Uniqueness and multiplicity criteria for an nth order chemical reaction

New and very strong criteria are presented for a priori prediction of the conditions for which the steady-state lumped parameter model of an nth order chemical reaction (n ≥ 0) in an adiabatic CSTR has either a unique or multiple solutions. The criteria show that the higher the order of the reaction the smaller is the region in the parameters space for which multiplicity can occur.New uniqueness and multiplicity criteria are developed also for an nth order reaction in a porous catalyst using a model, which accounts for intraparticle concentration gradients, while assuming a uniform intraparticle temperature different from the ambient one. The region in the parameters space for which steady state multiplicity can occur for this model is smaller than that for a corresponding lumped model, which ignores the intraparticle concentration gradients.     

ANALYSIS OF THE MULTIPLICITY PATTERNS OF A CSTR

Continuous changes in the residence time of a cooled continuously stirred tank reactor, in which a single, exothermic, first-order reaction occurs, may lead to one of six different multiplicity patterns. A simple technique is developed for the exact prediction of the multiplicity pattern existing for any set of parameter values and of the influence of changes in the parameter values on the transition from one pattern to another.     

A Resource Allocation Approach for the Generation of Service-Dependent Demand Matrices for Communications Networks

Estimating point-to-point demands from partially available information, such as total demand volumes originating and terminating at nodes and traffic volumes routed on links, has significant applications in various areas, such as communications network planning and transportation planning. Existing methods include matrix and link scaling methods, statistical methods, more complex mathematical programming models, and forecasting using demographic data. We present a new mathematical programming model based on equitable resource allocation. The model considers multiple services, e.g., data, video, and voice, and generates a point-to-point demand matrix for each service. Originating and terminating demands for each service and link loads, aggregated over all services, are viewed as resources. Each point-to-point demand is associated with a performance function that measures its weighted, normalized deviation from a target defined by a service-dependent community of interest matrix. The model formulation has a lexicographic minimax objective function and multiple knapsack resource constraints. The model has an intuitively appealing interpretation and a specialized algorithm can generate demand matrices for large network problems very fast.     

Hot zones formation during regeneration of diesel particulate filters

A diesel particulate filter (DPF) is used to remove particulate matter (PM) from the diesel engine exhaust. The accumulated PM is periodically removed by combustion, which sometimes leads to excessive temperature excursions that melt the ceramic filter. This behavior cannot be explained by operation under stationary feed conditions. We propose that these temperature excursions are a dynamic effect following a rapid change in the driving mode while the DPF is being regenerated. Specifically, a rapid decrease in the exhaust temperature can lead to a counterintuitive large transient temperature rise above that which would exist under a higher stationary feed temperature. This unexpected behavior is similar to the well‐known wrong‐way behavior in packed‐bed reactors, even though the axial‐dependent flow through the filter in a DPF is rather different from the constant axial flow through a packed bed. We present simulations that provide insight about the dependence of the amplitude of this wrong‐way temperature rise on the filtration velocity, the PM loading, dimensions of the DPF, and the amplitude of the rapid temperature decrease and when it occurs after the start of the regeneration. The insight provided by these simulations will help develop operation and control protocols that circumvent or at least decrease the probability of the occurrence of the destructive melting of the DPF. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Electric and Magnetic Fields Generated by SHS

Fast-moving reaction zones (combustion fronts) may generate transient electric potentials (up to 1.5 V) and weak magnetic fields (up to 20 nT) due to ionization processes and ion movement within and behind the reaction front. These time-varying electric and magnetic fields are most probably generated by an electric double layer within individual particles and a temporal excess of ion carriers within the sample. The shape and magnitude of the induced temporal signals depend on the reaction zone propagation mode, reaction mechanism, and reactant properties.     

A new route to synthesize La1?xSrxMnO3

Self-Propagating High-temperature Synthesis (SHS) was used to producecomplex oxides (La_1–x Sr _x MnO₃ with x = 0, 0.1 and 0.2), which are used as the cathode in solid oxide fuel cells (SOFCs). Thermodynamic predications and experiments show that La_1–x Sr _x MnO₃ can be prepared via SHS under moderate conditions from a mixture of La₂O₃ + SrO₂ + Mn, using either gaseous oxygen or solid NaClO₄ as the oxidant. Partial melting at the high combustion temperature increased product homogeneity. The electrical conductivity of the product was 180 S·cm^–1 at 1000°C in air, matching that of sample made by other synthesis processes. SHS enables a more economical production of La_1–x Sr _x MnO₃ than existing commercial processes.     

Steady-state multiplicity of lumped-parameter systems in which two consecutive or two parallel irreversible first-order reactions occur

This work examines and classifies the steady-state multiplicity features of lumped-parameter systems in which either two consecutive or two parallel, irreversible, first-order reactions are carried out. Several new and surprising features were discovered such as the occurrence of steady-state multiplicity for all Damköhler numbers in certain cases. The multiplicity may occur only if at least one of the reactions is exothermic. Simple criteria are presented for a priori prediction of the conditions which guarantee steady-state uniqueness or multiplicity.     

A RATIONAL APPROXIMATION OF THE EFFECTIVENESS FACTOR

A fast, approximate method of calculating the effectiveness factor for arbitrary rate expressions is presented. The method does not require any iterative or interpolative calculations. It utilizes the well known asymptotic behavior for small and large Thiele moduli to derive a rational function which gives an approximation valid for all Thiele moduli. The approximation converges to the proper asymptotic values for small and large Thiele moduli and gives only small errors for intermediate values of φ. The method fails in the range in which either steep slopes or multiplicity exist in the η(φ) graph.     

Carbon combustion synthesis of nanostructured perovskites

A novel, economical, and energy-efficient process to produce nanostructured particles of several perovskite oxides, such as ferroelectrics BaTiO₃, SrTiO₃ and LiNbO₃, is described. This process, referred to as carbon combustion synthesis of oxides (CCSO) is a modified SHS process that uses carbon as a fuel instead of a pure metal. In CCSO of nanostructured materials, the exothermic oxidation of carbon nanoparticles (∼5 nm) with a surface area of 80 m²/g generates a thermal reaction wave with temperature of up to 1200°C that propagates through the solid submicron reactant mixture, converting it to the desired complex oxide product. The carbon is not incorporated in the solid product since it is released in a gaseous form (CO₂) from the sample. The quenching front method combined with XRD and Raman spectroscopy revealed that crystalline tetragonal BaTiO₃ particles formed in the early stage of the combustion, before the temperature reached its maximum. A major difference between the thermal transport processes during CCSO and conventional SHS is the extensive emission of CO₂. The release of CO₂ enables synthesis of highly porous (up to 70%) powders having a particle size in the range of 60–80 nm with a surface area of up to 12.4 m²/g.