Steady State and Dynamic Models

In considering kinetic models which can display oscillatory behaviour, it is useful to recall the Langmuir-Hinshelwood approach to a simple reaction such as the oxidation of CO, taking place in a closed system and consider the commonly adopted assumptions  

The adsorption of the gases on surface metal sites followed by reaction could be written as  

Cutlip, C. Hawkins, D. Mukesh, W. Morton, and C. N. Kenney, submitted to 

The adsorption-desorption steps are fast compared with surface reaction so the term in can be neglected in equation (3). 

A steady state is established between gas-phase and surface concentrations so the time derivatives in equations (2) and (3), etc. are effectively zero. 

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Figure 1 Overview of transport models for predicting oral drug absorption. Absorption models are classified into three categories based on their dependence on the spatial and temporal variables. These three categories are quasi-equilibrium, steady-state, and dynamic models. 

Lazman M., Algebraic geometry methods in analysis of quasi steady state and dynamic models of cataljdic reactions. Proceedings of the 4th International Conference on Unsteady-State Processes in Catalysis USPC-4, Montreal, Quebec, Canada, October 26-29, 2003, Dr. H. Sapoundjiev (Ed.), Natural Resources Canada, 92-93 (2003a). 

In this section we have developed steady-state and dynamic models for a hetere-geneous system. Specifically, we have chosen the bubbling fluidized bed catalytic reactor, which has many industrial applications. We have built the model for a consecutive reaction A —> B —> C with the component B being the desired component. 

Show that the steady- state and dynamic models for a double-pipe, counter-current heat exchanger can have the same form as the model of a packed bed absorber. Discuss the assumptions inherent in both the heat exchanger and the absorber models which might lead to significant differences in the kinds of model equations used to describe each system. 

This chapter presents an overview of reactive absorption, which is one of the most important industrial reactive separation operations. Industrially relevant systems and equipment are highlighted, the modeling basics and peculiarities are detailed, and the methods of model parameter estimation are discussed. Both steady-state and dynamic modeling issues are addressed. The implementation of the theoretical description is illustrated with a number of up-to-date applications and validated against laboratory-, pilot- and industrial-scale experiments. 

Schwedock, M. J., L. C. Windes, and W. H. Ray, Steady state and dynamic modelling of a packed bed reactor for the partial oxidation of methanol to formaldehyde-H. Experimental results compared with model predictions, Chem. Eng. Commun., 78, 45-71 (1989). 

Cho, Y. S., and Joseph, B. Reduced-Order Steady-State and Dynamic Models for Separation Processes, AIChE J, 29, 261-269, 270-276 (1983). 

In selecting a computation model, it is important to make a clear distinction between steady-state and dynamic models. For instance, steady-state soil models. 

Hence, the development of a Plant Simulation Model is the proper approach to deal with industrial simulation problems. The progress in software technology makes possible today the development of integrated steady state and dynamic models. However, these require significant investment in qualified staff. Recently, generic simulation products have been proposed for applications in refining and petrochemical industries, which can be customised for specific processes. 

Most of the published literature on reactive distillation (RD) has been focussed mainly on aspects such as conceptual design with the aid of residue curve maps, steady-state multiplicity and bifurcations, and development of equilibrium (EQ) stage and rigorous non-equilibrium (NEQ) steady-state and dynamic models [1, 2]. Relatively little attention has been paid to hardware design. In this chapter the concepts underlying the selection of the appropriate hardware for RD columns are discussed. For RD column design, detailed information on hydrodynamics and mass transfer for the chosen hardware is required, but this information is often lacking. Modern tools such as computational fluid dynamics (CFD) can be invaluable aids in hydrodynamic and mass-transfer studies. 

Khare, N.P., Lucas, B., Seavey, K.C., Liu, Y.A. Steady-state and dynamic modeling of gas-phase polypropylene processes using stiired-bed reactors. Ind. Eng. Chem. Res. 43, 884-900 (2004)... 

The objective of this chapter is to give a comprehensive overview of both basics and peculiarities of RD modeling. A detailed description covers balance equations, mass and heat transfer, reaction kinetics including reaction-mass-transfer coupling, as well as steady-state and dynamic modeling issues. The achievements in the theoretical description are illustrated with several case studies supported by laboratory- and pilot-scale experimental investigations. 

Smaller excursions and faster responses to setpoint changes and load disturbances move the operation back to the desired steady state faster and with less variation in the yield and productivity (and, of course, the product quality). This relies mainly on steady-state and dynamic models. 

Formulate steady-state and dynamic models for the tubular heat exchanger shown in Figure P4.14 Hint We will get a partial differential equation for the dynamic model). 

Rigorous heterogeneous steady-state and dynamic models for this immobilized packed-bed fermentor with/without membranes should be developed and used to analyze and optimize this novel configuration (refer to the section in Chapter 6 regarding distributed modeling of fermentation). 

Equation oriented Steady-state and dynamic modeling... 

In the proposed framework, HYSYS. PLANT simulation package is used to validate both the steady state and dynamic models even though the switchability fiom steady state to dynamic mode is not a trivial procedure, as it will be shown in the case study section. 

Ray, W., Windes, L. and Schwedock, M. (1989). Steady-State and Dynamic Modelling of a Packed-Bed Reactor for the Parhal Oxidahon of Methanol to Formaldehyde, Chem. Eng. Comm., 78, pp. 1-43. 

The rigorous steady-state and dynamic models used in this book are solved using Matlab programs or Aspen Technology simulation software (Aspen Plus and Aspen Dynamics). 

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