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Jan-2008

### Ethylene furnace heat flux correlations

Equations are presented that correlate and predict heat flux as a function of operating, burner and furnace parameters for all major ethylene-cracking furnace configurations

Joseph Colannino
John Zink Company LLC

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Article Summary
This article presents mathematical heat flux models for ethylene furnaces in one of three configurations: fired by floor burners only, fired by wall burners only, and fired by floor burners in conjunction with one or more rows of wall burners (Figure 1). It is assumed that the floor burners do not release their heat instantly, but over some distance. To determine the explicit functionality, we use an analogy from jet theory and a global energy balance on the furnace. For the wall-fired-only case, we presume that the low heat release and short flame lengths allow us to treat the radiant heat as a point source. Additionally, we couple these two models for the floor plus wall-fired case. We will see that the model establishes similar conditions for field and test units, and may be used to generate real-time heat flux curves from flue-gas temperatures. These results have been incorporated into a state-of-the-art configuration program, which is also described.

One aim of this discussion is to show that it is possible to characterise normalised heat flux profiles as a function of two parameters: the elevation at which the maximum heat flux occurs (zmax) and the heat flux at the floor (y0). In turn, these two parameters are determined by operating conditions and furnace and burner design —statistically, all are significant contributors to y0 and zmax. This highlights the need to work with burner design engineers at the earliest possible stage in the design of ethylene units to predict the heat flux profile.

Heat flux profile
The distribution of heat flux (the heat flux profile) is an important criterion for the performance of ethylene-cracking units. The heat flux profile is the fraction of radiant heat incident to a tube at a given elevation. Figure 2 shows a typical heat flux profile for a furnace that is fired from the floor. To understand why heat flux profile is important, we will briefly overview the cracking process.

Production of ethylene via thermal cracking
Ethylene production proceeds via the thermal cracking of a hydrocarbon feedstock. For example, ethane and propane may crack in a complex series of steps to ultimately form ethylene and byproducts, as follows:

Ethane cracking: H3CCH3 " H2C=CH2 + H2
Propane cracking: H3CCH2CH3 " H2C=CH2 + CH4

The amount of ethylene production normalised by the maximum possible yield is known as the fractional conversion or conversion efficiency. Thermal cracking reactions such as the previously shown ethane and propane cracking (to ethylene) are highly endothermic and require heat. The process heat is supplied by special burners in an ethylene-cracking furnace operating at approximately 1200ºC. The reacting feedstock inside the tube will abstract heat from the tube wall, thus cooling the tube metal. The result is process outlet temperatures (ie, coil outlet temperatures – COTs) that are hundreds of degrees lower than the surrounding furnace temperature. However, if heat is applied non-uniformly, a side reaction may proceed to deposit carbonaceous polymers on the inside tube wall known as coke (ie, coking inside the tube wall). Coke sticks to the tube walls and insulates the process fluid from the furnace. This can result in local overheating of the tube surface and ultimately, if neglected, tube rupture. After sufficient deposition, the tube may be seen to be glowing from the furnace side. For this reason, tube surface temperatures are carefully monitored.

During normal operation, coke accumulates at a low rate on internal tube surfaces. Periodically, the furnace temperature is drastically lowered and some steam or steam and air are added to the feedstock. This procedure interrupts the production of ethylene but removes the coke. Periodic applications of steam and air are known as a steam-air decoke cycle. For decoking, you can write a generic reaction, as follows:

C + a H2O + (2 – b – a)/2 O2 " (1- b) CO + b CO2 + a H2

where a is the steam/carbon ratio of the influent, and b is the CO/CO2 ratio of the effluent.

The time between decoking episodes is the run length. It is desirable to increase run length, conversion efficiency, and preserve tube and equipment life. However, these are interrelated in complex ways. For example, higher temperatures can increase conversion but may also increase coking, reduce run time and shorten tube life. An appropriate heat flux profile balances and optimises these competing influences.

Furnace configurations
From a burner perspective, ethylene furnaces come in three basic varieties — floor fired, wall fired, and floor plus wall fired – as previously noted. To begin examining each configuration, we will consider the floor-firing-only case.

Heat flux from floor firing
Consider heat released from floor burners along the furnace length (qh) and being absorbed by process tubes, or otherwise removed from the furnace (qp), and finally exiting the furnace into the convection section (qc). Then, a simple heat balance for a two-dimensional furnace is as follows:

qh - qp = qc.

Typically, process engineers are interested in the normalised heat flux (0 < y < 1); that is, the heat flux (MW/m2) divided by the maximum heat flux. A specialised heat flux probe (Figure 3) converts radiant heat flux to an mV signal. You move the heat flux probe to various elevations along the centreline of the test heater and record each mV reading. After the readings are complete, you determine a normalised heat flux profile by dividing each mV reading by the maximum mV reading. You may use statistical procedures to smooth the heat flux profile and estimate the true maximum with greater accuracy.1

Generally, heat flux probing is done in special test furnaces designed for this purpose. Figure 4 shows one such ethylene furnace simulator – the internal furnace dimension of this particular simulator is 11m from floor to the beginning of the convection section.

Now qh and qp vary with the normalised furnace height (0 < z < 1), where z = 0 is the floor elevation and z = 1 is the top of the furnace. Accordingly, the following differential equation represents the heat flux as a function of elevation:

dy = qh (z) – qp (z)
dz
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