Roasted Onion Reaction Flavor Example and How to Determine Each Parameter in the Predictive Model

This document gives a detailed reaction flavor example built around a roasted onion or savory sulfur reaction flavor, with a step-by-step explanation of how to determine each parameter used in the burn-risk predictive model.

1) Example process

Assume a batch reactor is used to make a roasted onion-type reaction flavor from:

• D-xylose or glucose as reducing sugar
• Cysteine as sulfur precursor
• Methionine or onion-derived sulfur source
• Hydrolyzed vegetable protein or yeast extract
• Water
• Optional pH adjustment with sodium bicarbonate or phosphate buffer

Example batch composition

• Water: 55 wt%
• Xylose: 8 wt%
• Cysteine: 3 wt%
• Methionine: 1 wt%
• Yeast extract or HVP: 20 wt%
• Salt, buffer, and minors: 13 wt%

Process conditions

• 300 L stainless jacketed kettle
• Anchor agitator
• Batch size: 240 kg
• Start at 25°C
• Heat to 95°C to dissolve
• Hold 15 min
• Heat to 112–118°C for reaction development
• Final hold 20–40 min depending on profile
• Nitrogen blanket optional

The concern is that onion-like sulfur notes are easily pushed into burnt cabbage, rubber, sulfur-char, bitter roast, and black particles. This makes it a strong case for a quantitative burn-risk model.

2) Predictive model structure for this example

Core variables used are \(T_b\), \(T_w\), \(T_f\), \(q''\), \(h_b\), \(k_m\), \(C_f\), \(k_b\), \(E_b\), and \(BI\).

3) How to determine each parameter

Parameter 1: Bulk temperature, \(T_b\)

Meaning: average temperature of the reactor contents.

How to measure: use one calibrated RTD or thermocouple in the bulk, preferably two probes at different heights for large vessels. Record every 10–30 seconds.

Example: measured bulk temperature during the final stage is 116°C.

Bulk temperature is easy to measure, but it does not predict burning by itself.

Parameter 2: Jacket temperature, \(T_j\)

Meaning: effective heating-medium temperature.

How to get it: measure steam-jacket condensate temperature, or thermal oil / hot water inlet and outlet.

Example: thermal oil inlet = 135°C and outlet = 127°C.

Parameter 3: Overall heat transfer coefficient, \(U\)

Meaning: overall ability of heat to move from jacket to bulk.

How to estimate: use plant heat-up data during nonreactive heating:

Example:

• \(M = 240\ kg\)
• \(C_p = 3.6\ kJ/kg\cdot K\)
• \(A = 3.8\ m^2\)
• \(dT_b/dt = 0.022\ K/s\)
• \(T_j - T_b = 20\ K\)

Parameter 4: Heat flux, \(q''\)

Meaning: heat entering per unit wall area.

Using \(U = 250\ \text{W/m}^2\text{·K}\) and \(T_j-T_b = 15\ K\):

Parameter 5: Process-side heat transfer coefficient, \(h_b\)

Meaning: how effectively the bulk liquid removes heat from the process wall.

Method A: estimate from a correlation:

Example values:

• \(\rho = 1150\ kg/m^3\)
• \(N = 0.8\ s^{-1}\)
• \(D_i = 0.75\ m\)
• \(\mu = 0.45\ Pa\cdot s\)
• \(C_p = 3600\ J/kg\cdot K\)
• \(k = 0.42\ W/m\cdot K\)
• \(D = 1.0\ m\)

Parameter 6: Wall temperature, \(T_w\)

With \(q'' = 3750\) and \(h_b = 235\):

So:

Parameter 7: Film temperature, \(T_f\)

Meaning: actual temperature of the fluid layer touching or nearly touching the wall.

A practical shortcut is:

For a moderately viscous batch, use \(\phi = 0.75\):

Parameter 8: Density, \(\rho\)

How to measure: pycnometer, density cup, or mass of known volume at process temperature.

Example: \(\rho = 1150\ kg/m^3\).

Parameter 9: Heat capacity, \(C_p\)

How to estimate: DSC, literature, or weighted average from composition. For water-rich savory systems, often 3.2–3.9 kJ/kg·K.

Example:

Parameter 10: Thermal conductivity, \(k\)

How to estimate: transient hot-wire method or literature. Typical aqueous systems are 0.4–0.6 W/m·K.

Example:

Parameter 11: Viscosity, \(\mu\)

How to measure: rheometer or Brookfield viscometer at relevant temperatures and solids levels.

Example:

• at 95°C, \(\mu = 0.18\ Pa\cdot s\)
• at 116°C after reaction thickening, \(\mu = 0.45\ Pa\cdot s\)

As viscosity rises, \(Re\) drops, \(h_b\) drops, and wall temperature rises.

Parameter 12: Film refresh rate, \(k_m\)

Estimate from:

Suppose \(\delta_{eff} = 1.5 \times 10^{-3}\ m\):

This implies a wall-film refresh time of about:

Parameter 13: Susceptible concentration, \(C_f\) and \(C_b\)

Use one lumped “burnable precursor concentration” at first.

Suppose:

Assume wall enrichment factor \(\alpha_c = 1.20\):

Parameter 14: Burn kinetics constant, \(k_b\)

Measure using small sealed tubes or a lab reactor at several temperatures, then fit Arrhenius behavior. Example fitted values:

• at 120°C: \(k_b = 2.5\times10^{-4}\ s^{-1}\)
• at 125°C: \(k_b = 5.3\times10^{-4}\ s^{-1}\)
• at 130°C: \(k_b = 1.1\times10^{-3}\ s^{-1}\)

Suppose the fit gives:

Parameter 15: Activation energy, \(E_b\)

From the Arrhenius plot:

If the slope is \(-11070\):

Parameter 16: Reaction order, \(n\)

Determine by running concentration-series tests at fixed temperature. Suppose the data suggest:

Parameter 17: Burn index, \(BI\)

Use the cumulative damage expression:

If conditions are constant:

Suppose:

• \(T_f = 401.12\ K\)
• \(E_b = 92,000\ J/mol\)
• \(k_{b,0} = 1.4\times10^9\ s^{-1}\)
• \(C_f/C_{ref} = 1.20\)
• \(n = 1.3\)
• \(t = 1800\ s\)

This suggests strong burn risk.

4) Full worked example

Step 1: Heat flux

Step 2: Wall temperature

Step 3: Film temperature

Use \(\phi=0.75\):

Step 4: Burn rate constant

Step 5: Concentration factor

Step 6: Burn index

Interpretation: high scorch risk.

5) Effect of changing one parameter

Case A: Increase agitation

If better agitation raises \(h_b\) from 235 to 320 W/m²·K:

If \(\phi=0.70\):

Case B: Lower jacket temperature by 5°C

If \(T_j = 126^\circ C\) instead of 131°C:

With \(\phi=0.75\):

Burn risk drops sharply.

Case C: Reduce hold time

If hold time drops from 30 min to 15 min, then:

This may move the batch from burnt to merely over-roasted.

6) How to experimentally determine the model in a real flavor lab or plant

• Step 1: measure physical properties such as density, heat capacity, viscosity, and thermal conductivity
• Step 2: determine heat-transfer behavior using plant heating data to estimate \(U\) and then \(h_b\)
• Step 3: determine burn kinetics at several temperatures to fit \(k_{b,0}\) and \(E_b\)
• Step 4: estimate wall enrichment from reflux, agitation, and deposit comparisons
• Step 5: back-fit a useful \(BI\) threshold from plant no-burn and burn runs

7) What parameters are hardest to determine?

• Hard engineering parameters: \(h_b\), \(k_m\), and direct \(T_f\)
• Hard chemistry parameters: \(k_{b,0}\), \(E_b\), and how to define burnable precursor concentration

That is why most plants begin with a semi-empirical calibrated model rather than a purely theoretical one.

8) Best practical way to start

Measure directly: \(T_b\), \(T_j\), time, rpm, viscosity, and batch mass. Estimate: \(U\), \(h_b\), and \(T_f\). Determine experimentally: \(E_b\), \(k_{b,0}\), and the critical \(BI\) threshold.

9) Practical summary table

10) Main lesson

For roasted onion reaction flavors, burn risk is not controlled by bulk temperature alone. It is driven by wall-film temperature, viscosity increase, sulfur precursor concentration near the wall, time at high temperature, and mixing strength. Two batches at the same 116°C bulk temperature can behave very differently because \(T_f\), \(h_b\), \(k_m\), and hold time differ.