Thermally safe operation of liquid-liquid semibatch reactors Part II: Single diffusion controlled reactions with arbitrary reaction order

The thermally safe operation of an indirectly cooled semibatch reactor in which an exothermic liquid-liquid reaction occurs corresponds to conditions of potentially very high macrokinetic conversion rates compared with the supply rate of the coreactant, which accumulation in the system remains consequently low. This leads to the definition of a target temperature that can be compared with the real temperature-time profile, in order to develop boundary diagrams which summarize all the possible thermal behaviors of the reactor and can be used for safe scale-up purposes. The variable parameters which appear in such diagrams are an exothermicity and a reactivity number derived from the expressions of the conversion rates in the kinetically or diffusion controlled regime, respectively.In this work the influence of the microkinetic rate of reaction on the shape and location of the boundary diagrams for single liquid-liquid diffusion controlled reaction systems is discussed, extending to this regime the results previously obtained for kinetically controlled reactions.Also in the case of diffusion controlled reactions, it is shown that for many practical systems, using boundary diagrams based on (1,1) reaction orders can lead to both unsafe or not necessary low production operating conditions. Consequently, a number of new boundary diagrams for arbitrary reaction orders is presented and some rules-of-thumb useful to their application are discussed.     

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.     

Economic criteria in the design of cascades of CSTR's for the performance of enzyme-catalyzed reactions

The mass balances on substrate in each unit of a series of CSTRs performing an enzyme-catalyzed reaction described by Michaelis-Menten kinetics (with parameter K^m) are written and the necessary and sufficient condition that must besatisfied by the intermediate concentrations in order to obtain a minimum overall capital investment is found on the assumption that the cost of each reactor unit scales up on its capacity according to a fractional factor exponential rule (with parameter n). The asymptotic situations of pseudo-zero order and pseudo-first order behavior are explored. The ratio between consecutive concentrations leading to a minimum overall capital investment decreases as K_m decreases at a rate that is slower for higher n, and tends to unity as the pseudo-first order situation is approached. If fractional values of n are considered, local minima of the capital investment associated with the overall reactor cascade exist only in certain ranges of substrate conversion; below the lower limits of such ranges, the number of reactor units should actually be decreased. A graphical procedure aimed at obtaining the intermediate optimal concentrations is presented.     

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.     

The free energy correlation for FeH2O system at 25°C and the thermodynamic consideration of the mechanisms on active iron

For a better understanding of the FeH₂O system at 25°C the standard free energies were summarized and the unknown values were estimated for the species Fe(OH)^m±_n, FeO^m±_n, Fe|H₂O|, etc. graphically.As has been explained on the basis of several mechanisms for the active iron, a detailed discussion is possible concerning the thermodynamic credence for the proposed mechanisms.It was demonstrated that the equilibrium E_H-pH, log a_i diagram furnishes a general graphic representation of the more important properties of the mechanism under study.     

Design stage optimization of an industrial low-density polyethylene tubular reactor for multiple objectives using NSGA-II and its jumping gene adaptations

Design stage optimization of an industrial low-density polyethylene (LDPE) tubular reactor is carried out for two simultaneous objectives: maximization of monomer conversion and minimization of normalized side products (methyl, vinyl, and vinylidene groups), both at the reactor end, with end-point constraint on number-average molecular weight (M_n,f) in the product. An inequality constraint is also imposed on reactor temperature to avoid run-away condition in the tubular reactor. The binary-coded elitist non-dominated sorting genetic algorithm (NSGA-II) and its jumping gene (JG) adaptations are used to solve the optimization problem. Both the equality and inequality constraints are handled by penalty functions. Only sub-optimal solutions are obtained when the equality end-point constraint on M_n,f is imposed. But, correct global optimal solutions can be assembled from among the Pareto-optimal sets of several problems involving a softer constraint on M_n,f. A systematic approach of constrained-dominance principle for handling constraints is applied for the first time in the binary-coded NSGA-II-aJG and NSGA-II-JG, and its performance is compared to the penalty function approach. A three-objective optimization problem with the compression power (associated with the compression cost) as the third objective along with the aforementioned two objectives, is also studied. The results of three-objective optimization are compared with two different combinations of two-objective problems.     

Micromixing effects on a parallel reaction in flow reactors

Using the micromixing concepts of Danckwerts and Zwietering, the Peclet number Pe has been correlated mathematically to the degree of segregation J for the axial dispersion model. The results were applied to compare the micromixing effects on a model, mixed-order parallel reaction system in continuous flow reactors. Axial dispersion model, and Ng and Rippin's two-environment model were used to find the micromixing effects in tubular and stirred tank reactors, respectively. The performance of these reactors, with varying geometries, has been evaluated in terms of overall conversion, selectivity, and yield under identical operating and reaction conditions. The overall conversion increases in a tubular reactor with the increase in J, irrespective of the kinetic orders. However, in a stirred tank reactor, the conversion is found to be micromixing-sensitive, depending on the order of reaction. For m = 1 and n = 2 (case 1), the conversion is fairly insensitive to micromixing effects while it decreases for m = 0.5 and n = 1 (case 2) with increasing J. For the same extent of micromixing, a tubular reactor gives, in both cases, a higher conversion than a stirred tank reactor. The selectivity, in either case, decreases in both reactors with increasing segregation effects. However, in each case, the selectivity of a tubular reactor was fairly close to that of a stirred tank reactor at the same value of J. As far as the yield is concerned, both reactors achieve nearly the same value, without significant micromixing effects.     

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.     

Exact criteria for uniqueness and multiplicity of an nth order chemical reaction via a catastrophe theory approach

The development of a simple, generalized technique for the exact determination of regions of unique and multiple solutions to certain nonlinear equations via a catastrophe theory-implicit function theorem approach, is presented. The application of this technique to the nth order chemical reaction in the nonadiabatic and adiabatic CSTR yields exact, explicit bounds for all n ≥ 0. To our knowledge, this is the first report of exact, explicit bounds for these systems, except for n = 0, 1 for the adiabatic CSTR, and n = 1 for the nonadiabatic CSTR. For the nonadiabatic CSTR, these bounds show that the higher the reaction order, the smaller the region in parameter space for which multiplicity can occur for all γ and x_2c, (dimensionless activation energy and coolant temperature, respectively). This behavior is similar to that reported by Van den Bosch and Luss[1] for the adiabatic CSTR. The zeroth order reaction in the nonadiabatic CSTR exhibits more complex behavior and assumes characteristics of both high and low reaction orders insofar as increasing and/or decreasing the uniqueness space, in comparison to all other n > 0.An exact implicit bound between regions of uniqueness and multiplicity is also derived for the nth order reaction in a catalyst particle with an intraparticle concentration gradient and uniform temperature, and is fully demonstrated for the first order reaction. In addition, explicit criteria, sufficient for uniqueness and multiplicity of the catalyst particle steady state, stronger than those of Van den Bosch and Luss, are also developed by combining the present technique with bounds suggested by these authors.     

Ternary hydrogen-bonded polymer solutions

Ternary-phase diagrams have been experimentally determined at 100°C for systems containing a series of poly(n-alkyl methacrylates), poly(ethylene oxide) (PEO), and a solvent [4-ethyl phenol (EPh)]. A totally miscible phase diagram is experimentally determined for the poly(methyl methacrylate)/PEO/EPh system, while a closed-loop diagram is observed for the analogous system containing poly(ethyl methacrylate). The corresponding phase diagrams of analogous mixtures containing poly(n-propyl methacrylate) or poly(n-butyl methacrylate) exhibit large heterogeneous areas. Theoretically predicted phase diagrams calculated using an association model developed in our laboratory are in general accord with these observations for ternary hydrogen-bonded polymer/polymer solutions. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 1265–1271, 1998     

Modelling the Kinetics of Photoinitiated Polymerization of Di(meth)acrylates

The kinetics of photoinitiated polymerization of six analogous di(meth)acrylates and diacrylates was analysed according to the autocatalytic model R_p=kp^m(1-p)ⁿ (where R_p is polymerization rate, p is conversion degree, k is reaction rate constant and m and n are exponents), in order to find the influence of the reaction temperature and atmosphere, as well as monomer structure, on the parameters k, m and n. The best fit between the model prediction and experimental data was for the polymerization of diacrylates in an inert gas atmosphere. The autocatalytic exponent, m, for polymerization in argon of both di-methacrylates and diacrylates was found to be close to unity, whereas the reaction order exponent, n, was twice as high for the former compared with the latter (in the range of c. 3–5 and c. 1·3–2, respectively). An increase in the polymerization temperature caused a drop in both exponents. This drop is much more rapid in the case of the exponent n. Changes in the m and n exponents with temperature, as well as the difference in n exponents for the polymerization of acrylates and methacrylates, may be related to changes and differences in the mobility of reactive species during the reaction. The influence of atmospheric oxygen on the polymerization parameters is manifested by a very high increase in value of the exponent n. In the photochemically initiated process, an increase in the polymerization rate with temperature results mainly from a rapid decrease in the exponent n and, to a much lesser degree, from an increase in the reaction rate constant k. © of SCI.     

Pyrolysis of alkylcyclohexanes in or near the supercritical phase. Product distribution and reaction pathways

Cyclohexane and seven n-alkylcyclohexanes (alkyl side-chain C_mH_2m + 1, m = 1, 2, 3, 4, 6, 8, 10) were pyrolyzed in or near the supercritical phase in a batch reactor at 450°C under relatively high (≥ 2 MPa) and continuously increasing pressure for 6–480 min. The thermal stability of alkylcyclohexanes decreases with increasing side-chain length. The major reaction pathways of alkylcyclohexanes are strongly dependent on the side-chain length. For cyclohexane and methylcyclohexane, the dominant reaction is isomerization to form alkylcyclopentanes via ring contraction. The tendency to isomerization decreases with increasing side-chain length. For alkylcyclohexanes with m ≥ 3, the major reaction at early decomposition stages is β-scission, leading to CC bond cleavage in the side-chain at or near the ring followed by H-abstraction. The decomposition resulted in three pairs of most abundant products: cyclohexane plus 1-C_mH_2m, methylenecyclohexane plus n-C_{(m − 1)}H_{2(m − 1) + 2}, and cyclohexene plus n-C_mH_{2m + 2}. Under the conditions used, alkylcyclohexanes do not undergo ring-opening cracking to any significant extent. An empirical equation was developed to correlate the rate constant with the molecular structure of alkylcyclohexanes using a group contribution method.     

CFD evaluation of internal manifold effects on mass transport distribution in a laboratory filter-press flow cell

The internal manifold geometry strongly influences the flow distribution inside an electrochemical reactor. The mass transport coefficient is a function of the flow pattern and is a key parameter in successful electrochemical reactor design and scale-up. In this work, a commercial computational flow dynamics (CFD) package was used to describe the flow pattern in the FM01-LC reactor at controlled volumetric flow rates (corresponding to mean linear flow velocities past the electrode surface between 0.024 and 0.11 m s^?1). Numerical Re numbers were obtained for each local flow velocity at different positions in the reactor channel. From a known mass transport correlation (based on dimensionless groups, i.e. Sh, Re, Sc), numerical k _m values were obtained (in the range 200 < Re < 1,000) at different positions in the reactor channel. Computed k _m numbers are compared against experimental values. This computational approach could be useful in reactor design or selection since it facilitates a fast, preliminary reactor flow and mass transport characterisation without experimental electrochemical measurements.     

Parametric sensitivity of a CSTR

It is shown that the generalized sensitivity criterion recently developed in the context of thermal explosions and tubular reactors can be easily applied in the case of a CSTR as well. An illustrative example concerning sensitivity analysis of a single nth order irreversible exothermic reaction in a nonadiabatic CSTR is presented. A generalized region of parametric sensitivity is identified where the reactor temperature is parametrically sensitive simultaneously to all the input parameters. Asymptotic analysis for large heats of reaction is performed to investigate limiting behaviour, which leads to the classical Semenov limit in the case of large activation energies. It is shown that parametric sensitivity can occur even when unique steady states exist for all Damköhler number (Da) values. Furthermore, if operating conditions are chosen so as to avoid completely the possibility of parametric sensitivity for all Da, then the possibility of steady-state multiplicity is automatically avoided.     

Multiplicity,stability and dynamics for isothermal autocatalytic reactions in CSTR

Multiplicity, stability and dynamics for autocatalytic reactions of the type A? → rR + ? with overall rate expression r_A = kC_A^mC_Rⁿ in a continuous stirred tank reactor (CSTR) are studied. Exact multiplicity criteria are defined in the parameter space. Stability analysis shows that no periodic oscillation is possible for the system. When multiplicity occurs, some minimum of R present initially in the reactor is required in order for the high steady state to be achieved. Loci of transient extreme for product are also investigated. Multiplicity and uniqueness criteria are further compared with reported experimental data in literature.     

The response of linear cascades to variations of holding times

An arbitrary system of isothermal first order reactions with no volume change on reaction is considered. A comparison is made between the response of the system in a cascade of ideal continuous stirred tank reactors and an ideal tubular reactor to variations of holding times.The performance criterion chosen is a linear combination of the exit concentrations and, contrary to what has been published previously, examples are given to show that for an m tank cascade non-equal tank cascades can be locally stationary and even localy extreme. In spite of this (except for certain trivial and degenerate cases) it can be shown that the global extrema occur for equal tank cascades. Furthermore, these extrema are dominated by those for an m + 1 tank cascade and these are all dominated by those of the turbular reactor.Cases where the performance criterion is augmented by a cost associated with the total holding time or where the total holding time is constrained (equality or inequality) are also discussed. In the first case the above results are essentially unchanged, while in the constrained cases examples are given to show that non-equal tank cascades can be optimal.     

Hydrogen production from oxidative steam reforming of ethanol in a palladium-silver alloy composite membrane reactor

In this investigation, we studied the oxidative steam reforming reaction of ethanol in a Pd-Ag/PSS membrane reactor for the production of high purity hydrogen. Palladium and silver were deposited on porous stainless steel (PSS) tube via the sequential electroless plating procedure with an overall film thickness of 20 μm and Pd/Ag weight ratio of 78/22. An ethanol-water mixture (n_water/n_ethanol = 1 or 3) and oxygen (n_oxygen/n_ethanol = 0.2, 0.7 or 1.0) were fed concurrently into the membrane reactor packed with Zn-Cu commercial catalyst (MDC-3). The reaction temperatures were set at 593-723 K and the pressures at 3-10 atm. The hydrogen flux in the permeation side increased proportionately with increasing pressure; however, it reduced slightly when increasing oxygen input. This is probably due to the fast oxidation reaction that consumes hydrogen before the onset of the steam reforming reaction. The effect of oxygen plays a vital role on the ethanol oxidation steam reforming reaction, especially for a Pd-Ag membrane reactor in which a higher flux of hydrogen is required. The selectivity of CO₂ increased with increasing flow rate of oxygen, while the selectivity of CO remained almost the same.     

Conversion of syngas to hydrocarbons in a tube-wall reactor using CoFe plasma-sprayed catalyst: experimental and modeling studies

Catalyst activity and product selectivity studies of the conversion of synthesis gas to various hydrocarbon fractions were performed in a single-tube tube-wall reactor (TWR) using a CoFe plasma-sprayed catalyst with the operating conditions: temperature 250–275°C, pressure 0.1–1.03 MPa, exposure velocity 139–722 μms⁻¹, and a H₂:CO ratio of 2.0. The catalyst activity in terms of CO conversion was highest (98.5% m/m) at an exposure velocity of 139 μms⁻¹, temperature of 275°C, and in the pressure range 0.69–1.03 MPa. The selectivity to hydrocarbons was 43–50% (m/m) in the pressure range 0.69–1.03 MPa whereas the selectivity to C₅ + hydrocarbons was over 40% of the total hydrocarbons produced. The production of propylene was higher than ethylene under similar process conditions. The performance of the TWR was predicted by a numerical model. The model is based on the complete two-dimensional transport equations and reaction rate equations, developed for the CoFe catalyst. Predictions are made for the temperature along the axis of the reactor, for CO and H₂ conversions as functions of the reactor length and the exposure velocity, and the axial H₂O and CO₂ concentrations.