Vladimir Z. Yakhnin

Convective instability induced by differential transport in the tubular packed-bed reactor

Abstract Convective (or spatial) instability, which manifests itself as the tuned amplification of perturbations in the course of their propagation along a non-isothermal packed-bed tubular reactor, is shown to occur in the exothermic standard reaction A → B + heat. The instability is caused by the interplay of the differential transport of heat and matter and of the activator-inhibitor kinetics inherent in non-isothermal, exothermic reactions (where heat plays the role of autocatalytic species or activator, and matter represents the inhibitor). The differential transport is caused by the inert reactor packing which acts as a thermal reservoir and slows down the diffusive and advective transport of heat relative to that of matter. This instability appears to be relevant to an earlier observation (Puszynski and Hlavacek, 1980, Chem. Engng Sci. 35 , 1769–1774) of sustained temperature oscillations in a packed-bed reactor at high Lewis number.

Patchiness and Enhancement of Productivity in Plankton Ecosystems due to the Differential Advection of Predator and Prey

The diffusive instability is considered as one important mechanism that accounts for the patchiness of ecosystems, e.g. the phytoplankton/zooplankton system. We show here that spatial differentiation of the plankton communities may occur alternatively through the differential flow instability. A differential flow (advection) between phyto-and zooplankton species arises naturally in the shear flow of a marine current due to the diurnal, differential vertical migration of the counteracting plankton species. Model calculations using an extension of Scheffers plankton model and literature values of the kinetic parameters predict a travelling wave pattern of biological activity on the spatial scale from a few kilometers to ca 100 km, depending on the parameter values, in agreement with the scales of observed structures. Most importantly we find that the productivity (the spatial average of biomass and production rate) of both predator and prey subpopulations may be enhanced in the patterned state by factors of the order of 2 and 20. The mechanism is discussed by which the productivity of both counteracting species may change (i.e. be enhanced) through the differential flow.

Amplification of inlet temperature disturbances in a packed-bed reactor for CO oxidation over Pt/Al2O3

Abstract The commonly used packed-bed catalytic reactor can exhibit complex dynamic features such as wrong-way behavior, differential-flow instability, different kinds of traveling waves and bifurcation behavior. Understanding these phenomena is essential for developing reliable reactor control systems. Of primary interest to the present study is the differential flow instability, which may cause amplification of small amplitude inlet perturbations of concentration, temperature, and flow rate into large temperature excursions. CO oxidation served as a model reaction to demonstrate resonance amplification of inlet temperature perturbations in a tubular reactor packed with 0.02 wt % Pt / Al 2 O 3 catalyst. Very low-frequency inlet perturbations did not cause large temperature increases in the reactor because the separation of thermal and concentration waves becomes insignificant when the system changes slowly between steady states. High-frequency perturbations, on the other hand, were attenuated as the waves propagated through the reactor bed. However, amplification at intermediate frequencies could be considerable. Amplification could be suppressed by increasing the axial thermal conductivity of the bed or by using highly concentrated catalyst.

Stationary and traveling hot spots in the catalytic combustion of hydrogen in monoliths

In the course of catalytic combustion of hydrogen (1–5% H2 in air) in monolith reactors, strongly localized stationary and traveling hot spots arise in response to a sudden and persistent rise of gas flow velocity. Such hot spots may occur, e.g. in a catalytic converter following the acceleration of a car or in a catalytic combustor as a result of a load increase. This phenomenon is illustrated by simulations using a two-phase reactor model. The temperature overshoot of the adiabatic limit is typically of the order of the adiabatic temperature rise itself. The following mechanism underlies this behavior. Light fuel is supplied to the catalytic wall by fast diffusion (in the direction perpendicular to flow), while the heat released by reaction is removed from the wall by the slower, mixture-averaged heat conduction. This leads to accumulation of heat at the catalytic surface that eventually saturates at high temperatures. The hot spots may exhibit intricate dynamics, propagating downstream or upstream, or they may remain stationary. The direction of propagation depends on the relative strength of convective downstream and conductive upstream contributions to the overall displacement of reaction fronts. Generally, the hot spot tends to drift downstream at low flow velocities, remain stationary at intermediate flow velocities, and drift upstream at high flow velocities.

Differential flow instability of the exothermic standard reaction in a tubular cross-flow reactor

Abstract A differential-flow-induced instability, which generates travelling waves, may occur in the exothermic reaction A → B + heat in a packed bed tubular cross-flow reactor. It is caused by the differential flow (not to be confused with cross flow) between heat acting as autocatalyst and the reacting matter, at elevated Lewis numbers. The uncoupling of heat and matter transport releases the inherent tendency of the autocatalyst to grow. A stability analysis of the governing equations is presented. Simulations of the travelling wave patterns show that multiple solutions coexist and are asymptotically stable.

Convective instability and its suppression in packed-bed- and monolith reactors

Abstract Non-isothermal packed-bed- and monolith reactors tend to be convectively unstable: in response to changes in operating conditions (start-up, shut-down, load change), they may develop pronounced travelling waves of temperature and chemical composition. The instability results from a tendency for runaway, inherent in exothermic reactions and from a differential flow of heat and matter – their convective transport at different velocities. The latter is a consequence of thermal inertia of the catalyst bed, that slows down transport of heat relative to that of matter. The properties of these differential flow-induced waves, experimentally studied in an isothermal, autocatalytic reaction, are briefly reviewed. Transient temperature waves, or moving hot spots constitute safety hazards, shorten service life of catalyst and, in production applications, impair selectivity and product quality. In this paper we propose methods for keeping the instability under control. A new class of stabilized reactors is described that have a reduced tendency to amplify process disturbances and to develop moving hot spots. It is based on axial thermal coupling (e.g. through shared walls) of two or more dynamically dissimilar reactors that develop different temperature waves in response to identical perturbation. These waves, which are generally out of phase, interact through radial heat flow between the component reactors and suppress each other in a way similar to destructive interference. The resulting, improved stability enables one to operate the reactor more aggressively with a gain in throughput. On the other hand, it translates into enhanced safety and quality of operation and into prolonged service life of equipment.

Temperature excursions in reactors packed with segregated layers of catalyst and inert solids

Abstract A recent numerical studies by Yakhnin and Menzinger (Proc. 8th Int. Symp. on Catalyst Deactivation, Brugge, Belgium, 10tober, Vol. 126, 1999, pp. 291–298) suggests that activity inhomogeneity in a catalyst bed can create larger temperature excursions after changes in feed temperature than would be encountered in beds with homogeneous catalyst activity. Until now, this finding has not been confirmed experimentally. Inhomogeneous catalyst activity was simulated by constructing a packed bed reactor by successive layers of catalyst and the inert support. Oxidation of carbon monoxide (CO) with oxygen in a nitrogen carrier gas over an industrial 0.2 wt % Pt/ γ –alumina catalyst was employed. This reaction is exothermic and inhibited by CO. Step changes and periodically varying inlet temperature were used to generate disturbances. Both wrong-way behaviour and differential flow instability were observed. Temperature excursions in the layered bed significantly exceeded those in a bed of homogeneous activity at the same operating conditions.

Absolute instability of a tubular packed-bed reactor with recycling

Abstract The stationary state of a non-isothermal tubular packed-bed reactor with partial recycling of the product flow or simply of the reaction heat, is shown to be absolutely unstable. This instability is closely related to the convective instability of a fixed-bed reactor without recycling [Yakhnin et al. , 1994, Chem. Engng Sci. (in press)] which manifests itself as the ability of the system to amplify perturbations in the course of their spatial propagation. Recycling causes these amplified perturbations to be reinjected, thereby keeping the reactor from settling into its stationary state. This results in self-sustained periodic waves that circulate through the reactor.

Control of activator-inhibitor systems by differential transport

Abstract When an activator-inhibitor system switches from a spatially uniform to a patterned state by a differential transport instability — the differential flow instability, or the diffusive or Turing instability — the values of variables, such as concentrations or reaction rates, including their averages, may drastically change. Analysis shows that such control of productivity by differential transport is a general property of nonlinear activator-inhibitor systems. By simulations and experiments using the Belousov-Zhabotinsky reaction, we show that average concentrations of the key species may be significantly enhanced when the reaction is run in the presence of a differential flow.

Deactivation avalanches through the interaction of locally deactivated catalyst with traceling hot spots

Abstract Packed-bed reactors with exothermic reactions tend to amplify transient perturbations of input parameters such as feed temperature, composition, flow rate, etc. These can grow into large-amplitude temperature (and concentration) waves-traveling hot spots (THS)-with peak temperatures well above the adiabatic temperature rise. Thus, THS accelerate thermal degradation of the catalyst. If the deactivation is localized (i.e. inactive pellets are surrounded by active catalyst) the THS develop much higher temperatures than they would in a uniformly active bed. The dynamics responsible for this secondary temperature overshoot and further accelerated deactivation is related to ‘wrong-way behavior’. This sequence constitutes a new dynamical mechanism of catalyst deactivation in which a low-activity domain acts as nucleating center for self-accelerated, avalanche-like, catalyst deactivation.