Tube Metal Temperature Factor, FT (from Example in Figure 3):
FT
Bulk Fluid Temperature, Tb °F = 520
Maximum Tube Metal Temperature:
Tm = Tb + ÆTf + ÆTc + ÆTw °F = 849
FIGURE 12 Sample Calculation - Effects of Internal Fouling Summary:
Clean Tm (from Figure 10) (Approx.) °F = 663
Tm with Fouling Allowance (from Figure 10) °F = 700
Tm with 1/4 in. Coke Layer °F = 849
FIGURE 12 (CONT’D)
Work Aid 1 - Calculating Heat Transfer in Boilers and Furnaces
MAXIMUM RADIANT HEAT DENSITY CALCULATION SHEET
The following procedure can be used to calculate maximum radiant heat density in furnaces.
Plant Location Furnace Service Coil Given:
Tube Outside Diameter, Do in. =
Average Wall Thickness, ta in. =
Tube Spacing, c-c (center-to-center) in. =
Flue Gas Temperature, Tg °F =
Average Radiant Tube Metal Temperature, Ta °F =
Average Heat Flux, fr Btu/hr-ft2 =
Height of Radiant Section, Hr ft =
Tube Arrangement:
Solution:
Tube Spacing: c-c/Do = ( )/( ) = Circumferential Heat Flux Factor, FC (from Work Aid 2) = Longitudinal Heat Flux Factor, FL (from Figure 2) =
Estimated Maximum Tube Metal Temperature, Tm °F =
Tube Metal Temperature Factor, FT:
FT
Convective Heat Flux, fc (Usually = 0) Btu/hr-ft2 = Calculate Maximum Radiant Heat Flux:
fm = FC FL FT fr + fc
= ( )( )( )( ) + ( ) Btu/hr-ft2 =
Work Aid 2 - Calculating Heat Transfer in Boilers and Furnaces
Note 1: Curve 1 = Double row against wall, triangular spacing.
Curve 2 = Double row with equal radiation from both sides and two diameters between rows, equilateral spacing.
Curve 3 = Single row against wall.
Curve 4 = Single row with equal radiation from both sides.
Note 2: These curves are valid when used with a tube-center-to-refractory-wall spacing of 1-1/2 times the nominal tube diameter. Any appreciable variation from this spacing must be given special consideration.
Source: API RP 530.
FIGURE 13 Ratio Of Maximum Local-To-Average Heat Flux
Work Aid 3 - Calculating Internal Heat Transfer Coefficient
TUBE INSIDE FILM COEFFICIENT CALCULATION SHEET The following procedure can be used to calculate inside film coefficients for boiler or furnace tubes.
Tube Outside Diameter, do in. =
Average Wall Thickness, ta in. =
Coke Thickness, tc in. =
Number of Tube Passes, n =
Solution:
Flow Diameter, dx = do - 2 (ta + tc) = ( ) - 2 ( + ) in. = Dx = (dx in.) / 12 ft = Flow Area, Ax = n (p/4) (Dx)2 = ( ) (p/4) ( )2 ft2 = Mass Velocity, G = W/Ax = ( ) / ( ) lb/hr-ft2 =
Estimated Temperature Rise Across Film, ÆTf °F =
Estimated Wall Temperature, Tw = Tb + ÆTf, °F =
Liquid Phase Coefficient:
Reynolds Number, NRe = DxG / µ = ( ) ( ) / ( ) = Prandtl Number, NPr = Cpµ / k = ( ) ( ) / ( ) =
Viscosity at Wall Temperature, µw cP =
2.42 (cP) = lb/hr-ft =
Vapor Phase Coefficient:
Reynolds Number, NRe = DxG / µ = ( ) ( ) / ( ) = Prandtl Number, NPr = Cpµ / k = ( ) ( ) / ( ) = Film Coefficient (Eqn. 9):
hv = 0. 021 k
Dx N Re 0. 8 N Pr 0. 4 Tb + 460 Tw + 460
0. 5
= 0. 021 ( )
( )( )0.8 ( )0.4
(
+ 460)
+ 460
( )
0.5
Btu/hr-ft2-°F = Two-Phase Coefficient (Eqn. 12):
htp = hl Wl + hv Wv
= ( )( ) + ( )( )
Btu/hr-ft2-°F = Work Aid 4 - Calculating Maximum Tube Metal Temperatures
Specific Heats of the Vapor for Constant Pressure
Source: Thermodynamic Properties of Steam Including Data for the Liquid and Solid Phases by John H. Keenan and Frederick G. Keyes, 33rd Printing, © 1936. Reprinted by Permission of John Wiley & Sons, Inc.
FIGURE 14 Thermal Properties Of Steam Absolute Viscosity of Saturated and Superheated Steam
With Permission from Babcock & Wilcox.
FIGURE 15
Viscosity of Liquid Water
FIGURE 16
Thermal Conductivity of Liquid Water
FIGURE 17 THERMAL PROPERTIES OF STEAM (CONT’D)
Thermal Conductivity of Steam
FIGURE 18 THERMAL PROPERTIES OF STEAM (CONTÍD) Work Aid 5 - Calculating Maximum Tube Metal Temperature
The following procedure can be used to calculate maximum tube metal temperatures.
Plant Location Boiler/Furnace Service Coil Given:
Tube Outside Diameter, Do in. =
Average Wall Thickness, ta in. =
Bulk Fluid Temperature, Tb °F =
Tube Material =
Maximum Heat Flux, fm (from Work Aid 1) Btu/hr-ft2 = Film Coefficient, hi (from Work Aid 4) Btu/hr-ft2-°F =
Solution:
Inside Diameter, Di = Do - 2ta = ( ) - 2 ( ) in. =
Fouling Factor, F (from Table 1.A, AES-F-001) =
Or: Coke Thickness, tc in. = Thermal Conductivity, kw (from Work Aid 6 at TMT): Btu-in./hr-ft2-°F =
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
Total Temperature Difference = ÆTf+ÆTc+ÆTw °F =
Bulk Fluid Temperature, Tb °F =
Maximum Tube Metal Temperature:
Tm = Tb + ÆTf + ÆTc + ÆTw °F =
Check Assumptions Made in Previous Calculations:
Check Inside Film Coefficient (from Work Aid 3):
Liquid Phase Coefficient:
Calculated Wall Temperature, Tw = Tb + ÆTf °F =
Viscosity at Wall Temperature, µw cP =
2.42 (cP) = lb/hr-ft =
Vapor Phase Coefficient: Thermal Conductivity, kw (at Tma) Btu-in./hr-ft2-°F =
∆Tw' = Original ∆Tw x Original kw
Revised kw =
°F =
Revised Maximum Tube Metal Temperature:
Tm' = Tb + ∆Tf' + ∆Tc' + ∆Tw' °F =
Recalculate Maximum Radiant Heat Flux (from Work Aid 1):
Recalculate FT (Eqn. 3): Maximum Radiant Heat Flux (Eqn. 2):
fm' = FC FL FT fr + fc
= ( )( )( )( )+ ( ) Btu/hr-ft2 =
% Difference in fm:
Resulting Difference in Tm:
Work Aid 6 - Calculating Maximum Tube Metal Temperatures
k for 9Cr: 177 + 0.0207 (T) (Btu - in.)/(hr - ft2 - °F)
Figure 19 Thermal Conductivity Of Common Tube Materials
REFERENCE
Saudi Aramco Standards
AES-F-001 Process Fired Heaters.
32-AMSS-021 Water-Tube Boilers.
API Publications
Recommended Practice 530 Calculation of Heater-Tube Thickness in Petroleum Refineries.
ASME Publications
1967 ASME Steam Tables.
Other Publications
Berman, H.L., "Fired Heaters," Chemical Engineering Magazine, June-September 1978 issues.
Port, R.D., and Herro, H.M., "The Nalco Guide to Boiler Failure and Analysis," McGraw-Hill, Inc., New York (1991).
GLOSSARY
bulk temperature The average temperature of the process fluid at any tube cross section.
coil A series of straight tube lengths connected by 180°
return bends, forming a continuous path through which the process fluid passes and is heated.
convection section The portion of a heater, consisting of a bank of tubes, which receives heat from the hot flue gases, mainly by convection.
economizer A tube bank for transferring heat from the flue gas to the boiler feedwater before the BFW enters the steam drum.
extended surface Surface added to the outside of bare tubes in the convection section to provide more heat transfer area.
This may consist of cylindrical studs butt-welded to the tube, or fins continuously wound around and welded to the tube.
film A thin fluid layer adjacent to a pipewall which remains in laminar flow, even when the bulk flow is turbulent. The velocity profile in the film is approximately linear, with zero velocity existing at the wall.
film coefficient The convective heat transfer coefficient of the film.
film temperature The maximum temperature in the film, at the tubewall.
flue gas A mixture of gaseous products resulting from combustion of the fuel.
fouling The building up of a film of dirt, ash, soot, or coke on heat transfer surfaces, resulting in increased resistance to heat flow.
header The fitting which connects two tubes in a coil. In common usage, "header" refers to cast or forged 180°
"U-bends" ("return bends").
heat density The rate of heat transfer per unit area to a tube, usually based on total outside surface area. Typical units are Btu/hr-ft2. Also called "heat flux."
heat duty The total heat absorbed by the process fluid, usually expressed in MBtu/hr (million Btu per hour). Total fired heater duty is the sum of heat transferred to all process streams, including auxiliary services such as steam superheaters and drier coils.
mass velocity The mass flow rate per unit of flow area through the coil. Typical units are lb/s-ft2.
one-side fired tubes Radiant section tubes located adjacent to a heater wall have only one side directly exposed to a burner flame.
Radiation to the back side of the tubes is by reflection/re-radiation from the refractory wall.
pass A coil which transports the process fluid from fired heater inlet to outlet. The total process fluid can be transported through the heater by one or more parallel passes.
radiant section The section of the fired heater in which heat is transferred to the heater tubes primarily by radiation from high-temperature flue gas.
shield section The first two tube rows of the convection section.
These tubes are exposed to direct radiation from the radiant section and usually receive about half of their heat in this manner. They are usually made of more resistant material than the rest of the tubes in the convection section. Extended surfaces are not used in this section.
sootblower A steam lance (usually movable) in the convection section for blowing soot and ash from the tubes, using high-pressure steam.
superheater Heat transfer surface downstream of the steam drum, which is designed to raise the steam temperature above the saturation temperature. The superheater is arranged within the boiler to absorb heat by radiation, convection, or both.
two-side fired tubes Radiant section tubes which are exposed on both sides to direct radiation from the burners.