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3.2 Calculation of Batch Composition
ОглавлениеAn accurate chemical analysis of every raw material is a prerequisite for batch preparation (Chapter 1.2). On this basis, one swiftly determines the batch composition by solving a system of linear equations where data are arranged in a specific way (Table 2). First, the total number of different oxides in the raw material basis is determined (6 in the example shown). The target glass composition is entered as an oxide column vector YTARGET. The large matrix shaded in gray contains the results of raw‐material analyses. It is arranged in the order of carriers of the respective glass oxides. For each oxide that is not represented by a specific raw material, the entry 1 is filled in the matrix. If an oxide has more than one carrier raw material (in the example, Al2O3 has two carriers, namely feldspar and Calumite®), then their ratio has to be specified, and the respective column entries are merged to a single column in proportion of this ratio. Through these operations, the gray area takes the form of a square matrix M. Next, a preliminary vector RPRE of the batch composition is obtained from the product RPRE = M −1·YTARGET. It may contain negative figures since it is impossible to make for example an iron‐free glass from iron‐containing raw materials. To derive the actual batch‐composition vector R, these negative figures are thus set to zero. The real glass composition is then given by the product YREAL = M·R before YREAL is normalized to 100 wt % and R to 1000 kg of resulting glass, or 2000 kg of sand (see following paragraph), or to any other convenient reference mass.
Table 2 Batch calculation scheme.
| The glass | The raw material basis | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Raw material | Sand | None | Feldspar | Calumite® | None | Dolomite | Limestone | Soda ash | None | |||
| For oxide | SiO2 | TiO2 | Al2O3 | Al2O3 | Fe2O3 | MgO | CaO | Na2O | K2O | |||
| Ratio | 0.5 | 0.5 | ||||||||||
| Y TARGET | Y REAL | |||||||||||
| Oxide | wt % | wt % | Oxide | kg/kg | kg/kg | kg/kg | kg/kg | kg/kg | kg/kg | kg/kg | kg/kg | kg/kg |
| SiO2 | 72.00 | 71.80 | SiO2 | 0.9960 | 0.6920 | 0.3550 | 0.0002 | 0.0040 | ||||
| TiO2 | 0.00 | 0.04 | TiO2 | 0.0001 | 1.0000 | 0.0080 | ||||||
| Al2O3 | 1.50 | 1.50 | Al2O3 | 0.0009 | 0.2010 | 0.1250 | ||||||
| Fe2O3 | 0.00 | 0.03 | Fe2O3 | 0.0002 | 0.0020 | 1.0000 | 0.0007 | |||||
| MgO | 3.00 | 2.99 | MgO | 0.0650 | 0.2160 | 0.0057 | ||||||
| CaO | 9.50 | 9.47 | CaO | 0.4090 | 0.3070 | 0.5502 | ||||||
| Na2O | 14.00 | 13.96 | Na2O | 0.0620 | 0.0170 | 0.5868 | ||||||
| K2O | 0.00 | 0.21 | K2O | 0.0370 | 0.0110 | 1.0000 | ||||||
| Sum | 100.00 | 100.00 | Sum | 0.9972 | 1.0000 | 0.9920 | 0.9920 | 1.0000 | 0.5232 | 0.5606 | 0.5868 | 1.0000 |
| Batch composition vector R in kg raw material per t of glass. | ||||||||||||
| kg/t | 674.28 | 0.00 | 44.02 | 44.02 | 0.00 | 123.39 | 70.61 | 231.99 | 0.00 |
The results of the considered raw‐material analysis is reported in the shaded gray area of the matrix.
Table 3 Redox factors R(i) of selected active raw materials i; these factors refer to batch compositions normalized to a sand amount of 2000 kg.
| Raw material i | Chemical formula | R(i) per 2000 kg sand |
|---|---|---|
| Carbon | C : 100, 85, 65% | −6.70 |
| Iron sulfide | FeS | −1.60 |
| Pyrite | FeS2 | −1.20 |
| Fluorspar | CaF2 | −0.10 |
| Calumite | Multicomponent slag | −0.073 |
| Iron red | Fe2O3 | +0,25 |
| Chili saltpeter | NaNO3 | +0.32 |
| Heavy spar | BaSO4 | +0.40 |
| Gypsum | CaSO4·2 H2O | +0.56 |
| Potassium dichromate | K2Cr2O7 | +0.65 |
| Salt cake; sulfate | Na2SO4 | +0.67 |
| Gypsum anhydrite | CaSO4 | +0.70 |
| Sodium dichromate | Na2Cr2O7 | +0.77 |
| Manganese oxide | MnO2 | +1.09 |
Final adjustment of the batch composition still requires allotments of the appropriate agents for controlling glass color, fining (as described in Section 5.2), redox conditions, and, thus, valence states and oxygen complex formation of polyvalent ions (cf. Chapter 5.6) at the industrial scale. For adjustment of the redox state, the so‐called redox number concept [2] is widely accepted and empirically applied in industry. This incremental system assigns a specific redox factor Ri to every member of a set of redox‐active ingredients i (Table 3). In the example of Table 4, the batch composition from Table 2 is complemented by 4 kg of sulphate (the amount of soda ash being reduced accordingly to maintain an identical amount of Na2O in the glass). Then the batch composition is normalized to amounts mIII(i) per 2000 kg of sand, and the total redox number of the batch is calculated from the weighted sum R = ∑ Ri·mIII(i). It is true that this number R does not have a straightforward scientific meaning but it allows one to set in a well‐defined way the redox state to a desired level. For redox numbers in the interval −25 < R < 25, a fair estimate of the Fe2+/Fetotal ratio for is given by 0.4 – 0.015·R. Because the chemical composition of the batch can no longer be corrected after charging, these rather simple calculations are mandatory for any successful melting process.
Finally, the raw materials are automatically weighed in proportions determined by batch calculations, conveyed to a mixer, and thoroughly mixed. During mixing, typically 2–3% of water is added to suppress dust formation and segregation induced either originally by transportation or subsequently by mixing. In batches containing soda ash, small amounts of this product dissolve in the water before reprecipitating on other batch grains. This process termed “impregnation” actually enhances the kinetics of batch melting.
