Improving comminution efficiency using classification: An attainable region approach

The AR for the fundamental processes of breakage and mixing was constructed in an earlier paper (Khumalo, N.; Glasser, D.; Hildebrandt, D.; Hausberger, B.; Kauchali, S. (2006). The application of the attainable region analysis to comminution. Chem. Eng. Sci., 61, 5969-5980). This work presents the AR constructed when the process of classification is combined with the processes of breakage and mixing. The process of classification extends the AR. An additional variable of energy consumption is introduced, increasing the dimensionality of the geometric construction from 2-D to 3-D. The AR shows that there is a linear relationship between consecutive particle size distributions with grinding time. However total energy consumption results in concavities when plotted against mass fraction in the median size class.This work demonstrates the degree to which there is an advantage of including the additional fundamental process of classification to particle breakage. The attainable region (AR) of a three particle size distribution can easily be represented graphically. Process targets can be inferred from these graphs. In our chosen system, the classification process has the effect of reducing total energy consumption by 95% to reach an objective of producing 92% of the material in the fines size class. This has cost implications since energy is often the predominant operating cost in size reduction systems. This work also shows that the benefits of classification are a function of the grinding extent for a system which consists of mono-sized feed particles. This suggests that classification should be introduced after some grinding at some point which is easily identified by analysing the AR construction.     

Use of the attainable region analysis to optimize particle breakage in a ball mill

Particle size reduction is one of the most widely encountered, yet least energy efficient, processes. Therefore, potentially significant energy and cost savings exist with even the slightest increase in milling efficiency. Often one would like to mill particles to a certain size, and no smaller, while minimizing energy use and milling time. We use the attainable region (AR) analysis to optimize the comminution of silica sand particles in a bench top laboratory ball mill. When the mill is loaded with a large number of grinding media (J=volume of media/mill volume=10.7%), the breakage profiles are indistinguishable over all rotation rates investigated. However, operation at lower grinding media fill level (J=1.5%) reveals separation between the grinding profiles for different rotation rates, suggesting more efficient breakage occurs at a lower grinding media fill level for a given rotation rate. Our results show that operation at multiple speeds, fast at first and then slower (φ_c=0.03), takes advantage of the initially overlapping grinding profiles and produces a similar particle size distribution with a decreased amount of processing time—less than half the time required for the single rotation rate milling. A natural extension of this idea is continuous milling, where the first mill can operate at a higher energy input for a shorter amount of time and the second mill can operate at a lower energy input for a longer amount of time.     

An attainable region analysis of the effect of ball size on milling

A theoretical investigation of the effect of ball diameter on milling kinetics using the attainable region methodology is presented. Under a predefined fineness of the grind in the product, attainable region plots are produced and results qualitatively interpreted.Initially, parameters describing the selection function, the breakage function, and the ball size effect are defined using batch experimental results obtained on a particular coal. Then, assuming a first-order kinetics law and a normalizable breakage, particle size distributions are generated for the following grinding times: 0.5-1-2-4-10-30-60 min. Several single-sized feed materials ranging from 26,500 μm down to 425 μm together with ball diameters between 10 and 50 mm are considered for simulation. Finally, the obtained data is analyzed with the attainable region technique. The targeted objective is chosen to be the amount of material less than 75 μm produced at each stage of batch milling.Results show that the attainable region plots lie nearly on top of each other irrespective of ball size. One thing though, smaller media sizes seem to exhibit a more differentiated behavior suggesting that size reduction could be more effectively controlled with smaller media. Similar trends are also observed with coarser feed materials.     

An experimental validation of a specific energy-based approach for comminution

In a recent paper [Khumalo, N., Glasser, D., Hildebrandt, D., Hausberger, B., Kauchali, S., 2006. The application of the attainable region analysis to comminution. Chemical Engineering Science 61, 5969-5980] it was shown that the attainable region approach could prove useful in designing better comminution circuits. Fundamental to this approach was the assumption that the rate of comminution was only determined by the specific energy within the device. This paper shows experimentally that this assumption holds for a batch ball mill.The system presented here considered breakage of mono-sized feed particles in a laboratory ball mill into two distinct progeny size classes. The population balance model was successfully used to model the experimental products and the results were represented geometrically in a two-dimensional space. The resulting geometric structure can be used to solve process synthesis and optimization problems simultaneously.It was found that the breakage rate parameter out of size class 1 changes with time but exhibits an exponential relationship with an asymptote. It is hypothesized that this asymptote is the rate of breakage at long grind times or in well-mixed, steady-state continuous systems. It is shown that the parameters of the process depend only on the specific energy. This was one of the assumptions that was made in the construction of the attainable region. Thus, equipment selection and operating conditions only require one to match the required specific energy.     

Energy and population balances in comminution process modelling based on the informational entropy

The results of theoretical and experimental studies of a comminution process are presented. There are two random functions: the selection function and the breakage function in the stochastic model based on a population balance. This model enables prediction of particle size distributions of comminution products after determination of both random functions. Maximum entropy method is used in the entropy model for determining the breakage function. Two cases are analysed, based on continuous and discrete particle size distribution functions of the fed material. Apart from mass balance, the energy balance of comminution process is also used. Searched form of breakage function is determined with the application of methodology of calculus of variations. The results of experimental identification of both models are presented. The parameters that occur in the discrete form of the selection and breakage functions were the identification objects. The results of experimental investigations of quartz sand single comminution in a laboratory jet mill provided an identification base. The experimentally identified results of the entropy model confirmed the adequacy of the theoretical analysis and demonstrated the possibility of adequate prediction of particle size distributions resulting from single comminution.     

Modelling of comminution processes in Spex Mixer/Mill

It is well known that mathematical models which simulate comminution processes represent a useful tool in several fields of academic and industrial research, with particular emphasis on nano-material and pharmaceutical production. In the present work a mathematical model which is able to quantitatively describe comminution processes in a ball milling system (i.e., Spex-Mixer/Mill) has been developed. The proposed approach takes into account three different contributions: dynamics of the vial, dynamics of spheres motion and simulation of the comminution process. The vial dynamics has been modelled by taking advantage of an appropriate roto-translation matrix. Model results have been successfully compared with literature experimental data. The spheres motion within the Spex Mixer/Mill has been simulated using a 3D dynamic model based on classical mechanics as well as the so-called discrete element method, which is widely adopted to quantitatively describe multi-body collision behaviour. In particular, existing models of impact with dissipation as well as the classical Hertz impact theory have been taken into account. This part of the global model allows one to obtain, for different operating conditions, the impact specific energy and impact velocity as a function of time. The latter ones represent input parameters for the simulation of comminution processes that is performed through suitable population balances, where different breakage functions as well as appropriate breakage probabilities have been considered. Model results are reported in terms of granulometric distribution of powders within the mixer-mill as a function of time, minimal grain size obtainable and time needed to complete the comminution process for various operating conditions (i.e., mill frequency and charge ratio).     

From single particle impact behaviour to modelling of impact mills

An approach to quantify the impact grinding performance of different materials is presented. Based on a dimensional analysis and on fracture mechanical considerations two material parameters, f_Mat. and W_m,min, are derived from theoretical considerations. f_Mat. characterises the resistance of particulate material against fracture in impact comminution. W_m,min gives the mass specific energy which a particle can absorb without fracture. Using this approach various materials in a wide size range, e.g. different polymers, crystalline substances, glass and limestone, can be characterised quantitatively. The derived material parameters are applied to the systematic and multi-scale modelling of grinding in impact mills. A population balance model is presented and the results of the simulation for two different impact mills are shown. The developed model allows for a clear separation of the influence of material properties, mill specific features and operating conditions, thus enabling a deeper understanding of the impact grinding process.     

Review: An investigation of single particle breakage tests for coal handling system of the gladstone port

Aspects of the literature on single particle breakage test have been reviewed in this article. The test procedures that are commonly used by the researchers in examining and measuring the breakage characteristics of the ore and coal particles are also discussed. It appears that most of the common size distribution function fitting techniques were not suitable for accurate representation of the size distributions obtained from a pendulum breaking process. The single impact test, double impact test (drop weight test, pendulum test) and slow compression test can be used to study the behaviour of the single particle breakage events. The single impact test, slow compression test and drop weight test cannot measure the energy utilization pattern in single particle breakage events, but this can be determined from the pendulum test.The energy utilized for breakage was predominantly dependent upon the size and shape of the specimen, level of input energy and the breakage properties of the specimen. This review highlights that the size distribution curves were linear in the fine particle region and have varying curvature in the coarser region, the gradient of the linear fine particle region of the size distribution curves increases with an increase in the specific comminution energy. The comminution energy increases with input energy at lower levels of input energy but at the higher levels of input energy the comminution energy did not show the same proportional increase. At a given level of input energy, the size distribution resulting from the breakage of the particles by the pendulum apparatus can be represented by a one-parameter family of curves.     

Towards a methodology for the systematic analysis and design of efficient chemical processes: Part 1. From unit operations to elementary process functions

A successful intensification of a chemical process requires a holistic view of the process and a systematic debottlenecking, which is obtained by identifying and eliminating the main transport resistances that limit the overall process performance and thus can be considered as rate determining steps on the process level. In this paper, we will suggest a new approach that is not based on the classical unit operation concept, but on the analysis of the basic functional principles that are encountered in chemical processes.A review on the history of chemical engineering in general and more specifically on the development of the unit operation concept underlines the outstanding significance of this concept in chemical and process engineering. The unit operation concept is strongly linked with the idea of thinking in terms of apparatuses, using technology off the shelf. The use of such “ready solutions” is of course convenient in the analysis and design of chemical processes; however, it can also be a problem since it inherently reduces the possibilities of process intensification measures.Therefore, we break with the tradition of thinking in terms of “unit apparatuses” and suggest a new, more rigorous function-based approach that focuses on the underlying fundamental physical and chemical processes and fluxes.For this purpose, we decompose the chemical process into so-called functional modules that fulfill specific tasks in the course of the process. The functional modules itself can be further decomposed and represented by a linear combination of elementary process functions. These are basis vectors in thermodynamic state space. Within this theoretical framework we can individually examine possible process routes and identify resistances in individual process steps. This allows us to analyze and propose possible options for the intensification of the considered chemical process.     

Using the attainable region analysis to determine the effect of process parameters on breakage in a ball mill

Ball milling is one of the most common unit operations used for size reduction across a range of industries. However, it is also a notoriously inefficient process, often contributing substantially to operational costs. In this work, we investigate the influence of rotation rate, grinding media fill level and grinding media size on the optimal production of a product of intermediate size. We find that changing the grinding media size at otherwise identical conditions produces different breakage products as well as nonmonotonic trends with varying rotation rate and grinding media fill levels. In addition, we show how to use the attainable region analysis to explore the parameter space in a reduced time without having to perform tests at every parameter combination. Finally, we examine how the complex interplay between rotation rate, grinding media fill level and grinding media size can control the mechanism of breakage occurring inside a ball mill. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

The application of a task-based concept for the design of innovative industrial crystallizers

A new task-based design approach [Menon, A. R., Pande, A. A., Kramer, H. J. M., Grievink, J., & Jansens, P. J. (2007). A task-based synthesis approach toward the design of industrial crystallization process units. Industrial & Engineering Chemistry Research, 46, 3979] is applied to design a crystallization process unit. Task-based design involves the conceptual built-up of a process (unit) from functional building blocks called tasks, which represent fundamental physical events. The motivation for developing this approach is to get a better control over the physical events governing crystalline product quality. To deliver a proof of concept, two lines of research are followed. First of all, several small scale experiments are designed to demonstrate practical feasibility of the approach. The new equipment allows for isolation and manipulation of individual crystallization tasks. Second, a model based on the experimentally tested tasks is developed for a crystallizer design and used in dynamic optimization of three case studies. The results show that completely different and tight product specifications can be achieved with the same design simply by changing the operational policy of the crystallizer. This remarkable increase in flexibility to achieve a broad range of product qualities is the result of the ability to control the rate at which individual crystallization tasks are executed as well as the material flows between those tasks.     

On the influence of mixing on crystal precipitation processes—application of the segregated feed model

The segregated feed model (SFM), a compartmental mixing model, is used to predict the influence of mixing on crystal precipitation. In this method, the population balance is solved simultaneously with the mass balances using crystallisation kinetic, solubility and computational fluid dynamics (CFD) mixing data. Mean properties are calculated for the three different zones of the reactor (two feed zones and bulk zone). It is predicted that during continuous operation, the product particle size exhibits oscillating behaviour before reaching steady state after about ten residence times. In contrast, the second moment (surface area) sharply increases during the first residence time and remains constant thereafter.Different mixing conditions are modelled by varying the mesomixing and micromixing times, which can be regarded as convective and diffusive exchange parameters between the compartments of the reactor. The overall nucleation rate is found to strongly depend on the mixing conditions, as it depends in a highly non-linear manner on the level of supersaturation. In consequence, the nucleation rate varies over three orders of magnitude between ‘good’ and ‘poor’ mixing conditions. Using the SFM, the effect of different feed points, feed rates, feed tube diameters, energy dissipation rates, impeller types and vessel sizes on the nucleation rate and the particle size during crystal precipitation is illuminated. Predictions of the model compare favourably with batch and continuous experimental data for calcium oxalate.     

Understanding the role of restructuring in flocculation: The application of a population balance model

The effect of shear on floc properties was observed through population balance to comprehend the mechanisms of flocculation, in particular the role of restructuring. Little fundamental attention has been given before to the shear influence responsible for creating compact aggregates, while the floc characteristics might differ in other conditions. It is crucial to understand how aggregates evolve to steady state, if their properties are to be ‘tailored’ to suit subsequent solid-liquid separation. From a previous experimental study (Langmuir 18(6) (2002) 1974), restructuring was observed to occur extensively in the flocculation of latex particles in couette-flow, and was proposed to be responsible for the decrease in floc size on their transition to equilibrium. On the other hand, flocs of larger primary particles were more susceptible to breakage, with densification occurring as a result of fragmentation and re-aggregation. Denser flocs were found when structural deformation dominated, particularly in the initial stage of the process, while comparatively tenuous ones were observed when formation and breakage kinetics were the governing mechanisms. The distinct manners in which aggregates of different primary particle sizes evolved with time, were replicated with a population balance that incorporated the floc structural variation; verifying that restructuring indeed played a crucial role under certain flocculation conditions.     

The kinetics of the granulation process: Right from the early stages

In this study, experimentation and modelling were carried out to understand the granulation process. This work assesses whether there is a significant difference in the aggregation rate of the wet granulation process between the very early stages and later stages of high shear granulation. Measurements of the size distribution and binder content from the beginning of the process, just after liquid binder addition, were carried out. A population balance model based on two different kernels, the Equi Kinetic Energy (EKE) kernel and two-dimensional population balance equations with a Size Independent (SI) kernel, was applied to the high shear granulation process. It was concluded that the population balance equations with SI kernel best described the aggregation in the high shear granulation process. The value of aggregation rate constant in the early stages is smaller than aggregation kernel in the later stages.     

Computationally efficient solution of population balance models incorporating nucleation, growth and coagulation: application to emulsion polymerization

A computationally efficient solution technique is presented for population balance models accounting for nucleation, growth and coagulation (aggregation) (with extensions for breakage). In contrast to earlier techniques, this technique is not based on approximating the population balance equation, but is based on employing individual rates of nucleation, growth and coagulation to update the PSD in a hierarchical framework. The method is comprised of two steps. The first step is the calculation of the rates of nucleation, growth and coagulation by solving an appropriate system of equations. This information is then used in the second step to update the PSD. The method effectively decomposes the fast and the slow kinetics, thereby eliminating the stiffness in the solution. In solving the coagulation kernel, a semi-analytical solution strategy is adapted, which substantially reduces the computational requirement, but also ensures the consistency of properties such as the number and mass of particles.     

The effect of primary particle surface energy on agglomeration rate in fluidised bed wet granulation

The effect of primary particle surface wettability by a binder solution on the rate of agglomeration in a fluid-bed top-spray granulation process was investigated. A model system consisting of hydrophilic and hydrophobic spherical primary particles with a narrow size distribution, and an aqueous solution of hydroxy propyl-cellulose (HPC) as binder, was used. The surface energy of the primary particles was measured by inverse gas chromatography (IGC) and their wettability was characterised by static and dynamic contact angle. Granulation was carried out in a desktop fluid-bed granulator and the resulting granule size distribution and granule microstructure were analysed. The hydrophobic particles gave a wider granule size distribution (larger maximum granule size) than hydrophilic ones under otherwise identical conditions, and the granules were notably rounder and more compact. However, the fraction of un-granulated fines was also higher in the case of hydrophobic primary particles. SEM analysis of granule microstructure revealed that the hydrophilic particles were coated by the binder solution, which left a smaller amount of binder available to form bonds at particle contacts. On the other hand, all of the binder was found to form solid bridges in the case of hydrophobic primary particles. A population balance model was used to explain the observed granulation behaviour.     

Population balance models for the thermal degradation of PMMA

A widely accepted view of the thermal degradation of polymers such as PMMA is that an initiation reaction produces radical fragments that undergo rapid depropagation and are also converted back to molecules by a termination reaction. This mechanism is applied to a population of linear molecules and radicals and the evolution of the population is modelled by appropriate discrete sets of ordinary differential equations. In particular, end-chain and random initiation reactions with first-order termination are analysed and compared with experimental data. We find on comparison with TG data for PMMA that the initiation reaction is important in dictating the qualitative behaviour of the overall rate of thermal degradation. Furthermore, the behaviour of degradation rate with initial degree of polymerisation is also investigated and interpreted within the framework of the model.     

Optimal moving and fixed grids for the solution of discretized population balances in batch and continuous systems: droplet breakage

The numerical solution of droplet population balance equations (PBEs) by discretization is known to suffer from inherent finite domain errors (FDE). Tow approaches that minimize the total FDE during the solution of discrete droplet PBEs using an approximate optimal moving (for batch) and fixed (for continuous systems) grids are introduced. The optimal grids are found based on the minimization of the total FDE, where analytical expressions are derived for the latter. It is found that the optimal moving grid is very effective for tracking out steeply moving population density with a reasonable number of size intervals. This moving grid exploits all the advantages of its fixed counterpart by preserving any two pre-chosen integral properties of the evolving population. The moving pivot technique of Kumar and Ramkrishna (Chem. Eng. Sci. 51 (1996b) 1333) is extended for unsteady-state continuous flow systems, where it is shown that the equations of the pivots are reduced to that of the batch system for sufficiently fine discretization. It is also shown that for a sufficiently fine grid, the differential equations of the pivots could be decoupled from that of the discrete number density allowing a sequential solution in time. An optimal fixed grid is also developed for continuous systems based on minimizing the time-averaged total FDE. The two grids are tested using several cases, where analytical solutions are available, for batch and continuous droplet breakage in stirred vessels. Significant improvements are achieved in predicting the number densities, zero and first moments of the population.     

A model-based nucleation study of the combined effect of seed properties and cooling rate in cooling crystallization

Crystallization is a widely used unit operation for the production of pharmaceuticals, fertilizers, and fine chemicals. A commonly used crystallization operational objective is to produce large crystals under minimum nucleation rates. For cooling crystallization there are two key methods for minimizing nucleation, programmed cooling and seeding. In this paper, we evaluate the cooling and seeding methods through the detailed modeling of nucleation phenomena coupled with a population balance and dynamic optimization of this mathematical formulation. Extensive simulation results showed that initial seeding parameters, as proclaimed by others, do have a significant effect on the final product crystal size distribution. It also showed the significance of a combined seeding-cooling approach where a joint cooling and seeding optimization gives superior performance to just optimizing the seed. Importantly, the developed model was highly instrumental in rapidly determining optimal combined seeding-cooling profiles via dynamic model-based optimizations.