Direct-fired heaters find wide application throughout the chemical process industries (CPI) and are common in petroleum refineries, where they are used to preheat petroleum or petroleum-derived feedstocks in advance of downstream process operations.
Since excessive internal tube fouling occurs above certain temperatures, designers often try to keep temperatures down by over-specifying the heat transfer surface area. Later on, if the capacity of the heater needs to be changed or if the heater needs to be used for a different service altogether, the engineer needs to investigate how the new conditions will influence fouling.
This article demonstrates mathematically how to determine the effects of a different heat flux specification on run length (the time interval between shutdowns for cleaning or decoking). Such analysis is helpful in understanding the changes in operating costs associated with decoking the heater either more or less frequently.
This discussion focuses on the performance of direct-fired heaters in delayed-coking service, which experience the most-severe operating conditions of any type of petroleum-refining application. The stringent design strategies discussed here are also applicable to fired-heaters used in other refinery and chemical process applications.
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| Figure 1. This schematic shows a typical direct-fired heater radiant section, and provides dimensional data and temperatures that correspond to the equations provided in this article. |
When heat transfer duty increases for a given amount of heat transfer surface area (as measured by the resulting increase in heat flux), it would appear that an increase in peak tube metal temperatures and more-rapid coke deposition would result. The calculations presented below verify that this is, in fact, the case.
However, the extent of increased fouling is not necessarily catastrophic. The example shown here for a heater of the design in Figure 1 illustrates that by increasing heat flux from 10,000 to 17,700 Btu/h-ft, the relative run length would be 0.36 or 36% of the run length for the heater as originally designed. If the original heater has a run length of 33 months, then the reapplied heater would have a run length of 1 year. In many cases, it would take many years for the increased operating costs to add up to the cost of a new heater.
Heat transfer conditions
Direct-fired heaters used in delayed-coking service usually come with two sections — a radiant section and a convection section.
In general, the heating surfaces in the convection section may be used for feed preheating, followed by final heating to the design outlet temperature in the radiant section. The convection section may also be used for other types of preheating, such as steam superheating.
Radiant section. The radiant section consists of a refractory-lined enclosure that houses one or more tubular heating coils, through which the process fluids flow. The heating coils are arranged so as to surround a central grouping of one or more burners fueled by natural gas (or other gases).
This section usually uses tubular heating surfaces that are either arranged vertically or horizontally in an enclosure that has a cylindrical or rectangular cross-section. The equations presented below are valid for cabin-type heaters that have a rectangular cross-section and horizontal tubes. Minor modifications would be needed to use these equations to evaluate the performance of a heater with a cylindrical cross-section.
The arrangement of the heating coils forms a combustion chamber into which the high-temperature combustion products generated by the burners flow. Heat is transferred from the combustion products flowing past the coils to the process fluids flowing through them, with the principal mode of heat transfer occurring via radiation across the walls of the coils (Figure 1).
The radiant section of a typical direct-fired heater most often has two merging zones. The first is a lower firing zone that corresponds to a section of the heater wherein the fuel-air mixture exiting the burners is burned very nearly to completion, and the combustion products are simultaneously cooled by the surrounding heat-transfer surfaces. The length of this section should be very nearly equal to the flame length. In the second zone — located above the first — the combustion products are further cooled prior to entering the convection section.
Convection section. The convection section typically preheats process fluids before they enter the radiant section. It consists of a refractory-lined enclosure that has a rectangular cross-section.
Inside the enclosure are multiple rows of closely spaced, horizontal tubes. These tubes form channels through which combustion products leaving the radiant section pass at relatively high velocity. As this happens, heat is transferred, principally via convection, from the combustion products to the heating surfaces and process fluids. Combustion products typically leave the convection section at a reduced temperature (lower exhaust temperatures corresponds to higher overall thermal efficiencies).
Temperature and fouling
The temperature of the combustion products generated in the heater vary from very high at the bottom of the radiant section (from a maximum equal to the adiabatic flame temperature at about 3,500°F), to intermediate at the top of the radiant section (also the inlet of the convection section), to very low at the top of the convection section (about 400°F leaving the convection section). The temperature gradient from top to bottom depends on the heat in the combustion products leaving the burners, and the amount of heat removed by the heat transfer surfaces, as determined by the temperature and heat transfer characteristics of both the combustion products and heat transfer surfaces.
Because of the high temperatures in the radiant section, the hydrocarbon fluids at the inside wall of the tubular heating elements in this section tend to experience a degree of thermal decomposition, leaving behind coke deposits that can adhere to the inner surface of the coil. As coke deposits (and deposits from dirt and other impurities in the fluids) build up, they form an insulating layer that restricts heat flow through the tube wall. Eventually, when the tube wall reaches its design temperature (referred to as an end-of-run condition), the heater must be shut down and decoked (for instance, by using steam-air decoking or controlled burning), or mechanically cleaned (by using rotary cutting tools). Periodic removal helps avoid tube damage while ensuring optimum heat-transfer and system performance.
The time interval between shutdowns for decoking or cleaning is referred to as run length. Ideally, the run length should be made as long as possible, but decisions related to appropriate run length must be balanced against the higher capital costs associated with such activities. For instance, it might be prohibitively costly to provide enough heat transfer area to lower the tube-metal temperatures to the level needed to drastically increase the run length.
Heat transfer calculations
Simultaneous solution of Equations (1) through (18) below describe how heat is transferred from the combustion products to the tubular heat-transfer surfaces in the radiant section by both radiation and convection. The radiant section described in the author’s patent [ 1 ] and shown in Figure 1 provides an illustrative example.
Calculate Q r–t, the total heat transferred by radiation from the burner flames to the tubular heating surfaces at either side of the burner flame envelopes, using Equation (1):
(1)
See box, right, for discussion of term a.
Emissivity calculations (Eeff). Eeff, the effective emissivity between two parallel surfaces, is given by Equation (2a) and Ref. [ 2 ]):
(2a)
For the purpose of solving Equation (1), E 1 is equal to E tubes, which can be easily found in popular references [ 5 ]. At an average temperature of 1,200°F (the design tubes metal temperature T MT) the average emissivity of the tubes (the cold plane) is 0.8. E 2is equal to E fg, which must be evaluated as two gases (one hot and one cold) using Equation (2b).
(2b)
E hot avg is equal to the arithmetic average of the top and bottom calculated emissivities for the hot plane using Equation (3). E cold avgis calculated in a similar fashion but for the cold plane.
(3)
Here, mf is mole fraction of the given subsance, and L is the thickness of the plane at top and bottom. In a burner flame,L is equal in thickness to the flame diameter at the top of the flame, and equal to 0 at the bottom of the flame; see Figure 1).
Surface area of the burner flame envelope (Aflame).
(4)
Ideally, the flame length, L f, as given by Equation (5) should be equal to or somewhat less than H bott.
(5)
D flame avg is the arithmetic average of Dburner and D flame top, as shown in Figure 1. D flame top is calculated from Equation (6):
(6)
Velocity of circulating fluegas stream (V circ).The circulating fluegas stream, described above and depicted in Figure 1 is generated as a result of fluegas entrainment by the burner jet. The volumetric gas-entrainment rate for a free jet (that is, one that is not constrained by a surrounding medium) is a function of the length-to-diameter of the jet and the volumetric flowrate of the burner gas. However, since a jet enclosed by a heater enclosure is not truly a free jet, different tactics must be used to calculate the circulation rate, since that rate must be considered to be limited by burner velocity. The following equation may be used:
(7)
Note that the above equation considers that a single burner velocity head, generated by the burner, is used to overcome a loss of four velocity heads, corresponding to the circulating stream making four 90-degree turns inside the enclosure.
Heat transfer coefficient for heat transfer from the circulating stream to the tubes (HTCotubes).Heat transfer by convection (from the relatively high-velocity, circulating fluegas stream and tubular heating coil at the inside walls of the radiant-section enclosure) contribute to the total heat flow absorbed by the coils. Equation (8) has been appropriately modified from Ref. [ 4 ]:
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| Figure 2. Shown here are the arrangements of components in the radiant and convection sections of a typical direct-fired heater |
(8)
The quantity of heat transferred by convection to this surface, Q c-circ-t, is given by:
(9)
Meanwhile, heat transferred by convection from the flame envelope to the circulating fluegas stream must also be considered, and may be calculated using the following equation, also appropriately modified from Ref. [ 4 ]:
(10)
The quantity of heat transferred by convection from the flame envelope to the circulating fluegas stream, Q c-circ, is given by:
(11)
Also note the following relationship, where Eeff is given by Equation (2a) E 1 = E fg and is evaluated at T fg-avgand E 2is evaluated at Tcirc:
(12)
The heat transferred by radiation from the circulating fluegas to the planar tubes, Qr-circ-t, is given by:
(13)
Equation (14) shows that the heat entering the circulating gas stream by radiation and convection is equal to the heat leaving the circulating gas stream by radiation and convection. The temperature of the circulating fluegas stream is determined by equating the radiant and convective heat inputs entering the circulating fluegas stream to the radiant and convective heat inputs leaving, and solving for the unknown circulating fluegas temperature. Thus:
(14)
Note that Equations (15) through (18) for both zones must be satisfied in order to obtain a proper solution of Equations (1) thru (14):
(15)
(16)
(17)
(18)
T bott in may be taken to be the adiabatic flame temperature, although heat flow from the burner flame at this point is essentially zero since flame thickness and emissivity at this point are also zero.
Equations (1) through (18) can be used to evaluate the performance of both the upper and lower zones of the radiant section, and have been used to calculate the performance of a delayed-coking heater with a total radiant-heat absorption of 100-million Btu/h. Dimensional data provided in Figure (1) are based on data summarized in Ref. [ 1 ]. Data calculated via the equations provided herein are summarized in Table 1.
Comparing relative run lengths
In the case of the two-zone, direct-fired heater discussed above, it is assumed that direct radiation to a single tube emanates horizontally and obliquely from a point corresponding to the radiating center (which is also the geometric center) of a cross-sectional plane passing vertically through the combustion chamber and burners (Figure 2).
Identify critical tube location.To properly evaluate the relative run length of a given radiant section for two different conditions, first a so-called critical tube location must be identified. The critical tube location is where the combination of maximum heat flux and resulting local-fluid temperature are such that the maximum allowable coke thickness is at its lowest point in the heater (and therefore is the limiting factor in run length). As a rule of thumb, the critical tube location is usually where the fluegas temperature is the highest. In the case of the heater illustrated in Figures 1 and 2, the critical tube location happens to correspond to the radiating center of the combustion chamber (the burner cross-section).
Calculate maximum radiant heat flux (qmax).Once a critical tube location has been identified, the maximum heat flux must be calculated.
(19)
Where
(20)
Note that the factor 1.8 in Equation (19) is for tubes on 2-dia. centers fired on one side only and backed by refractory.
Determine coke deposition temperature (TMT,avg).
(21)
Where T MT,eor = the maximum tube design temperature (in this case, 1,200°F).
Determine coke deposition thickness (Lc).Once a critical tube location has been identified, the maximum-allowable, coke-deposition thickness can be determined.
(22)
Where K c is the thermal conductivity of coke (13.6 Btu-in/h-ft2-°F).
Determine the thermal decomposition constant (K1).The coke-deposition temperature, ( T MT avg) in degrees R, can then be used to calculate a decomposition velocity constant [ 5 ].
(23)
K 1 is actually defined by Equation (24).
(24)
Since the run length for a given heater is proportional to L c/ K 1, the relative run length for the proposed heater having a lesser amount of tubular heat transfer surface than that of a heater of traditional design can be determined by dividing L c/ K 1 for the proposed heater by L c/ K 1for the traditional design. This relationship results in the relative run lengths calculated and given in Table 1.
Edited by Suzanne Shelley
References
1. Cross, A., U.S. Patent 7,395,785. “Reducing Heat Transfer Surface Area Requirements of Direct Fired Heaters Without Decreasing Run Length,” July 8, 2008; http://www.uspto.gov.
2. Kern, D.Q., “Process Heat Transfer, First Ed.,” McGraw-Hill, New York, 1959.
3. Perry, R.H., and Green, D.W., “Perry’s Chemical Engineers Hand Book, Sixth Ed.,” McGraw-Hill, New York.
4. McAdams, W.H., “Heat Transmission, Third Ed.,” McGraw-Hill, New York, 1954.
5. Nelson, W.L., “Constants for Rates of Thermal Decomposition of Hydrocarbons and Petroleum Fractions, Fuels, Combustion and Furnaces,” McGraw-Hill, New York, 1946.
Author
Alan Cross (73-34 244th St., Little Neck, NY, 11362; Email: across8588@aol.com) has had more than 30 years of professional design experience with direct-fired heaters with ABB Lummus Heat Transfer (now CB&I Lummus Technology). He holds a B.S.Ch.E. from The City College of New York, and an M.S.Ch.E. from the Polytechnic University of New York, and is a member of the American Institute of Chemical Engineers. He has authored several patents related to direct-fired heaters, and has several other patents pending related to the design of coal-fired process heaters, compact, low-cost, fired heaters capable of processing low- and high-boiling petroleum-based fluids using design strategies that reduce the fouling of internal tube surfaces from coke deposition. He is also engaged in design studies relating to the development of low-cost, innovative, catalytic steam- methane reformer heaters and hydrocarbon-cracking heaters, with the expectation of patenting and prototyping the proposed equipment, as a result of the very substantial material cost savings indicated by preliminary estimates.
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