A population balance model for high shear granulation

In a previous paper, Hoornaert et al. (Powder Technol. 96 (1998); 116-128) presented data from granulation experiments performed in a 50 L Lodige high shear mixer. In this study that same data was simulated with a population balance model. Based on an analysis of the experimental data, the granulation process was divided into three separate stages: nucleation, induction, and coalescence growth. These three stages were then simulated separately, with promising results. it is possible to derive a kernel that fit both the induction and the coalescence growth stage. Modeling the nucleation stage proved to be more challenging due to the complex mechanism of nucleus formation. From this work some recommendations are made for the improvement of this type of model.

Modelling the effect of shear history on activated sludge flocculation

The aim of this paper is to investigate the effect of shear history on activated sludge flocculation dynamics and to model the observed relationships using population balances. Activated sludge flocs are exposed to dramatic changes in the shear rate within the treatment process, as they pass through localised high and low mixing intensities within the aeration basin and are cycled through the different unit operations of the treatment process. We will show that shear history is a key factor in determining floc size, and that the floc size varies irreversibly with changes in shear rate. A population balance model of the flocculation process is also introduced and evaluated.

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.

Optimal control and operation of drum granulation processes

Process optimisation and optimal control of batch and continuous drum granulation processes are studied in this paper. The main focus of the current research has been: (i) construction of optimisation and control relevant, population balance models through the incorporation of moisture content, drum rotation rate and bed depth into the coalescence kernels; (ii) investigation of optimal operational conditions using constrained optimisation techniques; (iii) development of optimal control algorithms based on discretized population balance equations; and (iv) comprehensive simulation studies on optimal control of both batch and continuous granulation processes. The objective of steady state optimisation is to minimise the recycle rate with minimum cost for continuous processes. It has been identified that the drum rotation-rate, bed depth (material charge), and moisture content of solids are practical decision (design) parameters for system optimisation. The objective for the optimal control of batch granulation processes is to maximize the mass of product-sized particles with minimum time and binder consumption. The objective for the optimal control of the continuous process is to drive the process from one steady state to another in a minimum time with minimum binder consumption, which is also known as the state-driving problem. It has been known for some time that the binder spray-rate is the most effective control (manipulative) variable. Although other possible manipulative variables, such as feed flow-rate and additional powder flow-rate have been investigated in the complete research project, only the single input problem with the binder spray rate as the manipulative variable is addressed in the paper to demonstrate the methodology. It can be shown from simulation results that the proposed models are suitable for control and optimisation studies, and the optimisation algorithms connected with either steady state or dynamic models are successful for the determination of optimal operational conditions and dynamic trajectories with good convergence properties. (c) 2005 Elsevier Ltd. All rights reserved.

Kinetic study of the thermal degradation of high density polyethylene

The thermal degradation of high density polyethylene has been modelled by the random breakage of polymer bonds, using a set of population balance equations. A model was proposed in which the population balances were lumped into representative sizes so that the experimentally determined molecular weight distribution of the original polymer could be used as the initial condition. This model was then compared to two different cases of the unlumped population balance which assumed unimolecular initial distributions of 100 and 500 monomer units, respectively. The model that utilised the experimentally determined molecular weight distribution was found to best describe the experimental data. The model fits suggested a second mechanism in addition to random breakage at slow reaction rates. (c) 2005 Elsevier Ltd. All rights reserved.

Normal values of balance tests in women aged 20-80

OBJECTIVES: To determine normal values for four commonly used clinical functional balance tests from community-dwelling women aged 20 to 80 and to identify any significant decline due to aging. DESIGN: A cross-sectional study was undertaken to provide normative values for four clinical balance tests across 6 decade cohorts. SETTING: The Betty Byrne-Henderson Center for Women and Aging, Royal Womens' Hospital, Brisbane, Australia. PARTICIPANTS: Four hundred fifty-six community-dwelling, independently ambulant women with no obvious neurological or musculoskeletal-related disability, aged 20 to 80, were randomly recruited from a large metropolitan region. MEASUREMENTS: The clinical balance measures/tests were the Timed Up and Go test, step test, Functional Reach test, and lateral reach test. Multivariate analysis was used to test the effect for age, height, and activity level. RESULTS: Normal data were produced for each test across each decade cohort. Gradual decline in balance performance was confirmed, with significant effect for age demonstrated. CONCLUSION: New normative data across the adult age decades are available for these clinical tests. Use of clinical balance tests could complement other balance tests and be used to screen women aged 40 to 60 whose performance is outside the normal values for age and to decrease later falls risk.

Simplest tasks have greatest dual task interference with balance in brain injured adults

Attention difficulties and poor balance are both common sequel following a brain injury. This study aimed to determine whether brain injured adults had greater difficulty than controls in performing a basic balance task while concurrently completing several different cognitive tasks varying in visuo-spatial attentional load and complexity. Twenty brain injured adults and 20 age-, sex- and education level-matched controls performed a balance-only task (step stance held for 30s), five cognitive-only tasks (simple and complex non-spatial, visuo-spatial, and a control articulation task), and both together (dual tasks). Brain injured adults showed a greater centre of pressure (COP) excursion and velocity in all conditions than controls. Brain injured adults also demonstrated greater interference with balance when concurrently performing two cognitive tasks than control subjects. These were the control articulation and the simple non-spatial task. It is likely that distractibility during these simple tasks contributed to an increase in COP motion and interference with postural stability in stance. Performing visuo-spatial tasks concurrently with the balance task did not result in any change in COP motion. Dual task interference in this group is thus unlikely to be due to structural interference. Similarly, as the more complex tasks did not uniformly result in increased interference, a reduction in attentional capacity in the brain injured population is unlikely to be the primary cause of dual task interference in this group. (C) 2004 Elsevier B.V. All rights reserved.

Somatosensation, circulation and stance balance in elderly dysvascular transtibial amputees

Objective: To establish the relationship between poor lower limb somatosensory and circulatory status with standing balance, falls history, age and mobility level in dysvascular transtibial amputees (TTAs). Design: Within-subjects evaluation of somatosensation, circulation and stance balance measures in dysvascular transtibial amputees. Setting: Physiotherapy department of a tertiary metropolitan hospital in Australia. Participants: Twenty-two community-dwelling unilateral dysvascular transtibial amputee volunteers, aged between 54 and 86 recruited from a metropolitan hospital outpatient amputee clinic. Main outcome measures: Lower limb vibration sense, light touch sensation and circulatory status were related to centre of pressure excursion during quiet stance, dynamic balance measures of forward and lateral reach distance, and demographic information such as falls history and mobility level. Results: Overall, poor somatosensory status was associated with poor stance balance. There was an association between poor vibration and circulation and increased centre of pressure excursion in quiet stance and reduced reach distance, whereas poor light touch was linked with even weight-bearing in quiet stance. Poor vibration sense was associated with a history of frequent falls. Conclusions: Compromised lower limb somatosensation and circulation was linked with poor balance and a history of frequent falls in the elderly dysvascular amputee population.

Accounting for management costs in sensitivity analyses of matrix population models

Traditional sensitivity and elasticity analyses of matrix population models have been used to p inform management decisions, but they ignore the economic costs of manipulating vital rates. For exam le, the growth rate of a population is often most sensitive to changes in adult survival rate, but this does not mean that increasing that rate is the best option for managing the population because it may be much more expensive than other options. To explore how managers should optimize their manipulation of vital rates, we incorporated the cost of changing those rates into matrix population models. We derived analytic expressions for locations in parameter space where managers should shift between management of fecundity and survival, for the balance between fecundity and survival management at those boundaries, and for the allocation of management resources to sustain that optimal balance. For simple matrices, the optimal budget allocation can often be expressed as simple functions of vital rates and the relative costs of changing them. We applied our method to management of the Helmeted Honeyeater (Lichenostomus melanops cassidix; an endangered Australian bird) and the koala (Phascolarctos cinereus) as examples. Our method showed that cost-efficient management of the Helmeted Honeyeater should focus on increasing fecundity via nest protection, whereas optimal koala management should focus on manipulating both fecundity and survival simultaneously, These findings are contrary to the cost-negligent recommendations of elasticity analysis, which would suggest focusing on managing survival in both cases. A further investigation of Helmeted Honeyeater management options, based on an individual-based model incorporating density dependence, spatial structure, and environmental stochasticity, confirmed that fecundity management was the most cost-effective strategy. Our results demonstrate that decisions that ignore economic factors will reduce management efficiency.