Low‐dimensional models for real time simulations of catalytic monoliths

Joshi, Saurabh Y.; Harold, Michael P.; Balakotaiah, Vemuri

doi:10.1002/aic.11794

Cited by 57 publications

(29 citation statements)

References 22 publications

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“…The reference [6] describes one possible assumption in which the effectiveness factor for a single species is applied throughout. & An alternative use of the Thiele modulus which avoids effectiveness factors is to generate an "internal mass transfer coefficient" as developed in a series of papers partially represented by [7][8][9][10]. In very simple terms, this approach approximates the effect of washcoat diffusion within the given reaction-diffusion problem with that of a simpler linear problem at the extremes of Thiele modulus and posits a smooth transition between the extremes [8].…”

Section: Comparison With Thiele Modulusmentioning

confidence: 99%

“…The species rates are considered averages for use in Eq. (9). Beyond these approximations, there is a more subtle but important assumption made in this approach at the key step when the average rate is replaced with the rate of the average, Eq.…”

Section: Comparison With Thiele Modulusmentioning

confidence: 99%

“…Without ‖D inv ‖≪1, this result requires an additional assumption at best when working with internal mass transfer coefficients, and is highly questionable for the rapidly-varying washcoat profiles of large Thiele modulus at worst. In the cited papers for example, the spatially variations of the concentrations are assumed small compared to their averages without further comment in [9] and [10]. In [8], the equivalent of the second-order terms of Eq.…”

Section: Comparison With Thiele Modulusmentioning

confidence: 99%

“…(12) are ignored as higher order. The small parameter that would represent the magnitude of these higher-order terms is not explicit, but we may assume the author either refers to the same argument as [9] and [10], or that the small parameter is the perturbation parameter of [7], which is equivalent to ‖D inv ‖. In any case, we believe that there is no general argument that allows replacing the average rate with the rate of the average in a nonlinear setting that does not rely upon approximately flat profiles.…”

Section: Comparison With Thiele Modulusmentioning

confidence: 99%

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An Asymptotic Solution for Washcoat Pore Diffusion in Catalytic Monoliths

Bissett

2015

Emiss. Control Sci. Technol.

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When modeling monolithic exhaust aftertreatment reactors, washcoat pore diffusion resistance is often neglected with satisfactory results, but interest in the effect remains, especially for dual layer catalysts where the intention is to explicitly exploit the effect, for example, to enhance selectivity. To bring analyses that include washcoat pore diffusion resistance into convenient and everyday usage, an asymptotic solution based on small dimensionless washcoat pore diffusion resistance is derived and presented herein. When this solution is integrated within a common formulation for modeling monolithic exhaust aftertreatment reactors, it solves the leading-order reaction-diffusion equations within the washcoat analytically so the computational burden associated with discretizing and numerically solving along the washcoat thickness dimension is avoided. No further ad hoc approximations are required; in particular, the full complexity and nonlinearity of the reaction system is preserved. Catalytic surface coverages and dual layer catalysts are included. The method can be implemented in a manner that generalizes but is similar to the more standard solution method for no pore diffusion resistance. Although the asymptotic solution cannot substitute for the full solution in all cases, we argue that this asymptotic regime includes the most practical applications. Vector of scaled mass fractions of channel gas

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Section: Comparison With Thiele Modulusmentioning

confidence: 99%

Section: Comparison With Thiele Modulusmentioning

confidence: 99%

Section: Comparison With Thiele Modulusmentioning

confidence: 99%

Section: Comparison With Thiele Modulusmentioning

confidence: 99%

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An Asymptotic Solution for Washcoat Pore Diffusion in Catalytic Monoliths

Bissett

2015

Emiss. Control Sci. Technol.

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“…As evidenced by many of these effective approximations, there are always pros and cons for such approximations. Sometimes, approximation is only the way to simulate 43 and, sometimes, approximation is necessitated by the availability of software and codes. Nevertheless, the approximations had always been validated by comparing with the full-order model and/or experimental data.…”

mentioning

confidence: 99%

Data Science Approaches for Electrochemical Engineers: An Introduction through Surrogate Model Development for Lithium-Ion Batteries

Dawson-Elli

Lee

Pathak

et al. 2018

J. Electrochem. Soc.

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Data science, hailed as the fourth paradigm of science, is a rapidly growing field which has served to revolutionize the fields of bio-informatics and climate science and can provide significant speed improvements in the discovery of new materials, mechanisms, and simulations. Data science techniques are often used to analyze and predict experimental data, but they can also be used with simulated data to create surrogate models. Chief among the data science techniques in this application is machine learning (ML), which is an effective means for creating a predictive relationship between input and output vector pairs. Physics-based battery models, like the comprehensive pseudo-two-dimensional (P2D) model, offer increased physical insight, increased predictability, and an opportunity for optimization of battery performance which is not possible with equivalent circuit (EC) models. In this work, ML-based surrogate models are created and analyzed for accuracy and execution time. Decision trees (DTs), random forests (RFs), and gradient boosted machines (GBMs) are shown to offer trade-offs between training time, execution time, and accuracy. Their ability to predict the dynamic behavior of the physics-based model are examined and the corresponding execution times are extremely encouraging for use in time-critical applications while still maintaining very high (∼99%) accuracy. Data science, also known as data-intensive scientific discovery, is hailed as the fourth paradigm of science.1 A field focused on extracting knowledge or understanding from data, it includes the subdomains of machine learning, classification, data mining, databases, and data visualization. In the age of internet-scale data, these techniques are not only powerful, but also necessary to extract the signal from the noise and to have the throughput to do so in a reasonable amount of time. It has revolutionized the fields of bio-informatics, climate science, word recognition, advertising, medicine, and is finding more applications daily. In Google's Translate application, substantial improvements over previous methods were achieved using artificial neural network (ANN) structures, making 60% fewer errors than the previous state-ofthe-art algorithm.2 In climate science, where models are sophisticated and numerous, data science techniques are used to determine which of 20 models will give the best prediction on future and historical data, the accuracy of which surpasses the accuracy of the average of all models, the current benchmark.3 As chemical engineers are increasingly tasked with the analysis of more complex data sets, these same data science tools which have revolutionized other fields become more relevant. 4 When data sets grow, they must be managed intentionally in order to be useful. Data management, a subfield of data science, fills this role and gives the tools to be able to correct for missing data points, ensure consistency of the data, and transform the content of the data such that it is suitable for use in other aspects of data science....

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On the quantification of the controlling regimes in automotive catalytic converters

Santos

Costa

2010

AIChE Journal

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The conversion of pollutants in automotive catalytic converters is influenced by a number of physical and chemical processes that take place in the gaseous and solid phases as the exhaust gases flow through the converter. A detailed understanding of the complex processes involving flow dynamics, heat and mass transport and heterogeneous surface reactions is of crucial importance to improve the converter design. The main objective of the present study is to quantify the magnitudes of the external and internal mass transfer as well as chemical reaction limiting processes as a function of the converter operating temperature. To this end, experimental data, obtained for a three way catalyst (TWC) under real world operating conditions, are analyzed and compared against analytical expressions that allow for the quantification of the different limiting processes involved. The results demonstrate that (i) the external mass transfer resistance overlaps the reaction resistance only at moderate operating temperatures and not immediately above the ignition temperature as generally considered in the literature, (ii) the transport phenomena (external and internal mass transfer) represents 90% of the total resistance for temperatures higher than 792 K, (iii) the internal mass transfer in the porous washcoat presents a larger resistance than the external mass transfer from the bulk fluid to the washcoat wall even at high operating temperatures, and (iv) based on the quantification of the individual resistances as a function of the TWC operating temperature, it was demonstrated both the influence of the substrate cell density and of the effective diffusivity on the TWC conversions.

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Low‐dimensional models for real time simulations of catalytic monoliths

Cited by 57 publications

References 22 publications

An Asymptotic Solution for Washcoat Pore Diffusion in Catalytic Monoliths

An Asymptotic Solution for Washcoat Pore Diffusion in Catalytic Monoliths

Data Science Approaches for Electrochemical Engineers: An Introduction through Surrogate Model Development for Lithium-Ion Batteries

On the quantification of the controlling regimes in automotive catalytic converters

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