Effect of surface diffusion on the selectivity of catalytic reactions

Analysis is made on the effect of surface diffusion on the selectivity of a catalyst for a consecutive reaction A→B→C in a well-mixed stirred tank reactor. The catalyst is composed of an α region despersed on the β region. A→B is assumed to occur on the α region and B→C on the β region. Migration of B from α to B proceeds both by surface diffusion and gas phase transport. Influence of the flow rate through the reactor, the crystallite size of α, and the loading of the catalyst on the selectivity for C in the presence of surface diffusion are discussed. Under otherwise identical conditions, selectivity is increased by surface diffusion. The optimum condition for the production of C is also discussed.     

Rational design of shape selective separation and catalysis—I: Concepts and analysis

A molecule can enter a zeolite channel when it fits the size and shape of the opening. Zeolites have been used commercially for their ability to admit selectively molecule A but not molecule B. The search and design of zeolites for separation has been based on finding a channel with a diameter that is larger than molecule A, but smaller than molecule B. This method is not sufficiently accurate when the molecule is not a sphere or the channel is not a circle. We present here first a more accurate screening method based on comparing both the major and minor diameters of the molecule projection, called the “footprint”, with the diameters of the channel. Then we present an even better method that is based on the activation energy required to strain and distort a molecule to fit a given channel, thus leading to a lowering of its Boltzmann concentration in this channel. This paper compiles the activation energies encountered among thirty-eight (38) molecules and two hundred and seventeen (217) zeolite channels into a database, and shows how one can use this database to identify the most promising zeolites for the separation of a set of molecules of interest. Such a screening method would help to identify a zeolite that has much lower activation energy for molecule A than for molecule B. The appropriate temperature range for separation would be centered around the optimal temperature T^*, where the degree of selectivity is at a maximum. The separation of the three pentane molecules was selected as an illustration.     

The prediction of the performance of packed-bed catalytic reactors in the air-oxidation of o-xylene

The kinetics of the catalytic air-oxidation of o-xylene to phthalic anhydride over various commercial V₂O₂ and TiO₂-V₂O₂ catalysts are extended and a model derived which correctly predicts the temperature and yield profiles in a quasi-isothermal fixed-bed reactor of commercial dimensions. The model predicts the relative freedom from thermal “run-away” of commercial fixed-bed reactors and is used to demonstrate the possibilities of operation at elevated Xylene concentrations.In what follows, XH, TA, PI and PA refer to o-xylene o-tolualdehyde, phthalide and phthalic anhydride respectively, sometimes abbreviated to A, B, C and D.     

Multicomponent film-penetration theory with linearized kinetics—II. Particular cases and tests

The matrix results required for the evaluation of all interfacial flows at the film theory limit are presented for the multiple reaction system A → C ? B with linear kinetics and the single reaction system A + 2B ? C with linearized kinetics. The yield of C is calculated in the former case and the enhancement factor for A is calculated in the latter case when B is nonvolatile and the reaction is irreversible.The single reaction, A + 2B ? C, as well as A + B ? C + D, is considered further for testing the linearized solution against the exact numerical calculations of the enhancement factor with the nonlinear kinetics. The results indicate that the linearization theory can be applied with a maximum error of 10 per cent and, in most cases, with a considerably smaller error over the complete range of gas—liquid contact times.     

Optimal temperature policy in a riser reactor

The nature of the optimal axial temperature distribution in a riser reactor to maximise the yield of the intermediate B, in the reaction sequence A→B→C was investigated by way of the selective oxidation of naphthalene to phthalic anhydride. For this case, imposition of an axial profile could not improve the yield over that obtainable by operating at the optimum isothermal temperature. This result appears to be general, and suggests that optimal yields could be obtained by operation at the optimum isothermal temperature, which should prove easier to implement in practice than a specified temperature distribution.     

Multiplicity and uniqueness for binary,exothermic reaction in a non-adiabatic continuous stirred tank reactor

Exact multiplicity and uniqueness criteria for steady state in a non-adiabatic continuous stirred tank reactor are studied through simple tangent analysis for binary, exothermic reaction of the type A + bB → Products with rate expression r_A = kC_A^m C_Bⁿ, where A is the limiting reactant. Important parameters for multiplicity criteria are reaction orders m and n, stoichiometric coefficient b, the ratio p of feed concentration of A to that of B, dimensionless activation energy α, dimensionless heat of reaction β, dimensionless heat transfer coefficient γ and dimensionless coolant temperature. Necessary conditions for the system to have multiple exit conversions (temperatures) are defined in the (m, n, b, p, α, β, γ) space. Multiplicity is guaranteed by limiting the dimensionless space time ? in a proper range in addition to the necessary conditions. Effects of various parameters on multiplicity and uniqueness are numerically calculated and graphically represented. Theoretical prediction for multiplicity are further compared with multiplicity data reported in literatures.     

Heterogeneous catalytic reactor design with optimum temperature profile II: application of non-uniform catalyst

A new methodology has been developed to design non-isothermal, non-adiabatic heterogeneous catalytic fixed bed and tubular reactors with optimal temperature profiles inside a reactor. Catalyst characteristics such as pellet diameter, shape and activity distributions inside a pellet are considered simultaneously for reactor design. Various types of non-uniform activity distributions inside a pellet are modelled and optimised for the maximisation of an objective such as yield or selectivity. Dirac-δ, layered and general non-uniform distribution profiles such as egg-shell, egg-yolk and middle peak distributions are applied for the reactor design. The research demonstrates that different catalyst distribution profiles can approach the optimum performance. Whilst it is known that the Dirac-δ profile (and its step-function equivalent) always gives the best performance for clean catalyst, other profiles can approach this performance and might offer advantages in catalyst manufacture and under degraded conditions. A profile-based synthesis approach is applied to generate various shapes of activity profiles for multiple sections along the reactor during the optimisation of non-uniform catalyst pellets. A case study with the ethylene oxidation process illustrates that the catalyst characteristics, such as activity distribution profiles inside a pellet, sizes and shapes can be manipulated to control the temperature through the reactor very effectively, leading to significant improvements in selectivity or yield. The non-uniform catalyst pellet is further applied to various reactor configurations such as inert mixing and side stream distributions. This work is the first to consider all of these effects simultaneously.     

Multiplicity of the steady in the fluidized bed reactors—III: Yield of the consecutive reaction A → B → C

The simplified non-isothermal model for fluidized bed reactors developed earlier (Parts I, II) is extended here to the case of exothermic consecutive reaction, A → B → C. It is shown that simple adiabatic operation is not possible when the second reaction, B →- C is relatively fast because the desired operating temperature corresponds to an unstable steady state. A simple control scheme is suggested to stabilize the unstable steady state. Conditions for the existence of unstable steady state giving rise to limit cycle behaviour are discussed using local stabdity analysis. Limit cycles are shown on the phase plane and the effect of controller gain is investigated.     

The effect of imperfect mixing on an idealized kinetic fermentation model

Mixing patterns in stirred reactors are analyzed in this study from the point of view of the hysteresis behavior of final product rate as a function of the intermediate concentration in the sequential reaction A → B → C. A two-tank system model with an internal recycle stream is studied, in order to simulate the effect of imperfect mixing in a single batch reactor. The extent of mixing between positions at which product and intermediate species concentrations are measured in the reactor is revealed in both the direction of the hysteresis function and the relative magnitude of the inscribed area. Another approach, which apparently simplifies the analysis, is to measure the concentration of B in each of the two tanks and cross-plot the two variables. This latter technique not only avoids the errors resulting from differencing the data, but also leads to correlations between the circumscribed areas and the degree of mixing.     

Single and two-phase pressure drop in serpentine mini-channels

The pressure differential of single and two-phase flow in mini-channel serpentine geometries was investigated to determine the effects of flow patterns and radius of curvature of the serpentine on pressure drop. The friction factor for single phase flow through a straight channel was comparable to existing literature, while that in the serpentine geometry fell between conventional theory for straight channels and fully developed flow in helical coils. Extension of the single phase results to two-phase flow using a separated flow model led to the development of empirical correlations for two-phase pressure drop in the straight and serpentine configurations. Five operating regions were identified within the serpentine, each with distinct pressure drop characteristics dependent on the flow pattern and extent of bubble deformation. Two of the operating regions corresponded to bubbly and slug/unstable-annular flow, while the boundaries between the three remaining regions occurred at We_LGL_C = 2.7 and 15.5; corresponding to the onset of mild cap deformation and continuous bubble breakup, respectively.     

A mixing model for diagnosing reacting tracers and tracing reactants in chemical and biochemical processes

It has previously been shown (Tanner et al., 1985) that biochemical and chemical reaction processes of the Type A → B → C can lead not only to kinetic hysteresis between the rate of formation of C and the concentration of species B in batch processes, but also hysteresis between those variables in a closed, imperfectly mixed (two zone) batch reactor. Furthermore, crossplotting the intermediate reactant, B, in one region of the poorly mixed reactor against B from the other major region leads to a clockwise hysteresis curve which is defined by both its area and the coordinate phase angle. This paper shows that the earlier analysis (Tanner et al., 1985) can be extended to the more general system A → B, where A in one region of the vessel is crossplotted against A measured in the other region. With an initial concentration of A* in one zone equal to its highest concentration, the inscribed area double-valued crossplot of A, uniquely defines the system in terms of the inter-vessel flowrate to reaction rate constant ratio, D/k.     

On the dynamics of a stirred tank with consecutive reactions

The pattern of multiplicities of the steady states of a stirred tank reactor in which A → B → C takes place has been known for some time to be complex. We show that even in regions of parameter space for which there is only one steady state the dynamical behavior can be very complicated. Since the number of parameters is very large a complete exploration of the space is impossible, but by careful transection of a small, but significant, region we show that repeated bifurcation of limit cycles leads into a pattern of periodic and chaotic behaviour that returns to a simple limit cycle and then reflects itself.     

Effect of depth on onset of engulfment in rectangular micro-channels

The mixing behavior at different Reynolds numbers is analyzed for different T-shaped micro-channels with a rectangular cross-section. The focus is on analyzing the effect of aspect ratio on the critical Reynolds number at which engulfment occurs. Soleymani et al. (2008) have recently proposed an empirical equation based on extensive numerical simulations to determine this critical Reynolds number. This is valid only when the depth of the channels (C) is lower than the widths of the mixing (A) and inlet (B) channels i.e. when A/C and B/C are both greater than unity. We find that when they are both less than unity there is a delay or even absence of engulfment even when Re is increased. The predictions of these simulations are validated experimentally for two geometries.     

Optimal operation policies in batch reactors

Optimal operation policies in batch reactors are obtained using dynamic optimisation technique. Two different types of optimisation problems, namely, maximum conversion and minimum time problems are formulated and solved and optimal operation policies in terms of reactor temperature or coolant flow rate are obtained. A path constraint on the reactor temperature is imposed for safe reactor operation and an endpoint constraint on undesired waste production (by-product) is imposed to minimise environmental impact.Two different types of models are considered within the optimisation framework. The shortcut model allows determination of optimal reactor temperature profile to be used for detailed design of the reactor. The detailed model allows optimising operating conditions for an already designed batch reactors.     

Averaging theory and low-dimensional models for chemical reactors and reacting flows

A novel approach based on the Liapunov-Schmidt technique of bifurcation theory is presented for the spatial averaging of a class of convection-diffusion-reaction models. It is used to derive low-dimensional averaged models for different types of homogeneous and catalytic reactors, as well as coupled homogeneous-heterogeneous systems. For the homogeneous isothermal case, the averaged models consist of a pair of balance equations for each species A_j in terms of the mixing-cup (C_j,m) and spatially averaged (〈C_j〉) concentrations. The first (global) equation traces the evolution of C_j,m with residence time while the second (local) equation, which is independent of the reactor type, gives the local concentration gradient as a difference between C_j,m and 〈C_j〉 in terms of the local variables (such as species diffusivities, shear and reaction rates). For the wall-catalyzed reaction case, the averaged models are described by a pair of equations for each species in terms of C_j,m and the surface concentration C_j,s and are similar to the classical two-phase models of catalytic reactors. For the coupled homogeneous-heterogeneous case, the averaged models consist of three balance equations for each species in terms of C_j,m, 〈C_j〉 and C_j,s, and contain four mass transfer or exchange coefficients. The accuracy, convergence and the region of validity of the averaged models are examined for some special cases. Finally, the usefulness of the averaged models in predicting the reactor behavior is illustrated with an example for each of the three cases, homogeneous, heterogeneous and coupled homogeneous-heterogeneous case.     

Theoretical study of the application of porous membrane reactor to oxidative dehydrogenation of n-butane

This paper is the theoretical study of the oxidative dehydrogenation of n-butane in porous membrane reactors. Performance of the membrane reactors was compared with that of conventional fixed-bed reactors. The porous membrane was employed to add oxygen to the reaction side in a controlled manner so that the reaction could take place evenly.Mathematical models for the fixed-bed reactor and the membrane reactor were developed considering non-isothermal condition and both radial heat and mass dispersion. From this study, it was found that the hot spot problem was pronounced particularly near the entrance of the conventional fixed-bed reactor. In addition, the assumption of plug flow condition did not adequately represent the reaction system. The effect of radial dispersion must be taken into account in the modelling.The use of the porous membrane to control the distribution of oxygen feed to the reaction side could significantly reduce the hot spot temperature. The results also showed that there were optimum feed ratios of air/n-butane for both the fixed-bed reactors and the membrane reactors. The membrane reactor outperformed the fixed-bed reactor at high values of the ratio. In addition, there was an optimum membrane reactor size. When the reactor size was smaller than the optimum value, the increased reactor size increased the reaction and heat generation and, consequently, the conversion and the selectivity to C₄ increased. However, when the reactor size was larger than the optimum value, oxygen could not reach the reactant near the stainless steel wall. It was consumed to react with the product, C₄. As a result, the yield dropped. Finally, it was found that the increase of wall temperature increased the yield and that the feed air temperature could help control the temperature profile of the reaction bed along the reactor length.     

A study of the dependence of radial spread of liquid in random beds on local conditions of irrigation

Local values have been determined experimentally of the coefficient of radial spread in trickle beds randomly packed by 2O mm spheres and 15 and 25 mm Raschig rings in dependence on local conditions of irrigation. Three regions, A, B, C, have been found of different behaviour of trickling liquid. In regions A and B the coefficient remains constant but mutually different. This difference has been attributed to different regime of flow. In region C the coefficient depends on local value of the density of irrigation and the gradient of the density of irrigation. In spite of these findings the distribution of liquid in random beds may be described with the aid of a single suitably selected effective value of the coefficient of radial spread.     

Simulation and thermodynamic analysis of conventional and oxygen permeable CPO reactors

A one-dimensional steady-state heterogeneous model has been used to simulate the conventional CPO reactor. With the mechanism of O₂ permeable membrane, the model has been developed to simulate O₂ membrane reactor. The output temperature and the mole flow rates of different species in the tube side and the shell side can be calculated. They are the basis for the exergy analysis of the conventional CPO reactor with air, the conventional CPO reactor with pure O₂, and the O₂ permeable membrane CPO reactor. The simulation and exergy analysis results indicate that when the inlet conditions are the same, for a given methane conversion, the exergy efficiencies η₂ and η₁ of conventional CPO reactor with pure oxygen is lowest among the three reactors, because of the large amount of accumulative exergy required for obtaining pure oxygen.The exergy efficiencies η₁ and η₂ of membrane reactor are comparable with conventional CPO reactor with air and much higher than conventional CPO reactor with pure oxygen. As the membrane reactors can carry out simultaneous separation and reaction, in the mean time, removal of nitrogen from the product stream can be accomplished; the membrane reactor has advantages compared to other types of reactors.The operation of the membrane CPO reactor is more favourable when the inlet temperature is increased and the operation pressure is decreased from a thermodynamic point of view.     

Reactor performance and stability in an alternating reaction-reheat paraffin dehydrogenation system

The classical fixed bed C₃–C₄ paraffin dehydrogenation process is a cyclic operation in which the reactor alternates between reaction and reheat cycles. During the reheat cycle, the necessary energy for the dehydrogenation reaction is stored in the fixed bed by passing hot air through it. In this established technology, both the hydrocarbon reactant and the reheat hot air are fed into the fixed bed from the same end (top) of the reactor. This is termed parallel flow (cocurrent) operation. An alternative feeding fixed bed has the hydrocarbon reactant and the reheat air entering from the opposite ends of the reactor. This is termed reverse flow (countercurrent) operation. This alternate creates an ideal temperature profile for an equilibrium limited endothermic reaction (rising temperature profile along the reactor). The transient flow behavior of both parallel and reverse flow reactors has been modelled and the dynamics of temperature profile development for both concepts have been analyzed. Based upon the model predictions, the characteristics as well as the reactor stability of the both concepts have been discussed.     

Periodic operation of isothermal plug-flow reactors with input multiplicities

The performance of isothermal plug-flow tubular reactors under periodic inlet concentrations is theoretically analyzed for improvement in yield for homogeneous consecutive reactions A→ B → C which, under conventional steady-state operation, show input multiplicities in the flow rate on the yield of B. Two values of flow rate give an identical yield of B under steady-state operation. For periodic operation, a rectangular pulse is assumed for the inlet concentration. It is shown in three numerical examples that under concentration forcing the yield is significantly different for these two inlet flow rates. Under periodic operation the larger value of flow rate gives a higher yield of B.