New graphical method for the representation of the calcium-carbonate equilibria: Application to the water treatment
Although many good methods exist for computing calcium-carbonate equilibria, we considered that it was still possible to improve the representation to the problem and for this reason we have developed a new method of calculation. In this paper we have restricted ourselves to the graphical aspect of the question, referring the reader to the original bibliography at the end of the paper and as well we have not taken into account the kinetic aspects of the reactions involving the dissolution or precipitation of CaCO3. From this perspective, an original graph has been designed choosing for co-ordinates the pH (abscissa) and [CO3 total] (ordinate). The construction of such a graph requires only two fundamental laws, i.e. 1) The solubility product relationship of calcium carbonate. This relationship, with the introduction of an auxiliary variable: ∆=[Ca2+] - [CO3 total] can be transformed itself into an équivalent relationship, more convenient for the computation of the various curves composing the graph. 2) A second relationship, taking into account the H+-ions in their free or bound state (with the C03 group or the H20 solvent). For this purpose, one introduces a total concentration, called potential total acidity (in abbreviated form PTA), the définition of which is: PTA=2[H2CO3]+[HCO-3]+[H2O]+[H+] In addition, one uses also another variable derived from PTA to which we gave the name : carbonated potential acidity with the following definition: δ=2[H2CO3]+[HCO-3] Both variables PTA and ∆ have jointly the interesting property of remaining constant during the evolution of the water towards equilibrium according to the equation: CaCO3+H+⇌Ca2++HCO-3 The variable may also be considered as practically constant in the field of natural waters. We have taken advantage of this property to build up two networks of curves that make up the overall graph, i.e., a) the curves satisfying the condition : PTA=constant (these curves are named " iso-acidity curves "), and b) the curves whose characteristics are : =constant, and which are named " iso-equilibrium curves ". The paper describes how to use the graph and brings out its ease of use for both the qualitative and quantitative prediction of the behaviour of water in contact with calcium carbonate. In particular, the graph illustrates such essential water characteristics as equilibrium pH, stabilisation pH and stabilisation index, characteristics whose meanings are defined in the paper. The graph is shown to be a useful tool for the characterisation of waters as well as for the evaluation of most chemical treatments. The case of the mixture of different waters is also treated. Numerous examples for using the graph under different circumstances are developed in the paper, which should be useful for those whose job is connected with industrial water treatment. The graphical method here described, in conjunction with an associated computer programme, also constitutes an excellent introduction to the more complete computing methods developed elsewhere but which could not be treated in the limited frame of this publication. The graph turns out to be a useful tool for the characterisation of waters as well as for the evaluation of different chemical treatments, such as softening, carbonation, decarbonation, acidification, alkalinisation, aeration, etc. The case of the mixture of different waters is also treated. Numerous examples for using the graph under different circumstances are developed. The paper shows how it is possible, on the basis of the diagram, to predict the evolution of the water when different reagents are added, when the temperature changes or when one mixes different waters. The diagram should be a useful aid for those people whose job is connected with industrial water treatment. A computing program is necessary to draw the curves, to obtain the water characteristics with a better accuracy than can be read from the graphs. This programme, named Carbeq+, is commercially available (see below for the bibliographical reference). The values necessary for the computation and the drawing of the curves are : 1. temperature of analysis and temperature of computation 2. pH, alkalinity, calcium concentration 3. the ionic strength, which can be calculated either from the knowledge of the complete analysis of the water, or if that one is not available, by using an empirical relation based on either the conductivity or the salt content. The program computes then the equilibrium pH, the stabilisation pH and the stabilisation index and draws the graphs described in the paper. The graphical method here described, in conjunction with the associated computer programme, constitutes also an excellent introduction to the more complete computing methods developed elsewhere but which could not be treated in the limited frame of this publication. Note that the case of the influence of the gaseous carbon dioxide phase on the equilibrium is not treated in this paper, but it is taken into account in the Carbeq+ programme mentioned above.