Although radiative heat transfer has not yet been added to the capabilities of AHTL, it is quite well possible to do meaningful calculations. Here, an example of a refinery heater (reboiler) is presented. It is a cylindrical heater, with an overhead convection bank, with eight passes. The convection bank has eight rows. The lowest three are bare 6" tubes, the upper are finned 5" tubes per pass. The radiant coil has two 6" and four 8" tubes per pass. The process flow is vaporizing hydrocarbon, the physical properties of which are given by this table, which is the actual AHTL input format. Please refer to the heater data sheets for a detailed description (sheet1,sheet2,sheet3).

Calculations according to the Lobo-Evans method put the bridgewall temperature (BWT) at about 867 degrees centigrade. As the actual temperature in practice is always appreciably lower, the heat transferred in the radiant section is chosen such, that the bridgewall temperature is 830.8 degrees centigrade, which is an educated guess, that will give more realistic calculation results. This was achieved by setting a fixed heat transfer coefficient on the radiant tube outer surface to achieve this. All other heat transfer coefficients in the heater are calculated using the appropriate correlations, except those at the refractory walls. These calculations can be inspected in detail in the "detailed heat transfer output" section in the AHTL output.

The wall model of AHTL allows for specification of a heat maldistribution factor (on both sides of the wall, actually). On the outside of the radiant tubes it has been set to 1.8*1.3=2.34, which is customary for this specific heater design.

Another interesting item is the tube wall temperature calculation of the shock rows. Whereas the wall tubes have an alpha=0.9 (in alpha*A_cold_plane), the shock rows absorb all radiation. The constant quasi heat transfer coefficient used to achieve the required BWT is about 70 [W/m2/K]. Thus, the shock rows should have a coefficient of 70/0.9=78 [W/m2/K]. From this, the first row receives "direct to one row", which is 75% or about 60 [W/m2/K] and the second 20 [W/m2/K]. Since the upper part of the radiant section is in practice cooler, a value of 50 [W/m2/K] hase been used for the first shock row. The convective part is calculated using the Fishenden correlation. A maldistribution factor of 1.9 has been specified for the shock rows.

This shows that the approach of AHTL is very flexible and provides a lot of insight, since all calculations can be inspected to the last detail. If radiant heat transfer were implemented already, it would have been sensible (it is already possible) to calculate the front and back side of the shock rows as separate surfaces, with a maldistribution factor closer to one and to correctly model radiant heat transfer from the actual refractory geometry. This would increase the accuracy of the calculations, while the validity of the results is easy to verify. It should be mentioned here, that the AHTL framework is well suited to accommodate radiant zoning models.

The process calculations use a homogeneous 2-phase model. The balance equations are calculated without neglecting any contribution. Thus, the impulse balance includes static heads and acceleration losses (nice for easy flue gas side draft calculations; they are finalized during the simulation run, no additional draft calculations are required), the energy balance includes potential and kinetic energy. While in this case, these contributions may be small, this is not always so. For instance, in a cracking heater, the fluid velocity in the radiant tubes is around 200 [m/s]. The kinetic energy at this velocity is 0.5*200^2 = 20000 [J/kg], which is considerable.

Heat losses through the heater casing have been calculated in the same simulation, concurrently to the process calculations. The solid material properties were taken from an input file, using actual refractory property tables. In this way, it is not necessary to do lining calculations separately. Another bonus, however, is that for instance in turn-down cases, the heat losses are still correctly calculated, whereas in classical design programs, the heat loss is specified as a percentage of the firing rate, which is plain wrong and unnecessary these days. This feature is also neat when simulating air preheat with the air/ flue gas ducting included. The heat lost is transferred to a third stream: ambient air.

The AHTL output file is large. To print it out, it is recommended to print it in a small non-proportional font (such as courier) in landscape. Line length is 140 characters per line. The stream output is expected to be self-explanatory. This really is also true for both the wall output and the heat transfer coefficient calculation output. It is important, however, to understand the node numbering convention. The first wall defined is at the process tube wall at the process inlet. This wall extends to half the first tube station (the uppermost row). The second wall starts from there to the fluid node at the outlet of the uppermost row, and so on. The process has eight convection tubes, one cross-over tube and six radiant tubes per pass, in total 15 control volumes and 16 nodes. Each control volume is bounded by two walls, that is 30 walls in total.

Each wall has two surfaces. The outer surface is always the first one, so all outer surfaces of the process side are surface number 1,3,5,...,59. The tube inside surface numbers are 2,4,6,...,60.

Shielded radiant refractory is wall number 31, arch and hearth have for ease been combined into wall 32, refractory at the shock rows is wall 33 and at finned rows is wall 34. The same convection of even and uneven surface numbers applies. A finer casing refractory wall distribution could have been chosen, but since the heat loss is relatively small, this should suffice.

Process node numbering is ever increasing; the HC process flow is the first stream (nodes 1-16), the flue gas flow is the second stream (nodes 17-26). The ambient air stream has only two nodes and the heat lost is added to the second one (nodes 27-28).

Bearing this in mind, one can understand the reference numbers of the detailed heat transfer output. It mentions a surface number, a temperature reference number (from which the process temperature for heat transfer is to be taken) and a target number that specifies to which process node number the heat transferred is to be added.

If these conventions are understood, it is possible to fully cross-reference the output of the stream, wall and heat transfer models.

As AHTL renders the heat transfer problem completely transparent, this should help to validate any third party heater software or to analyze operational problems in the field. Heat Transfer Consult offers consulting services in this respect.