Adsorption equilibrium models: Computation of confidence regions of parameter estimates

Tolazzi, Natália; Steffani, Evandro; Barbosa-Coutinho, Elisa; Júnior, João Baptista Severo; Pinto, José Carlos; Schwaab, Marcio

doi:10.1016/j.cherd.2018.08.027

Cited by 18 publications

(15 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This approximation is valid when comparing the measurement variance for the three experiments (Exp4, Exp5, and Exp6) that represent replications (details in Section ). The parameter covariance matrix V θ ( P × P ) is then given by , bold-italicV θ = s normalR 2 false( bold-italicB normalT bold-italicB false) − 1 where B is the sensitivity matrix of dimension ( N × P ). The matrix B was obtained as a block matrix with N e sensitivity matrices B e of dimension ( K e N y × P ). bold-italicB = [ lefttrue B 1 B 2 ⋮ B N e ] bold-italicB e = ∂ bold-italicy e ∂ bold-italicθ where y e is the vector that contains all k discrete time points of all measured variables for a calibration experiment e bold-italicy e = false{ y false( 1 , k false) , 0.25em y false( 2 , k false) , ··· , 0.25em y false( N <...…”

Section: Population Balance Modelingmentioning

confidence: 99%

Modeling and Predictive Control of Cooling Crystallization of Potassium Sulfate by Dynamic Image Analysis: Exploring Phenomenological and Machine Learning Approaches

Moraes

Lima

Lage

et al. 2023

Ind. Eng. Chem. Res.

View full text Add to dashboard Cite

Representative mathematical modeling is essential for understanding the batch cooling crystallization processes. Efficient process design and operation are relevant to achieving high-quality criteria and minimizing variation between batches. This work first presents the modeling of batch cooling crystallization based on online dynamic image analysis. A flow-through microscope was used to track the temporal evolution of the crystal population. A population balance modeling (PBM) approach, parameter estimation, and validation were obtained for the batch cooling crystallization of potassium sulfate in water. The performed experiments provided new experimental data, giving dynamic information about the crystal size throughout each run. The kinetic model parameters for crystal nucleation and growth were estimated using a hybrid optimization algorithm, followed by the confidence region construction using a more exploratory particle swarm algorithm. In the parameter estimation framework, in addition to solute concentration, the first fourth-order moments computed throughout all experiments were included in the objective function. A linear size-dependent growth rate was found to capture well the dynamics of the potassium sulfate crystal size distribution. The experimental results evidenced that the crystal shape of potassium sulfate is predominantly constant, allowing the adequacy of the developed model. The validated PBM was also employed as a digital twin of the crystallization process to develop a machine-learning-based control for the process. Then, a surrogate model based on a recurrent neural network, called an echo state network (ESN), was applied in a nonlinear model predictive controller approach (ESN-NMPC). The ESN model could predict the moments of the population balance model up to five steps (5 min) forward. The ESN-NMPC achieved the desired control scenarios for the crystal size and its coefficient of variation. Its performance was comparable to the controller that uses the PBM as the internal model (PB-NMPC).

show abstract

Section: Population Balance Modelingmentioning

confidence: 99%

Modeling and Predictive Control of Cooling Crystallization of Potassium Sulfate by Dynamic Image Analysis: Exploring Phenomenological and Machine Learning Approaches

Moraes

Lima

Lage

et al. 2023

Ind. Eng. Chem. Res.

View full text Add to dashboard Cite

show abstract

“…On the other hand, when we are dealing with complex nonlinear problems with multiple optima (as in the case of surface complexation model fitting), the assumption that the confidence region is an ellipsoid is obviously very far from reality because these regions could be not only nonelliptical but even unbounded, nonconvex and composed of unconnected parts. In this case, likelihood confidence regions could be used as a more accurate representation of obtained solution uncertainty (Schwaab et al, 2008;Tolazzi et al, 2018).…”

Section: Figurementioning

confidence: 99%

U(VI), Np(V), Eu(III) sorption on goethite: A wide-ranging multiradionuclide dataset and uncertainty-aware parametrization of surface complexation models

Romanchuk¹,

Svitelman²,

Blinov³

et al. 2022

Front. Nucl. Eng.

View full text Add to dashboard Cite

Obtaining reliable thermodynamic sorption data is essential for establishing databases that can be used for the numerical safety evaluations of radioactive waste storage and disposal facilities. For this purpose, new experimental data on the sorption of U(VI), Np(V), and Eu(III) onto synthesized goethite in a wide range of experimental conditions were collected. Thermodynamic surface complexation models based on different approaches were developed and parametrized to fit a large dataset, including experimental data from the current work as well as available literature data. The proposed heuristic optimization procedure allowed identifying and comparing different parametrization variants and their uncertainties for considered models. The developed models pass the test on additional Cd(II) and Zn(II) data, simultaneously providing a reliable description of the sorption process for five cations and could probably be extended using the obtained linear free energy relationship.

show abstract

“…greater than or close to 0.9. Redlich-Peterson model combines elements of the Langmuir and Freundlich models, so that in low concentrations it follows the Langmuir model and in high concentrations it follows Freundlich model [32]. However, when the value of β is close to 1, the parameters qm and KR are reduced to the parameters qm and K L of Langmuir [32].…”

Section: Adsorption Isothermsmentioning

confidence: 99%

“…Redlich-Peterson model combines elements of the Langmuir and Freundlich models, so that in low concentrations it follows the Langmuir model and in high concentrations it follows Freundlich model [32]. However, when the value of β is close to 1, the parameters qm and KR are reduced to the parameters qm and K L of Langmuir [32]. Another interpretation that can be adopted is that the R-P model indicates a Freundlich isotherm when the constants KR and a R >>1 and β =1 [33].…”

Section: Adsorption Isothermsmentioning

confidence: 99%

Tannery wastes-derived gelatin and carbon nanotubes composite beads: adsorption and reuse studies using tartrazine yellow dye

et al. 2022

View full text Add to dashboard Cite

Tartrazine yellow is a dye commonly used in the food, textile, cosmetic and pharmaceutical industries. The effluents generated containing this contaminant must be treated since it presents potential carcinogenicity to the cells. The adsorption stands out among the other techniques used to remove dye from wastewater due to its ease of operation and implementation, and high removal rate. However, the production of effective and low-cost adsorbents is a constant challenge. Gelatin is a promising compound for the production of adsorbent composites, enabling the improvement of its low mechanical properties and accelerated degradation, by the addition of carbonaceous, such as carbon nanotubes (CNT's). Taking into account economic and environmental aspects, gelatin can be recovered from chromium-tanned leather wastes (RCTLW). Thus, this work aimed to study the adsorption of the tartrazine yellow dye by adsorbent composites based on:(1) commercial gelatin/CNT's beads and (2) RCTLW gelatin/CNT's beads. Commercial and RCTLW gelatin composite beads showed an adsorption capacity of 202.39 and 131.32 mg.g -1 , respectively, estimated by the Langmuir model. In adsorption kinetics, the density continued to increase after 300 min for both the composite materials, with better prediction of the pseudo-first order model. In the reuse study, the commercial and RCTLW gelatin composite beads proved to be usable for up to 10 cycles, with regenerations of 45 to 68% and 45 to 61%, respectively. In general, the composite beads of gelatin showed promise for the adsorption of dyes, mainly RCTLW gelatin, since it makes possible the use and minimization of wastes.

show abstract

Adsorption equilibrium models: Computation of confidence regions of parameter estimates

Cited by 18 publications

References 31 publications

Modeling and Predictive Control of Cooling Crystallization of Potassium Sulfate by Dynamic Image Analysis: Exploring Phenomenological and Machine Learning Approaches

Modeling and Predictive Control of Cooling Crystallization of Potassium Sulfate by Dynamic Image Analysis: Exploring Phenomenological and Machine Learning Approaches

U(VI), Np(V), Eu(III) sorption on goethite: A wide-ranging multiradionuclide dataset and uncertainty-aware parametrization of surface complexation models

Tannery wastes-derived gelatin and carbon nanotubes composite beads: adsorption and reuse studies using tartrazine yellow dye

Contact Info

Product

Resources

About