Bubble assemblage model for fluidized bed catalytic reactors

Publisher Summary This chapter focuses on two idealized patterns (of all possible flow patterns), plug flow and back-mix flow. Plug flow assumes that fluid moves through the vessel “in single file” with no overtaking or mixing with earlier or later entering fluid. Back-mix flow assumes that the fluid in the equipment is perfectly mixed and uniform in composition throughout the vessel. All patterns of flow other than plug and back-mix flow may be called nonideal flow patterns because for these the design methods are not nearly as straightforward as those for the two ideal flow patterns. The treatment of nonideal flow patterns discussed in the chapter divides naturally into two parts: flow of single fluids and flow of two fluids. The main emphasis falls on the nonideal flow of single fluids through process equipment. Conversion in a reactor with nonideal flow can be determined either directly from tracer information or by use of flow models. The distribution of residence times gives information on how long various elements of fluid spend in the reactor but not on the detailed exchange of matter within and among the elements. The exact nature of the surrounding molecules is of no importance. Thus, the distribution of residence times yields sufficient information for the prediction of the average concentration in the reactor effluent. Because of a lack of applications, conversion expressions for two region models have not been developed for homogeneous systems. For heterogeneous systems, the appropriate expressions can be found in the works of the individual investigators.

Patterns of Flow in Chemical Process Vessels

Publisher Summary A chemical reaction is no exception, because it does possess some true mechanism that is descriptive of every microscopic detail of the reaction. In practice, of course, a complete description of this mechanism cannot be obtained and approximations must be made. This chapter presents statistical methods for developing mathematical descriptions, either theoretical or empirical, of reacting systems. The term model is used to describe a wide range of chemical engineering subjects. Chemical engineering modeling activities in general can be thought of as belonging to one of the three members of a nested set. The outermost member is plant modeling. This entails the description of, for example, an entire refinery complex, taking into full account topics ranging from crude resources to geographical product distributions. Several models, such as plant model, economic model, process model, mechanistic model, power-function models, hyperbolic models, reaction-rate model are discussed to explain chemical reactions in different ways. Certain diagnostic parameters are exploited recently to allow discrimination among several rival models. These diagnostic parameters can be grouped into two broad classes. There are two primary advantages to the use of diagnostic parameters in reaction-rate modeling. First, the use of these parameters allows an easy analysis of the adequacy of the model. Second, in some cases, the diagnostic analysis will not only indicate a model inadequacy but also can suggest the precise nature of the inadequacy. Then, the model can be appropriately changed to remove this inadequacy.

Mathematical Modeling of Chemical Reactions

Kinetic models analysis

Publisher Summary Flow properties of the fluidized catalyst bed (FCB) are different from those of other conventional fluidized beds. The different treatment required is very significant for research and development on fluidized catalytic beds. This chapter discusses the factors affecting the flow properties. These properties include particle size distribution, also heat and mass transfer, and mixing properties. In the FCB, the dilute phase plays an important role in advancing the catalytic reaction when reaction rates are high. This factor provides a basis for identifying the appropriate reaction model and clarifying the effect of the dilute phase on selectivity and stability. The simplified theory for a bubble column is applied to understand particle circulation in the FCB. As a result, it is possible to analyze flow patterns of bubbles and “emulsion.” This chapter considers the uses of fluidized beds for catalytic reactions, using a viewpoint quite different from studies directed toward the physical handling of solid particles or toward gas–solid noncatalytic reaction. Particle size distribution has a great effect on most aspects of fluidization. Fluid beds are usually operated in the turbulent-flow region to obtain good contact and sufficient throughput of reactant gas. The uniformity and contact efficiency of a fluid bed can be improved by immersion of a surface within the bed.

Transport Phenomena and Reaction in Fluidized Catalyst Beds

Conventional data generation and analysis procedures used to select a descriptive Hougen-Watson reaction rate model have been reviewed and some statistical objections to these conventional procedures have been presented. In an attempt to assess the practical importance of these objections, a recently published example was analyzed with both conventional techniques and nonlinear least squares procedures, which more closely conform to theoretical weighting requirements. Comparisons were made between the results of the conventional linear least squares analysis of isothermal data and those of nonlinear least squares analyses of both isothermal and nonisothermal data. It was found that the nonlinear least squares procedures were useful for a rational selection of an acceptable model and estimation of its parameters.

General observations were made concerning good regions for further experimentation if a discrimination among rival models is desired. Additional well-designed experiments were found to be necessary to allow a reduction of the confidence region of the parameters of the Hougen-Watson models to an acceptable size.

Nonlinear least squares analysis of catalytic rate models

A method is reviewed which allows data points to be chosen in such a fashion that precise estimates of the parameters in nonlinear reaction rate models can be obtained. This method allows each future data point to be selected such that the confidence region of the estimated parameters is smaller with it than with any other possible data point within the region of experimentation. This procedure is applied for Hougen-Watson models with hypothetical experimental data which were generated with the guidance of an example from the current chemical engineering literature. It is found that, for the same number of data points, the parameters in the model can be estimated eighteen times more precisely by using this suggested experimental design than by another commonly used design. Confidence regions are presented for the parameters of the Hougen-Watson models with two types of designs.



It is found that the positions of the data points in the well-designed experiments are more sensitive to the functional form of the model than to the current estimates of the magnitudes of the parameter values.

Obtaining precise parameter estimates for nonlinear catalytic rate models

Effect of fluidization on catalytic cumene dealkylation

A method of estimating the true conditions of operation of a bubble-cap tray is presented. Intermediate between the Murphree and the Lewis methods, which represent the extremes of actual operation, this method involves the use of a correlation to determine the degree of liquid mixing on the tray and the use of new relations between the Murphree vapor efficiency, the Lewis case I efficiency, and the true local efficiency. For the last, partial liquid mixing is taken into account.

Data were obtained on an 18-in. O.D. three-tray bubble-cap tower containing ten 3-in. bubble caps a tray. Partial liquid mixing was correlated for changes in vapor and liquid rates, pressure, temperature, and weir height for the system ethylene dichloride-toluene.

Efficiency data on acetone-water, ethanol-water, and ethylene dichloride-toluene showed the following effects: (1) low concentration of lwo boiler usually, but not always, resulted in low true local efficiencies, always with high Murphree efficiencies; (2) vapor velocity effects are more intimately connected with slot velocity than superficial velocity (and hence entrainment); (3) raising the pressure gives higher efficiencies; (4) an increase in liquid depth increases the true local efficiency but may have no effect on the Murphree efficiency.

C. C. Watson

Papers

Nonlinear least squares analysis of catalytic rate models

Obtaining precise parameter estimates for nonlinear catalytic rate models

Effect of fluidization on catalytic cumene dealkylation

Correlation of bubble-cap fractionating-column plate efficiencies