Geochemical equilibrium modeling

6. REACTIVE TRANSPORT MODELING OF EXTERNALLY-INDUCED AGING OF

6.4. Results

6.4.2. Geochemical equilibrium modeling

To address the uncertainties in the measurements of reacted fraction in Chapter 4 and to

understand better the behavior of the thermodynamic model, the parameters 𝛼_𝐵𝐹𝑆 and 𝛼_𝐹𝐴𝐹 were varied over the intervals [0.6,1.0] and [0.0,0.8], respectively, using a Latin hypercube sampling (LHS) design of experiments [139]. A total of 100 model runs were computed with varied 𝛼𝑞, and modeling outputs were compared to the results of the Method 1313 pH-dependent leaching test at four equivalent base additions of -1.8 [meq/gram] to 0.68 [meq/gram] corresponding to pH points spanning the range of pH 8.7 to 13.0 as listed in Table 6.3. Shown in Fig. 6.2a is the pH response as a function of acid or base addition with continuous simulation between the

experimental points at which the residual was calculated. The curve in Fig. 6.2a labeled “RF”

corresponds to the thermodynamic response calculated with reacted fractions of 𝛼_𝐹𝐴𝐹 = 0.20 and 𝛼𝐵𝐹𝑆 = 0.83 whereas the curve label “1313” shows the same calculation performed using primary species masses calculated using availabilities from Method 1313. Shown in Fig. 6.2b is a contour plot of the mean error computed at all 100 sample points. Unsurprisingly, the pH response is much more sensitive to the reacted fraction of FAF than BFS because FAF

constitutes more than twice the total mass of BFS specified in the mix design. The rectangular region highlighted in Fig. 6.2b is centered on the mean values of 𝛼𝐵𝐹𝑆 and 𝛼𝐹𝐴𝐹 and spans one standard deviation to either side of the mean. The band of minimum pH residuals situated at approximately on 𝛼_𝐹𝐴𝐹 = [0.01,0.22] is encompassed this “uncertainty region” although it is relatively far from the mean measured value of 𝛼𝐹𝐴𝐹. Additionally, annotated on the intensity scale of Fig. 6.2b is the mean error computed when using 𝑀𝑖 computed from Method 1313 in lieu of reacted fraction quantities and the same thermodynamic parameters.

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Figure 6.2: a) The response of system pH in both simulation (blue and green lines) and experiment (gray boxes) as a function of milliequivalents of base added per gram of solid material. “1313” denotes the simulation wherein 𝑀𝑖 was determined through Method 1313 availability measurement and “RF” denotes the determination of 𝑀𝑖 through the reacted fraction BSE-EDX analysis. b) Contour plot of the mean error in pH computed from comparison of model responses to pH-dependent batch leaching as a function of varied reacted fractions. The magnenta rectangle is centered on the measured values of 𝛼_𝐵𝐹𝑆 and 𝛼_𝐹𝐴𝐹 and spans two standard deviations in those measurements, as determined in Chapter 4. The text label “1313” indicates the mean error predicted when the availabilities measured from Method 1313 are used in lieu of the reacted fraction quantities. The yellow star indicates the reacted fractions of 𝛼𝐵𝐹𝑆 = 0.83 and 𝛼𝐹𝐴𝐹 = 0.20 used for calculation of pH in a).

Presented in Fig. 6.3 are the mean errors computed for the primary species Ca, Si, Mg, and Al.

Errors have been calculated in base 10 logarithms in order to scale relative solubilities to a more comparable range. Thus, a mean error of one corresponds to an order of magnitude difference in prediction and experiment. Similar to pH, the mean errors of Ca, Si, Mg, and Al are highly correlated to 𝛼_𝐹𝐴𝐹. Interestingly, the minima for the primary species present in Fig. 6.3 do not necessarily coincide with the minima for pH. The region of minima for Ca (Fig. 6.3a) are banded at a slightly higher value of 𝛼𝐹𝐴𝐹 than was pH, whereas the Mg minima are nearly coincident with the minima for pH, a correlation that is likely a result of the sensitivity of Mg solubility to pH. The responses of Al and Si are also highly correlated with the exception that the region of minima for Al is bounded for low values of 𝛼𝐹𝐴𝐹 whereas Si is not.

Figs. 6.4a and 6.4b illustrates the contour plots of Na and K errors, respectively. Both primary species tend to decrease with decreasing 𝛼_𝐹𝐴𝐹, primarily, although the concentrations of Na

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depend upon 𝛼_𝐵𝐹𝑆 as well. Because no solid phase reactions are specified for Na and K, the trends in Fig. 6.4 are a direct reflection the extent of reaction. Also shown in Fig. 6.4 are the measured availabilities of Na and K; since the availabilities are generally lower than the reacted fraction amounts, the mean error observed using available concentrations is generally lower, which suggests an omitted mechanism of alkali uptake in the thermodynamic description.

Figure 6.3: Contour plots of the mean errors in major primary species computed from comparison of model responses to pH-dependent batch leaching. The magenta rectangle

delineates the BSE-EDX measurements of 𝛼𝐵𝐹𝑆 and 𝛼𝐹𝐴𝐹 ± one standard deviation, as measured in Chapter 4. The arrow labeled “1313” corresponds to the error computed by defining

component masses with availabilities measured via Method 1313.

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Figure 6.4: Contour plots of the mean errors in alkali primary species computed from comparison of model responses to pH-dependent batch leaching. The magenta rectangle

delineates the BSE-EDX measurements of 𝛼_𝐵𝐹𝑆 and 𝛼_𝐹𝐴𝐹 ± one standard deviation, as measured in Chapter 4. The arrow labeled “1313” corresponds to the error computed by defining

component masses with availabilities measured via Method 1313.

Examination of Figs. 6.2-6.4 indicates that the region near 𝛼𝐵𝐹𝑆 = 0.83 and 𝛼𝐹𝐴𝐹 = 0.20 contains near-minimal values for the considered primary species and also lies within the

uncertainty region of measured reacted fractions. Therefore, the composition of 𝛼_𝐵𝐹𝑆= 0.83 and 𝛼_𝐹𝐴𝐹 = 0.20 was chosen as a reasonable approximation of the mass of the partial equilibrium assemblage for subsequent mass transport modeling.

The results of pH-dependent modeling and experiment for Ca, Si, Mg, and Al are depicted in Fig. 6.5. Also shown are the results of the pH dependence test using available 𝑀𝑖 measured in Method 1313. The general trends between the two methods of determining 𝑀_𝑖 are very much the same; the simulation of Mg is nearly identical between the two methods, and the predictions are within an order of magnitude of the experimental values. Al and Si are better predicted with availabilities above pH of approximately 11, and in the case of Al, the difference is nearly an order of magnitude. This result may be indicative of over-estimation of the reacted fractions in Chapter 4 in conjunction with an incongruent reaction of the FAF and BFS materials. The reacted fraction prediction of Ca solubility lies closer to the measured values, and the reason for this may be the higher Ca/Si ratio for the availability measurements.

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Figure 6.5: Experimentally measured values (gray squares) of component solubility from the Method 1313 leaching protocol and geochemical equilibrium modeling results using both availabilities (“1313”) and reacted fractions (“RF”).

Overall, neither model attains the full range of measured pH values as a result of acid and base addition, but the agreement between model and prediction is fairly good in the vicinity of the own pH of SVC. It is anticipated that the development of a C-A-S-H solid solution model may greatly improve the description of both Al and Si, as the ad hoc approach to mimic C-A-S-H stoichiometry resulted in improved model predictions.

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