Tube-wall reactor reaction

The solution of Eq. (173) poses a rather formidable task in general. Thus the dispersed plug-flow model has not been as extensively studied as the axial-dispersed plug-flow model. Actually, if there are no initial radial gradients in C, the radial terms will be identically zero, and Eq. (173) will reduce to the simpler Eq. (167). Thus for a simple isothermal reactor, the dispersed plug flow model is not useful. Its greatest use is for either nonisothermal reactions with radial temperature gradients or tube wall catalysed reactions. Of course, if the reactants were not introduced uniformly across a plane the model could be used, but this would not be a common practice. Paneth and Herzfeld (P2) have used this model for a first order wall catalysed reaction. The boundary conditions used were the same as those discussed for tracer measurements for radial dispersion coefficients in Section II,C,3,b, except that at the wall. 

Figure 7-16 A highly simplified sketch of an automohile engine and catalytic converter with typical gas compositions indicated before and after the automotive catalytic converter. The catalytic converter is a tube wall reactor in which a noble-metal-impregnated wash coat on an extruded ceramic monolith creates surface on which reactions occur.

This problem may look at first to be the same geometry as for diffusion in a single pore, but this situation is quite drSerent hr the single pore we had reaction controlled by diffusion down the pore, while in the tube wall reactor we have convection of reactants down the tube. 

Figure 7-20 Sketch of tube wall reactor with a porous catalyst film of thickness t on walls. Expected reactant concentration profiles with reaction-limited, mass-transfer-limited, and pore-diffusion-limited reaction.

A tube-wall reactor, in which the catalyst is coated on the tube wall, is conceptually ideally suited for highly exothermic and equilibrium-limited reactions because the heat generated at the wall can be rapidly taken away by the coolant. Previous work (1) has numerically demonstrated that for highly exothermic selectivity reactions, the optimized tube-wall reactor is superior from both steady state production and dynamic points of view to the fixed-bed reactor. Also, the tube-wall reactor is being advanced as a possible reactor for carrying out methanation in coal gasification plants (2). From a reaction engineering point of view, it therefore seems appropriate to analyze the reactor for the analytically resolvable case of complex first-order isothermal reactions. 

It is our purpose to optimize the performance of a tube-wall reactor with the reaction rate constants as parameters, and also with respect to some other key design parameters. 

Open-tube reactor The conditions of analysis using an open-tube wall reactor with an enzyme immobilzed at the inner wall are very similar to assays with soluble enzymes in flow systems. A monomolecu-lar enzyme layer covalently bound to the etched inner wall of polystyrene or nylon tubes [365] has a rather low activity requiring a long tube to provide a sufficient amount of reaction product for detection. For this reason it is more advantageous to bind enzyme(s) to a polycarboxylic gel layer attached to the inner wall of a small-bore nylon tube providing a thick porous enzymatic annulus in a tubular envelope [366]. 

TI Carbon monoxide hydrogenation over cobalt catalyst in a tube-wall reactor Part II Modeling studies KW Fischer Tropsch synthesis modeling, carbon monoxide hydrogenation cobalt catalyst, tube wall reactor Fischer Tropsch reaction IT Hydrogenation catalysts... 

Good heat transfer on the outside of the reactor tube is essential but not sufficient because the heat transfer is limited at low flow rates at the inside film coefficient in the reacting stream. The same holds between catalyst particles and the streaming fluid, as in the case between the fluid and inside tube wall. This is why these reactors frequently exhibit ignition-extinction phenomena and non-reproducibility of results. Laboratory research workers untrained in the field of reactor thermal stability usually observe that the rate is not a continuous function of the temperature, as the Arrhenius relationship predicts, but that a definite minimum temperature is required to start the reaction. This is not a property of the reaction but a characteristic of the given system consisting of a reaction and a particular reactor. 

In the tubular reactor, a large amount of reaction heat is removed through the tube walls. 

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

Heat-transfer resistance Across two-phase interface in fast reactions Gas side of tube wall in liquid-cooled gas-phase or G/S reactors Within solid particles in solid-fluid reactions... 

When writing the boundary conditions for the above pair of simultaneous equations the heat transferred to the surroundings from the reactor may be accounted for by ensuring that the tube wall temperature correctly reflects the total heat flux through the reactor wall. If the reaction rate is a function of pressure then the momentum balance equation must also be invoked, but if the rate is insensitive or independent of total pressure then it may be neglected. 

Other variables of importance in designing these tubular pyrolysis reactors include the mass velocity (or flow velocity) of the gaseous reaction mixture in the tubes, pressure, steam-to-hydrocarbon-feedstock ratio, heat flux through the tube wall, and tube configuration and spacing. Pressure drop in the reactor is of major importance, especially because of the extremely high flow velocities normally employed. 

---