Burners are critical for the successful operation of industrial furnaces. Presented here is a set of equations that can be used to calculate characteristics of burner operation, including flame length, flame diameter, ignitability and flameout conditions. Equations are based on pre-mix burners operating at atmospheric pressure and firing natural gas only. Premix burners create short and compact flames compared to raw gas burners, and are designed to function with fuel-gas mixtures that have consistent specific gravity and composition.
For direct-fired heaters to function correctly, burners must be capable of providing sufficient heat liberation from the fuel to meet heater processing requirements — based on the lower heating value (LHV) of the fuel. A fuel’s LHV can be defined as the amount of heat produced by combusting a specified volume, and returning the combustion products to 150C. For the heater to operate at the design process flowrate, the burners need to provide the heat necessary to maintain process fluid temperature and meet vaporization requirements at the heating coil outlet.
- The number, size and placement of burners must allow each coil to operate at the same design outlet temperature
- Design tube-metal temperature cannot be exceeded at any point on the coils
- Burner size must allow an outlet velocity that does not result in malfunction over the range of flow conditions
- Burner flame length should be less than firebox height (for vertical cylindrical heaters) or less than firebox length (for end-wall-fired heaters)
- Excessive flame height and diameter should be avoided to prevent flame impingement on tubes
- Burner spacing should be sufficient to allow burner-to-burner, as well as burner-to-tube clearance
The following equations can help establish optimal burner diameter:
Establishing burner-to-burner clearance and burner spacing should be based on maximum burner flame diameter. Further, burner flame diameter should be evaluated at maximum burner-flame length. Sufficient burner-to-burner, outside diameter clearance should take into account the placement of structural elements between burners.
Sufficient burner-to-burner clearance prevents interference between the flame bodies and unburned fuel cores generated by adjacent burners, which results in the absence of unburned fuel within the burner flame when maximum flame length is reached. Burner center-to-center spacing should be at least one fully combusted flame diameter.
Clearance between the burner-flame (at maximum diameter) and the outside diameter of tubular heating surfaces should be set such that burner-to-tube flame impingement is avoided. Doing so will prevent tube damage due to overheating and will make best use of heating surfaces.
At high burner velocities, flame loss can occur if the heat gain due to burner ignition is less than the heat loss from the burner flame. Burner velocities may be pushed well above that used in normal heater operation in an effort to achieve higher heater capacity. Aside from flame loss while the heater is in operation, flameout can also be characterized by difficulty maintaining a stable flame at startup, or an inability to ignite the burner. The following equations can help predict the circumstances under which flamout conditions might occur:
The heat generated by combustion is dependent on the flame propagation velocity. In a situation with 0% excess air, the ratio of fuel-to-fuel+air is about 0.1. In that case, evaluation of the flame propagation velocity is straightforward. However, at fuel-to-fuel+air ratios higher or lower than 0.1, it is more difficult. The following equations can help predict flame propagation velocity in those cases:
Qlib heater= Heater liberation, Btu/h
Nb= Number of burners
Db = Burner diameter, ft
Vb= Burner exit velocity, ft/s
Cfuel = Fuel, ft3
LHV = Lower heating value of fuel, Btu/lb
Cair+fuel = Volume of air and fuel mixture, ft3
SVfuel = Specific volume of fuel, ft3/lb
Df max = Maximum flame diameter, ft
Lf = Flame length, ft
SVflame= Specific volume of flame, ft3/lb
Vf = Flame propagation velocity, ft/s
Qgain = Burner heat gain, Btu/h
Qloss = Burner heat loss, Btu/h
As = Flame front area, ft2
(HTC)c (HTC)f, (HTC)r = Natural convective, forced- convective, and radiative heat transfer coefficients, respectively, Btu/h-ft2-F
Tflame = Flame temperature, R
Tsurr = Surrounding temperature, R
Eg = Flame emissivity
Cp = Gas specific heat, Btu/lb-F
A = Frequency factor in the Arrhenius equation
H = Heat of activation, Btu/lb-mol R
R= Gas constant, 1.987 Btu/lb-mol R
T= Gas Temperature, R
dCm/dt= Fuel concentration change, mol per ft3/s
K = Reaction velocity constant, s–1
Wf= Fuel, lb/h
*The text was adapted from the article “Fired-Heater Burner Performance,” by Alan Cross. It appeared in the April 2008 issue of Chemical Engineering.