Electrical properties of V2O5–WO3/TiO2 EUROCAT catalysts evidence for redox process in selective catalytic reduction (SCR) deNOx reaction

Electrical conductivity measurements on EUROCAT V₂O₅–WO₃/TiO₂ catalyst and on its precursor without vanadia were performed at 300°C under pure oxygen to characterize the samples, under NO and under NH₃ to determine the mode of reactivity of these reactants and under two reaction mixtures ((i) 2000 ppm NO + 2000 ppm NH₃ without O₂, and (ii) 2000 ppm NO + 2000 ppm NH₃ + 500 ppm O₂) to put in evidence redox processes in SCR deNO_x reaction.It was first demonstrated that titania support contains certain amounts of dissolved W⁶⁺ and V⁵⁺ ions, whose dissolution in the lattice of titania creates an n-type doping effect. Electrical conductivity revealed that the so-called reference pure titania monolith was highly doped by heterovalent cations whose valency was higher than +4. Subsequent chemical analyses revealed that so-called pure titania reference catalyst was actually the WO₃/TiO₂ precursor of V₂O₅–WO₃/TiO₂ EUROCAT catalyst. It contained an average amount of 0.37 at.% W⁶⁺dissolved in titania, i.e. 1.07 × 10²⁰ W⁶⁺ cations dissolved/cm³ of titania. For the fresh catalyst, the mean amounts of W⁶⁺ and V⁵⁺ ions dissolved in titania were found to be equal to 1.07 × 10²⁰ and 4.47 × 10²⁰ cm⁻³, respectively. For the used catalyst, the mean amounts of W⁶⁺ and V⁵⁺ ions dissolved were found to be equal to 1.07 × 10²⁰ and 7.42 × 10²⁰ cm⁻³, respectively. Since fresh and used catalysts have similar compositions and similar catalytic behaviours, the only manifestation of ageing was a supplementary progressive dissolution of 2.9 × 10²⁰ additional V⁵⁺ cations in titania.After a prompt removal of oxygen, it appeared that NO alone has an electron acceptor character, linked to its possible ionosorption as NO⁻ and to the filling of anionic vacancies, mostly present on vanadia. Ammonia had a strong reducing behaviour with the formation of singly ionized vacancies. A subsequent introduction of NO indicated a donor character of this molecule, in opposition to its first adsorption. This was ascribed to its reaction with previously adsorbed ammonia strongly bound to acidic sites. Under NO + NH₃ reaction mixture in the absence of oxygen, the increase of electrical conductivity was ascribed to the formation of anionic vacancies, mainly on vanadia, created by dehydroxylation and dehydration of the surface. These anionic vacancies were initially subsequently filled by the oxygen atom of NO. N^o atoms, resulting from the dissociation of NO and from ammonia dehydrogenation, recombined into dinitrogen molecules. The reaction corresponded to

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. In the presence of oxygen, NO did not exhibit anymore its electron acceptor character, since the filling of anionic vacancies was performed by oxygen from the gas phase. NO reacted directly with ammonia strongly bound on acidic sites. A tentative redox mechanism was proposed for both cases.     

Integral approximation—an approach to reduced models for particulate processes

In this contribution, a model reduction technique for population balance systems describing particulate processes is presented. This technique is based on integral approximation and allows the derivation of highly accurate moment models. In contrast to other model reduction methods which can be found in literature, this integral approximation technique can be applied for arbitrarily complex phenomena specifications. The applicability of the presented method will be demonstrated for different example processes by comparing the dynamic behavior of the original population balance models with those of the derived reduced models of moments.     

An analytical tuning approach to multivariable model predictive controllers

Multivariable model predictive control is a widely used advanced process control methodology, where handling delays and constraints are its key features. However, successful implementation of model predictive control requires an appropriate tuning of the controller parameters. This paper proposes an analytical tuning approach to multivariable model predictive controllers. The considered multivariable plants are square and consist of first-order plus dead time transfer functions. Most of the existing model predictive control tuning methods are based on trial and error or numerical approaches. In the case of no active constraints, closed loop transfer function matrices are derived and decoupling conditions are addressed. For control horizon of one, analytical tuning equations and achievable performances are obtained. Finally, simulation results are used to verify the effectiveness of the proposed tuning strategy.     

Time Deformation,Continuous Euler Processes and Forecasting

Abstract. A continuous Euler model has time‐varying coefficients. Through a logarithmic time transformation, a continuous Euler model can be transformed to a continuous autoregressive (AR) model. By using the continuous Kalman filtering through the Laplace method, this article explores the data application of a continuous Euler process. This time deformation of an Euler process deforms specific time‐variant (non‐stationary) behaviour to time‐invariant (stationary) data on the deformed time scale. With these time‐invariant data on the transformed time scale, one may use traditional tools to conduct parameter estimation and forecasts. The obtained results can then be transformed back to the original time scale. Simulated data and actual data such as bat echolocation and the US residential investment growth are used to demonstrate the usefulness of time deformation in forecasting. The results indicate that fitting a traditional autoregressive moving‐average (ARMA) model on an Euler data set without imposing time transformation leads to forecasts that are out of phase while the forecasts of an Euler model stay mostly in phase.     

Catalyst surface at a fractal of cost—a quest for optimal catalyst loading

Intuition tells us that any decrease in the catalytically active surface area should result in an equivalent decrease in the reaction yield and efficiency. Our findings counter this by showing that the active surface and hence the catalyst loading can be reduced drastically in the diffusion-limited heterogeneous reaction systems, while the conversion rate remains essentially unchanged by using fractals for spatial distribution of the catalyst load. The results of this study provide an unusual circumstance for optimal design of chemically active surfaces and can be used to drastically reduce cost of heterogeneous chemical and biological reactors, sensors, and electrodes of fuel cells. The proposed approach can be exploited to its fullest extent in chemical microsystems by utilizing the latest advances in our abilities to manipulate matter on the micro/nano scale.     

Empirical equations for the thermodynamic properties of aqueous sodium chloride

Equations for the thermodynamic properties of aqueous sodium chloride near its vapour pressure are presented. The equations are functions of temperature and concentration, and may be used to estimate aqueous sodium chloride's solubility, density, vapour pressure, specific enthalpy and entropy. They are valid for temperatures from 0 to 300°C, and concentrations extending to saturation with suitable accuracy. The thermodynamic equations are represented graphically and compared with published experimental data. These equations should prove to be a useful tool for modeling desalination equipment, particularly distillation processes.     

An analytic solution to the transient diffusion-reaction problem in particles dispersed in a slurry reactor

In this work, we present the solution of the equations that govern the reactant transport in a well mixed system that contains particles where diffusion and first-order reaction occur. The transport equations are coupled by an interfacial boundary condition that includes mass transfer resistance. The statement of the problem allows arbitrary time depending feed functions. The evaluation of the solution obtained by the Laplace method requires the solution of an eigenvalue problem. We discuss the evaluation of the solution, and typical results for three different feed functions: step, pulse and oscillatory functions are presented. The resulting equations are able to show the effect of internal and external mass transfer limitations on the particle and fluid concentrations and on kinetic experimental results.     

Population balances for particulate processes—a volume approach

Population balance models have been used in chemical engineering since the 1960s and have evolved to become the most important tools for design and control of particulate processes. In this paper we show that the intrinsic particle parameter that determines changes in the process and should thus be included in the population balance is the particle volume. The basic population that is modeled should be the mass distribution, or the volume distribution if the density is constant. The population balance thus describes the change of the volume distribution of volume with time. Furthermore, we suggest that the “birth” and “death” terms that are often used to describe discrete events in particulate processes can almost always be replaced by a rate of change term.To design and control existing and future processes, a multi-dimensional population balance model is required. We propose a volume-based model in which the particle properties that are modeled are the volumes of solid, liquid, and air, respectively. In the most general case the model will consist of a properties vector and a distribution tensor. Depending on the complexity of the process, one or more of the properties may be omitted from the model. This is shown in three examples of increasing complexity: comminution, sintering, and granulation.     

Modelling of membrane nanofiltration—pore size distribution effects

The effects of log-normal pore size distributions on the rejection of uncharged solutes and NaCl at hypothetical nanofiltration membranes have been assessed theoretically. The importance of pore radius-dependent properties such as solvent viscosity and dielectric constant is increased by the introduction of a pore size distribution in calculations. However, the effect of porewise variation in viscosity is less apparent when considered at a defined applied pressure rather than at a defined flux, showing a further advantage of basing theoretical analysis of nanofiltration in terms of applied pressure.Truncated pore size distributions gave better agreement than full distributions with experimental rejection data for a Desal-DK nanofiltration membrane. Such truncation is in agreement with the findings of atomic force microscopy (AFM). Analysis of uncharged solute rejection data alone could not give useful information about membrane pore size distribution. Neither could such a distribution be obtained quantitatively directly from AFM images. However, use of the shape of the distribution obtained by AFM in conjunction with experimental rejection data for an uncharged solute allows calculation of corrected distributions. Importantly, incorporation of such a corrected pore size distribution in calculations of NaCl rejection gave better agreement with experimental data, compared to calculations assuming uniform pores, at high pressure, the region of industrial interest.