Tray model

The simulations involve the solution of the rigorous tray-by-tray model of each sequence, given by equations 1 to 6, together with the standard equations for the PI controllers for each control loop (with the parameters obtained through the minimization of the lAE criterion). The objective of the simulations is to And out how the dynamic behavior of the systems compare under feedback control mode. To carry out the closed-loop analysis, two types of cases were considered i) servo control, in which a step change was induced in the set point for each product composition under SISO feedback control. 

A tray model is shown in Figure 6.1-5. This tray model has the inlet and outlet vapours well mixed, with compositions of yN+l and yN respectively. It is further assumed that the... 

Distillation tray models Young and Stewart (1992, 1995) 2b 1,1,1 AE GREG 152-157... 

The simplified tray model assumes idealized hydraulic conditions that enhance mass transfer (high tray efficiency) and maintain a low vapor pressure drop. Proper tray design aims at minimizing the effect of factors that tend to diminish good tray hydraulics. Inefficient performance may either be inherent in the tray type or design for a particular situation or may be the result of operating the column outside the design conditions. A look at some of these factors follows. 

A dynamic model of a distillation column can be assembled from simpler units, as trays, heat exchangers (condenser, reboiler), reflux drum, valves and pumps (Fig. 4.5). Tray modelling has to answer two issues (1) accurate description of material and energy holdup, and (2) accurate pressure drop calculation. 

Figure 4.5 Dynamic model for a distillation column Tray modelling...

Ciric and Gu (1994) present a MINLP-based approach for the design of RD columns for systems where multiple reactions take place and/or where reactive equilibrium or thermal neutrality caimot be assured. This method is based on the combination of a rigorous tray-by-tray model and kinetic-rate-based expressions to give basic constraints of an optimization model that minimizes the total annual cost. The major variables are the number of trays in the column, the feed tray location, the temperature and composition profiles within the column, the reflux ratio, the internal flows within the column and the column diameter. 

The product property model generates the product properties listed in Table 7. During projects, other product roperty calculations are added as needed. The online application at Suncor-Samia does not use the simplified fiactionator model. Instead, it uses fully rigorous tray-by-tray models for the HCC fractionation section. 

Based on physical considerations, a model structure can be derived which correlates the two dependent variables (vapor flow or production and top composition or quality) to the state variables (bottom composition and bottom contents) and the control variables (energy supply and the reflux). Fuzzy logic can be nsed to derive the description from the observations, without the need for rigorous tray-to-tray modeling. 

By use of the tray-to-tray model mentioned previously, one may calculate the required changes in distillate or reflux at column top, and boilup or bottom-product flow at column base required to hold terminal composition constant in the face of changes in the variables listed. 

The relationship of this type of model to a tme differential analysis has been discussed for the case of linear equiHbrium and first-order kinetics (74,75). A minor extension of this work leads to the foUowing relations for a bed section in which dow rates of soHd and Hquid are constant. For the number of theoretical trays,... 

The model of theoretical equiHbrium trays with entrainment is readily treated by computer with methods analogous to those used for the design of fractionating columns. 

Distillation Columns. Distillation is by far the most common separation technique in the chemical process industries. Tray and packed columns are employed as strippers, absorbers, and their combinations in a wide range of diverse appHcations. Although the components to be separated and distillation equipment may be different, the mathematical model of the material and energy balances and of the vapor—Hquid equiUbria are similar and equally appHcable to all distillation operations. Computation of multicomponent systems are extremely complex. Computers, right from their eadiest avadabihties, have been used for making plate-to-plate calculations. 

Fractional equihbrium stages have meaning. The 11.4 will be divided by a tray efficiency, and the rounding to an integral number of actual trays should be done after that division. For example, if the average tray efficiency for the process being modeled in Fig. 13-36 were 80 percent, then the number of actual trays required would be 11.4/0.8 = 14.3, which would be rounded to 15. 

The iC values (vapor-liquid equihbrium ratios) in Equation (13-123) are estimated from the same equation-of-state or aclivity-coefficient models that are used with equilibrium-stage models. Tray or packed-section pressure drops are estimated from suitable correlations of the type discussed by Kister (op. cit.). 

From the above list of rate-based model equations, it is seen that they total 5C -t- 6 for each tray, compared to 2C -t-1 or 2C -t- 3 (depending on whether mole fractious or component flow rates are used for composition variables) for each stage in the equihbrium-stage model. Therefore, more computer time is required to solve the rate-based model, which is generally converged by an SC approach of the Newton type. 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

The rate-based model gave a distillate with 0.023 mol % ethylbenzene and 0.0003 mol % styrene, and a bottoms product with essentially no methanol and 0.008 mol % toluene. Miirphree tray efficiencies for toluene, styrene, and ethylbenzene varied somewhat from tray to tray, but were confined mainly between 86 and 93 percent. Methanol tray efficiencies varied widely, mainly from 19 to 105 percent, with high values in the rectifying section and low values in the stripping section. Temperature differences between vapor and liquid phases leaving a tray were not larger than 5 F. 

Based on an average tray efficiency of 90 percent for the hydrocarbons, the eqiiilibniim-based model calculations were made with 36 equilibrium stages. The results for the distillate and bottoms compositions, which were very close to those computed by the rate-based method, were a distillate with 0.018 mol % ethylbenzene and less than 0.0006 mol % styrene, and a bottoms product with only a trace of methanol and 0.006 mol % toluene. 

The second classification is the physical model. Examples are the rigorous modiiles found in chemical-process simulators. In sequential modular simulators, distillation and kinetic reactors are two important examples. Compared to relational models, physical models purport to represent the ac tual material, energy, equilibrium, and rate processes present in the unit. They rarely, however, include any equipment constraints as part of the model. Despite their complexity, adjustable parameters oearing some relation to theoiy (e.g., tray efficiency) are required such that the output is properly related to the input and specifications. These modds provide more accurate predictions of output based on input and specifications. However, the interactions between the model parameters and database parameters compromise the relationships between input and output. The nonlinearities of equipment performance are not included and, consequently, significant extrapolations result in large errors. Despite their greater complexity, they should be considered to be approximate as well. 

Analysts must recognize the above sensitivity when identifying which measurements are required. For example, atypical use of plant data is to estimate the tray efficiency or HTU of a distillation tower. Certain tray compositions are more important than others in providing an estimate of the efficiency. Unfortunately, sensor placement or sample port location are usually not optimal and, consequently, available measurements are, all too often, of less than optimal use. Uncertainty in the resultant model is not minimized. 

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