Davidbrooker1 Improving Granulation Techniques.pdf

Thesis

David Brooker

E1445 Thesis Design

Improving Granulation Techniques Of 'N-Gold' Fertilizer Department of Chemical Engineering David Brooker Supervisor: Jim Litster Tony Brown 15/10/99

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ABSTRACT An investigation was undertaken into the granulation of 'N-Gold'; a urea based fertiliser produced at Incitec's Gibson Island granulation facility. Uncharacteristically high recycle ratios in the order of 7:1 are observed in the production of 'N-Gold' leading to high production costs. The study was aimed at identifying methods that can be used to reduce the amount of fertiliser recycled in the circuit. Following a sampling audit of the process, a range of methods were used to investigate the granulation of 'N-Gold' including size analysis, image analysis, x-ray diffraction and a computer simulation. The investigation found that both random and preferential coalescence mechanisms contribute to the granulation process. As the moisture content in the system increases, the range of the granulator outlet size distribution spreads due to a greater contribution by the preferential coalescence mechanism. Within the granulator, a large proportion of the fine material below 225 microns is successfully agglomerated. Much of this fine material is produced during the crushing and screening stages of the circuit aiding in the size enlargement process. Image analysis indicates the formation of four different particle types; large agglomerates in the particle size range; deformagle agglomerates attached to non-deformable crystals; agglomerates of non-deformable particles; large spherical agglomerates outside the product size range. In addition there are many particles that pass through the granulator without undergoing any size enlargement. The majority of these particles are in the intermediate size range of 0.225mm to 1mm. The x-ray diffraction results indicate that components other than urea are present in 'NGold'. It is likely that this is due to the binder content of the system. Further study is required to identify the composition of the impurities. The results of the sampling process were used to model the 'N-Gold' process on the Nimbus simulation package developed by Jang (1996). A combination of sampling and modeling limitations reduced the effectiveness of the model validation on 'N-Gold' granulation. The results provide a solid foundation for future modeling of the process. It has been concluded that the non-deformable particles in the size range of 0.225 mm to 1mm in the urea feed are a major contributing factor to the large recycle ratios. Grinding the urea fines feed before it is granulated would greatly improve the granulation efficiency. In addition effective control of the moisture content in the system will ensure that granulation proceeds by both random and preferential coalescence mechanisms.

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Table of Contents Chapter 1 1.0 Introduction 1.1 Fertiliser Granulation 1.2 Thesis Objectives

6 6 7

Chapter 2 2.0 Literature Review 2.1 Granulation Mechanisms of Fertilisers 2.2 Effects of Binder Content and Viscosity on Granulation 2.3 Effect of Initial Size Distribution 2.4 Effect of Circuit Performance on Granulation 2.5 Granulation Modeling and Simulation 2.6 'N-Gold' Analysis 2.7 Scope of Work

8 8 10 11 11 12 13 13

Chapter 3 3.0 Plan of Study 3.1 Data Collection 3.2 Quantity of Samples 3.3 Sample Analysis 3.4 Model Fitting and Simulation 3.3.1 Model Development 3.3.2 Model Fitting

14 14 14 15 15 15 15

Chapter 4 4.0 Experimental Procedure 4.1 Sampling 4.1.1 Sampling Procedures 4.2 Size Analysis 4.2.1 Particle Size Analysis Procedure 4.3 Moisture Content Analysis 4.4 Image Analysis 4.4.1 Stereomicroscope 4.4.2 Camera 4.4.3 Scanning Electron Microscope 4.5 X-Ray Diffraction

16 16 16 17 18 19 19 19 19 20 20

Chapter 5 5.0 Results / Discussion 5.1 Analysis of Data Collection Reliability 5.1.1 Sampling Errors 5.1.2 Precision of Sampling 5.1.3 Sieving Enduced Errors

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David Brooker 5.2 Results of 'N-Gold' Data Collection 5.3 Morphology of Particles 5.3.1 Scanning Electron Microscope Analysis 5.4 X-Ray Diffraction Analysis 5.5 Recycle Ratio Reduction Techniques 5.6 Conclusion

23 26 32 32 36 36

Chapter 6 6.0 Granulation Simulation 6.1 Model Development 6.2 Model Fitting - Granulation Drum 6.2.1 Size Distribution 6.2.2 Physical Constants 6.2.3 Empirical Constants 6.3 Model Fitting for Granulator 6.3.1 Initial Conditions 6.3.2 Model Fitting 6.4 Conclusion

37 38 38 39 40 42 42 42 46

Chapter 7 7.0 Conclusion

47

Chapter 8 8.0 Nomenclature

48

Chapter 9 9.0 References

49

Appendix 1

Physical Properties of Fertilisers

51

Appendix 2

Granulation Simulation

52

Appendix 3

Sampling Error

53

Appendix 4

Precision of Sampling

54

Appendix 5

Raw Data

55

Appendix 6

Nimbus Code

51

Appendix 7

Granulator Initial Conditions

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List of Figures Figure 1 - 'N-Gold' Granulation Circuit Figure 2 - Major Granulation Mechanisms Figure 3 - Pendular, Funicular and Capillary States of the Mobile Liquid Phase Figure 4 - Variation of Recycle Ratio with Solution Phase Ratio (Adetayo 1995) Figure 5 - Sampling Points Figure 6 - Granulator Exit Sampler and General Purpose Sampling Device Figure 7 - Sieve Shaker Figure 8 - Camera used for Image Analysis Figure 9 - Precision of Sampling Results Figure 10 - Effect of Sieving Process on Particle Size Distribution Figure 11 - Size Distribution of Urea Fines Figure 12 - Comparison of the U-Fines Feed to the Granulator Exit Flowrate Figure 13 - Change in Size Distribution over the Granulator, Run 1 Figure 14 - Change in Size Distribution over the Granulator, Run 2 Figure 15 - Change in Size Distribution over the Granulator, Run 3 Figure 16 - Change in Size Distribution over the Granulator, Run 4 Figure 17 - Change in Size Distribution over the Granulator, Run 5 Figure 18 - Effect of Moisture Content on Range of Particle Size Distribution Figure 19 - Effect of Binder Flowrate and Steam Pressure on the Particle Size Range Figure 20 - Comparison of Size Distribution for Granulator and Drier Exit, Run 1 Figure 21 - Morphology of U-Fines Figure 22 - Morphology at Granulator Exit Figure 23 - Effect of Particle Deformation on Bond Strength (Adetayo, 1993) Figure 24 - Electron Microscope Image 52x Magnification Figure 25 - Electron Microscope Image 1033x Magnification Figure 26 - X-Ray Diffraction Results Figure 27 - Granulation Circuit of Di-Ammonium Phosphate (Jang, 1996) Figure 28 - Granulation Circuit for 'N-Gold' Process Figure 29 - Effect of Size Independent Kernel on Granulation Figure 30 - Effect of Size Dependent Kernel on Granulation Figure 31 - Effect of Changing β (u , v ) (Adetayo) Figure 32 - Comparison of Sampling to Simulation Results, Run 1 Figure 33 - Comparison of Sampling to Simulation Results, Run 2 Figure 34 - Comparison of Sampling to Simulation Results, Run 3 Figure 35 - Comparison of Sampling to Simulation Results, Run 4 Figure 36 - Comparison of Sampling to Simulation Results, Run 5 Figure 37 - Effect of Moisture Content on Size Distribution

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1.0 INTRODUCTION 1.1 Fertilizer Granulation This thesis investigates problems associated with the granulation process during the production of 'N-Gold'. 'N-Gold' is a urea-based fertilizer produced by granulating urea fines (u-fines) at Incitec's granulation plant on Gibson Island. Granulation is the general term relating to the gathering of smaller particles into a larger mass. There are many methods of granulation including compression, extrusion, agglomeration, globulation, nodulization and sintering. The method of granulation used depends on the application and type of particle to be granulated. The fertilizer industry is one of many industries that use agglomeration to increase particle size. Granulated fertilizer has excellent storage, handling and transportation properties and allows the controlled release of nutrients. 'N-Gold' is a relatively new product that is not produced elsewhere in the world. As a result little information exists about its granulation properties. Figure 1 shows the granulation circuit at Incitec. A particulate phase is mixed with a liquid binder in the granulation drum, which adds a shearing force to facilitate size enlargement. The granulated material is then dried in a co-current rotary drier. The fertilizer then passes through a set of oversize and undersize screens to separate out the product. The oversized material is then crushed and recycled with the undersized stream.

Liquid Feed Powder Feed

Granulation Drum

Rotary Drier

Dry Granule

Product Undersize Recycle Recycle

Screen Oversize

Crusher

Figure 1: 'N-Gold' Granulation Circuit The granulation circuit poses two main problems: 1. A relatively small amount of particles are in the desired size range. As a result large recycle streams are necessary, often exceeding of 7:1. 2. Problems of surging, drifting mass flow rates and large size distributions along with large time constants mean that the process is difficult to optimize and control.

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Compared with the other fertilizers produced at Incitec, the 'N-Gold' production process exhibits unusually large recycle ratios with low product rates. This leads to an increase in cost due to low production rates. 1.2 Thesis Objectives The aim of this thesis is to analyse the 'N-Gold' production process and identify methods of improving the granulation efficiency of 'N-Gold', allowing a reduction of the recycle ratio and improved circuit control. This will result in increased profit for Incitec. To achieve this, the following objectives have been addressed: v Perform a plant audit on the 'N-Gold' granulation process v Analyse the data using a range of particle characterization techniques v Simulate the 'N-Gold' granulation circuit using existing modeling facilities v Identify methods to reduce the recycle ratio and improve circuit control. This thesis continues on from the work of G. Davis in 1996 who investigated the granulation of 'N-Gold' and an ammonium sulfate based fertilizer.

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2.0 LITERATURE REVIEW 2.1 Granulation Mechanisms of Fertilizers A range of mechanisms for granule growth has been discussed in literature. These include the nucleation, coalescence and layering (Snow, 1997). Figure 2 outlines these main size enlargement processes.

Coalescence

Nucleation

Layering

Figure 2: Major Granulation Mechanisms Experimental observations of granulation processes indicate that the mechanisms of size enlargement are often unique to a given class of materials (Adetayo and Ennis, 1997). This has also found to be true between different types of fertilizers. Fertilizers can be set aside from other granulated materials for a number of reasons. 1. Fertilizer granules are hard and cannot easily be deformed. This reduces the ability of the particles to dissipate breakup forces during granulation resulting in lower growth rates (Adetayo and Ennis, 1997). 2. The second factor effecting the granulation of fertilizers is their solubility. Sherrignton (1968) found that the differing solubilities of particles partly explained the variation in granulation properties of different fertilizers. Therefore the chemical composition of the particle has a significant effect on the granulation process. Appendix 1 summarizes the physical characteristics of a range of fertilizer compounds. It can be seen that 'N-Gold' has significantly higher solubility then other fertilizers. This difference partly explains the granulation differences between 'N-Gold' and other fertilizers produced at Incitec. Adetayo et al. (1993) proposed that the main mechanism of granulation for fertilizers is coalescence with a minor effect resulting from layering. Ennis et al. (1991) proposes a two stage coalescence mechanism: 1. The first stage of granulation is a fast and short-lived process. Size enlargement proceeds by random coalescence where nearly all collisions result in new agglomerates. Therefore a successful coalescence is independent of the particle size and collision velocity. This process has the effect of narrowing the particle size distribution. The extent of granulation by the first stage of coalescence is determined

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by the point at which the resultant Stokes number is equal to the critical stokes number. The resultant Stokes number for rotary drum granulation is

given by: St v =

8ρ g r ω R 9µ

Where ρ g = Granule density, g/cm3 r = Effective granule size, m ω = Drum speed, s-1 R = Radius of granulation drum, m µ = Binder Viscosity, P At low moisture contents this is the only mechanism. 2. When sufficient moisture is provided a second stage of granulation occurs called preferential coalescence. Under preferential coalescence not all collisions are successful. Granulation is influenced by factors such as the material type, solution viscosity, surface tension, particle deformability and liquid content. A successful collision relies on granule compaction to squeeze binder to the granule surface. This two-stage growth mechanism was validated by Adetayo et al (1995) for granulation of di-ammonium phosphate fertilizer. Zhang (1996) has used the mechanism in the development of the dynamic model of the fertilizer granulation circuit. For optimum circuit performance the process should be controlled between the two stages of granulation. This has the effect of removing all the fines from the recycle without broadening the particle size distribution (Adetayo, 1993). An alternative approach to modeling fertilizer granulation mechanisms was developed by Bathala et al. (1998). They proposed that the granulation process is governed by layering mechanisms. Under this process size enlargement occurs by layers of small particles forming on existing particles. The growth rate is assumed to be inversely proportional to the existing particle size and the size to which it grows. Iverson and Litster (1997) proposed the most recent development in granulation mechanisms. They constructed of a regime map to describe the granule growth as a function of the particle deformability and the pore saturation. The proposed mechanism is based on two broad regimes: 1. Steady Growth. This regime is for a highly deformable system capable of withstanding the separating forces in the granulator. 2. Induction. This occurs for systems with strong, non-deformable and slow consolidating particles.

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The regime map is based on properties of the powder binder system. It therefore has the potential to be used for the prediction of the granulation behaviour without the need for granulation experiments. 2.2 Effects of Binder Content and Viscosity on Granulation For any granule agglomeration or growth to occur, a minimum amount of binder must be added to the process. The binder facilitates coalescence through the formation of a mobile liquid bridge that generates interfacial forces and capillary suction between particles. This mobile liquid phase can form in three states, pendular, funicular and capillary. These three states are indicated by Figure 3. In the pendular state the liquid is held in discrete lens shaped rings at the point of contact between particles. An increase of binder leads to the funicular state where a continuous fluid network with interspersed air is generated. At the point of complete saturation the capillary state is formed. In this state all the pore spaces are filled (Snow et al, 1997).

Pendular

Funicular

Capillary

Figure 3: Pendular, funicular and capillary states of the mobile liquid phase. The amount of binder required to reach each of these states is related to the powder porosity, particle surface area and binder-powder wetting characteristics. In addition to theses properties the factors effecting agglomerate formation include: v Initial binder mixing distribution. v Time required for the binder to spread and penetrate pores. (ie. Binder wetting, spreading and adsorption characteristics) v Time taken for the binder to strengthen. This is effected by the evaporation of solvent, reactive transformations, cooling and other solidification mechanisms. The extent of granulation is a function of binder content present during granulation. This is termed the liquid phase ratio. The mean granule diameter increases with the amount of free liquid available for coalescence. As the liquid phase ratio increases both the rate and extent of granulation increases (Adetayo and Ennis, 1997). Adetayo et al. (1995) shows that as the liquid phase ratio increases the recycle ratio of the granulation circuit goes through a minimum. This minimum recycle ratio is reached when the majority of particles leaving the granulator are in the desired product size range. Figure 4 shows a plot of the recycle ratio as a function of solution phase ratio. The plot was developed using the results of a steady state fertilizer simulation developed by Adetayo et al. (1995).

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Figure 4: Variation of recycle ratio with solution phase ratio. (Adetayo, 1995) 2.3 Effect of Initial Size Distribution Granulation experiments performed by Adetayo et al (1991) showed that the inlet size distribution fed into the granulator has a significant effect on the resultant particle size distribution of the granulated material. It was found that as the amount of fines in the feed increased the median particle diameter passes through a maximum for a given moisture content. This indicates that there is an optimum feed rate at which the urea fines can be added to maximize the extent of granulation. The effect of removing the coarse particles from the feed was also investigated. It was found that the amount of coarse particles in the feed strongly effects the particle size distribution. 2.4 Effect of Circuit Performance on Granulation In addition to the granulator, the granulation circuit also contains a drier, crusher and screen. The effect of these units has a significant effect on the performance of the circuit. Adetayo et al. (1995) investigated the effect varying the granulation circuit parameters on the performance of the steady state circuit. They found that increased crusher efficiency will reduce the recycle ratio and improve circuit control. The crusher has the effect of changing the particle size distribution fed to the granulator. An efficient crusher will narrow the particle size distribution in the feed by reducing the number of coarse particles. The steady state results agree with the experimental observations of Adetayo et al (1993) who found that the amount of coarse particles had a significant effect on the particle size distribution being fed into the granulator. The steady state analysis carried out by Adetayo et al. (1995) also showed that an increase in the screen performance had a significant effect on the reduction of the recycle ratio. The screen however had no effect on the allowable operating region and therefore, did not effect the circuit stability.

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2.5 Granulation Modeling and Simulation In the modeling of granulation process the particle size distribution is the most important quantity. The change of the size distribution with time and position in the granulator is followed using a population balance. The general form of the population balance is given by: Q ∂n(v, t ) Qin ∂(G * − A*)n(v.t ) = nin (v) − ex nex (v) − + Bnuc(v) ∂t V V ∂v

+

1 2N t

∫ β (u, v − y

0

−

1 Nt

∞

u, t )n(u, t )n(v − u, t )du

∫ β (u, v − 0

u, t )n(u, t )n(v − u, t )du

(Snow et al., 1997)

Where: V = Volume of granulator Q = Inlet and exit flowrates from granulator. G (v ) = Layering rate A(v ) = Attrition rate Bnuc (v) = Nucleation rate β (u , v, t ) = Coalescence kernel N t = Total number of particles per unit volume In general this population balance cannot be solved by analytical methods. It is therefore necessary to solve it using numerical techniques. Hounslow (1988) proposed a method to discretize the size domain such that vi + 1 / vi = 2 . This method is widely used in population balance modeling. An important factor in the fitting of the population balance to the granulation process is the coalescence kernel ( β (u , v, t ) ). The kernel dictates the birth and death rates during granulation. The development of the correct coalescence kernel requires an understanding of the granulation mechanisms and will therefore vary depending on the application. Recent research has identified improvements in the modeling of granulation of fertilizers. In 1995 Adetayo et al. developed a simulator of a steady state fertilizer granulation circuit. The population balance used the two-stage coalescence kernel developed by Ennis et al. (1991). This simulation was validated by a series of experiments on the granulation of a di-ammonium phosphate fertilizer. Zhang (1996) adapted this simulation to develop a dynamic model of a fertilizer granulation circuit.

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An alternative approach to modeling a dynamic fertilizer granulation process was developed by Bathala et al. (1998) using a model based on layering mechanisms (see section 2.1). This model was validated on a nitrogen-potassium fertilizer system. 2.6 'N-Gold' Analysis Limited research has been carried out on the granulation performance of 'N-Gold' to date. Davis (1996) carried out an investigation into the differences between 'N-Gold' and ammonium sulfate. This investigation concentrated on sampling from the granulation circuit at Incitec. Davis found that 'N-Gold' exhibits similar granulation properties to other commercial fertilizers. The investigations also found that 'N-Gold' has a minimum obtainable recycle ratio of 5.6:1. Davis results agreed with Adetayo et al. (1995). He found that the minimum recycle ratio was reached as the moisture content is increased. Davis (1996) concluded that the granulation properties of 'N-Gold' are sufficiently similar to other fertilisers to allow the adaptation of existing simulation packages to model 'NGold' granulation. 2.7 Scope of Work Work in the area of fertilizer granulation has increased the understanding of the underlying mechanisms. The aim of this thesis is to identify why limited granulation of 'N-Gold' occurs when compared with the other fertilizers produced at Incitec. Davis (1996) investigated the granulation of 'N-Gold'. His research was however limited to the analysis of the particle size distribution. This thesis will continue from previous work by performing further analysis of 'N-Gold'. In addition the data collected on the processing of 'N-Gold' will be used to model the granulation of 'N-Gold'. Significant research has been carried out in the modeling of granulation processes. The existing fertilizer granulation simulator developed by Zhang (1996) will be used. Zhang's model suits the purpose as it has been validated for fertilizer granulation and it is a dynamic model. A dynamic model is important in the analysis of circuit control.

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3.0 PLAN OF STUDY 3.1 Data Collection A plant audit was carried out over the 'N-Gold' granulation facility. The audit was performed over a period of three days in March 1999. Additional sampling was proposed for the period June-August. Due to a changed plant schedule this sampling could not proceed. The aim of the audit was to identify the granulation characteristics of 'N-Gold' under normal operating conditions. Table 1 outlines the data collected from the 'N-Gold' granulation circuit. Table 1: Data Requirements Stream Particle Size Moisture Distribution Content X X Recycle to Granulator (s) (s) X X Fertilizer flow into (s) (s) Granulator Binder flow into Granulator Steam flow into Granulator X X Fertilizer flow out of (s) (s) Granulator X X Fertilizer Flow out of (s) (s) Drier Air Flow into Drier Air Flow out of Drier

Temperature X (s) X (s)

X (s) X (s) X (p) X (p)

Flowrate X (p) X (p) X (p) X (m) X (p)

s - Data taken from plant sample p - Data taken from plant control panel m - Data taken from plant reading

The temperature of the fertilizer throughout the circuit was measured using an infra red non-contact temperature sensor. The accuracy of the measurement is ± 0.1oC. 3.2 Quantity of Samples 'N-Gold' is only produced several times each year. Each production run of 'N-Gold' continues for several weeks. To maximize the value of the audit, data is required from the 'N-Gold' process under a variety of operating conditions. There was no possibility however, of setting the operating conditions under which the plant operates. A total of five sets of samples were taken.

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3.2 Sample Analysis The following analysis has been performed on the samples: v Size Analysis. Sieving was used to analyse the size distribution. v Moisture Content. v Image Analysis. Image analysis allowed visual examination of the smaller particles within the sample. v X-Ray Diffraction. X-ray diffraction was used to analyze the chemical make-up of the particles and check for the presence of binder. 3.3 Model Fitting and Simulation The dynamic simulator developed by Zhang (1996) was used in the analysis of the 'NGold' process. The characteristics of the simulator are shown in appendix 2. 3.3.1 Model Development The current simulator models the production of di-ammonium phosphate. This model was adapted to suit the 'N-Gold' process. The changes that were made include: 1. The addition of a mixing unit to mix the urea fines and the recycled material. 2. The elimination of the unsuitable mechanisms from the granulator. 3.3.2 Model Fitting The data collected from the plant audit was used to fit the simulator to the 'N-Gold' process. Three main factors needed to be adjusted: 1. Specifying initial conditions. 2. Adjusting physical constants. 3. Identifying appropriate empirical constants.

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4.0 EXPERIMENTAL PROCEDURE The following section outlines the procedures involved in carrying out plant sampling and the analysis of the results. 4.1 Sampling Sampling was concentrated around the granulation drum. The location of each of the sampling points is outlined in figure 5. 1. 2. 3. 4.

Granulator Feed Urea Fines Feed Granulator Exit Drier Exit Liquid Feed

Granulation Drum

Urea Fines 2

4 Rotary Drier

3

Dry Granule

Product

1 Undersize Recycle

Screen Oversize

Recycle Crusher

Figure 5: Sampling Points 4.1.1 Sampling Procedures The quality of the samples taken for size analysis was limited by the error in the sampling procedures. Good sampling tools and appropriate sampling techniques can minimize this error. There are two main sources of error in sampling of particulate solids. These are delimitation and extraction errors. Delimitation errors arise when not all of the particles in a stream have equal probability of being sampled. Extraction errors occur when the probability of the particles occurring on the edge of the increment being sampled is size dependent.

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In order to take a representative sample the following rules should be followed: v A powder should always be sampled while in motion. v The whole of the stream of powder should be sampled for many short increments of time in preference of part of the stream being taken for the whole time. It is therefore necessary to design the correct sampling equipment to obtain a representative sample. The following criteria should be followed in the design of a sampler (Snow et al, 1997): v Cutter width should be at least 3 times the diameter of the falling stream v Cutter length should be at least 10mm or three times greater then the largest particle v Sampler should not become more than half full. Even when correct techniques eliminate bias, sampling variance will still arise. This variance is a result of short and long term fluctuations in the process being sampled. The long-term fluctuations are a result of effects generated by the process including fluctuations in the flow rate. Short term fluctuations result from variability within particles. Figure 6 shows the sampling tools used in the plant audit. The sizes of the tools are limited by the size of the access points in the granulator circuit.

0 10

250

100

100

0 10

250

B

A

Figure 6: A - Granulator exit sampler; B - General purpose sampling device 4.2 Size Analysis Sieving was used to analyze the particle size distribution of the fertilizer samples. A 2 sieve series between 0.053 and 11.2 mm aperture was used in the analysis. In this series the area of successive screens has a constant ratio of 2. A 2 sieve series has been chosen as it provides acceptable loading on each of the screens.

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The factors effecting the accuracy of sieving are: v v v v v v

Sieving time Characteristics of the particle Particle load on the sieve Method of shaking the sieve Geometry of the sieve surface Angle of presentation of the particle to the aperture.

The amount of separation achieved is a function of the sieving time. By maintaining a constant sieving time, constant sieving equipment and approximately constant sample size the variance in the analysis of samples can be minimized. A Retsch AS200 Analytical Sieve Shaker has been used in the analysis of the particle size. The amplitude of the vibration was set to 50. This corresponds to a vibration height of approximately 1.6mm. The sieve shake is shown in figure 7.

Figure 7: Sieve Shaker 4.2.1Particle Size Analysis Procedure 1. The original sample size taken from the granulator circuit is in the order of 1 kg. To keep an acceptable particle load on the sieve the sample size needed to be reduced to approximately 200-300g. The sample will therefore be split twice using a chute splitter. The chute splitter will introduce a variance of approximately 3.4% (Snow et al, 1997). 2. The number of sieves used in the analysis was too large to be held by the sieve shaker, therefore the fertilizer was screened in two stages. The first stage involved passing the material through sieves with an aperture ranging from 11.2mm→ 0.71mm. The sieving time for this stage is 10 minutes.

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3. The second stage of the sieving involves passing the undersized material from the first pass through sieves with an aperture ranging from 0.5mm→ 0.053. The sieving time for this stage is 10 minutes. 4.3 Moisture Content Analysis The moisture content of 'N Gold' was found by drying the fertilizer in a drying oven. 'NGold' begins to melt at 80 to 90 oC depending on the level of impurities. The drying process is outlined below: 1. Initial weight of sample recorded. 2. Sample dried in oven at 70 -75oC for 24 hours. 3. Final Mass of Sample recorded. 4.4 Image Analysis Image analysis allows the physical examination the particles throughout the granulation circuit. Three methods were used to capture the images of the particles. 4.4.1 Stereomicroscope An Olympus CH-I stereomicroscope with an image capture facility was used to perform thee image analysis on the particles of size 250 microns and below. The eyepiece magnification was 10x with a set of objective lenses ranging from 5-85x magnification. 4.4.2 Camera A single lens reflex camera was used to capture the image of particles in the size range of 710 microns and above. A Pentax single ten was set up with a 115mm telephoto lens, a 2x doubler and a standard 50mm lens mounted in the reverse direction on the front of the telephoto lens. This configuration gives a 22x magnification. An electronic flash was used to side light the particle with a mirror positioned opposite the flash to act as a back fill light source. The flash synchronization speed was set at 1/60 second. The aperture size was set at f16 for the 50mm lens and f11 for the telephoto. The configuration is shown in figure 8.

Figure 8: Camera used for Image Analysis

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4.4.3 Electron Scanning Microscope The Philips XL30 scanning electron microscope was used to take detailed images of the fertilizer surface. An accelerating voltage of 10kV was used. The samples were carbon coated to minimise charging. To remove any absorbed water within the particles, they were first evacuated overnight. This process may have effected the morphology of the particles. 4.5 X-Ray Diffraction X-Ray diffraction was used to collect data on the chemical makeup of the 'N-Gold' particles. A Siemans D5000 goniometer with Cu Kα radiation was used in the analysis. Search / match software was used to identify the peaks in the output.

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5.0 Results / Discussion 5.1 Analysis of Data Collection Reliability 5.1.1 Sampling Errors Errors are induced into the results due to sampling of the fertiliser in the granulation circuit. An estimate of the short term errors induced into the process can be made using Gy's theory (Smith and James, 1981)

1 1 3 σ 2 = ρx(100 − x)  − lα v hd 95 M M  s  Where ρ = Density of particle l = Degree of liberation x = Property being measured (mass fraction) α v = Volume shape factor M s = Mass of sample h = Spread of size distribution d 953 = 95% passing size of distribution

M = Mass from which sample is taken

The sampling error for the samples taken at the granulator outlet has been calculated in appendix 3. The maximum sampling error was found to be 15.53%. 5.1.2 Precision of Sampling In order to test the precision of the sampling techniques a series of four samples were taken in quick succession from the entrance to the granulator. A plot of the mass fraction of the size distribution for each sample is shown in figure 9. 0.35 Test A

0.3

Test B

Mass Fraction

Test C

0.25

Test D

0.2 0.15 0.1 0.05 0 0.01

0.1

1

10

Size (mm)

Figure 9: Precision of Sampling Results

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The plot shows that there is a small variation in the size distribution of the four samples. It can be seen that test sample B has twice the proportion of fines when compared with the other samples. This variation can be explained by changes in the particle size distribution in the granulator entrance over the sampling time and by limitations associated with taking a representative sample from the granulator feed. To quantitatively assess the variance in the sample, the standard error at each size interval was calculated. The standard deviation at each size interval is given by: σ = 2

Σ( yi − y ) 2 n− 1

where: y =Average mass at given size interval yi = Mass at given size interval n = Number of size intervals. Appendix 4 shows the calculation of the standard deviation and standard error at each size interval. The average error over each of the 17 size intervals was found to be 1.5%. The greatest error of 4.4% was found to occur in the size range of 1.4 to 2mm. The small errors indicate that there is only a small difference in the size distribution for the four samples. This is insignificant when compared to the sampling errors outlined in section 5.1.1. It can therefore be concluded that the sampling procedures produce precise results. 5.1.3 Sieving Induced Errors The effect of the sieving process on the size distribution of the particles has been investigated by repeatedly sieving the same sample. Figure 10 shows a plot of the particle size distribution after sieving for 5, 7,10 and 15 minutes. 0.25 5min 7min

Mass Fraction

0.2

10min 15min

0.15

0.1

0.05

0 0.01

0.1

1

10

Size (mm)

Figure 10: Effect of Sieving Process on Particle Sieve Distribution

23

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David Brooker

The plot shows that there is a negligible shift in the particle size range as the sieving time is increased. Any change in the particle size distribution is a result of fines generation and increased separation efficiency. When the effect of the sieving process is compared with the precision of the sampling shown in figure 8, it can be seen the sieving has an insignificant effect on the particle size distribution. 5.2 Results of 'N-Gold' Data Collection Table 2 outlines the 'N-Gold' operating conditions resulting from the audit of the granulation circuit. Four sampling points were used, the feed to the system (u-fines), the granulator entrance, the granulator exit and the drier exit. Five sets of samples were collected. (Appendix 5 shows the raw sampling data.) Table 2: 'N Gold' Operating Conditions Run Liquid D50 Gran D50 Gran Gran Exit Entrance Exit %H2O Feed (L/s) 1 0.31 0.68 1.1 0.02 2 0.34 0.93 1.19 0.011 3 0.22 0.95 1.28 0.0183 4 0.31 1.08 1.28 0.034 5 0.30 1.09 1.4 -

Gran Exit Temperature (o C) 46.3 51.2 46.1 46 46.4

Steam Pressure 21 34 22 22 22

Mass % in Product Size Range (2-4mm) 8.5 2 14 16 26.5

Table 3 outlines the average spread of the size distribution at each sampling point. The spread of the distribution has been measured as D90-D10. The table shows that the particle size distribution is broadened as the particles pass through the granulator. The drier has little effect on the breadth of the particle size distribution. Table 3: Spread of Particle Size Distribution Sample D10 D90 U-Fines 0.132 1.87 Granulator Entrance 0.22 1.8 Granulator Exit 0.55 2.55 Drier Exit 0.25 2.21

24

D90-D10 1.74 1.58 2.00 1.96

Thesis

David Brooker

Figure 11 shows the size distribution for the u-fines, the feed for the granulation circuit.

Mass Fraction

0.4 0.35

Run 1

0.3

Run 3

Run 2 Run 4

0.25

Run 5

0.2 0.15 0.1 0.05 0 0.01

0.1

1

10

100

Size (mm)

Figure 11: Size Distribution Urea Fines It can be seen that the size distribution of the urea feed varies considerably for the different samples. A likely cause of this variation is a result of the urea fines collection system. The feed is collected from a stockpile before being feed into the granulator. As a result the size distribution will vary depending on where within the pile the feed is collected. The distribution is bimodal in shape. The first peak occurs at approximately 0.3mm with the second peak at 1.5mm. The flowrate of the u-fines is approximately 6.5 kg/s. This u-fines stream is then mixed with the recycle stream (approximately 45 kg/s) to form the feed for the granulator. Figure 12 shows a comparison of the normalised size distribution for the granulator feed and the u-fines. 0.4 0.35

U Fines Gran Ent

Mass Fraction

0.3 0.25 0.2 0.15 0.1 0.05 0 0.01

0.1

1

10

100

Size (mm)

Figure 12: Comparison of the U-Fines Feed to the Granulator Entrance Flowrate

25

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David Brooker

There is a considerably larger amount of fines in the granulator feed when compared with the u-fines. These additional fines have two possible origins: 1. Poor granulation of the fine material in the granulator and as a result fines are accumulating in the circuit. 2. Additional fines are being generated in the granulation circuit. The likely source would be the crusher. Figure 13 through to figure 17 shows the change in the particle size distribution in the granulator for each of the five runs. All five runs show a shift in the particle size distribution to the right indicating that size enlargement has occurred. It can be seen that the majority of the particles in the size range 0-125 microns are consumed during granulation. This indicates that the fines seen in the granulator entrance are a result of fines generation within the granulator circuit, not accumulation.

0.35 0.3

Gran Ent Gran Exit

Mass Fraction

0.25 0.2 0.15 0.1 0.05 0 0.01

0.1

1

10

100

Size (mm)

Figure 13: Change in Size Distribution over the Granulator, Run 1 0.4 0.35

Gran Ent Gran Exit

Mass Fraction

0.3 0.25 0.2 0.15 0.1 0.05 0 0.01

0.1

1

10

100

Size (mm)

Figure 14: Change in Size Distribution over the Granulator, Run 2

26

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David Brooker

0.4 Gran Ent

0.35

Gran Exit

Mass Fraction

0.3 0.25 0.2 0.15 0.1 0.05 0 0.01

0.1

1

10

100

Size (mm)

Figure 15: Change in Size Distribution over the Granulator, Run 3 0.3 Gran Ent

Mass Fraction

0.25

Gran Exit

0.2 0.15 0.1 0.05 0 0.01

0.1

1

10

100

Size (mm)

Figure 16: Change in Size Distribution over the Granulator, Run 4 0.4 0.35

Gran Ent Gran Exit

Mass Fraction

0.3 0.25 0.2 0.15 0.1 0.05 0 0.01

0.1

1

10

100

Size (mm)

Figure 17: Change in Size Distribution over the Granulator, Run 5

27

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David Brooker

Identifying the mechanisms by which granulation occurs is important in gaining an understanding the granulation process. Adetayo et al (1993) proposed a two stage granulation mechanism based on experiments of mono-ammonium phosphate and diammonium phosphate fertilisers. In the first stage, random coalescence, nearly all collisions are successful. The probability of coalescence equals the probability of encountering binder during a collision. Under these conditions collisions between large particles and fines remove fine particles from the distribution. This has the effect of narrowing the size distribution. Inspection of the size distributions indicates that the granulation of 'N-Gold' occurs predominately by this reaction. The fines within the system are consumed and there is a general shift to the right in the distribution. The second stage of granulation proposed by Adetayo et al (1993) is the size independent kernel. Under the second stage, granulation occurs by preferential coalescence, not all the collisions are successful. The particles may grow significantly larger then in the first stage and as a result the size distribution is broadened. This second mechanism will only occur at high enough moisture contents. Figure 18 shows that the size distribution of the 'N-Gold' outlet broadens with increasing moisture content. This is evidence of the effect of preferential coalescence in the granulator. As the particle moisture content increases, a greater proportion of the granulation occurs by preferential coalescence. For coalescence to occur under these conditions the collision relies on the granule compaction to squeeze additional liquid to the granule surface. The granules deform on collision increasing the contact area of the colliding particles (Adetayo et al, 1993).

Range of Distribution (D90-D10)

3 2.5 2 1.5 1 0.5 0 0

0.5

1

1.5

2

2.5

3

3.5

Size (mm)

Figure 18: Effect of Moisture Content on Range of Size Distribution There are two main variables that effect both the moisture content and level of granulation in the system, the binder flowrate and the steam pressure. As figure 19 shows there is no correlation between either the binder flowrate or the steam pressure and the breadth of the distribution.

28

4

Thesis

David Brooker 2.8 Breadth of Distribution (D90-D10)

2.5 2 1.5 1 0.5 0 0.2

2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1

0.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

20

0.38

22

24

26

28

30

32

34

Steam(PSI)

Binder Flowrate (L/s)

A B Figure 19: Effect of Binder Flowrate (A) and Steam Pressure (B) on the Particle Size Range It is difficult to draw any solid conclusions from these results. The 'N-Gold' granulation circuit has proven to be an unstable process, producing large variations in the recycle flowrate. As the liquid flow into the granulator is held approximately constant, the moisture content (liquid flow / recycle flow) will also undergo large fluctuations. Figure 20 shows that there is no net breakage or agglomeration of 'N-Gold' in the drier. 0.4 0.35

Gran Exit Drier Exit

0.3 Mass Fraction

Breadth of Distribution (D90-D10)

3

0.25 0.2 0.15 0.1 0.05 0 0.01

0.1

1

10

100

Size (mm)

Figure 20: Comparison of Size Distribution for Granulator and Drier Exit, Run 1

29

36

Thesis

David Brooker

Size enlargement within the granulation drum is occurring by two mechanisms, random and preferential coalescence. The amount of size enlargement is however small. Table 2 shows that for run 2 only 2% of the fertiliser out of the granulator is in the product size range. There are two operating conditions in run 2 that standout from the other runs. The first is that the moisture content at the granulator exit of run 2 is the lowest out of the five runs. This leads to a narrow size distribution due to the small contribution of preferential coalescence to size enlargement. The second standout feature of run 2 is the high steam pressure. The pressure in run 2 is approximately 12 psi higher then the other runs. This increased temperature did not effect the moisture content of the system but it did have an effect on the outlet temperature. The temperature of run 2 is 5 degrees higher then the other runs. The steam has a significant effect on the energy input of the system. There are insufficient variations in steam pressures within the samples taken to identify the effect of steam pressure and temperature on granulation. 'N-Gold' however, has a melting point that is considerably lower then other fertilizers, 80-90oC depending on the level of impurities. Further investigation is required to identify the effect of temperature on the fertilizer including particle deformation. The results have shown that the fine material within the granulator, up to 250 microns, is almost entirely consumed in the granulator. Approximately 30% of the particles are in the size range of 250 microns to 1mm. These particles are notoriously difficult to granulate. 5.3 Morphology of Particles Individual particles have been removed from the bulk sample to identify the morphology of particles within the granulation circuit. The image analysis was performed using a single lens reflex camera (SLR) and a stereomicroscope (SM). Section 5.2 identified that the u-fines form a bi-modal distribution. The two main particle types that make-up this distribution are shown in figure 21. Particle A is a prill particle. It is an undersized by-product of the prilling operations at Incitec. The prills are hard spherical urea particles.These prill particles comprise the majority of the particles in the 1-2mm size range. Some 710 micron prills were also present. Particle B is a smaller urea crystal. These crystals comprise the size ranges from 90 to 710 microns. Visual analysis of the u-fines indicates that there are no agglomerates within the feed. The u-fines are then mixed with the recycle where they enter the granulator. Several particle types emerge at the granulator exit. These are shown if figure 22. Particle A is a large 'N-Gold' particle in the product size range. It is an agglomerate of many smaller particles.

30

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David Brooker

Figure 22: Morphology of Particles

31

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David Brooker

Particle B is a flat non-deformable crystal joined to a larger particle. The larger particle has deformed upon collision with the crystal. This is further evidence of the preferential coalescence within the system. Particle C is two prill particles that have come together without deforming. The probability of coalescence between two non-deformable particles is low due to the reduced contact area. This is shown diagrammatically by Adetayo (1993) in figure 23.

Non Deformable Particles

Weak Bond

Deformable Particles

Strong, increased area of contact

Figure 23: Effect of Particle Deformation on Bond Strength (Adetayo, 1993) Due to the weak bond formation, the amount of prill - prill agglomerates out of the granulator is low. This form of agglomerate requires the presence of binder during collision. On leaving the granulator, the fourth particle type, particle D, is a disc shaped agglomerate. The workers at Incitec named these particles "Smarties". These particles are found throughout the larger size ranges, 2mm to 8mm. Workers at Incitec reported that the number of "smarties" increase with increasing binder flowrate. These particles may be a result of large amounts of binder accumulating with a small amount of urea. The final types of particles found in the system are unagglomerated prill and crystalline particles. These particles either pass through the granulator without undergoing any size enlargement or form weak bonds which are quickly broken again. These particles make up the size range below 710 microns but are also present in the larger size ranges. It is evident from the analysis of the morphology of the particles that although size enlargement is occurring within the system, a large number of particles are passing through the granulator unagglomerated. The majority of the particles in the U-Fines stream are single, non-deformable particles. For the u-fines to attach to each other, binder needs to be present at the point of collision. Alternatively the u-fines can join to the larger agglomerates that have been recycled into the granulator. These larger particles appear to be more deformable resulting in stronger bond formation.

32

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David Brooker

5.3.1 Scanning Electron Microscope Analysis A scanning electron microscope was used to identify the surface structure of the urea prills. Figure 24 shows a prill attached to a smaller particle at a magnification of 52x. The image displays the porous nature of the particle. Figure 25 shows a prill at 1033x magnification. This image identifies that the prills are composed of small crystal like grains with a size in the order of 5 microns. 5.4 X-Ray Diffraction Analysis X-ray diffraction (XRD) has been performed on a range 'N-Gold' particles in an attempt to identify their chemical composition. Figure 26 shows the XRD output for four particle types: Plot A: Fine urea crystals (90ηm) removed from the granulator exit. Plot B: A portion of bulk urea sample from the 710 micron size range. Plot C: An agglomerate 1mm in size. Plot D: Material scraped from the surface of a large agglomerate. The fine lines through each plot show the peak position of urea, the major component of 'N-Gold'. It is clear that all plots show the characteristic urea composition. There are however additional peaks in plots A, B and C. This indicates that material other then urea is present in the sample. This indicates that material other then urea is present in the samples. Attempts were made to match the additional peaks to known compounds. The results were however inconclusive. The logical source of the additional component is the binder. Further analysis is required.

33

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David Brooker

Figure 24: Prill at 53x Magnification

34

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David Brooker

Figure 25: Prill at 1033x Magnification

35

Thesis

David Brooker

Figure 26: XRD Results

36

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David Brooker

5.6 Conclusion The following conclusions can be made following the analysis of the 'N-Gold' data. v Coalescence occurs by random and preferential coalescence. v The moisture content in the system is directly related to the range of the size distribution at the granulator outlet. v Much of the fine material that successfully agglomerates is produced in the crushing and screening stages of the granulation circuit. v A large number of granules in the size range 0.225mm to 1mm pass through the granulator without undergoing size enlargement. 5.7 Recycle Ratio Reduction Techniques It has been identified that the majority of the fine material (0 to 0.225 microns) is granulated successfully. The intermediate size range of 0.225 to 1mm however has poor granulation properties. This is largely due to their non-deformable nature resulting in a tendency to rebound during collisions. It is therefore proposed that to improve the granulation of 'N-Gold' the urea feed be passed through a grinder. This will have the effect of increasing the amount of fine material and reduce the intermediate size range. It has also been identified that the moisture content in the granulator is proportional to the rate of preferential coalescence. Preferential coalescence has the effect of spreading the particle size distribution. By controlling the moisture content in the system a suitable particle distribution spread will maximise the amount of fertilizer in the product size range.

37

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David Brooker

6.0 Granulation Simulation 6.1 Model Development Simulating the granulation process of 'N Gold' using a mathematical model provides a useful way to analyse the granulation circuit. By performing a population balance over the granulation circuit the change in particle size distribution of the fertilizer can be followed. The simulation package can then be used to better understand the process operating conditions. In addition a mathematical simulation provides a useful way to analyse the process control aspects of the granulation circuit. Jang (1996) developed a Nimbus simulation for a di-ammonium phosphate (DAP) granulation circuit. The model composed of a granulator, rotary drum drier, vibrating screen, crusher and conveyor belt. The circuit is controlled by a feedback / feedforward control loop. Figure 27 shows a block diagram representing the units within the model and how they are connected.

NH3

Water

Slurry

Reactior

Air in

Layering

Granulator Stage 1

Granulator Stage 2

Direr

Dry_rate

Senf Sum

PI Senn

Convey Belt

Crusher

Screens

Product

Sens Forward

Senr Seng

Figure 27: Granulation Circuit of Di-Ammonium Phosphate as Modeled by Jang (1996) The mechanisms associated with each of the major units within the model are outlined in appendix 2. This model has been validated on the granulation circuit at Incitec. By adjusting the model parameters and mechanisms the model has been fitted to the 'N Gold' process. The following sections of the model developed by Jang are not suitable for the 'N Gold' process and have been removed: 1. The slurry feed of DAP to the granulation drum. 2. The reaction of mono-ammonium phosphate with ammonia in the granulation drum. 3. The layering of slurry on to the recycled particles. 4. The control loop is not required for the simulation.

38

Thesis

David Brooker

The following units have been added to the model: 1. A source of urea fines. 2. A mixer to combine the urea fines feed with the recycled product. Figure 28 shows a block diagram representing the adjusted model.

Air in Granulator

Urea Fines Feed

Mixer

Convey Belt

Granulator Stage 1

Granulator Stage 2

Crusher

Direr

Screens

Dry_rate

Product

Figure 28: Granulation Circuit for 'N Gold Process The Nimbus codes for the urea fines source and the mixer are shown in appendix 6. 6.2 Model Fitting - Granulation Drum The critical part of the granulation circuit is the granulation drum. The granulation drum has been separated into two stages based on the work of Adetayo et al (1993): Stage 1: Random coalescence, size independent kernel. Stage 2: Preferential coalescence, size dependent kernel. It has been shown in Section 5.2 that both these mechanisms contribute to the granulation of 'N-Gold'. There are three areas of the granulation drum model that must be adjusted to fit to the 'N Gold' process, the particle size distribution, the physical constants and the empirical constants. 6.2.1 Size Distribution The size interval used on the 'N-Gold' sampling trials differ from the size interval used to validate the model on the DAP circuit. The code for the first and second stages of granulation were adjusted to suit a sieve series used in the 'N-Gold' sampling trials outlined in section 4.2. The adjusted code is shown in appendix 6.

39

Thesis

David Brooker

6.2.2 Physical Constants The granulation model uses the physical constants of the particles in developing the rate constant for the circuit. The physical constants required for the model are outlined in Appendix 1. The effect of changing the physical constants on the rate of granulation for given moisture content has been investigated. The calculation of the rate of granulation using the properties of 'N-Gold' and di- ammonium phosphate for moisture content of 3% is shown below. The rate constant in the granulation drum is given by:  A1 S sat  β ij =  0 ; S sat < S crit  A (v + v ) ; S > S j sat crit  2 i

Where A1 = Parameter for random kernel

A2 = Parameter for preferential kernel S sat = Fractional saturation of granules S crit = Critical granule saturation vi , v j = Volume of particles

ρ f = Density of fertiliser salt

ρl = Density of fertiliser solution p = Particle porosity

X w = Moisture content S s = Solubility of fertiliser salt in water

The first stage of granulation uses the physical properties to calculate Ssat and therefore the rate constant. Ssat is given by: S sat =

X w ρ f (1 − p )(1 + S s ) ρl p(1 − X w S s )

For 'N-Gold' Ssat is: 0.03 * 1.34(1 − 0.35)(1 + 1.19) S sat = 1.29 * 0.35(1 − 0.03 * 1.19 ) = 0.1315 For DAP Ssat is: 0.03 * 1.5(1 − 0.35)(1 + 0.7) S sat = 1.3 * 0.35(1 − 0.03 * 0.7 ) = 0.1125

40

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David Brooker

The size independent kernel rate constant for both 'N-Gold ' and DAP is therefore given by:

'N-Gold'

Rate Constant β ij = 0.1315 A1

DAP

β ij = 0.1125 A1

For a given value of A1 it can be seen that the rate of the size independent kernel is greater for 'N-Gold' then for DAP fertilizer. The problem exists however that the granulation efficiency of 'N-Gold' is smaller then DAP. It is therefore evident that the empirical constant, A1 , needs to be adjusted to fit the 'N-Gold' process. 6.2.3 Empirical Constants The performance of the granulation simulation can be adjusted by changing the values of the empirical constants, A1 and A2 . Figure 29 shows the effect of a change in A1 while A2 is held constant. Increasing A1 has the effect of increasing the rate of the size independent kernel mechanism. The figure shows that as A1 is increased a greater proportion of the fine material (0.053 - 0.125 mm) is consumed. This has the effect of shifting the size distribution to the right. This is because the as the name suggests the growth of the particles is independent of size. Therefore the greatest growth occurs in the fines where there is the greatest amount of particles. 450 400 a1=20

350 Mass Flowrate

a1=45

300

a1=0

250 200 150 100 50 0 0.01

0.1

1

10

100

Size (mm)

Figure 29: Effect of the Size Independent Kernel on Granulation

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Figure 30 shows the effect of changing A2 while holding A1 constant. This has the effect of

changing the size dependent kernel on granulation. Figure 30 shows that increasing A2 spreads the particle size distribution. This results from the larger particles growing faster then the smaller particles. 450 400

a2=0.016 a2=0.16

Mass Flowrate

350

a2=1.6

300 250 200 150 100 50 0 0.01

0.1

1

10

100

Size (mm)

Figure 30: Effect of the Size Dependent Kernel on Granulation These results agree with Adetayo (1993) as shown in Figure 31. The spikes seen in the particle size distribution at 11mm are a result of the numerical methods used in the model. The calculations are performed using a number balance. The results are then converted to a mass balance for the output. In the large size ranges, a small number of particles will result in a large mass, producing the spike in the distribution.

Figure 31: Effect of Changing β (u , v )

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David Brooker

6.3 Model Fitting for the Granulator Initial Conditions The first step in fitting the model to the sampled data is providing the necessary initial conditions. The model requires the particle size distribution in two forms. The first is a mass flowrate into and out of each of the units in the model. These values can be taken directly from the sieving results. Within each stage of the granulator, an orthogonal collocation approach is used to model the spatial variations. Each stage has been separated into 5 collocation points. The calculations are performed using a population balance. Therefore the initial conditions at each of the collocation points is required in the form of the number of particles. The number of particles can be calculated from the mass of particles using the following equation:

ni =

xi / Li

3

Σxi / Li

3

Where: ni = Number fraction in size i

xi = Mass fraction in size i Li = Mean size of fraction

In addition to the particle size distribution the length of the granulator drum, moisture content and residence time are also required. Appendix 7 outlines the initial conditions for Run 1. Fitting In fitting the model to the real data, the model was run to steady state and the empirical constants, A1 and A2 , are varied until a suitable fit to the data could be achieved. The best possible fit for each of the five runs is shown in figures 32 through 36.

43

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David Brooker

400 350

Actual Outlet Actual Outlet

Mass Flowrate (kg/h)

300

Simulation

250 200 150 100 50 0 0.01

0.1

1

10

100

Size (mm)

Figure 32: Comparison of Actual Results to Simulation, Run 1 400

Mass Flowrate( kg/min)

350 300

Actual Outlet Actual Inlet Simulation

250 200 150 100 50 0 0.01

0.1

1

10

100

Size (mm)

Figure 33: Comparison of Actual Results to Simulation, Run 2 MAss Flowrate (kg/min)

450 400 350

Actual Outlet Actual Inlet Simulation

300 250 200 150 100 50 0 0.01

0.1

1

10

100

Size (mm)

Figure 34: Comparison of Actual Results to Simulation, Run 3

44

David Brooker

Mass Flowrate (kg/min)

Thesis 450 400

Actual Outlet

350 300

Actual Inlet Si mul ation

250 200 150 100 50 0 0.01

0.1

1

10

100

Size (mm)

Figure 35: Comparison of Actual Results to Simulation, Run 4

350

Mass Flowrate (kg/min)

300

Actual Outlet Actual Inlet Simulation

250 200 150 100 50 0 0.01

0.1

1

10

100

Size (mm)

Figure 36: Comparison of Actual Results to Simulation, Run 5 It can be seen that there are difficulties in producing accurate simulation fits to the data. The largest errors lie in the fines region of the distribution. Only the fines in the in the size range of 0 to 225 microns are sufficiently removed. There is then an increase in the number of particles in the region of 225 microns to 1mm. This indicates that the fines are coalescing with other fines but are not attaching / layering to the larger particles in the distribution. The addition of a layering mechanism to the granulator may provide a better fit to the data. Under the layering mechanism the fine, unagglomerated particles would attach to the larger particles in the system. An additional limitation of the model is the upper limit in the random coalescence mechanism that exists. Beyond a certain value of a1 the numerical methods within the model fail. This limits the consumption of fines in the model. The maximum value of A1 differs for each of the five runs. It is effected by the conditions of the system.

45

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Table 4 shows the empirical constants provide the best fit for each of the five runs. It can be seen that the constant may vary up to 50%. The granulation calculations in the simulation are largely dependent on the moisture content in the system. Section 5.2 showed that the large fluctuations in the recycle flow resulted in no correlation between moisture content and extent of granulation. It can therefore not be expected that the model will accurately predict the changes in the particle size distribution of the sampled data. Table 4: Empirical Constants Run a1 a2 1 45 1.5 2 20 0.5 3 30 0.4 4 40 0.5 5 20 0.7 Figure 37 shows the effect of varying the moisture content by ± 50% on the granulator outlet size distribution. As the moisture content increases there is a small increase in the amount of fines removal and a small shift to the right in the size distribution. Apart from the inlet size distribution the only difference in each of the models is the moisture content. It is evident that the moisture content is having an insignificant effect on the particle size distribution. 1400 Cummulative Mass

1200 1000

+50% 2% H2O -50%

800 600 400 200 0 0.01

0.1

1

10

Size (mm)

Figure 37: Effect of Moisture Content on Size Distribution

46

100

Thesis

David Brooker

6.4 Conclusion The validation of the model was limited by errors in the sampling results. It has been identified that in order to model the 'N-Gold' processes effectively, a series of changes to the simulation need to be made. 1. Incorporate a layering mechanism into the granulation process. 2. Review the numerical methods of the simulation to allow greater effect of the random coalescence on granulation. 3. Model the binder flowrate and distribution within the granulation drum. 4. Model the energy balance over the granulation circuit including the energy input associated with the steam. .

47

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7.0 Conclusion The investigation into the granulation of 'N-Gold' has identified that two mechanisms contribute to its granulation. These mechanisms are random and preferential coalescence. As the moisture content in the system increases, the range of the granulator outlet size distribution spreads due to a greater contribution by the preferential coalescence mechanism. Within the granulator a large proportion of the fine material below 225 microns is successfully agglomerated. Much of this fine material is produced during the crushing and screening stages of the circuit. Image analysis indicates the formation of four different particle types; large agglomerates in the particle size range; deformagle agglomerates attached to non-deformable crystals; agglomerates of non-deformable particles; large spherical agglomerates outside the product size range. In addition there are many particles that pass through the granulator without undergoing any size enlargement. The majority of these particles are in the intermediate size range of 0.225mm to 1mm. X-ray diffraction analysis showed, as expected, that the major component of 'N-Gold' is urea. There are however additional components within the granules. Attempts were made to match the additional peaks to known compounds. The results were however inconclusive. The logical source of the additional component is the binder. Further analysis is required to identify the non-urea components. The granulation simulation developed by Jang (1996) was adapted to suit 'N-Gold' granulation. Both random and preferential coalescence mechanisms were successfully modeled. The effectiveness the simulation was limited by a combination of the unstable granulation processes during sampling due to unreliable data and sections of the model that do not fit 'N-Gold'. It has been identified that to produce a closer fit of experimental data to the simulation results, the following changes in the model should be made: 5. Incorporate a layering mechanism into the granulation process. 6. Review the numerical methods of the simulation to allow greater effect of the random coalescence on granulation. 7. Model the binder flowrate and distribution within the granulation drum. 8. Model the energy balance over the granulation circuit including the energy input associated with the steam. It has been concluded that the non-deformable particles in the size range of 0.225 mm to 1mm in the urea feed are a major contributing factor to the large recycle ratios. Grinding the urea fines feed before it is granulated would greatly improve the granulation efficiency. In addition effective control of the moisture content in the system will ensure that granulation proceeds by both random and preferential coalescence mechanisms.

48

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8.0 NOMENCLATURE A1 = Parameter for random kernel A2 = Parameter for preferential kernel A(v ) = Attrition rate Bnuc (v) = Nucleation rate d 953 = 95% passing size of distribution G (v ) = Layering rate h = Spread of size distribution l = Degree of liberation Li = mean size of fraction M = Mass from which sample is taken M s = Mass of sample

N t = Total number of particles per unit volume ni = number fraction in size I n = Number of size intervals. p = Particle porosity Q = Inlet and exit flowrates from granulator. r = Effective granule size, m R = Radius of granulation drum, m S sat = Fractional saturation of granules S s = Solubility of fertiliser salt in water S crit = Critical granule saturation vi , v j = Volume of particles V = Volume of granulator xi = mass fraction in size i

X w = Moisture content y =Average mass at given size interval yi = Mass at given size interval α v = Volume shape factor β (u , v, t ) = Coalescence kernel ρ g = Granule density, g/cm3 ρ f = Density of fertiliser salt

ρl = Density of fertiliser solution µ = Binder Viscosity, P ω = Drum speed, s-1

49

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9.0 References Adetayo, A. A. and Ennis, B. J., 1997. 'Unifying Approach to Modeling Granule Coalescence Mechanisms', AIChE Journal, 43(4), pp.927-934. Adetayo, A. A., Litster, J.D. and Cameron, I.T., 1995. 'Steady State Modelling and Simulation of a Fertilizer Granulation Circuit, Computers chem. Engng, 19(4), pp. 383393. Adetayo, A. A., Litster, J.D. and Desai, M., 1993. 'The Effect of Process Parameters on Drum Granulation of Fertilizers with Broad Size Distributions', Chemical Engineering Science, 48(23), pp.3951-3961. Bathala C. R., Dodlaty V. S. M., Madaboosi, S.A. and Chamarti D.P.R., 1993. 'Modeling of Continuous Fertilizer Granulation Process for Control', Particle Particle System Characterization, 15, pp. 156-160. Davis, G., 1996, Collection of Granulation Circuit Data for Plant Evaluation and Simulation, Undergraduate Thesis, Department of Chemical Engineering, University of Queensland. Ennis, B. J., 1996. 'Agglomeration and size enlargement Session summary paper', Powder Technology, 88, pp. 203-225. Iverson, S.M. and Litster, J.D., 1998, Growth Regime Map for Liquid-Bound Granules, Powder Technology and Fluidization, 44 (7), pp. 1510-1518. Iveson, S.M., Litster, J.D. and Ennis, B.J., 1996, 'Fundamental studies of granule consolidation Part 1: Effects of binder content and binder viscosity', Powder Technology, 88, pp. 15-20. Litster, J.D. and Sarwono. R., 1996. 'Fluidized drum granulation: studies of agglomerate formation', Powder Technology, 88, pp. 165-172. Reddy, B.C., Murthy, D.V.S. and Rao, C.D.P., 1997, 'Continous Rotary Drum Granulation of N-K Fertilizers', Part. Part. Syst. Charact. 14, pp. 257-262. Sherington, P.J., (1968), The Chemical Engineer, pp. 201. Smith, R and James, G.V., 1981, The Sampling of Bulk Materials, London: Royal Society of Chemistry. Snow, R.H., Allen, T., Ennis, B.J. and Litster, J.D., 1997, 'Size reduction and Size Enlargement', Perry's Chemical Engineers Handbook, 7, pp. 20-56 to 20-89.

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Zhang, J., 1996, Dynamics and Control of Fertilizer Granulation Circuit, Postgratuate Thesis, Department of Chemical Engineering, University of Queensland. Hounslow, M.J. and Ryall, R.L. and Marshall, V.R., 1988, A Discretized Population Balance for Nucleation, Growth, and Aggregation, AIChE, 34 (11), pp. 1821-1832. Ennis, B.J., Tardos, G. and Pfeffer, R., 1991, A Microlevel-Based Characterization of Granulation Phenomena, Powder Technology, 65, pp. 257-272.

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APPENDIX 1 'N-Gold' Properties Table 1 shows a comparison of the properties of 'N-Gold' and the other fertilizers produced at Incitec. Table 1: Physical Properties of Fertilizer Urea AS MAP DAP True Density (g/cm3) 1.34 1.7 1.6 1.5 Solubility (g/ml)

119

Density of fertilizer Solution(ρl, g/cm3) Solubility (Ss, g/ml) Porosity of Granule (p)

1.29

1.3

1.19 0.35

0.7 0.35

Viscosity

78

46

3.4

3.7

52

75

8.5

Thesis

David Brooker

APPENDIX 2 Dynamic Fertilizer Model Zhang (1996) has developed a dynamic model for the granulation of di-ammonium phosphate. This model was adapted from the steady state model developed by Adetayo et al. (1995). The model includes the granulation drum, drier, screen, and crusher. Granulation Drum A dynamic model of the granulation drum has been developed that uses Hounslow's descritized population balance and the two-stage coalescence kernel proposed by Ennis [10]. (See section 2.1). The coalescence kernel is given by:

 AS sat  β ij =  0 ; S sat < S crit k (v + v ) ; S > S j sat crit  2 i In the development of the model, the assumptions have been made that no particle breakage occurs and that the operating temperature is constant along the drum. Incorporated in to the granulation drum model is the reaction between mono-ammonium phosphate and ammonia to give di-ammonium phosphate. Drier A distributed parameter model of a rotary drum drier has been used. The model describes the behaviour under co-current conditions. The key assumption in the development of the drier model is that there is no particle breakage or granulation occurring within the drier. The accuracy of the assumption will be tested through the analysis of the particle size distributions before and after the drier in the N-Gold process. Screen The screen model is based on the probability that a particle will pass through the aperture of the screen. Crusher A matrix model has been used to model the crusher; this was validated for fertilizer processes by Adetayo [1]. The key assumptions of the model are: v Single fracture breakage occurs v The breakage is assumed to be constant within a size interval v The system is assumed to be perfectly mixed v Efficiency is not a function of flowrate. The input data requirements for each of the units are shown below. Granulator Drier Crusher / Screen Particle Size Distribution Air Flowrate Solid Flowrate Solid Flowrate Solid Flowrate Particle Size Distribution Binder Flowrate Moisture Content Water Content Temperature Input Requirements for Granulation Circuit

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APPENDIX 3 Sampling Error Calculations Density

1.34 D95

Run 1 Run 2 Run 3 Run 4 Run 5

2.5 1.94 4.2 4 3.6 Run 1

Sieve Size

Mass on Sieve

Mass Fraction

Run 2

Run 3

Mass on Mass Sieve Fraction

Mass on Sieve

Mass Fraction

Run 4

Run 5

Mass on Mass Sieve Fraction

Mass on Mass Sieve Fraction

11.2

0

0

2.35

0.01136

2.35

0.011624

0

0

8

0

0

2.76

0.013342

2.76

0.013653

0.55

0.00186

5.6

0.87

0.004175

0.85

0.003848

7.27

0.035143

7.27

0.035962

5.84

0.01978

4

5.13

0.024621

0.7

0.003169

12.67

0.061246

12.67

0.062673

28.19

0.09548

2.8

14.09

0.067623

6.01

0.027209

21.04

0.101706

21.04

0.104076

51.86

0.17566 0.20289

2

35.21

0.168986

59.35

0.268698

41.8

0.202059

41.8

0.206767

59.9

1.4

67.49

0.323911

81.02

0.366806

59.96

0.289844

59.96

0.296597

67.7

0.22931

1

38.65

0.185496

36.38

0.164705

32.2

0.155653

32.2

0.15928

32.76

0.11096

0.71

22.25

0.106786

18.31

0.082896

13.3

0.064292

13.3

0.065789

20.97

0.07103

0.5

12.18

0.058457

8.64

0.039116

5.32

0.025717

5.32

0.026316

12.71

0.04305

0.335

6.77

0.032492

4.71

0.021324

1.66

0.008024

1.66

0.008211

6.94

0.02351

0.25

3.06

0.014686

2.33

0.010549

5.5

0.026587

0.79

0.003908

4.24

0.01436

0.18

0.98

0.004703

0.78

0.003531

0.36

0.00174

0.36

0.001781

1.5

0.00508

0.125

0.38

0.001824

0.63

0.002852

0.22

0.001063

0.22

0.001088

0.86

0.00291

0.09

0.7

0.00336

0.53

0.002399

0.17

0.000822

0.17

0.000841

0.61

0.00207

0.053

0.37

0.001776

0.41

0.001856

0.2

0.000967

0.2

0.000989

0.53

0.0018

0

0.23

0.001104

0.23

0.001041

0.09

0.000435

0.09

0.000445

0.07

0.00024

Total

208.36

1

220.88

1

206.87

1

202.16

1

295.23

Error

7.01

4.64

14.25

15.53

9.90

Mass

Granulator Exit Cumulative Plot 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Run 1 Run 2 Run 3 Run 4 Run 5

0

2

4

6

8

Size (mm)

54

10

12

Thesis

David Brooker

APPENDIX 4 Error Calculations for Precision Analysis Test A 11.2 8

0 0.0079

5.6 4

Test B

Test C 0 0

Test D

ybar

Standard Deviation

0 0

0 0.00209

0 0.0025

0 2.9E-05

0 6.2E-06

0.0036

0.00147 0.00503

0.00315

0.0033

8.4E-08

0.0122

0.00634 0.02806

0.01273

0.0148

7E-06

2.8

0.0235

0.01833 0.02077

0.03042

0.0233

Error

0 6.2E-06

0 1.7E-07

0 0.003734

0 0.74674

3.4E-06

2.9E-06

2.6E-08

0.001465

0.292936

7.2E-05

0.00017

4.4E-06

0.00928

1.856067

7.1E-08

2.4E-05

6.2E-06

5.1E-05

0.005222

1.044363

2

0.0944

0.08012 0.09277

0.12018

0.0969

6E-06

0.00028

1.7E-05

0.00054

0.016801

3.360297

1.4

0.3079

0.26485 0.30472

0.31299

0.2976 0.00011

0.00107

5E-05

0.00024

0.022108

4.421538

1

0.2218

0.20524 0.21474

0.20477

0.2116

0.0001

4.1E-05

9.6E-06

4.7E-05

0.008189

1.63781

0.71

0.1133

0.11086 0.11381

0.10208

0.11

1.1E-05

7.4E-07

1.4E-05

6.3E-05

0.005435

1.08693

0.5

0.0686

0.0769 0.07371

0.06115

0.0701

2.1E-06

4.6E-05

1.3E-05

8E-05

0.006868

1.37363

0.335

0.0378

0.04686 0.04223

0.03321

0.04

5E-06

4.7E-05

4.9E-06

4.6E-05

0.00586

1.171925

0.25

0.0191

0.01686

0.0192

0.01768

0.0182

7.4E-07

1.8E-06

9.9E-07

2.6E-07

0.001124

0.224831

0.18

0.0265

0.04092 0.01246

0.02569

0.0264

7.4E-09

0.00021

0.00019

4.8E-07

0.011628

2.325596

0.125

0.0216

0.04263 0.02583

0.02411

0.0285

4.8E-05

0.0002

7.4E-06

2E-05

0.009557

1.911354 1.540912

0.09

0.0163

0.03307 0.01843

0.01874

0.0216

2.9E-05

0.00013

1E-05

8.3E-06

0.007705

0.053

0.014

0.02991 0.01564

0.01685

0.0191

2.6E-05

0.00012

1.2E-05

5.1E-06

0.007297

1.459336

0

0.0115

0.02562 0.01263

0.01415

0.016

2E-05

9.3E-05

1.1E-05

3.4E-06

0.006514

1.302803

Average Error

55

1.515122

Thesis

David Brooker

APPENDIX 5 Raw Data - 'N-Gold' Mass Fractions Urea Fines Run 1

Granulator Exit Run 2

Run 3

Run 4

Run 5

Run 1

Run 2

Run 3

Run 4

Run 5

11.2

0.000

0.000

0.004

0.020

0.000

11.2000

0.0000

0.0000

0.0135

0.0114

8

0.001

0.002

0.003

0.020

0.000

8.0000

0.0000

0.0000

0.0253

0.0133

0.0019

5.6

0.002

0.004

0.006

0.051

0.001

5.6000

0.0042

0.0038

0.0128

0.0351

0.0198

4

0.007

0.008

0.007

0.028

0.002

4.0000

0.0246

0.0032

0.0339

0.0612

0.0955

2.8

0.137

0.015

0.019

0.037

0.008

2.8000

0.0676

0.0272

0.1040

0.1017

0.1757

2

0.310

0.222

0.219

0.185

0.110

2.0000

0.1690

0.2687

0.2154

0.2021

0.2029

1.4

0.178

0.334

0.334

0.286

0.269

1.4000

0.3239

0.3668

0.3208

0.2898

0.2293

1

0.063

0.155

0.150

0.149

0.144

1.0000

0.1855

0.1647

0.1462

0.1557

0.1110

0.71

0.060

0.072

0.069

0.085

0.107

0.7100

0.1068

0.0829

0.0748

0.0643

0.0710

0.5

0.050

0.046

0.052

0.108

0.067

0.5000

0.0585

0.0391

0.0258

0.0257

0.0431

0.335

0.080

0.037

0.071

0.023

0.073

0.3350

0.0325

0.0213

0.0125

0.0080

0.0235

0.25

0.080

0.043

0.040

0.008

0.100

0.2500

0.0147

0.0105

0.0060

0.0266

0.0144

0.18

0.033

0.046

0.023

0.000

0.108

0.1800

0.0047

0.0035

0.0030

0.0017

0.0051

0.125

0.001

0.013

0.001

0.000

0.010

0.1250

0.0018

0.0029

0.0020

0.0011

0.0029

0.09

0.000

0.003

0.000

0.000

0.000

0.0900

0.0034

0.0024

0.0027

0.0008

0.0021

0.053

0.001

0.000

0.000

0.000

0.000

0.0530

0.0018

0.0019

0.0010

0.0010

0.0018

0.000

0.000

0.000

0.000

0.0000

0.0011

0.0010

0.0000

0.0004

0.0002

0

Granulator Entrance

Drier Exit

Run 1 Run 2 Run 3 Run 4 Run 5 11.2 0.000 0.000 0.000 0.052 0.000 8 0.000 0.000 0.001 0.002 0.000 5.6 0.001 0.001 0.011 0.008 0.004 4 0.001 0.002 0.008 0.012 0.045 2.8 0.004 0.005 0.025 0.029 0.100 2 0.055 0.085 0.104 0.119 0.152 1.4 0.211 0.351 0.318 0.352 0.258 1 0.209 0.227 0.185 0.195 0.130 0.71 0.137 0.110 0.120 0.091 0.077 0.5 0.101 0.068 0.054 0.045 0.052 0.34 0.078 0.050 0.037 0.022 0.041 0.25 0.063 0.041 0.038 0.020 0.039 0.18 0.037 0.021 0.041 0.017 0.029 0.13 0.033 0.009 0.043 0.013 0.036 0.09 0.025 0.016 0.012 0.010 0.016 0.05 0.028 0.008 0.002 0.008 0.014 0 0.018 0.006 0.000 0.005 0.006

11.2 8 5.6 4 2.8 2 1.4 1 0.71 0.5 0.335 0.25 0.18 0.125 0.09 0.053 0

56

Run 1 Run 2 Run 3 Run 4 0.000 0.000 0.000 0.000 0.003 0.001 0.002 0.020 0.005 0.007 0.060 0.051 0.026 0.007 0.057 0.028 0.102 0.030 0.108 0.037 0.148 0.206 0.239 0.186 0.361 0.283 0.303 0.288 0.189 0.184 0.127 0.149 0.082 0.103 0.053 0.085 0.044 0.070 0.021 0.108 0.022 0.048 0.007 0.023 0.011 0.038 0.018 0.023 0.003 0.013 0.002 0.000 0.001 0.005 0.001 0.000 0.001 0.004 0.001 0.000 0.001 0.002 0.001 0.000 0.000 0.001 0.000 0.000

Thesis

David Brooker

APPENDIX 6 Simulation Code (Code was developed by Jang (1996). Changes have been made to suit the 'N-Gold' process.) Urea Fines Source function_block U-Fines (* global variables declaration *) var_external initialization : bool ; time : real ; max_time : real ; print_level : int ; error_tolerance : real ; no_comps : int ;

(* (* (* (* (* (*

enables user code at time zero *) simulation time *) time for end of simulation *) degree of print output *) integration error acceptable *) number of components *)

end_var (* global data type declarations *) type stream : (* mass flow streams *) structure pressure : real ; temperature : real ; z_flow : array (1 .. no_comps) of real ; end_structure ; energy : structure z_rate : real ; end_structure ;

(* energy stream *)

signal : structure z_value : real ; end_structure ;

(* information signal *)

end_type var_in_out o1 : Stream ; (* feed *) end_var var_input x: array (1 .. 21) of real; term: real; end_var var i: int; end_var var_output resid_1: array (1 .. 21) of real; end_var function error (errcode: int;) end_function for i:=1 to 21 do resid_1(i):=x(i)-o1.z_flow(i); end_for end_function_block

Granulator Stage 1 function_block granu1 (* global variables declaration *) var_external

57

Thesis initialization : bool ; time : real ; max_time : real ; print_level : int ; error_tolerance : real ; no_comps : int ;

David Brooker (* (* (* (* (* (*

enables user code at time zero *) simulation time *) time for end of simulation *) degree of print output *) integration error acceptable *) number of components *)

end_var

(* global data type declarations *) type stream : (* mass flow streams *) structure pressure : real ; temperature : real ; z_flow : array (1 .. no_comps) of real ; end_structure ; energy : structure z_rate : real ; end_structure ;

(* energy stream *)

signal : structure z_value : real ; end_structure ;

(* information signal *)

end_type var_in_out i1: stream; o1: stream; end_var var_input x_n2: array(1 .. 20) of real; x_n3: array(1 .. 20) of real; x_n4: array(1 .. 20) of real; x_n5: array(1 .. 20) of real; x_xw: array(1 .. 5) of real; length: real; tr: real; densty: real; end_var var_output resid_out: array(1 .. 21) of real; deriv_n2: array(1 .. 20) of real; deriv_n3: array(1 .. 20) of real; deriv_n4: array(1 .. 20) of real; deriv_n5: array(1 .. 20) of real; deriv_xw: array(1 .. 20) of real; end_var var a1: array(1 .. 5) of real; a2: array(1 .. 5) of real; a3: array(1 .. 5) of real; a4: array(1 .. 5) of real; a5: array(1 .. 5) of real; i: int; j: int; sum1: real; sum2: real; sum3: real; sum4: real; beta: array(1 .. 5) of real; ntotal1: real; ntotal2: real; ntotal3: real;

58

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David Brooker

ntotal4: real; ntotal5: real; mntotal1: real; mntotal2: real; mntotal3: real; mntotal4: real; mntotal5: real; dmntotal2: real; dmntotal3: real; dmntotal4: real; dmntotal5: real; d: array (1 .. 20) of real; meand: array (1 .. 5) of real; in_fi: array(1 .. 20) of real; in_f: array(1 .. 20) of real; out_fi: array(1 .. 20) of real; out_f: array(1 .. 20) of real; dbar: array(1 .. 20) of real; end_var function error(errcode: int;) end_function (* program for birth death rate calculation*) a1(1):=0.0-13.0/length ; a1(2):=14.78831/length; a1(3):=0.0-2.66667/length; a1(4):=1.87836/length; a1(5):=0.0-1.0/length; a2(1):=0.0-5.32378/length; a2(2):=3.87298/length; a2(3):=2.06559/length; a2(4):=0.0-1.29099/length; a2(5):=0.67621/length; a3(1):=1.50000/length; a3(2):=0.0-3.22749/length; a3(3):=0.0; a3(4):=3.22749/length; a3(5):=0.0-1.50/length; a4(1):=0.0-0.67621/length; a4(2):=1.29099/length; a4(3):=0.0-2.06559/length; a4(4):=0.0-3.87298/length; a4(5):=5.32379/length; a5(1):=1.00/length; a5(2):=0.0-1.87836/length; a5(3):=2.66667/length; a5(4):=-14.78831/length; a5(5):=13.000/length; d(1):=0.053; d(2):=0.09; d(3):=0.125; d(4):=0.18; d(5):=0.25; d(6):=0.335; d(7):=0.5; d(8):=0.71; d(9):=1; d(10):=1.4; d(11):=2; d(12):=2.8; d(13):=4.0; d(14):=5.6; d(15):=8; d(16):=11.2; d(17):=12.7; d(18):=16; d(19):=20.16; d(20):=25; for i:=1 to 20 do if i==1 then dbar(i):=(d(i)+0.198)/2; else dbar(i):=(d(i)+d(i-1))/2;

59

Thesis

David Brooker

end_if end_for beta(1):= i1.z_flow(21)*(1.0+1.19)*1.34/(1.0i1.z_flow(21)*1.19)/1.29*(1.0-0.38)/0.38*6 ; for i:=2 to 5 do beta(i):= x_xw(i)*(1.0+1.19)*1.34/(1.0x_xw(i)*1.19)/1.29*(1.0-0.38)/0.38*6 ; end_for ntotal1:=i1.z_flow(1)-i1.z_flow(1); ntotal2:=i1.z_flow(1)-i1.z_flow(1); ntotal3:=i1.z_flow(1)-i1.z_flow(1); ntotal4:=i1.z_flow(1)-i1.z_flow(1); ntotal5:=i1.z_flow(1)-i1.z_flow(1); mntotal1:=i1.z_flow(1)-i1.z_flow(1); mntotal2:=i1.z_flow(1)-i1.z_flow(1); mntotal3:=i1.z_flow(1)-i1.z_flow(1); mntotal4:=i1.z_flow(1)-i1.z_flow(1); mntotal5:=i1.z_flow(1)-i1.z_flow(1); meand(1):=i1.z_flow(1)-i1.z_flow(1); meand(2):=i1.z_flow(1)-i1.z_flow(1); meand(3):=i1.z_flow(1)-i1.z_flow(1); meand(4):=i1.z_flow(1)-i1.z_flow(1); meand(5):=i1.z_flow(1)-i1.z_flow(1); for i:=1 to 20 do ntotal1:=ntotal1+i1.z_flow(i)*tr/length/densty/(3.14/6*dbar(i)**3); ntotal2:=ntotal2+x_n2(i); ntotal3:=ntotal3+x_n3(i); ntotal4:=ntotal4+x_n4(i); ntotal5:=ntotal5+x_n5(i); mntotal1:=mntotal1+i1.z_flow( i); mntotal2:=mntotal2+x_n2(i)/tr*length*densty*(3.14/6*dbar(i)**3); mntotal3:=mntotal3+x_n3(i)/tr*length*densty*(3.14/6*dbar(i)**3); mntotal4:=mntotal4+x_n4(i)/tr*length*densty*(3.14/6*dbar(i)**3); mntotal5:=mntotal5+x_n5(i)/tr*length*densty*(3.14/6*dbar(i)**3); end_for for i:=1 to 20 do meand(1):=meand(1)+i1.z_flow(i)*tr/length/densty/(3.14/6*dbar(i)**3) /ntotal1*dbar( i); meand(2):=meand(2)+x_n2(i)/ntotal2*dbar(i); meand(3):=meand(3)+x_n3(i)/ntotal3*dbar(i); meand(4):=meand(4)+x_n4(i)/ntotal4*dbar(i); meand(5):=meand(5)+x_n5(i)/ntotal5*dbar(i); if i==1 then in_fi(i):=i1.z_flow(i)*tr/length/densty/(3.14/6*dbar(i)**3)/ntotal1 /(d(i)); in_f(i):=i1.z_flow(i)*tr/length/densty/(3.14/6*dbar(i)**3)/ntotal1; out_fi(i):=o1.z_flow(i)*tr/length/densty/(3.14/6*dbar(i)**3)/ntotal5 /(d(i)); out_f(i):=o1.z_flow(i)*tr/length/densty/(3.14/6*dbar(i)**3)/ntotal5; else in_fi(i):=i1.z_flow(i)*tr/length/densty/(3.14/6*dbar(i)**3) /ntotal1/(d(i)-d(i-1)); in_f(i):=in_f(i-1)+i1.z_flow(i)*tr/length/densty/(3.14/6*dbar(i)**3) /ntotal1; out_fi(i):=o1.z_flow(i)*tr/length/densty/(3.14/6*dbar(i)**3) /ntotal5/(d(i)-d(i-1)); out_f(i):=out_f(i-1)+o1.z_flow(i)*tr/length/densty/(3.14/6*dbar(i)**3) /ntotal5; end_if end_for for i:=1 to 20 do sum1:=x_n2(i)-x_n2(i); sum2:=x_n2(i)-x_n2(i); sum3:=x_n2(i)-x_n2(i); sum4:=x_n2(i)-x_n2(i); if i > 1 then sum1:= sum1+0.5*beta(2) *x_n2(i-1)*(x_n2(i-1)); sum2:= sum2+0.5*beta(3) *x_n3(i-1)*(x_n3(i-1)); sum3:= sum3+0.5*beta(4)

60

Thesis

David Brooker

*x_n4(i-1)*(x_n4(i-1)); sum4:= sum4+0.5*beta(5) *x_n5(i-1)*(x_n5(i-1)); end_if for j:=1 to 20 do if j <= i-2 then sum1:=sum1+2.0**(j-i+1)*beta(2) *x_n2(i-1)*x_n2(j) ; sum2:=sum2+2.0**(j-i+1)*beta(3) *x_n3(i-1)*x_n3(j) ; sum3:=sum3+2.0**(j-i+1)*beta(4) *x_n4(i-1)*x_n4(j) ; sum4:=sum4+2.0**(j-i+1)*beta(5) *x_n5(i-1)*x_n5(j) ; end_if if j <= i-1 then sum1:= sum1-2.0**(j- i)*beta(2) *x_n2(i)*x_n2(j); sum2:= sum2-2.0**(j- i)*beta(3) *x_n3(i)*x_n3(j); sum3:= sum3-2.0**(j- i)*beta(4) *x_n4(i)*x_n4(j); sum4:= sum4-2.0**(j- i)*beta(5) *x_n5(i)*x_n5(j); else sum1:= sum1-beta(2) *x_n2(i)*x_n2(j); sum2:= sum2-beta(3) *x_n3(i)*x_n3(j); sum3:= sum3-beta(4) *x_n4(i)*x_n4(j); sum4:= sum4-beta(5) *x_n5(i)*x_n5(j); end_if end_for deriv_n2(i):=0.0-(a2(1)*i1.z_flow(i) *tr/length/ densty/(3.14/6*dbar(i)**3) +a2(2)*x_n2( i) +a2(3)*x_n3( i)+a2(4)*x_n4(i) +a2(5)*x_n5( i))*length/tr +sum1/ntotal2; deriv_n3(i):=0.0-(a3(1)*i1.z_flow(i) *tr/length/ densty/(3.14/6*dbar(i)**3) +a3(2)*x_n2( i) +a3(3)*x_n3( i)+a3(4)*x_n4(i) +a3(5)*x_n5( i))*length/tr +sum2/ntotal3; deriv_n4(i):=0.0-(a4(1)*i1.z_flow(i) *tr/length/ densty/(3.14/6*dbar(i)**3) +a4(2)*x_n2( i) +a4(3)*x_n3( i)+a4(4)*x_n4(i) +a4(5)*x_n5( i))*length/tr +sum3/ntotal4; deriv_n5(i):=0.0-(a5(1)*i1.z_flow(i) *tr/length/ densty/(3.14/6*dbar(i)**3) +a5(2)*x_n2( i) +a5(3)*x_n3( i)+a5(4)*x_n4(i) +a5(5)*x_n5( i))*length/tr +sum4/ntotal5; resid_out(i):= x_n5(i)*length/tr*densty*(3.14/6*dbar(i)**3) -o1.z_flow(i); end_for dmntotal2:=0.0-(a2(1)*mntotal1+a2(2)*mntotal2 +a2(3)*mntotal3+a2(4)*mntotal4 +a2(5)*mntotal5)*length/tr; dmntotal3:=0.0-(a3(1)*mntotal1+a3(2)*mntotal2 +a3(3)*mntotal3+a3(4)*mntotal4 +a3(5)*mntotal5)*length/tr; dmntotal4:=0.0-(a4(1)*mntotal1+a4(2)*mntotal2 +a4(3)*mntotal3+a4(4)*mntotal4 +a4(5)*mntotal5)*length/tr;

61

Thesis

David Brooker

dmntotal5:=0.0-(a5(1)*mntotal1+a5(2)*mntotal2 +a5(3)*mntotal3+a5(4)*mntotal4 +a5(5)*mntotal5)*length/tr; deriv_xw(2):=0.0-((a2(1)*i1.z_flow(21)*mntotal1 +a2(2)*x_xw(2)*mntotal2 +a2(3)*x_xw(3)*mntotal3 +a2(4)*x_xw(4)*mntotal4 +a2(5)*x_xw(5)*mntotal5)*length/tr +x_xw(2)*dmntotal2)/mntotal2; deriv_xw(3):=0.0-((a3(1)*i1.z_flow(21)*mntotal1 +a3(2)*x_xw(2)*mntotal2 +a3(3)*x_xw(3)*mntotal3 +a3(4)*x_xw(4)*mntotal4 +a3(5)*x_xw(5)*mntotal5)*length/tr +x_xw(3)*dmntotal3)/mntotal3; deriv_xw(4):=0.0-((a4(1)*i1.z_flow(21)*mntotal1 +a4(2)*x_xw(2)*mntotal2 +a4(3)*x_xw(3)*mntotal3 +a4(4)*x_xw(4)*mntotal4 +a4(5)*x_xw(5)*mntotal5)*length/tr +x_xw(4)*dmntotal4)/mntotal4; deriv_xw(5):=0.0-((a5(1)*i1.z_flow(21)*mntotal1 +a5(2)*x_xw(2)*mntotal2 +a5(3)*x_xw(3)*mntotal3 +a5(4)*x_xw(4)*mntotal4 +a5(5)*x_xw(5)*mntotal5)*length/tr +x_xw(5)*dmntotal5)/mntotal5; resid_out(20+1):=x_xw(5)-o1.z_flow(20+1); end_function_block

Granulator Stage 2 function_block try (* global variables declaration *) var_external initialization : bool ; time : real ; max_time : real ; print_level : int ; error_tolerance : real ; no_comps : int ;

(* (* (* (* (* (*

enables user code at time zero *) simulation time *) time for end of simulation *) degree of print output *) integration error acceptable *) number of components *)

end_var

(* global data type declarations *) type stream : (* mass flow streams *) structure pressure : real ; temperature : real ; z_flow : array (1 .. no_comps) of real ; end_structure ; energy : structure z_rate : real ; end_structure ;

(* energy stream *)

signal : structure z_value : real ; end_structure ;

(* information signal *)

end_type

62

Thesis

David Brooker

var_in_out i1: stream; o1: stream; o2: signal; end_var var_input x_n2: array(1 .. 20) of real; x_n3: array(1 .. 20) of real; x_n4: array(1 .. 20) of real; x_n5: array(1 .. 20) of real; x_xw: array(1 .. 5) of real; length: real; tr: real; densty: real; constn: real; end_var var_output resid_1: array(1 .. 21) of real; resid_2: real; deriv_n2: array(1 .. 20) of real; deriv_n3: array(1 .. 20) of real; deriv_n4: array(1 .. 20) of real; deriv_n5: array(1 .. 20) of real; deriv_xw: array(1 .. 5) of real; end_var var a1: array(1 .. 5) of real; a2: array(1 .. 5) of real; a3: array(1 .. 5) of real; a4: array(1 .. 5) of real; a5: array(1 .. 5) of real; i: int; j: int; ii: int; sum1: real; sum2: real; sum3: real; sum4: real; term: real; ntotal1: real; ntotal2: real; ntotal3: real; ntotal4: real; ntotal5: real; mntotal1: real; mntotal2: real; mntotal3: real; mntotal4: real; mntotal5: real; psum: real; sum: real; d: array(1 .. 20) of real; meand: array(1 .. 5) of real; fi: array(1 .. 20) of real; f: array(1 .. 20) of real; dbar: array(1 .. 20) of real; tn: real; end_var function error(errcode: int;) end_function (* program for birth death rate calculation*) a1(1):=0.0-13.0/length ; a1(2):=14.78831/length; a1(3):=0.0-2.66667/length; a1(4):=1.87836/length; a1(5):=0.0-1.0/length; a2(1):=0.0-5.32378/length; a2(2):=3.87298/length; a2(3):=2.06559/length; a2(4):=0.0-1.29099/length; a2(5):=0.67621/length; a3(1):=1.50000/length;

63

Thesis

David Brooker

a3(2):=0.0-3.22749/length; a3(3):=0.0; a3(4):=3.22749/length; a3(5):=0.0-1.50/length; a4(1):=0.0-0.67621/length; a4(2):=1.29099/length; a4(3):=0.0-2.06559/length; a4(4):=0.0-3.87298/length; a4(5):=5.32379/length; a5(1):=1.00/length; a5(2):=0.0-1.87836/length; a5(3):=2.66667/length; a5(4):=-14.78831/length; a5(5):=13.000/length; d(1):=0.053; d(2):=0.09; d(3):=0.125; d(4):=0.18; d(5):=0.25; d(6):=0.335; d(7):=0.5; d(8):=0.71; d(9):=1; d(10):=1.4; d(11):=2; d(12):=2.8; d(13):=4.0; d(14):=5.6; d(15):=8; d(16):=11.2; d(17):=12.7; d(18):=16; d(19):=20.16; d(20):=25; for i:=1 to 20 do if i==1 then dbar(i):=(d(i)+0.198)/2; else dbar(i):=(d(i)+d(i-1))/2; end_if end_for sum:=i1.z_flow(1)-i1.z_flow(1); psum:=i1.z_flow(1)-i1.z_flow(1); for i:=1 to 20 do sum:=sum+o1.z_flow(i); end_for for i:=10 to 13 do psum:=psum+o1.z_flow(i); end_for ii:= i1.z_flow(1)-i1.z_flow(1); (* for j:=1 to 20 do for i:=1 to 20 do ii:=ii+1; beta(20*(j-1)+i):= 0.0156*constn*(2**(i-0.5)+2**(j-0.5)) ; end_for end_for*) ntotal1:=i1.z_flow(1)-i1.z_flow(1); ntotal2:=i1.z_flow(1)-i1.z_flow(1); ntotal3:=i1.z_flow(1)-i1.z_flow(1); ntotal4:=i1.z_flow(1)-i1.z_flow(1); ntotal5:=i1.z_flow(1)-i1.z_flow(1); mntotal1:=i1.z_flow(1)-i1.z_flow(1); mntotal2:=i1.z_flow(1)-i1.z_flow(1); mntotal3:=i1.z_flow(1)-i1.z_flow(1); mntotal4:=i1.z_flow(1)-i1.z_flow(1); mntotal5:=i1.z_flow(1)-i1.z_flow(1); tn:= i1.z_flow(1)-i1.z_flow(1); for i:=1 to 20 do ntotal1:=ntotal1+i1.z_flow(i)*tr/length/densty/(3.14/6*dbar(i)**3); ntotal2:=ntotal2+x_n2(i); ntotal3:=ntotal3+x_n3(i);

64

Thesis

David Brooker

ntotal4:=ntotal4+x_n4(i); ntotal5:=ntotal5+x_n5(i); mntotal1:=mntotal1+i1.z_flow( i); mntotal2:=mntotal2+x_n2(i)/tr*length*densty*(3.14/6*dbar(i)**3); mntotal3:=mntotal3+x_n3(i)/tr*length*densty*(3.14/6*dbar(i)**3); mntotal4:=mntotal4+x_n4(i)/tr*length*densty*(3.14/6*dbar(i)**3); mntotal5:=mntotal5+x_n5(i)/tr*length*densty*(3.14/6*dbar(i)**3); tn:=tn+x_n5(i)/tr*length; end_for for i:=1 to 20 do if i==1 then fi(i):=x_n5(i)/ntotal5/(d(i)); f(i):=x_n5(i)/ntotal5; else fi(i):=x_n5(i)/ntotal5/(d(i)-d(i-1)); f(i):=f(i-1)+x_n5(i)/ntotal5; end_if end_for for i:=1 to 20 do sum1:=x_n2(i)-x_n2(i); sum2:=x_n2(i)-x_n2(i); sum3:=x_n2(i)-x_n2(i); sum4:=x_n2(i)-x_n2(i); if i > 1 then sum1:= sum1+0.5*$Rate*3.14/6*( dbar(i-1)**3+dbar(i-1)**3) *x_n2(i-1)*(x_n2(i-1)); sum2:= sum2+0.5*$Rate *3.14/6*( dbar(i-1)**3+dbar(i-1)**3) *x_n3(i-1)*(x_n3(i-1)); sum3:= sum3+0.5*$Rate *3.14/6*( dbar(i-1)**3+dbar(i-1)**3) *x_n4(i-1)*(x_n4(i-1)); sum4:= sum4+0.5*$Rate *3.14/6*( dbar(i-1)**3+dbar(i-1)**3) *x_n5(i-1)*(x_n5(i-1)); end_if for j:=1 to 20 do if j <= i-2 then sum1:=sum1+2.0**(j-i+1)* $Rate *3.14/6*( dbar(j)**3+dbar(i-1)**3) *x_n2(i-1)*x_n2(j) ; sum2:=sum2+2.0**(j-i+1)* $Rate *3.14/6*( dbar(j)**3+dbar(i-1)**3) *x_n3(i-1)*x_n3(j) ; sum3:=sum3+2.0**(j-i+1)* $Rate *3.14/6*( dbar(j)**3+dbar(i-1)**3) *x_n4(i-1)*x_n4(j) ; sum4:=sum4+2.0**(j-i+1)* $Rate *3.14/6*( dbar(j)**3+dbar(i-1)**3) *x_n5(i-1)*x_n5(j) ; end_if if j <= i-1 then sum1:= sum1-2.0**(j- i)* $Rate *3.14/6*(dbar(j)**3+dbar(i)**3) *x_n2(i)*x_n2(j); sum2:= sum2-2.0**(j- i)* $Rate *3.14/6*(dbar(j)**3+dbar(i)**3) *x_n3(i)*x_n3(j); sum3:= sum3-2.0**(j- i)* $Rate *3.14/6*(dbar(j)**3+dbar(i)**3) *x_n4(i)*x_n4(j); sum4:= sum4-2.0**(j- i)* $Rate *3.14/6*(dbar(j)**3+dbar(i)**3) *x_n5(i)*x_n5(j); else sum1:= sum1-$Rate *3.14/6*( dbar(j)**3+dbar(i)**3) *x_n2(i)*x_n2(j); sum2:= sum2-$Rate *3.14/6*( dbar(j)**3+dbar(i)**3) *x_n3(i)*x_n3(j); sum3:= sum3-$Rate *3.14/6*( dbar(j)**3+dbar(i)**3) *x_n4(i)*x_n4(j); sum4:= sum4-$Rate *3.14/6*( dbar(j)**3+dbar(i)**3) *x_n5(i)*x_n5(j); end_if end_for term:=1.0; deriv_n2(i):=0.0-(a2(1)*i1.z_flow(i)*term *tr/length/ densty/(3.14/6*dbar(i)**3) +a2(2)*x_n2( i) +a2(3)*x_n3( i)+a2(4)*x_n4(i) +a2(5)*x_n5( i))*length/tr +sum1/ntotal2;

65

Thesis

David Brooker

deriv_n3(i):=0.0-(a3(1)*i1.z_flow(i)*term *tr/length/ densty/(3.14/6*dbar(i)**3) +a3(2)*x_n2( i) +a3(3)*x_n3( i)+a3(4)*x_n4(i) +a3(5)*x_n5( i))*length/tr +sum2/ntotal3; deriv_n4(i):=0.0-(a4(1)*i1.z_flow(i)*term *tr/length/ densty/(3.14/6*dbar(i)**3) +a4(2)*x_n2( i) +a4(3)*x_n3( i)+a4(4)*x_n4(i) +a4(5)*x_n5( i))*length/tr +sum3/ntotal4; deriv_n5(i):=0.0-(a5(1)*i1.z_flow(i)*term *tr/length/ densty/(3.14/6*dbar(i)**3) +a5(2)*x_n2( i) +a5(3)*x_n3( i)+a5(4)*x_n4(i) +a5(5)*x_n5( i))*length/tr +sum4/ntotal5; resid_1(i):= x_n5(i)/term*length/tr*densty*(3.14/6*dbar(i)**3) -o1.z_flow(i); end_for meand(1):=i1.z_flow(1)-i1.z_flow(1); meand(2):=i1.z_flow(1)-i1.z_flow(1); meand(3):=i1.z_flow(1)-i1.z_flow(1); meand(4):=i1.z_flow(1)-i1.z_flow(1); meand(5):=i1.z_flow(1)-i1.z_flow(1); for i:=1 to 20 do (* meand(1):=meand(1)+i1.z_flow(i)*d(i)/mntotal1; meand(2):=meand(2)+x_n2(i)/tr*length *densty*(3.14/6*dbar(i)**3)*d(i)/mntotal2; meand(3):=meand(3)+x_n3(i)/tr*length *densty*(3.14/6*dbar(i)**3)*d(i)/mntotal3; meand(4):=meand(4)+x_n4(i)/tr*length *densty*(3.14/6*dbar(i)**3)*d(i)/mntotal4;*) meand(5):=meand(5)+x_n5(i)/tr*length*dbar(i)/tn; end_for deriv_xw(2):= (a2(1)*i1.z_flow(20+1)+a2(2)* x_xw(2)+a2(3)*x_xw(3) +a2(4)*x_xw(4)+a2(5)*x_xw(5))*(0.0-length/tr); deriv_xw(3):= (a3(1)*i1.z_flow(20+1)+a3(2)* x_xw(2)+a3(3)*x_xw(3) +a3(4)*x_xw(4)+a3(5)*x_xw(5))*(0.0-length/tr); deriv_xw(4):= (a4(1)*i1.z_flow(20+1)+a4(2)* x_xw(2)+a4(3)*x_xw(3) +a4(4)*x_xw(4)+a4(5)*x_xw(5))*(0.0-length/tr); deriv_xw(5):= (a5(1)*i1.z_flow(20+1)+a5(2)* x_xw(2)+a5(3)*x_xw(3) +a5(4)*x_xw(4)+a5(5)*x_xw(5))*(0.0-length/tr); resid_1(20+1):=x_xw(5)-o1.z_flow(20+1); (* resid_2:=o2.z_value-x_xw(5);*) end_function_block

66

Thesis

David Brooker

APPENDIX 7 Initial Conditions - Granulator

Collocation Points Granulator Stage 1 1

5.234

2

A B C D E

Mass of Particles 1 2 11.2

Stage 2

2.775

3A

B

3

F G H I J

C

Number of Particles E F

D

G

H

I

J

1.136

8

0.224

0.890

1.334

0.000

0.000

0.000

0.000

0.000

0.000 0.000

0.000

0.000

0.000

5.6

0.765

2.415

3.514

0.000

0.000

0.000

0.000

0.000

0.000 0.000

0.000

0.000

0.000

4

1.224

4.164

6.125

0.000

0.000

0.000

0.000

0.001

0.001 0.001

0.001

0.001

0.001

2.8

2.932

7.275 10.171

0.001

0.002

0.002

0.003

0.004

0.005 0.005

0.006

0.007

0.008

2 11.870 16.872 20.206

0.009

0.015

0.021

0.027

0.033

0.039 0.046

0.052

0.058

0.064

1.4 35.191 31.467 28.984

0.067

0.098

0.128

0.159

0.190

0.220 0.251

0.281

0.312

0.342

1 19.471 17.127 15.565

0.157

0.226

0.296

0.366

0.435

0.505 0.575

0.645

0.714

0.784

0.71

9.109

7.501

6.429

0.263

0.371

0.479

0.587

0.695

0.803 0.911

1.019

1.127

1.235

0.5

4.526

3.353

2.572

0.462

0.625

0.788

0.950

1.113

1.275 1.438

1.600

1.763

1.926

0.34

2.160

1.345

0.802

0.731

0.909

1.086

1.263

1.441

1.618 1.795

1.972

2.150

2.327

0.25

1.957

2.378

2.659

6.903

11 15.040

43.5

0.18

1.651

0.765

0.174

7.450

0.13

1.292

0.580

0.106

20.3

0.09

1.035

0.463

0.082

72.6

0.05

0.826

0.388

0.097

194.1

0

0.534

0.240

0.044 1653.8

Moisture Content Granulator Length Granulator Residence Time

19

23

27

31

35.4

39.5

7.730

8

8

8

8

8.4

8.6

8.7

20 19.973

20

20

20

19

19.3

19.1

19.0

8

72 71.091

70

70

69

68

67.3

66.6

65.8

206.3

212

218

225

231

236.7

242.8

248.9

1641 1627.6

1614

1601

1588

1575 1562.1 1549.0

1536.0

200

Granulator Stage 1 Stage 2 0.02 0.02 1 7 0.625 4.375

67