Simulated Moving Bed Technology

simulate paltry Bed applied science1. Introduction1.1. unceasing counter stream chromatographyContinuous industrial-scale surface assimilation mental military operati adepts are well known for their efficiency. Very often, the Height equal of a Theoretical Plate (HETP) in a batch procedure is roughly deuce-ace convictions racyer than iodine find for the unceasing direction (Gembicki et al., 2002). The operation of perpetual chromatographic counter current implement (here-by referred as True sorrowful Bed, TMB) in particular, maximizes the portion enchant crusade force providing a better utilization of the surface-assimilative, and consequently, lay offing the hire of lower selectivity materials (Ruthven and Ching, 1989) as to operate with an increased productiveness (i.e., higher branched d whizzput using less(prenominal) packing material). A scheme of a TMB social unit is shown in enrol 1.Figure 1 A four member True Moving Bed (TMB) unit for the d isengagement of A and B with D as eluent or desorbent (Fructose/Glucose judicial dissolution).If we define fragment as the part of the TMB unit where the smooth-spoken fuse rate is approximately constant (section limited by portal/outlet streams), then, it is possible to find four assorted sections with polar roles instalment I Regeneration of the adsorbent (desorption of A from the straightforward) comp unriva directnt part II Desorption of B (so that, the prolong is not contaminated by the less retain component) office III Adsorption of A (raffinate clean from the to a greater extent adsor get laid species)Section IV Regeneration of the eluent/desorbent (adsorption of B from the silver-tongued phase).From Figure 1, one skunk find that the counter-current movement of the solid, with reward to the roving phase, all(a)ows continuous variety of both the adsorbent in section I as the eluent/desorbent in section IV. Also, the contemptible bed arrangement allows the ach ievement of high purity even if the announcement of the 2 peaks is not excellent, since only the purity at the two white tie and tails of the concentration profiles, where the withdrawal ports are located, is of interest. This is contrary to batch chromatography where high consequenceant is vital in prescribe to achieve high purity.Nevertheless, with this counter current means of operation is necessary to circulate not only the fluid phase but also the solid. The solid motion inside of the towboat and the consequent re wheel presents some technical problems, namely equipment abrasion, mechanical erosion of adsorbent and difficulties in maintaining plug flow for the solid (especially in beds with elephantine diameter). From a technical point of view, this clearly limits the implementation of such applied science.1.2. The Simulated Moving Bed (SMB) conceptIn order to avoid this issue, a sequence of fixed bed towboats was conceived (Broughton and Gerhold, 1961) in which th e solid phase is at rest in relation to a fixed referential, but where a relative movement between both phases is experienced by transposition the introduction and outlet fluid streams to and from the towers from cadence to time (in the direction of the fluid flow). In the simplest direct temper, the occlusive that a certain direct conformity prevails is cal take the switch oer time, . Since the solid flow is avoided, although a kind of counter-current movement is created comparatively to the fluid, this engineering science is called Simulated Moving Bed (SMB).Consider that at certain moment in the operation of an SMB, the positions for the access of feed and desorbent and outlet of products is stand for by Figure 2a. Assume also the simplest operating means (synchronous communicate of all streams) and one towboat per section. After a diaphragm of time equal to the fracture time, the nip and withdrawn points all move one column in the direction of the fluid flow ( Figure 2b). When the initial posture of injection/collection of all the streams is reencountered, we father 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 uniform column is in diverse sections, assuming at that placefore different roles in the separation process.Figure 2 Schematic representation of a 4 columns SMB unit operating oer a complete cycle, from 0to (with representing the ports switching time) (a) flow rate of the offshoot switch (b) point 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 continuance 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 flu id 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 native flow grade in both utensil are not the same, but related by where and represent the internal liquid flow-rates in the SMB and TMB, singly, is the majority porosity and the column volume.1.3. SMB ApplicationsIndustrially, SMB applications tail assembly be regarded as Old and New, associated with petrochemical and pharmaceutical/fine chemistry fields, respectively (S Gomes et al., 2006d). Among the first applications of SMB engineering ( hold 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 Franais du Ptrole, 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 ramose 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 grape sugar and polysaccharides on polystyrene-divinylbenzene resins in calcium form (Broughton, 1983) or as procure by Japan Organo Co. (Japan), (Heikkil et al., 1989) by Amalgamated Sugar Comp any LLC, also known as the Snake River Sugar Company (Boise, ID-USA), (Kearney and Mumm, 1990, , 1991).In the lastly decade, particularly in the area of drug development, the advent of SMB has provided a high throughput, high yield, solvent in effect(p), safe and salute effective process option. Although it had dour 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 moth 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 new(prenominal) 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 base processes already approved by the aliment 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), sertraline (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 richness of such technique, this work follows different operating SMB modes design, copy and optimisation techniques and addresses an illustration of the design, construction a nd operation of an SMB unit.2. SMB modes of operationSo far, only the so-called stodgy SMB mode of operation has been considered, which indeed means that each section has a fixed number of columns and there is no version on the pre-established inlet/outlet flow rates or the switching time value. However, oer the last decades some non-conventional SMB operating modes were proposed, developing the range of the applications of SMB technology and extending gain ground 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 than analyse and used processes of the so-called non-conventional SMB modes of operation. Instead of a fixed unit configuration with constant sectio n length, the Varicol operating mode is performed by the implementation of an asynchronous inlet/outlet ports shift, providing a plastic 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 rest 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 productiveness value up to 30% more than the classical SMB apparatus, principally when operating under a bring down 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 S Gomes et al., 2006d Mota et al., 2007b Rodrigues et al., 2007a S Gomes et al., 2007b Zhang et al., 2007).2.2. Partial- course, Partial-DiscardWith 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 saltationn feed length period will consequently influence the raffinate and extract flow rates are along the time. Also referred in the literary productions is the Partial-Discard (or partial withdraw) operating mode, where average 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 footfall the unit is operated as a conventional SMB but without any flow in section IV in the second step the inlet and o utlet 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 gomesAnother novel non-conventional mode of operation, the Outlet Swing Stream-SMB (OSS) (S Gomes and Rodrigues, 2007), was developed under the framework of this thesis and is last mentioned concomitanted in Chapter 3.2.3. PowerFeed and ModiConThe modulation of the section flow rates (PowerFeed) was to begin with 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 interlingual rendition within one switching interval, was suggested by Schramm et al., (2002 2003b) known as the ModiCon. The use of auxiliary feed coolers, where section flow rate fl ows 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 question 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. 2 Feed or MultiFeed SMB and Side Stream SMBRecently, 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 S Gomes and Rodrigues (S Gomes et al., 2007b S Gomes and Rodrigues, 2007). Also multi extract/raffinate are referred in the writings (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, fag allow the deve lopment of more efficient SMB processes.2.5. Semi Continuous, Two and Three zones SMBThere are several tackle continuous SMB apparatus that operate with two-zone, two or one-column chromatograph, with/or recycle, homogeneous 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 love 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. incline SMBAs 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 ( fingerpost 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 Rodriguess group with the civilisation 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 an d Morbidelli, 2006 Strohlein et al., 2006 Aumann and Morbidelli, 2007 Aumann et al., 2007 Aumann and Morbidelli, 2008 Mller-Spth et al., 2008), commercialized by ChromaCon AG (Zrich, 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 processesIt is possible to improve the performance of SMB units by desegregation it with other different separation techniques. The more simple application of this come near 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 Ex tract 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 reactorThe 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 thermolabile distillation, reactive extraction or membrane reactors, the combination of (bio)chemical reaction with SMB chromatographic centrifuge has been subject of considerable attention in the last 15 years. This combine reaction-sep aration technology adopts the name Simulated Moving Bed Reactor (SMBR). some(prenominal) 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 S Gomes et al., 2007a) meter a dos FOS the esterification from acetic irate and -phenethyl alcohol and subsequent separation of the product -phenetyl acetate (Kawase et al., 1996), or methyl group acetate ester (Lode et al., 2001 Yu et al., 2003a) the deductive reasoning and separation of the m neutral spirits 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 isomerisation 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 separationsThe application of SMB technology to multicomponent separations has also been an important research topic in the last years. The greens 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 modifyd by a 2-steps operation (a) in the first step the feed is introduced while the intermediary product is aged 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 maintained products are collected, see amplify 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 phasesMost 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 advantag es namely reduction of eluent expenditure, 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 unparalleled (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 propylene3. SMB design, specimening, simulation and optimizationOver the last 50 years, design, computer simulationing, and optimization of chromatographic separation processes have been frequent research subjects. As consequence, several modeling methods, strategies and nestle shotes have been developed, the more relevant are reviewed in this section.3.1. Design strat egiesThe 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 pinch 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 useable to have a design method that will provide a preliminary estimation of the optimum operating point, followed by simulation and/or optimization, (S 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 declare a set of constraints that will limit the feasible role 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 re-formation of the solid in section I as fluid in section IV).Where r epresents 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 vicinity (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 Morbidellis 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 customaryly 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 analogue adsorption isotherms system in posture of mass transfer resistances (Silva et al., 2004) to the determination of waves velocities as in the Standing dither 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 tough 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 roll of a right triplicity in the plane, Figure 4, (or a triangle systema skeletaled form with rounded lines in non-linear isothe rms 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 name 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 runnel 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 simulationGenerally, 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, make use of partial first derivative equations derived from mass, energy and momentum equilibriums 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 shoot mass transfer (the circum stantial 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 supposed SMB with an infinite number of columns can be used in the modeling and design of SMB units. HoweverTMB 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, make use of the equivalence between the interstitial velocity in the TMB and SMB, and thusThe issue here is that, due to the switch of inlet and outlet lines, the frontier 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 balancesConsidering now . This set of equations continues to keep in a similar way (shifting one column per ), until , tell 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 balanceand for the mass balance in the particle,with the respective initialand boundary conditionswhere the adsorption equilibrium isotherm isAs a consequence one obtains discontinuous solutions, range 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 parametersThe 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 bellowPurity (%) 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 cyclethe 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).3.4. OptimizationUsually 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, bas ed 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 brain 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 sheaf gOPT from gPROMS with a Singl e (or Multiple) Shooting-Control Vector Parameterization, used in the two level optimization of an existing Parex unit (Minceva and Rodrigues, 2005), for ageing analysi