Realities of heat flux in fired heaters
Uneven radiant heat flux distribution is a major cause of poor reliability in refinery fired heaters.
GRANT NICCUM and STEVE WHITE
Process Consulting Services
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Fired heaters in refinery heavy oil service are common limits to unit throughput and run length. Aside from cases where a heater is simply at maximum firing, many units are limited by poor heater reliability. Unreliable heaters tend to begin coking rapidly at start-up and require frequent decoking to lower pressure drop and tube metal temperatures. In crude/vacuum, FCC, delayed coker, and many other units, maximising heater reliability extends run length and increases profitability.
Fired heaters coke due to high oil temperature and residence time. Reliable heaters that meet run length expectations are designed by optimising the heater layout and the process side mass velocity. When it comes to heater sizing and layout, radiant section heat flux is one of the most important parameters. Excessive radiant tube peak heat flux is a common cause of radiant tube coking. Peak radiant heat flux is listed on the API heater datasheet, but does the datasheet number really reflect reality? Specific heater layout parameters can heavily influence the answer to this question, and analytical tools are available to explore the question during the design process to avoid surprises at start-up. These same design parameters and analytical tools also provide critical insights into practical revamp solutions for existing problem heaters.
Definition of heat flux
In the context of fired process heaters, heat flux is the amount of heat absorbed through the heater tubes per unit outside surface area. Heat flux is typically expressed in units of kcal/h-m2 (BTU/h-ft2). For fired heater design and evaluation, it is typical to discuss the heat flux for a specific section rather than for the heater as a whole. For example, the radiant section average heat flux is the total duty absorbed in the radiant section divided by the total radiant tube outside surface area.
While average heat flux is a useful concept for high level heater design and evaluation, it does not capture the harshest conditions, which are better represented by ‘peak’ heat flux. Peak heat flux represents the maximum heat flux in a specific heater section and can be used to calculate maximum expected oil film and tube metal temperatures (TMT).
Many heaters are specified with a maximum allowable radiant section average heat flux. Average heat flux specifications are useful because the calculation is simple and, for a given heater design, peak flux varies proportionally with average flux. For well-designed heaters, average heat flux is a good gauge of likely reliability, along with process side mass velocity (not discussed here). However, in some cases the specific heater design (geometry, burner selection, and so on) leads to peak heat fluxes that are significantly higher than expected. When this happens, heaters can have severe reliability problems at average fluxes that might normally be considered safe.
Consequences of high heat flux
Two major crude heater problems associated with high oil temperatures are cracking and coking. As oil temperature increases, the oil tends to crack and produce light ends and off-gas, and it can also form hard coke attached to the inside tube walls. The highest oil temperatures in a fired heater occur in the oil film at the inner wall of the tubes (see Figure 1). The temperature at the inner tube wall, tw,i, can be calculated using Equations 1 and 4. Equation 4 shows that the temperature rise across the oil film is directly proportional to the heat flux. As heat flux increases, so does the likelihood of coking and cracking:
Tube inside wall temperature
tw,i = tb + ∆tf 
Tube outside wall temperature (clean)
tw,o = tb+ ∆tf + ∆tw 
Tube outside wall temperature (fouled)
tw,o = tb+〖Δtf + ∆tc + ∆tw 
Oil film temperature rise 
Tube wall temperature rise 
Coke layer (fouling) temperature rise 
Many refinery heaters operate against limits on maximum TMT in the radiant tubes. Building on the equation for the inside wall temperature, Equations 2 and 5 allow for the calculation of the outside tube metal temperature for a clean tube. Adding a term to incorporate a fouling factor allows for calculation of the outside metal temperature of a fouled tube (Equations 3 and 6). For crude heaters, typical design fouling factors are in the range 0.0012-0.0020 h-m2-°C/kcal (0.006-0.010 h-ft2-°F/BTU) which roughly corresponds to the thermal resistance of 3-6 mm (⅛-⅟4 in) of coke thickness.
Determining maximum heat flux
Most commercial fired heater modelling software is based on the assumption of a ‘well-stirred’ firebox, meaning that the flue gas temperature is uniform throughout. Well-stirred firebox models do not account for firebox/burner geometry or flame characteristics. By assuming a constant flue gas temperature and calculating the heat transfer to each radiant tube in one or more segments, these programs iteratively solve for the average heat flux of each tube. In the process, they must also solve for the process side bulk temperature, internal heat transfer coefficient, film temperature, fouling ΔT, and outside tube metal temperature for each tube segment.
Once the average heat flux for a radiant tube in a well-stirred firebox is known, the ratio of peak radiant heat flux to average radiant heat flux around the circumference of the tube, Fc, is a geometric function of the tube layout and the tube centreline spacing. For a single row of tubes with typical tube spacing of twice the tube outside diameter, Fc is about 1.8 for single fired tubes and 1.2 for double fired tubes. This implies that, for the same peak heat flux, double fired heaters can be designed for 1.8/1.2 = 1.5 times the average heat flux and thus less radiant tube surface area.
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