Terms in Kinetic Models for Nonelementary Reactions

The types of intermediates we may postulate are suggested by the chemistry
of the materials. These may be grouped as follows.


Free Radical
Free atoms or larger fragments of stable molecules that contain one or more unpaired electrons are called free radicals.The unpaired electron is designated by a dot in the chemical symbol for the substance. Some free
radicals are relatively stable, such as triphenylmethyl


Ions and Polar Substances

Electrically charged atoms, molecules, or fragments of molecules. such as
N3-, Na+, OH-, 
called ions. These may act as active intermediates in reactions.


Transition Complexes.

The numerous collisions between reactant molecules result in a wide distribution of energies among the individual molecules. This can result in strained bonds, unstable forms of molecules, or unstable association
of molecules which can then either decompose to give products, or by further collisions return to molecules in the normal state. Such unstable forms are called transition complexes. Postulated reaction schemes involving these four kinds of intermediates can be of two types.
Nonchain Reactions.
Chain Reactions.






By Rajendra

• Equilibrium means a condition of balance.
•  In thermodynamics the concept includes not only a balance of forces, but also a balance of other influences. 
• Each kind of influence refers to a particular aspect of thermodynamic (complete) equilibrium. 
• Thermal equilibrium refers to an equality of temperature, mechanical equilibrium to an equality of pressure, and phase equilibrium to an equality of chemical potentials 
• Chemical equilibrium is also established in terms of chemical potentials. For complete equilibrium the several types of equilibrium must exist individually.
• To determine if a system is in thermodynamic equilibrium, one may think of testing it as follows:Isolate the system from its surroundings and watch for changes in its observable properties. If there are no changes, it may be concluded that the system was in equilibrium at the moment it was isolated. The system can be said to be at an equilibrium state. When a system is isolated, it cannot interact with its surroundings; however, its state can change as a consequence of spontaneous events occurring internally as its intensive properties, such as temperature and pressure, tend toward uniform values. When all such changes cease, the system is in equilibrium. At equilibrium. temperature and pressure are uniform throughout. If gravity is significant, a pressure variation with height can exist, as in a vertical column of liquid.

EQUATIONS OF STATE

The equation which relate pressure-temperature-volume of substance,

• the equation of state are useful for calculating properties of pure fluids and mixtures, for example, density of gas or liquid, vapor pressure, vapor-liquid equilibrium (vle), liquid-liquid equilibrium (lle), enthalpy, and entropy.
• Mostely used form equations are

                1. Van der Waals equations

                2. Perturbation equations

                3. Virial and extended virial equations

Pump Related Terms

Vapor pressure, cavitation, and NPSH are subjects widely discussed by engineers, pumps users, and pumping equipment suppliers, but understood by too few. To grasp these subjects, a basic explanation is required.




VAPOR PRESSURE


Vapor pressure is the pressure absolute at which a liquid, at a given temperature, starts to boil or flash to a gas. Absolute pressure (psia) equals the gauge pressure (psig) plus atmospheric pressure.


Water and water containing dissolved air will boil at different temperatures. This is because one is a liquid and the other is a solution. A solution is a liquid with dissolved air or other gases. Solutions have a higher vapor pressure than their parent liquid and boil at a lower temperature. While vapor pressure curves are readily available for liquids, they are not for solutions. Obtaining the correct vapor pressure for a solution often requires actual laboratory testing.


CAVITATION


When a liquid boils in the suction line or suction nozzle of a pump, it is said to be “flashing” or “cavitating”
(forming cavities of gas in the liquid). This occurs when the pressure acting on the liquid is below the vapor pressure of the liquid. The damage occurs when these cavities or bubbles pass to a higher pressure region of the pump, usually just past the vane tips at the impeller “eye,” and then collapse or “implode.” Cavitation can create havoc with pumps and pumping systems in the form of vibration and noise. Bearing failure, shaft breakage, pitting on the impeller, and mechanical seal leakage are some of the problems caused by cavitation.


NPSH


Net Positive Suction Head is the difference between suction pressure and vapor pressure. In pump design
and application jargon, NPSHA is the net positive suction head available to the pump, and NPSHR is the net positive suction head required by the pump. The NPSHA must be equal to or greater than the NPSHR for a pump to run properly. One way to determine the NPSHA is to measure the suction pressure at the suction
nozzle, then apply the following formula:

NPSHA = PB – VP ± Gr + hv

where PB = barometric pressure

in feet absolute,

VP = vapor pressure of the liquid at maximum pumping temperature in feet absolute,

Gr = gauge reading at the pump suction, in feet absolute (plus if the reading is above barometric

pressure, minus if the reading is below the barometric pressure), and

hv = velocity head in the suction pipe in feet absolute.

NPSHR can only be determined during pump testing. To determine it, the test engineer must reduce the NPSHA to the pump at a given capacity until the pump cavitates. At this point the

vibration levels on the pump and system rise, and it sounds like gravel is being pumped. More

than one engineer has run for the emergency shut-down switch the first time he heard cavitation on

the test floor. It’s during these tests that one gains a real appreciation for the damage that will occur if a pump is allowed to cavitate for a prolonged period.

By Rajendra

What do you know about POOL BOILING??

1) Pool boiling occurs when a heater is submerged in a pool of initially stagnant liquid.


2) When the surface temperature of the heater exceeds the saturation temperature of the liquid by a sufficient amount, vapor bubbles nucleate on the heater surface.

3) The bubbles grow rapidly in the superheated liquid layer next to the surface until they depart and move out into the bulk liquid. While rising as the result of buoyancy, they either collapse or continue their growth, depending on whether the liquid is locally subcooled or superheated.


4) Nucleation is a molecular-scale process in which a small bubble (nucleus) of a size just in excess of the thermodynamic equilibrium is formed.


5)Initial growth from the nucleation size is controlled by inertia and surface tension effects. 
The growth rate is small at first but increases with bubble size as the surface tension effects become less significant.


6) When the growth process reaches the asymptotic stage, it is controlled
by the rate of heat transferred from the surrounding liquid to facilitate the evaporation
at the bubble interface.


7) If the bubble, during its growth, contacts the subcooled liquid, it may collapse.


8) The controlling phenomena for the collapse process are much the same as for the growth process but are encountered in reverse order.

By Rajendra

Size and Type of Heat Exchanger

Heat exchangers basics, the knowledge of heat exchanger and its importance in industry should be known
Do you have any idea, how to size heat exchanger and its type designated ?
First we will  consider sizing part; what do you mean by sizing designations? How to designate shell diameter, shell thickness , heat exchanger length, tubes dimensions, baffle size etc. Theoretical explanation is as fallows:

1. TEMA standards (Tubular Exchanger Manufacturing Association) and Heat Exchanger Institute (HEI) standards have specified the nomenclature for the size and type of shell and tube heat exchanger.
2. Size is designated by the nominal shell diameter and the tube length.
3. The tube length for a straight tube unit is the distance between the outermost tube faces. For a U-tube unit, it is the distance between the outermost face of the tubesheet  and the bend tangent.

Type of heat exchanger is designated by a set of letters associated with the front end, the shell and rear end as in figure.

1. Split-ring floating head (S) exchanger with removable channel and cover (A), single-pass shell (E), 23.5 inch (590 mm) inside diameter with tubes 16 ft (4880 mm) long. Size 23-192 (590-4880), Type AES
2. U-tube exchanger (U) with bonnet-type stationary head (B), split flow shell (G), 19 in (480 mm) inside diameter with tubes 7 ft ( 2130) straight length. Size 19-84 (480-2130), Type BGU
3. Fixed tubesheet exchanger with removable channel and cover (A), bonnet-type rear head (M), two-pass shell (F), 33 1/8 inch (840 mm) inside diameter with tubes 8 ft (2440 mm) long. Size 33-96 (840-2440), Type AFM

[TO SEE FIGURE CLEARLY CLICK ON IT]

By Rajendra

DIstillatoion

The fundamental basis of distillation is the physical equilibrium between the liquid and vapor phases of a system. Equilibrium is the condition reached after an infinite time of contact between the phases. In practice, liquid-vapor systems normally reach a state close to equilibrium in a comparatively short time of contact. At equilibrium, the composition in the vapor phase is usually different from that in the liquid. (If this is not the case, then an azeotrope is present, as discussed later.) The relationship of equilibrium concentrations of a component between phases is described by the equilibrium ratio . Other terms used for this ratio can include distribution coefficient, equilibrium constant, K-constant , or simply volatility.


Relative volatility is a useful tool to judge the feasibility and ease of a distillation separation. In general, the larger the relative volatility between two key components, the easier and less costly will be the separation of those keys. If the relative volatility between the keys is unity, then their separation by ordinary distillation is impossible. Such a situation exists with azeotropes. The relationship between relative volatility and difficulty of separation may be illustrated by application of a simple relationship


By Rajendra

Selecting Chemical Reaction

If you are a designer, you want to produce particular product say "P" and you are having set of reactions which gives the same product "P"

A+B-------> P

C+D--------> P

E+F+G------>P

When there are number of reactions for same product, the task is to which one you will choose?


Some of the Useful hints are


1) Aim to maximize incorporation of reactant atoms into final product
  Suppose product P is made of atoms like "A" "B" "C" "D", then choose reactants which contains theses atoms/ elements more


2) Choose the reactants that are as close as possible in chemical structure to final product


3)Choose reactants to minimize risk of explosions, Fires, or release of toxic materials. If use hazardous materials is unavoidable , design for minimum reactor volume.


4) Use highly-purity raw materials to avoid side reactions. Consider purifying raw material before feeding to reactor, if possible


5)Use catalyst if at all possible


6)Choose reactions that proceed simultaneously at temperature and pressure as close to ambient conditions as possible  so that operating and fixed cost will be less 

By Rajendra

The Gibbs Phase Rule........What do you Know??

Have you remembered Gibb's phase rule, for what it is applied or to just calculate the "F" for namesake and sit cold. There is something beyond this , Look at exapmles
Suppose in a container these exists


1)Pure water
2)Water-Steam
3)Ice-Water-Steam
4)component Ethanol-water and 2 phases


From these examples what do you feel, to know about condition in the container or to define completly whats exactly state in the contianer something is reqiured. What is that? Number of variables you can define , but how many of them minimum should be defined so that others can be predicted; how many of these variables are independent ? The answer lies in simple but useful rule called
Gibb's Phase rule:
Josiah Willard Gibbs F=C+2-π

          π = Number of phases presents

C = number of components

                                F = number of variables that independently set

Look first at a single- component, in examlpe 1 , water; π=1, C=1 so the F=2 means we should specify two variables (pressure and temperature) of the system, In other words , there are multiple combination of  T and P at which liquid water exists.

For second case , C=1, π=2 ;F=1+2-2=1;  It means we can specify additional one varible ; either T or P. One is known second can be calculated

For third case : F=1+2-3=0 will come. It means no need to specify, three phases exists in exualibrium at only one T and P at which it is possible; Triple point and Nature has set these value fixed. Then one silly question will come in someones mind that , if I add some water , Ice cubes in a container where steam is alredy present ; that means "Triple Point".  Here importance of the  term EQUALIBRUM comes into picture where phases exists with each other comfortably.

For fourth case:  F= 2+2-2 =2 ; Two independetn variables must be specified from T, P, xE and yE

You ask questions to youself

Does F<0 (negetive) possible?

Does F= Complex Number possible?

Does F= Infinity possible ?


Biography

Josiah Willard Gibbs

1839-1903

Gibbs was a theoretical physicist and chemist considered by many to be one of the greatest scientists of his time. An engineer by training, he became (1871) Professor of Mathematical Physics at Yale. His papers on "Graphical Methods in the Thermodynamics of Fluids" (1873), "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces" (1873) and the most famous "On the Equilibrium of Heterogeneous Substances" (1876 and 1878) form the basis for much of modern thermodynamics, phase rule and statistical mechanics. He published the first quantitative theory of the emf of an electrolytic cell (Gibbs-Helmholtz Eq) and worked out his own "Elements of Vector Analysis". He was a tall, dignified gentleman, excellent horseman, did his share of household chores (an expert on heterogeneous equilibria, he mixed the salads) and was approachable and kind (if unintelligible) to students. He was aware of the significance of his work but did nothing to publicize it, content that posterity would appraise him.

By Rajendra

Direct-Fired Heaters: Evaluate Thermal Performance And the Effects of Fouling

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.

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.

Surface-area reduction

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.

Nomenclature

Term Units Definition

a unitless Factor converting a single row of tubes backed by refractory to a planar surface (see box, p. 49)

A_circ ft²Surface area of the circulating stream

A_flameft²Surface area of the circulating stream; equal to A_circ (Equation 4)

A_tft²Total planar tube surface

A_oft²Total outside radiant heat transfer surface

Cp_circ Btu/lb°F Average specific heat at the average circulating fluegas, or the

average Cp based on a specified temperature interval

D_burner ft Burner inside dia.

D_{flame avg} ft Average flame dia. (see Figure 1)

D_{flame top} ft Diameter at the top of the flame

D_tubeft Outside tube diameter

E_circunitless Emissivity of the circulating gas stream

E_effunitless Effective emissivity between two parallel surfaces (one hot plane and one cold plane). Note: Calculation ofE _eff in Equation (2a) requires the following substitutions: Equation (1) E ₁= E _tubes and E ₂= E _fg; Equation (12) E ₁=E _fg and E ₂= E _circ; Equation (13) E ₁= E _circ and E ₂= E _tubes

E_fgunitless Emissivity of the fluegas, obtained from Equation (3), which was obtained by curve fitting a figure obtained from Ref. [ 3 ]

E_{cold avg}unitless Average emissivity of the top cold plane

E_{hot avg}unitless Average emissivity of the hot plane

E_tubesunitless Emissivity of the tubes, as obtained from Ref. [ 3 ]

H_bottft Height of the lower zone

H_topft Height of the top zone

HTCo_flameBtu/h-ft²-°F Convective heat transfer coefficient at the outside of the flame

envelope (Equation 10)

HTCo_insideBtu/h-ft²-°F Heat transfer coefficient inside tube

HTCo_tubesBtu/h-ft²-°F The tubular outside heat transfer coefficient from the circulating stream to the tubes (Equation 8)

K₁ unitless Thermal decomposition constant of process fluid

L ft Thickness of the fluegas layer

L_cin. Maximum allowable coke thickness

L_fft Flame length

L_tft Tube length

N_b Total number of burners

P atm Total pressure

q_avg Btu/hr-ft²Average radiant heat flux

q_max Btu/hr-ft²Maximum radiant heat flux

Q_bott Btu/h Total heat absorption in the bottom zone of the radiant section (Equation 18)

Q_c-circ-t Btu/h Heat transferred by convection from the circulation stream to the outside tube surfaces (Equation 18)

Q_c-circ Btu/h The quantity of heat transferred by convection from the flame

envelope to the circulating fluegas stream (Equation 11)

Term Units Definition

Q_{heat loss} Btu/h Radiant and convective heat loss from radiant section enclosure

Q_libBtu/h Total burner heat liberation

Q_{r –circ}Btu/h Heat transferred by radiation from the burner flame envelope to the circulating fluegas (Equation 12)

Q_r–circ–t Btu/h Heat transferred by radiation from the circulating fluegas to the planar tubes (Equation 13)

Q_r–t Btu/h The total heat transferred by radiation from the burner flames to the tubular heating surfaces at either side of the burner flame envelopes, with burner flames being generated by two rows of burners firing upward from the hearth (Equation 1)

Q_topBtu/h Total heat absorption in the top zone of the radiant section

(Equation 17)

Q_total Btu/h Total process heat absorption (Equations 15 and 16)

Sp.vol._{burner gas} ft³/lb Specific volume of fuel-air mix at the temperature exiting the burner

Sp.vol._circft³/lb Specific volume of the circulating gas

Sp.vol._{flame top}ft³/lb Specific volume of the flame at the temperature exiting the lower zone

t s Time

T_adb °F Adiabatic flame temperature (about 3,500°F for natural gas)

T_{bott in} °F Temperature of the fluegas entering the bottom zone of the radiant section; same as T_adb

T_{bott out} °F Temperature of the fluegas leaving the bottom zone of the radiant section

T_circ °F or R* Average temperature of circulating fluegas

T_f °F or R* Average process fluid temperature, in °F except in Equation (5)

T_flame °F Average flame temperature

T_fgR Fluegas temperature

T_fg-avg R The average fluegas temperature based on the fluegas temperature entering and leaving the zone

T_MT °F or R* Design temperature of tube metal surface at outside diameter; Subscripts: sor = start of run; eor = end of run; avg = average

T_{top in} °F Temperature of the fluegas entering the top zone of the radiant section; same as T_{bott out}

T_{top out} °F Temperature leaving the top zone of the radiant section and entering the convection section

V_burner ft/s Burner exit velocity, which is also equal to V _f, the flame velocity

V_circ ft/s Velocity of the circulating fluegas stream, as limited by V _burner;see Equation (7)

Vp ft/s Flame-propagation velocity for the fuel-air mixture [ 3 ]; Note: 1 ft/s is a typical value for natural gas and other hydrocarbon mixtures under ordinary burning conditions

V_flameft/s Velocity of the flame envelope

W_{air+fuel total}lb/h Total flowrate of the burner fuel-air mix

W_fglb/h Burner fluegas flow

* In the case of convective heat transfer [Equations (9) and (11)], use °F; in the case of heat transfer via radiation [Equations (1), (12) and (13)], use R

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 (E_eff). E_eff, the effective emissivity between two parallel surfaces, is given by Equation (2a) and Ref. [ 2 ]):

(2a)

Planar tube surfaces

Note that the procedure for the calculation of heat exchange between the burner flame, the circulating combustion products and the tubular heating surfaces assumes that each of the above-mentioned entities are parallel planes. While the flame surface and circulating combustion product surfaces may be considered parallel planes, the tube surfaces cannot.

To covert the outside tubular surface to an equivalent parallel plane or planar surface that is consistent with the flame and combustion product surfaces, the center-to-center distance between tubes is multiplied by the tube length, the number of tubes and the term a (see the Equation (1), the Nomenclature box, and the paragraph that follows).

Noting that factor a is a function of the tube diameter and the spacing of the tubes, and may be found in [2, 3], the use of the term planar tube surface is then considered to be the surface as calculated by the aforementioned procedure.❑

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 avg}is 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 (A_flame).

(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 D_burner 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 (HTCo_tubes).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 ]:

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 E_eff is given by Equation (2a) E ₁ = E _fg and is evaluated at T _fg-avgand E ₂is evaluated at T_circ:

(12)

The heat transferred by radiation from the circulating fluegas to the planar tubes, Q_r-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 (q_max).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 (T_MT,avg).

(21)

Where T _MT,eor = the maximum tube design temperature (in this case, 1,200°F).

Determine coke deposition thickness (L_c).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.