Results of the LDA algorithm applied to SVC mortar with phyllosilicates in the field of. Experimentally measured and simulated tank concentrations of Al as a function of the square root of leaching time for DI, NC, MS and NS leaching.
Motivation
A good example of mechanistic-based modeling of inaccessible regimes is the prediction of the long-term performance of cementitious barriers used in nuclear waste management applications. An "externally induced aging process" is defined herein as a disturbance of the physicochemical cement-based system due to its dissimilarity with the surrounding environment.
Research Goal and Specific Objectives
In Chapter 5, the extent of reaction is used to determine the masses of the "partial equilibrium composition", that is, the mass of major constituents within the reacted portion of a blended cement system. A set of solid-phase equilibrium constants developed for the description of Portland cement systems is used together with the reacted mass to calculate the pH-dependent solubility of the same blended cement system.
IONIC TRANSPORT IN CEMENT-BASED MATERIALS
Introduction
However, what has not been clearly established is an explicit comparison of Fickian and NP. The purpose of this paper is to directly compare the Fickian and NP mass transport models in the context of a practical problem: aggressive leaching of a Portland cement.
Models and methods
- Simulation geometry
- Reactive transport model formulation
- Geochemical reaction
- Solution strategy
- Numerical method
Thus, when 𝐷𝑖 and 𝜏 are constant in time, the FD approximation of the Fickian model is a linear system. Due to the Coulombic coupling and activity terms in Eq. 2.7), numerical approximation of the NP model is somewhat more complicated than the Fickian one.
Model parameterization
- Initial and boundary conditions
- Thermodynamic constants
- Activity coefficients
- Ionic diffusion coefficient estimation
Therefore, in the present study, the values of unknown 𝐷𝑖𝑢 have been estimated empirically as a function of both the size and the charge of the unhydrated ion. All estimated values of 𝐷𝑖𝑢 for unmeasured ions are listed in Appendix C. Figure 2.2: a) Fitted linear regressions of 𝐷𝑖𝑢 values as a function of the ratio of ion charge 𝑍𝑖 to the estimated van der Waals volume.
Results and discussion
- Example 1: Comparison of Fickian and LEN transport in an inert porous medium
- Example 2: Dilute external leachant
- Example 3: Concentrated single-salt leachant
- Example 4: Concentrated multi-ionic leachant
Similarly, the peaks of Ca, Si and Al concentrations are closer to the sample surface in the Fick model. Similar to the other non-precipitating species, Cl (Fig. 2.11c) has not reached steady state in the LEN model after 280 days of leaching.
Conclusions
However, for the case of ammonium nitrate leaching, large deviations from Fickian diffusion were observed for the LEN model due to the confluence of charge-coupling phenomena and highly pH-dependent primary species solubilities. These trade-offs can have important implications for the release of trace elements, which can be effectively controlled by the chemistry and transport of major species in the LEN model. Furthermore, the differences between the Fickian and LEN models are not uniformly biased for the three leaching cases investigated herein, underscoring the possibility that any regressed value of effective Fickian diffusion coefficient may be a strong function of the conditions under which it is obtained .
SOLUTION OF THE NONLINEAR POISSON-BOLTZMANN EQUATION
Introduction
Observations of different cation/anion diffusivities coupled with the measurement of significantly high membrane potentials and zeta potentials in cementitious materials and their constituent phases led Chatterji and Kawamura [88, 92] to suggest the electrical double layer (EDL). as the underlying cause of different diffusivat ions and to propose a qualitative description of the process. Quantitative descriptions of EDL theory have their roots in the early 20th century [93–95], and since then, numerous investigations have aimed to illuminate the bilayer manifestations in various materials. The PBE solutions are then used to determine 1) the degree of divergence of the linear and nonlinear solutions for expected conditions in cementitious materials and 2) whether the effect of EDL on diffusion may be significant for the relevant range of pore sizes encountered. in cement materials.
Experimental Methods
- Sample preparation
- Pore water expression
- Porosimetry
Nitrogen adsorption/desorption experiments were performed on vacuum-dried samples using a Micromeritics ASAP (Accelerated Surface Area and Porosimetry System) 2010. Pore size distribution and pore volume with pore diameters between 2 and 600 nm were calculated using BJH (Barret, Joyner , and Halenda), used for both adsorption and desorption isotherms. An estimate of the specific surface area was also made using the Brunauer-Emmett-Teller theory applied to the nitrogen adsorption isotherm [108].
EDL modeling
3.4) is by far the most common version of the PBE; However, electrophoretic measurements of hydrated cement and its constituent solid phases indicate that the magnitude of the electrokinetic (zeta) potential (which we assume approximates the potential of the Helmholtz level, 𝜓𝛿) for cement is typically in the order of tens of millivolts, in in which case the exponential terms may not be neglected [89, 92]. The value of potential at given node, 𝜓0, is expressed as a function of the values of 𝜓 at the nearest neighboring nodes, the constant term and the power series of 𝜉. Once satisfactory convergence of the solution is obtained, the concentration of any particular ion can be calculated from the Boltzmann distribution.
Results and Discussion
- Porewater concentrations
- Porosimetry
- EDL Modeling
- Academic examples
- Application to blended cement mortar
- Interpretation of diffusion cell experiments
A number of observations are apparent from the comparison of the full nonlinear PBE solution for the three cases, shown in Fig. If the pore diameter is small enough relative to the thickness of the EDL, anions will be excluded from the pore. This Nernst-Planck formulation, however, neglects the accompanying change in potential gradient in the presence of a concentration gradient.
Conclusions
BACKSCATTERED ELECTRON MICROSCOPY AND ENERGY DISPERSIVE X-
Introduction
Creating particle regions in this way provides both spatial and compositional correlation between pixels in a given region. Therefore, all pixels within a region are assumed to be samples of a single underlying mean composition, effectively increasing the total number of X-rays, thus the precision associated with a single composition measurement. The slag and fly ash particles used in this study, however, present a challenge as there are currently no archetypes for the composition of these particles.
Materials and experimental methods
- Sample preparation
- Scanning and processing
- Sources of experimental uncertainty
Furthermore, as will be discussed in the next section, the resolution of the electron beam itself is on the order of 1 μm. The darker regions of each histogram to the left of the diameter on the x-axis indicate the fraction of particles smaller than the nominal diameter of the probe at the corresponding value. With an estimate of the approximate diameter of the interaction volume, the fractions of anhydrous particles smaller than the probe volume (and necessarily on average the partial volume) can be calculated from the particle size distributions of isolated, unreacted binding particles, measured by laser diffraction [138].
![Table 4.2: Mix design of the blended cement mortar studied herein. Particle sizes were determined from information provided by [138]](https://thumb-ap.123doks.com/thumbv2/123dok/10742070.0/91.918.107.767.695.895/table-design-blended-studied-particle-determined-information-provided.webp)
Particle identification method
- Segmentation
- Anhydrous particle database – cluster analysis
- Particle classification - discriminant analysis
- Calculation of reacted fraction
According to DDLP, a candidate threshold 𝑆(𝑛) is chosen randomly; however, in this work, 𝑆(𝑛) is chosen as the threshold for which the variance of the interval. The PAVA constructs a monotonically non-decreasing estimator of the histogram interval ℎ(𝑎,𝑡), or conversely the monotonically non-increasing estimator of ℎ(𝑡+ 1,𝑏). Therefore, the goal of the segmentation algorithm developed in this work is to “divide and rule”.
Results and Discussion
- Anhydrous particle database
- Database cross-validation
- Estimation of reacted fractions
The values of cement clinker materials (C3Styp, C2Styp, C3Atyp, C4AFtyp) were not measured here, but instead correspond to typical values [162]. The results of the LDA algorithm applied to a random field of view in SVC are shown in Fig. The colors of the bars in c correspond to the coloring in b. c) Anhydrous phase fractions assigned to specific classes in the anhydrous particle database.
Conclusions
Results of the classification method applied to a realistic 30-month-old mixed cement mortar indicate very satisfactory results for the identification of blast furnace slag particles. The identification of fly ash particles is complicated by the presence of quartz and phyllosilicate minerals in the fine aggregate fraction of the mortar, which exhibit elemental compositions similar to those of fly ash. Results from three sampling sites indicate that the estimated degree of reaction for blast furnace slag is 83% with a coefficient of variation of 0.02 and for the fly ash 35.8% with a coefficient of variation of 0.27.
CHARACTERIZATION AND MODELING OF MAJOR CONSTITUENT
- Introduction
- Methods
- Material preparation
- pH-dependent leaching test
- Geochemical modeling
- Results and discussion
- Conclusions
The total elemental composition of the binder materials for the major constituents, as determined by X-ray fluorescence spectroscopy (XRF), is given in Table 5.2. After the leachate was tumbled, the pH and electrical conductivity of the leachates were measured and the leachate was vacuum filtered. The modeled solubility of Cafalls (Fig. 5.1a) within an order of magnitude of the measured values over the pH range of interest (8 The present work builds on this idea by using standard leaching protocols as a means to investigate the validity of component masses calculated from measurements of reacted fractions. The first objective of this work is to vary the range of parameters of the reacted fractions over a possible range to evaluate the sensitivity and accuracy of the partial equilibrium representation of the SVC. The second aim of the current work is to investigate the response of the thermodynamic model to chemical aging as a result of exposure to external leaching solutions. The pH point at 12.0±0.5 is obtained without the addition of acid or base and is called the "native pH" of the material. Sequential grinding and polishing with diamond paste of the exposed face, followed by 20 seconds of sonication in acetone, was performed to eliminate artificial porosity created by sawing. The NC solution was chosen as a vehicle for the formation of carbonates independent of the pH depression associated with gas phase carbonation. Because of the well-mixed assumption, the concentration 𝑝 at 𝑥= 0 is both the concentration at the surface of the porous medium and the concentration of the tank. The solid domain, that is 0≤ 𝑥 ≤ 𝑎, is divided into 21 nodes using a geometrically increasing node spacing with a minimum node spacing of 0.75 mm to meet the requirements of the local equilibrium assumption [48]. The simulation time step was set to a value of 100 s for the first three hours after refreshing the tank solution to improve the accuracy of the FD scheme; otherwise, a constant time step of three hours was used. Figure 6.2b shows a contour plot of the mean error calculated over all 100 sample points. In addition, the pH of the reservoir solution (Figure 6.9) is also relatively unchanged by the value of tortuosity. 6.13, Mg release is generally predicted to be within the magnitude of the measured value. That measured pH is typically lower than predicted may be indicative of a systematic bias in the pH measurement due to atmospheric carbonation, but an alternative hypothesis not addressed in this work is that soluble reduced sulfur species may be present in anionic form such that hydroxide concentrations are suppressed in the SVC pore water. The thermodynamic description of Al-bearing calcium silicate hydrate and a more coherent description of hydrotalcite phases have been identified as areas of research likely to lead to significant improvements in reactive transport model predictions of blended cements. Furthermore, a deeper understanding of the phenomena responsible for alkali uptake and retention may prove beneficial for the improvement of long-term performance assessment. Masses of the primary species of the three external solutions considered: deionized water Calculated equilibrium concentrations of primary species in the native Portland cement Ionic species used for estimation of unknown ionic diffusion coefficients Apparent diffusivities reported in the literature from diffusion cell experiments on Proportion of mix components Expressed pore water concentrations Results of ASTM C 642 density and water accessible porosity determination, mercury Statistics computed from the beta distribution fit to the N 2 adsorption incremental volume Major element composition of the component materials Mix design of the blended cement mortar Raw material properties of the mortar Major element composition of the binder materials Solid phases considered in the SVC assemblage Major element composition of the component materials Mix design of the blended cement mortar Equivalent base additions and resultant pH for the Method 1313 leach test![Table 5.1: Raw material properties of the mortar used in this study. Particle size information was determined from particle size information provided by [138]](https://thumb-ap.123doks.com/thumbv2/123dok/10742070.0/122.918.104.795.161.382/material-properties-particle-information-determined-particle-information-provided.webp)
REACTIVE TRANSPORT MODELING OF EXTERNALLY-INDUCED AGING OF
Introduction
Materials and methods
Reactive transport modeling
Results
Conclusions
CONCLUSIONS AND FUTURE WORK
