Rate-based model

From the above list of rate-based model equations, it is seen that they total 5C -t- 6 for each tray, compared to 2C -t-1 or 2C -t- 3 (depending on whether mole fractious or component flow rates are used for composition variables) for each stage in the equihbrium-stage model. Therefore, more computer time is required to solve the rate-based model, which is generally converged by an SC approach of the Newton type. 

A study of industrial apphcatious by Taylor, Kooijmau, and Woodman [IChemE. Symp. Ser. Distillation and Absorption 1992, A415-A427 (1992)] concluded that rate-based models are particularly desirable when simulating or designing (1) packed columns, (2) systems with strongly uonide liquid solutions, (3) systems with trace compo-... 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

The rate-based model gave a distillate with 0.023 mol % ethylbenzene and 0.0003 mol % styrene, and a bottoms product with essentially no methanol and 0.008 mol % toluene. Miirphree tray efficiencies for toluene, styrene, and ethylbenzene varied somewhat from tray to tray, but were confined mainly between 86 and 93 percent. Methanol tray efficiencies varied widely, mainly from 19 to 105 percent, with high values in the rectifying section and low values in the stripping section. Temperature differences between vapor and liquid phases leaving a tray were not larger than 5 F. 

The present economic and environmental incentives for the development of a viable one-step process for MIBK production provide an excellent opportunity for the application of catalytic distillation (CD) technology. Here, the use of CD technology for the synthesis of MIBK from acetone is described and recent progress on this process development is reported. Specifically, the results of a study on the liquid phase kinetics of the liquid phase hydrogenation of mesityl oxide (MO) in acetone are presented. Our preliminary spectroscopic results suggest that MO exists as a diadsorbed species with both the carbonyl and olefin groups coordinated to the catalyst. An empirical kinetic model was developed which will be incorporated into our three-phase non-equilibrium rate-based model for the simulation of yield and selectivity for the one step synthesis of MIBK via CD. 

The liquid phase kinetics of the selective hydrogenation of mesityl oxide in acetone were studied for the purpose of developing a robust kinetic model to be integrated into an existing non-equilibrium rate-based model for the simulation of the CD process for MIBK production. A typical concentration versus time profde is illustrated in Figure 2. MIBK was produced with veiy high selectivity with essentially all of the MO converted to MIBK. Products from the... 

Some important general aspects of rate-based modeling as well as further peculiarities of the specific process applications and the different solution strategies are given in Appendices A and B. 

Despite the recent rapid development of computer technology and numerical methods, the rate-based approach in its current realization still often requires a significant computational effort, with related numerical difficulties. This is one of the reasons the application of rate-based models to industrial tasks is rather limited. Therefore, further work is required in order to bridge this gap and provide chemical engineers with reliable, consistent, robust, and comfortable simulation tools for reactive separation processes. 

Yuxiang Z, Xien X. Study on catalytic distillation processes. Part B. Simulation of catalytic distillation processes—quasi-homogenous and rate-based model. Trans IChemE 1992 70 465 470. 

APPENDIX A. A DETAILED DESCRIPTION OF RATE-BASED MODELING... 

The mass balance equations of the traditional multicomponent rate-based model (see, e.g., Refs. 57 and 58) are written separately for each phase. In order to give a common description to all three considered RSPs (where it is possible, of course) we will use the notion of two contacting fluid phases. The first one is always the liquid phase, whereas the second fluid phase represents the gas phase for RA, the vapor phase for RD and the liquid phase for RE. Considering homogeneous chemical reactions taking place in the fluid phases, the steady-state balance equations should include the reaction source terms ... 

The rate-based models suggested up to now do not take liquid back-mixing into consideration. The only exception is the nonequilibrium-cell model for multicomponent reactive distillation in tray columns presented in Ref. 169. In this work a single distillation tray is treated by a series of cells along the vapor and liquid flow paths, whereas each cell is described by the two-film model (see Section 2.3). Using different numbers of cells in both flow paths allows one to describe various flow patterns. However, a consistent experimental determination of necessary model parameters (e.g., cell film thickness) appears difficult, whereas the complex iterative character of the calculation procedure in the dynamic case limits the applicability of the nonequilibrium cell model. 

The rate-based models usually use the two-film theory and comprise the material and energy balances of a differential element of the two-phase volume in the packing (148). The classical two-film model shown in Figure 13 is extended here to consider the catalyst phase (Figure 33). A pseudo-homogeneous approach is chosen for the catalyzed reaction (see also Section 2.1), and the corresponding overall reaction kinetics is determined by fixed-bed experiments (34). This macroscopic kinetics includes the influence of the liquid distribution and mass transfer resistances at the liquid-solid interface as well as dififusional transport phenomena inside the porous catalyst. 

The component mass balance equations of the traditional multicomponent rate-based model (see, e.g., Refs. [15, 16]) are written separately for each phase. As chemical reactions take place in the fluid phases, the steady-state balance equations should include the reaction source terms ... 

In this section, four examples illustrating the application of the rate-based modeling approach discussed above are presented. First three reactive absorption processes -namely absorption of NOx, coke gas purification and CO2 absorption by aqueous... 

The predictions of the analytical model [100] and the calculations performed in Ref. [70] using the rate-based model described above are compared with experimental data in Fig. 9.23. It can be seen that the theoretical results obtained with both... 

Reactive absorption occurs in multiphase multicomponent fluid systems, and a single modeling approach for all - in part very different - processes, is desirable. Such an approach is suggested here, whereby an application of a reactive rate-based model as a suitable and accurate method is recommended. This method employs a kinetic description of diffusion and reaction steps. 

Despite highly developed computer technologies and numerical methods, the application of new-generation rate-based models requires a high computational effort, which is often related to numerical difficulties. This is a reason for the relatively limited application of modeling methods described above to industrial problems. Therefore, a further study in this field - as well as in the area of model parameter estimation - is required in order to bridge a gap and to provide process engineers with reliable, consistent, robust and user-friendly simulation tools for reactive absorption operations. 

R. Kleerebezem, et ah, Rate-based modelling of SO2 absorption into aqueous NaHC03/Na2CC>3 solutions accompanied by the desorption of CO2, Chem. Eng. Sci., 2003, 58, 3589-3600. 

Egorov, Y., Menter, F., Kloeker M., Kenig, E.Y. On the combination of CFD and rate-based modelling in the simulation of reactive separation processes. Chem. Eng. Process., Vol. 44, 631-644, 2005. 

Eldrige, R.B., A comparison of steady-state equilibrium and rate based models for packed reactive-distillation columns,... 

In this case study we will model, simulate and design an industrial-scale BioDeNOx process. Rigorous rate-based models of the absorption and reaction units will be presented, taking into account the kinetics of chemical and biochemical reactions, as well as the rate of gas-liquid mass transfer. After transformation in dimensionless form, the mathematical model will be solved numerically. Because of the steep profiles around the gas/liquid interface and of the relatively large number of chemical species involved, the numerical solution is computationally expensive. For this reason we will derive a simplified model, which will be used to size the units. Critical design and operating parameters will be identified... 

Real distillation processes, however, nearly always operate away from equilibrium. In recent years it has become possible to simulate distillation and absorption as the mass-transfer rate-based operations that they really are, using what have become known as nonequilibrium (NEQ) or rate-based models [Taylor et ah, CEP (July 28, 2003)]. 

In recent years a new approach to the modeling of distillation and absorption processes has become available the nonequilibrium or rate-based models. These models treat these classical separation processes as the mass-transfer rate governed processes that they really are, and avoid entirely the (a priori) use of concepts such as efficiency and HETP [Krishnamurthy and Taylor, AZChE/., 31, 449-465 (1985) Taylor, Kooijman, and Hung, Comput. Chem. Engng., 18, 205-217 (1994)]. 

The liquid composition, flow, and temperature profiles are shown in Fig. 13-56. In this particular system the vapor and liquid temperatures estimated by the rate-based model are quite close (as often is the case in distillation operations). 

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