content ΔH(Tex) of the glass at the exit temperature Tex. The standard enthalpy difference between inputs and products constitutes the chemical energy demand
(15)
The heat content of the melt at Tex is given by ΔH(Tex). For convenience, all enthalpy values are inserted in absolute figures, disregarding the minus sign given in thermochemical tables. The overall intrinsic heat demand Hex (exploited heat of the process) is given by
(16)
where yCULLET denotes the weight fraction of cullet per amount of glass produced.
It is true, real raw materials typically do not contain their main mineral phase only, but also contain minor amounts of side minerals. For example, a real quartz sand may contain, beside its main phase quartz, minor amounts of feldspar minerals, magnetite, spinel, etc.; a natural dolomite is typically composed of different minerals forming solid solutions in the system Ca–Mg–FeII–CO3 with an overall composition not too far from the pure phase CaMg(CO3)2. An accurate determination of the enthalpy values H°i of real raw materials would thus require the evaluation of multicomponent phase diagrams. However, such an approach would hardly be accepted by the technological community. Beyond this, the gain of accuracy against a simpler approach is minor only. Thus, with the reservation to a more rigorous treatment [7, 8], only the enthalpy values H°i of pure raw materials are given here in units of MJ/kg:
| Raw material i | Enthalpy H°i in MJ/kg |
| Pure quartz sand | 15.150 |
| Pure albite (NaAlSi3O8) | 14.952 |
| Pure dolomite CaMg(CO3)2 | 12.549 |
| Pure calcite CaCO3 | 12.058 |
| Soda ash | 10.659 |
| Sodium sulfate | 9.782 |
| Carbon | 0.000 |
| Calumite® | 13.561 |
For the batch gases, the following values hold:
CO2: 8.941; H2O: 13.422; SO2: 4.633; O2: 0.000.
The energy calculation for the real glass composition of Table 2 (where the tiny amount of TiO2 has been allotted to SiO2) is summarized in Table 5. The position of the glass composition in the phase diagram in units of kg of equilibrium compounds per t of glass is found by the following simplified procedure:
NAS6 = 51.440 Al2O3 – 55.697 K2O,
KAS6 = 59.102 K2O,
hm = 6 Fe2O3,
FS = 7.345 Fe2O3,
MS = 24.907 MgO,
NC3S6 = 35.112 CaO,
NS2 = 29.386 Na2O + 19.346 K2O – 17.867 Al2O3 – 10.824 CaO,
S = difference to 1000 kg.
Oxide amounts are to be inserted in wt %. For the components k, the shorthand notation hm = FeO·Fe2O3, F = Fe2O3, M = MgO, C = CaO, N = Na2O, K = K2O, S = SiO2 is used. Column m(k) in Table 5 lists the resulting amounts of the constitutional components of the glass. By this procedure, one finds that the standard enthalpies of formation of the glass and melt are 14 189.7 MJ/t at room temperature and 12 665.9 MJ/t at 1300 °C, respectively. The enthalpy physically stored in the melt at 1300 °C relative to the glass at 25 °C is thus 1523.8 MJ/t. By the weighted sum of the heat capacity of compounds k, the latter value can be adjusted to any other exit temperature of the melt. For the batch given in Table 4, column “mII(i)”, a chemical energy demand of ΔH°chem = 461.8 MJ/t is obtained. Fusion of the selected batch with 50% cullet (yCULLET = 0.5) thus requires an intrinsic energy demand of
(17)
A well‐constructed and operated melting furnace (end port, air‐gas fired) reaches an efficiency of heat exploitation ηex of 48%. Thus, the actual energy demand Hin of the melting process amounts to Hin = Hex/ηex = 3637 MJ/t. This result is very much in line with industrial experience. Calculations of this kind are of high importance for the evaluation of glass furnace performance [9], for furnace design, as well as for the energy optimization of batch and glass compositions.
7 Perspectives
Although the energetics of the fusion process may be considered as satisfactorily assessed, the kinetic aspects of fusion are not yet well enough understood. The efficiency of heat exploitation ηex of a furnace varies according to a hyperbolic law of the type ηex = 1/(A + B·p) with the production rate p (t/h). Thus, furnaces are preferentially operated at the highest achievable rates. The limits for p are determined by the rate of heat transfer or the time demand of the fusion process required to achieve an acceptable glass quality. As of now, however, one does not even known which of the above constraints controls the melting rate. As a matter of fact, the answer depends on both furnace and batch design.
Table 5 Calculation scheme for the energetics of a soda‐lime silicate glass (composition in wt %).a
| Oxide | wt % | Compound k | H°k,GL | H k,1300 | c P,k,L | m(k) | m(k)· H°k,GL | m(k)· Hk,1300 |
|---|---|---|---|---|---|---|---|---|
| MJ/kg | MJ/kg | kJ/kg·K | kg/t |
|
