measuring and modelling the classification and ...

MEASURING AND MODELLING THE CLASSIFICATION AND DISSOLUTION OF FINE CRYSTALS IN A DTB CRYSTALLISER Sean K. Bermingham1’2, Andreas M. Neumann1, Peter J.T. Verheijena and Herman J. M. Kramert 1Laboratory for Process Equipment, Delft University of Technology, Leeghwaterstraat 44, 2628 CA Delft, The Netherlands 2process Systems Engineering, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands Abstract

A predictive model framework for DTB crystallisers is presented. The overall model contains relations for secondary nucleation, growth, attrition, fines classification and dissolution, but only contains two parameters that need to be estimated. These parameters can be estimated using experimental data from a different crystalliser than the one that is to be simulated. In this paper the influence of fines removal is studied for a 1.1 m3 DTB crystalliser. Experimentally observed and simulated product median crystal sizes are compared for fines withdrawal rates of 2 and 3 l’s1 and dissolution residence times of 10 and 100 s. The predictive capabilities of the framework are good with respect to the average product median size, but unsatisfactory with respect to its oscillations. The results are promising considering the absence of parameters that are dependent of crystalliser scale, type and operating conditions. Keywords Fines classification, dissolution, removal, DTB crystalliser, compartment modelling Introduction Solution crystallisation processes can be performed in a wide variety of crystalliser types. The most common types include the mixed tank crystalliser, forced circulation crystalliser, draft tube crystalliser, draft tube baffle crystalliser and fluidised bed or OsIo crystalliser. Crystalliser type selection is influenced by design specifications such as production capacity, product quality, plant availability, flexibility, capital costs and maintenance costs. With respect to the quality of crystalline products, the crystal size distribution (CSD) is one of the more important aspects. The resulting CSD is determined by the residence time and the rates at which crystals are born, grow, dissolve, are attrited, break, agglomerate, etc. These rates are a function of (local) process conditions such as supersaturation, energy dissipation, pressure, and temperature. In their turn, the process conditions are a result of the selected crystalliser type and scale as well as the chosen operating conditions. The most important aspects as regards the relation between the product CSD and selected crystalliser type are: ¯ The mean specific power input of the circulation device required for crystal suspension. A lower mean specific power input generally leads to !ess crystal attrition and hence an increased average crystal size; ¯ The presence of classification devices for the selective removal of crystals in a particular size range. Product classifiers are used to manipulate the product CSD by only discharging crystals above a certain size. Fines classification in combination with subsequent dissolution is employed for the selective remova! of small crystals from a crystalliser. Fines removal increases the average crystal

size by decreasing the volume specific crystal surface area in the crystalliser and consequently increasing the crystal growth rate. In practice, selection or rejection of a crystalliser type is mainly based upon company experience with existing plants and pilot plant results. As a consequence, the design itself is often conservative and the design process may be lengthy and very costly. A more systematic design procedure, e.g. as exists for distillation, is obviously desirable. Such a procedure requires first principle models which can predict the influence of design and operational variables on the performance of the crystalliser and on the product quality. However, most punished crystalliser models are descriptive, which may be adequate for control purposes (e.g. Eek et al., 1995 and Miller et ai., 1994), but not predictive as required for design purposes.

~l:x]rometric condensor

~

Cross-sectional area annular zone: the area perpendicular to the direction of the fines flow in the annular zone. Superficial velocity in annular zone: volumetric fines withdrawal rate divided by cross-sectional area annular zone. Temperature increase fines: temperature difference between the exiting and entering fines stream of the heat exchanger. Volume fines dissolution loop: volume of the fines flow from the heat exchanger to the crystalliser inlet. Residence time dissolution loop: volume fines dissolution loop divided by the volumetric fines withdrawal rate.

Figure ]: An industrial DTB crystalliser.

Objective In this paper, we will focus on the development of a predictive model for draft tube baffle (DTB) crystallisers. In Fig. 1 an industrial DTB crystalliser is depicted and a definition is given of some terms used throughout this paper. A distinguishing feature of DTB crystallisers is the continuous removal of fines. Table 1: Relation between equipment dimensions and operating conditions on the one hand and process conditions on the other. Results in the following changes in the process conditions below

An increase in

Solids concentration in cr~,stalliser

Superficial velocity in annular zone

Temperature increase fines

Residence time dissolution loop

Cross-sectional area annular zone Volume fines dissolution loop Volumetric fines withdrawal rate

‘5

Heat input per unit volume Volumetric product withdrawal rate

ii

Table 2: Relation between process conditions on the one hand and the fines classification cut size and degree of fines dissolution on the other.

An increase in

Results in the following, changes in Degree of Fines classification fines dissolution cut size

Solids concentration in crystalliser Superficial velocity in annular zone Temperature increase fines Residence time dissolution loop

+

A proper description of the fines removal system requires models that account for changes in classification behaviour and degree of dissolution as a result of differences in equipment dimensions and operating conditions (see Tables 1 and 2). In addition, kinetic models are needed to predict the rate at which crystals are born (nucleation), grow out and are attrited. Finally, depending on the hydrodynamics and kinetics, the spatial distribution of process conditions needs to be accounted for. Note that in their present form, the models do not include agglomeration. In order, to be fully predictive, the resulting overall crystalliser model may contain intrinsic kinetic parameters only. In other words, the parameters should be independent of crystalliser scale, crystalliser type and operating conditions. If this is not the case, the product CSD which can be obtained with a certain crystalliser type, i.e. design alternative, can only be determined after realisation of the design. The predictive capabilities of the overall crystalliser model will be tested with the use of experimental results. Model framework First, a brief presentation is given of the theory behind the three sub-models describing the various phenomena that occur in a DTB crystalliser. Secondly, the concept of compartmental modelling is introduced. Material, energy and population balances as well as thermodynamic and physical property relations are not treated here. Nucleation, growth, dissolution and attrition in the crystaIliser

For the description of these phenomena the model framework of Gahn (1996, 1999) is used. The kinetics of nucleation, growth and attrition are calculated on the basis of the detailed impeller geometry, impeller frequency, material properties including mechanical properties, CSD, solute concentration and local energy dissipation. The framework consists of three sub-models: a procedure to determine the total number of crystals colliding per second with the impeller edges and the impeller blades, and the corresponding impact energy per collision. a relation between the impact energy and the number density distribution of attrition fragments produced due to a single collision of a crystal comer with the impeller blade or edge. a relation to derive the growth rate of the fragments formed by the attrition process. Attrition fragments resulting from a collision of a crystal comer with an impeller contain a certain amount of internal strain, which results in an increased solubility, c*r~, in comparison to the solubility, c*, of ideal, stress free crystals: Cr*eal(L)=c*.exp(Fx)R~-.L

(1)

thus reducing the driving force for crystal growth, Ac(L). Growth rates of attrition fragments will therefore be lower than those of larger crystals, and may even be negative. As a result, attrition fragments may dissolve under macroscopic growth conditions. Assuming a combined diffusion and

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second order surface reaction controlled growth, the size dependent growth rate of a crystal, G(L), can be obtained as follows:

Note that the condition of deformation, P~, and the surface reaction coefficient, kr, are the only parameters which have to be derived from crystallisation experiments. The mass transfer rate

coefficient, k~(L), can be calculated using a Sherwood relation developed by Herndl (1982). Classification in the annular zone Due to the low upward superficial velocity in the annular zone, classification occurs as a result of gravitational forces/settling. With increasing size, the terminal slip velocity of a particle increases. Consequently, the ratio between the particle concentration at the top, n~,,es(L), and the bottom, nb,,¢,(L), of the annular zone decreases with increasing particle size, L. The classification performance of the annular zone can be expressed by means of a classification function, lz¢~,,es(L), which is defined as:

(3) (z.) ,...,.,..,,,,.s (.z.) = h,,,,s (z.).

For an existing crystalliser with an unclassified product removal, nprod(L) = n~,adL), the classification function can be determined from CSD measurements of the fines and product stream. In other cases, e.g. crystalliser type selection for a new design, hydrodynamic models are required. Computational fluid dynamics (CFD) techniques v~0uld be ideal for this purpose as regards the amount and detail of information. However, with respect to human as well as computational effort, particle slip velocity models are deemed more suitable. Two classification function models based on particle slip velocities are proposed: The ideal classification function: h.n,,~s (L )=~ ~’’~’

L < Le,,

(4)

L >_ Le,.

(5)

~bulk

h¢,,~s (L ) =0

The cut size, Lc,,,, of the classification function is defined as the particle size for which the magnitude of the slip velocity is half that of the superficial velocity in the annular zone. Note that the slip velocity, Uszip(L), and superficial velocity, U~,p, have different signs, as they are respectively downward and upward. A non-ideal classification function:

For both classification function models, the particle slip velocities are calculated according to a model proposed by Barnea and Mizrahi (1973). Their model applies to the Stokes, transition and turbulent regimes. The factor gq,,~Jeo,,~ in equations 4 and 6 is related to the change in solids concentration as a result of classification, e~,t~, and eo,,~ denote the liquid fraction in the fines stream and bulk of the crystalliser respectively. Note that both models assume a fiat velocity profile throughout the annular zone. Dissolution in the fines removal loop The kinetics of crystal dissolution are also described with equation 2. This implies the following two assumptions: the order of the surface reaction with respect to the supersaturation and the surface reaction coefficient are the same for growth and dissolution conditions. Compartmental modelling Compartmental modelling is aimed at accounting for the spatial distribution of the CSD, energy dissipation, supersaturation, etc. inside a crystalliser. The individual compartments are considered to be well

iv

mixed, but may have classified exit streams. In each compartment, the kinetics are evaluated for the local process conditions and the material, energy and population balances are solved. An extensive motivation for compartmental modelling and a methodology for subdividing a crystalliser into multiple compartments is given by Kramer et al. (1999). This subdivision is performed on the basis of hydrodynamic analyses and characteristic times of crystallisation phenomena. Fig. 2 shows the compartment structures used for the simulations throughout this paper: (a) ideally mixed DT, (b) ideally mixed DTB with ideal fines dissolution, (c)ideally mixed DTB with real fines dissolution, and (d) DTB with real fines dissolution and compartmentalised main body. apour

~

Feed Product

(a)

Feed Product

(b)

Feed Product

(c) Feed

(d) Figure 2: Compartment structures employed for simulations with the compartmental model.

Experimental To validate the model framework presented in this paper, a number of experiments have been performed on an 1100 litre DTB crystalliser (Fig. 3). This crystalliser was operated in a continuous, evaporative mode at a constant temperature of 50 °C using ammonium sulfate/water as the model system. All experiments were performed with a product residence time of 75 minutes and a heat input of 120 kW. m3. In order to have an unclassified product stream, i.e. IZprod(L) = llb,,lk(L), product is isokinetically removed from the down-comer of the crystalliser. The CSD of the product flow is measured on-line with a Malvern 2600c laser diffraction instrument (equipped with a 1000 turn lens) which is implemented in a separate measuring !oop. This loop is required in order to reduce the original product solid concentration of approximately llvol.% to a solid concentration of approximately 1.5vo1.%; the maximum solid concentration which avoids multiple scattering and thus enables an accurate measurement using the laser diffraction measurement systems. A detailed description of this measuring procedure and a comparison with other CSD measurement techniques performed on the same crystalliser is given by Neumann et al. (1999).. The fines flow is withdrawn via six equally spaced withdrawal points located at the top of the annular zone. The CSD of this flow is measured on-line using a Malvern MasterSizer X laser diffraction instrument (equipped with a 300 mm lens). Next, the stream passes through a plate heat exchanger in which the heat necessary for evaporation is added to the system. The resulting temperature increase of the fines flow leads to dissolution of crystals. The degree of fines dissolution is not only determined by the level of undersaturation present after the heat exchanger, but also by the volume between the heat exchanger and the crystalliser inlet. The volume of this part of the fines loop is referred to as the fines dissolution loop volume. Together with the fines withdrawal rate this volume determines the time available for dissolution. In this

configuration, the fines dissolution loop volume can be varied between 0.020 and 0.200 m3 with the use of a dissolution vessel. Volume main body [ms] Volume annular zone [m3]

1.100 0.775 Volume dissolution vesset[m3] 0.180 0.020 Volume piping after heat exchanger [m~] Volume dissolution loop [m3] 0.200 / 0.020 0.5 Diameter draft tube [m] Diameter main body [m] 0.7 1.2 Diameter annular zone [m] 0.485 25

Angle of blades [o] Power number [-] Pumping number [-] Edge of impeller [m] Breadth of impeller [m]

Malvern MasterSizerX

Feed

3-blade marine

Impeller type Diameter impeller [m]

Fines removal

0.40

0.32 0.006 0.15 Annular zone

Impeller~ Inside draft tube

Dilution

Heat exchanger

OPUS Malvern 2600c

Bar

"down-comer"

Dissolution vessel

ii 0.Sm ii 1.2 m

Figure 3." Schematic drawing (left), cross-sectional view (bottom rtght) and specifications (top right) of the 1.1 m~ DTB crystalIiser. Table 3." Experiments performed on the 1.1 m~ DTB crystalliser Run

Crystalliser temperature [°C] Product residence time Is] Heat input [kW.m"3] Product density [kg.m3] Impeller frequency Isq] Feed temperature [°C] Feed density [kg’m~] Volume dissolution loop [m?] Fines withdrawal flow [m3’s1]

I

II 50 4500 120 1300 6.167 50 1250

III

0.200 0.002

0.020 0.002

0.020 0.003

Three experiments have been performed on this crystalliser to investigate the classification and dissolution of fine crystals. The conditions of these experiments are summarised in Table 3. Run I and Run II are aimed at studying the influence of the dissolution loop volume, whereas Run II and Run III are concerned with the influence of the fines withdrawal rate. The classification behaviour of the annular zone is determined by comparing the CSD of the withdrawn fines and the product crystals. As there are no CSD

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measurement of the fines just before being returned to crystalliser, the effects of fines dissolution are studied on the basis of product CSD only, Measured and calculated fines classification functions The median size of the product crystals and withdrawn fines obtained from Run III are depicted in Fig. 4 and 5 respectively. Fig. 5 also shows the obscuration of the fines CSD measurement, which is a measure for the volume fraction of crystals in the fines stream. Fines rmdian (Run ILl) --Fines obscuratinn (Run 111) i

~Pmduct rmdian (Run 11I) [

200 i

1200 1050

ts°l 100

750

5O

~/

450

! 0 30

0

300 5

10

15

20

25

0

30

10

[5

25

20

TLme (hrs)

Thr~ (hrs)

Figure 5." fines median crystal size and fines obscuration (Run II1).

Figure 4: product median ; crystal size (Run 11I).

[~Cut size lines classhqcation (Run i~ ’

l--Fract on below 120pmm produc (Run lIl) I

2OO 150 i00 50 0 10

15

20

25

Time (hrs)

Figure 6: volutne fraction of crystals below 120 pm in the product (Run III).

30

, tO

15

20

25

Tirm (hrs)

Figure 7: cut size of fines classification fitnction (Run III).

The dynamics of the obscuration trend are in good agreement with the trend of the product CSD. This is further illustrated by the trend of the volume fraction of crystals below 120 gm in the product (Fig. 6). Product and fines CSD’s measured at roughly the same time (< 3 minutes apart) were used to determine the time-variant fines classification function. The cut size of this function oscillates between 80 and 130 btm (see Fig. 7). The oscillations in Fig. 4 through 7 indicate that the variations in cut size are most probably a result of changes in the volume fraction solids in the fines and the volume fraction fines in the product stream. Changes in solids concentration may result in different degrees of hindrance for settling particles, consequently changing the slip velocities and thus the classification function. However, this explanation is unlikely as the resulting cut size trend would be counter phase to the observed trend. A more likely explanation is a decreased accuracy of the CSD measurements at low fines concentrations. The fines measurement is hampered by low obscurations and the product measurement by a low ratio of small over large crystals. The classification functions determined at higher fines obscuration levels are therefore taken to be the most reliable. Fig. 8 shows classification functions determined under these conditions and a comparison with calculated classification functions for Runs II and III, i.e. fines withdrawal rates of respectively 2 and 3 1.s~. The ideal and non-ideal classification models both provide good predictions of the cut size, but only moderate estimates of the whole function. The shape of these functions can easily be approximated with an S-curve, but that would introduce fit parameters into the models, which is in conflict vii

with our objective. Furthermore, the question remains whether the greatest error is present in the measurements or in the model. 1

o.9 0.8 o.7

--- Measured ...... Ideal ~ Non-ideal

-- Measured ...... Ideal ~ Non-ideal

0.6

0.5 0.4 0.3 0.2

0.t 0

50 100 150 200 250 300 350 400 450 500 Particle size [urn]

50 100 i50 200 250 300 350 400 450 500 Particle size [urn]

Figure 8: measured and calculated classy’cation functions for fines withdrawal rates of 2 l’s-~ (left) and of 3 l.s4 (right)

Influence of fines removal on the product CSD

In this section we will compare the measured and calculated effects of fines classification and dissolution on the product CSD of Runs I through III to evaluate the predictive capabilities of the DTB crystalliser model framework presented in this paper. As mentioned earlier, the total model only contains two parameters that need to be estimated for a certain model system, i.e. the condition of deformation, F~, and the surface reaction coefficient, k, As the crystalliser model has been set up to be scale and type independent, these parameters can be determined from experiments with an arbitrary crystalliser. The parameter values used in this work were determined by Neumann et al. (1998) from experiments on a 0.022 m? litre DT crystalliser. Table 4: Simulations for model evaluation (no. 1-5) and for model validation (no. 5-7). 4 5 6 1 2 3 Simulation ~) DTB DTB DTB DTB DTB crystalliser (i. 1 m DT non-ideal non-ideal non-ideal ideal non-ideal classification kinetics kinetics ideal ideal kinetics dissolution 4 1 1 4 1 1 # compartments Fig. 2.d Fig. 2.b Fig, 2.b Fig. 2.c Fig. 2.d Fig. 2.a comp. structure 0.200 0.200 0.020 Diss. loop [m~] 0.200 0,200 0.002 0.002 0.002 0.002 0.002 Fines flow [m3"s"l] II I Comparable to Run

7 DTB

non-ideal kinetics 4 Fig. 2.d 0.020

0.003 III

Before evaluating the model framework as a whole, the effect of different classification models (ideal, non-ideal), disgolution models (ideal, physical) and compartmentalisation on the predicted product CSD is investigated. Five simulations have been performed for the conditions of Run I using different sub-models and compartment structures (see Table 4, Sim. 1 through Sire. 5). From the simulated product median sizes shown in Fig. 9 the following conclusions can be drawn: The choice of classification function has little effect on the steady state median size but changes the period of the oscillation considerably. With a fines residence time of 100 seconds, and a temperature increase of 19 °C fines dissolution is practically complete. The spatial distribution of process conditions plays no role. As expected, fines removal increases the product median size and decreases the period of oscillation. Note that these conclusions may not hold when studying another crystalliser or even the same crystalliser with different operating conditions (Bermingham, 1999). Consequently, the simulations of Runs I through III

viii

are all performed with non-ideal classification, dissolution kinetics and four compartments for the main body.

ideal classification (Sire 2)

classification (Sire. 3) ]

ideal dissolution (Sire. 3) ~dissolution "kinetics (Sim. 4) i

700 500 3OO 5

10

15

20

25

0

3O

I5 Tirm (hrs)

Tin~ (hrs)

l

(Sire.4)~4

(Sim. 5) j

20

30

I---DT (Sire. 1) --DTB (Sire. 5)

7oo.

, 0

5

10

15

20

4000

25

10

15

20

25

30

Tim~ (hrs)

Time (hrs)

Figure 9: Simulated influence of different classification models (top left), dissolution models (top right), compartment structures (bottom left) and of no fines removal (bottom right).

The influence of the dissolution loop volume and the fines withdrawal rate on the product median size is presented in Fig. 10 and 11, respectively. The experimentally observed influence of the dissolution loop volume is minimal, but opposite to the simulated influence, which is also minimal. The average median size of Runs I and II, approximately 680 btm, and the simulated steady state median size of simulations 5 and 6, approximately 640 I-tm, are in good agreement. As regards the dynamics, the periods are also in good agreement but the amplitudes differ significantly. 200 Iitre (Siw_ 5) ~ 10 litre (Sire 6) i

i ~--- 200 litre (Run 1) -- 10 litre (Run II) !

1200 1050

750

450 3001 10

15 Th’ne (hrs)

20

25

30

10

15 Time (hrs)

20

25

30

Figure 10: Experimentally observed (left) and simulated (right) influence of the dissolution loop volume on the median size of the product CSD Comparison of the measured product median sizes of the Runs II and III show a significant increase in amplitude and period and a minor increase in average median size when increasing the fines flow from 2 to 3 l’sq. The simulated median also increases slightly with increasing fines flow. The dynamics are again less pronounced. Moreover, the change in period is opposite to that observed experimentally.

ix

~--2 litre/sec (Sire. 6) ~ 3 litre/sec (Sin-,

--2 litre!sec (Run II) ~3 litre/sec (Run 11I)~ L 1200

1200

10~0

1050 90O 750

750

030 450

450

300

300 5

l0

15

20

25

30

20

25

Titm (h~s)

Figure 11: Experimentally observed (left) and simulated (right) influence of the fines flow rate on the median size of the product CSD

Discussion and Conclusions The predictive capabilities of the presented model framework for DTB crystallisers are good with respect to the average median size, but unsatisfactory as regards the amplitude of the oscillations. The most promising outcome is the fact that the whole model framework only contains two parameters that need to be estimated, and not necessarily on the crystalliser for which the model was derived. The addition of primary nucleation can most probably improve the description of the dynamic behaviour, but doing so introduces new parameters which are not independent of crystalliser scale, type and operating conditions. Acknowledgement The authors express their gratitude to the Dutch Foundation of Technology (STW), Akzo Nobel, BASF, Bayer AG, DOW Chemicals, DSM, E.I. DuPont de Nemours and Purac Biochem for their financial support of the UNIAK research program. References Barnea, E. and J. Mizrahi (1973). A Generalised Approach to Fluid Dynamics of Particulate Systems. Chem. Eng. J., 5, 171. Bermingham, S.K., A.M. Neumann, H.J.M. Kramer, P.J.T. Verheijen, G.M. van Rosmalen and J. Grievink (1999). A design procedure and predictive models for solution crystallisation processes, to be presented at the 5’h International Conference on Foundations of Computer-Aided Process Design, Colorado, USA, 18-23 July 1999. Eek, R.A., H.A.A Pouw, O.H. Bosgra (1995). Design and experimental evaluation of stabilizing feedback controllers for continuous crystallizers. Powder Technology, 82, 21-35. Gahn, C. (1996). The effect of impact energy and the shape of crystals on their attrition rate. J. Crystal Growth, 166, 1058-1063. Gahn, C. and A. Mersmann (1999). Brittle fracture in crystallisation processes. Part B. Growth of fragments and scaleup of suspension crystallizers. Chem Engng Sci., 54, 1283-1292. Herndl, G. (1982). Stoffiibergang in gerahrten Suspensionen, Ph.D. thesis, TU Mtinchen. Kxamer, H.J.M., S.K. Bermingham and G.M. van Rosmalen (1999). Design of industrial crystallisers for a required product quality. J. Crystal Growth., 198/199, 729-737. Miller, S.M. and J.B. Rawlings (1994). Model identification and control strategies for batch cooling crystallisers, AIChE J., 40, 1312-1326. Neumann, A.M., Kxamer, H.J.M., Zhenhua, M., Scarlett, B. (1999). On-line measurement techniques for industrial crystallisation processes. 14~’ Symposium on Industrial Crystallisation, Cambridge, U.K, 12t~’-16t~’. Neumann, A.M., S.K. Bermingham, HJ.M. Kramer and G.M. van Rosmalen (1998). Modelling the dynamic behaviour of a 22 litre evaporative draft tube crystallizer. Proceedings of the International Symposium on Industrial Crystallization, Tianjin, China, 21-25 September 1998. pp. 222-226.