Building a Steady-State Model

In this section we use an extractive distillation column as an example to demonstrate how to build a steady-state simulation. This is one column of an overall two-column system for separating isopropanol and water. The detailed design and control of the overall distUlation system will be given in Chapter 10. 

Design and Control of Distillation Systems for Separating Azeotropes. By William L. Luyben and 1-Lung Chien Copyright 2010 John Wiley Sons, Inc. 

The purpose of the solvent entrainer in this extractive distillation column is to alter the relative volatility between IPA and water, making IPA go to the top of the column and water go to the bottom of the column. The upper section of the column (above the entrainer feed location) is called the rectifying section, and its purpose is to separate the IPA and the entrainer. The middle section of the column (between the entrainer feed stage and the fresh feed stage) is called the extractive section. The purpose of this section is to suppress water from going up the column. The bottom section of the column (below the fresh feed location) is called the stripping section, and its purpose is to keep IPA from going down the column. The bottoms product of the column is the mixture of water and the entrainer, and it is fed to another downstream entrainer recovery column to separate these two components, so the entrainer can be recycled back to the extractive distillation column. 

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In this chapter, the detailed step-by-step instructions to build a steady-state model are given with an extractive distillation column example. The unit operation blocks such as RadFrac,... 

Decanter, Heater, and HeatX used in this book are also explained. For the situation when a particular chemical component cannot be found in Aspen, a way to add a nondatabank component into an Aspen simulation is also demonstrated with an example. Following step-by-step instructions in this chapter, the reader should have a basic knowledge of building a steady-state model. 

Also, because initiation of homogeneous explosives results in overdriven detonations in the practical case, they will not exhibit build-up. The nitromethane experimental data seem to scale and to be adequately described by a steady-state model. The nitromethane overdriven detonation may decay to a steady-state detonation or may decay to a flow that continues to be time dependent (oscillates), perhaps requiring greater experimental resolution to detect. 

Indoor air quality models that include chemistry and all other important source and loss mechanisms have been developed by a variety of authors (Nazaroff and Cass, 1986 Weschler, Shields and Naik, 1989). These models can be used to determine if a relevant change is likely to occur, by balancing pollutant source rates with removal rates to arrive at a predicted indoor concentration. The key components are shown here for a steady-state, well-mixed mass-conservation model of a building ... 

Using available flowsheeting software, it is possible to produce a computerized tool that will permit us to learn or even mirror the plant behaviour under different operating conditions or with different raw materials and product specifications. Such as tool is called the steady state plant simulation model. The steady state model, whieh is simpler to build, and has a wide variety of applications in its own right, it can be used directly in revamping and a wide variety of other engineering projeets. 

Fig. 5.16. Time evolution of the site occupation by O and CO of the two prominent adsorption sites at the RuO2(110) model catalyst surface shown in Fig. 5.14. The temperature and pressure conditions chosen (T = 600K, pco = 20atm., P02 = 1 atm.) correspond to optimum catalytic performance, cf. Fig. 5.15. Under these conditions, kinetics builds up a steady state surface population in which O and CO compete for either site type at the surface, as reflected by the strong fluctuations in the site occupations (from [53])...

The second concern is the assumption that Mg is deactivated when it reacts with RX. This assumption aligns the D model for Mg w-ith the reaction scheme treated by Andrieux and Saveant 1128.125)]. in which the reducing agent K is consumed as it reacts. Otherwise. Mg would build up continuously in the reaction zone and not reach a steady state. 

Seigel et al. [51] developed a multi-phase, two-dimensional model. The model was a two-dimensional steady state model, which studied transport limitations due to water build up in the cathode catalyst region. They considered water in three phases liquid, gas and dissolved (membrane phase). They found that treating the catalyst layer as a very thin interface imderestimates the transport limitations due to water build-up. Hence, they modeled the catalyst layer as a finite region. Their model showed that 20-40% of the water building up at the cathode catalyst layer comes fi om water which is transported across the membrane. This problem may be coimteracted by applying a pressure differential to force back diffusion of water, i.e., from cathode to anode. 

Stirred tanks typically contain one or more impellers mounted on a shaft, and optionally, baffles and other internals. Although it is a straightforward matter to build a 3D mesh to contour to the space between these elements, the mesh must be built so that the solution of the flow field incorporates the motion of the impeller. This can be done in two ways. First, the impeller geometry can be modeled directly, or explicitly, and the grid and solution method chosen so as to incorporate the motion of the impeller using either a steady-state or time-dependent techniqne. This approach is discussed in detail in Section 5-5. Second, the motion of the impeller can be modeled implicitly, using time-averaged experimental velocity data to represent the impeller motion. The second approach is the subject of this section. 

Many indoor pollutants can be modeled as nonreactive and as having a constant source, no appreciable sink, and a negligible concentration in outdoor air. To estimate the pollutant concentration inside a building at steady state (i.e., (rf(Cu side)/rfO building equals zero), Eq. (4.14) can be simplified to... 

CFD is appropriate in cases where the detailed flow field is of interest in a configuration with mostly known or at least steady-state boundary conditions (surface temperatures). Combined thermal and ventilation modeling is more suited to cases where the dynamic behavior of the building masses and the changing driving forces for the natural ventilation are of importance. 

Now, we need a solution to the plug flow with dispersion model for steady-state operation of an air-stripping tower. The mass transport equation for this situation, assuming minimal trichloroethylene builds up in the bubble, is... 

In combustion systems it is generally desirable to minimize the concentration of intermediates, since it is important to obtain complete oxidation of the fuel. Figure 13.5 shows modeling predictions for oxidation of methane in a batch reactor maintained at constant temperature and pressure. After an induction time the rate of CH4 consumption increases as a radical pool develops. The formaldehyde intermediate builds up at reaction times below 100 ms, but then reaches a pseudo-steady state, where CH2O formed is rapidly oxidized further to CO. Carbon monoxide oxidation is slow as long as CH4 is still present in the reaction system once CH4 is depleted, CO (and the remaining CH2O) is rapidly oxidized to CO2. 

This is the kinetic equation for a simple A/AX interface model and illustrates the general approach. The critical quantity which will be discussed later in more detail is the disorder relaxation time, rR. Generally, the A/AX interface behaves under steady state conditions similar to electrodes which are studied in electrochemistry. However, in contrast to fluid electrolytes, the reaction steps in solids comprise inhomogeneous distributions of point defects, which build up stresses at the boundary on a small scale. Plastic deformation or even cracking may result, which in turn will influence drastically the further course of any interface reaction. 

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