Journal articles: 'Chemical reactors Mathematical models'

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Devika, P. D., P. A. Dinesh, G. Padmavathi, and Rama Krishna Prasad. "Numerical Methods for Mathematical Models of Heterogeneous Catalytic Fixed Bed Chemical Reactors." Mapana - Journal of Sciences 11, no. 1 (May 28, 2012): 49–64. http://dx.doi.org/10.12723/mjs.20.4.

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Mathematical modeling of chemical reactors is of immense interest and of enormous use in the chemical industries. The detailed modeling of heterogeneous catalytic systems is challenging because of the unknown nature of new catalytic material and also the transient behavior of such catalytic systems. The solution of mathematical models can be used to understand the interested physical systems. In addition, the solution can also be used to predict the unknown values which would have been otherwise obtained by conducting the actual experiments. Such solutions of the mathematical models involving ordinary/partial, linear/non-linear, differential/algebraic equations can be determined by using suitable analytical or numerical methods. The present work involves the development of mathematical methods and models to increase the understanding between the model parameters and also to decrease the number of laboratory experiments. In view of this, a detailed modeling of heterogeneous catalytic chemical reactor systems has been considered for the present study.

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RONDONI, L. "MATHEMATICAL MODELS OF CHEMICALLY REACTING GASES." Mathematical Models and Methods in Applied Sciences 06, no. 02 (March 1996): 245–68. http://dx.doi.org/10.1142/s0218202596000572.

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Modeling and analysis of models of complex chemical reactions constitute wide branches of research in chemistry, physics and mathematics. Here a model is proposed which is amenable to rigorous mathematical study, which makes clear the dynamics of the systems described by such a model. In particular, only combinations of chemical reactions which preserve the number of particles, and which have equal forward and backward reaction rates are allowed. Reactions which do not satisfy such requirements can be considered, provided they are suitably modified. Also, it is required that the densities of the chemicals in the reactions be low, so that the applicability of the theory is restricted to mixtures of gases.

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Kalyuzhnyi, Sergey, and Vyacheslav Fedorovich. "Integrated mathematical model of UASB reactor for competition between sulphate reduction and methanogenesis." Water Science and Technology 36, no. 6-7 (September 1, 1997): 201–8. http://dx.doi.org/10.2166/wst.1997.0592.

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The existing mathematical models of anaerobic treatment processes were mainly developed for ideally mixed reactors with no concentration gradients on substrates, intermediates, products and bacteria inside the reactor. But for conventional UASB reactors with low upward velocity, the distribution of these components along the reactor height is very far from uniform. This paper presents an integrated mathematical model of the functioning of UASB reactor taking into account this non-uniformity as well as multiple-reaction stoichiometry and kinetics. In general, our integrated model includes the following blocks: a) kinetic block, including the growth and metabolism of acidogenic, acetogenic, methanogenic and sulphate-reducing bacteria; b) physico-chemical block, for the calculation of pH in each compartment of the liquid phase; c) hydrodynamic block, describing liquid flow as well as the transport and distribution of the components along the reactor height; d) transfer block, describing a mass transfer of gaseous components from the liquid to gas phase. This model was calibrated to some experimental studies of the functioning of UASB reactors made by in 1994. Hypothetical computer simulations are presented to illustrate the influence of different factors (recycle number, hydraulic retention time, quality of seed sludge, SO42−:COD ratio etc.) on the operation performance of UASB reactor.

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Kaczmarczyk, Robert, and Sebastian Gurgul. "A Thermodynamic Analysis of Heavy Hydrocarbons Reforming for Solid Oxide Fuel Cell Application as a Part of Hybrid Energy Systems." Energies 14, no. 2 (January 9, 2021): 337. http://dx.doi.org/10.3390/en14020337.

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A thermodynamical analysis of steam reforming of Associated Petroleum Gas (APG) was conducted in the presented research. The reforming process of heavy hydrocarbons for small scale power generation is a complex issue. One of the main issues is that a set of undesired chemical reactions deposit solid carbon and, consequently, block the reactor’s catalytic property. The experimental investigation is crucial to design an APG reforming reactor. However, a numerical simulation is a key tool to design a safe operating condition. Designing the next generation of reactors requires a complex coupling of mathematical models, kinetics, and thermodynamic analysis. In practice, the thermodynamic analysis should be applied in each control volume to assure realistic results. This is not easy to apply in practice since both thermodynamic analysis and CFD modeling can be time-consuming. In this paper, the authors suggest using a mathematical formalism called Parametric Equation Formalism to calculate the equilibrium composition. The novelty lies in the mathematical approach in which any complex system at equilibrium can be reduced to the problem of solving one non-linear equation at a time. This approach allows implementing a thermodynamic analysis easily into CFD models to assure the reasonability of obtained results and can be used for research and development of solid oxide fuel cells as a part of hybrid energy systems.

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Kaczmarczyk, Robert, and Sebastian Gurgul. "A Thermodynamic Analysis of Heavy Hydrocarbons Reforming for Solid Oxide Fuel Cell Application as a Part of Hybrid Energy Systems." Energies 14, no. 2 (January 9, 2021): 337. http://dx.doi.org/10.3390/en14020337.

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A thermodynamical analysis of steam reforming of Associated Petroleum Gas (APG) was conducted in the presented research. The reforming process of heavy hydrocarbons for small scale power generation is a complex issue. One of the main issues is that a set of undesired chemical reactions deposit solid carbon and, consequently, block the reactor’s catalytic property. The experimental investigation is crucial to design an APG reforming reactor. However, a numerical simulation is a key tool to design a safe operating condition. Designing the next generation of reactors requires a complex coupling of mathematical models, kinetics, and thermodynamic analysis. In practice, the thermodynamic analysis should be applied in each control volume to assure realistic results. This is not easy to apply in practice since both thermodynamic analysis and CFD modeling can be time-consuming. In this paper, the authors suggest using a mathematical formalism called Parametric Equation Formalism to calculate the equilibrium composition. The novelty lies in the mathematical approach in which any complex system at equilibrium can be reduced to the problem of solving one non-linear equation at a time. This approach allows implementing a thermodynamic analysis easily into CFD models to assure the reasonability of obtained results and can be used for research and development of solid oxide fuel cells as a part of hybrid energy systems.

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Spatenka, Stepan, Vlastimil Fila, Bohumil Bernauer, Josef Fulem, Gabriele Germani, and Yves Schuurman. "Modelling and simulation of microchannel catalytic WGS reactor for an automotive fuel processor." Chemical Industry and Chemical Engineering Quarterly 11, no. 3 (2005): 143–51. http://dx.doi.org/10.2298/ciceq0503143s.

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The water-gas shift (WGS) is one of the major steps for H2 production from gaseous, liquid and solid hydrocarbons. It is used to produce hydrogen for ammonia synthesis, to adjust the hydrogen-to-carbon monoxide ratio of synthesis gas, to detoxify gases. The WGS reactor is widely used as a part of fuel processors which produce hydrogen-rich stream from hydrocarbon-based fuels in a multi-step process. The WGS unit is placed downstream the fuel reformer in order to increase overall efficiency of hydrogen production and to lower CO content in reformate. Fuel processors stand for considerable option for fuelling PEM fuel cells for both portable and stationary applications. Micro-structured reactors are used with benefits of process miniaturization, intensification and higher heat and mass transfer rates compared with conventional reactors. Micro-structured reactor systems are essential for processes where potential for considerable heat transfer exists as well as for kinetic studies of highly exothermic reactions at near-isothermal conditions. Modelling and simulation of a microchannel reactor for the WGS reaction is presented. The mathematical models concern a single reaction channel with porous layer of catalyst deposited on the metallic wall of the microstructure unit. Simplified one-phase and more sophisticated two-phase models, with separate mass and energy balances for gas and solid phase at different levels of complexity, were developed. The models were implemented into gPROMS process modelling software. The models were used for an estimation of parameters in a kinetic expression using experimental data obtained with a new WGS catalyst. The simulations provide detailed information about the composition and temperature distribution in gas phase and solid catalyst inside the channel.

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Moustafa, T. M., M. Fahmy, and S. S. E. H. Elnashaie. "Applications of Mathematical and Computer Models for the Evaluation of Novel Catalytic Reactors." Developments in Chemical Engineering and Mineral Processing 8, no. 5-6 (May 15, 2008): 571–86. http://dx.doi.org/10.1002/apj.5500080509.

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Zhang, Tongwang, Bin Zhao, and Jinfu Wang. "Mathematical models for macro-scale mass transfer in airlift loop reactors." Chemical Engineering Journal 119, no. 1 (June 2006): 19–26. http://dx.doi.org/10.1016/j.cej.2006.03.005.

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Maksimova, Nadezhda N. "INVESTIGATION OF MATHEMATICAL MODELS OF THE CHEMICAL REACTIONS KINETICS." Messenger AmSU, no. 97 (2022): 6–12. http://dx.doi.org/10.22250/20730268_2022_97_6.

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Fry, D. L. "Mathematical models of arterial transmural transport." American Journal of Physiology-Heart and Circulatory Physiology 248, no. 2 (February 1, 1985): H240—H263. http://dx.doi.org/10.1152/ajpheart.1985.248.2.h240.

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A finite-element model (FEM) and corresponding five-parameter analytical model (AM) were derived to study the one-dimensional transport of chemically reactive macro-molecules across (x) arterial tissue. Derivations emphasize chemical activity [a(x)], its gradient, and water flux as driving forces for chemical reactions and transport. The AM was fitted to 28 measured 125I-albumin transmural concentration [c(x)] curves giving parameter estimates of diffusivity (DA), convective velocity (nu A), and so on as functions of pressure (P), location (z) along the vessel, etc. The FEM was used to study 1) intimal-medial a(x) associated with molecular sieving and medial edema, 2) reversible binding, and 3) errors of AM in analysis of c(x). Results are as follows. Average relative error for the 28 AM fits was 5.3%. Only estimates of DA and nu A had acceptable coefficients of variation. DA (approximately 0.10 X 10(-7) cm2 X s-1) decreased with P, increased with z to a maximum, and then decreased; nu A was approximately proportional to P (approximately 0.12 X 10(-7) cm X s-1 X mmHg-1) and decreased slightly with z; distribution coefficient (epsilon F) decreased with z and was smaller for serum than for simple albumin reagent. Assumed boundary conditions for AM were associated with approximately 1.4% error in AM c(x). Parameter estimates were sensitive to wall inhomogeneity, e.g., approximately 15% error. In conclusion, the AM and FEM simulated measured c(x) well; the FEM is useful for study of mechanisms, experimental designs, and AM errors; trends of AM parameter estimates suggest dependence on P, z, and composition of reagent for further FEM and experimental study.

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Alekseev, M. V., N. G. Sudobin, A. A. Kuleshov, and E. B. Savenkov. "Mathematical Simulation of Thermomechanics in an Impermeable Porous Medium." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 4 (91) (August 2020): 4–23. http://dx.doi.org/10.18698/1812-3368-2020-4-4-23.

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The paper reports on mathematically simulating behaviour of a porous medium featuring isolated interstices filled with a chemically active substance by using a mathematical model of thermomechanics in the matrix and thermochemical processes inside the pores. We used three-dimensional thermomechanical equations to describe the behaviour of the medium. A lumped-element model accounting for chemical reactions and phase equilibrium describes the processes in pores. We outline the mathematical model of the medium and the respective computational algorithm. We provide parametric computation results using realistic thermophysical and thermodynamical parameters, composition of the organic substance found inside pores (products of thermal decomposition of kerogen) and chemical reactions, which show that it is necessary to employ complex, interconnected models to simulate the process class under consideration

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Zambrano, D., J. Soler, J. Herguido, and M. Menéndez. "Conventional and improved fluidized bed reactors for dry reforming of methane: Mathematical models." Chemical Engineering Journal 393 (August 2020): 124775. http://dx.doi.org/10.1016/j.cej.2020.124775.

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Cassani, Andrea, Alessandro Monteverde, and Marco Piumetti. "Belousov-Zhabotinsky type reactions: the non-linear behavior of chemical systems." Journal of Mathematical Chemistry 59, no. 3 (February 28, 2021): 792–826. http://dx.doi.org/10.1007/s10910-021-01223-9.

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AbstractChemical oscillators are open systems characterized by periodic variations of some reaction species concentration due to complex physico-chemical phenomena that may cause bistability, rise of limit cycle attractors, birth of spiral waves and Turing patterns and finally deterministic chaos. Specifically, the Belousov-Zhabotinsky reaction is a noteworthy example of non-linear behavior of chemical systems occurring in homogenous media. This reaction can take place in several variants and may offer an overview on chemical oscillators, owing to its simplicity of mathematical handling and several more complex deriving phenomena. This work provides an overview of Belousov-Zhabotinsky-type reactions, focusing on modeling under different operating conditions, from the most simple to the most widely applicable models presented during the years. In particular, the stability of simplified models as a function of bifurcation parameters is studied as causes of several complex behaviors. Rise of waves and fronts is mathematically explained as well as birth and evolution issues of the chaotic ODEs system describing the Györgyi-Field model of the Belousov-Zhabotinsky reaction. This review provides not only the general information about oscillatory reactions, but also provides the mathematical solutions in order to be used in future biochemical reactions and reactor designs.

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Masavetas, K. A. "Mathematical properties common in all mechanism models of chemical reactions." Mathematical and Computer Modelling 10, no. 4 (1988): 263–74. http://dx.doi.org/10.1016/0895-7177(88)90005-2.

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Pilling, M. J. "Mathematical Models of Chemical Reactions. Theory and Applications of Deterministic and Stochastic Models." Journal of Photochemistry and Photobiology A: Chemistry 49, no. 3 (October 1989): 409–10. http://dx.doi.org/10.1016/1010-6030(89)87138-2.

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Cvetinovic, Dejan, Predrag Stefanovic, Vukman Bakic, and Simeon Oka. "Review of the research on the turbulence in the laboratory for thermal engineering and energy." Thermal Science 21, suppl. 3 (2017): 875–98. http://dx.doi.org/10.2298/tsci160221330c.

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Paper gives a review of the most important results of turbulence research achieved by the Laboratory for Thermal Engineering and Energy. Paper presents detailed overview of the history of the scientific research provided in the laboratory, from the beginning in the mid-60s to today, pointing out the main reasons initiating the investigations in this field. After the first period, which was mainly devoted to the research of the structure of the turbulence, since the beginning of the 80s, research is mainly oriented to the flows at high temperatures including chemical reactions and to the development and improvement of differential mathematical models as a modern and very efficient tool in the technological development. This research significantly contributed to the development of pulverized coal burners, plasma-chemical reactors, and optimization of pulverized coal fired boilers operating parameters and prediction of the greenhouse gases emissions. Most recent period includes experimental and numerical studies of the coherent structures in turbulent fluid jets, mathematical modeling of various turbulent thermal flow processes including two-phase turbulent flow in the multiphase heat exchangers and mathematical modeling of the atmospheric boundary layer.

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Novkovic, Djordje, Jela Burazer, and Aleksandar Cocic. "Comparison of different CFD software performances in the case of an incompressible air flow through a straight conical diffuser." Thermal Science 21, suppl. 3 (2017): 863–74. http://dx.doi.org/10.2298/tsci161020329n.

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Paper gives a review of the most important results of turbulence research achieved by the Laboratory for Thermal Engineering and Energy at the Vinca Insitute of Nuclear Sciences. Paper presents detailed overview of the history of the scientific research provided in the laboratory, from the beginning in the mid-60s to today, pointing out the main reasons initiating the investigations in this field. After the first period, which was mainly devoted to the research of the structure of the turbulence, since the beginning of the 80s, research is mainly oriented to the flows at high temperatures including chemical reactions and to the development and improvement of differential mathematical models as a modern and very efficient tool in the technological development. This research significantly contributed to the development of pulverized coal burners, plasma-chemical reactors, and optimization of pulverized coal fired boilers operating parameters and prediction of the greenhouse gases emissions. Most recent period includes experimental and numerical studies of the coherent structures in turbulent fluid jets, mathematical modeling of various turbulent thermal flow processes including two-phase turbulent flow in the multiphase heat exchangers and mathematical modeling of the atmospheric boundary layer.

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Basha, Omar M., Laurent Sehabiague, Ahmed Abdel-Wahab, and Badie I. Morsi. "Fischer–Tropsch Synthesis in Slurry Bubble Column Reactors: Experimental Investigations and Modeling – A Review." International Journal of Chemical Reactor Engineering 13, no. 3 (September 1, 2015): 201–88. http://dx.doi.org/10.1515/ijcre-2014-0146.

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Abstract This paper presents an extensive review of the kinetics, hydrodynamics, mass transfer, heat transfer and mathematical as well as computational fluid dynamics (CFD) modeling of Low-Temperature Tropsch Synthesis (LTFT) synthesis in Slurry Bubble Column Reactors (SBCRs), with the aim of identifying potential research and development areas in this particular field. The kinetic expressions developed for F-T synthesis over iron and cobalt catalysts along with the water gas shift (WGS) reactions are summarized and compared. The experimental data and empirical correlations to predict the hydrodynamics (gas holdup, Sauter mean bubble diameter, and bubble rise velocity), mass transfer coefficients and heat transfer coefficients are presented. The effects of various operating variables, including pressure, temperature, gas velocity, catalyst concentration, reactor geometry, and reactor internals on the hydrodynamic and transport parameters as well as the performance of SBCRs are discussed. Additionally, modeling efforts of SBCRs, using axial dispersion models (ADM), multiple cell recirculation models (MCCM) and computational fluid dynamics (CFD), are addressed. This review revealed the following: (1)Numerous F-T and WGS kinetic rate expressions are available for cobalt and iron catalysts and one must be careful in selecting the appropriate expressions for LTFT. Iron catalyst suffers from severe attrition and subsequent deactivation in SBCRs and accordingly building a costly catalyst manufacturing facility onsite is required to maintain a steady operation of the F-T reactor; (2)Experimental data on the hydrodynamic and transport parameters at high pressures and temperatures, typical to those of actual F-T synthesis, remain scanty when compared with the plethora of studies conducted using air–water systems in small reactors at ambient conditions; (3)Several empirical correlations for predicting the hydrodynamic and mass as well heat transfer parameters are available and one should select those which consider the reactor diameter, gas mixtures and the potential foamability of the F-T liquids; (4)The effect of cooling internals configuration and sparger design on the hydrodynamic and transport parameters, local turbulence, mixing and catalyst attrition are yet to be seriously addressed; (5)The impact of operating variables on the hydrodynamic and transport parameters as well as the overall performance of the SBCRs should be investigated using actual F-T fluid–solid systems under typical pressures and temperatures using a large-scale reactor (>0.15 m ID) in the presence of gas spargers and cooling internals; (6)Significant efforts are still required in order to advance CFD modeling of SBCRs, particularly those pertaining to the relevant closure models, such as drag, lift and turbulence. Also, cooling internals configuration and the design as well as orientation of gas spargers should be accounted for in the CFD modeling; and (7)Proper validations of the CFD formulations using actual systems for F-T SBCR are needed.

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Kadinski, L., Yu N. Makarov, M. Schäfer, M. G. Vasil'ev, and V. S. Yuferev. "Development of advanced mathematical models for numerical calculations of radiative heat transfer in metalorganic chemical vapour deposition reactors." Journal of Crystal Growth 146, no. 1-4 (January 1995): 209–13. http://dx.doi.org/10.1016/0022-0248(94)00570-2.

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Till, Zoltán, Bálint Molnár, Attila Egedy, and Tamás Varga. "CFD Based Qualification of Mixing Efficiency of Stirred Vessels." Periodica Polytechnica Chemical Engineering 63, no. 1 (July 10, 2018): 226–38. http://dx.doi.org/10.3311/ppch.12245.

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In this work, we focus on the most crucial units in a chemical technology, the chemical reactors. Using a commercially available CFD software package, COMSOL Multiphysics, 3D mathematical models of a batch reactor with different impeller geometries have been investigated. The reasonable agreement between the experimental and simulation results indicates the validity of the developed CFD model. The effect of the impeller design, e. g. number of blades on the mixing efficiency is evaluated based on the simulation studies. The proposed measure to determine the energy efficiency of mixing (i. e. mixing index) is based on the calculated velocity field and energy usage. The information about the homogeneity of the mixed phase in the system can be extracted from the developed velocity field. Hence, we proposed histograms of velocity fluctuations on a logarithmic scale as an efficient tool to measure the achieved homogeneity of the phase in case of different impellers and rotational speeds.

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Chakachaka, Vimbainashe, Charmaine Tshangana, Oranso Mahlangu, Bhekie Mamba, and Adolph Muleja. "Interdependence of Kinetics and Fluid Dynamics in the Design of Photocatalytic Membrane Reactors." Membranes 12, no. 8 (July 29, 2022): 745. http://dx.doi.org/10.3390/membranes12080745.

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Photocatalytic membrane reactors (PMRs) are a promising technology for wastewater reclamation. The principles of PMRs are based on photocatalytic degradation and membrane rejection, the different processes occurring simultaneously. Coupled photocatalysis and membrane filtration has made PMRs suitable for application in the removal of emerging contaminants (ECs), such as diclofenac, carbamazepine, ibuprofen, lincomycin, diphenhydramine, rhodamine, and tamoxifen, from wastewater, while reducing the likelihood of byproducts being present in the permeate stream. The viability of PMRs depends on the hypotheses used during design and the kinetic properties of the systems. The choice of design models and the assumptions made in their application can have an impact on reactor design outcomes. A design’s resilience is due to the development of a mathematical model that links material and mass balances to various sub-models, including the fluid dynamic model, the radiation emission model, the radiation absorption model, and the kinetic model. Hence, this review addresses the discrepancies with traditional kinetic models, fluid flow dynamics, and radiation emission and absorption, all of which have an impact on upscaling and reactor design. Computational and analytical descriptions of how to develop a PMR system with high throughput, performance, and energy efficiency are provided. The potential solutions are classified according to the catalyst, fluid dynamics, thickness, geometry, and light source used. Two main PMR types are comprehensively described, and a discussion of various influential factors relating to PMRs was used as a premise for developing an ideal reactor. The aim of this work was to resolve potential divergences that occur during PMRs design as most real reactors do not conform to the idealized fluid dynamics. Lastly, the application of PMRs is evaluated, not only in relation to the removal of endocrine-disrupting compounds (EDCs) from wastewater, but also in dye, oil, heavy metals, and pesticide removal.

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Bałdyga, Jerzy, and Magdalena Jasińska. "Energetic Efficiency of Mixing and Mass Transfer in Single Phase and Two-Phase Systems." Chemical and Process Engineering 38, no. 1 (March 1, 2017): 79–96. http://dx.doi.org/10.1515/cpe-2017-0007.

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Abstract In this work a concept of energetic efficiency of mixing is presented and discussed; a classical definition of mixing efficiency is modified to include effects of the Schmidt number and the Reynolds number. Generalization to turbulent flows is presented as well. It is shown how the energetic efficiency of mixing as well as efficiencies of drop breakage and mass transfer in twophase liquid-liquid systems can be identified using mathematical models and test chemical reactions. New expressions for analyzing efficiency problem are applied to identify the energetic efficiency of mixing in a stirred tank, a rotor stator mixer and a microreactor. Published experimental data and new results obtained using new systems of test reactions are applied. It has been shown that the efficiency of mixing is small in popular types of reactors and mixers and thus there is some space for improvement.

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Asadollahfardi, Gholamreza, Matin Molaei, Masoud Taheriyoun, and Ivan Leversage. "Comparison of ultraviolet (UV) radiation intensity between a single lamp and a double lamp in a reactors." Water Practice and Technology 9, no. 4 (December 1, 2014): 558–65. http://dx.doi.org/10.2166/wpt.2014.062.

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Disinfection of drinking water is a challenging and controversial issue. Chemical and ultraviolet (UV) methods are used to deactivate bacteria. Some of the chemical disinfection causes threats to public health since they produce toxic chemical compounds. Recently, several researchers conducted experiments and mathematical models to deactivate pathogenic bacteria from wastewater and drinking water using UV. The intensity of UV is very effective in deactivating bacteria. The authors compared the radiation intensity of a single and double lamp in a UV reactor for water treatment using computational fluid dynamics. The results indicated that the mean volume emission rate of single lamp and double lamp in the reactor was similar. However, the energy distribution of single lamps was much better than the double lamp in the reactor. The sensitivity analysis using three different UV transmittances (UVT), 70, 80 and 90%, indicated that the increase in % UVT value improved the energy distribution in the UV reactor.

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Yue, Lindsey, Leanne Reich, Terrence Simon, Roman Bader, and Wojciech Lipiński. "Progress in thermal transport modeling of carbonate-based reacting systems." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 5 (May 2, 2017): 1098–107. http://dx.doi.org/10.1108/hff-03-2016-0087.

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Purpose Carbonate-based heterogeneous reacting systems are investigated for the applications of thermochemical carbon dioxide capture and energy storage. This paper aims to review recent progress in numerical modeling of thermal transport phenomena in such systems. Design/methodology/approach Calcium oxide looping is selected as the model carbonate-based reacting system. Numerical models coupling heat and mass transfer to chemical kinetics are reviewed for solar-driven calcium oxide looping on the sorbent particle, particle bed, and reactor levels. Findings At the sorbent particle level, a transient numerical model of heat and mass transfer coupled to chemical kinetics has been developed for a single particle undergoing cyclic calcination and carbonation driven by time-periodic boundary conditions. Modeling results show cycle times impact the maximum sorbent utilization and solar-to-chemical energy efficiency. At the reactor level, a model of heat and mass transfer coupled to chemical kinetics of calcination of a packed-bed reactor concept has been developed to estimate the reactor’s performance. The model was used to finalize reactor geometry by evaluating pressure drops, temperature distributions, and heat transfer in the reactor. Originality/value Successful solar thermochemical reactor designs maximize solar-to-chemical energy conversion by matching chemical kinetics to reactor heat and mass transfer processes. Modeling furthers the understanding of thermal transport phenomena and chemical kinetics interactions and guides the design of solar chemical reactors.

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Leonzio, Grazia. "Mathematical modeling of a methanol reactor by using different kinetic models." Journal of Industrial and Engineering Chemistry 85 (May 2020): 130–40. http://dx.doi.org/10.1016/j.jiec.2020.01.033.

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Arcadia, Christopher E., Amanda Dombroski, Kady Oakley, Shui Ling Chen, Hokchhay Tann, Christopher Rose, Eunsuk Kim, Sherief Reda, Brenda M. Rubenstein, and Jacob K. Rosenstein. "Leveraging autocatalytic reactions for chemical domain image classification." Chemical Science 12, no. 15 (2021): 5464–72. http://dx.doi.org/10.1039/d0sc05860b.

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Kinetic models of autocatalytic reactions have mathematical forms similar to activation functions used in artificial neural networks. Inspired by these similarities, we use a copper-catalyzed reaction to perform digital image recognition tasks.

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Zhang, Fangyuan, Brittany Macshane, Ryan Searcy, and Zuyi Huang. "Mathematical Models for Cholesterol Metabolism and Transport." Processes 10, no. 1 (January 13, 2022): 155. http://dx.doi.org/10.3390/pr10010155.

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Cholesterol is an essential component of eukaryotic cellular membranes. It is also an important precursor for making other molecules needed by the body. Cholesterol homeostasis plays an essential role in human health. Having high cholesterol can increase the chances of getting heart disease. As a result of the risks associated with high cholesterol, it is imperative that studies are conducted to determine the best course of action to reduce whole body cholesterol levels. Mathematical models can provide direction on this. By examining existing models, the suitable reactions or processes for drug targeting to lower whole-body cholesterol can be determined. This paper examines existing models in the literature that, in total, cover most of the processes involving cholesterol metabolism and transport, including: the absorption of cholesterol in the intestine; the cholesterol biosynthesis in the liver; the storage and transport of cholesterol between the intestine, the liver, blood vessels, and peripheral cells. The findings presented in these models will be discussed for potential combination to form a comprehensive model of cholesterol within the entire body, which is then taken as an in-silico patient for identifying drug targets, screening drugs, and designing intervention strategies to regulate cholesterol levels in the human body.

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Bunimovich, Leonid A., and Mark F. Demers. "Deterministic Models of the Simplest Chemical Reactions." Journal of Statistical Physics 120, no. 1-2 (July 2005): 239–52. http://dx.doi.org/10.1007/s10955-005-5254-8.

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Maksymenko-Sheiko, Kyrylo V., Tetiana I. Sheiko, Denys O. Lisin, and Nykyta D. Petrenko. "Mathematical and Computer Modeling of the Forms of Multi-Zone Fuel Elements with Plates." Journal of Mechanical Engineering 25, no. 4 (December 30, 2022): 32–38. http://dx.doi.org/10.15407/pmach2022.04.032.

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Seeing the significant increase in the number of nuclear power plants, as well as models and modifications of nuclear reactors, it becomes important to find out/establish the advantages of certain plants. At the same time, designers face a number of questions for which optimal solutions have not yet been found. At nuclear plants, there is the largest turnover of financial funds and the smallest gain in economy brings huge profits, but one should not forget about reliability and costs during the plant construction. This is a complex problem that is solved at the design stage. Calculations of the reactor at the design stage make it possible to determine the main parameters of the active zone, temperature values, etc. Thermohydraulic calculation of the active zone of the reactor is one of the cornerstones in justifying the safe operation of the nuclear power plant. Calculations of coolant parameters and temperatures of fuel elements are carried out at all stages of designing and proving the safety of nuclear power plants. Twisted pipes and finned heat transfer surfaces are widely used in engineering to increase the effective heat transfer coefficient. In particular, longitudinal, transverse, and spiral edges are used for finning the shells of fuel elements of nuclear reactors and the outer surfaces of steam generator pipes. Finning not only increases the heat transfer surface on the side where the heat transfer coefficient has a low value, but also significantly affects the hydrodynamics of the flow, and thus affects this coefficient. It is obvious that the better the medium is mixed in the main flow and in the intercoral zone, the higher the heat transfer coefficient is. The most profitable forms of fuel elements shells finning are chevron and polyzonal finning, which are performed in the form of a multiturn spiral with a large step. The R-function theory turned out to be quite convenient for building mathematical models of finned shells of fuel elements with straight and helical plates, as well as for building the corresponding objects on a 3D printer. From a practical point of view, the relevance of the problem is also determined by the significant spread of twisted cylindrical bodies, twisted channels, coils in the energy, chemical, oil, gas, metallurgical industries and in heat engineering equipment. The flows that arise at this time make it possible to intensify the processes of heat and mass exchange and achieve savings in energy resources

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Miranda-Quintana, Ramón Alain, and Paul W. Ayers. "Fractional electron number, temperature, and perturbations in chemical reactions." Physical Chemistry Chemical Physics 18, no. 22 (2016): 15070–80. http://dx.doi.org/10.1039/c6cp00939e.

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The mathematical framework of conceptual density functional theory is extended to use the eigenstates and eigenvalues of perturbed subsystems. This unites, justifies, and extends, several previously proposed models.

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Sedej, Owen, and Eric Mbonimpa. "CFD Modeling of a Lab-Scale Microwave Plasma Reactor for Waste-to-Energy Applications: A Review." Gases 1, no. 3 (July 24, 2021): 133–47. http://dx.doi.org/10.3390/gases1030011.

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Rapidly increasing solid waste generation and energy demand are two critical issues of the current century. Plasma gasification, a type of waste-to-energy (WtE) technology, has the potential to produce clean energy from waste and safely destroy hazardous waste. Among plasma gasification technologies, microwave (MW)-driven plasma offers numerous potential advantages to be scaled as a leading WtE technology if its processes are well understood and optimized. This paper reviews studies on modeling experimental microwave-induced plasma gasification systems. The system characterization requires developing mathematical models to describe the multiphysics phenomena within the reactor. The injection of plasma-forming gases and carrier gases, the rate of the waste stream, and the operational power heavily influence the initiation of various chemical reactions that produce syngas. The type and kinetics of the chemical reactions taking place are primarily influenced by either the turbulence or temperature. Navier–Stokes equations are used to describe the mass, momentum, and energy transfer, and the k-epsilon model is often used to describe the turbulence within the reactor. Computational fluid dynamics software offers the ability to solve these multiphysics mathematical models efficiently and accurately.

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Makoba, Mmoloki, Daniel Erich Botha, Mpho Thabang Rapoo, László Zsolt Szabó, Thapelo Shomana, Paul Serban Agachi, and Edison Muzenda. "A Review on Botswana Coal Potential from a Pyrolysis and Gasification Perspective." Periodica Polytechnica Chemical Engineering 65, no. 1 (July 6, 2020): 80–96. http://dx.doi.org/10.3311/ppch.12909.

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Coal pyrolysis and gasification are promising options for the future of Botswana as the country has large coal reserves with severe limitations in terms of export options. Coal characterization facilities will be required in order to harness its full potential and methods such as proximate, ultimate and chemical structure analysis (FTIR, Raman spectroscopy and X-ray diffraction techniques) were investigated. The paper presents a brief history of pyrolysis and gasification, typical types of the reactors as well as factors that influence product selection for Botswana coal. Coal pyrolysis and gasification are complex processes and it is difficult to define the mechanisms of product formation. However, there are several kinetic models that are relevant to the sub-bituminous coal of Botswana which were proposed by researchers to describe the formation of the compounds and mathematical models that were validated by other researchers on mass and heat transfer as also presented herein.

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Hoppej, Dominik, and Miroslav Variny. "Industrial-Scale Hydrogen Production Plant Modelling." Advances in Thermal Processes and Energy Transformation 4, no. 1 (2021): 09–15. http://dx.doi.org/10.54570/atpet2021/04/01/0009.

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Considering the process characteristics, hydrogen production via steam methane reforming is a vital part of oil refinery not just in terms of materials, but of energy integration as well. This work extends the mathematical model describing hydrogen production by ATE (Approach to Equilibrium) parameters implemented within the chemical reactors’ models. Equations for ATE parameter prediction, i.e. mass flow of process feed (natural gas) and reaction temperature, were formulated. Verification of the whole model as well as of its parameters was performed using process data from a real hydrogen plant. The extended mathematical model is suitable for the evaluation of the influence of increased hydrogen content in natural gas on plant´s material and energy efficiency, as renewable hydrogen injection and co-transport in natural gas pipelines in future is proposed by the European Union as a means of decreasing carbon dioxide emissions.

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Orazbayev, Batyr, Dinara Kozhakhmetova, Ryszard Wójtowicz, and Janusz Krawczyk. "Modeling of a Catalytic Cracking in the Gasoline Production Installation with a Fuzzy Environment." Energies 13, no. 18 (September 11, 2020): 4736. http://dx.doi.org/10.3390/en13184736.

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The article offers a systematic approach to the method of developing mathematical models of a chemical-technological system (CTS) in conditions of deficit and fuzziness of initial information using available data of various types. Based on the results of research and processing of the collected quantitative and qualitative information, mathematical models of the reactor are constructed. Formalized and obtained mathematical statements of the control problem for choosing effective modes of operation of technological systems are based on mathematical modeling. Based on the obtained expert information, linguistic variables were described and a database of rules describing the operation of the input parameters of the reactor unit of the catalytic cracking unit was obtained.

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Afanasyev, Vitaliy, Zheng Keli, Alexei Kulagin, Hui-hui Miao, Yuri Ozhigov, Wanshun Lee, and Nadezda Victorova. "About Chemical Modifications of Finite Dimensional QED Models." Nonlinear Phenomena in Complex Systems 24, no. 3 (October 12, 2021): 230–41. http://dx.doi.org/10.33581/1561-4085-2021-24-3-230-241.

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Suggestion of modifications of finite-dimensional quantum-electrodynamic (QED) models are proposed for interpreting chemical reactions in terms of artificial atoms and molecules on quantum dots placed in optical cavities. Moving both photons and atoms is possible between the cavities. Super dark states of diatomic systems are described, in which the motion of atoms between cavities is impossible due to quantum interference. Chemical processes with two level atoms and three level atoms with lambda spectrum are schematically modeled by solving the single quantum master equation with the Lindblad operators of photon leakage from the cavity and influx into it; association and dissociation reactions then differ only in the initial states. An example is given of the optical interpretation of the transition of an electron from atom to atom in terms of the multilevel Tavis-Cummings-Hubbard model with an estimate of the accuracy. Polyatomic chemical reactions are too complex for accurate modeling. Our method of rough interpretation helps to obtain their long-term results, for example, the form of stationary states of reagents, such as dark and super dark states.

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Khan, Faiz Muhammad, Amjad Ali, Nawaf Hamadneh, Abdullah, and Md Nur Alam. "Numerical Investigation of Chemical Schnakenberg Mathematical Model." Journal of Nanomaterials 2021 (November 9, 2021): 1–8. http://dx.doi.org/10.1155/2021/9152972.

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Schnakenberg model is known as one of the influential model used in several biological processes. The proposed model is an autocatalytic reaction in nature that arises in various biological models. In such kind of reactions, the rate of reaction speeds up as the reaction proceeds. It is because when a product itself acts as a catalyst. In fact, model endows fractional derivatives that got great advancement in the investigation of mathematical modeling with memory effect. Therefore, in the present paper, the authors develop a scheme for the solution of fractional order Schnakenberg model. The proposed model describes an auto chemical reaction with possible oscillatory behavior which may have several applications in biological and biochemical processes. In this work, the authors generalized the concept of integer order Schnakenberg model to fractional order Schnakenberg model. We provided the approximate solution for the underlying generalized nonlinear Schnakenberg model in the sense of Caputo differential operator via Laplace Adomian decomposition method (LADM). Furthermore, we established the general scheme for the considered model in the form of infinite series by the aforementioned technique. The consequent results obtained by the proposed technique ensure that LADM is an effective and accurate techniques to handle nonlinear partial differential equations as compared to the other available numerical techniques. Finally, the obtained numerical solution is visualized graphically by MATLAB to describe the dynamics of desired solution.

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Balakotaiah, Vemuri, and Saikat Chakraborty. "Averaging theory and low-dimensional models for chemical reactors and reacting flows." Chemical Engineering Science 58, no. 21 (November 2003): 4769–86. http://dx.doi.org/10.1016/j.ces.2002.11.002.

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Vermolen, F. J., C. Vuik, E., and S. Van der Zwaag. "Review on some Stefan Problems for Particle Dissolution in Solid Metallic Alloys." Nonlinear Analysis: Modelling and Control 10, no. 3 (July 25, 2005): 257–92. http://dx.doi.org/10.15388/na.2005.10.3.15124.

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This paper is a review of a suite of mathematical models of increasing complexity on particle dissolution in metallic alloys. This work deals with models for multi-component particle dissolution in multi-component alloys, where various chemical species diffuse simultaneously, and a two-dimensional model incorporating interfacial reactions as in the model of Nolfi [1]. The work is mathematically rigorous where asymptotic solutions and solution bounds are derived but is also of a practical nature as particle dissolution kinetics is modelled for industrially relevant conditions.

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Mishra, Prakash, and Farhad Ein-Mozaffari. "Critical review of different aspects of liquid-solid mixing operations." Reviews in Chemical Engineering 36, no. 5 (July 28, 2020): 555–92. http://dx.doi.org/10.1515/revce-2018-0017.

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AbstractMechanically stirred slurry tanks are utilized in several industries to perform various unit operations such as crystallization, adsorption, ion-exchange, suspensions polymerization, dispersion of solid particles, leaching and dissolution, and activated sludge processes. The major goal of this review paper is to critically and thoroughly analyse the different aspects of previous research works reported in the literature in the field of liquid-solid mixing. This paper sheds light on the advantages and limitations of various particle concentration measurement methods employed to assess the suspension quality and the extent of solid suspensions in slurry reactors. Attempts are being made to identify and compare various mathematical models and methods to quantify particle dispersion and distribution in slurry reactors. It has been shown that various factors such as geometric configurations, agitation conditions, and physical characteristics of liquid and solid have pronounced influence on local suspension quality and power consumption. Computational fluid dynamics (CFD) modeling can be extremely useful in assessing the suspension of solid particles in slurry tanks. A critical review of different scale-up procedures employed for solid suspension and distribution in liquid-solid systems is presented as well. The findings of this review paper can be useful for future research works in liquid-solid mixing.

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Jank, Gerhard, Thomas Nonte, Eberhard Steinmetz, and Herbert Wilhelmi. "Experimental investigations of flow, turbulence and subspace formation on cold models of gas-stirred reactors with a view to describing mixing processes by mathematical models." Chemical Engineering & Technology 16, no. 3 (June 1993): 161–71. http://dx.doi.org/10.1002/ceat.270160304.

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Sheintuch, Moshe, and Olga Nekhamkina. "Thermal patterns in simple models of cylindrical reactors." Chemical Engineering Science 58, no. 8 (April 2003): 1441–51. http://dx.doi.org/10.1016/s0009-2509(02)00677-2.

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Khan, Zoheb, Vishal H. Bhusare, and Jyeshtharaj B. Joshi. "Comparison of turbulence models for bubble column reactors." Chemical Engineering Science 164 (June 2017): 34–52. http://dx.doi.org/10.1016/j.ces.2017.01.023.

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Bhattacharya, Madhuchhanda, Michael P. Harold, and Vemuri Balakotaiah. "Low-dimensional models for homogeneous stirred tank reactors." Chemical Engineering Science 59, no. 22-23 (November 2004): 5587–96. http://dx.doi.org/10.1016/j.ces.2004.07.068.

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Gobbert, Matthias K., Timothy S. Cale, and Christian A. Ringhofer. "The Combination of Equipment Scale and Feature Scale Models for Chemical Vapor Deposition Via a Homogenization Technique." VLSI Design 6, no. 1-4 (January 1, 1998): 399–403. http://dx.doi.org/10.1155/1998/24073.

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In the context of semiconductor manufacturing, chemical vapor deposition (CVD) denotes the deposition of a solid from gaseous species via chemical reactions on the wafer surface. In order to obtain a realistic process model, this paper proposes the introduction of an intermediate scale model on the scale of a die. Its mathematical model is a reaction-diffusion equation with associated boundary conditions including a flux condition at the micro structured surface. The surface is given in general parameterized form. A homoganization technique from asymptotic analysis is used to replace this boundary condition by a condition on the flat surface to make a numerical solution feasible. Results from a mathematical test problem are included.

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Yang, Chao, Guangsheng Luo, Xigang Yuan, Jie Chen, Yangcheng Lu, Xiaojin Tang, and Aiwu Zeng. "Numerical simulation and experimental investigation of multiphase mass transfer process for industrial applications in China." Reviews in Chemical Engineering 36, no. 1 (December 18, 2019): 187–214. http://dx.doi.org/10.1515/revce-2017-0050.

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Abstract This paper presents a comprehensive review of the remarkable achievements by Chinese scientists and engineers who have contributed to the multiscale process design, with emphasis on the transport mechanisms in stirred reactors, extractors, and rectification columns. After a brief review of the classical theory of transport phenomena, this paper summarizes the domestic developments regarding the relevant experiments and numerical techniques for the interphase mass transfer on the drop/bubble scale and the micromixing in the single-phase or multiphase stirred tanks in China. To improve the design and scale-up of liquid-liquid extraction columns, new measurement techniques with the combination of both particle image velocimetry and computational fluid dynamics have been developed and advanced modeling methods have been used to determine the axial mixing and mass transfer performance in extraction columns. Detailed investigations on the mass transfer process in distillation columns are also summarized. The numerical and experimental approaches modeling transport phenomena at the vicinity of the vapor-liquid interface, the point efficiency for trays/packings regarding the mixing behavior of fluids, and the computational mass transfer approach for the simulation of distillation columns are thoroughly analyzed. Recent industrial applications of mathematical models, numerical simulation, and experimental methods for the design and analysis of multiphase stirred reactors/crystallizers, extractors, and distillation columns are seen to garnish economic benefits. The current problems and future prospects are pinpointed at last.

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GONTAR, V., and O. GRECHKO. "GENERATION OF SYMMETRICAL COLORED IMAGES VIA SOLUTION OF THE INVERSE PROBLEM OF CHEMICAL REACTIONS DISCRETE CHAOTIC DYNAMICS." International Journal of Bifurcation and Chaos 16, no. 05 (May 2006): 1419–34. http://dx.doi.org/10.1142/s0218127406015398.

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An automatic procedure for generating colored two-dimensional symmetrical images based on the chemical reactions discrete chaotic dynamics (CRDCD) is proposed. The inverse problem of derivation of symmetrical images from CRDCD mathematical models was formulated and solved using a special type of genetic algorithm. Different symmetrical images corresponding to the solutions of a CRDCD mathematical model for which the parameters were obtained automatically by the proposed method are presented.

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Trninić, Marta. "Mathematical modelling of primary and secondary pyrolysis: State of the art." FME Transactions 48, no. 4 (2020): 733–44. http://dx.doi.org/10.5937/fme2004733t.

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Pyrolysis process converts biomass into liquid, gaseous and solid fuels. Chemical kinetics play a key role in explaining the characteristics of pyrolysis reactions and developing mathematical models. Many studies have been undertaken to understand the kinetics of biomass pyrolysis; however, due to the heterogeneity of biomass and the complexity of the chemical and physical changes that occur during pyrolysis, it is difficult to develop a simple kinetic model that is applicable in every case. In this review, different methods to describe biomass primary and secondary pyrolysis with different types of kinetic mechanisms are discussed.

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Bobkov, Vladimir I., Margarita V. Chernovalova, and Andrey M. Sokolov. "Mathematical Models for an Energy Intensive Multistage Roasting Process of Pelletized Industrial Waste from Apatite-Nepheline Ores." Materials Science Forum 1052 (February 3, 2022): 473–81. http://dx.doi.org/10.4028/p-0i5ger.

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In this article, we describe mathematical and computer models for the complex, energy-consuming, multistage, integrated chemical and power engineering processes of calcination and sintering of pelletized industrial waste from apatite-nepheline ores, accumulated in the dumps of mining and processing plants. The models take into account the negative effect of vitrification and the subsequent destruction of pellets in case the operating temperature condition in the high-temperature roasting zone of indurating conveyor furnaces is violated during the implementation of these thermally activated processes. Experimental and analytical methods have been developed for the analysis of integrated, thermally activated processes in a dense multilayer mass of pellets obtained from apatite-nepheline ores waste, taking place in indurating furnaces. The possibility of complex phenomena accounting for polymorphic transformations, chemical reactions in solid phases, reactions involving a liquid phase, as well as the formation of new phases and solid solutions as a result of reactions, must be considered when modeling these processes. This analysis makes it possible to increase the strength of pellets during sintering and the degree of calcination as a result of carbonates dissociation, as well as to detect and use the potential of increasing energy and resource efficiency in a complex, environmentally safe, chemical and power engineering system for the processing of industrial waste of apatite-nepheline ores from dumps of mining and industrial plants.

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Seckler, Marcelo Martins. "Crystallization in Fluidized Bed Reactors: From Fundamental Knowledge to Full-Scale Applications." Crystals 12, no. 11 (October 28, 2022): 1541. http://dx.doi.org/10.3390/cryst12111541.

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A review is presented on fifty years of research on crystallization in fluidized bed reactors (FBRs). FBRs are suitable for recovery of slightly soluble compounds from aqueous solutions, as it yields large, millimeter sized particles, which are suitable for reuse and permits low liquid residence times in the timescale of minutes. Full-scale applications for water softening have been applied since the 1980s, and since then, new applications have been developed or are in development for recovery of phosphorus, magnesium, fluoride, metals, sulfate, and boron. Process integration with membrane, adsorption, and biological processes have led to improved processes and environmental indicators. Recently, novel FBR concepts have been proposed, such as the aerated FBR for chemical-free precipitation of calcium carbonate, the seedless FBR to yield pure particulate products, a circulating FBR for economic recovery and extended use of seeds, as well as coupled FBRs for separation of chiral compounds and FBRs in precipitation with supercritical fluids. Advances are reported in the understanding of elementary phenomena in FBRs and on mathematical models for fluid dynamics, precipitation kinetics, and FBR systems. Their role is highlighted for process understanding, optimization and control at bench to full-scale. Future challenges are discussed.

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Davis, T. J., T. McAllister, V. Maslen, S. W. Wilkins, M. Faith, and P. Leech. "Mathematical and numerical models of CdTe deposition in a pre-cracking metalorganic chemical vapour deposition reactor." Journal of Crystal Growth 133, no. 3-4 (October 1993): 230–40. http://dx.doi.org/10.1016/0022-0248(93)90159-t.

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Journal articles on the topic 'Chemical reactors Mathematical models'

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