Design and control of an olefin metathesis reactive distillation column

This paper considers the design and control of a reactive distillation column in which one reactant is consumed and two products are formed (A?B+C). The volatilities are α_B>α_A>α_C, i.e. the reactant is intermediate boiling between the two products. The metathesis of 2-pentene is considered as the demonstrative example. The column has a single feed of the intermediate boiling reactant. The distillate contains mostly light component and the bottoms mostly heavy.Three designs are considered: the base case (low-conversion/low-pressure), a low-conversion/high-pressure case and a high-conversion/high-pressure case. The base design is obtained from the literature, and the other two steady-state designs are optimized with respect to the total annual cost. All the designs are found to be openloop stable. Five control structures are studied for the base design. Then the best two structures are applied to the remaining two designs. This category of reactive distillation exhibits less challenging problems than other categories since it uses a single feed, which eliminates the need for the control structure to perfectly balance two fresh feeds.Simulation results demonstrate that effective dynamic control is provided by a control structure that uses two temperatures to maintain the purities of both product streams. No internal composition measurement is required. This structure is found to be robust and stable and rejects loads and tracks setpoints very well.     

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.     

Simultaneous absorption with reversible instantaneous chemical reaction

The approach presented recently [1] for analyzing absorption and desorption mass transfer problems with instantaneous chemical reaction is extended to the case of simultaneous absorption of two gases, A and A′. The analysis is developed for arbitrary stoichiometry. The following simple case is discussed in detail:A + B₁?B₂A′ + B₁?B₃ where B₁ is the liquid phase reactant and B₂, B₃ the reaction products. The analysis takes into account the “shift” reaction, which for the simple case above is:A + B₃?A′ + B₂This reaction takes place in the region near the interface. The analysis differs from previous work which, with one exception, ignored the “shift” reaction and restricted attention to zero values of the concentrations of B₂ and B₃ in the bulk liquid.The analysis shows that the conditions where the physical driving forces (a_i-a_o) for absorption of both gases are large and positive does not imply that the chemical driving forces (α_i-α_o) are both positive. In fact, it is shown that cases arise where one component may desorb even though its physical driving force is positive.A simplified thermodynamic model useful for extrapolation of mixed CO₂ and H₂S equilibrium data in amine solutions to very low values of acid gas loading in solution is developed. Tower profiles for simultaneous absorption of CO₂ and H₂S in monoethanolmine solution are considered in light of the new analysis. The good kinetic selectivity measured for H₂S at the absorber lean end is due to the fact that carbon dioxide is not absorbed in the instantaneous reaction regime. At the absorber rich end, where a temperature bulge develops, CO₂ is absorbed in the instantaneous regime, causing H₂S to be desorbed even though its physical driving force favors absorption.     

Autocatalytic reactions in the isothermal,continuous stirred tank reactor: Oscillations and instabilities in the system A + 2B → 3B; B → C

The prototype, cubic autocatalytic reaction (A + 2B → 3B) forms the basis for the simplest homogeneous system to display “exotic” behaviour. Even under well-stirred, isothermal, open conditions (CSTR) we may find multistability, hysteresis, extinction, ignition and anomalous relaxation times. Allowing for the finite lifetime of the catalyst (B→inert products) adds another dimension. The dependence of the stationary-states on residence-time now yields isolas or mushrooms. Sustained oscillations (stable limit cycles) are also possible. The onset of oscillation corresponds to a change in the character of the stationary-state (from stable focus to unstable focus) and the conditions for this change can be evaluated analytically. The period of the oscillations and their amplitudes increase as the residence time is lengthened. A total of nine different phase-portraits in the a–b plane has been found.The isothermal system is less complex than the exothermic, first-order reaction in a CSTR, but there are strong analogies between the two.     

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.     

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.     

Autocatalytic reactions in the isothermal,continuous stirred tank reactor: Isolas and other forms of multistability

Autocatalytic reactions are often complicated, and analyses of their behaviour in open systems can seem too particular to permit useful generalisation. We study here the simplest of circumstances (uniform temperatures and concentrations in the isothermal CSTR) and the simplest of reaction schemes: (i) quadratic autocatalysis (A + B→2B); and (ii) cubic autocatalysis (A + 2B→3B). The catalyst B may be stable or have a finite lifetime (B→ inert products). Allowing for this finite lifetime adds another dimension to the interest.The phenomena encountered include multistability, hysteresis, critical extinctions, critical ignitions, and anomalous relaxation times (though infinite values do not arise). Patterns of stationary states as function of residence time can show isolas and mushrooms. All these aspects yield to simple algebraic analysis. The presence of the catalyst B in the inflow can make qualitative differences of a kind parallelled by an additional, non-catalytic reaction of the same stoichiometry (e.g. A→B). Invoking the reversibility of the reactions neither increases nor diminishes their variety, and thermodynamic considerations have little to do with the many different patterns of reactivity displayed.The local stability of the various stationary states has also been characterized. Quadratic autocatalysis shows limited variety (stable node, stable focus); cubic autocatalysis generates all the kinds of stationary state possible in a two-variable system. Again all the algebra is straightforward if not always simple. Sustained oscillatory behavior (limit cycles) also occur.All these remarks relate to isothermal systems, but there are the most striking parallels between isothermal autocatalysis and the exothermic, first-order reaction in the CSTR. Behaviour with an autocatalyst of complete stability corresponds to perfect heat insulation (adiabatic operation) in the non-isothermal, exothermic system.     

Mixing and fast chemical reaction-V: Influence of diffusion within the reaction zone on selectivity

The competitive, consecutive reations A + B = R, R + B = S are considered to occur within spherical or planar zones, initially containing only the reagent B and into which the reagent A diffuses. Depending upon whether B is immobile or can diffuse within the reaction zone, so will different distributions of the products R and S be obtained. These distributions have been computed by numerically integrating the diffusion-reaction equations. When B diffuses, less S is formed and increasing the volume ratio α = V_A/V_B of the reagent solutions also causes less S to be formed, provided that the mixing modulus is constant. The latter trend has been confirmed by conducting the coupling of 1-naphthol (A) and diazotised sulphanilic acid (B) at α = 10, 50 and 100. The product distributions were predicted well without fitting any constants by a model postulating a gradually thinning, planar reaction zone within which also B diffused.     

On a mechanism for autocatalysis

The mechanism proposed by Walles and Platt for an autocatalytic reaction A → B + C is analysed by the method of singular perturbations. This has some features of interest in that the stable root of the degenerate problem changes during the course of the reaction and an intermediate solution with a different dependence on the small perturbation parameter must be introduced. Comparison between the calculated and asymptotic solution shows good agreement with only the first two terms of the perturbation expansion.     

Localization of spherical nanoparticles within lamellar AB diblock copolymer melts through self-consistent field theory

Here we report the results of a three dimensional hybrid self-consistent field theoretic (HSCFT) model describing the equilibrium particle distribution of spherical nanoparticles within symmetric AB diblock copolymer melts. Holding the polymer composition and morphology fixed, we consider a comprehensive parameter space comprised of the Flory interaction parameter describing interactions between B segments and the particle surface compared to the segment-segment interaction parameter (χBP/χAB), the particle volume fraction (?_P), and the ratio of the particle diameter to block copolymer domain spacing (dP/dAB). Analysis of the free energy over this parameter space yields phase diagrams showing the conditions under which particles segregate to the intermaterial diving surface (IMDS) or the center of the domain. Interestingly, w e predict a particle concentration-dependent “reentrant” phase transition in which particles move from the domain interior, to the IMDS, and back as ?_P increases. These results are interpreted as a subtle consequence of the competition between enthalpic polymer-particle interactions and the chain packing frustration imposed by the particulate inclusion. These results are consistent with recent experiments on block copolymer nanocomposites.     

Compensation effect in the activation of fibrous chars prepared from viscose

Viscose chars have been prepared under several different conditions and with four inorganic impregnants. The reaction with CO₂ was studied at several temperatures and the Arrhenius parameters A and E were evaluated. For these related chars A and E were found to conform to the Compensation Effect, In A = β + αE; the isokinetic temperature was 900 K. It is also shown that for such a system of chars the experimentally determined variable In (rate constant) also varies linearly with E for chars activated at the same temperature. Whilst E for a given char is independent of the extent of activation, A is not.     

Eigenvalue-eigenfunction analysis of infinitely fast reactions and micromixing regimes in regular and chaotic bounded flows

We analyze the dynamics of a single irreversible reaction A+B→ Products, occurring in a bounded incompressible flow. Within the limits of infinitely fast kinetics, the system is reduced to an advection-diffusion equation for the scalar φ, representing the difference between the reactant concentrations. By the linearity of the governing PDE, the system evolution is determined by the properties of the eigenvalue-eigenfunction spectrum associated with the advection-diffusion operator. In particular, the dependence of the dominant eigenvalue Λ—yielding the time-scale controlling the asymptotic reactant decay—as a function of the molecular diffusivity, , for different stirring protocols is analyzed. We find , where the exponent α∈[0,1] depends upon the kinematic features of the stirring flow. When the kinematics is regular within most of the flow domain (e.g. two-dimensional autonomous flows or time-periodic protocols possessing large quasiperiodic islands) a purely diffusive scaling, α=1 settles as . The singular scaling α=0 is found in the case of globally chaotic kinematics, whereas mixed regimes, 0<α<1, occur in flows that are characterized by the coexistence of quasiperiodic and chaotic behavior. The analysis of spectral properties of the advection-diffusion operator provides a new classification of micromixing regimes, and new mixing indices for quantifying homogenization performances in the presence of diffusion.     

Dynamics of adsorptive reactors I — Instantaneous nonlinear adsorption and finite zero order irreversible reaction

The dynamics of adsorptive reactors, in which the coupling of nonlinear Langmuir adsorption with zero order reaction A → B occurs, is considered. The method of characteristics is used to develop, analytically, the responses of fixed bed (plug flow) adsorber/reactors to step, pulse or Dirac inputs of reactant A. An increase in the breakthrough time of the column is observed as a consequence of the coupling of both phenomena. The responses of CSTR adsorber/reactors to step or Dirac inputs of reactant A are derived, as well. A method for the determination of equilibrium and kinetic parameters is proposed.     

Kinetic instabilities in heterogeneously catalyzed reactions—I: Rate multiplicity with langmuir-type kinetics

The question under which conditions kinetic instabilities can be described by Langmuir type kinetics is studied using a fairly general model for the surface reactionpA + qB → C. This paper is concerned with the occurrence of rate multiplicities (ignition-extinction phenomena). It is shown that rate multiplicity can be caused by the competing chemisorption of A and B upon the same active sites of the catalyst. Rate multiplicity can occur if at least one of the chemisorption or reaction steps is of second order. No rate multiplicity can be expected, if either A or B reacts via an Eley-Rideal type mechanism.     

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.     

Polymerization of propylene catalyzed by α-diimine nickel complexes/methylaluminoxane: catalytic behavior and polymer properties

α-Diimine nickel dibromide complexes of dibromo[N,N’-bis(2,6-diisopropylphenyl)-2,3-butanediimine]nickel(II) (A) and dibromo[N,N’-(phenanthrene-9,10-diylidene)bis(2,6-diisopropylaniline)]nickel(II) (B) were synthesized under controlled conditions. The catalysts A, B and mixed of 1:1 weight ratio of them (C) were activated by methylaluminoxane and were used for propylene polymerization in a semi-batch reactor. In study of the catalytic systems behavior, activities, glass transition temperature (T _g) and viscosity average molecular weight (M _v) values related to the catalyst C were between those related to the catalysts A and B under same conditions. The highest and the lowest molecular weights of the obtained polymers were produced by the catalysts B and A which were about 80,000 and 70,000 (g/mol) under same conditions, respectively. The T _g of polypropylenes produced by the catalysts was about ?34 °C. The resulting polymers had similar behavior with ethylene-propylene copolymer which it could be due to formation of ethylene-type units in the polymer chain.     

Retraction of polypropylene tape

Retraction measurements have been made on 50 μm thick polypropylene tapes drawn on a yarn line under a variety of conditions. Small samples were annealed in silicone oil for different periods at temperatures up to the melting point. The retraction data were found to be described by a relation of the form R(%) = A + B log t, where A and B are constant for a given temperature, A being the intercept on the retraction axis for t = 1. As the temperature is increased towards the melting point, A increases, slowly at first and then much more rapidly. On the other hand, B reaches a maximum at a temperature T_k, and then decreases as the temperature is increased further. T_k corresponds to the point at which A, which represents a virtually instantaneous retraction as the sample reaches temperature, begins to increase rapidly. T_k promises to be useful in that it represents the susceptibility of a given polymer to retraction and corresponds fairly closely to the original draw temperature if the tape has not been heat set. D.s.c. analysis has demonstrated that the mechanism responsible for the instantaneous component of retraction is the partial melting out of crystallites. The small logarithmic retraction which is dominant below T_k is seen as resulting from a thermally activated process within the crystallites. The approach has enabled the effect of pre-anneals and heating rates to be understood and has also led to a general prediction of retraction behaviour under conditions of continuous heating.     

Simulation of an extractive electrochemical reaction operated under limiting current conditions in a parallel-plate reactor

An extractive electrochemical reaction, which uses an extractive liquid (β) to separate the adherent product (S) on the electrode surface (e) in order to allow the continuation of the reaction (R) occurring electrochemically in a reacting phase (α), was investigated with the aim of studying the kinetics and reactor design. A kinetic model based on the competitive surface coverage (θ) by the reactant and the product, was developed to describe the performance in a parallel-plate reactor. The electrochemical reaction rate, defined asKmAX _α/e(1-θ)(C _R/α-C _R/e), is equal to the extraction rate, defined asKdAX _β/Seθ(C _S ^β/sat -C _S/β) under steady-state conditions whereX is the dispersion function andA is the specific surface area. Simulation under limiting current conditions reveals that this system is dependent on the volume ratio of the two liquids, the dispersion effect and the reactor geometry and diffusion coefficients. Three dimensionless parametersΦ _k(=K _m/K _d),Φ _x (=X _α/e/X _β/Se) andΦ _v ( =X _β/X _α) were used to describe this extractive electrochemical reaction.     

Application of the Monte Carlo simulation method to the investigation of peculiar free‐radical copolymerization reactions: Systems with both reactivity ratios greater than unity (rA > 1 and rB > 1)

With a Monte Carlo simulationmethod, copolymer properties have been thoroughly studied, and the influence of the reactivity ratios and feed composition has been taken into consideration. Instantaneous alterations of the copolymer composition and copolymer heterogeneity, which is also called a randomness parameter, have been examined with data obtained from the simulation at each stage of the copolymerization reaction. The results prove the azeotropic behavior of copolymerization reactions in which both reactivity ratios are greater than unity, although some special reactivity ratio combinations ignore the azeotropic behavior. The copolymer composition reaches an azeotrope point at the end of the copolymerization reaction when the copolymerization is an azeotropic reaction. In addition, the randomness parameter takes its maximum value at the azeotrope point when reactivity ratio r_A is equal to reactivity ratio r_B. Finally, increasing the reactivity ratios causes no change in the trend of copolymer composition/feed composition curves when r_A is equal to r_B. However, the curves produced with larger r_A and r_B values show more fluctuations. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007     

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.