Shrinking Particle Model Research Articles

Fly ash treatment via conventional and microwave-assisted organic acid leaching: kinetics and life cycle assessment.

Heedless disposal of oil-based fly ash contributes to the contamination of the air, water, and soil. Acid leaching of industrial solid wastes is recognized as a versatile, cost-effective, and environmentally friendly solid waste treatment approach. The present study investigated the viability of conventional leaching (CL) and microwave-assisted leaching (MAL) of predominant heavy metals from Mazut-burnt fly ash. For this purpose, the practicality of four organic acids with various specifications (ascorbic, gluconic, citric, and oxalic acids) on the dissolution efficiency of fly ash components was examined. Utilization of oxalic acid led to achieving full V recovery, complete Fe removal, and Ni enrichment in the residue in both CL and MAL setups. The Ni content of the sample was enriched from 6% in the calcinated sample to 23.7% in the oxalic acid leaching residue. Using citric acid resulted in the co-extraction of V, Ni, and Fe with nearly 70% V, 50% Ni, and 89% Fe dissolved in CL. The dissolution efficiencies were slightly lower in MAL. Oxalic acid was selected as the most promising organic acid reagent for fly ash treatment, so its CL kinetics was studied and defined by the shrinking particle model. The model showed that the controlling steps in the leaching of V differ over time, changing from a chemical reaction before 60min to fluid film diffusion or mixing afterward. The kinetic study proved MAL as an effective technique in overcoming the leaching kinetic barriers. A life cycle assessment study was conducted to determine the environmental impacts of the proposed process. Accordingly, the MAL using oxalic acid was the most environmentally friendly process among the studied ones, and the utilization of microwaves leads to the reduction of the leaching processes' environmental impacts by decreasing the processing time.

Application of the Shrinking Particle Model for the Evaluation of Molecular Recyclability of PET versus Semi-Aromatic Polyesters

Application of the Shrinking Particle Model for the Evaluation of Molecular Recyclability of PET versus Semi-Aromatic Polyesters

Determination of the kinetic parameters of leaching from experimental data using the non-porous shrinking particle model: Effect of error propagation

All alternatives of the non-porous shrinking particle model (NSPM) referred to in the literature were reviewed and critically compared – they differ especially in their ability to reflect the role of three crucial model parameters: the order of reaction, liquid/solid ratio and activity coefficient of the leaching reagent. A procedure to calculate an experimental error related to the methodology of laboratory leaching tests (including the effect of different ore-particle size) has been proposed. Error propagation in the process of determination of the apparent order of reaction and activation energy from experimental data was analysed in detail, to estimate the systematic error of the simulation model developed. The simulation models tested were validated using the experimental data for the reaction system MgO-HCl-H2O. Based on the results obtained, some recommendations for an effective practical use of the NSPM have been suggested.

The effect of ultrasound on synthesis and energy storage mechanism of Ti3C2Tx MXene

Removal of aluminum (abbreviated to Al) accounts for the main step for synthesizing Ti3C2Tx MXene. To date, the synthesis of Ti3C2Tx MXene is hampered by the low removal efficiency of Al from Ti3AlC2. Ultrasound was therefore introduced to achieve efficient synthesis of Ti3C2Tx MXene by promoting the removal rate of Al from Ti3AlC2. It was found that ultrasonic aid can significantly boost the removal efficiency of Al. Additionally, distinct kinetics for the removal of Al was recognized as the advent of ultrasonic intervention: (i) the shrinking core model was used to describe the removal kinetics of Al in the case without ultrasound, whilst the shrinking particle model was capable for the case in presence of ultrasound; (ii) the activation energy for removal of Al with ultrasonic aid was 70.2 kJ/mol, indicating a chemical reaction-controlled process, whereas the corresponding value for the case without sonication was 28.1 kJ/mol, demonstrating a mixed kinetic feature of the removal process of Al. Morphological study showed that ultrasound can remove the surface-adhering reaction products and favors the formation of structures with flower-like morphology. The sample without sonication treatment exhibited typical capacitive behavior, whilst the contribution of diffusion-limited capacitance in addition to the capacitive behavior was readily observed for the sonication-treated sample. Surface chemistry study indicated the more prevalent oxidation of the sonication treated sample, which gave rise to a higher specific capacitance than those without sonication treatment.

Porosity and crystallinity dynamics of carbon black during internal and surface oxidation

The structure of carbon black (CB) is investigated during its oxidation by O2 at 550 and 800 °C by thermogravimetric analysis, microscopy, N2 adsorption and X-ray diffraction (XRD). That way, the dynamics of its porosity and crystallinity during surface and internal oxidation are elucidated, for the first time to the best of our knowledge. At 800 °C, oxidation takes place largely on the CB surface. This increases the CB specific surface area, SSA, from 240 to about 453 m2/g, closely following the classic shrinking particle model and hardly affects the porosity and crystallinity of CB. At 550 °C, O2 diffuses and reacts with the bulk of CB particles forming pores with radius smaller than 2 nm after 25 and 50% conversion. At higher conversions, these small pores fuse together resulting in hollow CB particles with high SSA, up to 939 m2/g. Fractal and XRD analyses of the resulting pore network reveals that internal oxidation at 550 °C reduces the interlayer distance of the crystallites constituting the CB, compacting its pore network. This increases the pore fractal dimension, Dfp, from 2.43 up to about 2.7, in good agreement with the Dfp measured during diesel soot oxidation. The dynamics of CB porosity and crystallinity quantified in detail here can assist the design of new highly porous CB grades and activated carbons as well as battery materials.

Effect of Pyrite on the Leaching Kinetics of Pitchblende in the Process of Acid In Situ Leaching of Uranium

In the process of acid in situ leaching of sandstone uranium ore, pyrite, which is a common associated mineral of pitchblende, would inevitably participate in the reaction. Therefore, it is important to study the influence of pyrite on the leaching kinetics of pitchblende. In this study, we compared the difference leaching rates of pitchblende in the systems of sulfuric acid–hydrogen peroxide, sulfuric acid–hydrogen peroxide–pyrite and sulfuric acid–pyrite and studied the influence of temperature and pyrite quantity on the leaching rate of pitchblende. The results show that the leaching process of pitchblende follows the shrinking particle model controlled by a chemical reaction, and the apparent activation energy Ea of the leaching reaction is (3.74 ± 0.40) × 10 kJ/mol. Pyrite itself cannot promote the dissolution of pitchblende; however, it can promote the leaching of pitchblende in the presence of an oxidizer. Increasing the quantity of pyrite in a certain range can increase the leaching rate of pitchblende, and the reaction order of pyrite is 0.36.

Preparation and Application of Nano-structured Lead Dioxide from Waste Lead Slag

To develop an efficient and green method to recycling lead slag, a novel strategy to fabricate nano-lead dioxide from lead slag was applied by the hydro-electrometallurgy. In leaching system, the optimum condition of leaching time 100 min, 80 °C, stirring rate 500 rpm, liquid/solid ratio 20 and 1 mol/L methanesulfonic acid resulted in lead recovery of 89% and residue obtained without toxicity. The kinetic study revealed that the methanesulfonic acid leaching of lead slag shows good agreement with a diffusion-controlled shrinking-particle model. Additionally, the apparent activation energy of MSA leaching of lead slag was determined using Arrhenius model as 13.621 kJ/mol. Furthermore, Nano-PbO2 recovered from waste lead paste was prepared for the electrolysis of water to produce ozone. The experimental results showed that the ozone production of nano-PbO2 recovered from waste lead slag was not significantly different from the nano-PbO2 prepared by pure reagents. In conclusion, waste lead slag can be recycled for the fabrication of nano-PbO2, which has a significant advantage on realizing the recycling of lead resources.

A Kinetic Study of Manganese Leaching from Low-Grade Psilomelane Ore by Acetic-Tannic Acid Lixiviant

Kinetic leaching of psilomelane using tannic acid as reductant and acetic acid as an acidic modifier is investigated in terms of tannic acid and acetic acid concentration, solid-liquid ratio, particle size and temperature. Kinetic modelling using three models: shrinking core, shrinking particle, and diffusion-interface transfer model revealed that at room temperature leaching (30 °C), experimental data are best modelled using diffusion-interface transfer model, indicating the dissolution of Mn is more affected by reaction rate among reactants and their concentration in bulk volume rather than by transfer across the boundary layer. At higher temperatures (≥ 50 °C), the shrinking particle model fits the experimental data best, suggesting the prominence of the diffusion process boundary layer. The apparent activation energy obtained at two temperatures were 13.1 and 52.7 kJ/mol for lower and higher temperatures. Plot between rate constant and concentration yields reaction order to be 1.28 for tannic acid and 0.73 for acetic acid. A semi-empirical model for each temperature range is proposed to describe the overall manganese leaching efficiency.

Numerical Experimentation and Validation of Shrinking Particle - Gas Reaction in a Pilot Plant Downer Reactor

ABSTRACT Downer reactors have been the choice for catalytic reactions necessitating control on intermediates, short residence time and high solid loading. The noncatalytic gas-solid reactions exhibit different hydrodynamics due to continuous variation of particle morphology during the reaction. This study addresses the challenges with numerical experimentation of reactive gas-solid system possessing shrinking particle characteristics and verification with the results from pilot scale test facility. Petcoke with ash content about 0.322% by weight is selected to justify the shrinking particle characteristics during combustion. The particle size ranges from 2 µm to 130 µm with an average size of 60 µm. The powder is cohesive with Hausner ratio of 1.43 and occupies cohesive regime in the Geldart’s classification. Ansys Fluent v19.0R1 is employed in simulating the reaction with a shrinking particle model and the kinetic parameters deduced with the help of TGA has been incorporated in the numerical model as well. The optimum multiphase interaction parameters using numerical experiments established with coupled CFD-RSM method also been included. The simulation tests are conducted for the same experimental conditions with the pilot plant test facility. The temperature profile and concentration profile are obtained for different solid/gas loading ratios and compared with the experimental data obtained with the pilot plant test facility. The study establishes the significance of appropriate drag models along with the interacting parameters for reliable and robust simulation. The simulation model presented here can be used for design and analysis of the performance of a downer reactor for reactive systems with shrinking particle characteristics.

Single-Particle Hyperspectral Imaging Reveals Kinetics of Silver Ion Leaching from Alloy Nanoparticles

Gold-silver alloy nanoparticles are have attracted attention for multiple applications, including heterogeneous catalysis, optical sensing, and antimicrobial properties. The inert element gold can act as a stabilizer for silver to prevent particle corrosion to slow down silver ion leaching and increase the durability of plasmonic alloy nanoparticles in sensing or catalytic applications. On the other hand, intentional release of antimicrobial silver ions has been used to fight infections caused by bacteria. Understanding silver ion leaching from gold-silver alloy nanoparticles is a therefore prerequisite to designing alloy nanoparticles with either unintended or intended corrosion. However, little is known about the mechanism and kinetics of silver ion leaching from bimetallic gold-silver nanoparticles and how it is correlated with particle size and silver content, especially not on a single-particle level. To characterize the kinetics of silver ion release from gold-silver alloy nanoparticles, we employed a combination of electron microscopy and single-particle hyperspectral imaging with an acquisition speed fast enough to capture silver ion leaching for a statistically relevant number of individual nanoparticles. Our studies confirmed a reduction in corrosion rate due to the alloying with as little as 10-20 mole% gold. Single-particle leaching profiles revealed two leaching stages, with a large heterogeneity in rate constants. We modelled the initial leaching stage with a shrinking-particle model with a rate constant that exponentially depends on the silver mole fraction. The second, slower leaching stage is controlled by diffusion of silver atoms through a passivating gold rich lattice, and a change in electrochemical potential of the nanoparticle. Individual nanoparticles with similar sizes and compositions exhibited completely different dealloying yields. Most nanoparticles released silver completely, but 25% of them appeared to arrest corrosion. Calculations of average size together with SEM revealed that nanoparticles became slightly porous. Our findings suggest that alloy nanoparticles, produced by scalable laser ablation in liquid, together with kinetic studies of silver ion leaching, provide an approach to selectively design the durability or anti-microbial bioactivity of alloy nanoparticles. Figure 1

Image analysis data for the study of the reactivity of the phases in Nd-Fe-B magnets etched with HCl-saturated Cyphos IL 101.

Three phases can be distinguished in Nd‒Fe‒B permanent magnets: a Nd2Fe14B matrix grain phase, a Nd-rich grain boundary phase and a Nd-oxide phases. Common reaction models for leaching, such as the shrinking-particle model, cannot simply be applied to composite Nd‒Fe‒B permanent magnets because of the different chemical reactivities of the crystalline phases mentioned above. Etching the surface of a Nd‒Fe‒B magnet to expose its microstructure to electron microscopy is a necessary practice to correlate the microstructure itself to the specific properties of the magnets. Aqueous solutions of mineral acids are often used for etching purposes. However, these solutions are too low viscous to easily control the etching front and they show little selectivity in the etching process. In our work, the ionic liquid Cyphos IL 101 was used to etch bulk magnets instead of aqueous HCl solutions. The bulk Nd‒Fe‒B magnets were first polished, then exposed to a solution of 3 M HCl in Cyphos IL 101 for different times and at different temperatures. Afterwards, the etched Nd‒Fe‒B magnets were washed with ethanol and acetone. The results were examined via scanning-electron microscopy and image analysis. A commercial software, ImageJ®, was employed for image analysis. The latter technique was used to correlate the etched area (%area) or the grain and oxide size to the etching temperature or the etching time. The grain or the oxide size were calculated as Feret diameter. Image analysis revealed to be a necessary tool to support and correct the findings first suggested by the simple scanning-electron microscopy. The data presented in this article might be reused to corroborate a new reactivity order of the three Nd‒Fe‒B phases, different from that traditionally reported in literature, which is – from the most to the least reactive – grain boundary > oxides > the Nd2Fe14B grain phase.

Generalized shrinking particle model of leaching: Effect of the order of surface chemical reaction, liquid-to-solid ratio and non-ideal behaviour of the liquid phase

A generalized non-porous shrinking particle model (G NSPM) of leaching has been verified and used for numerical simulations. Unlike the commonly used “simple” non-porous shrinking particle model (S NSPM), the G NSPM assumes n−th order chemical reaction, the influence of the L/S ratio and non-ideal behaviour of the leach solution. The leaching of dead-burned magnesite with hydrochloric acid has been chosen to verify the proposed mathematical model, as the (apparent) reaction order for HCl, n, may be both positive and negative, depending on the HCl concentration.Comparison of the simulations with experiments revealed that the S NSPM does not reflect the qualitatively different leaching behaviour at positive and negative n, especially at near-to-stoichiometric HCl/MgO ratio. The G NSPM reflects the effect of n not only qualitatively, but also with acceptable accuracy. At the stoichiometric HCl/MgO ratio, the mean squared error of the predictions obtained using the S NSPM was 100–130 rel. % as compared to those provided by the G NSPM.The common effect of the reaction order, n, L/S ratio (represented by the reduced HCl/MgO molar ratio, ϕ) and non-ideal behaviour of the acid were studied in detail by means of numerical simulations. The values of parameters n and ϕ can alter the leaching behaviour qualitatively. In contrast, the activity coefficient of HCl only slightly modifies the shape of the kinetic curves, but does not change the overall picture. The error of the time for complete conversion of MgO calculated using the S NSPM can reach more than 100 rel. % for n = − 0.5 and even up to several hundred rel. % for n = 1, because the conversion vs. time curves predicted by the G NSPM are markedly skewed towards longer leaching times.

Effect of a thermal pretreatment on dissolution kinetics of a limonitic laterite ore in chloride media

The effect of a thermal pretreatment on the kinetic parameters and rate-controlling step for nickel leaching dissolution in hydrochloric acid‑sodium chloride solutions from a low – grade Colombian nickel laterite (1.15% Ni, 0.12% Co and 41.1% Fe), was evaluated. The mineralogical analysis showed that nickel is associated with iron in the form of hematite (Fe2O3) and goethite (FeOOH) within the calcined and uncalcined ore, respectively. The hydrochloric acid and total chloride ions concentrations, as well as the leaching temperature, were shown to have a direct effect on nickel extraction. The experiments showed that ~92% of nickel can be dissolved after only 25 min in a 3 M HCl and 2 M NaCl solution when the leaching temperature was increased to 60 °C, after the sample had been previously calcined at 430 °C for 1 h. Nickel dissolution can be described by the chemical reaction-controlled shrinking particle model for both the calcined and uncalcined sample with apparent activation energies of 98 kJ/mol and 103 kJ/mol, respectively. This result suggests that a thermal pretreatment stage does not affect the nickel reaction mechanism, although it may liberate the nickel within the laterite structure.

The kinetics of Indonesian galena concentrate leaching in fluorosilicic acid and hydrogen peroxide as its oxidants

Lead smelting is known as a lead extraction technique which has negative impact to environment because it produces emissions of dust, SO 2 gas and lead. The leaching is conducted to reduce the smelting’s weaknesses by extracting the lead without damaging the environment. This technique, often called hydrometallurgical lead extraction, uses liquid media to extract the lead and separate it from the elemental sulphur (S 0 ) by filtration. Particle size, slurry density (solid percentage) and acid concentration affect the dissolution of Indonesian galena concentrate with fluorosilicic acid and hydrogen peroxide as oxidants. By means of these reagents, it is expected that the Pb extraction process from galena concentrate resulted from flotation of sulfide ore can be carried out at low temperatures and lead recovery can be accomplished from the leach solution by electrowining. Studying galena leaching kinetics is required to perform galena leaching with high Pb extraction percentages. Two kinetics models are commonly used to study leaching kinetics, namely shrinking core model (SCM) and shrinking particle model (SPM). These models are used to determine the mechanism which controls leach reaction and reaction rate constant or diffusion constant of the reacting species. Total plotting of sulfide fraction dissolves with time adjusted to the existing mathematical model, and fitting the curve from the dummy model to the experimental data, are two techniques that are utilized to obtain the best kinetics model which important in controlling the leaching reaction rate. Applying the Arrhenius equation, the relation of the reaction rate constant or the diffusion constant and the temperature is determined to calculate the leaching activation energy. The result from kinetics analysis showed that the leaching of Indonesian galena concentrate in fluorosilicic acid with hydrogen peroxide as oxidants followed the shrinking core model with diffusion through porous solid product layer as the reaction controller with activation energy of 45.81 kJ/mol or 10.91 kcal/mol.

Numerical Simulation of Soil Shrinkage by Using Cohesive Shrinking Particle Model

Numerical Simulation of Soil Shrinkage by Using Cohesive Shrinking Particle Model

Water chemistry influences on long-term dissolution kinetics of CdSe/ZnS quantum dots

Widespread usage of engineered metallic quantum dots (QDs) within consumer products has evoked a need to assess their fate within environmental systems. QDs are mixed-metal nanocrystals that often include Cd2+ which poses a health risk as a nanocrystal or when leached into water. The goal of this work is to study the long-term metal cation leaching behavior and the factors affecting the dissolution processes of mercaptopropionic acid (MPA) capped CdSe/ZnS QDs in aphotic conditions. QD suspensions were prepared in different water conditions, and release of Zn2+ and Cd2+ cations were monitored over time by size exclusion chromatography-inductively coupled plasma-mass spectrometry. In most conditions with dissolved O2 present, the ZnS shell degraded fairly rapidly over ~1 week, while some of the CdSe core remained up to 80 days. Additional MPA, Zn2+, and Cd2+ temporarily delayed dissolution, indicating a moderate role for capping agent detachment and mineral solubility. The presence of H2O2 and the ligand ethylenediaminetetraacetate accelerated dissolution, while NOM had no kinetic effect. No dissolution of CdSe core was observed when O2 was absent or when QDs formed aggregates at higher concentrations with O2 present. The shrinking particle model with product layer diffusion control best describes Zn2+ and Cd2+ dissolution kinetics. The longevity of QDs in their nanocrystal form appears to be partly controlled by environmental conditions, with anoxic, aphotic environments preserving the core mineral phase, and oxidants or complexing ligands promoting shell and core mineral dissolution.

Non-porous shrinking particle model of leaching at low liquid-to-solid ratio

A generalized non-porous shrinking particle model (NSPM) of leaching is proposed, which - unlike commonly used “simplified” mathematical models - takes into account the influence of the L/S ratio (by means of the so-called reduced A/B molar ratio, ϕ, which indicates how many times the leaching agent (A)-to-valuable substance (B) molar ratio actually used exceeds its stoichiometric value) and non-ideal behaviour of concentrated lixiviants. Moreover, n-th order chemical reaction with power-law kinetics is considered, which makes determination of the rate-determining step of the overall process more reliable.Correlation between the proposed model and experiment was tested using the hydrochloric acid leaching of dead-burned magnesite, which provides the opportunity to experimentally verify how the mathematical model fits the leaching data for both the positive and negative reaction order. Calculated values of the reaction order for HCl, n, different from unity (n = 0.28 and n = −0.23 obtained for low (0.20–1.03 M) and high HCl concentrations (2.06–3.83 M), respectively), together with relatively high values of the activation energy (57.5 J mol−1 and 56.6 J mol−1) indicate that the leaching rate is controlled by the intrinsic chemical reaction under the conditions considered in the present work. Simulations made using the calculated values of the parameters have shown that the proposed generalized NSPM model clearly reflects two most important experimental facts: (a) L/S ratio affects the leaching process; and (b) qualitatively different leaching behaviour has been observed for the positive and negative reaction order. Unlike the simplified NSPM model, the generalized model describes the leaching process quantitatively in the whole range of the parameter ϕ, for both n > 0 and n < 0. The simplified NSPM (which does not take into account the L/S ratio) describes the leaching process with sufficient accuracy when ϕ ≥ 10, but at ϕ < 10 the error grows exponentially with decreasing ϕ and can reach up to 11–17% rel. under the stoichiometric conditions (i.e., at ϕ = 1), in dependence on the value of n. It is assumed that the proposed generalized NSPM model provides a useful tool for planning kinetic experiments, identifying the kinetic model parameters and simulation of the leaching process even under stoichiometric conditions.

Direct sulfuric acid leaching of zinc sulfide concentrate using ozone as oxidant under atmospheric pressure

The use of ozone as an oxidant for the direct leaching of zinc sulfide (sphalerite) concentrate in sulfuric acid medium under atmospheric pressure was explored. The influence of acid concentration, feed gas injection rate, particle size distribution, stirring speed, temperature and slurry density on zinc extraction efficiency was examined. The experimental results showed that the leaching efficiency depends on all of these operating parameters except for stirring speed. It was found that essentially complete dissolution of zinc from the concentrate with the present method can be achieved in only about seven hours under the conditions of sulfuric acid concentration of 2 mol/L, particle size smaller than 74 µm, slurry density of 50 g/L, stirring speed of 420 rpm and feed gas injection rate of 1 L/min at ambient temperature. The experimental results suggest that the dissolution reactions produce independent elemental sulfur that is readily floated and can be easily separated rather than forming a layer on the surface of the reacted particle, as usually observed in a system with ferric-sulfate as oxidizing agent. It was therefore determined that the dissolved ozone play a key role in improving the rate of zinc dissolution from the concentrate. Analysis of the leaching kinetics indicate that the leaching rate follows the shrinking particle model, and the overall dissolution rate of zinc is controlled by a surface reaction.

Parameters estimation and model discrimination for solid-liquid reactions in batch processes

Process optimization and control rely highly on system modeling. A reliable model must be formulated with estimable parameters in order to closely predict system behavior in the operating domain. This paper focuses on the modeling and parameter estimation of organic solid-liquid reactions in batch reactors with limited lab-scale experimental data and industrial-scale plant data. Two possible mechanisms, shrinking particle model and dissolution model, are reviewed. A uniform dynamic model with a model indicating factor and several lumped parameters is developed for both mechanisms. A Bayesian estimation procedure is discussed and implemented to select an estimable parameter set, simplify the system model, obtain prior information and determine posterior parameter values. The quality of estimation results is analyzed and enhanced by examining the parameter covariance matrix at the optimal point. In the case of multiple candidate process models, model discrimination is then performed to choose the best representative one by comparing posterior probability shares. Finally, the selected model is validated and tested.This work has been selected by the Editors as a Featured Cover Article for this issue.

Development of a diffusion-limited shrinking particle model of cellulose dissolution in a carbon dioxide switchable system

A diffusion-limited shrinking spherical particle model was developed to describe cellulose dissolution in carbon dioxide switchable system (CO2-SWS) by assuming an instantaneous reaction of the CO2-SWS on the cellulose surface. CO2, the main precursor of the SWS, was mixed with 1,8-diazabicyclo [5.4.0] undec-7-ene, ethylene glycol and dimethyl sulfoxide under various operating pressures (P) and temperatures (T) to yield a CO2 switchable ionic liquid for cellulose dissolution. As dissolution proceeded, the cellulose particle radius decreased because of the disappearance of cellulose. The model–predicted diffusion coefficient (D), completed dissolution time (τ), and dissolution conversion (XC) were determined under various CO2-SWS operating conditions. The predicted τ and XC values were in good agreement with the observed results. The influence of the CO2-SWS operating conditions on the predicted numerical D, τ, and XC values were investigated using Spearman’s rho correlation. The results showed that the D values ranged from 10−20 to 10−17 m2 s−1 for the CO2-SWS–cellulose system depending on the system conditions.