The role of pellet thermal stability in reactor design for heterogeneously catalysed chemical reactions

For exothermic fluid-phase reactions, a reactor which is cooled at the wall can exhibit multiplicity or parametric sensitivity. Moreover, for heterogeneously catalysed exothermic fluid-phase reactions, each of the catalytically active pellets in the reactor can exhibit multiplicity. Both forms of multiplicity can lead to thermal instability and as such have to be taken into account in reactor design. Here the effect of both instabilities is quantified. To this end, simple first-order kinetics are assumed, and intraparticle resistances and reactor and particle dynamics are not considered. A one-dimensional model, consisting of microscale mass and heat balances, is chosen to describe the reactor. It is assumed that the fluid inlet temperature equals the coolant temperature. The pellet scale model is a combined mass and heat balance for the pellet and it assumes that the Chilton¿Colburn analogy holds. For its incorporation in the reactor model it is assumed that for every individual pellet heat removal to neighbouring pellets via the mutual contact spots is negligible as compared to the heat transferred to the surrounding fluid. Consequently every pellets is isolated from its neighbours. In the thermally most critical region, i.e. the hot-spot region, reactor stability is determined by three parameter groups: a dimensionless adiabatic temperature rise, an Arrhenius number or dimensionless activation temperature and the ratio of the number of heat transfer units to the number of reaction units. For pellet multiplicity, a fourth parameter group becomes significant in addition: the ratio of the reaction rate to the pellet mass transfer rate. This number depends on the pellet size. A general recipe is given which enables us to determine whether or not pellet thermal instability can become important in reactor operation. For the situation where it is significant, generalized diagrams are presented indicating which pellet sizes problems must be expected due to pellet multiplicity

Incorporation of statistical distribution of particle properties in chemical reactor design and operation: the cooled tubular reactor

Pellet heat and mass transfer coefficients inside packed beds do not have definite deterministic values, but are stochastic quantities with a certain distribution. Here, a method is presented to incorporate the stochastic distribution of pellet properties in reactor design and operation models. The theory presented is illustrated with a number of examples. It is shown that pellet-scale statistics have an impact on cooled tubular reactor design and operation. Cooled tubular reactor design is determined to a large extent by the objective that run away inside the reactor tubes be avoided. We obtain the highest conversion if conditions in the tubes are such that the pellet and reactor run-away mechanisms are in balance. This determines an optimum amount of particles on a diameter inside a cooled tubular reactor. This optimum is influenced by the distribution of transport coefficients over the pellets. Because of the pellet-scale statistical behaviour, a certain percentage of the tubes will always suffer run away if we operate close to the run-away region. If we have certain fluctuations in the coolant temperature, reactor pressure or load, any of these can damage a certain amount of tubes. As these fluctuations occur often, the performance of the cooled tubular reactor will deteriorate with time. The effects, as shown in this study, may cause an increase in inherent reactor instability. Therefore, if these effects are taken into account, a more conservative reactor design emerges

Radial heat transport in packed beds at elevated pressures

Values were measured for the effective radial heat conductivity λeff, r and the heat transfer coefficient at the wall αw in a packed bed. This was done for superficial velocities of 5 – 70 cm s−1 and at pressures from 1 – 10 bar. Values for λeff, r and αw were obtained by simultaneous fitting of measured axial and radial temperature profiles. The bed diameter was 5 cm; it was filled with 6.1 mm Raschig rings. Nitrogen gas was used in all cases. Values could be determined with reasonable accuracy. The agreement with correlations presented in the literature is good for λeff, r and less so for αw. The results obtained indicate that λeff, r and αw are a function of the product ‘velocity times pressure’ only. The correlations found can be represented by λeff, r/λg = 21 + 0.23Pe with an average relative error of 4% and Bi = 2.9Pe−0.40 with an average relative error of 5%. The experiments covered the range 25 < PE < 350. These correlations were obtained for one specific gas and one specific set-up.\u

The statistical character of packed-bed heat transport properties

Packed beds are essentially heterogeneous on a pellet scale. For random packed beds this heterogeneity causes a statistical character both on a pellet and bed scale. We discuss experimental results which deal with bed-scale statistics

Do the effective heat conductivity and the heat transfer coefficient at the wall inside a packed bed depend on a chemical reaction? Weaknesses and applicability of current models

Many studies have been on the effective heat conductivity (λeff) and the transfer coefficient at the wall (αw) inside packed beds. It has been mentioned that the values of λef and αw are changed when a chemical reaction occurs in the packed bed. We give an explanation for such a phenomenon. The properties λeff and αw are lumped parameters which usually are determined by both the measured temperature profiles and the model used to calculate the temperature profiles from λeff and αw. If either the experimental data are wrong or the model is erroneous the error will manifest itself in the values of λeff and αw. At least a part of the change in the values of λeff and αw due to a chemical reaction is caused by the fact that a homogeneous model with catalyst and gas having the same temperature is chosen, whereas a heterogeneous model with catalyst and gas having different temperatures should be used. If no reaction occurs the catalyst and gas will have the same temperature and the homogeneous model yields a good description. Hence, when fitting temperature profiles with this model the correct values of λeff and αw are found. If reaction does occur the catalyst and the gas will have different temperatures because the heat of reaction must be transferred from the catalyst to the gas. If, despite this fact, a homogeneous model is used to calculate the temperature profiles, an error is introduced which is reflected in the values of λeff and αw. As a consequence we create an apparent dependence of λeff and αw on the reaction rate. We derive criteria to determine which model must be used. We discuss results presented in the literature on the dependence of λeff and αw on the chemical reaction. The explanation is both qualitative and quantitative

A temperature overshoot on a catalyst pellet

An unexpected temperature overshoot was found for a Pd on alumina catalyst pellet in its course towards a new steady state, after a change in concentration of one of the reactants. The reaction mixture consisted of ethylene, hydrogen and nitrogen as inert. A speculative model is introduced, which can explain these overshoots by a slow adsorption of one of the reactants on the active sites of the catalyst

Simulation of a Casimir-like effect in a granular pile with avalanches

Using a modified Bak-Tang-Wiesenfeld model for sand piles, we simulate a Casimir-like effect in a granular pile with avalanches. Results obtained in the simulation are in good agreement with results previously acquired experimentally: two parallel walls are attracted to each other at small separation distances, with a force decreasing with increasing distance. In the simulation only, at medium distances a weak repulsion exists. Additionally, with the aim of avalanche prevention, the possibility of suppressing self-organized criticality with an array of walls placed on the slope of the pile is investigated, but the prevention effect is found to be negligible. © 2011 American Physical Society