Simulated Moving Bed Technology
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1.1. Continuous counter current chromatography
Continuous industrial-scale adsorption processes are well known for their efficiency. Very often, the Height Equivalent of a Theoretical Plate (HETP) in a batch operation is roughly three times higher than one find for the continuous mode (Gembicki et al., 2002). The operation of continuous chromatographic counter current apparatus (here-by referred as True Moving Bed, TMB) in particular, maximizes the mass transfer driving force providing a better utilization of the adsorbent, and thus, allowing the use of lower selectivity materials (Ruthven and Ching, 1989) as to operate with an increased productivity (i.e., higher processed throughput using less packing material). A scheme of a TMB unit is shown in Figure 1.
Figure 1 - A four section True Moving Bed (TMB) unit for the separation of A and B with D as eluent or desorbent (Fructose/Glucose separation).
If we define section as the part of the TMB unit where the fluid flow rate is approximately constant (section limited by inlet/outlet streams), then, it is possible to find four different sections with different roles:
- Section I: Regeneration of the adsorbent (desorption of A from the solid);
- Section II: Desorption of B (so that, the extract is not contaminated by the less retained component);
- Section III: Adsorption of A (raffinate clean from the more adsorbed species);
- Section IV: Regeneration of the eluent/desorbent (adsorption of B from the fluid phase).
From Figure 1, one can observed that the counter-current movement of the solid, with respect to the fluid phase, allows continuous regeneration of both the adsorbent in section I as the eluent/desorbent in section IV. Also, the moving bed arrangement allows the achievement of high purity even if the resolution of the two peaks is not excellent, since only the purity at the two tails of the concentration profiles, where the withdrawal ports are located, is of interest. This is contrary to batch chromatography where high resolution is vital in order to achieve high purity.
Nevertheless, with this counter current mode of operation is necessary to circulate not only the fluid phase but also the solid. The solid motion inside of the column and the consequent recycle presents some technical problems, namely: equipment abrasion, mechanical erosion of adsorbent and difficulties in maintaining plug flow for the solid (especially in beds with large diameter). From a technical point of view, this clearly limits the implementation of such technology.
1.2. The Simulated Moving Bed (SMB) concept
In order to avoid this issue, a sequence of fixed bed columns was conceived (Broughton and Gerhold, 1961) in which the solid phase is at rest in relation to a fixed referential, but where a relative movement between both phases is experienced by switching the inlet and outlet fluid streams to and from the columns from time to time (in the direction of the fluid flow). In the simplest operating mode, the period that a certain operating configuration prevails is called the switching time, . Since the solid flow is avoided, although a kind of counter-current movement is created relatively to the fluid, this technology is called Simulated Moving Bed (SMB).
Consider that at certain moment in the operation of an SMB, the positions for the inlet of feed and desorbent and outlet of products is represented by Figure 2a. Assume also the simplest operating mode (synchronous advance of all streams) and one column per section. After a period of time equal to the switching time, the injection and withdrawn points all move one column in the direction of the fluid flow (Figure 2b). When the initial location of injection/collection of all the streams is reencountered, we have completed one cycle (in a four equally zoned SMB, it takes to complete one cycle, where is the number of columns in each one of the four sections). As it is possible to see in Figure 2, during one cycle the same column is in different sections, assuming therefore different roles in the separation process.
Figure 2 - Schematic representation of a 4 columns SMB unit operating over a complete cycle, from 0to (with representing the ports switching time); (a) period of the first switch; (b) period of the second switch and (c) a TMB unit.
As mentioned before, the continuous movement of inlet and outlet lines into and from the column is almost impractical, therefore discreet jumps (with the length of one bed, during ) have to be applied.
The analogy between SMB and the TMB is then possible by the introduction of the relative velocity concept, where , with the fluid interstitial velocity in each section in the TMB, the interstitial velocity in the SMB unit and the solid interstitial velocity in the TMB. The solid velocity is evaluated from the switching time interval value in the SMB as , being the column length. As consequence, The internal flow rates in both apparatus are not the same, but related by where and represent the internal liquid flow-rates in the SMB and TMB, respectively, is the bulk porosity and the column volume.
1.3. SMB Applications
Industrially, SMB applications can be regarded as “Old” and “New”, associated with petrochemical and pharmaceutical/fine chemistry fields, respectively (Sá Gomes et al., 2006d). Among the first applications of SMB technology (back to 1960s) are the ones implemented by the UOP Inc. (Des Plaines, IL-USA) with the Sorbex® processes, such as: the Parex® unit for separation of p-xylene from mixtures with its C8-isomers (Broughton et al., 1970), separation also performed by the Aromax® process from Toray Industries (Tokyo, Japan) (Otani et al., 1973) and the Eluxyl® process by Axens/IFP (Institut Français du Pétrole, France) (Ash et al., 1994); the Ebex® for the separation of EthylBenzene (EB) from a mixed of C8-aromatic isomers (Broughton, 1981); the Molex® for the separation of n-paraffins from branched and cyclic hydrocarbons; and the Olex® process to separate olefins from parafins; the Cresex® and Cymex® for the separation of p-cresol and p-cymene from its isomers, respectively.
The application of SMBs in the sugar industry is also substantial, with the Sarex® process, for the separation of fructose from the corn syrup with dextrose and polysaccharides on polystyrene-divinylbenzene resins in calcium form (Broughton, 1983); or as patented by Japan Organo Co. (Japan), (Heikkilä et al., 1989); by Amalgamated Sugar Company LLC, also known as the Snake River Sugar Company (Boise, ID-USA), (Kearney and Mumm, 1990, , 1991).
In the last decade, particularly in the area of drug development, the advent of SMB has provided a high throughput, high yield, solvent efficient, safe and cost effective process option. Although it had long been established as a viable, practical, and cost-effective liquid-phase adsorptive separation technique, the pharmaceutical and biomolecule separations community did not show considerable interest in SMB technology until the mid-1990s. The application of the SMB concept to the fine chemical separations in the earlier 90s, led to the second “boom” on the number of applications of SMB technology (Negawa and Shoji, 1992; Nicoud et al., 1993; Kusters et al., 1995; Rodrigues et al., 1995; Cavoy et al., 1997; Francotte and Richert, 1997; Guest, 1997; Pais et al., 1997a; Pais et al., 1997b; Francotte et al., 1998; Grill and Miller, 1998; Lehoucq et al., 1998; Pais et al., 1998; Dapremont et al., 1999; Miller et al., 1999; Nagamatsu et al., 1999; Nicoud, 1999a, 1999b; Pedeferri et al., 1999; Strube et al., 1999; Juza et al., 2000; Kniep et al., 2000; Wang et al., 2001), among other “pioneers”.
Daicel Chemical Industries, Ltd (Japan) first published the resolution of optical isomers through SMB (Negawa and Shoji, 1992). Since then, several are the SMB based processes already approved by the Food and Drug Administration (FDA) and others regulatory agencies. Examples includes renowned products such as: Biltricide (Praziquantel) Cipralex/Lexapro (Escitalopram), Keppra (Levetiracetam), Modafinil/Provigil, Taxol (Paclitaxel), Xyzal (Levocetirizine), Zoloft (Sertraline), Zyrtec (Cetirizine), Celexa/Citrol/Cipram (Citalopram), Prozac (Fluoxetine hydrochloride), (Abel and Juza, 2007) o paper de real SMB e rajendran, among others biological separation, with a particular emphasis in protein separations meteer referencias a biologias e proteinas.
Given the importance of such technique, this work reviews different operating SMB modes; design, modeling and optimization techniques; and addresses an example of the design, construction and operation of an SMB unit.
2. SMB modes of operation
So far, only the so-called conventional SMB mode of operation has been considered, which indeed means that each section has a fixed number of columns and there is no variation on the pre-established inlet/outlet flow rates or the switching time value. However, over the last decades some non-conventional SMB operating modes were proposed, developing the range of the applications of SMB technology and extending further its potential. Some of these operating modes, worthy of note, are listened in the following Sections.
2.1. Asynchronous shifting SMB (the Varicol® process)
The asynchronous shifting SMB or Varicol® process (Adam et al., 2000; Bailly et al., 2000; Ludemann-Hombourger et al., 2000; Ludemann-Hombourger et al., 2002) commercialized by Novasep (Pompey, France), became one of the more studied and used processes of the so-called non-conventional SMB modes of operation. Instead of a fixed unit configuration with constant section length, the Varicol® operating mode is performed by the implementation of an asynchronous inlet/outlet ports shift, providing a flexible use of each section length, Figure 3.
Figure 3 - [11.51.51] Asynchronous SMB for a complete cycle; section II has 1 column during the first half of the switching time and 2 columns in the remaining time (within a switching time period), thus 1.5 columns; the opposite happens to section III.
By means of Varicol® mode of operation it is possible to increase the productivity value up to 30% more than the classical SMB apparatus, principally when operating under a reduced number of columns (Toumi et al., 2002; Zhang et al., 2002b; Pais and Rodrigues, 2003; Subramani et al., 2003b, 2003a; Toumi et al., 2003; Yu et al., 2003b; Sá Gomes et al., 2006d; Mota et al., 2007b; Rodrigues et al., 2007a; Sá Gomes et al., 2007b; Zhang et al., 2007).
2.2. Partial-Feed, Partial-Discard
With the Partial-Feed mode of operation two additional degrees of freedom are introduced: the feed length and the feed time (Zang and Wankat, 2002a; Zang and Wankat, 2002b). Feed during a given feed length period will consequently influence the raffinate and extract flow rates are along the time. Also referred in the literature is the Partial-Discard (or partial withdraw) operating mode, where just a part of the outlet products is used in order to improve the overall purity (Zang and Wankat, 2002b; Bae and Lee, 2006), or with the partial recirculation of the outlet products back to the feed (Kessler and Seidel-Morgenstern, 2008a; Kessler and Seidel-Morgenstern, 2008b; Seidel-Morgenstern et al., 2008).
The ISMB (Improved SMB) mode of operating, commercialized by the Nippon Rensui Co. (Tokyo, Japan) and FAST - “Finnsugar Applexion Separation Technology”, now Novasep-France, is also well known (Tanimura et al., 1989). In this process, during a first step the unit is operated as a conventional SMB but without any flow in section IV; in the second step the inlet and outlet ports are closed and the internal flow through the four sections allowing the concentration profiles to move to adjust their relative position with respect to the outlet ports (Rajendran et al., 2009). Meter referencias do mazzotti e nova de sa gomes
Another novel non-conventional mode of operation, the Outlet Swing Stream-SMB (OSS) (Sá Gomes and Rodrigues, 2007), was developed under the framework of this thesis and is latter detailed in Chapter 3.
2.3. PowerFeed and ModiCon
The modulation of the section flow rates (PowerFeed) was originally proposed by Kearney and Hieb (1992) and later studied in detail by other authors (Kloppenburg and Gilles, 1999b; Zhang et al., 2003b; Zhang et al., 2004b; Kawajiri and Biegler, 2006b). Another SMB operating concept, based on the feed concentration variation within one switching interval, was suggested by Schramm et al., (2002; 2003b) known as the ModiCon. The use of auxiliary feed tanks, where section flow rate flows into a tank to dissolve solid raw materials and fed into section III, has also been studied (Wei and Zhao, 2008). The cross combination of PowerFeed, Modicon and Varicol modes of operation is also a recurrent research matter, principally of optimization studies (Zhang et al., 2004a; Arau?jo et al., 2006a; Rodrigues et al., 2007b), providing more degrees of freedom and allowing better performance values.
2.4. Two Feed or MultiFeed SMB and Side Stream SMB
Recently, the introduction of multi feed streams in the SMB area, by analogy with distillation columns, led to the formulation of the Two Feed SMB, or MultiFeed, operating mode presented by Kim (2005) and later studied by Sá Gomes and Rodrigues (Sá Gomes et al., 2007b; Sá Gomes and Rodrigues, 2007). Also multi extract/raffinate are referred in the literature (Mun, 2006), known as side stream SMB (Beste and Arlt, 2002). These techniques, combined with the distillation know-how for the optimum location of multiple feeds, can allow the development of more efficient SMB processes.
2.5. Semi Continuous, Two and Three zones SMB
There are several semi continuous SMB apparatus that operate with two-zone, two or one-column chromatograph, with/or recycle, analogous to a four-zone SMB(Abunasser et al., 2003; Abunasser and Wankat, 2004; Arau?jo et al., 2005a; Arau?jo et al., 2005b; Jin and Wankat, 2005b; Mota and Arau?jo, 2005; Arau?jo et al., 2006b; Arau?jo et al., 2007; Rodrigues et al., 2008b), that allow a reasonable separation, some allowing centre cut for ternary or quaternary separations (Hur and Wankat, 2005b, 2005a, , 2006a, 2006b; Hur et al., 2007), under reduced equipment usage.
The discontinuous injection in a system with 2 or more columns, based on the concept of simulated adsorbent movement, as been applied by Novasep under the denomination of Cyclojet®, Hipersep®, Supersep™ (Supersep MAX™ with Super Critical CO2) and Hipersep®, (Grill, 1998; Valery and Ludemann-Hombourger, 2007).
2.6. Gradient SMB
As a further possibility for increasing the productivity, the introduction of gradients in the different separation sections of the SMB process is also described in literature. The gradient mode was suggested firstly for the SMB-SFC (SMB-supercritical fluid chromatography) process, where the elution strength can be influenced by a pressure gradient (Clavier and Nicoud, 1995; Clavier et al., 1996). Nowadays, there are more gradient-variants that allows the variation solvent elution strength by changing the temperature, the pH-value, the content of salt or the modifier concentration (Jensen et al., 2000; Antos and Seidel-Morgenstern, 2001; Migliorini et al., 2001; Abel et al., 2002; Antos and Seidel-Morgenstern, 2002; Abel et al., 2004; Ziomek and Antos, 2005; Mun and Wang, 2008a), or as in Rodrigues's group with the purification of proteins by Ion Exchange-SMB (IE-SMB) (Li et al., 2007; Li et al., 2008). Also worth of note is the MCSGP (Multicolumn Counter-current Solvent Gradient Purification) process (Aumann and Morbidelli, 2006; Strohlein et al., 2006; Aumann and Morbidelli, 2007; Aumann et al., 2007; Aumann and Morbidelli, 2008; Müller-Späth et al., 2008), commercialized by ChromaCon AG (Zürich, Switzerland), which combines two chromatographic separation techniques, the solvent gradient batch and continuous counter-current SMB for the separation of multicomponent mixtures of biomolecules.
2.7. Hybrid-SMB: SMB combined with other processes
It is possible to improve the performance of SMB units by integrating it with other different separation techniques. The more simple application of this approach is to combine in series the two different processes and then recycle back the outlets between (or within) the different units (Lorenz et al., 2001; Amanullah et al., 2005; Kaspereit et al., 2005; Amanullah and Mazzotti, 2006; Gedicke et al., 2007). Among these, an interesting hybrid SMB was presented by M. Bailly et al., (2005; Abdelmoumen et al., 2006), the M3C process; or the similar process: Enriched Extract operation (EE-SMB) (Paredes et al., 2006), in which a portion of the extract product is concentrated and then re-injected into the SMB at the same, or near to, the collection point. The use of SMB-PSA apparatus is also referred in the literature for gas phase separations, (Rao et al., 2005; Sivakumar, 2007; Kostroski and Wankat, 2008). The use of two SMB units with concentration steps between, for the separation of binary mixtures, was also developed under the denomination of hybrid SMB-SMB process (Jin and Wankat, 2007a).
2.8. The SMBR multifunctional reactor
The integration of reaction and separation steps in one single unit has the obvious economical advantage of reducing the cost of unit operations for downstream purification steps. Besides reactive distillation, reactive extraction or membrane reactors, the combination of (bio)chemical reaction with SMB chromatographic separator has been subject of considerable attention in the last 15 years. This integrated reaction-separation technology adopts the name Simulated Moving Bed Reactor (SMBR). Several applications have been published considering the SMBR: the enzymatic reaction for higher-fructose syrup production (Hashimoto et al., 1983; Azevedo and Rodrigues, 2001; Borges da Silva et al., 2006; Sá Gomes et al., 2007a); meter a dos FOS the esterification from acetic acid and -phenethyl alcohol and subsequent separation of the product -phenetyl acetate (Kawase et al., 1996), or methyl acetate ester (Lode et al., 2001; Yu et al., 2003a); the synthesis and separation of the methanol from syngas (Kruglov, 1994); the esterification of acetic acid with ethanol (Mazzotti et al., 1996b); the lactosucrose production (Kawase et al., 2001); the MTBE synthesis (Zhang et al., 2001); the diethylacetal (or dimethylacetal) synthesis (Silva, 2003; Rodrigues and Silva, 2005; Silva and Rodrigues, 2005a; Pereira et al., 2008); the ethyl lactate synthesis from lactic acid and ethanol (Pereira et al., 2009a; Pereira et al., 2009b); the biodiesel synthesis (Geier and Soper, 2007) falta uma; or the isomerization and separation of p-xylene (Minceva et al., 2008) faltam os franceses, are examples that prove the promising potential of this technique. Depending on the reactive system some interesting arrangements of the general SMBR setup can be found in the literature, a more detailed review of several SMBR applications can be found elsewhere (Minceva et al., 2008).
2.9. Multicomponent separations
The application of SMB technology to multicomponent separations has also been an important research topic in the last years. The common wisdom for such multicomponent process is the simple application of SMB cascades (Nicolaos et al., 2001a, 2001b; Wankatt, 2001; Kim et al., 2003; Kim and Wankat, 2004); nevertheless, there are some non-conventional operation modes that proved to have interesting performance, as the one introduced by the Japan Organo Co. (www.organo.co.jp), called JO process (or Pseudo-SMB); this process was discussed in detail (Mata and Rodrigues, 2001; Borges da Silva and Rodrigues, 2006, , 2008) and (Kurup et al., 2006a). The process is characterized by a 2-steps operation: (a) in the first step the feed is introduced while the intermediary product is recovered with the whole unit working as a fixed bed; (b) during the second step the feed stopped, the unit works as a standard SMB and the less and more retained products are collected, see Annex I for details. The use of two different adsorbents (Hashimoto et al., 1993), two different solvents (Ballanec and Hotier, 1992), or a variation of the working flow rates during the switching period (Kearney and Hieb, 1992), were also proposed.
2.10. SMB - Gas and Super Critical phases
Most of the industrial applications of SMB technology operate in the liquid phase; nevertheless, SMBs can also be operated under supercritical conditions; where a supercritical fluid, typically CO2, is used as eluent offering a number of advantages namely reduction of eluent consumption, favourable physicochemical properties and lower pressure drop and higher column efficiency (Clavier and Nicoud, 1995; Clavier et al., 1996; Denet and Nicoud, 1999; Depta et al., 1999; Denet et al., 2001; Johannsen et al., 2002; Peper et al., 2002; Peper et al., 2007). Also in the gas phase the recent developments have been remarkable (Storti et al., 1992; Mazzotti et al., 1996a; Juza et al., 1998; Biressi et al., 2000; Cheng and Wilson, 2001; Biressi et al., 2002; Rao et al., 2005; Lamia et al., 2007; Mota et al., 2007b; Sivakumar, 2007; Kostroski and Wankat, 2008). Meter a do propano propylene
3. SMB design, modeling, simulation and optimization
Over the last 50 years, design, modeling, and optimization of chromatographic separation processes have been frequent research subjects. As consequence, several modeling methods, strategies and approaches have been developed, the more relevant are reviewed in this section.
3.1. Design strategies
The design of an SMB based separation involves taking decisions at many levels, from the configuration of the unit (number of columns per section, column and particle size) to operating conditions (feed concentration, switching time, internal flow rates). Although simulation can be exhaustively done until the right combination of parameters is found for the expected performance, it is useful to have a design method that will provide a preliminary estimation of the optimum operating point, followed by simulation and/or optimization, (Sá Gomes et al., 2009a).
The equivalence between TMB and SMB can be quite useful in the SMB design procedure. Recalling the role of each SMB section (Figure 2c), one can state a set of constraints that will limit the feasible region and allow a complete separation (recover of the more retained species (A) in the extract stream, the less retained one (B) in the raffinate port, and regeneration of the solid in section I as fluid in section IV).
Where represents the solid flow rate, the average solid concentration of species in section and the bulk fluid concentration of species in section .
The flow rates constraints in Eq. 1b and 1.c will identify the separation region (section II and III), while Eq. (1 a) and Eq. (1 d) the regeneration one (section I and IV).
Usually, the fluid and solid velocities in each section are combined into one only operating parameter, such as the from Morbidelli's group or the , as used by Ruthven (1989). The identification of constrains, Eq. (1 a) to Eq. (1 d), led to the appearance of several design methodologies, which are usually approximated and/or graphical, providing a better insight to the possible operating regions. From the plates theory and McCabe-Thiele diagrams (Ruthven and Ching, 1989); passing by the analytical solutions for a linear adsorption isotherms system in presence of mass transfer resistances (Silva et al., 2004); to the determination of waves velocities as in the Standing Wave Design (SWD) methodology (Ma and Wang, 1997; Mallmann et al., 1998; Xie et al., 2000; Xie et al., 2002; Lee et al., 2005). A particular emphasis should be given to the strategy developed for binary and multicomponent separations modeled by linear and non-linear isotherms as in (Storti et al., 1989b; Storti et al., 1993; Mazzotti et al., 1994; Storti et al., 1995; Mazzotti et al., 1996c; Mazzotti et al., 1997b; Chiang, 1998; Migliorini et al., 2000; Mazzotti, 2006b), the so-called “Triangle Theory”, where the term is treated by assuming that the adsorption equilibrium is established everywhere at every time (Equilibrium Theory, (Helfferich, 1967; Klein et al., 1967; Tondeur and Klein, 1967; Helfferich and Klein, 1970), resulting in a feasible separation region formed by the above constraints Eq. (1 b) and Eq. (1 c), which in the case of linear isotherms takes the shape of a right triangle in the plane, Figure 4, (or a triangle shaped form with rounded lines in non-linear isotherms case), and a rectangular shape in the plane.
Recently, this methodology was also extended for the design of SMB units under reduced purity requirements, in which the separation triangle boundaries are “stretched” to account for different extract and/or raffinate purities (Kaspereit et al., 2007; Rajendran, 2008).
Figure 4 - “Triangle Theory”, separation and regeneration regions for linear isotherms, where represents the Henry constant for linear adsorptions isotherms (A: the more retained and B: the less retained species), is the intraparticle porosity; case of (S,R)--Tetralol enantiomers, see Section 4.3.2.
Nevertheless, the inclusion of mass transfer resistances can deeply affect the result of the design. By taking into account all mass transfer resistances, and running successive simulations, it is possible obtain more detailed separation/regeneration regions, as well as the separation study carried out for three different sections (II, III and I) or (II, III and IV) allowing the analysis of solvent consumption or solid recycling, as proposed in the “Separation Volume” methodology, (Azevedo and Rodrigues, 1999; Rodrigues and Pais, 2004a), or the influence of the solid flow rate in the separation region (Zabka et al., 2008a).
3.2. Modeling and simulation
Generally, one can model a chromatographic separation process, and consequently an SMB unit, by means of two major approaches: by a cascade of mixing cells; or a continuous flow model (plug flow or axial dispersed plug flow, making use of partial differential equations derived from mass, energy and momentum balances to a differential volume element ), (Rodrigues and Beira, 1979; Ruthven and Ching, 1989; Tondeur, 1995; Pais et al., 1998). Each of these approaches can include mass transfer resistances, thermal, and/or pressure drop effects. Nevertheless, most of the recent literature concerning SMB processes just makes use of the continuous approach, detailing the particle diffusion and/or film mass transfer (the Detailed Particle Model), or using approximations to the intraparticle mass transfer rate in a similar way as the Linear Driving Force (LDF) approach presented by Glueckauf (1955a), (Guiochon, 2002).
One can argue that an SMB unit is no more than the practical implementation of the continuous counter current TMB process, Figure 2. Consequently, the equivalence between the TMB and a hypothetical SMB with an infinite number of columns can be used in the modeling and design of SMB units. However
TMB model approach will just give reasonable results if a considerable number of columns per section is present.
The SMB model approach represents an SMB unit as a sequence of columns described by the usual system equations for an adsorptive fixed bed (each column ), thus represented by a PDE system. Nevertheless, the nodes equations can be stated to each section, making use of the equivalence between the interstitial velocity in the TMB and SMB, and thus:
The issue here is that, due to the switch of inlet and outlet lines, the boundary conditions to a certain column are not constant during a whole cycle but change after a period equal to the switching time.
Since the model equations are set to each column , one will obtain the concentration of species in the begin of each section , , from the following node mass balances:
Considering now . This set of equations continues to progress in a similar way (shifting one column per ), until , repeating then from the first switch.
As for the TMB model approach, both the Detailed Particle Model and LDF approach can be used with the SMB model approach; nevertheless, and for the sake of simplicity, just the last is detailed in this work.
The LDF approximation can now be obtained from , and thus obtaining for the bulk fluid mass balance:
and for the mass balance in the particle,
with the respective initial:
and boundary conditions:
where the adsorption equilibrium isotherm is:
As a consequence one obtains discontinuous solutions, reaching not a continuous Steady State but a Cyclic Steady State (CSS).
By applying the SMB model approach, both the Detailed Particle as LDF strategies, to the case study mentioned before, one obtains the CSS concentration profiles over a complete switching time, Figure 6.
3.3. Performance parameters
The performance of the SMB unit for a given separation is usually characterized by the following parameters: purity, recovery, productivity per the amount adsorbent volume and eluent/desorbent consumption per mass of treated product. The definitions of all these performance parameters, for the case of a binary mixture, are given bellow:
Purity (%) of the more retained (A) species in extract and the less retained one (B) in the raffinate stream, over a complete cycle (from to ):
Recovery (%) of more retained (A) species in extract and the less retained one (B) in raffinate stream, again over a complete cycle:
the productivity per total volume of adsorbent :
the eluent/desorbent consumption :
These parameters hold for both SMB and TMB model approaches; nevertheless, one can simplify: in the SMB model strategy the same equations can be stated for a switching time period (from to ) if the unit is symmetrical, i.e., there are no differences between each switching time period (either due to the implementation of non-conventional modes of operation, or to the use of more detailed models accounting for dead volumes or switching time asymmetries); in the TMB model approach there is no need of the integral calculation, since the solutions from this model strategy are continuous and thus, the performance parameters constant over the time (at the steady state).
Usually one can classify the optimization of SMB units according to the type of objective functions: (i) optimization of performance parameters (productivity, adsorbent requirements or desorbent/eluent consumption for given purities and/or recovery requirements); (ii) optimization based on the separation cost. In case (i) each objective function, based on a different set of performance parameters, can lead to a different optimum solution; therefore multi-objective functions procedure should be considered; in the second case (ii) all those different performance parameters can be homogenized/normalized by the separation cost, where separation dependent costs (adsorbent, plant, desorbent/eluent recovery cost, desorbent/eluent recycling, feed losses...) and separation independent costs (wages, labour, maintenance, among others) are taken into account and weighted by cost factors, which sometimes are difficult to characterize (Jupke et al., 2002; Chan et al., 2008).
To solve these problems, the use of powerful optimization algorithms, such as: IPOPT (Interior Point OPTimizer, (Wa?chter and Biegler, 2006), employed for liquid as gas phase SMB separations (Kawajiri and Biegler, 2006b, 2006a; Mota et al., 2007a; Mota and Esteves, 2007; Rodrigues et al., 2007b; Kawajiri and Biegler, 2008a, 2008b); the commercial package gOPT from gPROMS with a Single (or Multiple) Shooting-Control Vector Parameterization, used in the two level optimization of an existing Parex® unit (Minceva and Rodrigues, 2005), for ageing analysis (Sá Gomes et al., 2008b) and gas phase separation of propane/propylene (Sá Gomes et al., 2009a) or for optimal economic design (Chan et al., 2008); the Non-dominated Sorting Genetic Algorithm (NSGA) or the Jumping Gene based algorithms (Deb, 2001), such as NSGA-II-JG, applied by several groups to optimize SMB units, from p-xylene to chiral separations (Zhang et al., ; Zhang et al., 2002a; Subramani et al., 2003b; Zhang et al., 2003a; Wongso et al., 2004; Kurup et al., 2005; Wongso et al., 2005; Kurup et al., 2006c; Paredes and Mazzotti, 2007; Lee et al., 2008; Mun and Wang, 2008b), is recurrent, either in the refinement of the design strategies mentioned before, or as a diagnosis method (such as the use of superstructures SMB considering several hypothetic inlet/outlet recycles), allowing the identification of new SMB configurations or modes of operation.
4. Design, construction and operation of SMB units
The design, construction and operation of a new lab-scale flexible SMB unit, the FlexSMBâ€‘LSRE® detailed elsewhere (aper aiche sa gome), is addressed in this section.
4.1. Design and construction
4.1.1. Valves and pumps design
As mentioned before, there are several ways to operate an SMB unit; therefore, when designing a new SMB unit, particularly for research purposes, one should take into account its flexibility as a key objective (Chin and Wang, 2004). If one considers an SMB unit as a certain number of packed columns interconnected and feedâ€‘controlled by a specific valves and pumps arrangement, it will be easy to understand that the key factor related with an SMB unit expandability and flexibility is in fact its valves system. An extensive review on the different SMB units valves schemes patented over the years can be found elsewhere (Chin and Wang, 2004).
The FlexSMB-LSRE® is based on a two SD (Selectâ€‘Deadâ€‘end flow path) valves per stream in the extract and raffinate currents, one SD per stream in the feed and eluent/desorbent currents and one twoâ€‘way valve per column as detailed in Figure 6.2.
Figure 6.2 - FlexSMB-LSRE® pumps and valves scheme under a 6 columns configuration, operating a during the first step of a  classic SMB. Bold lines are the active connections; thick lines are stagnant volumes. (alterar a figura)
By using this valves and pumps scheme, it is possible to operate most of the non-conventional SMB operating modes and perform columns re-configuration simply by changing some parameters in the automation routines on the computer interface.
When assembling an SMB unit one should take into account that tubing and other equipment will introduce dead volumes; pumps and valves distribution may introduce dead volumes asymmetries, and thus the unit might present in the end some peculiarities which can limit its performance. Therefore, when constructing the FlexSMB-LSRE® a preliminary work was undertaken to study possible equipment and columns positing. As result, the tubing and equipment dead volumes were reduced by using of 1mm i.d. tubes and short dead end valves (SD, Valco Instruments Co., Inc.) were employed. To reduce the dead volumes asymmetries, tubes with the same length were used for the same function and all columns assembled in a carousel scheme, Figure 6.4.
Photo do SMB
To reduce the pumps flow rates fluctuations (fluid inlets, outlets and internal flow rates), four HPLC pumps (VWR International, USA) were used, assisted by two Coriolis flow meters (Bronkhorst High-Tech B.V., Netherlands). One purge valve was installed at the outlet of raffinate stream that together with a purge valve installed next to the extract pump serves to manually regulate the total system pressure, as well as security valves.
To avoid variations related to the ports switching velocity asymmetries a distributed connection scheme for the SD valves was used. The FlexSMB-LSRE® can operate with a maximum number of columns of 12. For a 6 columns apparatus, all columns were connected to the 12 ways SD valves using just the odd valve connecting positions (i.e., 1,3,…,9, 11) in order to reduce the switching time discrepancies. All equipment is connected to an integrated power supply that assures protection from electrical fluctuations as a possible current discharge.
The automation of any laboratorial/industrial unit is a critical task, and as it concerns to an SMB unit, it is probably even more crucial. In fact, a relevant part of these units' flexibility relies in its automation and control routines. The LabView (National Instruments, USA) platform, was chosen to automate the FlexSMB-LSRE unit and thus to connect the computer to all controllable equipment: (valves, pumps and flow meters). A LabView based application was then used to provide a user friendly interface between the operator and the equipment, Figure XX.
4.1.4. Columns packing and characterization
The common modeling strategies assume that all SMB columns have identical characteristics. However, it is quite difficult to find several columns manufactured with the same specifications (column tubes may have slightly different geometric dimensions, thus, different retention times for a given flow rate…), as well as one should take into account that packing procedure is quite irreproducible, and therefore, it results on local fluctuations of the packing density) (Mihlbachler et al., 2001; Mihlbachler et al., 2002). Consequently, once the operator introduces the theoretical optimized operating parameters, the differences between columns arise and different values from the ones expected can appear. Therefore, packing of SMB columns should be carefully done and columns should be repacked if do not present acceptable reproducibly good characterization results.
For the FlexSMB-LSRE® columns used for the case studies presented in the next Sections, the slurry packing method as chosen and each column packed by means of Analytical Slurry Packer from Alltech Associates Inc. (USA). For each column a slurry of approx. 18.5g of Chiral AD 20m, amylose tris-(3,5 dimethylphenylcarbamate coated onto 20μm silica-gel), provided by Chiral Technologies Europe (France) in approx. 36ml of 2-propanol (GC-grade from Sigma-Aldrich Chemie, Germany) was prepared (pure 2-propanol was chosen as slurry solvent taking into account its physical proprieties, namely its viscosity). For the case studies shown on this work, The column was filled with solvent (2-propanol) and the slurry poured its upper reservoir. Then, the analytical slurry packer pump was connected to the upper reservoir and operated for 10min, at a max solvent pressure of 20bar (approx. 300ml.min-1), the solvent used was a mixture of -hexane/2-propanol, 90/10%, volumetric fraction, (GC-grade from Sigma-Aldrich Chemie, Germany). The reservoir was opened and the excess solvent drained again; the column disconnected from the reservoir and the excess of solid in the top of the column cut with a blade.
Each column was evaluated for HETP numbers, tracer experiments were performed by injecting pulses of 100ml of a solution of 0.00667+/-0.00001g of TSO (Trans - Stilbene Oxide, racemic mixture standard for this type of operations) and 0.00700+/â€‘0.00001g of TTBB (1,3,5 - TriTert ButyBenzol, considered non adsorbed) in 25.00+/-0.05ml of heptane-2-propanol (95%-5%, volume fraction) mobile phase. An average HETP value of 0.03cm was found and the retention times obtained from the experiments has a maximum deviation of 5% among all the columns. Therefore, and accounting with the packing supplier specifications, the columns were considered suitable for the SMB operation.
The technology demonstration stage is a quite important step in the “R&D flow sheet”, and in fact, when it accounts to equipment development it is probably the most important one. To operate and demonstrate some of the potential of the FlexSMB-LSRE® unit, a set of different experiments was planned regarding both linear as non-linear adsorption isotherms, under different modes of operation (classic and non-conventional). However, the operation of SMB units is not as straightforward as other batch techniques, and a particular attention must also be directed for some aspects not accounted (or simplified) in the modeling stage.
4.2.1. Real SMB units modeling and design
It should be taken into account that the performance of a real SMB unit differs from the ones described by the commonly used modeling and design strategies. There are several factors that can influence the precision of the SMB model predictions, such as: uncertainty in adsorption equilibrium kinetics and hydrodynamics data (diffusivity, axial dispersion coefficients etc.) and bed voidage (packing asymmetries), as well as, extra column dead volumes (tubing, equipment, asymmetries), variation in the port switching velocity (asymmetries and delays), fluctuations in pump flow rates (fluid inlets, outlets and internal), which are not accounted for it in the most commonly used SMB models (Mun et al., 2006). Consequently, if one runs an experimental SMB unit based on the operating parameters obtained by a simple mathematical model, such as the one described in Section CCC, the experimental results may not match the ones that were predicted by the model.
Concerning the uncertainty in the equilibrium isotherm data, kinetics data, and even the asymmetries of columns packing, the more precise, and/or accurate, these factors are, better will be the SMB model predictions. Therefore, detailed and precise measurements of all these parameters have to be done a priori, so that they introduce a minimal discrepancy between the SMB model results and the experiments itself.
The remaining deviation factors, such as the tubing and equipment dead volumes, pumps and valves asymmetries, related to each SMB unit design and equipment particularities should be taken into account before starting to construct a new SMB unit, as detailed before. However, even after all the work done on the FlexSMB-LSRE unit, the unit still has: 11.5% of dead volumes; the port switching velocity variation (delay) can represent around 0.8 seconds; the fluctuation of the pumps flow rates are still considerable.
If the average internal flow rates in each section are kept constant during the SMB operation (as assumed by some SMB design procedure) the SMB performances would not be affected, despite their considerable local variations. This is due to the cyclic mode of operation of these units, leading to compensation of these variations with time. Nevertheless, there are still two major issues concerning the prediction of the SMB performances: the unit SMB design features related with the dead volumes and the switching time asymmetries or delay. To deal with discrepancies between the real SMB operation and that predicted with commonly used models that account only for the presence of SMB columns (and do not consider the surrounding equipment features) one can apply different compensation strategies. For instance, the asynchronous port shift in the Licosep units (Hotier and Nicoud, 1995; Hotier and Nicoud, 1996; Blehaut and Nicoud, 1998), and simplified by switching time compensating strategy (Sa gOmes). The second strategy was discussed by several authors, within the Triangle Theory spectrum (Migliorini et al., 1999b; Katsuo et al., 2009), or in the case of the Standing Wave Theory (Mun et al., 2003a; Mun et al., 2006).
The switching time compensating measure accounts only for equipment dead volumes, the switching time delay or asymmetry is still not compensated when this measure is used. They can be included in the switching time compensation measure as true delay in the switching time, as follows:
For the FlexSMB-LSRE®:
Where represents the switching time for an ideal SMB unit with zero dead volumes, the total dead volumes in section , ml.minâ€‘1, the unit's average flow rate and the sub switching time delay (see Figure 6.14).
The corrected separation region using the extension to the switching time compensating measure is shown in Figure 6.17.
As can be observed in Figure 6.17, the SMB-zero dead volumes separation region corrected by the dead volumes and switching time delay (asymmetries) almost matches the one obtained with the detailed model. By this means it is possible to easily obtain a precise and realistic separation region without running tedious simulations related with the more detailed SMB models.
4.2.2. Separation of racemic mixture of (S,R)--Tetralol enantiomers (linear Isotherms) by conventional SMB
As case study it is presented the resolution of a racemic mixture of (S,R)--Tetralol 9(S,R)-(±)-1,2,3,4 Tetrahydro-1-naphthol) at the concentration of 1.0g.dmâ€‘3 in a â€‘heptane/2â€‘propanol (95%/5% volumetric fraction) solvent basis, using the 6 stainless steel columns packed with CSP Chiralpak AD (diameter particle size of 20μm).
a) Determination of adsorption and kinetic parameters
Since the racemic mixture to be separated would be prepared at 1.0g.dmâ€‘3, near diluted conditions, the adsorption equilibrium was represented by means of a linear formula characterized by an Henry constant for each enantiomer , . Consequently, the sorption parameters were determined by means of pulse experiments in a stainless steel column (=25cm and I.D.=0.46cm) packed with Chiralpak AD (diameter particle size of 20μm) also using the Analytical Slurry Packer as described before. A racemic solution of 0.5g.dmâ€‘3 (S,R)--Tetralol (minimum 99% purity, Fluka Chemie, Switzerland) was prepared in a â€‘heptane/2â€‘propanol (95%/5% volumetric fraction, also from Sigma Aldrich, previously degassed and filtrated trough a 0.2m and 50mm I.D. NL 16-membrane filter (Schleicher & Schuell, Germany), and loaded into a 10μl loop that was then injected by means of a Knauer injection valve installed on a Gilson HPLC unit. The consequent peaks were measured by means of a UV detector set at 270nm. The procedure was repeated for four different flow rates (4.4ml.minâ€‘1; 8.5ml.minâ€‘1; 12.5ml.minâ€‘1; and 16.6ml.minâ€‘1). The peaks retention times () were then deducted from the equipment dead volumes (0.50ml for the injector and 0.01ml for the detector) and plotted in function of the measured flow rate, Figure 6.18.
The slopes obtained from both regression lines (Figure 6.18) were then used to determine the Henry adsorption constants of both enantiomers from and thus obtaining (R=A and S=B): and .
The same overall mass transfer coefficient as defined in Zabka and Rodrigues (2007), was used to lump both the intraparticle as film mass transfer resistances and defined by . Where was calculated from the Linear Driving Force (LDF) approximation suggested by Glueckauf (1955b) (with the effective pore diffusivity define by , the pore porosity, , the particle porosity obtained from , the molecular diffusivity calculated by the Wilke-Chang equation (1955) and extended to mixed solvents by Perkins and Geankoplis (1969) with the absolute temperature, the solution viscosity, calculated according to Teja and Rice method for liquid mixtures (1981), the solute molar volume and obtained form where are the molar fractions, the molar masses and are the association factors constants which account for solute-solvent interactions); and obtained from , with the Sherwood number, the Schmidt number defined by and the Reynolds number: .
The contribution of molecular diffusion to axial dispersion is assumed to be negligible and therefore the axial dispersion coefficient ( obtained from, (Zabka and Rodrigues, 2007).
b) Determination operating parameters and operation
After the determination of the equilibrium adsorption parameters it was possible to draw both the theoretical separation as the regeneration regions for the separation under study and choose suitable operating conditions,
Taking into account the equipment limitations as maximum pressure drop allowable (20bar), it was possible to calculate the following operating parameters: ml.min-1, =6.0ml.min-1, =1.0ml.min-1, =4.5ml.min-1, =2.5ml.min-1, =2.95min.
Applying the dead volumes and switching time delay correction (from eq. 6.3) it was found that the switching time compensating measure should be about 4% (based on an average flow rate of 25.0ml.minâ€‘1), and thus correcting the switching time for 3.05min.
About 5dm3 of nâ€‘heptane/2â€‘propanol (95%/5% volumetric fraction) solution was prepared and filtrated as mentioned before. This mixture served as Eluent as well as solvent for the preparation of 1dm3 of the racemic mixture of (S,R)--Tetralol at 1.0g.lâ€‘1 used as Feed.
The extract and raffinate flow rates were monitored by means of the total recovered mass in each outlet over complete cycles and weighted on a laboratorial balance with 0.01g of precision. The extract flow rate was also measured by means a Coriolis flow meter installed for control purposes at the extract stream outlet. The recycle flow rate was monitored by the other Coriolis flow meter. The experimental average flow rates, as well as geometric features, number of columns and SMB configuration are reported in Table 6.9.
Table 6.9 - Experimental operating conditions for the (S,R)--Tetralol racemic mixture separation .
Columns and packing parameters
SMB operating conditions (measured)
The different model equations presented in this work were numerically solved using the gPROMS v2.3.6 a commercial package from Process Systems Enterprise (www.psenterprise.com), by applying the OCFEM (Orthogonal Collocation on Finite Elements) with 2 collocation points per element, 50 elements in each column for the axial coordinate and 3 collocation points and 5 elements for the radial discretization (when necessary). After the axial and/or radial discretization step, the time integration is performed by the ordinary differential equation solver SRADAU a fully-implicit Runge-Kutta method that implements a variable time step, the resulting system is then solved by the gPROMS BDNSOL (Block decomposition NonLinear SOLver). An absolute and relative tolerance value was set to 10â€‘5.
The separation was undertaken throughout 28 cycles. During the operation, samples of extract and raffinate average concentrations were withdrawn (referent to a complete cycle, namely: cycle 2; 4; 6; 8; 10; 13; 15; 17; 19; 27),
To plot the FlexSMB-LSRE® concentration profile, from cycle 20 to cycle 25, a single sample in each cycle was withdrawn for 10 seconds, at the middle of the switching time period , by means of a 6 ports sampling valve installed on the outlet of column 6 for internal profile sample I, III, IV and V; and at the extract and raffinate ports for profiles samples VI and II, respectively, see Annex VIII. The same procedure was then repeated in cycle 27, but now with all sampling apparatus occurring within the same cycle. Both sampling procedures resulted in almost the same concentration profile, proving that collecting six samples per cycle will not influence too much the SMB internal profiles.
In Figure 6.21 the internal concentration profile obtained from cycle 20 to 27..
The simulated results fit well the experimental ones, even the “secondary plateau” noted next to the left of major plateau of the more retained species in section II and the right of the major plateau of the less retained species in section III (related with dead volumes of both extract and raffinate lines), are well predicted by the extended dead volumes model used.
All samples (extract and raffinate average concentrations, as well as internal profiles) were loaded into a 10μl loop and then injected by means of a Knauer injection valve installed on a Gilson HPLC unit into an analytical column CHIRALCEL OBH (25cm and 0.46cm I.D., supplied by Chiral Technologies, France) using as mobile phase the same solution used for eluent purposes.
The consequent peaks were measured by means of a UV detector set at 270nm and concentrations determined according with calibration curve obtained from linear regression of Area vs. Concentration ( of 5 standards (g.dm-3, of each enantiomer) with a with a All experiments (separation with the SMB unit and analytical procedures) were run at laboratorial conditions (approximately 25ºC).
4.3. Control of SMB units
In recent years the control of SMB units has also been wide investigated (Erdem et al., 2004b; Engell, 2007; Grossmann et al., 2008a; Grossmann et al., 2008b). Several reports on dynamic control strategies include nonlinear control strategies such as: the input-output linearizing control, where the controller action is based on a nonlinear state estimator using the TMB model (Kloppenburg and Gilles, 1999a); and model predictive control (MPC) (Natarajan and Lee, 2000; Erdem et al., 2004a; Dietz and Corriou, 2008); or design on the basis of neural networks (Wang et al., 2003). Also a model based SMB control where an optimal trajectory is calculated off-line was proposed by (Klatt et al., 2000; Klatt et al., 2002) and from wave reconstruction (Kleinert and Lunze, 2008). A more recent strategy based on the nonlinear wave propagation phenomena aims to control the central sections of the SMB unit by controlling the position of the concentration fronts (Schramm et al., 2003a). The control of chromatographic processes (SMB included) by means of the standard control procedures (P, PI or PID controllers), but detecting characteristic points of the unit where the history of a specific variable of the fractions of the mixture to be separated will be representative for the control action was also addressed (Valery and Morey, 2009).
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