Simulation of heat transfer in the convection section of fired process heaters

Heat transfer analysis of the radiation section in a fired process heater was carried out in order to determine the flue gas and process fluid temperatures in the zone separating the convection and the radiation sections. Such a determination is a pre-requisite for the heat transfer analysis of the convection section. A Matlab computer programme for the heat transfer analysis of the convection section was written and the results presented graphically including process heat load, the amount of absorbed heat per layer in the convection section and the temperature profiles of combustion gases, tube wall and process fluid.


Introduction
Fired heaters are a versatile class of equipment whereby fluids flowing in tubes mounted inside the furnace are heated by gases produced by the combustion of a liquid or gaseous fuel.These heaters are widely used in petroleum refining and other chemical process industries.
Fired heaters are built with two distinct heating sections: a radiant section in which process fluids are directly heated by radiation from the flame, and a convection section in which hot flue gases leaving the radiation section circulate at high speed through a tube bundle.Heat is recovered from the flue gases and transferred, chiefly by convection, to the process fluid, increasing thereby the overall thermal efficiency of the fired heater which is dependent to a large extent on the effectiveness of the recovery of heat from the flue gases [1].Given that the thermal efficiency depends also on the size of the heat exchange surface area in the furnace, the efficiency may be further increased by the use of finned or studded tubes in the convection section in order to increase the heat transfer area.
Fired heaters are usually classified as cylindrical or box-type heaters depending on the geometrical configuration of the radiant section or combustion chamber.In the cylindrical-type furnace, the radiation section is in the shape of a cylinder with a vertical axis, and the burners are located on the floor at the base of the cylinder.The heat exchange area covers the vertical walls and therefore exhibits circular symmetry with respect to the heating assembly.In box-type heaters, the radiant section has generally a rectangular or square cross section where the tubes may be arranged horizontally or vertically and the burners are located on the floor or on the lower part of the longest side walls where there are no tubes.

Heat transfer mechanisms in fired heater:
Heat is transferred in a fired heater by both convection and radiation in both sections of the furnace, where radiation is the dominant type of heat transfer in the radiant section and convection predominates in the convection section as the average temperature in this section is much lower.In both sections, the heat-absorbing surface is the outside wall of the tubes mounted inside the heater.
The total heat transfer to the process fluid can be estimated by the following equation: The radiant heat transfer follows the relationship: and convective heat transfer follows the relationship:

Thermal evaluation of the convection section
The convection section must make up the difference between the heat duty of the furnace and the part absorbed in the radiant section.By means of using finned tubes in the convection section it is often possible to attain heat flux in the convection section that is comparable to that in the radiation section.
The bases for the calculation of heat transfer in the convection section were laid for the first time by Monrad [2].Subsequently Schweppe and Torrijos [3] developed a method based on the work done by Lobo and Evans [4] on the radiation section.Other work done on the heat transfer in the convection section includes work by Briggs and Young [5] and the work of Garner [6] on the efficiency of finned tubes.
In general, heat transfer in the convection section is composed of the following: 1 Direct convection from the combustion gases.
Eq. ( 4), developed by Monrad [7,8] may be used to estimate a film coefficient based on pure convection for flue gas flowing normal to a bank of bare tubes: where Cp f luegas is the average specific heat of flue gas, and can be determined using equation (5) [10]: Eq. ( 4) does not take into account radiation from the hot gases flowing across the tubes, or re-radiation from the walls of the convection section.
2 Radiation from the gases As an approximation, the radiation coefficient of the hot gas may be obtained from the following equation [7][8][9]: 3 Radiation from refractory walls Re-radiation from the walls of the convection section usually ranges from 6 to 15% of the sum heat transfer by pure convection and the hot-gas-radiation coefficient.A value of 10% represents a typical average.Based on this value, the total heat transfer coefficient for the bare tubes convection section can be computed as [11]: 4 Radiation escaping from the combustion chamber into the first several rows of tubes in the convection section close to the radiation section, commonly referred to as the shield section as they "shield" the remaining tubes from the direct radiation from the radiant section.The shield section normally consists of two to three rows of bare tubes, but the arrangement varies widely for the many different heater designs.These rows are directly exposed to the hot gases and flame in the radiant section, and in order to estimate the radiation escaping from the combustion chamber into the convection section, the same formula already used in the radiant section may also be used [12]: where: and T w is the mean tube wall temperature and can be estimated using Eq. ( 10) in terms of the inlet and outlet process fluid temperatures, t 1 and t 2 , respectively [13]: Since all heat directed towards the shield tubes leaves the radiant section and is absorbed by these tubes, the relative absorption effectiveness factor, α, for the shield tubes can be taken to equal one.
Total heat transfer in the convection section is then equal to the sum of escaping radiation across the shield section, if applicable, and the heat transferred by convection and radiation into the tubes, Where: = coefficient of heat transfer by convection and radiation (overall heat exchange coefficient), which can be determined by Eq. ( 12) [14]: where: Per. Pol.Chem.Eng.Eq. ( 14) was obtained using the least square method for curvefitting the thermal conductivity data of the tube material used (Table 1) [15,16] in terms of tube temperatures.
For turbulent flow, 10000<Re<120000, and L/D o ≥60, the value of h i is given by [14]: where: k = 0.49744 − 29.4604 Eq. ( 16) was obtained using the least square method for curvefitting the thermal conductivity data of process fluid from [7] in terms of process fluid temperature.Eq. ( 17) was also obtained using the least square method for curve-fitting the viscosity values of process fluid data from [9] in terms of process fluid temperature.

Simulation of heat transfer
Davalos, Fermandez and Vallejo proposed a method for the simulation of direct vertical cylindrical fired heaters [17].This method may be used for predicting the overall behaviour of the Fig. 2. Temperature rofiles for combustion gases, tubewall and fluid process and absorbed heat per layer in the convection section convection section without giving information on the heat flux and temperature gradients.Such information may, however, be obtained by carrying out calculations for each segment of the tubes in the convection section.This implies the use of iterative methods.The temperatures of the flue gas and process fluid in the zone separating the convection and the radiation section may be also obtained by using this procedure for an analysis of the radiation section.
There are two primary sources of heat input to the radiant section, the combustion heat of fuel, Q rls , and the sensible heat of the combustion air, Q air , the fuel atomization fluid (for liquid fuel when applicable) and the fuel, Q f uel .The heat is taken out of the radiant section by the two heat transfer methods viz., heat absorbed by the tubes in the radiant Q R and the shield Q shld sections, heat loss through the casing, Q losses , and sensible heat of the exiting flue gas, Q f lue gases .The temperature of the flue gas can then be calculated by setting up a heat balance equation for the case where fuel gas is used as follows [18]: where: Where Where: Q r is radiant heat transfer Q conv is the convective heat transfer in radiant section Simulation of heat transfer in the convection section of fired process heaters 37 2010 54 1 Then, by means of appropriate heat balance: The Newton-Raphson method [19] was used to solve the heat balance equation and determine the effective gas temperature, for which two Matlab programmes were written.The intermediate flue gas and process fluid temperatures can then be calculated using the following algorithm: 1 Assume heat absorption by the first layer of tubes.
2 From the assumed heat absorption it is possible to calculate the temperatures of the flue gas and process fluid by means of an appropriate heat balance.
3 Calculate the log mean temperature difference.
4 Calculate the heat transfer coefficient for convection and radiation from the flue gas.
5 Determine the contributions of escaping radiation if the tubes in the convection section are close to the combustion chamber.
6 Compare the calculated heat absorption with the assumed value, and if the difference between the two values is less than the allowed error, proceed to the following layer of tubes.The total heat absorption in the convection section is determined by the summation of the amounts of heat absorbed in all layers.
Based on the above analysis, a Matlab computer programme was written for the convection section of a box-type fired heater used for heating crude oil in an atmospheric topping unit at Homs Oil Refinery (see Fig. 3 for flowchart).Table 1 shows the geometrical characteristics for the heater, and Table 2 shows its Process data sheet and the characteristics of the fuel (gas oil), flue gas, process fluid and air.By applying the analysis of the convection section for each layer of tubes separately, it was possible to ascertain the effects of using studded tubes.
The results obtained by this analysis are given in Table 3.The heat absorbed in the radiant section is 60% and the remainder is recovered from the hot flue gas in the convection section.By using finned or studded tubes in the convection section, the heat exchange surface area was increased to make possible the attainment of a heat flux in the convection section that is comparable to that in the radiation section, improving significantly by this means the overall thermal efficiency of the heater.
Fig. 1 shows a flow sketch for the furnace in which are indicated the combustion products, mass balance and overall energy balance and heat losses.Fig. 2 shows the temperature profiles for the process fluid, flue gas and tube wall and the amount of heat absorbed per layer in the convection section.

Conclusion:
Heat transfer analysis of the convection section of fired heaters necessitates knowledge of the effective gas and process fluid temperatures in the zone separating the convection and radiation section.For this purpose, heat transfer analysis of both convection and radiation sections of a box-type fired heater in a crude oil atmospheric topping unit was carried out.
A Matlab computer programme for the heat transfer analysis of the convection section was written and the results presented graphically including process heat load, the amount of absorbed heat per layer in the convection section and the temperature profiles of combustion gases, tube wall and process fluid.
The analysis carried out in this work demonstrated effectively the significant contribution of the convection section to the overall thermal efficiency of the heater.

Fig. 3 .
Fig. 3. Flowchart for the simulation of the convection section Tab. 1. Geometrical characteristics of box-type fired heater.
Tab. 2. Process data sheet for box-type fired heater.Results of the Box-Type Heater heat transfer Simulation Number of tubes in radiation section t 1 , t 2 Inlet and outlet process fluid temperatures, respectively ( • C) , w Velocity of the process fluid (m/s).Relative effectiveness factor of the tubes bank.λ Thermal conductivity of tube wall (kJ/m.K.h).µ Viscosity of the process fluid at the average temperature (Pa.s).µ w Viscosity of the process fluid at the tube-wall temperature (Pa.s).ρ Density of process fluid (kg/m 3 ).σ Stefan-Boltzman constant=2.041• 10 −7 kJ/h.m 2 .K 4 .
Simulation of heat transfer in the convection section of fired process heaters Tab. 3.