> ## Content Index > Fetch the complete content index at: https://www.flavorist.com/llms.txt > Use this file to discover other available public pages before exploring further. # Burn Risk - Part 2: Roasted Onion Reaction Flavor Example and How to Determine Each Parameter in the Predictive Model - URL: https://www.flavorist.com/roasted-onion-reaction-flavor-example-and-how-to-determine-each-parameter-in-the-predictive-model-part-2/ - Published: 2026-03-31T22:24:44.000Z - Updated: 2026-04-01T02:31:49.000Z - Author: Editor # 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. \\\[ T\_b = 116 + 273.15 = 389.15\\ \\text{K} \\\] 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. \\\[ T\_j \\approx \\frac{135+127}{2} = 131^\\circ C = 404.15\\ \\text{K} \\\] ### 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: \\\[ M C\_p \\frac{dT\_b}{dt} = U A (T\_j - T\_b) \\\] \\\[ U = \\frac{M C\_p (dT\_b/dt)}{A(T\_j-T\_b)} \\\] **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\\) \\\[ U = \\frac{240 \\times 3600 \\times 0.022}{3.8 \\times 20} \\approx 250\\ \\text{W/m}^2\\text{·K} \\\] ### Parameter 4: Heat flux, \\(q''\\) **Meaning:** heat entering per unit wall area. \\\[ q'' = U(T\_j - T\_b) \\\] Using \\(U = 250\\ \\text{W/m}^2\\text{·K}\\) and \\(T\_j-T\_b = 15\\ K\\): \\\[ q'' = 250 \\times 15 = 3750\\ \\text{W/m}^2 \\\] ### 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: \\\[ Nu = \\frac{h\_b D}{k} \\\] \\\[ Re = \\frac{\\rho N D\_i^2}{\\mu}, \\qquad Pr = \\frac{\\mu C\_p}{k} \\\] \\\[ Nu = 0.36 Re^{0.67} Pr^{0.33} \\\] **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\\) \\\[ Re = \\frac{1150 \\times 0.8 \\times 0.75^2}{0.45} \\approx 1150 \\\] \\\[ Pr = \\frac{0.45 \\times 3600}{0.42} \\approx 3857 \\\] \\\[ Nu \\approx 0.36 \\times 1150^{0.67} \\times 3857^{0.33} \\approx 560 \\\] \\\[ h\_b = \\frac{Nu \\cdot k}{D} = \\frac{560 \\times 0.42}{1.0} \\approx 235\\ \\text{W/m}^2\\text{·K} \\\] ### Parameter 6: Wall temperature, \\(T\_w\\) \\\[ q'' = h\_b (T\_w - T\_b) \\\] \\\[ T\_w = T\_b + \\frac{q''}{h\_b} \\\] With \\(q'' = 3750\\) and \\(h\_b = 235\\): \\\[ T\_w = 389.15 + \\frac{3750}{235} = 405.11\\ K \\\] So: \\\[ T\_w \\approx 131.96^\\circ C \\\] ### Parameter 7: Film temperature, \\(T\_f\\) **Meaning:** actual temperature of the fluid layer touching or nearly touching the wall. A practical shortcut is: \\\[ T\_f \\approx T\_b + \\phi(T\_w-T\_b) \\\] For a moderately viscous batch, use \\(\\phi = 0.75\\): \\\[ T\_f = 116 + 0.75(131.96 - 116) \\approx 127.97^\\circ C \\\] \\\[ T\_f = 401.12\\ K \\\] ### 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:** \\\[ C\_p = 3.6\\ kJ/kg\\cdot K \\\] ### 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:** \\\[ k = 0.42\\ W/m\\cdot K \\\] ### 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: \\\[ k\_m \\sim \\frac{h\_b}{\\rho C\_p \\delta\_{eff}} \\\] Suppose \\(\\delta\_{eff} = 1.5 \\times 10^{-3}\\ m\\): \\\[ k\_m \\sim \\frac{235}{1150 \\times 3600 \\times 1.5\\times10^{-3}} \\approx 0.038\\ s^{-1} \\\] This implies a wall-film refresh time of about: \\\[ 1/k\_m \\approx 26\\ s \\\] ### Parameter 13: Susceptible concentration, \\(C\_f\\) and \\(C\_b\\) Use one lumped “burnable precursor concentration” at first. Suppose: \\\[ C\_b = 220\\ kg/m^3 \\\] Assume wall enrichment factor \\(\\alpha\_c = 1.20\\): \\\[ C\_f = \\alpha\_c C\_b = 264\\ kg/m^3 \\\] ### 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: \\\[ E\_b = 92\\ kJ/mol, \\qquad k\_{b,0} = 1.4\\times10^9\\ s^{-1} \\\] ### Parameter 15: Activation energy, \\(E\_b\\) From the Arrhenius plot: \\\[ \\ln k\_b = \\ln k\_{b,0} - \\frac{E\_b}{R}\\frac{1}{T} \\\] If the slope is \\(-11070\\): \\\[ E\_b = 11070 \\times 8.314 \\approx 92,000\\ J/mol = 92\\ kJ/mol \\\] ### Parameter 16: Reaction order, \\(n\\) Determine by running concentration-series tests at fixed temperature. Suppose the data suggest: \\\[ n = 1.3 \\\] ### Parameter 17: Burn index, \\(BI\\) Use the cumulative damage expression: \\\[ BI = \\int\_0^t k\_b(T\_f)\\left(\\frac{C\_f}{C\_{ref}}\\right)^n dt \\\] If conditions are constant: \\\[ BI \\approx k\_b\\left(\\frac{C\_f}{C\_{ref}}\\right)^n t \\\] 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\\) \\\[ k\_b = 1.4\\times10^9 \\exp\\left(-\\frac{92000}{8.314\\times401.12}\\right) \\approx 1.47\\times10^{-3}\\ s^{-1} \\\] \\\[ (1.20)^{1.3} \\approx 1.27 \\\] \\\[ BI \\approx 1.47\\times10^{-3} \\times 1.27 \\times 1800 \\approx 3.36 \\\] This suggests strong burn risk. ## 4) Full worked example | Given | Value | | ------------------------------------------------ | ---------------------------------------- | | Batch mass | \\(M = 240\\ kg\\) | | Heat capacity | \\(C\_p = 3600\\ J/kg\\cdot K\\) | | Heat transfer area | \\(A = 3.8\\ m^2\\) | | Bulk temperature | \\(T\_b = 116^\\circ C = 389.15\\ K\\) | | Jacket temperature | \\(T\_j = 131^\\circ C = 404.15\\ K\\) | | Overall heat transfer coefficient | \\(U = 250\\ W/m^2\\cdot K\\) | | Density | \\(\\rho = 1150\\ kg/m^3\\) | | Viscosity | \\(\\mu = 0.45\\ Pa\\cdot s\\) | | Thermal conductivity | \\(k = 0.42\\ W/m\\cdot K\\) | | Estimated process-side heat transfer coefficient | \\(h\_b = 235\\ W/m^2\\cdot K\\) | | Activation energy | \\(E\_b = 92,000\\ J/mol\\) | | Pre-exponential factor | \\(k\_{b,0} = 1.4\\times10^9\\ s^{-1}\\) | | Order | \\(n=1.3\\) | | Concentration ratio | \\(C\_f/C\_{ref}=1.20\\) | | High-temperature hold | 30 min = 1800 s | ### Step 1: Heat flux \\\[ q'' = U(T\_j-T\_b) = 250(404.15-389.15)=3750\\ W/m^2 \\\] ### Step 2: Wall temperature \\\[ T\_w = T\_b + \\frac{q''}{h\_b}=389.15+\\frac{3750}{235}=405.11\\ K \\\] \\\[ T\_w = 131.96^\\circ C \\\] ### Step 3: Film temperature Use \\(\\phi=0.75\\): \\\[ T\_f = 116+0.75(131.96-116)=127.97^\\circ C \\\] \\\[ T\_f = 401.12\\ K \\\] ### Step 4: Burn rate constant \\\[ k\_b = 1.4\\times10^9\\exp\\left(-\\frac{92000}{8.314\\times401.12}\\right) \\approx 1.47\\times10^{-3}\\ s^{-1} \\\] ### Step 5: Concentration factor \\\[ (1.20)^{1.3} \\approx 1.27 \\\] ### Step 6: Burn index \\\[ BI = 1.47\\times10^{-3}\\times1.27\\times1800 \\approx 3.36 \\\] **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: \\\[ T\_w = 389.15+\\frac{3750}{320}=400.87\\ K \\\] \\\[ T\_w=127.72^\\circ C \\\] If \\(\\phi=0.70\\): \\\[ T\_f=116+0.70(127.72-116)=124.20^\\circ C \\\] \\\[ T\_f=397.35\\ K \\\] \\\[ k\_b = 1.4\\times10^9\\exp\\left(-\\frac{92000}{8.314\\times397.35}\\right) \\approx 8.47\\times10^{-4}\\ s^{-1} \\\] \\\[ BI = 8.47\\times10^{-4}\\times1.27\\times1800 \\approx 1.94 \\\] ### Case B: Lower jacket temperature by 5°C If \\(T\_j = 126^\\circ C\\) instead of 131°C: \\\[ q'' = 250(399.15-389.15)=2500\\ W/m^2 \\\] \\\[ T\_w = 389.15+\\frac{2500}{235}=399.79\\ K = 126.64^\\circ C \\\] With \\(\\phi=0.75\\): \\\[ T\_f = 116 + 0.75(126.64-116)=123.98^\\circ C \\\] Burn risk drops sharply. ### Case C: Reduce hold time If hold time drops from 30 min to 15 min, then: \\\[ BI = 3.36/2 = 1.68 \\\] 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 | Parameter | Meaning | How to determine | Example | | -------------- | ---------------------------- | -------------------------------------- | ----------------------------- | | \\(T\_b\\) | bulk temp | RTD / thermocouple | 116°C | | \\(T\_j\\) | jacket temp | utility inlet/outlet | 131°C | | \\(U\\) | overall heat transfer | plant heat-up data | 250 W/m²·K | | \\(q''\\) | heat flux | \\(U(T\_j-T\_b)\\) | 3750 W/m² | | \\(h\_b\\) | process-side HT coefficient | Nusselt correlation / calibration | 235 W/m²·K | | \\(T\_w\\) | wall temp | \\(T\_b+q''/h\_b\\) | 132°C | | \\(T\_f\\) | wall-film temp | wall-factor or film model | 128°C | | \\(\\rho\\) | density | density cup / pycnometer | 1150 kg/m³ | | \\(C\_p\\) | heat capacity | DSC / estimate | 3.6 kJ/kg·K | | \\(k\\) | thermal conductivity | meter / literature | 0.42 W/m·K | | \\(\\mu\\) | viscosity | Brookfield / rheometer | 0.45 Pa·s | | \\(C\_f\\) | wall precursor concentration | bulk concentration × enrichment factor | 1.2× bulk | | \\(E\_b\\) | activation energy | Arrhenius fit | 92 kJ/mol | | \\(k\_{b,0}\\) | pre-exponential factor | Arrhenius fit | \\(1.4\\times10^9\\ s^{-1}\\) | | \\(n\\) | concentration dependence | concentration-series kinetics | 1.3 | | \\(BI\\) | cumulative burn score | integrate over time | 3.36 | ## 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.