Modeling and Characterization of an in Situ Wet Mill Operation

Subscriber access provided by NEW YORK UNIV

Full Paper

Modelling and Characterization of an Insitu Wet Mill Operation David Antonio Acevedo, Vamsi Krishna Kamaraju, Brian Glennon, and Zoltan K Nagy Org. Process Res. Dev., Just Accepted Manuscript • DOI: 10.1021/acs.oprd.7b00192 • Publication Date (Web): 29 Jun 2017 Downloaded from http://pubs.acs.org on June 29, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Organic Process Research & Development is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Organic Process Research & Development

Modelling and Characterization of an Insitu Wet Mill Operation David Acevedoa, Vamsi K. Kamarajub, Brian Glennonb,c*, Zoltan K. Nagya a

School of Chemical Engineering, Purdue University, IN, USA 47907

b

c

APC Ltd, Building 11, Cherrywood Business Park, Loughlinstown, Co Dublin, Ireland

Synthesis and Solid State Pharmaceutical Centre (SSPC), School of Chemical and Bioprocess

Engineering, University College Dublin, Belfield, Dublin 4, Ireland * email: [email protected]

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table of Contents

Mill


Page 2 of 34

Page 3 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Abstract The integration of an in-situ wet mill and continuous mixed suspension mixed product removal crystallizer (MSMPR) is studied in this work for the cooling crystallization of Paracetamol from an aqueous isopropanol mixture. The continuous operation was monitored using Focused Beam Reflectance Measurement (FBRM) to determine the onset of steady state. The impact of various operational conditions of both continuous in-situ mill and MSMPR unit is studied. The paper demonstrates that the operational conditions (i.e. residence time, operational temperature) of the crystallization process affects the achievable steady state product characteristics. In addition, the influence of in-situ mill operating conditions (i.e. rotor speed) on important product and process qualities such as mean particle size, yield, and particle number is also discussed. Furthermore, breakage kernels were evaluated and validated through a parameter estimation routine. The insitu mill process can be assumed to be a combination of a nucleator generator and mill due to its impact on the mixing conditions as demonstrated by the parameter estimation framework. The model developed shows significant promise for process intensification and optimization studies in continuous crystallization process. Keywords: Crystallization, wet milling, MSMPR 1. Introduction Crystallization is one of the critical unit operations during the production of an active pharmaceutical ingredient or a pharmaceutical intermediate. Control of crystal attributes such as shape and size distributions is critical not only to the efficiency of the downstream operations but also to the efficacy of the final drug product. The control of these properties through optimal cooling crystallization, antisolvent crystallization, or a combination of both has been extensively



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

studied in literature.1-12 Large and uniform crystals are commonly the objective considered during the design and optimization of crystallization processes. However, smaller crystals are necessary to be produced for various purposes such as seed material for crystallizations or to enhance the bioavailability of crystals with low aqueous solubility.13,14 Towards this end, size reduction can be achieved by employing dry or wet milling operations. Dry mills are commonly used due to their scalability, and efficiency in generating fine particles.14-16 However, this type of operation may promote deformation of crystal lattice and potentially increases the number of operational steps.17,18 Wet milling is a commonly used approach which not only reduces the crystal size and results in a narrow size distribution but also eliminates the drawbacks associated with dry milling. Recent literature has shown that the average particle size achieved using a high-shear rotor-stator wet mill (HSWM) is in the range of 10-15 μm.18,19 Furthermore, the integration of rotor-stator wet mill with batch, semi-batch, and continuous crystallization process has been demonstrated.14, 20, 21 Yang et al. implemented a rotor-stator wet mill during a continuous cooling crystallization process.21 Higher yield and shorter startup duration were achieved when the continuous wet mill seed generation approach was implemented. A toothed rotor-stator wet mill was integrated to a batch cooling crystallization process in which an energy factor was correlated to the crystal size achieved.20 The mill geometry, tip speed, flow rate and slurry volume affect the wet mill energy factor and it was used as scaling factor between lab scale and pilot plant mills. Traditional scale-up approaches involve maintaining the tip speed of the rotor or equivalent batch turnovers. Harter et al. demonstrated the limitations in applying constant tip speed and equivalent batch turnover approach.18 It was demonstrated that the flow rate, starting particle size and concentration could impact the kinetics and final particle size.


Page 4 of 34

Page 5 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Moreover, a significant increase in nucleation rates has been observed due to the high shear environment.22,23 The design and scale-up of wet milling operations has promoted the development and study of mathematical models (empirical and mechanistic) for the prediction of particle properties and process conditions. A Slot Event Model was proposed and validated for a HSWM in which it is assumed that the slots within the rotor are responsible for the breakage of the particles.18 The frequency and probability determine the number of slot events, which then can be related to breakage events. Luciani et al. evaluated a modeling-aided scale-up approach of a HSWM by solving a population balance equation (PBE) with known breakage distribution functions and specific breakage rate while assuming no nucleation, dissolution, agglomeration and growth.13 The breakage modes that describe wet milling operations are massive fracture and attrition, which are caused by forces transferred from the slurry medium to the particles.20 The breakage of crystals by massive fracture produces two or more child particles of fine sizes compared to the parent crystal, whereas attrition results in crystals with similar size to that of the parent and a significant amount of fines.13 Towards this end, it is important to develop a mechanistic model in order to understand the effects of various wet mill properties on the obtained crystal size distributions. In this work, a continuous crystallization coupled with in-situ wet milling operation for paracetamol in water and isopropyl alcohol (IPA) mixture is studied. The continuous crystallization was performed in a Mixed Suspension Mixed Product Removal (MSMPR) crystallizer with a novel transfer unit characterized for paracetamol in water and IPA mixture in a previous work.24 The breakage rate model described by Luciani et al. is evaluated and extended to describe an in-situ wet mill operation. The impact of residence time and magma density on the mill efficiency is studied.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2. Material and Methods 2.1. Material 4-acetaminophenol (Paracetamol, >99%) purchased from Sigma Aldrich was recrystallized in an aqueous isopropanol (IPA, >99%, Sigma Aldrich) solution. The composition of the aqueous isopropanol solution was fixed to 4:1 (Water:IPA) through all the experiments performed. The solubility data for the considered system was obtained from literature.25 2.2. Experimental Setup The continuous crystallization process was performed in a 500 mL vessel in an Optimax (Mettler Toledo) system. Figure 1 shows the schematic of the MSMPR system. The transfer was performed by means of intermittent withdrawal using an automated Nitrogen pressure source (50 kPa) to transfer the product from the crystallizer to the feed/dissolution tank.24 The time intervals for the withdrawal were calculated as the ratio of the transfer volume to the feed flowrate. A Cole-Parmer Masterflex L/S Precision Modular Pump with Easy-Load II Head was used to transfer the saturated solution from the feed/dissolution tank to the crystallizer. The in-situ wet mill operation was performed using an IKA T 18 ULTRA-TURRAX® Disperser with S18N-19G dispersing element throughout all the experiments. Focused Beam Reflectance Measurement (FBRM) probe was used to monitor the changes in particle counts and chord length distributions.


Page 6 of 34

Page 7 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1.Schematic of continuous crystallization system. A. Peristaltic pump, B. In-situ Wet Mill, C. Thermocouple, D. FBRM.

The temperature was controlled through the Optimax control system. FBRM (Mettler Toledo AutoChem Ltd.) probe was employed to determine the onset of steady state and characterize the impact of the various mill conditions on the process dynamics and steady state product. The FBRM data was recorded every 5 seconds and averaged over 10 samples. Slurry samples of the steady state product were collected in order to analyze the CSD and solute concentration. The samples were obtained from the product line and were washed, filtered and vacuum dried. The concentration was determined gravimetrically by allowing the solution to evaporate in a vacuum oven at 40°C for a week; a week period was assumed to be enough time for the solids to be completely dried. The sample mass before and after drying was measured using a Mettler Toledo balance with an accuracy of ±0.0001 g. The Malvern Mastersizer 2000 coupled with the wet dispersion unit was used for off-line CSD analysis. A saturated solution of paracetamol in Water:IPA (4:1) was used as the dispersion medium. The volume-based particle size distribution in the range of 0.01 to 1000 µm was measured for each of the samples.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2.3. Procedure A saturated solution of Paracetamol at 40°C in Water: IPA mixture (4:1) was prepared using the solubility information from literature. The solution was then used to fill up the feed/dissolution tank and MSMPR crystallizer. The average working volume for the MSMPR crystallizer and feed-dissolution tank through all the experiments performed was 525 and 1000 mL, respectively. The feed/dissolution tank temperature was maintained using a temperature controlled hot plate at 50°C in order to ensure complete dissolution of crystals after each transfer. The saturated solution in the MSMPR crystallizer was cooled from 40°C to the final desired reactor temperature following a linear cooling profile. Table 1 shows the summary of experimental conditions evaluated during this work. The cooling rate was varied for one set of experiments in order to evaluate the impact of the startup material on the quasi steady state milled product. The startup procedure was varied for experiment 1 to identify if there is any different on the steady state material by starting the continuous milling-crystallization system from a batch or continuous procedure; no significant difference was observed between experiment 1 and 6. For simplification purposes, the authors would refer to the quasi steady state operation as steady state. Furthermore, the flowrate was varied in order to evaluate the impact of residence time on the final steady state product properties, i.e. CSD and solute concentration. The peristaltic pump was calibrated before each experiment to deliver the flowrate required to achieve the desired residence time.


Page 8 of 34

Page 9 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1. Operating conditions for continuous milling experiments in MSMPR system. Experiment 7 and 8 were used for validation purpose. Startup procedure cooling rate process (°C/min) MSMPR 0.5 Batch 0.5 Batch 0.5 Batch 0.5 Batch 1.5 Batch 0.5

exp

T (°C)

RT (min)

Nrpm×103 (rpm)

1 2 3 4 5 6

20 20 20 5 20 20

30 15 60 30 30 30

3-15 3-15 3-15 3-15 3 3-15

7

13

30

7

Batch

0.5

8

20

45

7

Batch

0.5

3. Mathematical Model The general form of the 1-D population balance model for a continuous MSMPR assuming a well-mixed system is given as ∂n(L, t ) ∂Gn(L, t ) 1 + = (n feed (L, t ) − n(L, t )) + φ (L, t ) ∂t ∂L τ

(1)

where n(L, t ) is the density distribution, L is characteristic length, G is the growth rate, τ is the residence time, and φ is the source term contribution on the density distribution due to nucleation, aggregation, and breakage. In this work, the aggregation of crystals was assumed to be negligible. Also, it was assumed that the system operates at constant volume, crystals nucleate at size zero, clear liquor feed, and well mixed suspension, mixed product removal. A high resolution finite volume (HRFV) method was used to solve the population balance equation involving nucleation, size independent growth, and breakage. The HRFV method was implemented to the homogenous equation of the population balance.26,27 The homogenous equation considering size independent growth is given by



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

dni 1 1 G(S )  j j  =−  ni + 1 − ni − 1  − 2 ∆Lτ dt ∆L  2 2 L

i+

ni =

 feed 1 1 feed   ni + 1 + ni − 1  + 2 ∆Lτ  2 2 

   ni + 1 + ni − 1   2 2

(2)

1 2

1 ndL ∆L L∫1 i−

Page 10 of 34

(3)

2

with ni , j being the average quantity in each cell where i represents bin number ( i = 1,2,..., N ) and N is the total number of bins. In this work, the secondary nucleation of crystals was considered since it is dominant in the MSMPR and due to the startup procedure implemented (refer to section 2.3). The secondary nucleation rate can be expressed as follows b'

 C − CS (T )  J = kb ' M t    CS (T )  j

(4)

where kb and b ' are the nucleation rate constant and order. The solubility concentration, C S , follows a polynomial expression.28 The magma density, M t , can be estimated from the third moment of the number density distribution based on Eq. (5) ∞

M t = ρ c kv ∫ L3n( L)dL

(5)

0

The growth rate of crystals follows an Arrhenius-type expression given by

 − Ea   C − Cs (T )  G = k g exp     RTR (K)  Cs (T ) 

g

(6)

where k g , Ea , and g are constants obtained from literature.28 The size independent growth and secondary nucleation rate depends on the supersaturation given by the difference between solute concentration and corresponding solubility at the given temperature. The solute concentration, C , can be obtained from the mass balance equation as dC 1 = ( C feed − C ) − ρC kv G ∫ L2 ndL dt τ


(7)

Page 11 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


where C feed is the solute concentration of the saturated feed solution, ρ C is the crystal density, and kv is the constant volumetric shape factor. The material properties, nucleation and growth kinetics constants used in this work are shown in Table 2. Table 2. Nucleation and growth kinetics parameters and Paracetamol crystals properties used for simulation work.28 Symbol

Units

Value

Symbol −4

kg

m/s

g

-

3.34 ×10 1.08

J/mol

1.44 ×10

#/kg s

295

EA kb'

'

b

Units

Value

-

2.14

j 4

1.62

ρc

kg/m

1332

kv

-

10

3

The rate of crystal breakage is considered after estimating the average cell quantities. The source term, φ , is assumed to consider only crystal breakage. The rate of crystal breakage is given by the birth and death of crystals due to fragmentation of the parent crystals. The breakage rate can be estimated from the specific breakage rate ( Si ) and breakage distribution function ( bi , j ) as follows i −1

Bi = − Si ni + ∑ bi , j S j n j

(8)

j =1

Numerous models have been proposed that describe the specific breakage rate and the breakage density distribution function for milling operations.29-32 In this work, the model presented by Austin et al. was implemented as an initial case study because it has been widely used to describe the breakage of organic crystals and it has been recently studied on wet-milling applications: 29 α

L  Si = S1  i   L1 

(9)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Bi , j

L = i L  j

  

Page 12 of 34

ε

(10)

bi , j = Bi , j − Bi +1, j

(11)

where S1 is the specific breakage rate for the coarsest particles, α and ε are model parameters, and Bi , j is the cumulative breakage distribution function. This model is based on several assumptions: (a) infinite number of child crystals are born from the breakage of a parent crystal, (b) the specific breakage rate is a monotonically increasing function of the particle size, (c) model parameters are material-specific, (d) there is a minimum particle size below which breakage is no longer possible, and (e) S1 is a function of rotation rate. In this work, a symmetry simplification for the cumulative breakage distribution function was considered in order to minimize the complexity of the model (Eq. 10).13 Furthermore, the minimum particle size in which further breakage does not occur was set to 75 µm. This was approximated from dynamic experimental results obtained from the FBRM data. It was observed that the total counts between 75 to 85 µm do not change significantly as the rotor speed changes. Therefore, it can be assumed that the breakage limit is around this range for this type of configuration within the operating range studied for the in-situ mill. The HRFV method was formulated by implementing a linear discretization of 100 bins ( N = 100 ) and the resulting set of ordinary differential equations were solved numerically in MATLAB R2015b using ode23s solver. The time domain was linearly discretized into 100 points for the total continuous operation simulation of 800 min. It was observed that for all conditions the system reaches steady state during this time. Therefore, the CSD at the end of the process (800 min) was considered as the steady state solution. The initial condition for each process was obtained from the off-line CSD and concentration characterization (refer to section 2). The


Page 13 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


process conditions and wet-mill properties used during this work are listed in Table 3. The PBM was used to estimate the parameters for various breakage models describing the in-situ wet milling operation.

Table 3. Summary of experimental conditions and HRFV parameters fixed throughout this work. Parameter

Unit

Value

Parameter

Value

Nt

Unit -

V

m3

525×10-6

C0

g/kg

96.2

N

-

100

Tsat

°C

40

Lmax

M

2000×10-6

C Feed

g/kg

96.2

ܴ௔

rpm

300

100

The specific breakage rate expression (Eq. 9) was varied to consider the impact of milling and MSMPR operational conditions since only S1 and α are process dependent. The specific breakage rate for the coarsest particles has been reported as a function of the rotor speed in the case of ex-situ high shear wet mill.29 In this work, the specific breakage rate constant is extended to include crystallization process conditions such as residence time and magma density. The various specific breakage rate expressions tested and parameters evaluated are shown in Table 4.

Table 4.Specific breakage rate selection function evaluated throughout the study. Model

Variables

Equation

A

N RPM

m S1 = kmill N rpm

B

N RPM ,τ

m1 − m2 S1 = kmill N rpm τ

C

N RPM , MT

m1 S1 = kmill N rpm M Tm3

The model parameters were estimated by fitting the simulated crystal size distribution ( n' ) to that obtained from the off-line CSD analysis. The distribution obtained from the off-line CSD analysis was converted to a number based distribution.28 The objective function (Eq. 12) was formulated as the difference between the simulated cumulative distribution and experimental



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 34

cumulative distribution subject to the parameter vector θ . The MATLAB function fminsearch was employed to obtain the breakage parameters for the various models evaluated. The 95% confidence intervals were estimated through the projection of uncertainty via linear error propagation.33,34 The parameters were scaled nonlinearly (i.e. ln(kmill ) ) in order to obtain a fast and efficient optimization procedure. 35 2  exp Lmax ' ' min ∑∑ ( nsim − nexp )  θ  k =1 0 

(12)

4. Results and Discussion 4.1. Characterization of continuous in-situ mill operation The continuous in-situ wet milling operation in a continuous cooling crystallization of paracetamol was performed as described in section 2. The process was monitored using an FBRM; the particle size and particle number of the steady state product were monitored. The continuous mill operation was initiated after the continuous MSMPR system reached steady state. The initial wet mill rotor speed was set to 3000 rpm, which is the lower limit of the equipment. The dynamic profile of total counts per seconds observed in Figure 2(a) shows a washout period (i.e. steady decrease in fine particles), which is expected for continuous MSMPR operations. A slight increase in the square weighted mean chord length (SWMCL) can be observed, which is related to the washout of sudden fines generated after the continuous in-situ mill operation was initiated (40 min). The in-situ wet mill rotor speed was changed after the system reached a quasi-steady state operation (125 min). A constant increase can be observed through the various set point changes between 3000 to 10000 rpm which can be attributed to slight increases in the rotor speed performed. A higher increase can be observed when the in-situ wet mill speed was changed from


Page 15 of 34

10000 to 15000 rpm. Furthermore, the measurements show higher variability at 15000 rpm. This demonstrate that the FBRM measurements are sufficiently accurate under the turbulent mixing conditions between rotor speeds of 3000 to 10000 rpm. Similar behavior is observed in the dynamic profile of counts per second for different size ranges shown in Figure 2(b).

20000

Chord length (µm)

15000 120 10000 80

counts, No Wt (#/s)

(a)

Median No Wt Mean Sqrt Wt Total counts

160

5000

40

0 250

0 0

50

100

150

200

time (min) 160

1000

(b)

100-110 40-50 50-60

140 120

Counts No Wt (#/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


800

100

600

80 400

60 40

200 20 0 0

50

100

150

200

0 250

time (min)

Figure 2. (a) Median No Wt (black), mean sqrt. wt.(red), and total count counts obtained for experiment 1. (b) Dynamic behavior of counts between 100-110 (red), 40-50(blue), and 50-60(black) µm. Square dotted lines show when mill speed was increased.

The dynamic behavior of counts between different size regions can be evaluated to determine the threshold in which crystal breakage occurs. The counts between 40 to 150 µm were evaluated and three regions are shown in Figure 2(b). The increase in the counts is observed for all the regions after the continuous in-situ mill operation is initiated at 3000 rpm. Significant increase is



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 34

observed for the counts between 40 to 60 µm during the various rotor speed changes until 10000 rpm. Counts between 60 to 100 µm showed similar behavior as fine crystals. No increase is observed in the counts per second for the 100 to 110 µm after the second set point change was performed (i.e., 3000 to 5000 rpm). The counts between 100 to 110 µm did not show significant change throughout the rest of the continuous operation. Hence, it can be assumed that new crystals generated due to breakage are below 100 µm since an increase in the counts is not observed when the rotor speed was increased. Also, it can be assumed that no crystal breakage occurs below this range (i.e., 400µm). However, the fit in model C follows similar trend as the one observed in the experimental results. The impact of the in-situ mill in the steady state CSD is better capture by considering the magma density in the specific breakage rate (model C). Although the fit does not show significant accuracy, all models were tested with respect to two validation experiments performed (e.g. experiment 7 and 8). The operating temperature and residence time was varied, while the rotor speed was fixed to 7000 rpm. The startup procedure and experimental conditions are shown in Table 1. The observed and predicted CSDs for all models considered are shown in Figure 9.

0.25

0.25 Exp A B C

0.2

0.2

0.15

pdf (-)

pdf (-)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 34

0.1

0.05

0.1

0.05

(a) 0 10 1

0.15

(b) 10 2

10 3

0 10 1

L ( m)

10 2

10 3

L ( m)

Figure 9. Observed and predicted CSDs for validation runs: (a) experiment 7 and (b) experiment 8.


Page 27 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The validation results show that the model cannot predict accurately the CSD distribution in all scenarios. The simulated distributions obtained in all scenarios are wider than the one observed experimentally. Furthermore, a significant number of fine crystals can be observed experimentally (

Modeling and Characterization of an in Situ Wet Mill Operation

Recommend Documents