Interval switch

Tran and Mujtaba (1997), Mujtaba et al. (1997) and Mujtaba (1999) have used an extension of the Type IV- CMH model described in Chapter 4 and in Mujtaba and Macchietto (1998) in which few extra equations related to the solvent feed plate are added. The model accounts for detailed mass and energy balances with rigorous thermophysical properties calculations and results to a system of Differential and Algebraic Equations (DAEs). For the solution of the optimisation problem the method outlined in Chapter 5 is used which uses CVP techniques. Mujtaba (1999) used both reflux ratio and solvent feed rate (in semi-continuous feeding mode) as the optimisation variables. Piecewise constant values of these variables over the time intervals concerned are assumed. Both the values of these variables and the interval switching times (including the final time) are optimised in all the SDO problems mentioned in the previous section. 

Other timing switch gear works with electronic digital clocks. The 1-s time interval derived from the mains frequency is counted in an integrating counter. The... 

The protection station must be carefully maintained (see Section 10.5). The function of the rectifier should be monitored at monthly intervals. The pipe/soil potentials of the pipelines should be measured at least once a year. The IR-free potentials should be determined as far as possible by the switching method, especially when new pipework is installed and connected to the protection system. 

Since usually the reference electrode is not equipped with a capillary probe (see Fig. 2-3), there is an error in the potential measurement given by Eq. (2-34) in this connection see the data in Section 3.3.1 on IR-free potential measurement. The switching method described there can also be applied in a modified form to potential-controlled protection current devices. Interrupter potentiostats are used that periodically switch off the protection current for short intervals [5]. The switch-off phase is for a few tens of microseconds and the switch-on phase lasts several hundred microseconds. 

Accumulators can be used to help stabilize the lube system against pressure transients such as that from the turbine power operator during a large correction. For a sizing rule of thumb, the system pressure should not vary by more than 10%, while the turbine servo travels full stroke in a one second interval. The role of accumulators for pump switching was covered earlier in the section on Startup Control. 

Demand-related failure rates are presented as failures per 10 demands and are for equipment that is normally static but is called upon to operate at indeterminate intervals, for example, a switch or standby generator. In this case, data are gathered that can be converted to reflect the number of failures per demand on the equipment. 

Introducing the dimensionless variables x = and 6 = t/t, where t is the switch time interval, and is the length of one SMB column, the model equations become ... 

Fig. 9-4. Cyclic steady state internal concentration profiles of the more retained component during a switch time interval (start, 25 %, 50 %, 75 %, and at the end of a switch time interval) for SMBS.

Fig. 9-5. Transient evolution (first 5 cycles) of the concentration of the more retained component in the extract for (a) SMB4, (b) SMBS, and (c) SMB 12. Solid line, TMB dotted line, SMB stepped dotted line, SMB approach with average concentration over a switch time interval o, SMB instantaneous concentration evaluated between switchings.

The influence of the switch time interval on the purity is shown in Fig. 9-10. A change on the switch time interval will lead to a change on the equivalent solid flow rate throughout the system. In all runs the inlet and outlet flow rates, as well as the internal liquid flow rates in all the four sections of the SMB unit, are kept constant. 

Increasing the switch time interval is equivalent to decrease the solid flow rate and the net fluxes of components in all sections of the TMB unit will be pushed in the same direction of the liquid phase. This implies that, first, the more retained species will move upwards in section III and will contaminate the raffinate stream and the less retained species will move upwards in section IV, will be recycled to section I, and will contaminate also the extract stream. The decrease of the switch time interval will have similar consequences. The equivalent solid flow rate will increase and the net fluxes of component in all four sections of the TMB unit will be pushed in the opposite direction of the liquid phase. This implies that, first, the less-retained species will move downwards in section II and will contaminate the extract stream and the more retained component will also move downwards in section I, will be recycled with the solid to the section IV, and will contaminate the raffinate stream. It is possible to obtain simultaneously high purities and recoveries in a SMB, but the tuning must be carefully carried out. 

The original optimization problem with five variables was, by choosing the liquid flow rate in section I by pressure-drop limitations and following Equations (35) and (36) to evaluate the switch time interval and the recycling flow rate, reduced to a two-variable optimization problem the choice of liquid flow rates in the two central sections. Table 9-5 summarizes the SMB operating conditions (and equivalent TMB conditions) used in the design of the 7 -711 plot. 

Feed concentration Switch time interval t = 3.3 min Flow rate in section I 2 = 31 mL min ... 

Interaction tests should be made on all unprotected structures in the vicinity of a proposed cathodic protection installation, and should be repeated annually or at some other suitable interval to ensure that alterations in the layout of plant or in the electrical conditions are taken into account. It is most convenient if the tests on all unprotected pipes or cables are made at the same time, the potential measurements being synchronised with the regular switching on and off of the protection current. It may then be convenient to continue with further tests to confirm that any remedial measures applied to one installation do not adversely affect other installations. 

Potential data loggers are now available to undertake close interval pipeline surveys. These increasingly popular surveys, determine a pipeline s pipe-to-soil potential at nominal intervals, of as little as 1 m. Additional information is gained by the recording at each point, of both the pipe-to-soil potential with the cathodic protection system ON , together with the potential some 100-300 ms after the cathodic protection system is switched OFF . This instantaneous OFF potential being devoid of any IR drop component present in the ON potential measurement. 

Its poles are determined to any order of by expansion of M. However, even in the lowest order in the inverse Laplace transformation, which restores the time kinetics of Kemni, keeps all powers to Jf (t/xj. This is why the theory expounded in the preceding section described the long-time kinetics of the process, while the conventional time-dependent perturbation theory of Dirac [121] holds only in a short time interval after interaction has been switched on. By keeping terms of higher order in i, we describe the whole time evolution to a better accuracy. 

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