552
Energy & Fuels 2001, 15, 552-558
Studies in Furnace Analysis: Prediction of Tunnel Kiln Performance by Application of the Integral Energy Equation Robert H. Essenhigh* Department of Mechanical Engineering, The Ohio State University, Columbus, Ohio 43210 Received June 5, 2000. Revised Manuscript Received December 22, 2000
Analysis of tunnel kiln performance to determine the relation between input energy (Hf) and useful output energy (Hs), by application of the integral energy equation, is shown to lead to a firing equation of standard form. This is a concave-upward curve, from an idle firing rate (Hfo) at zero output to, theoretically, an infinite firing rate at a maximum output (Hsm). The corresponding curve for the thermal efficiency, η ) Hs/Hf, then also follows the standard form, being an asymmetric, inverted U-shape. The auxiliary expressions obtained for the constants in the firing equation: idle heat, maximum output, and intrinsic efficiency (Rroo), are then all shown to have significant dependence on the heat exchanger elements incorporated in the tunnel kiln design. Unusually, for the optimum design configuration at the theoretical adiabatic limit, the thermal efficiency for this system converges to 100%, and the processing efficiency can converge to infinity. These are limits that are impossible to achieve in practical operations, but they provide a basis for evaluating expected design performance. The analytical structure is developed specifically for the tunnel kiln, represented as a firing section flanked by two (upstream and downstream) heat exchangers; but the general design and theoretical structure has potentially wider application, particularly with respect to the influence of heat exchangers in a furnace system where this has been given little earlier attention in the context of the furnace analysis protocol.
1. Introduction In this paper, the furnace analysis protocol1-3 based on the integral energy equation4,5 is applied to a tunnel kiln to evaluate the dependence of efficiency on its design characteristics. In a tunnel kiln, which is a straight chamber of refractory brick with a firing sectionlocated part way down the tunnel, the materials being fired, for example bricks or ceramics, are moved on cars continuously through the furnace from entry to exit, moving in counterflow to the products of combustion (POC) from the flame and/or to the combustion air. With this design, the tunnel kiln is, conceptually, one of the simplest of all industrial processing furnaces. Analytically, however, for reasons developed below, it is one of the more sophisticated, with potential in some firing configurations for unusually high thermal and processing efficiency characteristics, not believed to have been previously identified, that derive from the design. * E. G. Bailey Professor of Energy Conversion. (1) Essenhigh, R. H.; Thekdi, A. C.; Malhouitre, G.; Tsai, Y. Furnace Analysis: A Comparative Study. In Combustion Technology: Some Modern Developments; Academic Press: New York, 1974; Chapter 14. (2) Essenhigh, R. H. Comparative Thermal Behavior of Furnaces and Engines: Prediction of Thermal Efficiency in Real Time. In Proceedings of the 1989 (Beijing) Conference on “Thermodynamic Analysis and Improvement of Energy Systems”; International Academic Publishers (Pergamon-CNPIRC); Elsevier Science Publishers B. V.: Amsterdam, 1990; pp 116-125. (3) Essenhigh, R. H.; Boehman, A. L. Energy Fuels 1997, 11, 447456. (4) Moran, M. J.; Shapiro, H. N. Fundamentals of Engineering Thermodynamics; Wiley & Sons: New York: 1988. (5) Fox, R. W.; McDonald, A. T. Introduction to Fluid Mechanics, 5th ed.; John Wiley: New York, 1998.
In particular, for the optimum design configurations, the thermal efficiency, at the idealized theoretical limit of adiabatic operation, converges to 100%, and the processing efficiency, unusually, can converge at that limit to infinity. These two results are revisited for further evaluation in the Discussion and Conclusions at the end of this paper: they are limits that, of course, are impossible to achieve in practical operations, but they provide a basis for evaluating expected performance of alternative designs. The design element that is the source of the potentially high efficiencies is the existence of sections in the tunnel that can act as heat exchangers, upstream and/ or downstream of the firing section, as described more fully below, so that this kiln also represents one of the simplest examples of the general class of potentially high efficiency furnaces, of which boilers are a subset, having one or more stages of upstream and/or downstream heat recovery. A summary of comparative structures is given in Table 1 showing two stages of heat recovery for the tunnel kiln compared with three for the boiler. At the same time the two-stage recovery in the tunnel kiln is more conceptually complex than for the boiler since it includes heat recovery from the output processed material as well as from the exhaust whereas for the boiler, though it has three heat exchanger stages, this recovery is only from the boiler exhaust. Detailed but generally specifically targeted evaluation of the influence of heat exchangers on thermal efficiency, particularly of boilers,6,7 of course, has a long-standing history; but performance evaluation under the integral
10.1021/ef000119t CCC: $20.00 © 2001 American Chemical Society Published on Web 03/17/2001
Furnace Analysis
Energy & Fuels, Vol. 15, No. 3, 2001 553 Table 1. Structures in Heat Recovery
simple recovery
tunnel kiln
boiler
I. Air preheat by recovery from exhaust (cf: ref 2)
I. Material preheat by recovery from exhaust (section HEA in Figure 1) II. Air preheat by recovery from fired material (section HEB in Figure 1)
I. Superheater: Steam superheat by primary recovery from exhaust II. Economizer: Water (material) preheat by secondary recovery from exhaust III. Air Heater: Air preheat by tertiary recovery from exhaust
formulation of the furnace analysis protocol has evidently been limited so far to the case, only, of downstream heat recovery.2 This is identified in Table 1 as simple recovery though that earlier study2 also included extension to downstream work recovery in engines, thus identifying the broader and more general scope of this analytical procedure to second law (of thermodynamics) systems (engines) as well as first law (of thermodynamics) devices (furnaces and boilers). Thus, in the context of the furnace analysis protocol, with the potential existence in the tunnel kiln of both upstream and downstream heat exchanger sections, this further defines the tunnel kiln as a good platform target for more general analysis in evaluating the dependence of efficiency on the design characteristics of both furnaces and engines. Identification of those characteristics is the broader objective of this paper, and a further, longer term objective is to identify the need now for development of an experimental database of measurements on such operating furnaces, that at this time is not known to exist, for test and evaluation of the predictions set out in this paper. 2. Model Description The focus in this paper is primarily on first law devices though, as noted, the analysis also provides a platform for later extension to second law systems. 2.1. Construction. Tunnel kilns and similar units, such as billet heating and roller hearth furnaces, are generally built approximating to one of two formats, having a firing section either in the middle of the tunnel (double-ended design), or effectively at one end (nominally, single-ended design). Typical layouts are illustrated in, for example, the Hauck Industrial Combustion Data Handbook (Figures 51, 40, and 35).8 Figure 1 of this paper is then a generalization of, essentially, both single and double-ended patterns. This Figure illustrates a design with the firing section (F) in the middle of the tunnel, flanked by two regions (A and B) that either act as system component heat exchangers, or can be independent heating/cooling segments. In some industrial constructions, the firing section is itself staged, but for the analysis here, this is represented as a single component. With regard to the heat exchanger sections, physical elimination of segment B converts the “double-ended” format to explicitly single-ended; and retention of the segment B as an independent cooling section still implicitly retains the single ended configuration in terms of efficiency analysis. Either procedure (6) Singer, J. G., Ed. Combustion: Fossil Power Systems; Combustion Engineering, Inc.: Windsor, CT, 1981. (7) Stulta, S. C.; Kitto, J. B., Eds. STEAM, 40th ed.; Babcock and Wilcox: Barberton, OH, 1992. (8) Hauck Industrial Combustion Data Handbook; Hauck Mfg. Co.: Lebanon, PA, 1953.
Figure 1. Schematic of continuous tunnel kiln represented as a central firing section (F) flanked by two heat exchangers (A and B). Material flow is from left to right; air/POC flow is from right to left. Air and raw materials to be processed enter cold. Hf: input enthalpy from fuel into firing section. Hsr: enthalpy of preheated raw materials entering firing section. Har: enthalpy of preheated air entering firing section. Hg: POC exhaust enthapy leaving firing section. Hs: enthalpy of processed material leaving firing section. He: POC exhaust enthalpy leaving kiln. Hse: enthalpy of cooled processed material leaving kiln. Hso: enthalpy of raw material entering kiln. Hw: wall loss (assigned to firing section).
would also remove the second-listed stage for the tunnel kiln in Table 1 (air preheat by recovery from fired material). The material to be thermally processed enters cold, at the left in Figure 1, and moves left to right through the tunnel at a rate S units per hour, in counterflow to the combustion products and/or combustion air, with the processed material being first heated and then cooled in the process. In the segment A, which generally or universally operates as a heat exchanger, the incoming cold material is preheated by the combustion products that, exiting from the firing section, F, are flowing from right to left and (in the segment A) are being cooled in the process. The segment B can also operate as a heat exchanger in similar manner, with the hot, processed material travelling, again, from left to right, and in counterflow to the incoming (right-to-left) combustion air. With appropriate heat exchange, the processed material is cooled and preheats the incoming combustion air. In some designs, however, the segment B is either eliminated, or it is retained but operates as an independent cooling section without useful heat recovery, and as noted above, the furnace correspondingly operates effectively single-ended from the point of view of thermal analysis and performance. The analytical selection as single or double ended design is essentially determined by the burner designs used which, likewise, are determined by the operational thermal-treatment and control requirements of the furnace for the material being processed. If the burners (generally using gas) are premixed and self-stabilizing of standard (commonly, flame-retention tip) design, then all combustion air is provided through the burner ports, premixed with the gas; there is then no scope for air preheat, and segment B is either not in the construction or is only an independent cooling section. However, if the burners are gas-only jet-ports that supply raw gas directly injected into the furnace enclosure, the injected gas then burns on turbulent/diffusive mixing with the
554
Energy & Fuels, Vol. 15, No. 3, 2001
Essenhigh
(preheated) air, with the required combustion air induced by appropriate draft control at the left end of segment A, through the segment B into the firing section, with segment B then acting as a heat exchanger. This firing system was installed in a Harbison Walker refractories plant near State College, PA, included in annual plant visits by students in the Pennsylvania State University Fuel Technology Department program through the 1960s. The plant Manager at that time stated that this firing system resulted in very uniform firing of the (refractory) brick, whereas using flameretention tip burners resulted in three streams of overfired brick. These characteristics define the physical model of the system to be analyzed. 2.2. Analytical Procedure. The target of the furnace analysis protocol is to formulate an equation that defines the variation of thermal efficiency (η) with (useful) output (Hs). The basis procedure is set out in more detail elsewhere,1-3 and as basis for the further developments here, is summarized following. In summary, the primary analytical expression developed in the analysis, from which the thermal efficiency equation is obtained, is the firing equation that relates the rates of the thermal energy input (Hf) to the useful output (Hs); and obtaining this relation, as shown following (section 3), is the first stage of the furnace analysis procedure. The thermal efficiency dependence is then obtained from the standard formulation that, defined in the firing section, is given by
η ) Hs/Hf
(1)
The basis of the required procedure, as used here, is the development of energy balance equations by applying the integral energy equation [see below, section 3.1, eq 2] to a defined control volume (CV) as identified in Figure 1. This basic balance thus provides an equation that, using further supplementary relations, is then expanded into the firing equation. This approach originated in the studies by Hudson9 in 1890 and Orrock10 in 1926, yielding the Hudson-Orrock [H-O] equation as the original form of the Firing Equation, with later extensions, notably by Hottel, summarized by Hottel and Sarofim,11 and by Thring and Reber,12 mostly in the period from the 1930s through the 1950s. As noted in the Introduction the procedure is applicable both to first law and to second law devices, or generally, Furnaces and Engines,1-3,13 though the focus in this paper is on first law systems. In the simplest formulation,1-3 the analysis is confined to a single, governing CV. In the extension developed here, three further CVs are defined internal to the governing CV, and the system is illustrated in and defined by Figure 1, as noted above. The three (9) Hudson, J. E. Engineer 1890, 70, 449, 4, 83, 523. (10) Orrock, G. A. Trans. ASME 1926, 48, 218. (11) Hottel, H. C.; Sarofim, A. F. Radiative Transfer; McGraw-Hill: New York, 1967; Chapter 14. (12) Thring, M. W.; Reber, J. W. J. Inst. Fuel 1945, 18, 12. (13) Boehman, A. L.; Essenhigh, R. H. Application of Furnace Analysis to Internal Combustion Engines. In Proceedings of the 1995 Fall International Symposium “Combustion Research and Industrial Practice”; American Flame Research Committee (IFRF): Monterey, CA, 1995.
internal CVs are identified as the firing section, F, in the middle, flanked by the two heat exchangers, A and B. As shown following, energy balance equations are first written for the complete (governing) system, and then for all three inner segments; and the firing equation that is developed by appropriate reformulation of the equations is for the total system. Likewise, from the firing equation, the operational thermal efficiency, η, as defined by eq 1 is also for the total system, and the development of the predictive relationship for the thermal efficiency as expansion of eq 1 is the primary target of the analysis. This is also then extended to define the processing efficiency, ηP, as outcome of the development here, as shown below, in section 5.3 [eq 21]. 3. Analysis. 3.1. Basis Equation. The firing equation is obtained by reduction from the general energy equation4,5 defined in integral form on a control volume/surface (CV/CS). For clarity in this particular application this integral energy equation is written in a slightly expanded form4,5 with explicit separation of the conduction from the convection flux terms across the control surface (CS). In general, we then have:
(dE/dt)CV ) (A)
∫
Q - W + (∂/∂t) CV eFdV + (B) (C) (D)
∫CV (eFV) dA
(2)
(E)
where e ) (h + gz + V2/2) is the (standard definition) specific energy.4,5 In both furnace and engine applications, the gravity term, gz, can generally be set to zero; likewise, the KE term, V2/2, can also be set to zero in most furnace and in many engine applications (jetengines are an important exception). In the development here, only the residual specific-enthalpy term, h, is required. For this first-cut analysis, the system is set to steady-state. Equation 2 then reduces as follows: • At steady state, the time-dependent terms A and D are zero. These should be reconsidered nevertheless in extension of the analysis to furnace heat-up behavior, which in a large furnace (e.g., a glass tank) can take several days; or to load change response where, again, in large or very large furnaces, the change-time can be 1-100 h. • For a furnace (first law device) doing no mechanical work, term C is also zero, though, of course, it is nonzero for engines (second law devices: see refs 2 and 13). • Term B, as the enthalpy flux across the control surface (CS) of the defining CV by other than convective flows, is the (conduction-determined) wall loss, Hw. • Term E is the integral (sum) of the “convective” enthalpy flows across the control surface, due jointly to flow of materials being processed as well as of fluids. In the further analytical development, following, this is split as shown in eq 3 (below) into (1) the thermal input from the fuel (Hf); (2) the (net) thermal output from the processed material (Hs); and (3) the exhaust loss (He). 3.2. Reduced Equation. Applying these conditions to Figure 1 then, for the enthalpy balance on the outer CV and with appropriate expansion of term E as given
Furnace Analysis
Energy & Fuels, Vol. 15, No. 3, 2001 555
above, eq 2 reduces to
Hf ) Hw + He + (Hse - Hso) (1) (2) (3) (5) (4)
(3)
where, as defined above, term 1 is the thermal (enthalpy) input from the fuel, term 2 is the enthalpy in the leaving stock, term 3 is the exhaust loss to the stack; term 4 is the wall loss as already identified (term B of eq 2); and term 5 (Hso) is the input enthalpy of the materials under process: this is commonly set to zero by convention but it can be nonzero in cases where the input material is output from another furnace and it enters hot. In this formulation, as noted earlier, the stock is defined as moving from left to right, and the air/POC is moving in counterflow from right to left. We also then define the supplementary relations for the fuel thermal input, and for the exhaust output in terms of the fuel firing rate, F:
Hf ) Fhf
(3A)
He ) Fhe ) F[1 + Gs(1 + E%/100)]cp(Te - To) (3B) where hf is the enthalpy (heat) of combustion, Gs is the (mass) ratio of stoichiometric combustion air to fuel, E% is the excess air (%); cp is the average specific heat of the combustion-products mixture at the exhaust temperature or leaving temperature crossing the control surface, Te; and To is the ambient temperature. Equation 3B defines the specific enthalpy, he, in terms of the total flow of products of combustion (POC) per unit of fuel fired, not per unit mass of POC; this is standard convention in furnace analysis.1-3 The influence of excess air (E%) can be substantial in high-temperature furnaces as shown elsewhere14 in comparison of prediction with experiment (in firing coal-water fuels). 3.3. Heat Exchanger Application. Similarly, application of eq 2 to provide energy balances on the two heat exchangers, with wall losses assigned to the firing section, gives in terms of the parameters defined by Figure 1:
For heat exchanger A (HEA): Hg ) Fhg ) He + Hsr (4) For heat exchanger B (HEB): Hs ) Shs ) Har + Hse (5) where F is the Firing Rate into the firing section; and hg is the specific enthalpy of the POC (exhaust) leaving the firing section, per unit of fuel fired, defined above and as shown in eq 4. For HEA, the heat exchanger to the left of the firing section, the exhaust from the firing section enters HEA at enthaply Hg; it preheats the incoming stock to enthaply Hsr; and leaves the system to exit through the stack at enthaply He. Correspondingly, HEB is the heat exchanger to the right of the (14) Essenhigh, R. H.; Obloza, J. J.; Hammond, T. H. Energy Fuels 1994, 8, 179-187. (15) Essenhigh, R. H.; MacLellan, D. E. Studies in Furnace Analysis: Evaluation of Performance Characteristics of a Laboratory Furnace. In Proceedings of the 1995 Fall International Symposium “Combustion Research and Industrial Practice: From Equation to Equipment”; American Flame Research Committee (International Flame Research Foundation): Monterey, CA, 1995.
firing section in which the processed stock, entering HEB at at flow-rate S and at specific and total enthalpies hs and Hs, preheats the incoming combustion air to enthalpy, Har, and is itself cooled to its exit enthalpy, Hse. For the “single-ended” furnace when the segment B operates only as an independent cooling section without heat recovery, or does not exist, this is accommodated by setting Har ) 0. 4. Firing and Efficiency Equations Reduction of the governing equations, eqs 1-5, to the firing equation requires elimination of terms 3 and 4 in eq 3. This is done by linearization of the two terms in terms of the furnace output, Hs, as set out below in section 4.2, and likewise, by incorporating the thermal efficiency of the different sectors of the furnace.1-3 We start with the expressions for the efficiency properties. 4.1. Efficiency Definitions. The operational efficiency for the kiln is defined on the outer CV so that, for the terms defined in Figure 1, eq 1 for the outer CV takes the (modified) form
η ) Hse/Hf
(6)
For the two heat exchangers, with efficiencies defined as ηhA and ηhB, and with wall losses assigned to the firing section, as noted above, we get first for HEA, by definition and rearrangement:
ηhA) Hsr/Hg ) 1 - He/Hg ) 1 - (He/Hf)(Hf/Hg) ) 1 - (He/Hf)(Fhf/Fhg) ) 1 - (He/Hf)(hf/hg) (7a) so that, by further rearrangement and definition we get
(He/Hf) ) (Fhe/Fhf) ) (he/hf) ) (1 - ηhA)(hg/hf) (7b) Correspondingly, for HEB,
ηhB ) Har/Hs ) 1 - (Hse/Hs) ) 1 - Shse/Shs ) 1 - hse/hs (8) where hs and hse are the specific enthalpy values of the stock being processed (essentially proportional to its temperature), respectively: at exit from the firing section and at exit from the furnace. These specific enthalpy properties obviously have to be used with care since, if the segment B is an independent cooling section, not a heat exchanger, then ηhB ) 0, and for the performance analysis, hse ) hs, although the materials are nevertheless finally emerging cooled. 4.2. Linearization. The two terms, Hw and He, in eq 3 require formulation in terms of output, Hs. The standard formulation is as a linear function of output where the linear assumption originated, jointly, from experimental and empirical studies [refs 1 and 2; but see refs 3 and 15 for a theoretical basis and conditions for nonlinearity]. (1) For the wall loss, and using eq 8 to translate the firing section output, Hs, into the final output value, Hse, this is written in linear form as
Hw ) Hwo (1 + cHs/Hsm) ) Hwo (1 + c*Hse/Hsem) (9)
556
Energy & Fuels, Vol. 15, No. 3, 2001
Essenhigh
where Hsem is the (limiting and/or theoretical) maximum output (see section 4.3) used to normalize the operational output. Equation 3 is now reformed, first, by substituting the wall loss expression of eq 9, and then by factorizing out the He term and rewriting in the enthalpies ratio using the expressions from eq 7b: (He/Hf) ) (he/hf). Setting Hso ) 0, eq 3 can then be written as
Hf(1 - He/Hf) ) Hf(1 - he/hf) ) Hw + Hse ) Hwo + (1 + c*Hwo/Hsem)Hse
(10)
(2) For the exhaust loss specific-enthalpies ratio, (he/hf), this ratio, from eq 7b, is proportional to the specific enthalpy ratio leaving the firing section, (hg/hf) which, in turn, is written [refs 1 and 2, but see refs 3 and 14] as rising linearly with fired output from the firing section, Hs. Thus, we have o
o
m
hg/hf ) hg /hf + (1 - hg /hf)(Hs/Hs ) ) (1 - Roo) + Roo(Hs/Hsm) (11) where Hsm is the maximum firing section output (see above) at infinite firing rate and Roo is the (standard) formulation for the maximum Intrinsic efficiency.1-3 Using eq 11 to substitute for (hg/hf) in eq 7b, and using eq 8, eq 7b can be written in the alternative forms
He/Hf ) he/hf ) (1 - ηhA)[(1 - Roo) + Roo (Hs/Hsm)] ) (1 - ηhA) [(1 - Roo) + Roo(Hse/(1 - ηhB)Hsm)] ) heo/hf + (1 - heo/hf)(Hse/Hsem)
(12)
4.3. Maximum Output. At maximum output, it is assumed1-3 that the firing rate (F), and correspondingly, the firing enthalpy input, Hf, increase as a theoretical limit to infinity. At the outlet of the A heat exchanger, HEA, the outlet enthaply, He ) Fhe, so this, correspondingly, also converges to infinity even though he converges to zero as the HEA efficiency (ηhA) converges to unity. Consequently, even for a finite fraction of heat recovered from the exhaust, we have that He f Hf, and consequently the ratio he/hf ) He/Hf f 1. Inserting this condition in eq 12 we then have from the second line, after rearrangement, that
(Hsem/Hsm) ) (1 - ηhB)[1 + ηhA/(1 - ηhA)Roo]
(13)
Upon setting ηhB ) 0, to correspond to a single (downstream) heat exchanger, eq 13 then corresponds exactly to the relation given in ref 2 for the same maximum output increment for the simple recovery case listed in Table 1. Notably, as before,2 as ηhA f 1, then Hsem f ∞; however, when ηhB f 1, then Hsem f 0, which reemphasizes the need to interpret the results with care, as noted above (section 4.1), and as discussed further below in connection with the meaning of maxiumum intrinsic efficiency for the system. 4.4. Idle Conditions and Maximum Intrinsic Efficiency. Idle is defined as firing and other conditions at zero output (Hse ) Hs ) 0) so that, for conditions at Idle, designated by zero superscripts, we have the transformation obtained from eq 7b and given by reduction from eq 12:
(heo/hf) ) (1 - ηhA)(hgo/hf)
(14)
Likewise, at idle (Hse ) 0), eq 10 reduces to and can be rewritten as
Hwo ) (1 - heo/hf)Hfo ) RrooHfo
(15)
thus identifying the wall loss with the idle firing rate, Hfo, through the multiplier, Rroo. This multiplier is obtained from eq 12 by setting He ) Hf at maximum output (cf. refs 1 and 2), thus giving, by definition and formulation
Rroo ) (1 - heo/hf) ) Roo[(1 - ηhA)/(1 - ηhB)](Hsem/Hsm) (16a) ) 1 - (1 - ηhA)(1 - Roo)
(16b)
and thus also identifying Rroo as the maximum intrinsic efficiency for the system. Notably, eq 16b shows that the maximum value of Rroo ) 1 when ηhA f 1, in accordance with the prior developments.1-3 At the same time, however, eq 16a shows an evident dependence of Rroo on the efficiency of the heat exchanger B, with a nominal trend to infinity as ηhB f 1, but this must be interpreted with care since, from eq 13, we also have, for that condition, that Hsem f 0 so that the ratio converges to 0/0, and the convergence value must be determined from other sources. Conversely, we also have that Rroo nominally goes to zero as ηhA f 1, but correspondingly, also from eq 13, we then have that Hsem f ∞. The apparent problems derive from the dependence of the maximum output on the efficiencies, but they are resolved using eq 16b. However, they reinforce the significance of the accurate definition of useful output. 4.5. Firing Equation. The firing equation is now obtained from eq 10, first, by subtracting eq 15 to give
Hf(1 - he/hf) Hfo(1 - heo/hf) ) (Hf - Hfo)(1 - he/hf) + Hfo(he/hf - heo/hf) ) (Hw - Hwo) + Hse ) (1 + c*Hwo/Hsem)Hse
(17)
and then using eq 12 to eliminate (he/hf). This results, with rearrangement, in the firing equation in its standard form:1-3
Hf ) Hfo +
Hse o
Re (1 - Hse/Hsem)
(18)
where Reo is the intrinsic efficiency, given by
Reo ) Reoo/[1 + Reoo(Hfo/Hsm) + c*Hwo/Hsem)]
(19)
The intrinsic efficiency is the limit value of the heat utilization factor as defined by Thring and Reber:12
R ) Hs/(Hf - Hfo) ) Reo(1 - Hse/Hsem)
(20)
Furnace Analysis
and the maximum intrinsic efficiency factor is given, as shown above, by eq 16. 5. Efficiency Limits From these equations it is now possible to establish, as a primary outcome, the limiting values of the efficiency results, as identified in the Introduction. The first is that the limiting thermal efficiency is 100%, and the second is that the processing efficiency can become infinite. To obtain these results, we consider the consequence of increasing the physical length of the two heat exchangers, A and B, to infinity, so that their efficiencies converge to unity, and respectively, the exhaust gases leaving HEA and the stock leaving HEB are reduced to ambient temperature in both cases. At the same time, more broadly, these results invite further general examination with regard to the influence of heat exchangers in furnaces and related equipment such as boilers (as identified in Table 1); in particular, this present study also provides a platform for examination of the potential pattern resulting from the further addition of heat exchangers under different protocols. The focus in all cases is on the influence on the thermal efficiency. 5.1. Operational/Intrinsic Efficiency Limit. The operational and intrinsic efficiencies, η and Rro, are defined, respectively, by eqs 6 and 19 (cf. eq 16). It is well established1-3 that η and the heat utilization factor, R, defined in eq 20, are convergent when the output (Hs) is high and increasing; and they are divergent at low and decreasing output, with η going to zero but with R going to the (working) intrinsic efficiency, Rro, at zero output. This behavior is also a function of wall loss, however; and, as the furnace is more fully insulated, the convergence of the two factors is maintained to lower values of output (Hs). In the limit, of a totally adiabatic device, as the output goes to zero, the maximum operational efficiency also converges to the Intrinsic efficiency, Rro; and the Intrinsic efficiency has the maximum value of Rroo, given by eq 16. The maximum of the intrinsic efficiency is then obtained when there is complete heat recovery in the exhaust, theoretically obtainable by appropriately increasing the length of the heat exchanger A; correspondingly, this reduces the specific exhaust enthalpy, he, to zero (i.e., the exhaust is delivered at ambient). The operational and intrinsic efficiencies are then 1 (or 100%) as defined in terms of the exit value, hse, of the specific enthalpy of the material property (brick, ceramics, etc.). Notably, this result depends only on the heat exchanger, HEA, which is upstream from the incoming material to be processed, but downstream with respect to the exhaust. 5.2. Comparison with Firing Section Efficiency. The limit is different, however, if the comparison is made with the performance of the firing section. This limit depends partly on the heat recovered from the exhaust (by HEA) but also on obtaining the lowest limit value of the firing rate by maximum recovery in the heat exchanger B (HEB), again by appropriately increasing its length. For the firing section, the initial tradeoff is the reduction, by the air preheat, of the firing-rate offset. The reduced firing rate then, correspondingly, increases the residence time in the firing section, thus potentially
Energy & Fuels, Vol. 15, No. 3, 2001 557
allowing further reduction in firing rate due to the greater disproportion in heat transfer in favor of transfer to the material under process, as noted in the previous studies.2 Since the heat exchange in HEB is extracting heat from the fired brick, the limit is a tunnel of such length that the specific enthalpy, hse, and correspondingly the total enthalpy, Hse, of the emerging (cooled) brick are reduced to zero (ambient). At that point, as shown by eq 10, the only fuel requirement left is that needed to meet the idle wall loss requirements, Hwo. If the furnace is so fully insulated that it is adiabatic, the idle requirement goes to zero, and the thermal efficiency, based on the material property specific enthalpy, hs, becomes Hs/0, which is infinity. Such a limit is impossible to reach in practice, of course. What this theoretical extension shows, however, is the inherently high thermal efficiency of this design, using heat recovery from both the exhaust gas and from the processed material. 5.3. Process Efficiency. With such high efficiency values obtainable in such devices, it is common industrial practice, as being more operationally meaningful, to use a heat rate, defined as heat per unit of output, as an alternative parameter to thermal efficiency. In this case, this would be given by the ratio: Hf/S. For a preset value of hs, this ratio is essentially the inverse of the thermal efficiency for the firing section, as defined by eq 1. Thus, this identifies hs, the output specific enthalpy of the processed product leaving the firing section, as the key determining parameter for all measures of performance since this requirement must be met in order to process the material to a set condition, however much heat may be recovered after that. On this basis, an appropriate alternative to the heat rate is the processing efficiency, ηP, defined in terms of the firing section operations, or the thermal efficiency defined, as noted, on the firing section by eq 1 so that, with further transformation using eqs 6 and 8, we have
ηP ) Hs/Hf ) (Hs/Hse)(Hse/Hf) ) η/(1 - ηhB)
(21)
From this we see that, if the heat exchanger B is infinitely long so that its efficiency tends to unity (ηhB f 1) then, correspondingly, from eq 21 we evidently have that ηP f ∞. This is the result stated in the Introduction. Equation 21 is, nevertheless, an expression that also requires care in interpretation since it will also be evident that the condition: ηhB f 1 is obtained when the exiting enthalpy of the processed material Hse f 0 so that, correspondingly, η f 0, and the ratio [η/(1 - ηhB)] converges to 0/0. In this instance [cf., commentary in sections. 4.3 and 4.4] the ratio is infinity. Physically, this corresponds to the time-convergent condition that the kiln was appropriately heated, first, to the point that necessary material-processing was operational. At that condition, with no heat loss through the walls then, with all exhaust gas heat recovered by the incoming material in HEA, and correspondingly, all sensible heat in the processed material recovered by the incoming air in HEB, there is then no further thermal input required, but the throughput material is appropriately thermally processed. Clearly, the processing efficiency under that condition is infinite.
558
Energy & Fuels, Vol. 15, No. 3, 2001
Discussion and Conclusions The clear outcome of this analysis is the demonstration of the inherently high potential efficiency of tunnel kilns due to the heat exchanger elements of the design. The associated result of importance is the derivation of the same-form firing equation [eq 18] as in the previous studies1-3 with the corresponding associated pattern for the thermal efficiency variation with output. This by itself is a valuable addition to the compiled results of the furnace analysis protocol. The analytical formulation is, of course, targeted to the tunnel kiln and similar systems, with heat recovery exchangers both upstream and downstream of the firing section. Nevertheless, the analysis is also so sufficiently general, in principle, that it can be used as a basis or platform for further extensions, where the application to boilers would be a particular natural additional development. In formulating such possible extensions it is relevant that the analysis does incorporate a number of explicit or implicit assumptions or constraints that need to be identified as they may also be either too controlling or not relevant to other systems. Notably, it is assumed that, at a given output, the temperature of the exhaust gas at the combustion chamber exit is unchanged by preheat; and correspondingly, that the exhaust enthalpy is unchanged at a given stoichiometry. Likewise, in evaluating heat recovery from material being processed, the specific enthalpy of the material is assumed to be unchanged at the outlet of the firing section before entering the final heat exchanger. Further, it is assumed that the thermal efficiency of the heat exchangers involved are constant with variable load, and can also be increased to unity by increased length. All these assumptions can and need to be revisited although their more detailed influences are expected to be second, not first order; however, what is clearly absent at this time is an adequate database of operational behavior of such furnaces for test and evaluation, both, of this present analysis and of any further modifications and extensions. With regard to the theoretical approach, the procedure is quantitatively analytical so that it can also be used, in principle, to evaluate performance data obtained from experimental devices, as shown elsewhere,
Essenhigh
for example, in the comparative boiler study of ref 3, though noting that the procedure has not yet been applied in this way to tunnel kilns for lack, at this time, as noted earlier, of a relevant database for testing the analytical evaluation of these devices. However, since the procedure is based on an integral formulation, it is only performance-pattern or qualitatively predictive since the formulations contain parameters of unknown magnitude (such as the heat exchanger efficiencies) that require either experimental data values or separate mechanistic analytical predictive models for quantitative prediction of behavior of the individual components, and by extension, of the total system. However, this is potentially possible, and it defines targets for future developments. In conclusion, although these assumptions and constraints are important factors to be identified in extension to other systems, what is nevertheless more relevant as operationally governing in practical applications is either a determined rigidity or an allowed flexibility, in the thermal parameters that define actual operation of a given system. Thus: for material being heat-treated, such as firing brick or ceramics or heat treatment of steel parts, there is generally, jointly, a governing temperature requirement, and time-held at that temperature, for the processing to go to completion. After that, the material can be cooled and the enthalpy can be recovered; but the determining temperatures and processing times, which translates into, and thus specifies, the throughput rates, are set by the internal process requirements. This factor operates in defining input conditions to the heat exchanger HEB in the tunnel kiln. Conversely, however, as in a boiler, the output enthalpy of the processed materialssteamsis set by the external process requirements, such as a turbine, so that this becomes a fixed parameter external to the system. This may also be the case in certain other process operations, for example, heating steel billets for forging, where the materials exit-temperature is again pre-set and, within limits, is not adjustable. This identification is, thus, a starting point for definition of possible alternate subsets of systems for continuing analysis, with potential for different outcomes. EF000119T
