Heat Release Rate in Fires
Burning Rate
Burning Rate Calculation
ṁ” = q̇”net/L
ṁ” is the burning rate per unit area (g/m2·s)
q̇”net is the net heat flux at the fuel surface (net heat flux, kW/m2)
L is the specific heat of gasification (Specific heat of gasification, kJ/g)
Specific Heat of Gasification (L) is the energy required for solid or liquid to change state into vapor. This heat value is a thermodynamic property for liquid fuels. For solid fuels, the heat value varies with time, such as wood, which becomes charcoal with thermal insulation properties during combustion. Therefore, the L value of solids is variable.
Higher L values are more difficult to burn than lower L values
Table: Heat of gasification values
|
Fuel |
L (kJ/g) |
|---|---|
| Liquids: | |
|
Gasoline |
0.33 |
|
Hexane |
0.45 |
|
Heptane |
0.5 |
|
Kerosene |
0.67 |
|
Ethanol |
1.00 |
|
Methanol |
1.23 |
| Thermoplastic: |
|
|
Polyethylene |
1.8 – 3.6 |
|
Polypropylene |
2.0 – 3.1 |
|
Polymethylmethacrylate |
1.6 – 2.8 |
|
Nylon 6/6 |
2.4 – 3.8 |
|
Polystyrene Foam |
1.3 – 1.9 |
|
Flexible polyurethane Foam |
1.2 – 2.7 |
| Char Formers | |
|
Polyvinyl Chloride |
1.7 – 2.5 |
|
Rigid Polyurethane Foam |
1.2 – 5.3 |
|
Whitman Filter Paper no.3 |
3.6 |
|
Corrugated paper |
2.2 |
|
Woods |
4 – 6.5 |
- The general burning rate of fuel ranges between 5~50 g/m2·s
- If the burning rate is below 5 g/m2·s, combustion cannot continue
- Maximum Burning Rate (Maximum Burning Rate)
Maximum burning rate is the limit value of each fuel type indicating how high it can burn. The maximum burning rate is obtained from actual fuel burning experiments under sufficient oxygen conditions (Fuel-limited combustion).
Table: Maximum burning flux values
|
Fuel |
ṁ (g/m2·s) |
|---|---|
| Liquified propane | 100-130 |
| Liquified natural gas | 80-100 |
| Benzene | 90 |
| Butane | 80 |
| Hexane |
70-80 |
| Xylene |
70 |
| JP-4 | 50-70 |
| Heptane | 65-75 |
| Gasoline | 50-60 |
| Acetone |
40 |
| Methanol | 22 |
| Polystyrene (granular) | 38 |
| Polymethyl methacrylate (granular) |
28 |
| Polyethylene (granular) | 26 |
| Polypropylene (granular) |
24 |
| Rigid Polyurethane foam | 22-25 |
| Flexible Polyurethane foam |
21-27 |
| Polyvinyl chloride (granular) |
16 |
| Corrugated paper cartons |
14 |
| Wood crib | 11 |
Heat Release Rate (Heat Release Rate)
Heat Release Rate can be calculated from the fire combustion equation
Q̇ = ṁ”f AX∆HC
ṁ”f is the burning rate per unit area (g/m2·s)
Q̇ is the energy release rate (kW)
X is combustion efficiency ~60-70%
∆HC is the heat of combustion (Heat of combustion, kJ/g)
Table: Burning Rate per unit area and complete heat of combustion for various materials
|
Material |
Tefl |
∆HC |
|---|---|---|
|
Aliphatic Carbon-Hydrogen Atoms |
||
|
Polyethylene |
0.026 |
43.6 |
|
Polypropylene |
0.024 |
43.4 |
|
Heavy Fuel oil (2.6-23 m) |
0.036 |
—— |
|
Kerosene (30-80 m) |
0.065 |
44.1 |
|
Crude oil (6.5-31 m) |
0.056 | —— |
|
n-Dodecane (0.94) |
0.036 |
44.2 |
|
Gasoline (1.5-223 m) |
0.062 |
—— |
|
JP-4 (1-5.3 m) |
0.067 |
—— |
| JP-5 (0.6-1.7 m) | 0.055 | —— |
| n-Heptane (1.2-10 m) |
0.075 |
44.6 |
| n-Hexane (0.75-10 m) |
0.077 |
44.8 |
|
Transformer fluids (2.37 m) |
0.025-0.030 |
—— |
|
Aromatic Carbon-Hydrogen Atoms |
||
| Polystyrene (0.93 m) | 0.034 |
39.2 |
| Xylene (1.22 m) |
0.067 |
39.4 |
| Benzene (0.75-6.0 m) | 0.081 |
40.1 |
| Aliphatic Carbon-Hydrogen-Oxygen Atoms | ||
|
Polyoxymethylene |
0.016 |
15.4 |
| Polymethylmethacrylate, PMMA (2.37 m) |
0.03 |
25.2 |
|
Methanol (1.2-2.4 m) |
0.025 |
20 |
| Acetone (1.52 m) |
0.038 |
29.7 |
|
Aliphatic Carbon-Hydrogen-Oxygen-Nitrogen Atoms |
||
| Flexible Polyurethane foams |
0.021-0.027 |
23.2-27.2 |
|
Rigid Polyurethane foams |
0.022-0.025 |
25.0-28.0 |
|
Aliphatic Carbon-Hydrogen-Halogen Atoms |
||
|
Polyvinylchloride |
0.016 |
16.4 |
|
Tefzel (ETHE) |
0.014 |
12.6 |
|
Teflon (FEP) |
0.007 |
4.8 |
Table: Effective heat of combustion
|
Fuel |
∆HC (kJ/g) |
|---|---|
| Methane |
50 |
| Ethane |
47.5 |
| Ethene |
50.4 |
| Propane |
46.5 |
| Carbon monoxide |
10.1 |
| N-butane |
45.7 |
| c-Hexane |
43.8 |
| Heptane |
44.6 |
| Gasoline |
43.7 |
| Kerosene |
43.2 |
| Benzene |
40 |
| Acetone |
30.8 |
| Ethanol |
26.8 |
| Methanol |
19.8 |
| Polyethylene |
43.3 |
| Polypropylene |
43.3 |
| Polystyrene |
39.8 |
| Polycarbonate |
29.7 |
| Nylon 6/6 |
29.6 |
| Polymethyl methacrylate |
24.9 |
| Polyvinyl chloride |
16.4 |
| Cellulose |
16.1 |
| Glucose |
15.4 |
| Wood |
13-15 |
Table A.8.2.6 Unit Heat Release Rate for Commodities
|
Commodity |
Heat Release Rate |
|---|---|
| Wood pallets, stacked 0.46 m high (6%-12% moisture) |
1,420 |
| Wood pallets, stacked 1.52 m high (6%-12% moisture) |
4,000 |
| Wood pallets, stacked 3.05 m high (6%-12% moisture) |
6,800 |
| Wood pallets, stacked 4.88 m high (6%-12% moisture) |
10,200 |
| Mail bags, Filled, Stacked 1.52 m high |
400 |
| Cartons, Compartmented, Stacked 4.5 m high |
1,700 |
| PE letter trays, filled, stacked 1.5 high on cart |
8,500 |
| PE trash barrels in cartons, stacked 4.5 high |
2,000 |
| FRP shower stalls in cartons, stacked 4.6 high |
1,400 |
| PE bottles packed in compartmented cartons, stacked 4.5 high |
6,200 |
| PE bottles in cartons, stacked 4.5 m high |
2,000 |
| PU insulation boards, rigid foam, stacked 4.2 high |
1,900 |
| PS jars packed in compartmented cartons, stacked 4.5 m high |
14,200 |
| PS tubs nested in cartons, stack 4.2 m high |
5,400 |
| PS toy parts in cartons, stacked 4.2 high |
2,000 |
| PS insulation board, rigid foam, stacked 4.2 m high |
3,300 |
| PVC bottles packed in compartmented cartons, stacked 4.5 m high |
3,400 |
| PP tubs packed In compartmented cartons, stacked 4.5 m high |
4,400 |
| PP and PE film in rolls, stacked 4.1 m high |
6,200 |
| Methyl Alcohol |
740 |
| Gasoline |
2,500 |
| Kerosene |
1,700 |
| Fuel oil. No. 2 |
1,700 |
Pool Fire Burning Rate
Pool Fire Burning Rate
ṁ” = ṁ”∞ (1-e-kßD)
ṁ” is the burning rate of the fire pool (g/m2•s)
ṁ”∞ is the asymptotic burning rate of the fire pool (g/m2•s)
kß is the fire parameter depending on fuel type (m-1)
D is the diameter of the fire pool (m)
Deq = √4A/π
Image - Graph of pool fire burning rate versus pool fire diameter
Image - Characteristics of Pool Fire Source: https://pubs.acs.org
Table: Burning Rate of Pool Fire
|
Material |
Density (kg/m3) | ṁ” (kg/m2s) | ∆HC (MJ/kg) |
kß (m-1) |
|---|---|---|---|---|
| Cryogenics | ||||
|
Liquid H2 |
70 |
0.017 | 120 |
6.1 |
| LNG (mostly CH4) |
415 |
0.078 | 50 |
1.1 |
|
LPG (mostly C3H8) |
585 |
0.099 | 46 |
1.4 |
| Alcohols | ||||
|
Methanol (CH3OH) |
796 |
0.017 | 20 |
a |
|
Ethanol (C2H5OH) |
794 |
0.015 | 26.8 |
b |
|
Simple Organic Fuels |
||||
| Butane (C4H10) |
573 |
0.078 | 45.7 |
2.7 |
| Benzene (C6H6) |
874 |
0.085 | 40.1 |
2.7 |
|
Hexane (C6H14) |
650 |
0.074 | 44.7 |
1.9 |
| Heptane (C7H16) |
675 |
0.101 | 44.6 |
1.1 |
| Xylene (C8H10) |
870 |
0.09 | 40.8 |
1.4 |
| Acetone (C3H6O) |
791 |
0.041 | 25.8 |
1.9 |
| Dioxane (C4H8O2) |
1035 |
0.018 | 26.2 |
5.4b |
| Diethyl ether (C4H10O) |
714 |
0.085 | 34.2 |
0.7 |
| Petroleum Products | ||||
|
Benzine |
740 |
0.048 | 44.7 |
3.6 |
| Gasoline |
740 |
0.055 | 43.7 |
2.1 |
| Kerosene |
820 |
0.039b | 43.2 |
3.5 |
|
JP-4 |
760 |
0.051 | 43.5 |
3.6 |
| JP-5 |
810 |
0.054 | 43 |
1.6 |
| Transformer Oil, Hydrocarbon |
760 |
0.039 | 46.4 |
0.7 |
| Fuel oil, heavy |
940-1000 |
0.035 | 39.7 |
1.7 |
|
Crude oil |
830-880 |
0.022-0.045 | 42.5-42.7 |
2.8 |
| Solids | ||||
|
Polymethylmethacrylate (C5H8O2)n |
1184 |
0.02 | 24.9 |
3.3 |
|
Polypropylene (C3H6)n |
905 |
0.018 | 43.2 | |
|
Polystyrene (C8H8)n |
1050 |
0.034 | 39.7 |
a Value independent of diameter in turbulent regime
b Estimate uncertain, since only two points available
Example 1
An accident caused 20 liters of transformer oil to spill over an area of approximately 2 square meters. The oil caught fire. Calculate the Energy Release rate and the burning duration.
Solution
From the Pool Fire table for Transformer oil:
ρ = 760 kg/m3 ṁ”∞ = 0.039 kg/m3•s kß = 0.7 m-1 ∆Hc = 46.4 MJ/kg
Calculate D from a circle with area equal to 2 square meters
D = Deq = √4A/π = √4×2/π = 1.6 m
The energy release rate of transformer oil per unit area equals
ṁ” = 0.038 x (1- e-(0.7×1.6)) = 0.026 kg/m2•s
Total energy release rate equals
Q̇ = ṁ”f AX∆HC = (0.026)(2)(0.7)(46.4) = 1.69 MW
Total burning rate ṁ = Aṁ” = 0.052 kg/s
Total mass of spilled Transformer oil m = ρV = 760(20×10-3) = 15.2 kg
Total burning duration t = m/ṁ = 15.2/0.052 = 292 s ≈ min
Estimating Energy Release Rate from Actual Fuel Combustion
Estimating energy release rate through actual fuel combustion is practically tested using equipment called Oxygen Consumption Calorimeter (Cone Calorimeter) or Furniture Calorimeter
Method of Measuring Energy Release Rate using Cone Calorimeter
Cone Calorimeter Test is a device that measures heat quantity according to Cone Calorimeter testing theory, based on the principle that calories burned correlate with oxygen consumption. Using 1 g of oxygen generates 13.1 kJ of heat.
Image - Cone Calorimeter
Method of Measuring Energy Release Rate using Furniture Calorimeter Test
Furniture Calorimeter Test is a large device that uses the same principle as the Cone Calorimeter but has a larger cone and is used for burning various furniture items.
T-Square Fire
T-square fire refers to the period from when an object ignites (Growth Phase) where combustion spreads rapidly in proportion to time squared (T-square).
Q̇ = αt2
Q̇ is the energy release rate (kW)
α is the Growth Factor (kW/s2)
t is the combustion time starting from when the object ignites (s)
Growth Factor α
tg is the time from when an object starts burning until it can release 1000 kW of heat energy where
α = 1000/tg2
is an index indicating the fire spread rate of each fuel type
NFPA 204 Standard for smoke and heat ventilating has classified Growth Factor into 4 levels
Table: Fire Spread Speed Classification
|
Class |
Time to Reach 1000 kW (s) |
|---|---|
| Ultra-fast |
75 |
| Fast |
150 |
| Medium |
300 |
| Slow |
600 |
Image - T-Square Fire
Image - Growth Factor
Image - Rate of Energy Release for t-square Fire
Each fuel type has different Growth factor values
Table: Growth Factor α values
|
Fuel |
Growth Time (s) |
|---|---|
| Wood pallets, stacked 0.46 m high (6%-12% moisture) |
160-320 |
| Wood pallets, stacked 1.52 m high (6%-12% moisture) |
90-190 |
| Wood pallets, stacked 3.05 m high (6%-12% moisture) |
80-120 |
| Wood pallets, stacked 4.88 m high (6%-12% moisture) |
75-120 |
| Mail bags, Filled, Stacked 1.52 m high |
190 |
| Paper, Vertical rolls, stacked 6.10 m high |
60 |
| Cotton (also PE, PE/cot acrylic/nylon/PE), garments in 3.66 m high rack |
17-28 |
| Cartons, Compartmented, Stacked 4.57 m high |
22-43 |
| “Ordinary Combustibles” rack storage, 4.57 m – 9.14 m high |
40-270 |
| Paper products, densely packed in cartons, rack storage, 6.10 m high |
470 |
| PE letter trays, filled, stacked 1.52 high on cart |
180 |
| PE trash barrels in cartons, stacked 4.57 high |
55 |
| FRP shower stalls in cartons, stacked 4.57 high |
85 |
| PE bottles packed in compartmented cartons, stacked 4.57 high |
85 |
| PE bottles packed in compartmented cartons, stacked 4.57 high |
75 |
| PE pallets, stacked 0.91 m high |
150 |
| PE pallets, stacked 1.83 m-2.44 m high |
32-57 |
| PU mattress, single, horizontal |
120 |
| PU insulation boards, rigid foam, stacked 4.57 high |
8 |
| PS jars packed in compartmented cartons, stacked 4.5 m high |
55 |
| PS tubs nested in cartons, stack 4.2 m high |
110 |
| PS toy parts in cartons, stacked 4.2 high |
120 |
| PS insulation board, rigid foam, stacked 4.2 m high |
7 |
| PVC bottles packed in compartmented cartons, stacked 4.5 m high |
9 |
| PP tubs packed in compartmented cartons, stacked 4.5 m high |
25-40 |
| PP and PE film in rolls, stacked 4.1 m high |
40 |
| Distilled spirits in barrels, stacked 6.10 m high |
25-40 |
