Temperature diagrams for preventing decomposition or side reactions in liquid-liquid semibatch reactors

The operation of an indirectly cooled semibatch reactor in which an exothermic reaction occurs is usually considered safe if the characteristic time of the coreactant dosing is much higher than the characteristic times of all the other phenomena involved (chemical reaction and mass transfer), so that the conversion rate is controlled by the coreactant supply itself. Such operating conditions imply a small accumulation of the coreactant in the system and are characterized by a temperature evolution which quickly approaches a target temperature and remains close to it throughout the dosing period, at the end of which the conversion is almost complete.The so-called boundary diagrams are useful tools for identifying safe operating conditions without solving the mathematical model of the reactor. However, avoiding accumulation phenomena can be not sufficient for classifying a set of operating conditions as thermally safe when the maximum temperature reached by the system under normal operation exceeds a maximum allowable temperature (which can be related either to safety problems, when dangerous decomposition reactions can be triggered, or to productivity problems, when side reactions can significantly lower the product yield above a given threshold temperature).In this work the boundary diagrams for the prevention of excessive accumulation conditions in liquid-liquid semibatch reactors are coupled with new diagrams, called temperature diagrams. These new diagrams, involving the same dimensionless parameters used for the representation of the boundary diagrams, allow determining—for a given set of operating conditions—the maximum temperature increase with respect to the initial reactor temperature which can be expected to occur during normal operation. This information can be compared with the maximum allowable temperature for the reacting mixture. Then the operating conditions can be verified through the boundary diagrams in order to reject conditions of excessive coreactant accumulation.Several temperature diagrams are provided for various kinetically or diffusion controlled reactions with different reaction orders and their use together with a general procedure for calculating them is presented.     

Thermally safe operation of liquid-liquid semibatch reactors. Part I: Single kinetically controlled reactions with arbitrary reaction order

The thermally safe operation of an indirectly cooled semibatch reactor in which an exothermic reaction occurs corresponds to conditions of potentially very high effective reaction rate compared to the dosing rate of the coreactant, whose accumulation in the reaction system is consequently small. On this basis it is possible to build boundary diagrams in terms of suitable dimensionless parameters, which summarize all the possible thermal behaviors of the reactor and can be used for safe scaleup purposes.In this work the influence of reaction kinetics on the shape and location of boundary diagrams for a single liquid-liquid reaction in the slow regime is discussed. First of all, the theory of boundary diagrams, originally developed for (1,1) reaction order, is extended to a generic (n,m) rate of reaction expression. Then it is shown that in many practical systems, using boundary diagrams based on (1,1) reaction order can lead to both unsafe and unnecessary (from a safety point of view) low-production operating conditions. New boundary diagrams for a few (n,m) reaction orders are presented. Some rules-of-thumb are also discussed to identify in which cases a boundary diagram developed for a given (n,m) reaction order can be reasonably used to approximate the real kinetic behavior of the system of interest.Moreover, since building a boundary diagram for the specific kinetics considered can be necessary, a simple and general procedure for building such diagrams that can be easily implemented in a computer code is also presented.     

Reactions of solid particles with nonuinform distribution of solid reactant: The volume reaction model

The effect of non-uniform solid reactant distribution on conversion of solid particles in gas-solid reactions is analyzed based on the volume reaction model. Certain special features of such systems are pointed out. The possibility of ash layer formation in the kinetically controlled regime is discussed. Conditions leading to single or double ash layer formation, both at the center and surface of the particle, in the intermediate regime of diffusion with simultaneous reaction are described. Detailed mathematical equations which are useful for calculation of the conversion-time relationship for particles with non-uniform solid reactant distribution are presented. Comparison is made to reaction of uniform particles and differences in required reaction time for desired conversion are outlined.     

CO2 Capture Behavior of Shell during Calcination/Carbonation Cycles

The cyclic carbonation performances of shells as CO₂ sorbents were investigated during multiple calcination/carbonation cycles. The carbonation kinetics of the shell and limestone are similar since they both exhibit a fast kinetically controlled reaction regime and a diffusion controlled reaction regime, but their carbonation rates differ between these two regions. Shell achieves the maximum carbonation conversion for carbonation at 680–700 °C. The mactra veneriformis shell and mussel shell exhibit higher carbonation conversions than limestone after several cycles at the same reaction conditions. The carbonation conversion of scallop shell is slightly higher than that of limestone after a series of cycles. The calcined shell appears more porous than calcined limestone, and possesses more pores > 230 nm, which allow large CO₂ diffusion‐carbonation reaction rates and higher conversion due to the increased surface area of the shell. The pores of the shell that are greater than 230 nm do not sinter significantly. The shell has more sodium ions than limestone, which probably leads to an improvement in the cyclic carbonation performance during the multiple calcination/carbonation cycles.     

A model for the self-heating reaction of coal and char

A mathematical model of the self-heating reaction of coal or char in bulk has been developed. The model takes into account a local oxidation reaction which depends on temperature and the concentrations of unreacted and reacted oxygen. The transport processes of diffusion and convection take the mobile reactant, oxygen, from the boundary to the distributed reaction where heat energy is released, and then convey the latter back to the boundary. The equations of the model are evaluated numerically and results are in general agreement with those predicted by the Theory of Thermal Explosions appropriate to the assumptions of the model. Various situations arise in the heating regime, depending on whether the conversion reaction is controlled by thermal conduction, reactant diffusion, reactant convection, or thermal convection where no distinct separation exists between the various cases. Some guidelines emerge for evaluating safe storage conditions for coal or char where the criterion of safety has to be specified for different materials, probably as a maximum safe temperature and maximum time of storage.     

Dynamics of SO2 adsorption–oxidation in SOx traps for the protection of NOx adsorbers in diesel engine emissions

The SO₂ uptake behaviour at different temperature and SO₂ concentration of a reference SO_x trap is studied in a thermobalance apparatus and in a flow reactor under reaction conditions close to those in the emissions from a diesel engine. The data of the latter apparatus are also kinetically modelled to derive which controlling regime dominates the performances. The results evidence that at 200 °C the behaviour is largely controlled by the slow solid-state diffusion of the sulphate species, while above 300 °C there is an initial region controlled by the surface reaction, although for levels of SO₂ uptake above a weight increase of 4–5% (due to sulphation) the solid-state diffusion dominates the performances also at high temperature.     

The selectivity of porous catalysts: parallel reactions

The influence of intraparticle mass diffusion on the overall and relative rates of the parallel reactions A → B and A → C is examined for the case of an isothermal catalyst particle with no external concentration or temperature gradients. Calculations for three pairs of reaction orders: (0,1), (0,2) and (1,2), show that internal concentration gradients can cause the yield of the product formed in the higher-order reaction to decrease by as much as 80 percent. Extension of the analysis to other reaction orders is discussed. Criteria for close approach to various asymptotic limits are presented, together with an asymptotic expression which allows the maximum effect of pore diffusion on selectivity to be estimated for any pair of reaction orders.     

Model study of the direct causticization reaction between sodium trititanate and sodium carbonate

The solid state reaction between sodium tri‐titanate and sodium carbonate, forming mainly sodium pentatitanate, was investigated. Experiments were carried out in a micro‐differential reactor made of quartz glass at various temperatures between 800°C and 880°C and in a pilot fluidized bed reactor operated in a semi‐batch mode. In the former reactor, basic kinetic data was obtained by measuring the release of carbon dioxide. Different kinetic models were considered to describe the conversion, such as the Valensi‐Carter model for diffusion controlled reaction rates and the phase‐boundary model for first‐order reaction kinetics. Furthermore, a model that included both diffusion in the solid material and the chemical kinetics was derived. This model described the experimental data obtained in the micro‐differential reactor very well. However, for the fluidized bed experiments, these different kinetic models did not accurately describe the experimental data. Therefore, an improved model was developed, which also took into account the time taken for the reactants to achieve physical contact. This model gave good agreement with the experimental data.     

Separation of carbon dioxide from flue emissions using Endex principles

In an Endex reactor endothermic and exothermic reactions are directly thermally coupled and kinetically matched to achieve intrinsic thermal stability, efficient conversion, autothermal operation, and minimal heat losses. Applied to the problem of in-line carbon dioxide separation from flue gas, Endex principles hold out the promise of effecting a CO₂-capture technology of unprecedented economic viability. In this work we describe an Endex Calcium Looping reactor, in which heat released by chemisorption of carbon dioxide onto calcium oxide is used directly to drive the reverse reaction, yielding a pure stream of CO₂ for compression and geosequestration. In this initial study we model the proposed reactor as a continuous-flow dynamical system in the well-stirred limit, compute the steady states and analyse their stability properties over the operating parameter space, flag potential design and operational challenges, and suggest an optimum regime for effective operation.     

Multicomponent diffusion and chemical reaction of gases in porous catalysts—I: Ternary gasdiffusion and chemical reaction without volume change (ν = 0)

The overall conversion rate for catalytic reactions of gases in porous catalysts is often controlled by transport processes in the porous pellet. Since in general more than two gases take part in the reaction, one has to calculate the conversion rate by using the transport equations for multicomponent mixtures. These equations, however, are rather complicated; thus calculations of conversion rates are commonly done by using Fick's transport law.First of all it is shown that the equations for multicomponent diffusion can be reduced to simple linear laws by using the stoichiometric coupling of the fluxes. With these equations, the calculation of the conversion rate for a reaction of the general type: ν₁R₁ + ν₂R₂ ? ν₃R₃ is as simple as for the case of binary diffusion. Using the example of hydrogenolysis of ethane it is then demonstrated that in general Fick's law leads to higher conversion rates than the Maxwell-Stefan, diffusion equations. With this example some basic questions arising in the discussion of heterogeneous catalytic reactions in porous systems (e.g. the choice of the “key component”) are discussed in detail.     

Open tubular heterogeneous enzyme reactors: analysis of a theoretical model

A novel reactor, made by coating the inner wall of tubes with an enzyme resin layer, was mathematically modeled. Michaelis-Menten kinetics, laminar flow and isothermal conditions were assumed and substrate diffusion in both the streaming fluid and the catalyst annulus was taken into account. The behavior and effectiveness of the reactor are discussed in terms of characteristic dimensionless groups including the reactor coordinate which is inversely proportional to the average overall rate at a given conversion. An experimental criterion is given for the absence of all diffusional effects which may mask kinetic data. The calculated reactor coordinates can be approximated by the sun of their limiting values pertaining to the kinetically controlled and bulk diffusion controlled reaction thus permitting a simplified treatment of the reactor data and of problems of reactor design. Conditions for extracting kinetic parameters from experimental data are discussed.     

Effect of Polymer Growth Rate and Diffusion Resistance on the Behavior of Industrial Polyethylene Fluidized Bed Reactor

The two‐phase model developed for the UNIPOL polyethylene process is improved by introducing polymer diffusion resistance, this means modelling of polyethylene fluidized bed reactors has been examined on two levels, at small scale of individual polymer particle, and macroscale of the whole reactor. The model utilizes the multigrain model that accounts for the reaction rate at catalyst surface to explore the static and dynamic bifurcation behavior of the fluidized bed catalytic reactor. Detailed bifurcation diagrams are developed and analyzed for the effect of polymer growth factor and Thiele modulus (the significance of the porous medium transport resistance is characterized by Thiele modulus) on reactor dense phase monomer concentration and reactor temperature as well as polyethylene production rate and reactor single pass conversion for the safe temperature region. The observations reveal that significant diffusion resistance to monomer transport exists, and this can mask the intrinsic rate constants of the catalyst. The investigation of polymer growth factor indicates that, the nascent stage of polymerization is highly gas phase diffusion influenced. Intraparticle temperature gradients would appear to be negligible under most normal operating conditions.     

Investigation of shear effects on styrene free radical polymerization using a narrow channel reactor

Spinning disc reactor technology has been demonstrated to achieve significant enhancements in the rates of free radical polymerization. It is believed that these enhancements are related to the centrifugal and shear conditions that exist on the disk and it is the objective of this study to elucidate the role of shear in thin films in a plug flow regime. Polymerizing systems have been subjected to shear fields in the range of 0.4 to 2,173 s^?1 and comparisons between conversion profiles and polymer product properties have been made. It has been found that shear fields have little or no effect on these systems while the reaction is in the kinetically controlled regime and it is concluded that the observed rate enhancements of free radical polymerization on a spinning disk are not largely attributable to the high rates of shear experienced by the thin film as it traverses the disk. Our studies therefore continue to assess the role of flow divergence and centrifugal extension in the kinetics of polymerization. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94:1365–1369, 2004     

The energetic and/or economic optimisation or heterogeneous reactors

The first part of this paper presents the bases for the technico-economic optimisation of reactors.The optimum design of a reactor is by minimising an objective function which, depending on the choice of the decision-maker and for a given production rate, could be :- the cost in the national currency- the cost in foreign exchange- the consumption of primary energy- the consumption of exergy.In addition the decision-maker could in each case also aim to minimise :- the cost of equipment (investment)- the operating cost- the total cost, that is the weighted sum of the capital equipment cost and the operating cost for a chosen period of amortizement.These various optima are compared one with another, notably those which minimise money cost and those which minimise the consumption of primary energy. It is shown that between each there exist invariant ratios : for each optimum the contribution of each of the terms (equipment, operating…) to the total cost is a constant and is independent of economic factors. It is only a function of technical factors such as the flow regime (laminar or turbulent) transport process (diffusion, convection…).In the part two, the general concepts developped in part one are applied to the design of heterogeneous catalytic reactors (with fixed, fluidised or transported particles).A “simplissime” model is proposed which depends on only one parameter representing the hydrodynamic structure of the flow in the reactor. This model includes various types of flow structure : short circuit, recycle, total or partial macro-mixing, anisotropic jet hitting the active surface, etc… A general expression is established for the “Specific Operating Consumption of Mechanical Energy” (or SOCME) in joules per kg of useful product. The way the SOCME varies with the process parameters, especially the Reynolds number is examined for the main operating regimes of the reactor.- Volume effect regime : transport by convection - macro-mixing - short circuiting.- Surface effect regime : heterogeneous chemical reaction or transport by diffusion through the boundary layer.Operating conditions for which the limitation due to diffusion in the boundary layer is negligible are defined for the general case of any reactor.Illustration is given of how to apply these concepts to the optimisation of a fixed bed reactor where the requirement is to simultaneously :- maximise the productivity- minimise the energy consumption- minimise the construction cost of the reactor.Thus in any optimized reactor, the consumption of mechanical operating energy is a non-negligible fraction of the total optimisable expenditure (from 10 to 30 %) and this is valid even and especially in the chemical reaction regime. It may be concluded that in the future, reactors which will be required to consume less and less energy, should no longer be designed to operate in the chemical reaction regime but should be allowed to have certain physical rate limitations whether diffusional or convective.     

A novel reverse flow reactor coupling endothermic and exothermic reactions: Part II: Sequential reactor configuration for reversible endothermic reactions

The new reactor concept for highly endothermic reactions at elevated temperatures with possible rapid catalyst deactivation based on the indirect coupling of endothermic and exothermic reactions in reverse flow, developed for irreversible reactions in Part I, has been extended to reversible endothermic reactions for the sequential reactor configuration. In the sequential reactor configuration, the endothermic and exothermic reactants are fed discontinuously and sequentially to the same catalyst bed, which acts as an energy repository delivering energy during the endothermic reaction phase and storing energy during the consecutive exothermic reaction phase. The periodic flow reversals to incorporate recuperative heat exchange result in low temperatures at both reactor ends, while high temperatures prevail in the centre of the reactor. For reversible endothermic reactions, these low exit temperatures can shift the equilibrium back towards the reactants side, causing ‘back-conversion’ at the reactor outlet.The extent of back-conversion is investigated for the propane dehydrogenation/methane combustion reaction system, considering a worst case scenario for the kinetics by assuming that the propylene hydrogenation reaction rate at low temperatures is only limited by mass transfer. It is shown for this reaction system that full equilibrium conversion of the endothermic reactants cannot be combined with recuperative heat exchange, if the reactor is filled entirely with active catalyst. Inactive sections installed at the reactor ends can reduce this back-conversion, but cannot completely prevent it. Furthermore, undesired high temperature peaks can be formed at the transition point between the inactive and active sections, exceeding the maximum allowable temperature (at least for the relatively fast combustion reactions).A new solution is introduced to achieve both full equilibrium conversion and recuperative heat exchange while simultaneously avoiding too high temperatures, even for the worst case scenario of very fast propylene hydrogenation and fuel combustion reaction rates. The proposed solution utilises the movement of the temperature fronts in the sequential reactor configuration and employs less active sections installed at either end of the active catalyst bed and completely inactive sections at the reactor ends, whereas propane combustion is used for energy supply. Finally, it is shown that the plateau temperature can be effectively controlled by simultaneous combustion of propane and methane during the exothermic reaction phase.     

Effects of transport and phase equilibrium on fast, nearly irreversible reactive extraction

Integration of reaction and separation can be exploited to drive reversible reactions in the direction of the desired product using multiphase flow contacting. In the case of nearly irreversible, fast reactions, however, the dynamics of the product have little influence on the reactor efficiency in say liquid-liquid reactive extraction. A similar intensification in reaction efficiency to reactive separation can be achieved by exploiting phase equilibrium or asymmetry in mass transfer rates of the reactants. Here, a model for two-layer biphasic flow and homogeneous reaction is proposed for co-current reactive extraction, demonstrating that localization and intensification of reaction occurs in the region between the entrance and crossover. Crossover occurs if the reactant in stoichiometric deficit preferentially populates the reacting phase due to sufficient imbalance in either mass transfer coefficients or phase equilibrium. We develop an infinite Peclet number (convection dominates over bulk diffusion) model that indicates that crossover occurs when

     

A theoretical/experimental approach to the intrinsic oxidation reactivities of C/C composites and of their components

The oxidation reactivities of two C/C composites and of their available components (fibers, bulk matrices) are determined by measurement of mass loss rate in a cylindrical oxidation reactor under dry air and at atmospheric pressure. In order to identify reactional and diffusional regimes, and to provide a safe method for the identification of the intrinsic heterogeneous reaction rates at high temperatures, a modeling approach has been developed. Diffusion of the oxidant is considered throughout the reactor for all the samples (global-scale modeling) in combination with convection and reactions. Fibers have been arranged in unidirectional bundles in which diffusion is also considered (local-scale modeling). The importance of the reaction rate relatively to global-scale and local-scale diffusion has been evaluated. When reaction is slow enough, diffusion effects can be neglected; in the converse case, the intrinsic reaction rates are extracted from the experimental data using the models. Incidentally, the comparison of the fiber and matrix intrinsic reactivities supports the idea that the composites feature a complex oxidation behavior mainly based on a weakest link process. This result is illustrated and discussed using SEM and TEM investigations.     

Dynamic shear in continuous-flow rotating-disk catalytic reactors with stress-sensitive kinetics based on Curie's theorem in non-equilibrium thermodynamics

Stress-sensitive response is simulated in a modified parallel-disk reactor that implements steady and unidirectional dynamic shear in the creeping flow regime. Reactants chemisorb on the surface of the rotating plate, and catalytic sites are replenished from the bulk fluid via radial and tangential flow accompanied by transverse diffusion in the z-direction toward the active surface. Chemical reaction is enhanced by viscous shear at the interface between the bulk fluid and the rotating plate. This heterogeneous catalytic rotational reactor is modeled via radial convection and axial diffusion with angular symmetry in cylindrical coordinates. The reaction/diffusion boundary condition on the surface of the rotating plate accounts for stress-sensitive reactant consumption via the zr- and zΘ-elements of the velocity gradient tensor at the catalytic surface. Linear transport laws in chemically reactive systems that obey Curie's theorem predict the existence of cross-phenomena between scalar reaction rates and the magnitude of the second-rank velocity gradient tensor, selecting only those elements of ?v experienced by reactants that are chemisorbed on the surface of the rotating plate. Stress sensitivity via the formalism of irreversible thermodynamics introduces a zeroth-order contribution to heterogeneous consumption rates that must be quenched when reactants or active vacant sites are not present on the surface of the rotating plate. Rotating-disk reactor simulations are presented for simple 1st-order, simple 2nd-order, and complex heterogeneous stress-free kinetics, where the latter considers Langmuir-type dissociative adsorption of one of the reactants. Accurate design of rotating-disk reactors must consider stress-sensitivity when the shear-rate-based Damköhler number (i.e., ratio of the stress-dependent zeroth-order consumption rate relative to the rate of reactant diffusion toward the active surface) is greater than its threshold value which increases at higher stress-free Damköhler numbers. Modulated rotation of the catalytically active plate demonstrates that these rotating-disk reactors must operate above a threshold for the stress-sensitive Damköhler number, identified under steady shear conditions, before dynamic shear has a distinguishable effect on reactor performance.     

Solid-liquid and liquid-liquid slow and fast reactions: Enhancements by fine carbon particles

The role of fine carbon particles was studied in the alkaline hydrolysis of tridecyl formate and benzyl benzoate (liquid-liquid) and alkaline hydrolysis of phenyl benzoate and ethyl p-nitrobenzoate and oximation of cyclododecanone (solid-liquid). Enhancements by a factor of 1.2–5 were realized by the use of fine carbon particles whose sizes are smaller than the typical diffusion film thickness. The presence of fine carbon particles can cause a slow reaction occurring in the bulk to occur in the film (as in the oximation reaction) and can even enhance the rates of fast reactions which already occur completely in the film (as in the alkaline hydrolysis of ethyl p-nitrobenzoate and tridecyl formate). Theoretical models have been developed for different cases and a good agreement has been found between experimental and predicted values.     

Superlocal chemical reaction equilibrium in low temperature plasma

Low temperature plasmas (LTP) are a unique class of open-driven systems in which chemical reactions are unpredictable using established concepts. The terminal state of chemical reactions in LTP, termed the superlocal equilibrium state, is hypothesized to be defined by a proposed set of state variables. Using a LTP reactor wherein the state variables have been measured, it is shown that CO₂ spontaneously splits and the effluent speciation is independent of the influent speciation if the state variables are held constant and the residence time is long. CO₂ conversion at long residence times, which is expected to be nominally zero from equilibrium thermodynamics, can be as high as 70% in the LTP. The employed low pressure plasma reactor (P = 10 mbar) had a similar volume, productivity, and energy efficiency compared to an atmospheric pressure dielectric barrier discharge reactor, thanks to reaction rates that were three orders of magnitude faster.