Reactor kinetic model

Precious Metal Catalyst Mechanism and Reactor Kinetics Modeling... 

A simulation model for the reaction-regeneration steps in the transformation of methanol into hydrocarbons has been proposed and used for predicting the behaviour of a laboratory fixed bed pseudoadiabatic reactor. Kinetic models for both the main reaction and deactivation have been used, which take into account the attenuating role of water on both the zero time kinetics and the deactivation by coke deposition. The kinetics of coke combustion and the relationship between activity and coke content have been used for the design of the regeneration. The activity-coke content relationship is different in the reaction and regeneration steps. 

When used in the integral mode, total gas production by species is measured using teflon bags to collect all the reactor effluent. The dependence of total gas production on gas-phase residence time in the gas-phase zone of the reactor is determined using the combined data of many experiments. This data can be used to infer rates of gas production within the gas-phase reactor. Kinetic models of gaseous species formation can be obtained through a study of the effects of both temperature and residence time on species production. 

Vincent G, Marquaire P-M, Zahraa O (2009) Photocatalytic degradation of gaseous 1-propanol using an annular reactor kinetic modelling and pathways. J Hazard Mater 161 1173-1181... 

Mueller M A, Yetter R A and Dryer F L 1999 Flow reactor studies and kinetic modelling of the... 

Computer simulation of the reactor kinetic hydrodynamic and transport characteristics reduces dependence on phenomenological representations and idealized models and provides visual representations of reactor performance. Modem quantitative representations of laminar and turbulent flows are combined with finite difference algorithms and other advanced mathematical methods to solve coupled nonlinear differential equations. The speed and reduced cost of computation, and the increased cost of laboratory experimentation, make the former increasingly usehil. 

Over 25 years ago the coking factor of the radiant coil was empirically correlated to operating conditions (48). It has been assumed that the mass transfer of coke precursors from the bulk of the gas to the walls was controlling the rate of deposition (39). Kinetic models (24,49,50) were developed based on the chemical reaction at the wall as a controlling step. Bench-scale data (51—53) appear to indicate that a chemical reaction controls. However, flow regimes of bench-scale reactors are so different from the commercial furnaces that scale-up of bench-scale results caimot be confidently appHed to commercial furnaces. For example. Figure 3 shows the coke deposited on a controlled cylindrical specimen in a continuous stirred tank reactor (CSTR) and the rate of coke deposition. The deposition rate decreases with time and attains a pseudo steady value. Though this is achieved in a matter of rninutes in bench-scale reactors, it takes a few days in a commercial furnace. 

Dente and Ranzi (in Albright et al., eds.. Pyrolysis Theory and Industrial Practice, Academic Press, 1983, pp. 133-175) Mathematical modehng of hydrocarbon pyrolysis reactions Shah and Sharma (in Carberry and Varma, eds.. Chemical Reaction and Reaction Engineering Handbook, Dekker, 1987, pp. 713-721) Hydroxylamine phosphate manufacture in a slurry reactor Some aspects of a kinetic model of methanol synthesis are described in the first example, which is followed by a second example that describes coping with the multiphcity of reactants and reactions of some petroleum conversion processes. Then two somewhat simph-fied industrial examples are worked out in detail mild thermal cracking and production of styrene. Even these calculations are impractical without a computer. The basic data and mathematics and some of the results are presented. 

Cropley, J.B., Systematic Errors in Recycle Reactor Kinetic Studies, Chemical Engineeiing Piogiess, February 1987, 46-51. (Model building, experimental design)... 

Five percent random error was added to the error-free dataset to make the simulation more realistic. Data for kinetic analysis are presented in Table 6.4.3 (Berty 1989), and were given to the participants to develop a kinetic model for design purposes. For a more practical comparison, participants were asked to simulate the performance of a well defined shell and tube reactor of industrial size at well defined process conditions. Participants came from 8 countries and a total of 19 working groups. Some submitted more than one model. The explicit models are listed in loc.cit. and here only those results that can be graphically presented are given. 

Cropley made general recommendations to develop kinetic models for compUcated rate expressions. His approach includes first formulating a hyperbolic non-linear model in dimensionless form by linear statistical methods. This way, essential terms are identified and others are rejected, to reduce the number of unknown parameters. Only toward the end when model is reduced to the essential parts is non-linear estimation of parameters involved. His ten steps are summarized below. Their basis is a set of rate data measured in a recycle reactor using a sixteen experiment fractional factorial experimental design at two levels in five variables, with additional three repeated centerpoints. To these are added two outlier... 

The basic problem of design was solved mathematically before any reliable kinetic model was available. As mentioned at start, the existence of solutions—that is, the integration method for reactor performance calculation—gave the first motivation to generate better experimental kinetic results and the models derived from them. 

Remarks The aim here was not the description of the mechanism of the real methanol synthesis, where CO2 may have a significant role. Here we created the simplest mechanistic scheme requiring only that it should represent the known laws of thermodynamics, kinetics in general, and mathematics in exact form without approximations. This was done for the purpose of testing our own skills in kinetic modeling and reactor design on an exact mathematical description of a reaction rate that does not even invoke the rate-limiting step assumption. 

This involves knowledge of chemistry, by the factors distinguishing the micro-kinetics of chemical reactions and macro-kinetics used to describe the physical transport phenomena. The complexity of the chemical system and insufficient knowledge of the details requires that reactions are lumped, and kinetics expressed with the aid of empirical rate constants. Physical effects in chemical reactors are difficult to eliminate from the chemical rate processes. Non-uniformities in the velocity, and temperature profiles, with interphase, intraparticle heat, and mass transfer tend to distort the kinetic data. These make the analyses and scale-up of a reactor more difficult. Reaction rate data obtained from laboratory studies without a proper account of the physical effects can produce erroneous rate expressions. Here, chemical reactor flow models using matliematical expressions show how physical... 

CASE STUDY ENZYME KINETIC MODELS FOR RESOLUTION OF RACEMIC IBUPROFEN ESTERS IN A MEMBRANE REACTOR... 

A feed concentration of 15 g glucose and 15 g xylose per litre was used over a feed rate of 20-200 ml/hr. Samples were taken at successive points along the reactor length, and the usual analysis for glucose and xylose consumption, organic acid production and cell density were done. A kinetic model for the growth and fermentation of P. acidipropionici was obtained from these data. 

The kinetic models for the gas phase polymerization of propylene in semibatch and continuous backmix reactors are based on the respective proven models for hexane slurry polymerization ( ). They are also very similar to the models for bulk polymerization. The primary difference between them lies in the substitution of the appropriate gas phase correlations and parameters for those pertaining to the liquid phase. 

The kinetic models are the same until the final stage of the solution of the reactor balance equations, so the description of the mathematics is combined until that point of departure. The models provide for the continuous or intermittent addition of monomer to the reactor as a liquid at the reactor temperature. 

This section is divided into three parts. The first is a comparison between the experimental data reported by Wisseroth (].)for semibatch polymerization and the calculations of the kinetic model GASPP. The comparisons are largely graphical, with data shown as point symbols and model calculations as solid curves. The second part is a comparison between some semibatch reactor results and the calculations of the continuous model C0NGAS. Finally, the third part discusses the effects of certain important process variables on catalyst yields and production rates, based on the models. 

Reactor Variable Study. Assuming that the kinetic models are valid, we have a means to rapidly explore the effects of making certain changes in the catalyst or in the operating conditions. Fortunately, Wisseroth published the results for two runs at 100 C and two more runs at 20 atm in his Table 3 (1 ). 

To do this we developed a computer model to predict the kinetic conditions during the runaway stage. The kinetic model is used to estimate the reaction rates, temperatures, pressures, viscosities, conversions, and other variables which influence reactor design. 

The selectivity is 100% in this simple example, but do not believe it. Many things happen at 625°C, and the actual effluent contains substantial amounts of carbon dioxide, benzene, toluene, methane, and ethylene in addition to styrene, ethylbenzene, and hydrogen. It contains small but troublesome amounts of diethyl benzene, divinyl benzene, and phenyl acetylene. The actual selectivity is about 90%. A good kinetic model would account for aU the important by-products and would even reflect the age of the catalyst. A good reactor model would, at a minimum, include the temperature change due to reaction. 

Example 4.6 Use the kinetic model of Example 4.5 to determine the outlet concentration for the loop reactor if the operating conditions are the same as in Run 1. 

The results of Example 5.2 apply to a reactor with a fixed reaction time, i or thatch- Equation (5.5) shows that the optimal temperature in a CSTR decreases as the mean residence time increases. This is also true for a PFR or a batch reactor. There is no interior optimum with respect to reaction time for a single, reversible reaction. When Ef < Ef, the best yield is obtained in a large reactor operating at low temperature. Obviously, the kinetic model ceases to apply when the reactants freeze. More realistically, capital and operating costs impose constraints on the design. 

Chapter 10 begins a more detailed treatment of heterogeneous reactors. This chapter continues the use of pseudohomogeneous models for steady-state, packed-bed reactors, but derives expressions for the reaction rate that reflect the underlying kinetics of surface-catalyzed reactions. The kinetic models are site-competition models that apply to a variety of catalytic systems, including the enzymatic reactions treated in Chapter 12. Here in Chapter 10, the example system is a solid-catalyzed gas reaction that is typical of the traditional chemical industry. A few important examples are listed here ... 

Reactor design usually begins in the laboratory with a kinetic study. Data are taken in small-scale, specially designed equipment that hopefully (but not inevitably) approximates an ideal, isothermal reactor batch, perfectly mixed stirred tank, or piston flow. The laboratory data are fit to a kinetic model using the methods of Chapter 7. The kinetic model is then combined with a transport model to give the overall design. 

The glycolysis of PETP was studied in a batch reactor at 265C. The reaction extent in the initial period was determined as a function of reaction time using a thermogravimetric technique. The rate data were shown to fit a second order kinetic model at small reaction times. An initial glycolysis rate was calculated from the model and was found to be over four times greater than the initial rate of hydrolysis under the same reaction conditions. 4 refs. 

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