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Industrial problems like this require a multiscale analysis to develop solutions that meet the needs of industry. Linking and integration in multiscale modeling can be done, in general, in two fashions Vlachos et al. In the first one, named step-by-step procedure or hierarchical method, the integration is done in different sequential converging cycles and has the common characteristic that small level methods generate required input data for large level methods.
Thus, input conditions of each subsystem in a step-by-step multilevel examination remain constant through each single modeling method. An example of step-by-step mode-ling can be analyzed in the paper of Albo, Broadbelt, y Snurr who studied mass transport and residence times of particles in nonostructured membranes used in catalysis. The study focused on new membranes fabricated by a combination of anodic aluminum oxidation AAO and atomic layer deposition ALD Pellin et al.
This route offers many possibilities to adjust and control the contact between reagents and catalytic sites on the walls and the selectivity toward the desired products can be improved thereof. The understanding of mass transport inside the pores can help to design the optimal pore size for a particular application. The study by Albo et al. Atomistic scale: Self-diffusivity of species inside the pores was analyzed through molecular dynamics MD simulations of the system.
Alumina walls and the Lennard-Jones interaction between a molecule and the pore were represented by oxygen atoms and by the slit-pore potential, respectively. The results indicated that the surface diffusion disappeared as the temperature of the system was increased. Therefore, Knudsen diffusion was found to be the predominant mass-transport mechanism inside the pores under the typical conditions for selective catalytic oxidation.
Enlarged atomistic level with the identification of the Knudsen regime : the scheme of the Dual Control Volume Grand Canonical Molecular Dynamic simulation at Knudsen diffusion regime was utilized to access scales of time and length longer than those at atomistic level. The values of the obtained transmission probability indicated that the particles enter the pore multiple times before reaching the opposite end of the pore, especially for larger values of the aspect ratio of pore length to pore diameter. This fact can affect contact between the catalyst and diffusing molecules and therefore, influence the performance of the reactor operation.
Methyl ether sulfonation process MES carried out in a falling film reactor FFR presents multiple challenges such as the description of the reaction coordinate as well as the prediction of the profiles for momentum, mass and heat transfers. Simulation of the FFR was done with the help of a hierarchical modeling as follows:. According to the results on the thermodynamic grounds, the intermediates produced in the sulfonation and over-sulfonation steps were found to have the same relative stability.
This fact disregards the inclusion of these intermediates into the kinetic model and allows the use of a second order kinetic law for representing the reaction progress. The microscopic mass and energy balances are calculated by solving equations in partial derivatives for the liquid phase. Derived equations considered turbulent diffusivity for absorption with chemical reaction according to a second order kinetic law unveiled with the help of nanoscale modeling.
This set of equations was numerically solved using Laasonen implicit forms for first and second order derivates. The results of this model reproduce the experimental data for fa-lling film reactors; thus, a fast conversion region at the top gas phase control and a slow conversion region at the bottom of the reactor liquid phase control. The most important outlet data obtained by solving the mathematical model are the conversion of methyl ester, the density and viscosity of the sulfonic product. The proposed model can be suitable for use in design and operation of industrial falling film reactors even with petrochemical reactants.
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In the second fashion of the multiscale analysis, named hybrid or concurrent method, the integration is done in the same main iteration cycle until achieving of appropriate convergence. The concurrent methods can incorporate detailed interactions and system information such as spatiotemporal inhomogeneities on the surface in a more computationally efficient manner than the single methods and can be divided into low-level and high-level hybrids.
Developments on these methods have been concentrated on the low-level hybrids, i. We called low-level hybrid methods those that integrate in the same iteration cycle QM methods and classic atomic scale methods. Accordingly, we can count three subclasses of low-level concurrent methods: temporal, spatial and spatiotemporal hybrids. Methods that are hybrid in a temporal sense merge electronic structure calculations i.
With this hybrid, the system is simulated at a finite temperature with an electronic structure method rather than an empirical force field. This method and its various modifications have been very successful in material modeling and in calculations for heterogeneous and homogeneous catalysts in industrial applications Westmoreland et al. The second class of low-level hybrids is related to divide the complex system spatially.
In this sort, different methods are applied in different physical regions. Basically, this hybrid combines a more accurate more expensive method for the principal part of the system and a less accurate less expensive method for the rest of the system. This method allows bond breaking and forming processes of extended systems to be simulated in computationally tractable times Woo et al. The QM part is the region that requires electronic distribution to be properly studied. A third class of low-level concurrent method, called spatiotemporal, can be formed when spatial and temporal hybrid methods are combined Gao, ; Woo et al.
High-level concurrent methods resulting from the combination of both microscopic and macroscopic equations can improve the predictions of determining phenomena at detailed process conditions and therefore, they allow the appropriate change in operation to meet the require output of the systems. However, high-level hybrid methods that involve the combination between atomistic, mesoscopic and macroscopic scales are less common than the low-level hybrids that combine nanoscopic and atomistic levels.
One of the reasons of that scarceness is the lack of developments in theories and procedures for proper coupling between these scales. Another reason is the computational time which can make the simulation prohibitive for most of the cases. This strategy can be applied in semiconductor industry in which semiconductor devices, due to their size, show stress inhomogeneities caused by the high surface-to-volume ratio. Such inhomogeneities may affect the donor distribution by trapping donors in tensile stress regions Lidorikis et al. In this system, inclusion of atomically induced stresses at interfaces, where chemical bonding plays an important role, is enabled by applying MD simulation while most of the Si substrate is modeled by finite elements method FE as a continuum.
Simulation with this high-level hybrid demonstrated the same behavior as that obtained with large scale MD simulation Bachlechner, , but at much less computational effort. The handshake region is denoted by the dotted line HS. Another example of high-level hybrid method that couple macroscopic level with atomistic scale can be found in the work by Jensen, Hansen, Rodgers y Venkataramani In that work, different phenomena encountered in vapor deposition were analyzed in the same iteration cycle.
The underlying physical and chemical process occurred at time and length magnitudes ranged from nanoscopic to macroscopic finite elements scale. Prediction of performance of deposited structure and the ultimate device requires understanding of how process conditions influence thin film synthesis on the atomic scale and therefore, multiscale analysis is needed to see this effect on macroscopic phenomena. FE that simulated the reactor macroscopically, and kinetic Monte Carlo kMC method, which models the evolution of the surface morphology during growth, were integrated through the flux of species to the surface mesoscopic analysis.
The kMC method uses the flux given by the FE method as input, and returns the computed flux which is in turn used by FE as a boundary condition at the substrate. The solutions of both problems are iterated until a consistent flux is determined. The kMC method is embedded in the Newton iteration of the reactor scale FE model, which enables the linking through the surface flux boundary condition Vlachos, and aids in convergence of the reactor scale model Venkataramani, It is necessary to mention that neither chemical-physical transport at molecular level nor film morphology at micron scale can be studied by macroscopic conservation equations alone.
Moreover, a step-by-step methodology can also fail in representing those ever-changing conditions in CVD material is constantly exchanged between substrate and deposition chamber. This example demonstrates the needs of using multiscale analysis for understanding the complex processes. It is hoped that new developments on both theories and computational science facilitate the coupling between the domains, particularly in the case of chemical phenomena.
As the systems to be analyzed become more complex and the accuracy required become higher, hybrid methods are expected to become more and more popular, in both academic and industrial applications, as the method codes become more readily available Westmoreland et al. Abraham, F. Spaning the Length Scales in Dynamic Simulation. AIChe J. Computer simulation of liquids. Oxford Science Publications: New York. Fluid Mech.
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Science Eng. C, 27, Molecular Modeling in Heavy Hydrocarbon Conversions. CRC Press. Second edition. Molecular Modeling: Principles and Applications. Longman, USA. Science , 56, D, Jr. B, , Mesoscale modelling: recent developments and applications to nanocomposites, drug delivery and precipitation membranes.source url
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Nanotechnology, 2, Applied Catalysis A: General, , A dissertation submitted in partial fulfillment of the requirements of Doctor of Philosophy in Chemical Engineering. University of Delaware. Dynamics of Proteins and Nucleic Acids. Cambridge University Press, New York.
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International Technology Research Institute. World Technology Division. Catalysis Today , 50, Computational Chemistry. Services on Demand Article. English pdf Article in xml format Article references How to cite this article Automatic translation Send this article by e-mail. There are some areas where the molecular analysis is visualized as a common and strong "tool" for process engineering: Design: There is an emphasis on reducing the costs in the developmental time by omitting some phases of the activity that have traditionally been considered vital in the conceptual design of chemical processes e.
Quantum mechanical description of molecular systems Quantum mechanics, QM, explicitly represents the electrons in a calculation, making it possible to derive properties that depend upon the electronic distribution e. Simulation of the FFR was done with the help of a hierarchical modeling as follows: 1.
The coupling among different scales of modeling arises as a useful tool for developing molecular-based algorithms which can represent detailed conditions of systems that different isolated models cannot take into account. Different coupling methods were analyzed and exemplified in this review to demonstrate the applicability of such methodology in different industrial topics. The examples demonstrated that molecular tools increase the understanding of the studied processes and can give suitable input data for mathematical models at microscopic and macroscopic scales. Future developments in theories, hardware and software can make multilevel coupling widely applicable, and the molecular modeling a common tool in the analysis of engineering problems.
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