Feed tray models

The simplest distillation models to set up are the shortcut models. These models use the Fenske-Underwood-Gilliland or Winn-Underwood-Gilliland method to determine the minimum reflux and number of stages or to determine the required reflux given a number of trays or the required number of trays for a given reflux ratio. These methods are described in Chapter 11. The shortcut models can also estimate the condenser and reboiler duties and determine the optimum feed tray. 

A distillation column, for instance, would be modeled with a column section for the stripping section, a column section for the rectifying section, and single equilibrium stages for the feed tray, the condenser, and the reboiler. In order to solve the distillation column separation equations as one unit, two sets of Equation 12.33, each with the appropriate stripping factors for the corresponding section, would have to be solved simultaneously along with a component balance around the feed tray, the condenser, and reboiler equations. Such a solution does exist for conventional distillation and for certain extraction problems (Smith and Brinkley, 1960). 

Earlier chapters use simplified and binary models to analyze in a very informative manner some fundamentals such as the effect of reflux ratio and feed tray location, and to delineate the differences between absorption/stripping and distillation. Following chapters concentrate on specific areas such as complex distillation, with detailed analyses of various features such as pumparounds and side-strippers, and when they should be used. Also discussed are azeotropic, extractive, and three-phase distillation operations, multi-component liquid-liquid and supercritical extraction, and reactive multistage separation. The applications are clearly explained with many practical examples. 

The solution to the RD problems results in the optimum number of trays, the optimal feed tray location, reflux ratio, condenser and reboiler duties and liquid hold-ups on each tray. Since the model contains both continuous e.g. temperature and composition) and discrete i.e. number of trays) design variables, it should be solved by MINLP optimization technique. 

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 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... 

Figure 5.29. Models of feed tray (a) first mixing then attain equilibrium, and (b) mixing and attain equilibrium simultaneously.

At the first stage, the simplified model of feed tray (Fig. 5.29b) and assumption about hnearity of minimum reflux bundles are accepted. At this stage, the value (L/F) is determined taking into consideration the coordinates of stationary points from the condition of intersection of linearized minimum reflux bundles S - and (i.e., the smallest value of parameter L/V r is found at... 

First, a steady state model was built. The three reactors are modelled as CSTR and PFR rectors while the reaction kinetics are modelled with the available standard Arrhenius kinetic expressions in HYSYS.PLANT with the kinetic data available in the literature (see Ref. [45-48]). The four separation columns are modelled and simulated, at steady state, as full rigorous distillation columns based on the specifications of the inlet streams, colunms pressure profiles, required number of trays and feed tray location. Moreover, two more specifications are required for each column with both reboiler and condenser. These specifications could be the duties, reflux flow rate, draw streams rates, composition fractions, column recovery, etc. 

The mathematical model described in Section 5.2.1 indicates that two variables must be specified in order to define the performance of a column with fixed pressure, number of stages, feed tray location, and feed rate, composition, and thermal conditions. Three specifications are... 

Petroleum distillate fractionators are identical in appearance to the classical model studied in the classroom. They are fitted with condensers and reboilers and process generally one feed into two or, at the most, three products. The feed enters the tower at an intermediate tray so that there is always a stripping section below the feed tray and a... 

With all feed conditions and the column configuration specified (number of trays in each section, tray holdup in the reactive section, feed tray locations, pressure, and desired conversion), there is only one remaining degree of freedom. The reflux flowrate is selected. It is manipulated by a distillate composition controller to drive the distillate composition to 95 mol% C. The vapor boilup is manipulated to control the liquid level in the base. Note that the distillate and bottoms flowrates are known and fixed as the dynamic model is converged to the steady state that gives a distillate composition of 95 mol% C. The composition of the bottoms will be forced by the overall component balance to be 95 mol% D. 

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. 

Develop a mathematical model for the three-column train of distillation columns sketched below. The feed to the first column is 400 kg mol/h and contains four components (1, 2, 3, and 4), each at 25 mol %. Most of the lightest component is removed in the distillate of the first column, most of the next lightest in the second column distillate and the final column separates the final two heavy components. Assume constant relative volatilities throughout the system ai, CI2, and a3. The condensers are total condensers and the reboilers are partial. Trays, column bases, and reflux drums are perfectly mixed. Distillate flow rates are set by reflux drum... 

In order for a process to be controllable by machine, it must represented by a mathematical model. Ideally, each element of a dynamic process, for example, a reflux drum or an individual tray of a fractionator, is represented by differential equations based on material and energy balances, transfer rates, stage efficiencies, phase equilibrium relations, etc., as well as the parameters of sensing devices, control valves, and control instruments. The process as a whole then is equivalent to a system of ordinary and partial differential equations involving certain independent and dependent variables. When the values of the independent variables are specified or measured, corresponding values of the others are found by computation, and the information is transmitted to the control instruments. For example, if the temperature, composition, and flow rate of the feed to a fractionator are perturbed, the computer will determine the other flows and the heat balance required to maintain constant overhead purity. Economic factors also can be incorporated in process models then the computer can be made to optimize the operation continually. 

Rmin and the corresponding number of trays calculated ( 2N J. The shortcut models were replaced by rigorous RADFRAC units, where the reflux and distillate feed ratio were adjusted by means of design specifications, in order to meet the desired separation. The trays were sized using Aspen s facilities. Finally, the dimensions of the reflux drum and column sump were found based on a residence time of 5 min and aspect ratio H D = 2 1. Table 9.7 presents the results of distillation column sizing. 

Pure component physical property data for the five species in our simulation of the HDA process were obtained from Chemical Engineering (1975) (liquid densities, heat capacities, vapor pressures, etc.). Vapor-liquid equilibrium behavior was assumed to be ideal. Much of the flowsheet and equipment design information was extracted from Douglas (1988). We have also determined certain design and control variables (e.g., column feed locations, temperature control trays, overhead receiver and column base liquid holdups.) that are not specified by Douglas. Tables 10.1 to 10.4 contain data for selected process streams. These data come from our TMODS dynamic simulation and not from a commercial steady-state simulation package. The corresponding stream numbers are shown in Fig. 10.1. In our simulation, the stabilizer column is modeled as a component splitter and tank. A heater is used to raise the temperature of the liquid feed stream to the product column. Table 10.5 presents equipment data and Table 10.6 compiles the heat transfer rates within process equipment. 

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