Production efficiency, environmental sustainability, and glass quality –

a thermodynamic optimization of three conflicting objectives

Reinhard Conradt

Department of Mineral Engineering and Chair of Glass and Ceramic Composites

RWTH Aachen, Germany

Tel. +49-241-809-4966, Fax +49-241-8092-129,

E-mail conradt@ghi.rwth-aachen.de

ABSTRACT

Glass producers aim at using their installed melting aggregates at full capacity. At

the same time, they aim at minimizing the specific energy consumption, and

maximizing glass quality. Obviously, non of the above individual goals can be

reached to full extent without impairing the remaining two. In other words: The

mentioned objectives constitute the corners of an optimization task. This task is

accomplished by evaluating conventional heat balances, taking into account the

aspect of availability (or: exergy), applying the fundamentals of heat transfer, and

finally making use of the method of so-called finite-time thermodynamics. As a

result of this treatment, a performance diagram is presented displaying a distinct

curve for a given furnace in a pull rate vs. thermal efficiency diagram. The obtained

graph displays two characteristic working points. These are (1) a working point of

maximum pull rate (i. e., production efficiency), and (2) a working point of

maximum heat exploitation efficiency (i. e., environmental sustainability). These

working points clearly distinguish between wasteful and potentially optimal

2

configurations, with the term “optimal” referring to the specific optimization target.

The lowest pull rate which is still located within the potentially optimal range marks

a “quality point”. For a given furnace, glass quality enhancement beyond this point

can be reached under extremely wasteful conditions only.

INTRODUCTION

The efficiency of energy utilization of the conventional glass melting process

seems to have reached its technological limits. According to a recent energy

benchmarking report [1], the end-port fired horseshoe flame furnace with

regenerative flue gas heat recovery represents kind of an optimum configuration.

Yet there is a worldwide quest for further improvement. This quest is driven by the

continued increase of energy costs as well as by the commitment of individual

countries to reduce CO2 emission in accordance with the Kyoto protocol. New

concepts are discussed and tested, among which are conventional ones (like batch

pre-heating, enhanced combustion technology, use of top burners) and most

unconventional ones, like submerged combustion, jet melting, or segmentation of

the entire process. In view of these efforts, it seems necessary to reconsider the

theoretical basis of the glass melting process and to point out its physical limits as

derived from the 1rst and 2nd law of thermodynamics. This is done in terms of zero-

dimensional models yieldings general guidelines of optimization – irrespective of

their potential realization by technological means. In doing this, we must keep in

mind that optimization is an ambiguous target. It may be referred to power output, i.

e., to the maximum pull rate achieved with a given furnace, or to environmental

3

sustainability, i. e., to the minimum energy required to melt a given amount of

glass, or to maximum glass quality. None of the mentioned individual targets can

be reached to full extent without impairing the remaining two.

The paper starts with a 1rst law treatment, i.e., with a conventional heat balance.

Quantification of the balance is achieved by combustion calculations, as well as by

an assessment of the heat involved in the batch-to-melt conversion and the heat

content of the melt leaving the basin. The suggestions for optimization derived from

this treatment comprise the use of low-enthalpy batches, the enhancement of heat

recovery from the hot stream, and heat insulation measures. Such measures have

been applied with success in the past. However, from a principle point of view,

none of these measures provide a sufficient condition to push efficiencies beyond

the practical limits already reached.

In the second part of the paper, the issue of energy availability is briefly addressed.

This leads to a time-independent 2nd law treatment of the glass melting process

resulting in a quite different view of its efficiency. It is shown that the most severe

loss of availability is involved in the combustion process itself. From the point of

view of availability, it is an advantage to aim at the highest possible adiabatic flame

temperature, and to cool down the offgas to the possibly lowest temperature even

within the process. A later heat recovery is second-best choice only. Another

suggestion derived from this approach, however, may turn out to be quite

ambivalent if considered from the point of view of finite-time heat transfer. This is

4

the suggestion to realize heat transfer across the smallest possible temperature

gradients, which is equivalent to minimizing the increase of entropy.

The ambivalence is resolved when the process is treated in its time dependence,

first by applying the fundamentals of heat transfer, finally by applying the paradigm

of finite-time thermodynamics. Finite-time process thermodynamics was “invented”

by a number of theorists [2-3] as an answer to the first world oil crisis during the

early 70ties. The approach, nowadays used for the optimal configuration of power

plants, has hardly found access to the glass community. Yet, it provides some

interesting insights not obtainable by earlier approaches.

An editorial remark: Temperatures are given in units of K throughout this paper,

either as absolute temperatures T, or as temperature differences ∆T = T – T0 to the

environment; T0 = 298 K.

FIRST LAW HEAT AND POWER BALANCE

The glass melting process is a high-temperature process converting a batch of

primary or secondary raw materials to a homogeneous and workable melt. The

melt has to be made available

- at a certain temperature Tex (pull temperature),

- at a certain production rate mG given in t/h; the pull rate r, given in t/(m2⋅h), is

obtained by r = mG/A; A = melting area.

5

For a given glass composition, this corresponds to an amount of heat ∆HG =

cG·∆Tex physically stored in the melt at T = Tex relative to the environment at

T0 = 298 K. ∆HG is given in kWh/t, the heat capacity of the glass cG in Wh/(t·K).

∆HG corresponds, in turn, to a power qG,

GGG mHq ⋅∆= , (1)

with qG given in kW. No matter what actually happens inside the furnace, or how it

is constructed, its ultimate objective as a thermal reactor consists in generating an

amount of useful thermal power qG. Its objective as a chemical reactor consists in

bringing about the conversion batch → glass + batch gases characterized by the

chemical heat demand ∆H°chem (referred to 298 K). As the final steps of chemical

conversion (i. e., quartz dissolution, fining and refining) involve comparatively small

amounts of energy only, the time required to reach a desired degree of conversion

(i. e., a desired quality level) is not directly related to the constraints of heat

transfer. Thus, as Nemec pointed out [4], the aspect of glass quality yields its own

constraints for the process. For a given glass, ∆HG is a fixed quantity while ∆H°chem

is still open to manipulation by the choice of raw materials. If ∆H°chem is referred to

cullet-free batch, then ∆HG and ∆H°chem may be summarized like

GochemCex HHyH ∆+∆⋅−= )1( , (2)

6

where Hex denotes the so-called exploited heat and yC the cullet fraction (per t of

glass) used in the batch. The corresponding specific power is qex = Hex⋅mG. The

furnace requires an amount of energy input Hin > Hex made available at a

temperature TH. When provided by fossile or synthetic fuel, then TH is identical with

the so-called adiabatic combustion temperature Tad (see table 1).

Figure 1 illustrates the heat balance of a typical glass melting tank furnace with an

offgas heat exchanger system. The individual quantities are explained in the figure

itself. They may be read in an equivalent way as amounts of heat H in kWh/t, or as

power terms q in kW; amounts of t always refer to the quantity of melted glass. The

relative proportions of the individual terms in figure 1 depend on: the production

rate, the furnace age, the type of batch, the type of fuel and oxygen supply. They

thus represent a momentary production situation (a snap shot) or alternatively, an

average over a given time interval. Form figure 1, five principal balance equations

are derived describing the amounts of heat set free in the combustion space,

exchanged with the furnace body, transferred to the basin, conveyed to the heat

exchanger, and exchanged within the heat exchanger, respectively. Presented in

the quoted sequence and in terms of heat amounts, they read

Hsf = Hin + Hre = Hoff + Hwo + Hwu + Hex , (3)

Hfire = Hsf - Hoff = Hwo + Hwu + Hex , (4)

Hht = Hwu + Hex , (5)

Hoff = Hstack + Hwx + Hre , (6)

Hexch = Hoff - Hstack = Hwx + Hre . (7)

7

The meaning of the subscripts is explained in figure 1. The quantities Hin, Hoff, Hre,

and Hstack related to the hot stream entering or leaving the combustion space or the

heat exchanger, respectively, can be calculated via combustion calculations (as

explained in many textbooks) in a fully quantitative way. Likewise, based on own

work [5-6], the individual heat terms ∆H°chem and ∆HG in eq. (2), and hence, the

exploited heat, can be calculated in a fully quantitative way for a given pull

temperature Tex and any batch composition. Thus, by using eqs. (3) to (7), the

exact values of Hsf, Hfire, Hwx, and the sum of Hwo + Hwu can be derived, too.

Unfortunately, the individual wall losses Hwo and Hwu and the amount of heat Hht

transferred to the basin cannot be assessed by this approach. Nevertheless, a few

meaningful conclusions may be drawn from figure 1 and eqs. (3) to (7). Let us

express the heat input by the amount MF of fuel (kg per t of glass) and its net

calorific value HNCV (kWh per kg fuel),

,· NCVFin HMH = (8)

introduce the efficiency ηre of the heat exchanger system ηre = Hre/Hoff, and express

Hoff in terms of the volume VFH of the offgas, of the air demand VFair, both given in

m3 (at 298 K and 1 bar) per kg fuel, their heat capacities cH and cair, respectively,

and the air excess factor λ; T0 = 298 K. Then eq. (3) may be rearranged as

)T(T)cV1)(?c(V)?(1HHHH

M0offair

FairH

FHreNCV

exwuwoF −⋅⋅⋅−+⋅⋅−−

++= (9)

8

reflecting the significant influence of ηre and λ on the amount of fuel required.

According to eq. (9), energy utilization is optimized by a number of conventional

measures, i.e., by enhancing ηre, by minimizing λ ≥ 1, and by improving the heat

insulation of the furnace (i.e., by decreasing Hwo and Hwu). As the offgas volume

always exceeds the air volume, and always has a higher heat capacity than air,

approx. 75 % is a true physical upper limit of ηre even for an infinitely large heat

exchanger. Real heat exchangers nowadays approach 65 %. The option to

minimize Hex by using cullet - see eq. (2) – is also well established. One might also

think of minimizing ∆H°chem via the choice of raw materials, e.g., by replacing

alkaline earth carbonates by calcined products or by silicates. Such measures are,

however, effective only in batches with low cullet content. All above optimization

suggestions are valid for constant – and moderate – production rates. They may

not work at all if a furnace already operates in the vicinity of its performance limit

and are of little use to push the energy utilization efficiency beyond the practical

limits already reached.

SECOND LAW TREATMENT OF TIME-INDEPENDENT HEAT TRANSFER

The energy balance based on 1rst law principles has an essential weakness: It

counts energy amounts without taking into account their respective values relative

to the environment at T0 = 298 K. It is quite obvious that an amount of energy Hin

by itself is not sufficient to melt glass. Hin must be made available at a suitable

temperature level; otherwise it is useless for the purpose. In general terms, an

9

amount of heat Hin made available at a temperature level TH can be exploited to at

most

Ain = Hin ⋅ (1 – T0 / TH) , (10)

where Ain is termed „availability“ or „exergy“. Ain is smaller than Hin by the efficiency

ηC of the generalized Carnot heat engine, which is a direct 2nd law consequence

under the boundary condition of instantaneous (or time-independent) heat transfer.

TH determines how valuable Hin is. Transferring Hin to a lower temperature level

means depreciating it. During a process, energy is conserved but availability is lost.

From this point of view, optimizing energy utilization does not necessarily mean

reducing Hin, but minimizing availability losses. In this respect, availability balances

focus on the aspect of sustainability rather than efficiency. The corresponding

optimization task focuses on minimizing the entropy increase. The availability

approach, which is standard in energy conversion technology (see, e.g., [7]) has

found entry to the glass community in a few cases only [8-11]. Availability may be

presented in a way complementary to eq. (11) by

A = H1 – H0 – T0 (S1 – S0) , (11)

with 1 = state of influx, 0 = state of equilibrium with the environment, H = enthalpy

(heat), S = entropy. For pure CH4 as fuel, the difference H1 – H0 is equal to the net

calorific value HNCV = 802.3 kJ/mol (offgas water dissipates as atmospheric

humidity, not as liquid). The entropy term, by contrast, amounts to only 1.6 kJ/mol.

10

Consequently, the availability of energy chemically stored in the fuel is almost

equal to HNCV. This changes the very moment the fuel is ignited. Then

.11 00

−⋅

11

subscripts have the same meaning as in figure 1. As stated before, eqs. (1) to (3)

also hold for the heat fluxes q. The heat fluxes related to the hot stream passing

the combustion space are presented in terms of the mass flow rate mH and heat

capacity cH, respectively, of the offgas. Temperatures T are given in terms of

temperature differences ∆T = T – T0 to the environment (T0 = 298 K):

,offHHoff Tcmq ∆⋅⋅= (13)

,oadHHin Tcmq ∆⋅⋅= (14)

,adHHoffrein Tcmqq ∆⋅⋅=⋅+η (15)

where ∆Tad and ∆T°ad refer to the adiabatic combustion temperature with

preheated and ambient air, respectively. The term qwo is not taken into

consideration at this stage. Wall losses through the upper structure are non-

essential (avoidable) losses; they have no role for the function of the process. By

contrast, the wall losses through the basin are essential losses, at least in part.

They are not only necessary to promote convective stirring of the glass melt, but

also to establish a sufficient drain for qht. In this respect, a glass furnace is in no

way different form any other heat engine drawing heat form an upper reservoir,

rejecting heat to a lower one, thereby generating a useful power output. This

aspect has been addressed in earlier literature already [12]. Rearrangement of

eq. (1), expressed in terms of heat fluxes q, and combination with eqs. (13 – 15)

yields

12

;11

−

∆

∆⋅−−== wuo

ad

offre

oex

in

ex wT

T

qq

ηη (16)

η°ex is the overall efficiency of heat exploitation in the absence of wall losses qwo,

wwu = qwu/qin is a basin wall loss ratio. The unknown quantity ∆Toff is given by

( ) ( ) .exp htexadexoff NTUTTTT −⋅∆−∆+∆=∆ (17)

Here, in agreement with eqs. (14 – 15),

.offreo

adad TTT ∆⋅+∆=∆ η (18)

NTUht is the so-called number of transfer units related to the flux qht. NTUht may be

approximated by NTUht = αht/(cG·r); αht is a heat transfer number given in

W/(m2·K), cG is the heat capacity of the glass melt in Wh/(t·K) and r ist the pull

rate in t/(m2·h). The ratio b = αht/cG may be interpreted as a reference pull rate.

Inserting eq. (18) into (17), resolving for ∆Toff, and inserting ∆Toff in eq. (16) yields

the following relation between efficiency η°ex and pull rate r:

( )( ) .)exp()exp(1

11

00

0wuhto

ad

exo

ado

ad

ex

htre

reoex wNTUTT

TTTTTT

NTU−

−⋅

−−

+−−

⋅−⋅−

−−=

ηη

η (19)

13

The effect of the wall losses qwo through the upper structure is taken into account

by multiplying η°ex with wwo = qin/(qin + qwo). Since qin depends on the pull rate r

while qwo does not, wwo assumes a form like wwo = (1 + w/r)-1. Like b, w has the

meaning of a reference pull rate. Typically, b and w assume values of b = 2 to 8

and w = 0.5 to 2 t/(m2·d), respectively. For a given production situation

characterized by a given batch (see eq. (2)) and a given pull temperature Tex, the

actual heat demand Hin = Hex/ηex can be calculated as a function of the pull rate.

This is shown in figure 3 for Hex = 500 kWh/t, Tad = 3000 K (2700 °C), Tex = 1523 K

(1250 °C) and wwu = 0.2. The results feature the behavior actually found in

industry. The combination b = 8, w = 0.5 represents a large furnace with good

internal heat transfer and low wall losses. Such a furnace is especially efficient at

high pull rates. It reacts, however, to changes of the internal heat transfer in a very

sensitive way. Small furnaces typically exhibit high wall losses (here represented

by w = 2). Beyond this, with their small basin volumes resulting in short dwell times

of the melt, they do not reach the high-pull regime. They react very sensitive to

even moderate under-pull, but are less sensitive to changes of the internal heat

transfer than large furnaces.

FINITE-TIME THERMODYNAMICS

The approach presented in the previous section is helpful in predicting the

characteristic variation of the actual energy demand Hin with the pull rate for a

given furnace. The approach may be refined by using more sophisticated

expressions for NTUht, wwu, and wwu than done in the present paper. The

14

shortcoming of the approach consists in the fact that no constraint is put on the pull

rate r itself. Rather, r is treated as an independent variable. This makes sense for

simple heat exchangers in which the flow of cooling agent can be increased, in

principle, without limits. The limits related to glass quality have been pointed out by

[4]. But there are thermal constraints involved, too, which are not related to glass

quality. Therefore, let us complement the previous approach by the so-called finite-

time thermodynamics. In this approach, the glass furnace is treated as heat engine

generating an output qex of useful power. Thus, qex itself becomes the target of

optimization. In other words: Since qex is directly proportional to the pull rate r, the

approach focuses on the optimal and extremal points of r. Finite-time thermo-

dynamics has been developed earlier [2-3]; it has been used with success to

configure, e. g., power plants. The principle idea is sketched in figure 4: A

reversible heat conversion machine operates between a limited upper reservoir

and TH and an unlimited lower reservoir at T0 (i.e., the environment). The restricted

heat fluxes between the reservoir at TH and the machine, and between the

machine and the environment, respectively, decrease the temperature difference

Tht - Twu across which the machine operates. For simplicity, let us consider

Twu → TL (no heat resistance towards the environment). While the heat flux

( )htHht TTq −≈ (20)

increases with decreasing Tht, the power output

15

Chtht

Lht qT

Tqp η⋅=

−⋅= 1 (21)

decreases, and vice versa. As shown in literature [2-3, 13], the power output

depends on the actual value of Tth, which may be expressed by a dependence on

the Carnot type efficiency ηC (where pmax is found by the condition ∂p/∂Tht = 0):

( )2max1

1

/LH

LH

TT

TTpp

−

⋅

−−⋅

=η

η

(22)

yielding the well-known Curzon-Ahlborn efficiency

H

LAC T

T−= 1..η (23)

at the point of maximum power output p = pmax. The heat leak qwo is introduced in

the same was done in the previous section. Figure 5 shows the results for a zero, a

low, and a high heat leak qwo. It is interesting to note that in the realistic case of a

non-zero heat leak, the curves display two distinctly different optimal points, i.e.,

one referring to minimum entropy production (i. e., maximum sustainability), and

one to maximum power output. With increasing heat leak, both points approach

each other.

16

It has been debated whether or not the discussed scenario may be transferred to a

glass furnace. After all, glass melting obviously is a heat transfer process, not a

heat conversion process; beyond this, the endoreversibility of the processes in the

basin may be doubted. The latter point is resolved easily: The pull of hot glass and

its continuous replacement by a corresponding amount of batch constitutes a cycle

in the same way as the continuous supply of fuel and release of exhaust gas does

for an Otto engine. In fact, it has been shown [14] that endoreversibility is not a

prerequisite for the application of the method. The former point is by far more

difficult to resolve: The efficiency related to the intrinsic cycle must have a Carnot

type form; otherwise p(η) displays a steady decrease or increase only, but no

maximum. For the time being, let us lean on a general result from a theoretical

investigation [15] justifying the above approach in a most general way. The

justification is based on a common expression for the maximum entropy source

which is the same for operations with and without work. Thus, for a large number of

processes in which linear approximations are acceptable, models and optimization

results in both kinds of operations are identical [15]. Therefore, let us apply the

results from figure 5 to glass furnaces in general and interpret them accordingly.

This is done in figure 6. A furnace yielding 3.5 t/(m2·d) as upper limit of the pull

rate is taken as example. Again, two distinct optimal points appear, referring to pull

rates of 2.5 and 3,5 t/(m2·d) at heat exploitation efficiencies of 53 and 63 %,

respectively. The bold part of the curve marks the range within which the objectives

of production efficiency and energy exploitation efficiency can be optimized.

Operations aiming at high glass quality as the primary optimization target apply low

17

pull rates only. For these cases, the plot in figure 6 allows to define yet another

optimal point. It corresponds to the position on the lower branch of the curve at the

efficiency corresponding to maximum power output. This point shall be termed

“quality point”. At the quality point, maximum glass quality is obtained under the

constraint of an optimized energy utilization efficiency. Lowering the pull rate below

this point, however, leads to an extremely wasteful under-pull of the furnace. The

left part of the upper branch of the curve is of limited practical interest only. It

corresponds to an overdriven combustion space, is eventually entered in the

attempt to drive a furnace towards high pull due to economic pressure, and should

be avoided by any means.

CONCLUSION

A hierarchy of theoretical approaches was presented yielding an increasingly

distinct description of the thermal performance of glass furnaces. For the time

being, this is done on a quite abstract level only. Verification against a sufficiently

large number of data obtained from real furnaces will follow in a future paper. The

starting point of a numerical quantification of all approaches presented is the

conventional heat balance. It can be established in a fully quantitative way for

individual furnaces by retrospectively evaluating factory data typically recorded on

a day-by-day routine by every producer, and by calculating the intrinsic heat

demand ∆H°chem for the batch used in a most accurate way. The observation time

span should be extended over sufficiently long time spans comprising significant

changes of the pull rate. Based on such quantification, the more sophisticated

18

approaches can be quantified for individual furnaces, too. This means in detail, that

the conflicting optimization targets of production efficiency, heat exploitation

efficiency, and glass quality can be optimized for individual cases. For the latter

aspect of quality, a model as presented in [4] is implemented, balancing the

chemical versus the thermal constraints of an operation. In a situation where glass

industry is exposed to increasing pressure by economy and by environmental

regulations, a clear understanding of the achievable limits of individual operations

may be of great help.

19

REFERENCES

[1] R. G. C. Beerkens, J. van Limpt: Energy efficiency benchmarking of glass

furnaces. 62nd Conference on Glass Problems, Illinois 2001.

[2] F. L. Curzon, B. Ahlborn: Efficiency of a Carnot engine at maximum power

output. Am. J. Phys. 43 (1975), 22-24.

[3] B. Andresen, R. S. Berry, M. J. Ondrechen, P. Salamon: Thermodynamics

for processes in finite time. Acc. Chem. Res. 17 (1984), 266-271.

[4] L. Nemec: Energy consumption in the glass melting process. Pt. 1.

Theoretial relations. Pt. 2. Results of calculations. Glastechn. Ber. Glass Sci.

Technol. 68, (1995), 1-20, 39-50.

[5] R. Conradt, P. Pimkhaokham: An easy-to-apply method to estimate the heat

demand for melting technical silicate glasses. Glastechn. Ber. 63K (1990),

134-143.

[6] R. Conradt: Chemical structure, medium range order, and crystalline

reference state of multicomponent oxide liquids and glasses. J. Non-Cryst.

Solids 345 & 346 (2004), 16-23.

[7] K. Lucas: Thermodynamik – Die Grundgesetze der Energie- und

Stoffumwandlungen. Springer-Verlag, Berlin 2006.

[8] F. Bosnjakovic: The meaning of the second theorem of thermodynamics for

the heat balance of furnaces. (German). Glastechn. Ber. 32 (1959), 6-47.

[9] I. Huhmann-Kotz: Untersuchung und Beurteilung von Glasschmelzwannen

durch Exergiebilanzen. Glastechn. Ber. 51 (1959), 47-53.

20

[10] W. Trier: Glasschmelzöfen. Konstruktion und Betriebsverhalten. Kap.

5.1.5.5. Exergiebilanzen, Springer-Verlag, Berlin (1984), 91-93.

[11] S. Chengxu, X. Jianming: The exergy analysis of a glass tank furnace.

Glass Technol. 32 (1991), 217-218.

[12] D. Aufhäuser: The glass melting furnace as heat engine. (German).

Glastech. Ber. 6 (1928-29), 372-379.

[13] P. Salamon, K. H. Hoffmann, S. Schubert, R. S. Berry, B. Andresen: What

conditions make minimum entropy production equivalent to maximum power

production? J. Non-Eq. Thermodynamics 26 (2001), 78-83.

[14] J. Chen, Z. Yan, G. Lin, B. Andresen: On the Curzon-Ahlborn efficiency and

its connection with the efficiencies of real heat engines. Energy Concersion

& Management 42 (2001, 173-181.

[15] S. Sieniutycz: A synthesis of thermodynamic models unifying traditional and

work-driven operations with heat and mass exchange. Open Systems &

Information Dyn. 10 (2003), 31-49.

21

Table 1. Adiabatic combustion temperatures Tad in K for CH4 in different

combustion scenarios; λ = oxygen excess factor (lambda factor)

adiabatic temperature Tad in K

air-fuel,

ambient air (298 K)

air-fuel,

air pre-heated to1500 K

oxy-fuel

λ = 1.00 2332 3125 4746

λ = 1.02 2303 3102 4718

λ = 1.08 2221 3036 4634

22

heat exchanger melting tank

stack losses (stack)

recovered (re)

set free (sf)exchanged (fire)transferred (ht)

exploited heat (ex)

wall losses,basin (wu)

wall losses,upper structure (wo)

wall losses,heat exchanger (wx)

exchanged in theheat exchanger (exch)

heat input

(in)

offgas(off)

q = H·mG[kW] = [kWh/t]·[t/h]

Figure 1. Heat balance of a conventional glass furnace with offgas heat recovery;

the balance is valid for amounts of heat H per t of melted glass, or

power terms q = H⋅mG ; mG = production rate in t/h

23

qre = ηre·qoff, Tre

qin + qre, Tad qoff, Toff

qex, Tex

qwo, Two

qwu, Twu

qht, Tht

Figure 2 Heat flux balance of a glass furnace showing both heat fluxes and

corresponding temperature levels; ηre is the efficiency of the heat

exchanger; subscripts have the same meaning as in figure 1

24

0 1 2 3 41000

1500

2000

2500

3000

Hin in

kW

h/t

r in t/(m²·d)

w = 2

w = 0.5

b = 2

4

8

b = 4

8

Figure 3. Modeled dependence of the required heat input Hin as a function of

the pull rate r for the case: intrinsic heat demand Hex = 500 kWh/t,

adiabatic offgas temperature Tad = 3000 K (2700 °C), pull

temperature Tex = 1523 K (1250 °C), and basin wall loss ratio

wwu = 0.2; w is a parameter related to qwo presenting the wall losses

through the upper structure: b is a parameter presenting the heat

transfer rate qht from the combustion space to the basin; both w and b

are given in dimensions of a pull rate

25

TH

Tht

Twu

TL

(limited) upper heat reservoir

(unlimited) lower heat reservoir

endo-reversibleprocess

finite time heat transfer

exploitedpower p

qht

qL finite time heat transfer

heatleak qwo

Figure 4. Sketch of an endoreversible heat engine operating between two heat

reservoirs at TH and TL involving constrained heat transfer rates qht

and qL, respectively (so-called Curzon-Ahlborn machine [2]); the

actual temperature difference across which the machine operates

thus becomes Tht – Twu; in addition, a heat leak qwo is employed

26

0.0 0.2 0.4 0.6 0.8 1.0

1.0

0.0

low heatleak

high heat leak

no heat leak

efficiency η

maximumsustain-ability

maximum power output

p/p m

ax

Figure 5. Result for the Curzon-Ahlborn machine (see figure 4) with heat leak,

presented as a plot of relative power output p/pmax vs. thermal

efficiency η

27

0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

pull r

ate

in t/

(m²·d

)

efficiency ηex

maximum power output

maximumsustain-ability

sustainabilityvs. efficiency

quality vs.sustainability

efficiency vs. sustainability

under -pu

ll throug

h basin

over -d

riven c

ombu

stiom

space

wasteful configurations optimal configurations

„quality point“

Figure 6. Interpretation of the performance of a glass melting furnace in terms

of a Curzon-Ahlborn type behavior, presented as a plot of pull rate vs.

the efficiency of heat exploitation ηex = Hex/Hin; the bold part of the

curve marks the range within which the three optimization targets of

production efficiency, heat exploitation efficiency (environmental

sustainability), and glass quality can be balance against each other