Abstract
Recently, we developed a population balance framework describing the precipitation of calcium-silicate-hydrate, a key nanomaterial in the construction industry and with potential applications in biomedicine, environmental remediation, and catalysis. In this article, we first refine our computational workflow by developing a more efficient and robust method for the solution of the moment-transformed population balance equations. Then, we generalize our framework by coupling to PHREEQC, a widely used open-source speciation solver, to enhance the adaptability of the framework to new systems. Using this improved computational model, we perform global uncertainty/sensitivity analysis (UA/SA) to understand the effect of variations in the model parameters and experimental conditions on the properties of the product. With the specific surface area of particles as an example, we show that UA/SA identifies the factors whose control would allow a fine-tuning of the desired properties. This general approach can be transferred to other nanoparticle synthesis schemes as well.
Highlights
Calcium‐silicate‐hydrate (CaO‐SiO2‐H2O or C‐S‐H for short) is the most important phase formed during the hydration of cementitious materials [1]
We demonstrate the key influence of reagent addition rate, in a well‐mixed semi‐batch reactor, on the accessible specific surface area of the final product
SSACrystallite is calculated from the zeroth moment of crystallite size distribution and while we can estimate SSAParticle from and
Summary
Calcium‐silicate‐hydrate (CaO‐SiO2‐H2O or C‐S‐H for short) is the most important phase formed during the hydration of cementitious materials [1]. We give a detailed derivation of DQMOM and relevant subtleties critical to the robust and reliable performance of the method Having this improved simulation framework, we assess the behavior of the C‐S‐H precipitation model by applying global uncertainty/sensitivity analysis (UA/SA) with different model parameters as the source of uncertainty. The propagation of uncertainty into different model outputs such as crystallite dimensions, particle edge length, specific surface areas, and precipitation yield is examined thoroughly using three different methods, namely, PAWN (derived from the developers names, Pianosi and Wagener) [16,17], Elementary Effect Test [18,19], and variance‐based sensitivity analysis (VBSA) [19,20] The application of these complementary methods enables unambiguous appraisal of the model performance, which in turn facilitates complexity reduction, i.e., by fixing uninfluential parameters to reasonable values. This can be further compounded with adjustments in the solution chemistry to obtain a product with distinctly higher specific surface area
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