Modeling/simulation

M. Rafal and S. J. Sanders, "The ProChem System for Modeling/Simulation of Aqueous Systems," Proceedings of the Second International Mirlie House Conference onMqueous Systems, Warrenton, Va., May 10—14,1987. 

W. L. Luyben, Process Modeling, Simulation, and Controlfor Chemical Engineers, McGraw-HiU, Book Co., Inc., New York, 1973. 

Luyben, W. L. Frocess Modeling, Simulation and Control for Chemical Engineers, 2d ed., McGraw-HiU, New York (1990). 

High-pressure fluid flows into the low-pressure shell (or tube chaimel if the low-pressure fluid is on the tubeside). The low-pressure volume is represented by differential equations that determine the accumulation of high-pressure fluid within the shell or tube channel. The model determines the pressure inside the shell (or tube channel) based on the accumulation of high-pressure fluid and remaining low pressure fluid. The surrounding low-pressure system model simulates the flow/pressure relationship in the same manner used in water hammer analysis. Low-pressure fluid accumulation, fluid compressibility and pipe expansion are represented by pipe segment symbols. If a relief valve is present, the model must include the spring force and the disk mass inertia. 

There are many excellent textbooks on the subject of distillation, however with the explosion of information on the World Wide Web, process engineers can now gain almost instant access to calculation methods and model simulations which will walk the engineer through the important design steps. The following Web sites are recommended to be reviewed and accessed by the reader. 

The standard k- model simulates the turbulenee in the reaetor. For flow within the porous eatalyst bed, however, we suppress the turbulenee. We enter the appropriate physieal properties of the system, and employ standard boundary eonditions at the impermeable walls and the reaetor outlet. To represent the turbulenee of the feed stream at the inlet, we treat it as pipe-flow turbulenee. These model equations ean then be solved for instanee, via the well-known Simple algorithm [3]. To faeilitate fast eonvergenee, it is useful to make a reasonable initial guess of the pressure drop aeross the eatalyst bed. 

We close these introductory remarks with a few comments on the methods which are actually used to study these models. They will for the most part be mentioned only very briefly. In the rest of this chapter, we shall focus mainly on computer simulations. Even those will not be explained in detail, for the simple reason that the models are too different and the simulation methods too many. Rather, we refer the reader to the available textbooks on simulation methods, e.g.. Ref. 32-35, and discuss only a few technical aspects here. In the case of atomistically realistic models, simulations are indeed the only possible way to approach these systems. Idealized microscopic models have usually been explored extensively by mean field methods. Even those can become quite involved for complex models, especially for chain models. One particularly popular and successful method to deal with chain molecules has been the self-consistent field theory. In a nutshell, it treats chains as random walks in a position-dependent chemical potential, which depends in turn on the conformational distributions of the chains in... 

T. Zacharia, J. Vitek, J. Goldak, T. Debroy, M. Rappaz, H. Bhadeshia. Model Simul Mater Sei Eng 5 265, 1995. 

D. Givoli, J. E. Flaherty, M. S. Shephard. Simulation of Czochralski melt flows using parallel adaptive finite element procedures. Model Simul Mater Sci Eng 4 623, 1996. 

Pais L. S., Loureiro J. M., Rodrigues A. E. (1997b) Modeling, Simulation and Operation of a Simulated Moving Bed for Continuous Chromatographie Separation of l,l -bi-2-naphthol Enantiomers, J. Chromatogr. A 169 25-35. 

In the fluid flow model, simulation is based on Darcy s law for the steady flow of Newtonian fluids through porous media. This law states that the average... 

The Gartner model simulates charge collection by a potential-dependent space charge layer and considers diffusion into the space charge layer of charge carriers generated deep inside the semiconductor. The well-known Gartner formula for the photocurrent /ph is... 

Figure 6.25, Experimental71 (left) and modelled simulated" (right) dependence of the rate of CO oxidation on Pt deposited on J3"-A1203 as a function of pco, catalyst potential UWR and dimensionless catalyst work function Il(=A

The micro-mixed reactor with dead-polymer model simulated the product of the laboratory reactor well within experimental accuracy. 

Since our model simulated the Phase 11 results more accurately, we shall only discuss the Phase 11 results. 

In most cases models describing biogeochemical cycles are used to estimate the concentration (or total mass) in the various reservoirs based on information about source and sink processes, as in the examples given in Section 4.4. This is often called forward modeling. If direct measurements of the concentration are available, they can be compared to the model estimates. This process is referred to as model testing. If there are significant differences between observations and model simulations, improvements in the model are necessary. A natural step is then to reconsider the specification of the sources and/or the sinks and perform additional simulations. 

Figure 4-13 shows an example from a three-dimensional model simulation of the global atmospheric sulfur balance (Feichter et al, 1996). The model had a grid resolution of about 500 km in the horizontal and on average 1 km in the vertical. The chemical scheme of the model included emissions of dimethyl sulfide (DMS) from the oceans and SO2 from industrial processes and volcanoes. Atmospheric DMS is oxidized by the hydroxyl radical to form SO2, which, in turn, is further oxidized to sulfuric acid and sulfates by reaction with either hydroxyl radical in the gas phase or with hydrogen peroxide or ozone in cloud droplets. Both SO2 and aerosol sulfate are removed from the atmosphere by dry and wet deposition processes. The reasonable agreement between the simulated and observed wet deposition of sulfate indicates that the most important processes affecting the atmospheric sulfur balance have been adequately treated in the model. 

COHMAP Members (1988). Climate changes of the last 18 000 years Observations and model simulations. Science 241,1043-1052. 

A problem with the simplex-guided experiment (right panel) is that it does not take advantage of the natural factor levels, e.g., molar ratios of 1 0.5, 1 1, 1 2, but would prescribe seemingly arbitrary factor combinations, even such ones that would chemically make no sense, but the optimum is rapidly approached. If the system can be modeled, simulation might help. The dashed lines indicate ridges on the complex response surface. The two figures are schematic. 

The computer has become an accepted part of our daily lives. Computer applications in applied polymer science now are focussing on modelling, simulation, robotics, and expert systems rather than on the traditional subject of laboratory instrument automation and data reduction. The availability of inexpensive computing power and of package software for many applications has allowed the scientist to develop sophisticated applications in many areas without the need for extensive program development. 

Figure 1. Flow chart of the Polymer Analysis program. The program Is entered from a larger program, NMRl. A database must be chosen or created for the spectrum at hand and a statistical model chosen. Options In the main menu Include calculation of probabilities associated with the model, simulation of spectra, and modification of the peak table or database.

In this section, we will examine four examples that illustrate the steps, procedures, choices, and outputs involved in conducting some elementary cellular automata model simulations. The reader is advised to consult Chapter 10 to find the appropriate ways for entering parameters and making appropriate selections for each study. Following each prearranged example, some brief fiirther studies are indicated that will expand on, and fiirther illustrate, the concepts involved in the example. 

VOF or level-set models are used for stratified flows where the phases are separated and one objective is to calculate the location of the interface. In these models, the momentum equations are solved for the separated phases and only at the interface are additional models used. Additional variables, such as the volume fraction of each phase, are used to identify the phases. The simplest model uses a weight average of the viscosity and density in the computational cells that are shared between the phases. Very fine resolution is, however, required for systems when surface tension is important, since an accurate estimation of the curvature of the interface is required to calculate the normal force arising from the surface tension. Usually, VOF models simulate the surface position accurately, but the space resolution is not sufficient to simulate mass transfer in liquids. 

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