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 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.

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.

Weibull model selection for reliability modelling

A large number of models have been derived from the two-parameter Weibull distribution and are referred to as Weibull models. They exhibit a wide range of shapes for the density and hazard functions, which makes them suitable for modelling complex failure data sets. The WPP and IWPP plot allows one to determine in a systematic manner if one or more of these models are suitable for modelling a given data set. This paper deals with this topic.

Modelling solute transport in structured soils: Performance evaluation of the ADR and TRM models

The movement of chemicals through the soil to the groundwater or discharged to surface waters represents a degradation of these resources. In many cases, serious human and stock health implications are associated with this form of pollution. The chemicals of interest include nutrients, pesticides, salts, and industrial wastes. Recent studies have shown that current models and methods do not adequately describe the leaching of nutrients through soil, often underestimating the risk of groundwater contamination by surface-applied chemicals, and overestimating the concentration of resident solutes. This inaccuracy results primarily from ignoring soil structure and nonequilibrium between soil constituents, water, and solutes. A multiple sample percolation system (MSPS), consisting of 25 individual collection wells, was constructed to study the effects of localized soil heterogeneities on the transport of nutrients (NO3-, Cl-, PO43-) in the vadose zone of an agricultural soil predominantly dominated by clay. Very significant variations in drainage patterns across a small spatial scale were observed tone-way ANOVA, p < 0.001) indicating considerable heterogeneity in water flow patterns and nutrient leaching. Using data collected from the multiple sample percolation experiments, this paper compares the performance of two mathematical models for predicting solute transport, the advective-dispersion model with a reaction term (ADR), and a two-region preferential flow model (TRM) suitable for modelling nonequilibrium transport. These results have implications for modelling solute transport and predicting nutrient loading on a larger scale. (C) 2001 Elsevier Science Ltd. All rights reserved.

Experiments and modelling of phenanthrene biodegradation in the aqueous phase by a mixed culture

Pollution by polycyclic aromatic hydrocarbons(PAHs) is widespread due to unsuitable disposal of industrial waste. They are mostly defined as priority pollutants by environmental protection authorities worldwide. Phenanthrene, a typical PAH, was selected as the target in this paper. The PAH-degrading mixed culture, named ZM, was collected from a petroleum contaminated river bed. This culture was injected into phenanthrene solutions at different concentrations to quantify the biodegradation process. Results show near-complete removal of phenanthrene in three days of biodegradation if the initial phenanthrene concentration is low. When the initial concentration is high, the removal rate is increased but 20%-40% of the phenanthrene remains at the end of the experiment. The biomass shows a peak on the third day due to the combined effects of microbial growth and decay. Another peak is evident for cases with a high initial concentration, possibly due to production of an intermediate metabolite. The pH generally decreased during biodegradation because of the production of organic acid. Two phenomenological models were designed to simulate the phenanthrene biodegradation and biomass growth. A relatively simple model that does not consider the intermediate metabolite and its inhibition of phenanthrene biodegradation cannot fit the observed data. A modified Monod model that considered an intermediate metabolite (organic acid) and its inhibiting reversal effect reasonably depicts the experimental results.

A formal representation of assumptions in process modelling

In this work, we present a systematic approach to the representation of modelling assumptions. Modelling assumptions form the fundamental basis for the mathematical description of a process system. These assumptions can be translated into either additional mathematical relationships or constraints between model variables, equations, balance volumes or parameters. In order to analyse the effect of modelling assumptions in a formal, rigorous way, a syntax of modelling assumptions has been defined. The smallest indivisible syntactical element, the so called assumption atom has been identified as a triplet. With this syntax a modelling assumption can be described as an elementary assumption, i.e. an assumption consisting of only an assumption atom or a composite assumption consisting of a conjunction of elementary assumptions. The above syntax of modelling assumptions enables us to represent modelling assumptions as transformations acting on the set of model equations. The notion of syntactical correctness and semantical consistency of sets of modelling assumptions is defined and necessary conditions for checking them are given. These transformations can be used in several ways and their implications can be analysed by formal methods. The modelling assumptions define model hierarchies. That is, a series of model families each belonging to a particular equivalence class. These model equivalence classes can be related to primal assumptions regarding the definition of mass, energy and momentum balance volumes and to secondary and tiertinary assumptions regarding the presence or absence and the form of mechanisms within the system. Within equivalence classes, there are many model members, these being related to algebraic model transformations for the particular model. We show how these model hierarchies are driven by the underlying assumption structure and indicate some implications on system dynamics and complexity issues. (C) 2001 Elsevier Science Ltd. All rights reserved.

Classification and analysis of integrating frameworks in multiscale modelling

Chemical engineers are turning to multiscale modelling to extend traditional modelling approaches into new application areas and to achieve higher levels of detail and accuracy. There is, however, little advice available on the best strategy to use in constructing a multiscale model. This paper presents a starting point for the systematic analysis of multiscale models by defining several integrating frameworks for linking models at different scales. It briefly explores how the nature of the information flow between the models at the different scales is influenced by the choice of framework, and presents some restrictions on model-framework compatibility. The concepts are illustrated with reference to the modelling of a catalytic packed bed reactor. (C) 2004 Elsevier Ltd. All rights reserved.

A work domain analysis framework for modelling intensive care unit patients

Work domain analysis (WDA) has been applied to a range of complex work domains, but few WDAs have been undertaken in medical contexts. One pioneering effort suggested that clinical abstraction is not based on means-ends relations, whereas another effort downplayed the role of bio-regulatory mechanisms. In this paper it is argued that bio-regulatory mechanisms that govern physiological behaviour must be part of WDA models of patients as the systems at the core of intensive care units. Furthermore it is argued that because the inner functioning of patients is not completely known, clinical abstraction is based on hypothetico-deductive abstract reasoning. This paper presents an alternative modelling framework that conforms to the broader aspirations of WDA. A modified version of the viable systems model is used to represent the patient system as a nested dissipative structure while aspects of the recognition primed decision model are used to represent the information resources available to clinicians in ways that support lsquoif...thenrsquo conceptual relations. These two frameworks come together to form the recursive diagnostic framework, which may provide a more appropriate foundation for information display design in the intensive care unit.

Process systems modelling and applications in granulation: A review

Granulation is one of the fundamental operations in particulate processing and has a very ancient history and widespread use. Much fundamental particle science has occurred in the last two decades to help understand the underlying phenomena. Yet, until recently the development of granulation systems was mostly based on popular practice. The use of process systems approaches to the integrated understanding of these operations is providing improved insight into the complex nature of the processes. Improved mathematical representations, new solution techniques and the application of the models to industrial processes are yielding better designs, improved optimisation and tighter control of these systems. The parallel development of advanced instrumentation and the use of inferential approaches provide real-time access to system parameters necessary for improvements in operation. The use of advanced models to help develop real-time plant diagnostic systems provides further evidence of the utility of process system approaches to granulation processes. This paper highlights some of those aspects of granulation. (c) 2005 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.

Diagnostic goal driven modelling and simulation of multiscale process systems

A systematic goal-driven top-down modelling methodology is proposed that is capable of developing a multiscale model of a process system for given diagnostic purposes. The diagnostic goal-set and the symptoms are extracted from HAZOP analysis results, where the possible actions to be performed in a fault situation are also described. The multiscale dynamic model is realized in the form of a hierarchical coloured Petri net by using a novel substitution place-transition pair. Multiscale simulation that focuses automatically on the fault areas is used to predict the effect of the proposed preventive actions. The notions and procedures are illustrated on some simple case studies including a heat exchanger network and a more complex wet granulation process.

Exploratory modelling of grinding pressure within a compressed particle bed

With increasing industry interest in high pressure roll grinding (HPGR) technology, there is a strong incentive for improved understanding of the nature of grinding pressure that exists in the interior of a compressed particle bed. This corresponds to the crushing region of the HPGR. The relationship between applied pressure (stress) to the particle bed and induced pressure (stress) within particles and at contact points between particles is of particular interest. A detailed parametric investigation is beyond the scope of this exploratory paper. However, this exploratory investigation does suggest some interesting behaviour. The compressed particle bed within an 80 turn diameter piston has been modelled using Particle Flow Code for three dimensions. PFC3D is a discrete element code. The total number of simulated particles was 1225 and 2450 for two beds of different thickness. Particle diameters were uniformly distributed between 4 and 4.5 mm. The results of the simulations show that stress intensity within the simulated particle beds and within the observed particles increased with increase of the applied stress. The intensity of the average vertical stress in the selected particles tended to be comparable with the intensity of the pressure applied to the surface of particle bed and was only occasionally higher. However, the stress at contact points between particles could be several times higher. In a real crusher, such high stress amplification at contacts will quickly decrease due to local crushing and a resultant increase the size of the contact area. Therefore, its significance is likely to be relatively small in an industrial context. The modelling results also suggest that failure within the particle bed will progress from the crushing surface towards the depth of the bed. (c) 2006 Elsevier Ltd. All rights reserved.