Some examples of modeling in chemical engineering: thermal treatment of polymers, phase equilibrium calculations and process design

Presentation submitted to PSE Seminar, Chemical Engineering Department, Center for Advanced Process Design-making (CAPD), Carnegie Mellon University, Pittsburgh (USA), October 2012.

A formal framework for modelling complex network management systems

Society today is completely dependent on computer networks, the Internet and distributed systems, which place at our disposal the necessary services to perform our daily tasks. Subconsciously, we rely increasingly on network management systems. These systems allow us to, in general, maintain, manage, configure, scale, adapt, modify, edit, protect, and enhance the main distributed systems. Their role is secondary and is unknown and transparent to the users. They provide the necessary support to maintain the distributed systems whose services we use every day. If we do not consider network management systems during the development stage of distributed systems, then there could be serious consequences or even total failures in the development of the distributed system. It is necessary, therefore, to consider the management of the systems within the design of the distributed systems and to systematise their design to minimise the impact of network management in distributed systems projects. In this paper, we present a framework that allows the design of network management systems systematically. To accomplish this goal, formal modelling tools are used for modelling different views sequentially proposed of the same problem. These views cover all the aspects that are involved in the system; based on process definitions for identifying responsible and defining the involved agents to propose the deployment in a distributed architecture that is both feasible and appropriate.

X lberoamerican Conference on Phase Equilibria and Fluid Properties for Process Design (EQUIFASE): June 28-July 1, 2015 - Alicante (Spain): Book of Abstracts

The general purpose of the EQUIFASE Conference is to promote the Scientific and Technologic exchange between people from both the academic and the industrial environment in the field of Phase Equilibria and Thermodynamic Properties for the Design of Chemical Processes. Topics: Measurement of Thermodynamic Properties. Phase Equilibria and Chemical Equilibria. Theory and Modelling. Alternative Solvents. Supercritical Fluids. Ionic Liquids. Energy. Gas and oil. Petrochemicals. Environment and sustainability. Biomolecules and Biotechnology. Product and Process Design. Databases and Software. Education.

Constraining porewater chemistry in a 250m thick argillaceous rock sequence

The geochemistry of an argillaceous rock sequence from a deep borehole in NE-Switzerland was investigated. The focus was to constrain the porewater chemistry in low permeability Jurassic rocks comprising the Liassic, the Opalinus Clay formation, the 'Brown Dogger' unit and the Effingen Member (Malm). A multi-method approach including mineralogical analysis, aqueous and Ni-ethylenediamine extraction, squeezing tests and pCO(2) measurements as well as geochemical modelling was applied for this purpose. A consistent dataset was obtained with regard to the main solutes in the porewaters. A fairly constant anion-accessible porosity of similar to 50% of the total porosity was deduced for all analysed samples which displayed variable clay-mineral contents. Sulphate concentrations were shown to be constrained by a sulphate-bearing phase, presumably by celestite or a Sr-Ba sulphate. Application of a simple equilibrium model, including cation exchange reactions, calcite and celestite equilibrium showed good agreement with squeezing data, indicating the suitability of the modelling approach to simulate porewater chemistry in the studied argillaceous rocks. The modelling highlighted the importance of correct determination of the exchangeable cation population. The analysis corroborates that squeezing of the studied rocks is a viable and efficient way to sample porewater.

Homogeneous Spatial Units (HSU) - a Pan-European geographical basis for environmental and socio-economic modelling

The spatial data set delineates areas with similar environmental properties regarding soil, terrain morphology, climate and affiliation to the same administrative unit (NUTS3 or comparable units in size) at a minimum pixel size of 1km2. The scope of developing this data set is to provide a link between spatial environmental information (e.g. soil properties) and statistical data (e.g. crop distribution) available at administrative level. Impact assessment of agricultural management on emissions of pollutants or radiative active gases, or analysis regarding the influence of agricultural management on the supply of ecosystem services, require the proper spatial coincidence of the driving factors. The HSU data set provides e.g. the link between the agro-economic model CAPRI and biophysical assessment of environmental impacts (updating previously spatial units, Leip et al. 2008), for the analysis of policy scenarios. Recently, a statistical model to disaggregate crop information available from regional statistics to the HSU has been developed (Lamboni et al. 2016). The HSU data set consists of the spatial layers provided in vector and raster format as well as attribute tables with information on the properties of the HSU. All input data for the delineation the HSU is publicly available. For some parameters the attribute tables provide the link between the HSU data set and e.g. the soil map(s) rather than the data itself. The HSU data set is closely linked the USCIE data set.

Drivers of multi-scale plant community structure in agricultural field margins of South Korea

This data set describes the distribution of a total of 90 plant species growing on field margins of an agricultural landscape in the Haean-myun catchment in South Korea. We conducted our survey between July and August 2011 in 100 sampling plots, covering the whole catchment. In each plot we measured three environmental variables: slope, width of the field margin, and management type (i.e. "managed" for field margins that had signs of management activities from the ongoing season such as cutting or spraying herbicides and "unmanaged" for field margins that had been left untouched in the season). For the botanical survey each plot was sampled using three subplots of one square meter per subplot; subplots were 4 m apart from each other. In each subplot, we estimated three different vegetation characteristics: vegetation cover (i.e. the percentage of ground covered by vegetation), species richness (i.e. the number of observed species) and species abundance (i.e. the number of observed individuals / species). We calculated the percentage of the non-farmed habitats by creating buffer zones of 100, 200, 300, 400 and 500 m radii around each plot using data provided by (Seo et al. 2014). Non-farmed habitats included field margins, fallows, forest, riparian areas, pasture and grassland.

The effect of the CaO/SiO2 ratio on the phase equilibria in the ZnO-“Fe2O3”-(PbO + CaO + SiO2) system in air: CaO/SiO2 = 0.1, PbO/(CaO + SiO2) = 6.2, and CaO/SiO2 = 0.6, PbO/(CaO + SiO2) = 4.3

Experimental studies on phase equilibria in the multi-component system PbO-ZnO-CaO-SiO2-FeO-Fe2O3 in air have been conducted to characterize the phase relations of a complex slag system used in the oxidation smelting of lead and in typical lead blast furnace sinters. The liquidus in two pseudoternary sections ZnO-Fe2O3-(PbO + CaO + SiO2) with the CaO/SiO2 weight ratio of 0.1 and the PbO/(CaO + SiO2) weight ratio of 6.2, and with CaO/SiO2 weight ratio of 0.6 and the PbO/(CaO + SiO2) weight ratio of 4.3, have been constructed.

Modelling of froth transportation in industrial flotation cells: Part I. Development of froth transportation models for attached particles

Modelling of froth transportation, as part of modelling of froth recovery, provides a scale-up procedure for flotation cell design. It can also assist in improving control of flotation operation. Mathematical models of froth velocity on the surface and froth residence time distribution in a cylindrical tank flotation cell are proposed, based on mass balance principle of the air entering the froth. The models take into account factors such as cell size, concentrate launder configuration, use of a froth crowder, cell operating conditions including froth height and air rate, and bubble bursting on the surface. (C) 2004 Elsevier Ltd. All rights reserved.

Modelling nucleation in wet granulation

Nucleation is the first stage in any granulation process where binder liquid first comes into contact with the powder. This paper investigates the nucleation process where binder liquid is added to a fine powder with a spray nozzle. The dimensionless spray flux approach of Hapgood et al. (Powder Technol. 141 (2004) 20) is extended to account for nonuniform spray patterns and allow for overlap of nuclei granules rather than spray drops. A dimensionless nuclei distribution function which describes the effects of the design and operating parameters of the nucleation process (binder spray characteristics, the nucleation area ratio between droplets and nuclei and the powder bed velocity) on the fractional surface area coverage of nuclei on a moving powder bed is developed. From this starting point, a Monte Carlo nucleation model that simulates full nuclei size distributions as a function of the design and operating parameters that were implemented in the dimensionless nuclei distribution function is developed. The nucleation model was then used to investigate the effects of the design and operating parameters on the formed nuclei size distributions and to correlate these effects to changes of the dimensionless nuclei distribution function. Model simulations also showed that it is possible to predict nuclei size distributions beyond the drop controlled nucleation regime in Hapgood's nucleation regime map. Qualitative comparison of model simulations and experimental nucleation data showed similar shapes of the nuclei size distributions. In its current form, the nucleation model can replace the nucleation term in one-dimensional population balance models describing wet granulation processes. Implementation of more sophisticated nucleation kinetics can make the model applicable to multi-dimensional population balance models.

Modelling of entrainment in industrial flotation cells: the effect of solids suspension

Solids concentration and particle size distribution gradually change in the vertical dimension of industrial flotation cells, subject primarily to the flotation cell size and design and the cell operating conditions. As entrainment is a two-step process and involves only the suspended solids in the top pulp region near the pulp-froth interface, the solids suspension characteristics have a significant impact on the overall entrainment. In this paper, a classification function is proposed to describe the state of solids suspension in flotation cells, similar to the definition of degree of entrainment for classification in the froth phase found in the literature. A mathematical model for solids suspension is also developed, in which the classification function is expressed as an exponential function of the particle size. Experimental data collected from three different Outokumpu tank flotation cells in three different concentrators are well fitted by the proposed exponential model. Under the prevailing experimental conditions, it was found that the solids content in the top region was relatively independent of cell operating conditions such as froth height and air rate but dependent on the cell size. Moreover, the results obtained from the total solids tend to be similar to those from a particular gangue mineral and hence may be applied to all minerals in entrainment calculation. (C) 2004 Elsevier Ltd. All rights reserved.

Phase-space analysis of bosonic spontaneous emission

We present phase-space techniques for the modelling of spontaneous emission in two-level bosonic atoms. The positive-P representation is shown to give a full and complete description within the limits of our model. The Wigner representation, even when truncated at second order, is shown to need a doubling of the phase-space to allow for a positive-definite diffusion matrix in the appropriate Fokker-Planck equation and still fails to agree with the full quantum results of the positive-P representation. We show that quantum statistics and correlations between the ground and excited states affect the dynamics of the emission process, so that it is in general non-exponential. (c) 2005 Elsevier B.V. All rights reserved.

Modelling of entrainment in industrial flotation cells: Water recovery and degree of entrainment

Entrainment in flotation can be considered as a two-step process, including the transfer of the suspended solids in the top of the pulp region just below the pulp-froth interface to the froth phase and the transfer of the entrained particles in the froth phase to the concentrate. Both steps have a strong classification characteristic. The degree of entrainment describes the classification effect of the drainage process in the froth phase. This paper briefly reviews two existing models of degree of entrainment. Experimental data were collected from an Outokumpu 3 m(3) tank cell in the Xstrata Mt. Isa Mines copper concentrator. The data are fitted to the models and the effect of cell operating conditions including air rate and froth height on the degree of entrainment is examined on a size-by-size basis. It is found that there is a strong correlation between the entrainment and the water recovery, which is close to lineal. for the fines. The degree of entrainment decreases with increase in particle size. Within the normal range of cell operating conditions, few particles coarser than 50 mu m are recovered by entrainment. In general, the degree of entrainment increases with increase in the ail rate and decreases with increase in the froth height. Air rate and froth height strongly interact with each other and affect the entrainment process mainly via changes in the froth retention time, the froth structure and froth properties. As a result, other mechanisms such as entrapment may become important in recovering the coarse entrained particles. (c) 2005 Elsevier Ltd. All rights reserved.

Dual-symmetric Lagrangians in quantum electrodynamics: I. Conservation laws and multi-polar coupling

By using a complex field with a symmetric combination of electric and magnetic fields, a first-order covariant Lagrangian for Maxwell's equations is obtained, similar to the Lagrangian for the Dirac equation. This leads to a dual-symmetric quantum electrodynamic theory with an infinite set of local conservation laws. The dual symmetry is shown to correspond to a helical phase, conjugate to the conserved helicity. There is also a scaling symmetry, conjugate to the conserved entanglement. The results include a novel form of the photonic wavefunction, with a well-defined helicity number operator conjugate to the chiral phase, related to the fundamental dual symmetry. Interactions with charged particles can also be included. Transformations from minimal coupling to multi-polar or more general forms of coupling are particularly straightforward using this technique. The dual-symmetric version of quantum electrodynamics derived here has potential applications to nonlinear quantum optics and cavity quantum electrodynamics.

The cross-entropy method for continuous multi-extremal optimization

In recent years, the cross-entropy method has been successfully applied to a wide range of discrete optimization tasks. In this paper we consider the cross-entropy method in the context of continuous optimization. We demonstrate the effectiveness of the cross-entropy method for solving difficult continuous multi-extremal optimization problems, including those with non-linear constraints.