Enthalpy of Clinker Minerals

The following have been derived mainly from CODATA. Historically, tables of heat capacities have been used for deriving heat contents, but since these are invariably integrated with respect to temperature, it is more convenient to tabulate the integrals themselves. Formulae for these functions are extremely complex and unweildy (Note), and for modelling purposes it is best to use the table to derive simpler equations over the range of interest. The minerals have been selected as being representative of the minerals in clinker. While these minerals may not actually occur in clinker, they have thermal properies similar to those that do. They cover the range of elements normally quantified in a clinker analysis, so that, by making a linear combination, most clinkers can be emulated (Note 1). The resulting enthalpy data will be a close approximation to the true enthalpy of a clinker of a given composition. The clinker enthalpy data does not include the melting endotherm. This is important and substantial, but needs to be calculated separately: see Note 2. For convenience, all values are related to the state at 0°C. Values are in kJ/kg at a pressure of 101.325 kPa.

Note 1. There are more minerals than there are elements, so this is not a simple matrix conversion. Some are populated in a defined order, and their quantities are limited, as follows:-

MgO first goes into the pseudo-ferrite C₂MT, the amount of which is defined by the TiO₂ content. Any MgO remaining then goes into forsterite (actually in solid solution in the alite, belite and ferrite) but the amount of forsterite may not exceed 0.035 C₃S + 0.009 C₂S + 0.052 C₄AF. When this limit is reached, any surplus MgO remains as periclase.

SO₃ first forms arcanite until K₂O is used up, then forms thenardite until Na₂O is used up, and any surplus goes into anhydrite.

Any Na₂O left after thenardite formation goes into NA (actually solid solution in the C₃A).

Any K₂O left after arcanite formation goes into KA (actually solid solution in the C₃A).

The compostions of the minerals are as follows:-

Note 2. The clinker partially melts during formation, and absorbs latent heat in the process. The temperature range over which melting occurs depends upon a number of factors and is difficult to predict accurately, but a sufficiently useful treatment is as follows:

Amount of Liquid. The amount of liquid formed increases with temperature, in a manner defined by a complex function of bulk chemistry, dependent mainly upon the amounts of alumina, iron oxide and magnesia. The amount of liquid (excluding salt melts) in a clinker containing 1.5% MgO and (alumina + iron oxide) = 8% is exemplified below.

Latent Heat of Fusion. The latent heat of fusion of the liquid is a function of the clinker bulk chemistry as follows:

ΔH_m = 240.2 - 98(F + 0.33 M*) / (A + 0.746 F + 0.93 M*) + 41.5 M*

where ΔH_m is the enthalpy of fusion in kJ/kg of liquid: A is the %Al₂O₃ in the clinker: F is the %Fe₂O₃ in the clinker; and if M is the %MgO in the clinker, then M* = M if M < 2, otherwise M* = 2.

The heat energy that needs to be supplied to produce the liquid is obtained by multiplying the amount of liquid by the latent heat. For typical modern clinkers, about 60 kJ/kg is absorbed between 1320 and 1360°C, and as temperature rises, further melting requires an extra 0.08 kJ/kg/°C.