Switching interval

When a specific feed composition is given, the constraints on m1 and m4 as well as the complete separation region in the (m2, m3) plane can be determined,since these depend only on the parameters of the adsorption equilibrium isotherms and the feed composition itself. Based on these values an operating point can be selected, i. e. a set of four values of = 1,..., 4 fulfilling the complete separation requirements. Since the flow rate ratios are dimensionless groups combining column volumes, flow rates and switching intervals, the constraints on the flow rate ratios are independent of the size and productivity of the SMB unit. 

Equations (75) and (16) express the shortest duration of the two switching intervals as a function of specific magnet and power supply parameters. The dependence of the SfETdown on V)v does not directly transpire from Eq. (16), but the importance of in this context is evident from Eq. (12). We will discuss this point in more detail in the next Section. 

In general, an FFC relaxation rate measurement requires a series of elementary experiments in which the duration x of just one of the fixed-field intervals varies, while each of the switching intervals has always the same duration. Only in this way can one guarantee that the measured relaxation rate is correct and that it corresponds to the relaxation field present during the variable-duration interval (to be discussed later). 

The performance of the field-switching circuitry (power supply and magnet dynamics) affects the minimum duration of the switching intervals. Figure 20 illustrates the principal characteristics of the field-switching... 

Fig. 20. Schematic illustration of a main-field switching interval. The single pulser interval Swt (switching time), nested between a previous interval Pand a next interval N, is actually composed of three distinct phases (1,2,3). During phase (1) the magnetic field B is actively driven along a linear ramp from its previous value Bp to a close vicinity of its next value During the subsequent phase (2) it settles to its final...

Fig. 24. Examples of experimental relaxation curves The vertical scales are arbitrary, horizontal scales (x-values) are linear with a single label. In all cases, the axes cross at the origin (0,0). The upper two plots regard a slow-relaxing sample in which the switching effects described in the text are negligible. The bottom two plots regard a very fast relaxing sample in which switching-interval effects are very pronounced.

The optimization of individual switching intervals exploits two principles ... 

The duration of the ramp phase of a switching interval depends upon the field levels between which the switching actually occurs and can be therefore individually adjusted see Eq. (2). 

Figure 28 shows the diagram of the FFC version of the classical IR sequence. Notice that the first RF pulse has to be applied at the acquisition field Ba because the probe is tuned to the Larmor frequency at that field. This implies the presence of an extra field-switching interval unless, of... 

Fig. 28. FFC Inversion Recovery sequence. In the upper case the sample is first prepolarized in a filed Bp, then switched to the acquisition field Ba where the first RF pulse of 180° is applied and the sample magnetization is inverted. The field is then switched to B,. and the sample is allowed to relax for the variable time t. Finally, the field is switched again to the acquisition value and the magnetization is sampled by any of the sample-detection methods (here, a simple FID following a 90° RF pulse). Notice that, as shown in the lower diagram, in the special case when Bp = Ba it is possible to neatly avoid the extra switching interval prior to the inversion pulse.

Figure 5.18 illustrates the principle of SMB processes. The mobile phase passes the fixed bed columns in one direction. Counter-current flow of both phases is achieved by switching the columns periodically upstream in the opposite direction of the liquid flow. Of course, in a real plant the columns are not shifted but all ports are moved in the direction of the liquid flow by means of valves. The counter-current character of the process becomes more obvious when the relative movement of the packed beds to the inlet and outlet streams during several switching intervals is observed. After a number of switching or shifting intervals equal to the number of columns in the system, one so-called cycle is completed and the initial positions for all external streams are re-established. 

Classical SMB-systems are characterised by the synchronous and constant downstream shift of all inlet and outlet lines after a defined switching period. In that case four defined sections can be distinguished over the complete cycle time (Fig. 5.21a). Within these sections the columns are distributed equally (e.g. 2/2/2/2) or in any other given configuration where the number of columns per section is an integer number (e.g. 1/2/2/1). At periodic steady state, the same process conditions are always reached after one switching interval (tshift) and the number of columns per section is the same. 

For the classical SMB process described above, the composition and flow rate of the feed is constant for the whole switching interval. Following the approach by Zang and Wankat (2002) in the Partial-Feed process, two additional degrees of freedom are introduced, i.e. the feed duration and feed time. Figure 5.23a compares the feed flow... 

Partial-Feed processes switch the feed stream on and off within one time interval while the other inlet and outlet lines are active all the time. ISMB (Improved SMB) processes partition the switching interval in a different way. In the first part of the period (Fig. 5.24a), all external lines (desorbent and feed inlets as well as extract and raffinate outlets) operate. However, in contrast to a classical SMB unit, the outlet of section IV is not recycled during this part of the switching interval and, consequently, the flow rate in section IV is zero. The first. .injection period" is followed by a recirculation period in the second part of the switching interval (Fig. 5.24b). During this time all external ports are closed and recirculation is performed with a constant... 

During operation of an SMB plant the propagation of components to be separated are influenced by the internal fluid flow rates in the different sections as well as the switching time that simulates movement of the solid. By appropriate choice of operating parameters the movement of the less retained component is focused on the raffinate port while the more retained component is collected in the extract stream. Figure 7.16 shows an optimal axial profile of the liquid concentrations at the end of a switching interval after the process has reached a periodic steady state. The adsorption and desorption fronts of both components have to start or stop at given points to achieve complete separation at maximum productivity. 

For complete separation the desorption fronts of the two components must not exceed points 1 and 2 respectively, which are located one column downstream the desorbent and extract port. Since the concentration profile displayed in Fig. 7.16 demonstrates the situation at the end of a switching interval, all ports will move one column downstream in the very next moment. In the case were the desorption front of component B does exceed point 2, the extract stream, meant to withdraw the more retained component A only, will be polluted with B after the ports have been switched. The same applies to point 1. If component A is shifted into section IV the adsorbent will transfer it to the raffinate port and the raffinate will be polluted. For the adsorption fronts, components A and B must not violate points 3 and 4, respec-... 

Figure 7.16 Optimal axial concentration profile at the end of a switching interval.

Figure 7.21 shows the internal axial concentration profiles at the end of a switching interval for a system of linear isotherms and no competitive interaction of the two components. After switching all ports downstream in the direction of the liquid flow, the extract will be polluted with component B because the desorption front of B violates point 2 (Fig. 7.16). 

Zhang, Z., Mazzotti, M., Morbidelli, M. Power-Feed operation of simulated moving bed units changing flow-rates during the switching interval, J. Chromatogr. A, 2003, 1006, 87-99. 

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