Catalytic reactors wall heat transfer

Modeling of the packed bed catalytic reactor under adiabatic operation simply involves a slight modification of the boundary conditions for the catalyst and gas energy balances. A zero flux condition is needed at the outer reactor wall and can be obtained by setting the outer wall heat transfer coefficients /iws and /iwg (or corresponding Biot numbers) equal to zero. Simulations under adiabatic operation do not significantly alter any of the conclusions presented throughout this work and are often used for verification... 

Radial dispersion of mass and heat in fixed bed gas-solid catalytic reactors is usually expressed by radial Peclet number for mass and heat transport. In many cases radial dispersion is negligible if the reactor is adiabatic because there is then no driving force for long range gradients to exist in the radial direction. For non-adiabatic reactors, the heat transfer coeflScient at the wall between the reaction mixture and the cooling medium needs also to be specified. 

Mears [97] found that the reaction rates in fixed-bed catalytic reactors are highly affected by two heat transfer resistances resistance to radial heat transfer and resistance to particle-to-fluid heat transfer. Considerable effort has therefore been directed toward finding the effective radial conductivity and the fluid-to-wall heat transfer coefficient (which represents the radial heat transport) and particle-liquid heat transfer coefficient (which represents particle-to-fluid heat transport). 

The parameter p (= 7(5 ) in gas-liquid sy.stems plays the same role as V/Aex in catalytic reactions. This parameter amounts to 10-40 for a gas and liquid in film contact, and increases to lO -lO" for gas bubbles dispersed in a liquid. If the Hatta number (see section 5.4.3) is low (below I) this indicates a slow reaction, and high values of p (e.g. bubble columns) should be chosen. For instantaneous reactions Ha > 100, enhancement factor E = 10-50) a low p should be selected with a high degree of gas-phase turbulence. The sulphonation of aromatics with gaseous SO3 is an instantaneous reaction and is controlled by gas-phase mass transfer. In commercial thin-film sulphonators, the liquid reactant flows down as a thin film (low p) in contact with a highly turbulent gas stream (high ka). A thin-film reactor was chosen instead of a liquid droplet system due to the desire to remove heat generated in the liquid phase as a result of the exothermic reaction. Similar considerations are valid for liquid-liquid systems. Sometimes, practical considerations prevail over the decisions dictated from a transport-reaction analysis. Corrosive liquids should always be in the dispersed phase to reduce contact with the reactor walls. Hazardous liquids are usually dispensed to reduce their hold-up, i.e. their inventory inside the reactor. 

It is well known that during liquefaction there is always some amount of material which appears as insoluble, residual solids (65,71). These materials are composed of mixtures of coal-related minerals, unreacted (or partially reacted) macerals and a diverse range of solids that are formed during processing. Practical experience obtained in liquefaction pilot plant operations has frequently shown that these materials are not completely eluted out of reaction vessels. Thus, there is a net accumulation of solids within vessels and fluid transfer lines in the form of agglomerated masses and wall deposits. These materials are often referred to as reactor solids. It is important to understand the phenomena involved in reactor solids retention for several reasons. Firstly, they can be detrimental to the successful operation of a plant because extensive accumulation can lead to reduced conversion, enhanced abrasion rates, poor heat transfer and, in severe cases, reactor plugging. Secondly, some retention of minerals, especially pyrrhotites, may be desirable because of their potential catalytic activity. 

The One-Dimensional Pseudo Homogeneous Model of Fixed Bed Reactors. The design of tubular fixed bed catalytic reactors has generally been based on a one-dimensional model that assumes that species concentrations and fluid temperature vary only in the axial direction. Heat transfer between the reacting fluid and the reactor walls is considered by presuming that all of the resistance is contained within a very thin boundary layer next to the wall and by using a heat transfer coefficient based on the temperature difference between the fluid and the wall. Per unit area of the tube... 

Boundary conditions are part of the mathematical description of a process. For the energy balance, the condition at the vessel wall is that the rate of heat transfer by conduction equals the rate of transfer to the heat transfer medium. Similarly the rate of mass transfer at the wall equals the rate of reaction on the wall if that is catalytic, or equals zero when the wall is inert and impermeable. Clearly, the temperature, composition and pressure of the inlet to the reactor are part of the problem specification. 

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)]... 

Two other crucial factors are mass transfer and heat transfer. In Chapter 3 we assumed that the reactions were homogeneous and well stirred, so that every substrate molecule had an equal chance of getting to the catalytic intermediates. Here the situation is different. When a molecule reaches the macroscopic catalyst particle, there is no guarantee that it will react further. In porous materials, the reactant must first diffuse into the pores. Once adsorbed, the molecule may need to travel on the surface, in order to reach the active site. The same holds for the exit of the product molecule, as well as for the transfer of heat to and from the reaction site. In many gas/solid systems, the product is hot as it leaves the catalyst, and carries the excess energy out with it. This energy must dissipate through the catalyst particles and the reactor wall. Uneven heat transfer can lead to hotspots, sintering, and runaway reactions. 

The correct evaluation of catalytic properties demands that heat and mass transfer limitations are eliminated or properly accounted for. It also demands that the catalyst is in the working state, as opposed to the transient state observed at the beginning of most catalytic tests. The absence of gas-phase reactions or reactions catalyzed by the reactor wall should also be verified. This must be kept in mind in the following, in which measurement methods, kinetic analyses including the influence of heat and mass transfer and deactivation or, more generally, time-dependent effects will be examined. Regeneration of catalysts will be examined at the end. 

Theologos and Markatos (1992) used the PHOENICS program to model the flow and heat transfer in fluidized catalytic cracking (FCC) riser-type reactors. They did not account for collisional particle-particle and particle-wall interactions and therefore it seems unlikely that this type of simulation will produce the correct flow structure in the riser reactor. Nevertheless it is one of the first attempts to integrate multiphase hydrodynamics and heat transfer. 

Control of the temperature throughout the reforming catalyst bed can be established by use of a monolithic catalyst. The heat transfer control can be accomplished by combining three effects that monolithic catalyst beds can impact significantly (1) direct, uniform contact of the catalyst bed with the reactor wall will enhance conductive heat transfer (2) uniformity of catalyst availability to the reactants over the length of the flow will provide continuity of reaction and (3) coordination of void-to-catalyst ratio with respect to the rate of reaction will moderate gas-phase cracking relative to catalytically enhanced hydrocarbon-steam reactions. This combination provides conditions for a more uniform reaction over the catalyst bed length. 

The boundary condition of the governing partial differential equation that describes mass transfer in a reactor with catalytic walls, differs from the standard boundary conditions assumed in most texts on heat transfer in rod bundles (either constant wall temperature/concentration or constant heat/mass flux). However, the Sherwood number of a reactor with catalytic walls will lie between the values obtained for these two standard boundary conditions, which deviate less than 30% for relative pitches higher than 1.1. 

Mass transfer of reactants and products to and from the catalytically active surface in a reactor equipped with an OCFS is a function of the geometry of the structure and of the flow regime within it alone. Heat transfer to and from the reactor, on the other hand, is additionally a function of the flow regime between the structure and the reactor wall. For this reason mass transfer and heat transfer are treated separately in the following. 

---