This document provides savory flavorists with insight into the burning risk associated with reaction flavors during cooking, particularly during the temperature ramping (heating) process. Once reactors are designed and installed, they cannot be easily altered. Therefore, it is up to both the flavor creator and the production team to manage and reduce the burning risk for a reaction flavor.

While applying this model directly to flavor production may not be practical, the parameters that influence burn risk should still be considered during formulation and manufacturing. In principle, any factor affecting heat transfer and mass transfer warrants attention. For example, if viscosity is too high, it can impede both mass transfer and heat transfer, leading to potential issues.

Quantitative Heat and Mass Transfer Model for Predicting Burn Risk

This document presents a practical engineering model for predicting burn risk in a flavor reaction reactor, especially for Maillard, caramel, savory sulfur, extract concentration, and viscous thermal processes. It is not a full CFD (computational fluid dynamics) simulation. It is a plant-usable model that estimates when material near the wall is likely to scorch, char, or thermally degrade.

1) What “burn risk” means quantitatively

In reactor practice, burning usually starts when the material temperature at or near the hot surface becomes high enough, for long enough, that the rate of thermal degradation becomes significant.

So the risk depends on wall temperature, bulk temperature, heat transfer coefficient, mixing intensity, viscosity, residence time near the wall, thermal degradation kinetics, evaporation or concentration effects, and oxygen availability if relevant.

2) Core two-zone model

A useful simplification is a two-zone reactor model:

• Bulk zone: well-mixed average liquid
• Wall boundary layer zone: thin film near the heating surface where burning begins

Define \(T_b\) = bulk temperature, \(T_w\) = inner wall temperature, \(T_f\) = temperature of the near-wall fluid film, \(h\) = wall-to-bulk heat transfer coefficient, \(\delta\) = effective thermal boundary layer thickness, \(k\) = thermal conductivity, \(\rho\) = density, \(C_p\) = heat capacity, and \(\mu\) = viscosity.

2.1 Bulk energy balance

Where \(M\) is reactor mass, \(U\) is overall heat transfer coefficient, \(A\) is heat transfer area, \(T_j\) is jacket-side effective temperature, \(( -\Delta H_r )Vr\) is heat generated by reaction, \(\dot{m}_{evap}\lambda\) is evaporative cooling, and \(Q_{loss}\) is heat loss.

2.2 Wall-film energy balance

At steady state:

This shows that the wall-film temperature rises when heat flux is high, viscosity is high, mixing refresh is weak, thermal conductivity is low, and evaporation is low.

3) Burn kinetics model

Use Arrhenius kinetics for the unwanted burn pathway:

Where \(r_b\) is the burn formation rate, \(C_s\) is the concentration of susceptible material near the wall, \(n\) is the apparent order, \(k_{b,0}\) is the pre-exponential factor, and \(E_b\) is the activation energy.

3.1 Burn damage integral

Or more explicitly:

Interpretation:

• \(BI < BI_{crit,1}\): safe
• \(BI_{crit,1} < BI < BI_{crit,2}\): early overprocessing or darkening
• \(BI > BI_{crit,2}\): likely scorching, burnt notes, or wall fouling
• \(BI > BI_{crit,3}\): char formation likely

4) Mass transfer and concentration model near the wall

Burning often increases because the wall layer becomes more concentrated than bulk. Use a wall concentration balance:

Where \(C_f\) is wall-film concentration, \(C_b\) is bulk concentration, \(k_c\) is refresh mass transfer coefficient, \(r_b\) is burn rate, \(r_p\) is polymerization or fouling rate, and \(S_{dep}\) is a source term from settling or deposition.

If evaporation is important, approximate:

5) Fouling-growth feedback model

Once fouling begins, burn risk rises because the deposit acts as thermal resistance. Let \(x_f\) be fouling thickness and \(k_f\) be fouling thermal conductivity:

Fouling growth can be modeled as:

Where \(\tau_w\) is wall shear stress.

6) Burn risk number

• \(BRN \ll 1\): low risk
• \(BRN \approx 1\): borderline
• \(BRN \gg 1\): severe risk

7) Estimating key terms

7.1 Heat flux

Or if process-side wall temperature is known:

7.2 Wall temperature

7.3 Process-side heat transfer coefficient

7.4 Film refresh rate

or

7.5 Wall shear stress

8) Practical burn-threshold method

Define a critical temperature \(T_{crit}\) at which burning begins for a given residence time.

Risk condition:

9) A usable plant-level burn risk equation

Starter classification:

• \(BI < 0.3\): low risk
• \(0.3 \le BI < 1.0\): caution
• \(1.0 \le BI < 3.0\): high risk
• \(BI \ge 3.0\): scorch or fouling likely

10) Example: savory reaction flavor

Suppose:

• \(T_b = 115^\circ C = 388.15\ K\)
• estimated \(T_f = 132^\circ C = 405.15\ K\)
• \(E_b = 95\ kJ/mol\)
• \(k_{b,0} = 2.0 \times 10^9\ s^{-1}\)
• exposure time \(t = 1200\ s\)

If better agitation lowers \(T_f\) to \(124^\circ C = 397.15\ K\), then:

A modest drop in film temperature nearly halves burn risk.

11) How this model explains common failures

• High viscosity late in batch: \(Re\) falls, \(h_b\) drops, \(T_f\) rises, burn kinetics accelerate.
• Sulfur added too early: near-wall susceptible concentration increases, causing harsh sulfur burn notes.
• Fouling begins: local wall temperature climbs and risk accelerates.
• Small batch in large vessel: low wall refresh and stagnant zones push \(BRN\) upward.

12) Minimum experimental data needed

• Chemistry: onset temperature of burning, burn marker rate, activation energy \(E_b\), and concentration dependence \(n\)
• Engineering: bulk temperature, jacket temperature, agitator speed, viscosity, heat transfer estimate, and fouling appearance time
• Product markers: color increase, insoluble particles, char mass, sensory burnt score, furfural/HMF, sulfur collapse markers

13) Simplified spreadsheet version

At each time step, calculate:

1. \(h_b\) from a correlation
2. \(q'' = U(T_j-T_b)\)
3. \(T_f\)
4. \(k_b = k_{b,0}\exp(-E_b/RT_f)\)
5. concentration factor
6. incremental burn:
   \[ \Delta BI = k_b \left(\frac{C_f}{C_{ref}}\right)^n \Delta t \]
7. cumulative \(BI\)

14) Most important practical predictors

• Wall-to-bulk temperature difference \(\Delta T_{wb} = T_w - T_b\)
• Process-side heat transfer coefficient \(h_b\)
• Viscosity \(\mu\)
• Exposure time above critical film temperature \(t(T_f > T_{crit})\)
• Susceptible concentration near the wall \(C_f\)

15) Prevention rules derived from the model

In plain words: lower wall heat flux, improve agitation, reduce viscosity early, avoid local concentration spikes, shorten high-temperature hold, control fouling, prevent evaporation-driven surface drying, and use staged reactant addition.

16) Recommended burn-risk framework

• Level 1: screening model using bulk temp, jacket temp, viscosity, agitator speed, and time
• Level 2: calibrated plant model with measured \(U\), estimated \(h_b\), burn kinetics, concentration correction, and fouling factor
• Level 3: CFD-supported model for very viscous systems, scale-up, dead-zone analysis, and unusual geometries