solids drying.
Method, assumptions and limits
What it calculates
Constant-rate and falling-rate drying times for a tray or bed to reach a target moisture.
Equations
tc = Ls(X0 − Xc)/(ANc); tf = Ls(Xc − Xe)/(ANc) · ln[(Xc − Xe)/(X − Xe)].
Variables and units
X in kg water per kg dry solid; Nc in kg/(m²·h); Ls/A in kg dry solid per m²; times in h. (kg/m²)(kg/kg)/(kg/(m²·h)) = h.
Assumptions
Constant air conditions; falling rate linear in X − Xe; drying from the exposed surface. Drying droplets show analogous stages, on time scales set by droplet size and air conditions (see the drying page).
Valid range
The critical moisture is held at least 0.05 below the initial moisture and the target at least 0.005 above equilibrium; a warning appears when a slider is clamped.
What it does not establish
Real materials can show several falling-rate zones, shrinkage and case hardening; drying curves are measured.
Verification
Independent Python reference integrating dX/dt with scipy, in tests/numerics/ref/technologies-process-engineering.py.

A concentrated extract can flow laminar where water would be turbulent, which changes pressure drop, pump choice and cleanability

How it works

The Reynolds number decides the flow regime; only in turbulent flow does wall roughness change the friction factor. Raise the viscosity toward a concentrate and the operating point crosses the Moody chart's transition zone.

Darcy–Weisbach with the Colebrook and Haaland friction factorsΔp = f LD ρ v22
Re = ρ v Dμ
1√f = −2 log10(ε/D3.7
 + 2.51Re √f)
laminar (Re < 2,300): f = 64/Re
Velocity
Reynolds number · regime
Friction factor (Colebrook · Haaland)
Pressure drop
Head loss
Pump shaft power

Moody chart computed from the Colebrook equation, with the current operating pointModel output
System curve: pressure drop versus flow rate for the current pipe and fluidModel output
Moody LF. Friction factors for pipe flow. Trans ASME. 1944;66(8):671–684; Colebrook CF. J Inst Civ Eng. 1939;11(4):133–156; Haaland SE. J Fluids Eng. 1983;105(1):89–90; NIST Chemistry WebBook (water at 20 °C).
The Colebrook friction factor over Reynolds number and roughness: in the amber region only roughness mattersModel output
Colebrook CF. J Inst Civ Eng. 1939;11(4):133–156, solved by iteration; Moody LF. Trans ASME. 1944;66(8):671–684. The marked point follows the pipe-flow calculator. Drag to rotate.
Data table: Darcy friction factor
Reε/D 10⁻⁶10⁻⁴10⁻³10⁻²0.05
Method, assumptions and limits
What it calculates
Velocity, Reynolds number, friction factor, pressure drop, head loss and pump shaft power for flow in a straight pipe.
Equations
Re = ρvD/μ; laminar f = 64/Re below Re 2,300; otherwise Colebrook 1/√f = −2 log10(ε/(3.7D) + 2.51/(Re√f)), solved by iteration from the Haaland estimate; Δp = f(L/D)(ρv²/2); head = Δp/(ρg); shaft power = QΔp/η.
Variables and units
Flow 1–1,000 L/min (logarithmic slider); D in mm; L in m; μ 1.002–500 mPa·s (logarithmic); ρ in kg/m³; roughness 0.0015–0.5 mm (logarithmic); Δp in Pa: (m/m)(kg/m³)(m/s)² = Pa.
Assumptions
Newtonian fluid; fully developed flow in a straight circular pipe; fittings counted as equivalent length; default fluid water at 20 °C (998.2 kg/m³, 1.002 mPa·s, NIST). The roughness range starts at drawn tubing, 0.0015 mm (Moody 1944).
Valid range
Transitional flow (Re 2,300–4,000) is flagged because the friction factor there is uncertain.
What it does not establish
Concentrated extracts are often shear-thinning and need measured rheology; pump selection also needs NPSH and the pump curve.
Verification
Independent Python reference solving Colebrook with scipy root finding, in tests/numerics/ref/technologies-process-engineering.py.

A continuous step with a broad residence-time distribution under-processes some material and over-exposes the rest

How it works

In continuous equipment, material does not all spend the mean residence time τ inside. In a chain of N well-mixed tanks, one tank gives the broadest spread and many approach plug flow; the equivalent Péclet number describes the same spread for a pipe.

Tanks in series · dispersion modelE(θ) = N(Nθ)N−1 e−Nθ(N − 1)!
σθ² = 1N
σθ² = 2Pe − 2Pe²(1 − e−Pe)
Variance σθ²
Leaves too early
Stays too long
Equivalent Péclet number
Exit-age distribution E(θ) for tanks in seriesModel output

Danckwerts PV. Continuous flow systems: distribution of residence times. Chem Eng Sci. 1953;2(1):1–13; Levenspiel O. Chemical Reaction Engineering. 3rd ed. Wiley; 1999 (tanks-in-series and closed-vessel dispersion models). Shaded: leaves before the minimum time (amber) and stays beyond the maximum (red).
Method, assumptions and limits
What it calculates
The exit-age distribution of N equal well-mixed tanks, the fractions leaving before and after chosen times, and the Péclet number of a closed vessel with the same variance.
Equations
As above, with θ = t/τ; fractions from the cumulative distribution F(θ) = 1 − e−Nθ Σk=0N−1(Nθ)k/k!; Pe solved by bisection.
Variables and units
N whole number; τ in minutes; the time limits as percentages of τ. E is dimensionless.
Assumptions
Steady flow, equal tanks, no bypassing or dead zones; closed-vessel boundary conditions for the dispersion model.
Valid range
1 to 50 tanks; the Péclet equivalence is exact in variance only.
What it does not establish
Real equipment has dead zones and bypassing that this model cannot show; the distribution is measured with a tracer test.
Verification
Independent Python reference using scipy's gamma distribution and root finding, in tests/numerics/ref/technologies-process-engineering.py.
Explanation, details and sources
NumberDefinitionRatio ofWhere it matters here
Reynolds, ReρvL/μinertia to viscous forcesLaminar or turbulent pipe flow; stirred-tank regime (Re = ρND²/μ)
Prandtl, Prcpμ/kmomentum to thermal diffusivityHeat-transfer correlations for jackets and exchangers
Schmidt, Scμ/(ρD)momentum to mass diffusivityMass-transfer correlations; about 10³ for small molecules in water
Nusselt, NuhL/kconvective to conductive heat transferFilm coefficients inside the overall coefficient U
Sherwood, ShkfL/Dconvective to diffusive mass transferFilm around a particle; Sh = 2 for a sphere in still liquid
Péclet, PevL/D (= Re·Sc for mass)advection to diffusionAxial dispersion in continuous equipment; solute crowding in a drying droplet
Biot (mass), BikfR/Deffexternal to internal mass-transfer conductanceBi ≫ 1: diffusion inside the particle controls extraction, so stirring harder does not help
Mixing, homogenization and unit operations

A homogenizer concentrates energy that a stirred tank spreads over hours, and each unit operation separates or disperses by its own mechanism

Stirred-tank scale-up rules and a 3D power-per-volume map moved to the scale-up page.

A valve homogenizer concentrates energy that a stirred tank spreads over hours, and the product heats with every pass

How it works

The pressure drop across a homogenizing valve is an energy density: 1 MPa delivers 1 MJ/m³. A stirred tank's turbulence breaks droplets only down to a size set by the dissipation rate (Hinze 1955), far above nanoemulsion sizes. The smallest eddy (Kolmogorov length) is a first check of shear sensitivity; damage itself is measured.

Energy density · heating · breakupEv = Δp ΔT = Δpρcp
ηK = (ν³/ε)1/4
dmax = 0.725 (σ/ρ)3/5ε−2/5
Energy density delivered
Temperature rise per pass
Temperature rise, all passes
Stirred tank: Kolmogorov length
Stirred tank: largest stable droplet
Stirring time for the same energy
Largest stable droplet and smallest eddy versus energy dissipation rateModel output

Hinze JO. AIChE J. 1955;1(3):289–295 (dmax relation and constant 0.725); Kolmogorov microscale as in Paul EL, et al., eds. Handbook of Industrial Mixing. Wiley; 2003. The computed 2.5 K per 10 MPa (water-like product, 1,000 kg/m³ and 4.0 kJ/(kg·K)) agrees with the 2–2.5 °C per 10 MPa reported by Patrignani F, et al. Front Microbiol. 2019;10:246 and Romano E, et al. Int J Mol Sci. 2021;22(18):9896.
Method, assumptions and limits
What it calculates
Energy density and adiabatic temperature rise of valve homogenization; for a stirred tank, the mean dissipation rate, the Kolmogorov length and the Hinze largest stable droplet; the stirring time that would deliver the same energy density.
Equations
As above, with ε = (P/V)/ρ and ν = μ/ρ; stirring time = nΔp/(P/V).
Variables and units
Δp in Pa (Pa = J/m³); ρ = 1,000 kg/m³ and cp = 4.0 kJ/(kg·K) (water-like product); P/V in W/m³ on a logarithmic slider from 10 W/m³ to 10 kW/m³; σ in N/m; μ in Pa·s, logarithmic from 1 to 100 mPa·s. ε in W/kg = m²/s³; lengths in m.
Assumptions
All homogenizer energy ends up as heat in the product (adiabatic); the tank's mean dissipation rate stands in for the local rate, which near the impeller can be far higher; dilute dispersed phase; Hinze's relation holds in the inertial range, when dmax is well above the Kolmogorov length (the readout turns amber otherwise).
Valid range
10–200 MPa; 1–10 passes; 10 W/m³ to 10 kW/m³.
What it does not establish
It does not predict homogenizer droplet size, which depends on valve design, emulsifier adsorption speed and recoalescence, and is measured. Shear-sensitive ingredients need their own damage tests.
Verification
Independent Python reference in tests/numerics/ref/technologies-process-engineering.py.

Four unit operations that make or purify material, drawn from their operating principles

Hover or tab to a component for a short description. Measuring instruments are on the analytical page.

Supercritical CO₂ extraction: above 31.0 °C and 73.8 bar, CO₂ dissolves lipophilic constituents and releases them when the pressure dropsIllustrative schematic
NIST Chemistry WebBook, carbon dioxide phase-change data (critical and triple points); Reverchon E, De Marco I. J Supercrit Fluids. 2006;38(2):146–166. Plotted curves are illustrative shapes, not measured data.

Supercritical CO₂ extraction

What it makes, principle, botanical use and limits
Makes
Makes lipophilic extracts without organic-solvent residues: the CO₂ leaves as a gas when the pressure is released.
Principle
Liquid CO₂ is pumped to pressure and heated above its critical point, where it has liquid-like density and gas-like transport properties. Its solvent power changes with pressure and temperature. Pressure reduction in the separator precipitates the extract, and the CO₂ is recycled. Ethanol can be added as a cosolvent to reach more polar constituents.
Botanical use
Essential oils, oleoresins, seed oils and other lipophilic fractions.
Limits
High-pressure equipment is capital-intensive and safety-critical; polar glycosides extract poorly without cosolvent; batch vessel loading limits throughput.
Standard
No compendial chapter; the process would be designed and qualified within the quality system.
Key relationT_c = 304.18 K (31.0 °C) · p_c = 73.8 barCritical point of CO₂; triple point 216.58 K (−56.6 °C) and 5.185 bar.

Planned · Phase I–II Not purchased

High-pressure homogenizer: a coarse premix is forced through a narrow gap, where intense flow breaks droplets that emulsifier must then stabilizeIllustrative schematic
Håkansson A. Emulsion formation by homogenization: current understanding and future perspectives. Annu Rev Food Sci Technol. 2019;10:239–258. Plotted curves are illustrative shapes, not measured data.

High-pressure homogenizer

What it makes, principle, botanical use and limits
Makes
Makes fine emulsions and nanoemulsions from a coarse premix.
Principle
A positive-displacement piston pump forces the premix through the narrow gap of a homogenizing valve. Droplets break up in the intense flow downstream of the gap; emulsifier must cover the new interface quickly, or droplets recoalesce. The product can be passed several times.
Botanical use
Oil-in-water delivery systems for lipophilic botanical actives (see Delivery).
Limits
Each pass heats the product; over-processing can increase recoalescence. Smaller droplets do not by themselves guarantee stability or bioavailability.
Standard
No compendial chapter; droplet size would be verified by DLS or laser diffraction.
Key relationd = f(pressure, passes, formulation)Droplet size falls with pressure and passes until coalescence and emulsifier coverage set a floor; the curve shown is illustrative.

Planned · Phase I–II Not purchased

Ultrafiltration: feed sweeps along the membrane; small solutes pass, large ones are retained, and a polarized layer caps the fluxIllustrative schematic
Quezada C, et al. Prediction of permeate flux in ultrafiltration processes: a review of modeling approaches. Membranes. 2021;11(5):368. Plotted curves are illustrative shapes, not measured data.

Crossflow membrane ultrafiltration

What it makes, principle, botanical use and limits
Makes
Separates by molecular size: concentrates or fractionates an aqueous extract without heat.
Principle
A pump circulates feed tangentially along the membrane. Transmembrane pressure drives permeate through the pores while retained solutes accumulate in a boundary layer at the wall. At higher pressure that layer, not the pressure, limits flux.
Botanical use
Removing high-molecular-weight polysaccharides or proteins, or concentrating small constituents, depending on the cut-off chosen.
Limits
Fouling and concentration polarization reduce flux; cut-offs are nominal, so molecules of similar size separate incompletely; membranes need validated cleaning.
Standard
No compendial chapter.
Key relationJ = TMP / μ(R_m + R_c), J = k·ln(C_g / C_b)Resistance-in-series model and the gel-polarization limit, with mass-transfer coefficient k, gel concentration C_g and bulk concentration C_b.

Planned · phase not set Not purchased

Adsorption resin: an aqueous extract is loaded, sugars and salts are washed out, and an ethanol–water step elutes the enriched fractionIllustrative schematic
Li J, Chase HA. Development of adsorptive (non-ionic) macroporous resins and their uses in the purification of pharmacologically-active natural products from plant sources. Nat Prod Rep. 2010;27(10):1493–1510. Plotted curves are illustrative shapes, not measured data.

Macroporous adsorption-resin column

What it makes, principle, botanical use and limits
Makes
Makes an enriched fraction of a compound class, for example flavonoids or saponins, from a crude aqueous extract.
Principle
Non-ionic macroporous resins adsorb constituents mainly through hydrophobic interactions. Sugars and salts pass through during loading and washing; an ethanol–water step desorbs the retained fraction; the resin is then regenerated.
Botanical use
Enrichment and purification of pharmacologically active natural-product classes before drying.
Limits
Selectivity is at the level of a compound class; capacity and breakthrough must be measured for each extract; resin-derived residues must be controlled.
Standard
No compendial chapter.
Key relationLoad → wash → elute → regenerateBreakthrough sets the loading volume; the outlet trace shown is illustrative.

Planned · phase not set Not purchased

Explanation, details and sources

Solids suspension and heat transfer usually track power per volume; shear-sensitive emulsions track tip speed or energy density. A homogenizer delivers in one pass an energy density that a stirred tank needs hours to match.

Process safety and cleaning

An ethanol extraction train with a spray dryer combines flammable liquids and combustible dust, so hazard analysis comes before design freeze

Each hazard needs its own layers of protection, and the analyses that set them come before design freezeDesign requirements Cited codes and rules
Layers of protection the design would need for the flammable solvent, combustible dust and high pressure: analysis, prevention, detection and mitigation, each with its basisFlammable solventEthanol flashes at 13 °C (55 °F); flammablerange 3.3–19% in air (NIOSH)Combustible dustDried botanical powders can be combustibledusts: fuel, ignition, oxygen, dispersion andconfinement (OSHA)High pressureSupercritical CO₂ vessels and valvehomogenizersAnalyzeProcess hazard analysis by node:What-If, checklist, HAZOP, FMEA orfault tree, actions tracked to closure29 CFR 1910.119(e)(2)PSM may apply at 10,000 lb or more ofa liquid flashing below 100 °F in onelocation; coverage is a site-specificlegal question1910.119(a)(1)(ii) · for scale: the illustrativebatch charges 4,800 kg (about 10,600 lb) ofethanolDust hazards analysis for new andexisting facilitiesNFPA 660 (2025), which consolidated NFPA61, 652, 654 and othersIncluded in the process hazard analysisequipment design codes confirmed indetailed engineeringPreventNitrogen blanket on extractor,evaporator and receiversoxidantBonding and grounding; electrical areaclassificationignition · NFPA 30Evaporator strips ethanol, so the dryergets an aqueous feedfuel · stream 16 carries 0 kg ethanolCold condensing holds vent lossesdown; vacuum-pump exhaust awayfrom ignition sourcesfuel, ignition · stream 19: 30 kgMinimize dust escape; collect dust(CY-101, BF-101); clean residues at setintervalsfuel, dispersion · OSHA SHIBBond equipment to ground; suitableelectrical equipment; keep heatedsurfaces away from dustignition · OSHA SHIBRated components; interlocks on vesselclosuresDetectOxygen monitoring wherever nitrogen isusedasphyxiation risk in enclosed spacesSpark or ember detection andextinguishing systemsOSHA SHIBNot specified on this pageMitigateSet in detailed engineering andfire-code review with qualified partnersExplosion protection for the dryerchamber, cyclone, bag filter and mill,set by the dust hazards analysise.g. relief venting, explosion protectionsystems (NFPA 69), isolationPressure reliefLayers of protection the design would need for the flammable solvent, combustible dust and high pressure: analysis, prevention, detection and mitigation, each with its basisFlammable solventEthanol flashes at 13 °C (55 °F); flammable range3.3–19% in air (NIOSH)AnalyzeProcess hazard analysis by node: What-If,checklist, HAZOP, FMEA or fault tree,actions tracked to closure29 CFR 1910.119(e)(2)PSM may apply at 10,000 lb or more of aliquid flashing below 100 °F in onelocation; coverage is a site-specific legalquestion1910.119(a)(1)(ii) · for scale: the illustrativebatch charges 4,800 kg (about 10,600 lb) ofethanolPreventNitrogen blanket on extractor, evaporatorand receiversoxidantBonding and grounding; electrical areaclassificationignition · NFPA 30Evaporator strips ethanol, so the dryergets an aqueous feedfuel · stream 16 carries 0 kg ethanolCold condensing holds vent losses down;vacuum-pump exhaust away from ignitionsourcesfuel, ignition · stream 19: 30 kgDetectOxygen monitoring wherever nitrogen isusedasphyxiation risk in enclosed spacesMitigateSet in detailed engineering and fire-codereview with qualified partnersCombustible dustDried botanical powders can be combustible dusts: fuel,ignition, oxygen, dispersion and confinement (OSHA)AnalyzeDust hazards analysis for new andexisting facilitiesNFPA 660 (2025), which consolidated NFPA61, 652, 654 and othersPreventMinimize dust escape; collect dust(CY-101, BF-101); clean residues at setintervalsfuel, dispersion · OSHA SHIBBond equipment to ground; suitableelectrical equipment; keep heatedsurfaces away from dustignition · OSHA SHIBDetectSpark or ember detection andextinguishing systemsOSHA SHIBMitigateExplosion protection for the dryerchamber, cyclone, bag filter and mill, setby the dust hazards analysise.g. relief venting, explosion protectionsystems (NFPA 69), isolationHigh pressureSupercritical CO₂ vessels and valve homogenizersAnalyzeIncluded in the process hazard analysisequipment design codes confirmed in detailedengineeringPreventRated components; interlocks on vesselclosuresDetectNot specified on this pageMitigatePressure relief
NIOSH Pocket Guide to Chemical Hazards, ethyl alcohol (accessed October 22, 2026); NFPA 30, Flammable and Combustible Liquids Code; NFPA 660 (2025), as summarized by Osborn J. Processing Magazine, January 30, 2025; OSHA, Combustible Dust in Industry: Preventing and Mitigating the Effects of Fire and Explosions, SHIB 07-31-2005, updated November 12, 2014 (explosion pentagon; dust and ignition control and protection methods recommended by NFPA 654; NFPA 69); 29 CFR 1910.119(a)(1)(ii) and (e)(2) (OSHA, accessed October 22, 2026). Ethanol charge from the illustrative stream table; 1 kg = 2.20462 lb. This is a list of what a design would have to resolve, not a safety assessment of any facility.
Ethanol's saturated vapor reaches its lower flammable limit near 11 °C, so a room-temperature ethanol area is inside the flammable rangeNIOSH limits; reference equation
Ethanol's equilibrium vapor concentration in air at 1 atm rises with temperature and reaches the 3.3% lower flammable limit near 11 degrees C, close to its 13 degrees C flash point; it reaches 19% near 41 degrees CFlammable range of ethanol in air: 3.3–19% (NIOSH)flammable range in air, 3.3–19% (NIOSH)0.5%1%2%3.3%5%10%19%40%-10010203040liquid temperature, °Csaturated ethanol vapor3.3% reached at 10.9 °C (computed)flash point 13 °C (NIOSH)Why an ethanol room is a classified areaAbove about 11 °C the vapor over open ethanolcan be flammable: computed from the vaporpressure, it crosses 3.3% near the measuredflash point.Room temperature sits inside the range, soventilation, ignition control and bonding aredesigned in from the start.
NIOSH Pocket Guide, ethyl alcohol (flash point 55 °F/13 °C; LEL 3.3%, UEL 19%); vapor concentration = vapor pressure ÷ 101.325 kPa, with ethanol's vapor pressure from CoolProp, computed October 24, 2026.
A dust explosion needs all five elements, so each one is a place to put a controlOSHA bulletin
OSHA's dust explosion pentagon: fuel, ignition source, oxygen in air, dispersion of the dust in sufficient quantity and concentration, and confinement of the dust cloud; removing any one prevents an explosionExplosionFuel (combustible dust)Ignition sourceOxygen in airDispersionConfinementEach element is a control point (OSHA SHIB, NFPA 654 recommendations)Fueldust collection, housekeepingIgnitionbonding, grounding, rated equipmentOxygeninerting where justifiedDispersionclosed transfers, no blow-down cleaningConfinementventing, isolation, suppression
OSHA. Combustible Dust in Industry, SHIB 07-31-2005 (updated 2014): the explosion pentagon and the NFPA 654 recommendations it lists.
Text version of the hazards and layers
Flammable liquids

Ethanol flashes at 13 °C

Ethanol's flash point is 55 °F (13 °C) and its flammable range 3.3–19% in air (NIOSH). Extractor, evaporator and receivers would need nitrogen blanketing, bonding and grounding, and electrical area classification under the flammable-liquids code (NFPA 30). The evaporator strips ethanol so the dryer receives an aqueous feed; a solvent-laden feed would need a closed-cycle, inert-gas dryer.

Combustible dust

NFPA 660 requires a dust hazards analysis

Dried botanical powders can be combustible dusts. NFPA 660 (2025 edition), which consolidated NFPA 61, 652, 654 and other dust standards in December 2024, requires a dust hazards analysis for new and existing facilities. It would set explosion protection for the dryer chamber, cyclone, bag filter and milling.

Regulation

OSHA process safety management may apply

29 CFR 1910.119 covers processes with 10,000 lb or more of a flammable liquid (flash point below 100 °F) in one location, with an exception for liquids stored in atmospheric tanks below their normal boiling point without chilling. Whether a given design is covered is a site-specific legal question.

Combustible dust needs five elements to explode: fuel, an ignition source, oxygen in air, dispersion of the dust in sufficient quantity and concentration, and confinement of the dust cloud (OSHA's "explosion pentagon"). OSHA's bulletin lists dust-control and ignition-control recommendations from NFPA 654, among them minimizing dust escape, dust collection and filters, regular cleaning, suitable electrical equipment, bonding equipment to ground and separating heated surfaces from dust, and protection methods including pressure-relief venting for equipment, spark or ember detection and extinguishing systems, and explosion protection systems (NFPA 69).

  • Process hazard analysis. A structured review of each node, using What-If, checklist, HAZOP, FMEA or fault-tree methods, led by a qualified facilitator, with actions tracked to closure. Basis: methods listed in 29 CFR 1910.119(e)(2).
  • High pressure. Supercritical CO₂ vessels and homogenizers: pressure relief, interlocks on vessel closures, rated components. Basis: equipment design codes, confirmed in detailed engineering.
  • Utilities. Oxygen monitoring where nitrogen blankets or inerts (asphyxiation risk in enclosed spaces); vacuum-pump exhaust routed away from ignition sources; condenser coolant cold enough to hold vent losses down.

Cleaning: 21 CFR 111.27 (Cornell LII, accessed October 22, 2026).

Explanation, details and sources

Process safety is designed in, reviewed by qualified specialists and checked with the authority having jurisdiction. The items below set out what a design would have to resolve; they are not a safety assessment of any facility.

TopicWhat the design would includeBasis
CleaningEquipment installed to allow cleaning; cleaning and sanitizing between batches in wet processes; disassembly where needed; written procedures and records21 CFR 111.27(a)(3)(i) and 111.27(d) for dietary-supplement operations
Cleaning verificationResidue limits for the previous product and cleaning agents, checked by a suitable analytical method on swabs or rinsesEUTECNIQ proposal; acceptance limits set per product
Allergen and cross-contact controlScheduling, dedicated parts and cleaning validation where products differ in allergen profileEUTECNIQ proposal; confirmed against product labeling obligations
Quality by design and transfer

Quality by design links each critical quality attribute to the process parameters that move it

For a spray-dried botanical extract, a handful of process parameters drive most quality attributes

One loop, the dryer's outlet temperature (TIC-107), bears on degradants, residual ethanol and water contentProposed starting hypotheses
Cause-and-effect matrix linking eighteen process parameters, grouped by unit operation, to seven critical quality attributes, with the proposed control for each attributeUnit operationProcess parameterAssayFingerprintDegradantsResidualethanolWater, aw​Particlesize, flowMicrobialRaw materialLotLot (Raw material) moves chemical fingerprintBioburdenBioburden (Raw material) moves microbial qualityMilling M-101Particle sizeParticle size (Milling M-101) moves assay (marker content)Extraction R-101TemperatureTemperature (Extraction R-101) moves assay (marker content)Temperature (Extraction R-101) moves chemical fingerprintTemperature (Extraction R-101) moves degradation productsTimeTime (Extraction R-101) moves assay (marker content)Time (Extraction R-101) moves degradation productsSolvent composition and ratioSolvent composition and ratio (Extraction R-101) moves assay (marker content)Solvent composition and ratio (Extraction R-101) moves chemical fingerprintResin column C-101Cut point (AT-105)Cut point (AT-105) (Resin column C-101) moves assay (marker content)Evaporation E-101, E-103Temperature and time under vacuum (PIC-103)Temperature and time under vacuum (PIC-103) (Evaporation E-101, E-103) moves chemical fingerprintTemperature and time under vacuum (PIC-103) (Evaporation E-101, E-103) moves degradation productsEvaporator end pointEvaporator end point (Evaporation E-101, E-103) moves residual ethanolEluate concentrationEluate concentration (Evaporation E-101, E-103) moves residual ethanolSpray dryer D-101Outlet temperature (TIC-107)Outlet temperature (TIC-107) (Spray dryer D-101) moves chemical fingerprintOutlet temperature (TIC-107) (Spray dryer D-101) moves degradation productsOutlet temperature (TIC-107) (Spray dryer D-101) moves residual ethanolOutlet temperature (TIC-107) (Spray dryer D-101) moves water and water activityFeed rateFeed rate (Spray dryer D-101) moves water and water activityFeed solidsFeed solids (Spray dryer D-101) moves water and water activityFeed solids (Spray dryer D-101) moves particle size and flowAtomizationAtomization (Spray dryer D-101) moves particle size and flowDrying rateDrying rate (Spray dryer D-101) moves particle size and flowHygieneHold timesHold times (Hygiene) moves microbial qualityCleaningCleaning (Hygiene) moves microbial qualityWater qualityWater quality (Hygiene) moves microbial qualityProposed controlLoop tags refer to the pilot-train schematic and the P&ID fragmentSet-pointranges fromdesignedexperiments;UV cutAT-105;releaseassayRaw-materialqualification;comparisonwithreferencelotsVacuumevaporationPIC-103;outlettemperatureTIC-107HeadspaceGC atreleaseOutlettemperatureheld byfeed-ratetrim; KarlFischer andaw​ at releaseAtomizersetting; laserdiffractionRaw-materiallimits;hold-timelimits;microbiologyat releasethe page's CQA table names this parameter for this attribute (starting hypothesis, to be confirmed by designed experiments)
Definitions: ICH Q8(R2) Pharmaceutical Development, Step 4, August 2009, glossary. Parameter links are EUTECNIQ's proposed starting hypotheses, to be confirmed by designed experiments; "temperature history" and "time at temperature" are marked on each step the table names.
Text version: attributes, parameters and controls
Critical quality attributeProcess parameters that move itControl strategy (proposed)
Marker content (assay)Extraction temperature, time, solvent composition and ratio; particle size; resin cut pointSet-point ranges from designed experiments; UV-controlled cut (AT-105); release assay
Chemical profile (fingerprint)Raw-material lot, solvent composition, temperature historyRaw-material qualification; fingerprint comparison with reference lots
Degradation productsTime at temperature in extraction, evaporation and dryingVacuum evaporation (PIC-103); outlet-temperature control (TIC-107)
Residual ethanolEvaporator end point; eluate concentration; dryer outlet temperatureHeadspace GC test at release
Water and water activityDryer outlet temperature, feed rate, feed solidsOutlet temperature held by feed-rate trim; Karl Fischer and water activity at release
Particle size and flowAtomization, feed solids, drying rateAtomizer setting; laser diffraction in development and at scale-up
Microbial qualityRaw-material bioburden, hold times, cleaning, water qualityRaw-material limits; hold-time limits; microbiology at release

Response-surface optimization finds a region where high yield and low degradation overlap, not a single point

How it works

Twenty runs of a three-factor central composite design (temperature, ethanol fraction, time) are fitted with quadratic models for yield and a degradant. The data are simulated from an invented model; fitting and overlay are computed live.

Second-order response-surface model (coded units)ŷ = b0 + Σ bixi
 + Σ bijxixj + Σ biixi2
Yield model R²
Degradant model R²
Slice meeting both limits
Best predicted yield inside
Predicted responses at the selected timeSimulated data
Box GEP, Wilson KB. On the experimental attainment of optimum conditions. J R Stat Soc B. 1951;13(1):1–38; Montgomery DC. Design and Analysis of Experiments, 10th ed. Wiley; 2020 (response surface methods); ICH Q8(R2) Pharmaceutical Development (2009).
Method, assumptions and limits
What it calculates
Least-squares quadratic models for simulated yield and degradant data from a 20-run central composite design, the slice of the experimental region meeting both limits at the chosen time, and the best predicted yield inside it.
Equations
ŷ = b0 + Σbixi + Σbijxixj + Σbiixi²; b = (XᵀX)⁻¹Xᵀy; R² = 1 − SSE/SST; t = b/se(b) with 10 residual degrees of freedom.
Variables and units
Coded factors ±1 = 45–65 °C, 48–72% ethanol, 50–100 min; α = 1.682; yield in mg/g; degradant in % peak area. The region fraction is counted on a 72 × 72 grid inside the spherical experimental region.
Assumptions
Rotatable design: 8 factorial, 6 axial and 6 center runs. Responses, coefficients and noise are invented: data simulated from an invented quadratic model with fixed pseudo-random noise (seed 20261022).
Valid range
Inside the experimental region; outside it the model extrapolates and the plot is shaded.
What it does not establish
Regions drawn from mean predictions overstate assurance; an ICH Q8(R2) design space has to be demonstrated, with prediction uncertainty and confirmation runs.
Verification
Independent Python reference refits the same simulated data with numpy least squares, in tests/numerics/ref/technologies-process-engineering.py.
Pareto chart of standardized effects, marker yieldSimulated data
Bars are |t| = |coefficient ÷ standard error| from the least-squares fit (10 residual degrees of freedom). Terms beyond the reference line t0.975,10 = 2.228 are significant at α = 0.05; the rest are candidates for removal. Letters: A temperature, B ethanol, C time.

What ICH Q8(R2) means by design space

The definitions

"The multidimensional combination and interaction of input variables (e.g., material attributes) and process parameters that have been demonstrated to provide assurance of quality." Working within it is not considered a change; moving out of it is.

For a drug, the applicant proposes a design space and the regulator assesses it; a dietary supplement has no such filing.

A critical process parameter is one "whose variability has an impact on a critical quality attribute and therefore should be monitored or controlled"; the Pareto chart is one way to find candidates.

ICH Q8(R2), Pharmaceutical Development, Step 4, August 2009, glossary.
Explanation, details and sources

ICH Q8(R2) defines a critical quality attribute (CQA) as a property that should be within a limit to ensure product quality, and a critical process parameter (CPP) as one whose variability affects a CQA. For a dietary supplement no design space is filed, but the same logic gives specifications and process ranges a documented basis.

Technology transfer, process-validation stages, comparability and the proposed readiness gates are on the scale-up and tech-transfer page.

Simulation versus design

Every calculator on this page teaches a mechanism; none of them is a design

A calculator on this page and a validated design differ in their inputs, models, review and proofScope of the calculators
What separates the educational simulations on this page from a validated industrial design: inputs, models, review and proofEducational simulation (this page)Validated industrial designInputsIllustrative values, labeled as suchMeasured properties of the actual material and equipmentModelsTextbook equations with simplifying assumptions, statedin each methods panelModels calibrated and checked against pilot dataReviewNumerical checks against an independent PythonimplementationEngineering, safety and quality review; code complianceProofNone claimedEngineering and qualification runs in the real equipmentWhat separates the educational simulations on this page from a validated industrial design: inputs, models, review and proofInputsEducational simulation (this page) · Illustrativevalues, labeled as suchValidated industrial design · Measured propertiesof the actual material and equipmentModelsEducational simulation (this page) · Textbookequations with simplifying assumptions, statedin each methods panelValidated industrial design · Models calibratedand checked against pilot dataReviewEducational simulation (this page) · Numericalchecks against an independent PythonimplementationValidated industrial design · Engineering, safetyand quality review; code complianceProofEducational simulation (this page) · None claimedValidated industrial design · Engineering andqualification runs in the real equipment
The same four rows are in the table below. Calculators are checked against an independent Python implementation (tests/numerics); none is calibrated to equipment.
Show the table (4 rows)
AspectEducational simulation (this page)Validated industrial design
InputsIllustrative values, labeled as suchMeasured properties of the actual material and equipment
ModelsTextbook equations with simplifying assumptions, stated in each methods panelModels calibrated and checked against pilot data
ReviewNumerical checks against an independent Python implementationEngineering, safety and quality review; code compliance
ProofNone claimedEngineering and qualification runs in the real equipment
Explanation, details and sources

An educational simulation uses textbook equations and invented inputs to show how variables interact. A validated industrial design uses measured properties, vendor data, safety reviews and code compliance, and is proven in qualified equipment.

Discuss a scale-up or process question

Partners moving a botanical process from the bench toward manufacturing can describe it; EUTECNIQ would respond with a proposed development and transfer plan and its limits.