Feed plate model

Referring to Figure 2.3 of multivessel batch distillation (MultiBD) column, the model equations for condenser, reboiler and internal plates are the same as those presented for conventional batch distillation column (section 4.2). The model equations for the vessels are the same as those presented for feed tank of the MVC column (section 4.3.3). Note however, that there are no feed plate model equations as in the case of an MVC column. 

Here, the model equations for the feed plate (Figure 4.15) will be presented for model type III, IV and V. 

Simple Model - Type III Feed Tank and Feed Plate i = Vci i = 1 to nz a) Feed Tank... 

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. 

Inspection of this set of equations shows that they are a logical extension of those stated in Chap. 1, Eq. (1-43), for the binary system. A schematic representation of the component-material balances is shown in Fig. 2-1. The behavior assumed on the feed plate is demonstrated by model 2, which is shown in Fig. 2-2. 

Figure 2-2 Model 2 for the behavior of the feed plate. (Taken from Holland Introduction to the Fundamentals of Distillation, Proceedings of the Fourth Annual Education Symposium of the Instrument Society of America, April 5-7, 1972, Wilmington, Delaware.)...

The development of the recurrence formulas is outlined in Prob. 2-3. An improved form of these expressions was recently proposed by Boston and Sullivan.1 For the special case of a conventional distillation column in which model 2 (see Fig. 2-2) for the feed plate is assumed, the procedure proposed by Boston and Sullivan (see Prob. 2-3) may be used.to reduce the above formulas to the following form... 

When model 2, shown in Fig. 2-2, is used for the feed plates, the column vector / contains the vapor and liquid rates (vFi and lFi) for each feed. The elements of v,-and / may be displayed as follows... 

In addition to the above specifications, it is also supposed that the following variables and operating conditions are fixed the number of stages N, the feed plate location/ the model for the feed plate behavior, the complete definition of the feed (the composition, flow rate, and thermal condition), and the column pressure. Since D = 0, the condenser behaves as a total condenser, and thus... 

Parker (12) recommended the use of a distillation reactor for hydrolyzation of ethylene oxide to ethylene glycol. Miller (13), and subsequently Corrigan and Miller (14), analysed this process using a crude plate model and concluded that increased temperature in the distillation reactor adversely affected selectivity of the process as com )ared to the two-stage Shell process. However, this was disproved by Sive (15) who found no effect on selectivity of operating pressure or feed composition when modelling a packed distillation reactor for this process. 

The BASF model presented by Kaibel et al. (31) was further analysed by Mayer and Worz (33). They considered the reaction A + B 5 C + D and investigated the effect on conversion of feed plate location, number of plates and mutual variation in relative volatilities of A, B and D, all as a function of heat input in continuous and batch operations. For C as the most volatile component, it was found that a batch reboiler reactor is energetically a more attractive solution if D is more volatile than A. Otherwise a distillation reactor is preferable. 

The simplified model of feed tray, based on the assumption that feed plate is common for both sections and that the process of mixing and the process of equilibrium achievement go on simultaneously (Fig. 5.29b), is used in a number of works (Levy et al., 1985 Julka Doherty, 1990). According to this model, the composition x/ can be determined from the equations of both sections (i.e., point Xf should lie at the intersection of two sections trajectories) (x/ e Regf... 

At the second stage, one turns to more exact model of feed plate (Fig. 5.29a), using the result of the first stage as good initial approximation. 

For the simulation of SMB-separations efficient software packages,based on the Triangle-Theory, are commercially available. The number of columns, the column dimensions, the theoretical number of plates in the columns, the feed concentration, the bi-Langmuir adsorption isotherm parameters and the number of cycles need to be defined by the user. Then the separation is simulated and values for the flow rate ratios, the flow rates, the switching time and the quality of the separation, purity and yield, are calculated. Based on these values an actual separation can be performed. However, some optimization/further development is usually necessary, since the simulations are based on an ideal model and the derived parameters and results therefore can only be taken as indications for the test runs. 

The embedded model approach represented by problem (17) has been very successful in solving large process problems. Sargent and Sullivan (1979) optimized feed changeover policies for a sequence of distillation columns that included seven control profiles and 50 differential equations. More recently, Mujtaba and Macchietto (1988) used the SPEEDUP implementation of this method for optimal control of plate-to-plate batch distillation columns. 

A model for crystallization point of the urea melt sprayed into the granulator was developed based on acoustic spectra recorded from sensor position A during a trial period of 24 hours. A flow sheet of the liquid urea feed process can be seen in Figure 9.7. Sensor A is mounted onto an orifice plate inserted in the main supply pipeline of liquid urea (see Figures 9.6 and 9.7). The reference values used to calibrate the model are the crystallization temperature (called the jc point ), as determined by the pilot plant laboratory (heat table visual nucleation/crystallization detection). 

The equipment system scheme is essentially the same as that shown in Fig. 6.14 but with two differences (1) The orifice plates are used for metering airflow rates and (2) Since the equipment is much larger than that used in the model investigation and therefore the feeding rate is much larger, the screw feeder for wet material feeding in the quasi industrial test is not as complex as that shown in Fig. 6.14 in structure, but is a common one. 

Vapour phase enthalpies were calculated using ideal gas heat capacity values and the liquid phase enthalpies were calculated by subtracting heat of vaporisation from the vapour enthalpies. The input data required to evaluate these thermodynamic properties were taken from Reid et al. (1977). Initialisation of the plate and condenser compositions (differential variables) was done using the fresh feed composition according to the policy described in section 4.1.1.(a). The simulation results are presented in Table 4.8. It shows that the product composition obtained by both ideal and nonideal phase equilibrium models are very close those obtained experimentally. However, the computation times for the two cases are considerably different. As can be seen from Table 4.8 about 67% time saving (compared to nonideal case) is possible when ideal equilibrium is used. 

For single separation duty, Diwekar et al. (1989) considered the multiperiod optimisation problem and for each individual mixture selected the column size (number of plates) and the optimal amounts of each fraction by maximising a profit function, with a predefined conventional reflux policy. For multicomponent mixtures, both single and multiple product options were considered. The authors used a simple model with the assumptions of equimolal overflow, constant relative volatility and negligible column holdup, then applied an extended shortcut method commonly used for continuous distillation and based on the assumption that the batch distillation column can be considered as a continuous column with changing feed (see Type II model in Chapter 4). In other words, the bottom product of one time step forms the feed of the next time step. The pseudo-continuous distillation model thus obtained was then solved using a modified Fenske-Underwood-Gilliland method (see Type II model in Chapter 4) with no plate-to-plate calculations. The... 

Because of the strong effects of plate rotations on the rector performance for both RE and PC electrolyzers, the critical design parameters for these reactors are the Taylor number (a2w/4v)0 5 and the Reynolds number (aVf/v). Here a is the gap width between the plate, w the angular velocity of rotation (in radians per second), v the kinematic viscosity of the fluid, and V the velocity in the feed pipe. Since no asymptotic velocity profile is reached for PC, the length of the cell will be an important design parameter in a pump-cell electrolyzer. Detailed mathematical models for RE and PC electrolyzers are given by Thomas et al. (1988), Jansson (1978), Jansson et al. (1978) and Simek and Rousar (1984). 

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