Effect Analysis from Dynamic Regulation of Vacuum Pressure in an

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Ind. Eng. Chem. Res. 2008, 47, 9426–9436

Effect Analysis from Dynamic Regulation of Vacuum Pressure in an Adiabatic Batch Crystallizer Using Data and Image Acquisition Eusebio Bolanõs-Reynoso,*,† Omar Xaca-Xaca,† Jose Alvarez-Ramirez,‡ and Leticia Lopez-Zamora† DiVision de Estudios de Posgrado e InVestigacioń, Instituto Tecnologico de Orizaba, AV. Tecnologico No. 852, Col. Emiliano Zapata, C.P. 94320 Orizaba, Veracruz, Mexico, and Departamento de Ingenieria Quimica, UniVersidad Autonoma Metropolitana-Iztapala, AV. San Rafael Atlixco #186, Col. Vicentina, C.P. 09340, Mexico D.F.

The effect of dynamic regulation of vacuum pressure was analyzed in an adiabatic batch crystallizer using data and image acquisition, virtual instruments, and supervisor control to obtain a controlled vacuum pressure, confirming that the process follows programmed routes in the central computer to obtain both programmed vacuum pressure and cooling dynamic profiles inside the crystallizer (direct design approach). The dynamical regulation profile of vacuum pressure called “adiabatic natural cooling” was able to originate an abrupt cooling effect by adiabatic evaporation inside of the crystallizer (e.g., natural cooling in batch crystallizers operated to atmospheric pressure), benefiting the seeded crystal growth from cane sugar until it reached a size of 732.7 µm (% volume). In turn, the increase in crystal growth, formed mass, and the available supersaturation depletion in the system, contribute to final molasses reduction. From a process dynamics viewpoint, the use of dynamic regulation profiles of vacuum pressure reduces batch time and energy consumption (steam) in the process operation. 1. Introduction Crystallization is a process by which crystals from a solution or a fusion can be formed.1 Much effort that has been devoted to obtaining a quality product in batch crystallizers has focused on studying some kinetics factors, such as nucleation, crystal growth, and aggregation mechanisms. These factors depend on thermodynamics, kinetics (nucleation and growth rate), production-reduction terms (births and death of crystals),2 local and average levels of supersaturation, mixed degrees, impurities, temperature, operation pressures, pH, and solvent type.3 However, the problem of cane-sugar crystallization from an industrial process viewpoint has been rarely studied with an aim to develop first-principle approaches (phenomenological study) as seen in the field of pharmaceuticals, inorganic, amino acids, and proteins crystallization.2,4 Modeling of the growth rate dispersion for sugar-cane crystallization was modeled from first-principles by White et al.5 Some aspects of the secondary nucleation threshold and crystal growth of glucose monohydrate in aqueous solution were studied by Srisa-nga et al.,6 showing that the growth kinetics is linearly dependent on the supersaturation of total glucose in the system when the mutarotation reaction is not rate limiting. Quintana et al.2 and Salcedo et al.7 applied the firstprinciples approach in order to identify the metastable zone limit of cane-sugar crystallization from a saturated solution using a cooling batch crystallizer (glass vessel). They developed an optimal starting procedure from the mathematical modeling, kinetic parameter estimation, and a temperature control to force the process temperature (70-40 °C) to follow an index trajectory as time function (0-180 min). The traditional operation cycle of the industrial cane-sugar crystallization is divided into many sequential phases. During the first stage, the crystallizer is partially filled with a juice that contains dissolved saccharose, which is called mother liquor. * To whom correspondence should be addressed. E-mail: eusebio@ itorizaba.edu.mx. † Instituto Tecnologico de Orizaba. ‡ Universidad Autonoma Metropolitana-Iztapala.

This liquor is concentrated by evaporation to obtain a preset supersaturation value. In this phase, crystals seeds are introduced to induce their growth at low levels of supersaturation and to reduce the effect of spontaneous nucleation (primary).8 In the second phase, the water is evaporated with a constant vacuum pressure and the concentration of mother liquor increases, producing the crystal growth. In the standard vacuum crystallization process, the evaporation takes place and it is necessary to add more mother liquor or hot water to maintain a good level of the supersaturation and to increase the volume. The third phase consists of controlling the evaporation capacity. At the end of the process, the crystallizer is full of a sugar crystal suspension and final molasses (slurry) that are dropped in a storage tank before being centrifuged.9 The current crystallizer control involves the manipulation of feed velocity of sugar liquor and syrup, keeping constant the vacuum pressure for a larger number of batch process.10 It should be emphasized that, in most industrial conditions, the crystallization process for cane sugar is implemented by means of heuristic and traditional procedures that follow handmade recipes without considering the most recent advances developed in the crystallization field; namely, first-principles and rigorous direct design approaches for the supersaturation control.4,11 The first-principles approach for crystallization control has been proposed as an alternative to heuristic industrial procedures, although its implementation in industrial conditions is conditioned by the requirement of a mathematical model built from material, energy, and population balances.4,12 The main idea is to optimize some quantitative and qualitative variables such as temperature and crystal size distribution (CSD)4 among others. An important issue that should be considered for an optimal process operation is the identification of the metastable zone limit that specifies the default region for operating an industrial crystallization to avoid uncontrolled nucleation. The most efficient direct design approaches use a feedback control to follow a setpoint supersaturation curve (sometimes called index function)2,13 in the metastable zone limit.4,11

10.1021/ie071594i CCC: $40.75  2008 American Chemical Society Published on Web 10/30/2008

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To control some factors of influence in the CSD (e.g., temperature, agitation, velocity, and vacuum pressure), as well as to determine the CSD by means of image acquisition,2,14,15 new technological tools have been proposed. These include powerful processors, accurate temperature measurements, image acquisition by high-speed camera and electronic microscopes, signal conditioning, and data interface board (analogical/digital). These technological advances have allowed the development of measurement systems applications, control, and automation both for laboratories and industries.16 Actually, the systems called SCADA (supervisory control and data acquisition) have permitted the design of feedback control applications to different industrial processes and have provided communication with field devices (isolated controllers, PLC, robots, etc.), all of them manipulated from a host computer. On the other hand, as vacuum technologies have witnessed an important advance in the recent decades,17,18 vacuum pressure control inside a crystallizer has become a feasible technology with the implementation of dynamic regulation profiles and image and data acquisition, with a dynamic setpoint in the controller of vacuum pressure. The objective of this work is to make a detailed analysis of dynamic regulation effects of vacuum pressure in an adiabatic batch crystallizer using data and image acquisition. The idea is to characterize the effects of different vacuum pressure policies and conserve a concentration degree (supersaturation) controlled by a programmed route in a computer (direct design approach). In turn, it is expected that the study can lead to a framework to maximize the crystal size and the formed mass and reduce saccharose degree content in final molasses and the energy consumption (steam) in the process. 2. Methodology 2.1. Experimental Equipment. The equipment used was a stainless steel batch crystallizer with heating-cooling jacket (pilot plant), steam boiler, agitation motor, vacuum pump, and velocity investor (also known as velocity frequency driver) for both agitation and vacuum pump motors (Figure 1). The equipment, electronics, and instrumentation devices of the crystallizer are shown in Table 1. The pilot plant integrated a data acquisition system, which is used to follow and control the temperature, and handle the vacuum pressure (both online). An imaging acquisition system to register the crystal size distribution (pseudoline) by means of peristaltic pump, digital camera, and trinocular microscope19 was also implemented (see Table 2). 2.2. Supersaturation Manipulation. Figure 2 illustrates the block diagram for the manipulation of cane sugar supersaturation in the continuous phase, based on vacuum programmed profiles by means of a servo control to obtain a controlled vacuum pressure inside the crystallizer. The system allows the setting of a programmed route of vacuum pressure, which in turn defines in a unique form a cooling trajectory by adiabatic evaporation dynamics around a point of time-varying supersaturation limit. The procedure is based on the results by Quintana et al.,20 who identified the metastable zone limit for cane sugar. For convenience, the results of Quintana et al. were verified by using the equipment described in section 2.1. The concentration profile of cane sugar was carried out to unsaturated, saturated, first metastable, and intermediate zones. Moncada and Rodriguez’s equation20 describes the saturation line: °Brixeq ) -0.0007T 2 + 0.264T + 60.912

(1)

where °Brixeq is the saturation’s concentration at the equilibrium temperature point. The concentration interval of the last equation

ranges from 75.962 to 70.352 °Brix and temperature (T) ranges from 70 to 40 °C. The saturation zones were built according to experimental data and modeled according to the expressions reported by Quintana et al.,20 which have a rigorous support based in firstprinciples approach (kinetics parameter for growth and nucleation rates). The zones are governed by eq (2) considering the following limits:9 Ci ) SCi

(

°Brixi 100 - ° Brixi

)

(2)

where Ci is solute parts/100 solvents parts, °Brixi is solution concentration at specific temperature point, and SCi is specific saturation coefficient to each line: unsaturated (90), saturate (100), maximum limit to first metastable zone limit (120), maximum limit to intermediate zone (130). Hence, the supersaturation is given by: S ) Cexptl - Ceq

(3)

where Cexptl is experimental concentration at g sugar/g water, which is obtained in pseudoline by means of a peristaltic pump and refractometer (°Brix hand-held refractometer Atago) and Ceq is equilibrium concentration yield by eqs 1 and 2 at the saturation point to specific temperature point. 2.3. Dynamic Regulation Strategy of Vacuum Pressure. Preliminary experimental runs were made to obtain an operation strategy for the dynamic regulation of vacuum pressure from crystallization process, using different batch and constant evaporation times. To implement this strategy, a cane sugar solution was prepared with 9235.9 g of commercial sugar and 2922.7 g of water (75.962 °Brix to the saturation temperature of 70 °C) inside the crystallizer, seeding sugar crystal particles with diameter average D(4,3) of 195.3 µm in % volume and standard deviation S(4,3) of 19.52 µm, during the first minute of processing (68 °C and 18 inHg of vacuum pressure). The agitation velocity was set at 225 rpm and remained constant throughout the batch time (90 min). An average constant evaporation (0.2431 g water/sec) took place for 65 °C and 21.2 inHg of vacuum pressure by 30 min, to favor the water retirement, stabilize the batch and benefit the seeded crystals growth. This step is taken to minimize the spontaneous nucleation. After 30 min of processing, one dynamic regulation profile of vacuum pressure was applied during 60 min (designed for this work), causing a cooling trajectory by adiabatic evaporation from 65 to 41 °C (see Figure 3). 2.4. Dynamic Regulation Profiles of Vacuum Pressure. For the generation of “cubic” dynamic regulation profile of vacuum pressure (cubical-type cooling trajectory by adiabatic evaporation), the expression presented by Mayrhofer and Nyvlt21 was used and modified for the specific conditions described in this work; for example, adiabatic batch crystallization (Figure 4). The “linear” and “natural” dynamic regulation profiles of vacuum pressure (linear and natural type cooling trajectories by adiabatic evaporation, respectively) were obtained by means of polynomial adjustments in an interval from 21.5 to 25 inHg (Figure 4). This pressure interval was used by considering operation data reported by factories and bibliography support.9,22 A maximum vacuum pressure of 25 inHg was considered as feasible for operation of batch crystallizers9 and was validated by means of experimental runs. The implemented dynamic regulation profiles of vacuum pressure (inHg) as a time function (tsec in seconds) are (“cubic” profile [Mayrhofer and Nyvlt’s equation,21 modified for this work]):

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cubic profile ) 21.5 +

(

)

((tsec - 1800)) + 1200) 3 (25 - 21.5) 4800 (4)

The modification to Mayrhofer and Nyvlt’s equation21 consisted of suppressing the nucleation to the maximum when there are seeded crystals at the start of the batch. In this form, the initial stage in the Mayrhofer and Nyvlt’s equation21 was eliminated. It should be remarked that the temperature gradient during the initial cooling period is almost null and an energy loss takes place, leading to an unnecessary increase of the batch time and having an excessive nucleation that can reduce the efficiency of the growth stage for the seeded crystal.12 linear profile ) 19.75 + 0.000973tsec

(5)

natural profile ) 25 (6) Figure 4 shows the dynamic regulation profiles of vacuum pressure (eq 4 and 6), representing the indexed trajectories

tracked by the computer controller. The profiles were implemented by means of developed graphical programming with LabVIEW 7.1 (National Instruments, Inc.). The control final action according to dynamic regulation profile of vacuum pressure was generated by means of a velocity investor driver that acts on the process vacuum pump (Table 1). The dynamic regulation profile of vacuum pressure called “adiabatic natural cooling” displays an exponential behavior (Figure 4) because it follows the characteristic curve of maximum frequency from vacuum pump motor. This trajectory is known in the literature as natural cooling at atmospheric pressure.2,7,12,23,24 However, we have developed a new natural type cooling trajectory (profile) by adiabatic evaporation inside the crystallizer (Figures 3 and 4), produced by controlled vacuum pressure. Similarly, the “cubic” and “linear” dynamic regulation profiles of vacuum pressure produced an adiabatic cooling-type cubical and linear environment inside the crystallizer, respectively (Figures 3 and 4).

Figure 1. Vacuum batch crystallizer with integrated data and images acquisition system.

Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9429 Table 1. Electronics and Instrumentation Devices of a Vacuum Batch Crystallizer quantity

devices

1

stainless steel crystallizer of 12.77 L, heating-cooling jacket of 11.10 L, four vertical wall baffles of 17 cm (wide) by 3.5 cm (length), agitation arrow of 39 cm (length) agitator for closed tank, model NSDB of HP, direct transmission of 1750 rpm (1 phase, 60 cycles), 110 VCA totally closed, without ventilation, stainless steel 316 with bridle of 4 in. (diameter) in stainless steel, with agitating arrow of 26 in. (length) and 1/2 in. of diameter in stainless steel 316; velocity investor (driver) integrated with rank from 0 to 1750 rpm impeller marine type of 3 in. (diameter) with three blades of stainless steel 316 impeller flat palettes type of 3 in. (diameter) of stainless steel 316 thermocouple J type; temperature from 0 to 760 °C; wire length, 1 m hydraulic pump, model QB60 of Clean Water Puma; power, 1/2 HP for 127 VCA (1 phase), 3450 rpm, 35 L/min of capacity with 1 in. of input and output thermo-wells of 1 in. (NPT inlet diameter) in stainless steel heat insulation for high temperature made with glass fiber, 1 1/2 in. of thickness (18 kg of density) and steam barrier of aluminum foil paper; finished with aluminum blade of caliber 26, smooth, bevelled and it holds with galvanized wire; capacity of 80-150 °C vacuum pump, model FE-1400 of Felisa, power 0.33 HP and 0-60 Hz of frequency velocity investor (driver), model cat. 1305-AA04A-ES-HA2 series C of Allen-Bradley, 0.75 KW/1 HP steam boiler, model MBA9 of SUSSMAN; maxim pressure, 100 Psi; work voltage, 240 VAC; control voltage, 120 VAC thermodynamic trap of 1/2 in. NPT galvanized pipe system of 1/2 in. (diameter) for the circulation of heating-cooling water pressure controller valve (Norgren) of 1/2 in., with 21 Kg cm-2 of maxim input and 9 Kg cm-2 of maxim unloading stainless steel condenser, input of 1/2 in. and output of 1/4 in., with 27 in. (length) by 4 in. (diameter) plastic tank of 1100 L, with spiral cove stainless steel humid trap, with 13 in. (length) by 3 in. (diameter); input, output, and purge of 1/2 in.

1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1

Table 2. Electronics Devices for Data and Images Acquisition System quantity

devices

3

data acquisition hardware: PCI-6229M, PCI-6023E, and PCI-6025E. National Instruments, Inc. images acquisition hardware: PCI-1407. National Instruments, Inc. shielded carriers modules: SC-2345. National Instruments, Inc. shielded I/O connector block for DAQ: SCB-68. National Instruments, Inc. signal conditioning modules: 2 SCC-TC02 and 2 SCC-CI20. National Instruments, Inc. shielded terminal block: SCB-100. National Instruments, Inc. vacuum pressure transmitter, model 07356-02. Cole Parmer. professional compound microscope: 48923-30; trinocular. Cole Palmer. monochrome camera with video RS-170. Lens: 0.19 mm by pixel. National Instruments, Inc.

1 1 1 2 1 1 1 1

2.5. Virtual Instrument. Program “vacuum_regulation.vi” developed for this work using LabVIEW 7.1 (National Instruments, Inc.) is an interface of supervisory control and data acquisition (SCADA) that takes as its basis the program called “SCADA.vi”, whose aim is to acquire both vacuum pressure and temperature data and control the process through the dynamic regulation profiles of vacuum pressure and agitation trajectories. Program “vacuum_regulation.vi” consists of two parts: (a) a frontal panel, which is a virtual control board that contains both control and indicators buttons for each function, and (b) the block diagram that is integrated by the “G” graphical programming code of the developed system. These computer programs simplify the study of dynamic behavior of the canesugar crystallization process. 2.6. Images Acquisition System and CSD Calculation. For the pseudoline measurement at every sampling time of the experimental runs and its particles analysis (crystals) through captured images, the software IMAQ Vision Builder (National Instruments, Inc.) was used. This image approach is an alternative in measuring both length and area of particles in a direct way through IMAQ Vision’s software. The technique consists of acquiring an image using a monochromatic camera with video RS-170 and 60 Hz crisscross (8 bits of resolution) and handling the light beam from a microscope trinocular. The sample is transported from crystallizer to the imaging acquisition system by means of a peristaltic pump running at 1500 rpm.

The camera captures an image square that is to be processed and cleaned. This avoids undesirable light variations. The latter is achieved through the threshold technique that allows obtaining only an image in gray scale. Interesting areas are isolated to be independently analyzed, and black pixels (crystals) are counted. The black pixels are compared with acceptation limits to decide if the object is present or not according to binary images (background).25 Then, a threshold technique approach, similar to that reported in further multiscale segmentation image approach, was used to compute the CSD features.14,15 The measurements and analysis of particles were carry out against a previous calibration through a Neubauer’s recount camera (simple calibration) in order to get a direct conversion from 1 pixel (one pixel side) to 200 µm (length). A pixel is defined as the smallest homogeneous unit in color that is part of the digital image. The pixels appear as small squares in white, black, or gray shades (htpp://es.wikipedia.org/wiki/Pixel). In this work, a microscope with a 10× ocular lens with a 40× objective and an E square from Neubauer’s camera from 50 µm away, were used. This is equivalent to 20000 µm (10 × 40 × 50) per 100 pixels (length of pixel side). Thus, 1 µm is equal to 0.005 of the length of a pixel side.26 There are different approaches for CSD measurements and analysis, such as microscopy (electronic and handle), captured image by camera, electrozone sensing, and low angle laser light scattering (LALLS). Every technique can generate different measures of average diameter, as well as different properties of a particle. The suitable approach depends on the problem and on the available data.19 Therefore, different approaches allow different ways to directly obtain average numbers: microscopy produces D(1,0) (length), captured image by camera yields D(2,0) (superficial area), electrozone sensing gives D(3,0) (volume), and LALLS produces D(4,3) (equivalent volume). For this work, the program CSD Adq-Im26 was developed to make CSD complementary calculations to those of the IMAQ Vision Builder system. Our software CSD Adq-Im26 receives the crystal length in micrometers from IMAQ system as input data. Then, CSD Adq-Im26 makes the relationship between the direct measurement D(1,0), considering our results as the microscopy approach, and the derivate measurement D(2,1) produced by LALLS. Later on, the derivative diameters D(3,2), D(4,3), and D(1,0) are calcuated from each log-normal distribution of relative frequency from the LALLS approach. The latter


Figure 2. Open-loop control algorithm for supersaturation, using dynamic regulation profiles of vacuum pressure.

Figure 3. Strategy for implementation of dynamic regulation profiles of vacuum pressure.

approach (LALLS) obtains the derivative average diameter without necessarily requiring the particles total number from the slurry or solution at study. Finally, CSD Adq-Im26 carries out the calculations to obtain % number, % length, % surface, % volume, and others statistical properties from log-normal distributions of relative frequency, such as mean and standard deviation, distribution moments (considering the particle like a sphere),27 and calculations of average diameter (volume, area, length, number) and its deviations (variance) as well as the total number of particles (particles/cm3 mother liquor) from zero moment of the distribution, and both undersize and oversize graphics. The calculations were made following the mathematical formulism given by Marlven Instruments, Inc.28 with its commercial equipment of particle analysis based on low angle laser light scattering (LALLS). Figure 4. Dynamic regulation profiles of vacuum pressure.

3. Results and Discussion The virtual instruments development in software LabVIEW 7.1 of National Instruments, Inc. and the SCADA system implementation on the process has contributed to the phenomenologic study of adiabatic batch crystallization of cane sugar with dynamic regulation of vacuum pressure. From the planned strategy described in the methodology section, the metastable zone limit, CSD and formed crystal mass (FCM) were analyzed to study the system dynamic behavior and determine the operation conditions that improve both the crystal size and the amount of formed crystal mass. 3.1. Effect Analysis from Dynamic Regulation of Vacuum Pressure and Adiabatic Cooling. Figure 5 presents the behavior of the experimental runs, where it is observed that experimental routes of dynamic regulation of vacuum pressure follow in a favorable way the programmed routes as dynamic setpoint in the process central computer. Interferences and noise are observed in the vacuum pressure measurement mainly because of both electronic and mechanical noise (Figure 5a,c,e). This noise is caused by the velocity investor driver linked to

the vacuum bomb and the equipment vibration for agitation effects. Although some measurement and mechanical noise is observed in the vacuum pressure signal, it is poorly propagated into the temperature trajectory. This allows the damping of the measurement noise effects in the experimental CSD, which is corroborated by the results in Figure 5 that show only small deviations of the experimental trajectory inside the crystallizer for each of the three adiabatic cooling profiles produced by the dynamic regulation profiles of vacuum pressure. Notice that the interferences and noise at vacuum pressure are not transferred into adiabatic cooling profiles. Therefore, it can be considered that the absence of noise at the temperature profiles should lead to insignificant disturbances at supersaturation and the spontaneous nucleation effects will not be present in the crystallization. This is verified through both concentration zones in Figure 6d, which illustrates that the process has not achieved the second metastable zone limit (nuclei production and crystal growth zone). In this form, only the seeded crystal grew, as shown in Figure 7a,b,c, in bimodal distributions that could be related


Figure 5. Dynamic regulation profiles of vacuum pressure and adiabatic cooling: (a,b) cubic, (c,d) linear, and (e,f) natural.

to a spontaneous nucleation effects. Notice that the temperature trajectories for linear and cubic pressure cases are very similar, which reflects the fact that the corresponding pressure trajectories are quite similar. However, this is not a general feature of the crystallization process as is shown in Figure of the Appendix A where the temperature trajectory follows more closely the linear trajectory of the vacuum pressure. The dynamic regulation strategy of vacuum pressure (adiabatic cooling) reduces the batch time with regard to cooling batch crystallizations worked at atmospheric pressure2 due to the effect of 30 min of constant water evaporation (21.5 inHg, 65 °C). The energy consumption in the process operation decreases because of steam requirement is null during the cooling by adiabatic evaporation from 65 to 41 °C (21.5-25 inHg). 3.2. Concentration and Formed Crystal Mass Analysis. Figure 6 panels a and b illustrate the effect of dynamic regulation profiles of vacuum pressure (and its corresponding adiabatic cooling) over the concentration and formed crystal mass, respectively. Figure 6a shows that the “natural” dynamic regulation profile of vacuum pressure (adiabatic natural cooling) exhausts faster than the sugar concentration into the solution (from 3.16 to 2.43) than the “cubic” and “linear” dynamic regulation profiles of vacuum pressure. It is apparent that the adiabatic natural cooling profile presents

cooling rates higher than the other profiles due to the abrupt change of vacuum pressure (from 21.5 to 25 inHg in step form). Probably, this abrupt change induces a sharp change at the evaporation point of the substance that will originate higher evaporation rates, producing in this way a high concentration in the solution phase. Figure 6b shows that the FCM trajectory is very similar for each one of profiles in study during the first 30 min of constant evaporation (at 21.5 inHg). With the introduction of dynamic regulation profiles of vacuum pressure (from 30 to 90 min), differences are observed in the FCM trajectories. The operation conditions given for a“natural” dynamic regulation profile of vacuum pressure allowed the process to obtain the largest quantity of formed mass (4865.1 g) at the final batch time. Experimental data replication is shown in Appendix A. 3.3. Supersaturation and Concentrations Zones Analysis. Figure 6panels c and d illustrate the effect of dynamic regulation profiles of vacuum pressure over supersaturation and concentrations zones, respectively. Figure 6c shows a tendency that is similar for all supersaturation profiles, where supersaturation degree was depleted almost completely. The final point from the “natural” dynamic regulation profile of vacuum pressure (adiabatic natural cooling) presents a small value of supersaturation available. This indicates the existence of solute to be transferred into the seeded crystal growth. In


Figure 6. Effect of dynamic regulation profile on characteristic variables: (a) concentration, (b) formed crystal mass, (c) supersaturation, (d) concentrations zones, (e) crystal average diameter, and (f) standard deviation.

Figure 7. Percent volume from log-normal crystal size distribution: (a) cubic, (b) linear, and (c) natural.

fact, the larger possible depletion of supersaturation in the crystallization system (next to zero) contributes to the decrease of the sucrose amount in the final molasses of processing. Notice the abrupt temperature decrease at about 30 min in the natural cooling experiments, which is caused by a corresponding vacuum pressure increase to achieve a preset supersaturation range inside the first metastable zone limit. In turn, this promotes the growth of the crystal seed at the process starting and, consequently, avoids the undesired spontaneous nucleation. It is apparent that the crystal growth dampens the fast temperature trajectories (induced by the

vacuum pressure trajectories). Moreover, the relatively slow sugar cane mass transfer process reduces the adverse effects of temperature abrupt changes. Figure 6d shows that all concentration profiles are inside of the first metaestable zone (very close to the saturation line), allowing the seeded crystal growth and avoiding the spontaneous nucleation (primary). It has been pointed out that this process promotes the maximization of solute transfer from the continuous phase to the crystal face of cane sugar where integration and reaction rates take place).27,29,30 Data replication is shown in Appendix A.


Figure 8. Crystal growth sequence; “natural” dynamic regulation profile of vacuum pressure.

3.4. Crystal Size Distribution Analysis. Figure 6 panels e and f show the effect of dynamic regulation profiles of vacuum pressure over the crystal average diameter D(4,3) in % volume and its standard deviation S(4,3), respectively. Figure 6e illustrates that “natural” dynamic regulation profile produces a D(4,3) of 732.7 µm with S(4,3) of 78.1 µm, this being the largest crystal size originated by the profiles in this study. The “cubic” and “linear” dynamic regulation profiles of vacuum pressure produces a D(4,3) of 567.8 µm with S(4.3) of 64.1 µm, and of 585.2 µm with S(4.3) of 69.5 µm, respectively. Figure 7 presents the % volume experimental data, which suggest a log-normal crystal size distribution. Regarding the crystal average diameter for each one of the samplings carried out during the process, it is observed that the % volume from distributions has a favorable increase for each one of the implemented profiles, with certain irregularities due to the nonlinearity of the process. Figure 7c illustrates that the “natural” dynamic regulation profile of vacuum pressure presents 75% of the crystal distribution of the largest produced size (732.7 µm). This means that 75% of formed crystals have an average size from 732.7 µm at the end of batch time. Note from Figure 6e that a “switch back” is present around 400 µm (minute 45) and the % volume has three different values for the same particle size. This is possible because each point has three different standard deviations, producing different % volume from their specific log-normal distribution (Figure 7). Therefore, from the results analysis, it is established that the operating conditions from the “natural” dynamic regulation profile of vacuum pressure represents the most viable route to follow for the process according to the strategy described in sections 2.3 and 2.4. For this work, we have used the volume-weighted diameter (D(4,3) in % volume) for characterizing the suitability of a

crystal product because this diameter gives a reference close to industrial parameter D(3,0) called volume medium diameter (VMD); nevertheless, the last diameter VMD requires knowledge of the total number of particles to be characterized,19 which is frequently unknown. The volume-weighted diameter criterion has the deficiency of being insensitive to the fines density31 and could leave incorrect results when comparing supersaturation profiles. However, cane sugar crystallization at the industrial level is made without considering fines particles because seeded particles exist (small sugar crystals) since start of the process. Its target is to make the seeded crystals grow, avoiding the spontaneous nucleation. Therefore, most of the modeling of the industrial crystallizer for control and design purposes at cane sugar crystallizations consider the fines particles as insignificant and continue using the volume-weighted diameter criterion to characterize the suitability of a crystal product.20,32,33 3.5. Crystal Growth Sequence Analysis. From these images, the area in pixels was determined by means of IMAQ vision Builder software and subsequently converted into micrometers by means of Adq-im software as described in section 2.6. Figure 8 shows the crystal growth sequence obtained by the image acquisition system IMAQ Vision Builder of National Instruments, Inc. linked to an trinocular microscope (objective 4×), through samplings in the sugar crystallization process using the “natural” dynamic regulation profile of vacuum pressure. It is observed that the seeded crystal grows without presenting agglomerates and conserves the monoclinic form that characterizes the crystal shape.25 This suggests that agitation velocities at about 225 rpm are the appropriate ones for the crystallization system. 3.6. Discussion. Previous work on the crystallization polar substances such as ammonium sulfate, potassium chloride


Figure A.1. Replication dynamic regulation profiles of vacuum pressure and adiabatic cooling: (a,b) cubic, (c,d) linear, and (e,f) natural.

among others salts,12,34-36 has shown that larger crystals are formed for lower cooling rates. The underlying crystallization mechanisms present kinetics where growth and nucleation rates are very fast (mass transference of continuous phase to crystal), producing nuclei and growth itself inside a thin metastable concentration zone originated by a small permissible temperature range. If these crystallization processes increase their temperature range, they have the risk of going to an unstable concentration zone, where a spontaneous nucleation is produced.12,20 In this work, we have shown that controlling vacuum pressure is feasible to yield adiabatic cooling profiles at batch crystallizers with seeded cane sugar particles. We have found more and larger crystals on average form for the most rapid adiabatic cooling (natural). Some specific physiochemical properties of cane sugar support this finding, such as the relatively slow mass transference of continuous phase to crystal that is very slow due to resistances caused by an integration reaction and diffusiveconvective effects at the surface of growing crystals.13 Also, macro-resistances should be considered when viscosity increases from a temperature decrease effect. Although resistances quantification goes beyond of scope of this work presented, we consider that the mass transfer coefficient will be small (higher

resistances) and they will determine that mass transfer to face crystal of cane sugar will be too slow. Our result could be surprising when we have quantified more crystals and larger crystals on average from the most rapid adiabatic cooling (natural). 4. Conclusions Vacuum batch crystallization represents an alternative to achieving supersaturation in a system without modifying the solute properties by temperature effect. With the identification and configuration of control final elements, the implementation of the dynamic regulation profiles of vacuum pressure was achieved in the process through the SCADA system. The designed control configuration allowed maintaining the batch crystallizer inside a programmed route of vacuum pressure, producing adiabatic cooling profiles. From experimental runs analysis, it is concluded that the “natural” dynamic regulation profiles of vacuum pressure represents the route of more viable operation because it produces the largest crystal size (732.7 µm) with acceptable distribution (75%) and formed crystal mass amount (4865.1 g), contributing to depletion of final molasses


Figure A.2. Replication effect of dynamic regulation profile on characteristic variables: (a) concentration, (b) formed crystal mass, (c) supersaturation, (d) concentrations zones, (e) crystal average diameter, and (f) standard deviation.

from the process. Thus, the dynamic regulation strategy of vacuum pressure reduces the batch time and the energy consumption (steam) in the process operation. Acknowledgment The authors acknowledge the financial support of Fondo Mixto Conacyt-Gobierno del Estado de Veracruz (Fomix Veracruz), project 37571, and Direccion General de Educacion Tecnologica (DGEST)-Instituto Tecnologico de Orizaba (ITO), project 478.05_P, Universidad Autonoma Metropolitana-I (UAMI). We thank Oscar Velazquez Camilo (Conacyt’s PhD. scholarship) from UAM-I for his comments and collaborations in this paper. Appendix A. Measurement Noise Effect An interesting question is whether or not the unavoidable measurement and mechanical noises have a significant effect on the performance of the trajectory tracking. Figure 5 showed that the proposed strategy performs well for a piecewise linear trajectory. To illustrate that the measurement noise, as obtained with the technological devices nowadays, is within a reasonable band, we have duplicated the results in Figure 5 for three different trajectories (e.g., cubic, piecewise linear, and natural).

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ReceiVed for reView November 23, 2007 ReVised manuscript receiVed September 10, 2008 Accepted September 17, 2008 IE071594I

Effect Analysis from Dynamic Regulation of Vacuum Pressure in an

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