Furnaces. 3.2 Hot gases as heat source

Transcription

1 3.2 Hot gases as heat source Furnaces The chemical composition of the gases produced by the combustion of hydrocarbons depends upon the choice of fuel and the amount of excess air employed above the stoichiometric requirements. In practice, excess air is required to ensure complete combustion; typical values are 10% for gaseous fuels, 15 to 20% for liquid fuels, and 20% for pulverized fuel, although lower percentages can be achieved with efficient burners. As we know, gaseous combustion products radiate heat when raised to temperatures above their surroundings. When solid particles are present in the furnace gas stream they become incandescent, radiating both heat and light, so producing a glowing or luminous flame. Gaseous fuels burn with a nonluminous flame, but liquid and solid fuels produce luminous flames due to the presence of particles of carbonaceous material. For example, soot or coke resulting from the incomplete combustion of the hydrocarbons and mineral matter originally in the fuel. In general, solid fuel produces a more luminous flame than does liquid fuel. Carbon dioxide and water vapor are the main sources of radiation for nonluminous flames, and the total emissivity ε g of a volume of combustion gases is dependent upon the temperature Tg and product of partial pressure and effective path length PL. The total absorptivity of a gas also depends upon its temperature and partial pressure path length product, but in addition upon the temperature T s of the source of the radiation that is being absorbed. [1,9,10] 3.3 Heat Sink The rate at which heat is transferred by radiation from the hot gases to sink depends not only upon the emissivity of the gas and emissivity of the sink surface, but also upon the relative size of the sink. This is because the unconverted refractory lining radiates back into the furnace heat that it has received from the flame, and some of this is absorbed by the heat sink. This compound effect is illustrated in Fig. 3.6, where two extreme cases are shown. The diagram on the left represents the case in which the sink area is very small, and that on the right represents the case in which the sink is very large and completely covers the furnace walls. In the case of refractory surface, assuming no heat loses, is in equilibrium with the gases and reradiates all the heat falling upon it. The total radiation flux within the enclosure is equal to that emitted by a blackbody at temperature Tg. Under these circumstances the heat flux to the sink is independent of the gas emissivity, depending only on the emissivity of the sink itself. The rate of heat transfer to a very small sink at temperature T1 is therefore QgA1 >0 = A1ε1σ(Tg 4 T1 4 )...(6) In the second case,where the sink covers the whole of the interior of the furnace, the situation is analogous to the exchange between two parallel party reflecting surfaces. It was already known that the rate of heat transfer is given by Intermediate situations can be estimated by using the equation for the simple case when the sink and the refractory are intimately mixed (Hottel and Sarofim, 1967). This is called the speckled surface equation and is quite adequate for preliminary estimates of furnace performance. It gives Where C is the ratio of the sink area to the total area, i.e. A 1 /A t. Fig. 3.6 shows an example of the way of the effective emissivity (the term in the curly braces in Equation 8) varies with C. The example assumes a gas emissivity is close to that of the gas, ε g of 0.3 and a sink emissivity, ε 1, 0f 0.85, the latter being typical of tube surfaces. For large values of C the effective emissivity is close to that of gas, ε g, and is intensive to the value of the sink emissivity, ε 1. For this reason the emissivity of tube surfaces in the fire tube boilers, where the sink entirely encloses the hot gas stream, may often be taken as unity for calculation purposes. 1/6

2 Fig:3.6 [1] Fig. 3.6 Effect of heat sink area on effective emissivity. (a) small heat sink area; (b) large heat sink area; (c) blackbody analogous to (d) exchange between reflecting surfaces; Fig:3.7 Fig (3.7) an example(ε g, ε 1 ) speckled surface equation. [1] ε c =(1/(1/ε 1 +C(1/ ε g ) 1)),C=A 1 /A t 3.4 Effect of tube geometry on the heat sink characteristics So far the heat sink has been treated as a plain surface. In practice, however, it consists of one or more banks of tubes usually mounted close to the refractory wall, as shown diagrammatically in Fig Normally there is a space between the tubes and consequently some of the radiation from the hot gases is not intercepted and impinges on the refractory wall behind the tubes. Most of this heat is reradiated and part contributes to the heat flow to the sink. This is a complex situation and complete formal analysis is very difficult. Because of mutual shielding effects of adjacent tubes, the radiation heat flux varies circumferentially around the tubes, as shown diagrammatically in Fig [1] The surface of the tube facing inward (position 1 in the figure) receives maximum heat flux because it is subject to radiation from a total angle of 180. Point 2 receives radiation from a smaller angle and point 3 only from a very narrow beam; beyond this point there is an area of the tube that receives no direct radiation from the hot gases. There is, of course, an additional component of heat flux, mainly on the back of the tubes, due to reradiation, but this is much smaller in 2/6

3 magnitude. The ratio of peak to mean heat flux is a function of tube pitch to diameter ratio, B, as shown in Fig.3.9 [1] for three typically configurations. This factor is important in assessing the permissible heat rating of a furnace, because it is the peak heat flux, which is usually the limiting factor. A simplification of this complex situation was proposed by Hottel in which the heat sink is defined as an equivalent plain surface having an area equal to that covered by the tubes, as shown in Fig. 3.10, and an effective emissivity, eeff, which would give the same radiative heat transfer as the tube bank. The first step in calculating the equivalent emissivity of the plain surface is to determine the fraction, F, of radiation intercepted by the tubes. The equation for F is based on optical path geometry, namely, F = 1 (1/B){(B 2 1) 1/2 cos 1 (1/B)}...(9) This function is plotted in Fig.3.11 [1] for a single and a double row of tubes. The interception factor, F,can then be used in calculating the effective emissivity of the tube bank, including radiation from an adiabatic refractory backing,as: ε eff = 1/{(1/F(2 F)) + ((B/π)(1/ε 1 1))}...(10) Effective emissivity based on this equation is plotted in Fig [1] as a function of tube pitch to diameter ratio for a tube material emissivity of It is clear from the form of the equation and the shape of the curve that tube spacing has a very powerful effect. This is partly due to the fact that the actual tube surface area per unit of total projected area, A, is proportional to 1/B, a fact reflected in the reduction in the fraction, F, of radiation intercepted, which plays a predominant role in determining eeff. The foregoing equations apply to true banks adjacent to the refractory wall. A similar approach can be made to the case of a centrally mounted tube bank, but here a different form of equivalent plain area has to be used. Procedures for this type of furnace geometry are outlined in the Heat Exchanger Design Handbook (Truelove, 1983). 3/6

4 4. Furnace models The full mathematical description of practical furnaces is exceedingly complex, combining aerodynamics, chemical reactions, and heat transfer, and computer programs are necessary for detailed solutions. Advanced methods of calculation may be divided into zone methods and flux methods. Zone methods are employed when the heat release pattern from the flame is known. They start by dividing the furnace and its walls into discrete zones. The effective exchange areas between zones are determined, and the radiative heat transfer corresponding to the prescribed heat release pattern is calculated. In flux methods, instead of dividing the space into zones the radiation arriving at a point in the system is itself divided into a number of characteristic directions, representing averages over a specified solid angle. Flux methods are well suited for use in combination with modern methods of prediction of fluid flow and mixing pattern. Simultaneous solutions of the radiative heat transfer equations using flux methods and turbulent flow models are feasible. 4.1 Well Stirred furnace model [1 16] This is the simplest approach to the assessment of furnace performance. One of the first versions is the method of Lobo and Evans (Lobo and Evans, 1939), which was used in Process Heat Transfer (Kern, 1986). Subsequently an improved version, expressed in nondimensional terms, which made the calculations easier, was presented in the book Radiative Heat Transfer (Hottel and Sarofim, 1967). These authors also introduced additional terms to allow for incomplete mixing and wall losses. Their model, later reviewed by Hottel (1974), still forms the basis of most simple calculation procedures (e.g., Truelove, 1983). The furnace is modeled in three zones as shown, Fig.3.13 [1] namely, the central hot gas zone, the heat sink, and the refractory walls. The combustion region and the space occupied by hot products of combustion are lumped together in the central hot gas zone (hence the alternative title lumped model ), which transfers heat by radiation to the heat sink, here shown diagrammatically as a tube bank, and to the refractory walls containing the furnace. The following simplifying assumptions are made: The hot gases are perfectly mixed and at a uniform temperature, Tg. The heat sink is gray and has a uniform temperature, T1. The refractory surface is radiatively adiabatic, that is to say it radiates all the heat that is receives. The well stirred furnace model is based on a combination of the balance equation for the furnace (Equation 5), namely. (Q f Q g )/Q f =(T g T o )/(T f T o )...(11) And the expression for heat transfer to the sink based on the specked surface model (Equation 8),namely. Qf= A1{1/((1/εeff) + C(1/εg 1))} σ (Tg 4 T1 4 )=gr σ (Tg 4 T1 4 )...(12) Where, gr, the total heat transfer factor for radiation from gas to sink, is 4/6

5 gr= A1/{1/eeff+C(1/εg 1)}...(13) Note that ε eff (Equation 10) has replaced ε1, because the model is using the projected area, A1, of the tube bank as illustrated in Fig If the furnace contains a convectively heated section, the total heat transfer factor can be modified to introduce both radiation and convection,as Q g =g r σ(t g 4 T1 4 ) +αac (T g T 1 )...(14) Where,gr = total heat transfer factor for radiation from the gas to the sink, including reradiation from the refractory walls and multiple reflection. α= convective heat transfer coefficient from the gas to the sink. Ac = area of the sink subject to convective heat transfer. Because the convective component is usually small compared with that of radiation it may be submitted in the g r,term as follows.let αac (Tg T1)= (αac/4σt 3 g1)σ(t 4 g T 4 1)...(15) where T g1 (T g +T 1 )/2...(16) Then Qg=grc σ(tg 4 T1 4 )...(17) where g rc =g r +(α A c /4σT 3 g1 )...(18) Fig. 13 Simple well stirred Furnace model Equations (11) and (17) can be combined to give (Q g /σ g rc )+T 4 1 =T4 f {1 (Q g (T f T o )/Q f T f }4...(19) It is convenient to apply this expression in a nondimensional form involving the terms: Q, g =Qg(Tf To)/QfTf =reduced furnace density...(20) D, =Q f /σ g rc 3 f (T f T o ) =reduced firing density...(21) T, 1 =T1Tf =reduced sink temperature...(22) Equation (19) then reduced to Q, g D, +(T, 1 )4 ) =(1 Q, g )4...(23) References 1. Kern, D. Q. (1950). Process Heat Transfer.McGraw Hill. ISBN Rao, B.K.B.(1990). Modern Petroleum Refining Processes (2nd Edition Ed.) Oxford & IBH Publishers. ISBN James H. Gary and Glenn E. Handwerk (2001). Petroleum Refining: Technology and Economics (4th ed.). CRC Press. ISBN James. G. Speight (2006). The Chemistry and Technology of Petroleum (4th ed.). CRC Press. ISBN Reza Sadeghbeigi (2000). Fluid Catalytic Cracking Handbook (2nd ed.). Gulf 5/6

6 Publishing. ISBN Kister, Henry Z. (1992). Distillation Design (1st Edition ed.). McGraw Hill. ISBN Karl Kolmetz, Andrew W. Sloley et al. (2004), Designing Distillation Columns for Vacuum Service, 11th India Oil and Gas Symposium and International Exhibition, September 2004, Mumbai, India (also published in Hydrocarbon Processing, May 2005). 8. Leffler, W.L. (1985). Petroleum refining for the nontechnical person (2nd Edition ed.). PennWell Books. ISBN Editors: Jacqueline I. Kroschwitz and Arza Seidel (2004). Kirk Othmer Encyclopedia of Chemical Technology (5th ed.). Hoboken, NJ: Wiley Interscience. ISBN McCabe, W., Smith, J. and Harriott, P. (2004). Unit Operations of Chemical Engineering (7th ed.). McGraw Hill. ISBN Kister, Henry Z. (1992). Distillation Design (1st ed.). McGraw Hill. ISBN King, C.J. (1980). Separation Processes (2nd ed.). McGraw Hill. ISBN Perry, Robert H. and Green, Don W. (1984). Perry's Chemical Engineers' Handbook (6th ed.). McGraw Hill. ISBN Felder, R., Roussea, W. (2005). Elementary Principles of Chemical Processes (3rd ed.). Wiley. ISBN Beychok, Milton (May 1951). "Algebraic Solution of McCabe Thiele Diagram". Chemical Engineering Progress. 16. Seader, J. D., and Henley, Ernest J. (1998). Separation Process Principles. New York: Wiley. ISBN /6