4.3 Pore Solution Composition and its Influence on Hydration

Previous versions of CEMHYD3D considered only the formation of solid hydration products and offered no concrete information concerning the composition of the pore solution filling the pores during hydration. In version 3.0, a special module, pHpred.c, has been added to the CEMHYD3D codes to provide quantitative predictions of the pore solution composition and its electrical conductivity during the course of the hydration. Basically, the module considers the dissolution of sodium and potassium (sulfates) to supply ions in the pore solution. Further, the absorption of the Na+ and K+ ions by both the conventional and pozzolanic forms [5] of the C-S-H is considered.

Assumptions/Procedures:

1)      Equilibrium exists between the ionic species [Na+], [K+], [OH-], [SO₄--], and [Ca++], and the solids calcium hydroxide (Ca(OH)₂), gypsum (CaSO₄-2H₂O), and syngenite (K₂Ca(SO₄)₂-H₂O).

2)      The pore solution remains electrically neutral.

3)      Calculations are performed based on activities and not simply concentrations. Activities are calculated according to a modified version of the Davies equation [6].

4)      [K+] and [Na+] concentrations are calculated based on their measured release rate from the cement powder, adjusted due to their sorption by the primary and pozzolanic C-S-H phases produced during hydration, according to the procedure outlined by Taylor [5] and previously employed by van Eijk and Brouwers [7]. The user must thus provide estimates of the total and readily (1 h) soluble sodium oxide and potassium oxide mass fractions of the original cement (each as a percentage). These are typically provided in a datafile named alkalichar.dat, as will be outlined in the Execution of the Three-Dimensional Cement Hydration Model section to follow. For the readily soluble alkalis, 90 % are assumed to be released immediately and the remaining 10 % over the course of the first 1 h of hydration. The remainder of the alkalis is assumed to be released from the cement in proportion to its degree of hydration at any given time (beyond 1 h).

5)      The sulfate concentration is controlled by the presence of gypsum and goes to zero when the gypsum is basically consumed (and ettringite becomes unstable in the CEMHYD3D model).

6)      Equilibrium concentrations in the pore solution are first computed with respect to gypsum and calcium hydroxide, and then syngenite precipitation is considered. As syngenite precipitates, only the [K+] concentration is adjusted, as it is assumed that gypsum dissolution and calcium hydroxide precipitation will maintain the sulfate and calcium ion concentrations at their equilibrium levels.

7)      Once concentrations are calculated, pore solution conductivity is estimated using the approach outlined previously by Snyder et al. [8].

8)      The activity products, K_SP, for calcium hydroxide [9], calcium sulfate [9], and syngenite [10] are taken from the available literature and are provided in Table 1 Only that of calcium hydroxide is adjusted for the effects of temperature, based on the solubility data provided in Taylor [11].

Notation

γ = activity coefficient

K_SP = activity product

[X] = concentration of ionic species X

Equations:

Equations 1 and 2 are solved for the [SO₄--] and [OH-] concentrations, respectively, and substituted into equation 3 resulting in a fourth order equation for the [Ca++] concentration which is solved numerically [12] in the pHpred.c code.

Table 1: Activity products for solid phases of relevance to pHpred code [9, 10].

The above methodology has been used to predict pH, [K+], [Na+], etc. for several cements, with good agreement observed between the model predictions and experimental measurements [13].

In addition to predicting the development of the composition of the pore solution, it is also of interest to model its concurrent influence on hydration rates. In version 3.0 of CEMHYD3D, the pH and sulfate ion concentration of the pore solution are used to compute a "pHfactor" that can either increase or decrease the nominal dissolution rates of the four cement clinker phases. The following multi-step function is used to compute this pH factor:

pHfactor = [SO₄--] +

1.5 for pH < 12.5
1.0 12.5 ≤ pH < 12.75
0.667 12.75 ≤ pH < 13.0
0.333 13.0 ≤ pH < 13.25
0.0 13.25 ≤ pH < 13.75
-0.25 pH ≥ 13.75

The dissolution probabilities of the four major cement clinker phases, slag, and aluminosilicate phases (in fly ash, for example) are divided by the value of (1+pHfactor) to obtain the final influence of pore solution composition on hydration rates. Alternately, the pHfactor can be made to be a continuous function of pH and [SO₄--]; with the experimental data available to date, either the step or the continuous function provides a reasonable fit and neither approach is clearly superior to the other. But, the general effect of either procedure is the well-known one that higher pH (hydroxyl ion concentration) solutions tend to accelerate the hydration reactions of cements (fly ashes, and slags) [11]. The use of the CEMHYD3D v3.0 model to predict the hydration rates of cements with and without alkali additions will be presented in the Example Applications section to follow.