Process Considerations

This section covers important process considerations for fired heater design and operation, including thermal properties, heat transfer calculations, pressure drop analysis, and stack design principles.

Single Phase, Mixed Phase

The thermal properties of the process fluid flowing through the fired heater are extremely important to the fired heater designer. These properties not only have a direct effect on the amount of heat transferred, they also are important in predicting the pressure loss and furnace coking rates, etc.

Single Phase Fluids

For single phase fluids, liquid or vapor, the properties can normally be assumed to change on a straight line basis from the inlet to the outlet of the heater. Therefore, providing the designer with the properties of the process fluid at the inlet and outlet conditions will normally suffice.

The one exception to this is the viscosity. And this problem is made even worse when an attempt to extrapolate from two given points, such as the inlet and outlet, to get a value for the process fluid at a higher temperature which may occur due to the film temperature rise in the heat absorbing tubes. The following formula may be used to correct the viscosity using the two given values:

And the constants:

Variable	Description
μnew	Corrected viscosity, Cp
μin	Inlet viscosity, Cp
μout	Outlet viscosity, Cp
Tin	Inlet temperature, °R
Tout	Outlet temperature, °R
Tnew	New temperature, °R

Mixed Phase Fluids

For mixed phase process, obtaining the thermal properties of the fluid at the different points in the fired heater is much more difficult than with the single phase flow. However, for a heater with mixed phase at the inlet, the thermal heat transfer calculations may be performed using a straight line approximation similar to that used with single phase, without much loss in reliability of the results. It should be noted that when a heater has mixed phase at inlet and multiple tube passes, the actual flow conditions in the various passes may not be equal.

For the more normal situation, where the inlet process is a single phase liquid and vaporization begins at some unknown point in the heater, it becomes more difficult to estimate the properties. One way to do this is to set up a grid of the properties based on various pressures and temperatures. This works fairly well, but it is very important to assure that grid points near the dew point and the bubble point are included, if the points are going to be crossed in the heater design.

Heat Transfer Coefficients

The inside film coefficient needed for the thermal calculations may be estimated by several different methods. The API RP530, Appendix C provides the following methods:

Liquid Flow

For liquid flow with Re ≥ 10,000:

Vapor Flow

For vapor flow with Re ≥ 15,000:

Reynolds and Prandtl Numbers

Variable	Description
hl, hv	Heat transfer coefficient, liquid/vapor phase, Btu/hr-ft²-°F
k	Thermal conductivity, Btu/hr-ft-°F
di	Inside diameter of tube, ft
μb, μw	Absolute viscosity at bulk/wall temperature, lb/ft-hr
Tb, Tw	Bulk/wall temperature of vapor, °R
G	Mass flow of fluid, lb/hr-ft²
Cp	Heat capacity of fluid at bulk temperature, Btu/lb-°F

Two-Phase Flow

Where W_l and W_v are the weight fractions of liquid and vapor respectively.

In Tube Pressure Drop

The intube pressure drop may be calculated by any number of methods available today, but the following procedures should give sufficient results for heater design. The pressure loss in heater tubes and fittings is normally calculated by first converting the fittings to an equivalent length of pipe. Then the average properties for a segment of piping and fittings can be used to calculate a pressure drop per foot to apply to the overall equivalent length. This pressure drop per foot value can be improved by correcting it for inlet and outlet specific volumes.

Friction Loss

Variable	Description
Δp	Pressure drop, psi
di	Inside diameter of tube, in
G	Mass velocity of fluid, lb/sec-ft²
Vlm	Log mean specific volume correction
F	Fanning friction factor
Lequiv	Equivalent length of pipe run, ft

Log Mean Specific Volume

For Single Phase Flow:

• V₁ = Specific volume at start of run, ft³/lb
• V₂ = Specific volume at end of run, ft³/lb

For Mixed Phase Flow:

Variable	Description
Vi	Specific volume at point, ft³/lb
Tf	Fluid temperature, °R
Pv	Pressure of fluid at point, psia
MWv	Molecular weight of vapor
Vfrac	Weight fraction of vapor %/100
ρl	Density of liquid, lb/ft³

Fanning Friction Factor

The Moody friction factor, for a non-laminar flow, may be calculated by using the Colebrook equation relating the friction factor to the Reynolds number and relative roughness. And the Fanning friction factor is 1/4 the Moody factor. For a clean pipe or tube, the relative roughness value for an inside diameter given in inches is normally 0.0018 inch.

Gas Side Pressure Drop Across Tubes

The pressure drop of the flue gas across the tube bundle is needed for the stack draft calculations and for forced draft fan sizing. Several methods are available for calculating these pressure drops. The methods shown here are for bare tubes and finned tubes.

Bare Tube Pressure Drop

Variable	Description
Δp	Pressure drop, in H₂O
Gn	Mass velocity through minimum area, lb/hr-ft²
Dg	Gas density, lb/ft³
Nr	Number of tube rows

Finned Tube Pressure Drop

For finned tubes, the calculation is more complex and involves additional factors for fin configuration, tube layout (staggered vs. inline), and fin geometry. The basic approach uses similar principles but with modified coefficients based on the fin design.

Heater Stack Draft Analysis

Natural draft is the pressure differential created by a column of hot flue gas inside a stack compared to the cooler ambient air outside. This pressure differential provides the driving force to move the flue gas through the heater and up the stack.

Natural Draft Principles

For most stack designs, a gas velocity at the exit of about 15 to 25 ft/sec is sufficient to discharge the gases into the atmosphere at a rate that will assure they disperse properly. Additionally, most natural stacks are designed for 125% of the design flue gas flow to assure that if the furnace is operated above the design point that it will still operate safely.

Draft Calculation Components

Stack Draft Gain

Variable	Description
Gd	Draft gain, in H₂O
ρg	Density of flue gas, lb/ft³
ρa	Density of ambient air, lb/ft³
A	Height of gas path, ft

Stack Entry Loss

Stack Transition Loss

Included Angle	Ca
30°	0.02
45°	0.04
60°	0.07

Stack Damper Loss

Stack Friction Loss

Variable	Description
Vg	Average velocity of stack, ft/sec
Ds	Stack diameter, ft
Ls	Stack length, ft

Stack Exit Loss

Velocity Head

Ducting Pressure Losses

Fired heater designers utilize ducting for many purposes in a fired heater design. They are used for connecting flue gas plenums to stacks, distributing combustion air to burners, transferring flue gas to and from air preheat systems, etc. The pressure losses through ducting pieces may be individually analyzed or they may be analyzed as a system.

Straight Duct Run Friction Loss

Variable	Description
Δp	Pressure drop, in H₂O
Fr	Moody friction factor
ρg	Average gas density, lb/ft³
Vg	Velocity of gas, ft/sec
Le	Equivalent length of piece, ft
De	Equivalent diameter of piece, ft

Equivalent Diameter

For Round Duct:

For Rectangular Duct:

Moody Friction Factor

We can use the Colebrook equation to solve for the friction factor, with the roughness factor selected from the following:

Duct Surface	Roughness
Very rough	0.01
Medium rough	0.003
Smooth	0.0005

90° Elbow Losses

Round Section Elbow

Radius/Diameter (R/D)	Coefficient (Cl)
0.5	0.90
1.0	0.33
1.5	0.24
2.0	0.19

Rectangular Section Elbow

For rectangular elbows, the loss coefficient depends on both the Height/Width ratio and the Radius/Width ratio. Values range from 0.13 to 1.25 depending on the geometry.

Where V_h = Velocity head of gas, in H₂O

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