Modeling distillation column

Modelling a single tray is similar with a dynamic flash discussed before. The solution of the assembly of trays, increased with condenser, flash drum and reboiler, is a much more difficult problem, however. The equations presented below (for notations see Fig. 4.6) are known as MESH equations for modelling distillation columns at steady state enlarged with left hand terms for accumulation. 

The situation is very much poorer for stmctured rather than random packings, in that hardly any data on Hq and have been pubHshed. Based on a mechanistic model for mass transfer, a way to estimate HETP values for stmctured packings in distillation columns has been proposed (91), yet there is a clear need for more experimental data in this area. 

General Properties of Computerized Physical Property System. Flow-sheeting calculations tend to have voracious appetites for physical property estimations. To model a distillation column one may request estimates for chemical potential (or fugacity) and for enthalpies 10,000 or more times. Depending on the complexity of the property methods used, these calculations could represent 80% or more of the computer time requited to do a simulation. The design of the physical property estimation system must therefore be done with extreme care. 

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. 

Many industrial separations require a series of columns that are connected in specific ways. Some distillation programs can model such a system as a hypothetical single column with arbitrary cross-flows and connections and then carry out the distillation calculations for the modeled hypothetical column. Alternatively, such a system can be modeled as a process flow sheet using a process simulator. 

In the chemical engineering domain, neural nets have been appHed to a variety of problems. Examples include diagnosis (66,67), process modeling (68,69), process control (70,71), and data interpretation (72,73). Industrial appHcation areas include distillation column operation (74), fluidized-bed combustion (75), petroleum refining (76), and composites manufacture (77). 

Differential-Algebraic Systems Sometimes models involve ordinary differentia equations subject to some algebraic constraints. For example, the equations governing one equihbrium stage (as in a distillation column) are... 

RGA Example In order to illustrate use of the RGA method, consider the following steady-state version of a transfer function model for a pilot-scale, methanol-water distillation column (Wood and Berry, Terminal Composition Control of a Binaiy Distillation Column, Chem. Eng. Sci, 28, 1707, 1973) Ku = 12.8, K = -18.9, K. i = 6.6, and Koo = —19.4. It follows that A = 2 and... 

This matrix will contain information regarding loading characteristics such as flooding hmits, exchanger areas, pump curves, reactor volumes, and the like. While this matrix may be adjusted during the course of model development, it is a boundary on any possible interpretation of the measurements. For example, distillation-column performance markedly deteriorates as flood is approached. Flooding represents a boundary. These boundaries and nonlinearities in equipment performance must be accounted for. 

With respect to selecting measurements, emphasis should include measurements within the equipment such as tower internal temperatures and compositions, internal reac tor conditions, and intermediate exchanger temperatures in multipass exchangers. Trace component compositions provide particular insight into distillation-column performance. Those components that fall between the heavy and light keys and distribute in the products can usually be described by a variety of models and parameter estimates They provide little insight into the column performance. 

Example 11.7 Carbon dioxide is sometimes removed from natural gas by reactive absorption in a tray column. The absorbent, typically an amine, is fed to the top of the column and gas is fed at the bottom. Liquid and gas flow patterns are similar to those in a distillation column with gas rising, liquid falling, and gas-liquid contacting occurring on the trays. Develop a model for a multitray CO2 scrubber assuming that individual trays behave as two-phase, stirred tank reactors. 

Distillation is a well-known process and scale-up methods have been well established. Many computer programs for the simulation of continuous distillation columns that are operated at steady state are available. In fine chemicals manufacture, this concerns separations of products in the production of bulk fine chemicals and for solvent recovery/purification. In the past decade, software for modelling of distillation columns operated at non-steady state, including batch distillation, has been developed. In the fine chemicals business, usually batch distillation is applied. 

The principle of the perfectly-mixed stirred tank has been discussed previously in Sec. 1.2.2, and this provides essential building block for modelling applications. In this section, the concept is applied to tank type reactor systems and stagewise mass transfer applications, such that the resulting model equations often appear in the form of linked sets of first-order difference differential equations. Solution by digital simulation works well for small problems, in which the number of equations are relatively small and where the problem is not compounded by stiffness or by the need for iterative procedures. For these reasons, the dynamic modelling of the continuous distillation columns in this section is intended only as a demonstration of method, rather than as a realistic attempt at solution. For the solution of complex distillation problems, the reader is referred to commercial dynamic simulation packages. 

Figure 3.58. Model representation of a batch distillation column and typical plate n, as per Luyben (1973).

The conlinuous binary distillation column of Fig. 3.60 follows the same general representation as that used previously in Fig. 3.58. The modelling approach again follows closely that of Luyben (1973, 1990). 

Figure 3.60. Model representation of a continuous binary distillation column. PC is the cooling water controller, LC the reflux controller.

Relaxation methods are not competitive with the steady-state methods in the use of computer time, because of slow convergence. However, because they model the actual operation of the column, convergence should be achieved for all practical problems. The method has the potential of development for the study of the transient behaviour of column designs, and for the analysis and design of batch distillation columns. 

While we laud the virtue of dynamic modeling, we will not duphcate the introduction of basic conservation equations. It is important to recognize that all of the processes that we want to control, e.g. bioieactor, distillation column, flow rate in a pipe, a drag delivery system, etc., are what we have learned in other engineering classes. The so-called model equations are conservation equations in heat, mass, and momentum. We need force balance in mechanical devices, and in electrical engineering, we consider circuits analysis. The difference between what we now use in control and what we are more accustomed to is that control problems are transient in nature. Accordingly, we include the time derivative (also called accumulation) term in our balance (model) equations. 

Other synonyms for steady state are time-invariant, static, or stationary. These terms refer to a process in which the values of the dependent variables remain constant with respect to time. Unsteady state processes are also called nonsteady state, transient, or dynamic and represent the situation when the process-dependent variables change with time. A typical example of an unsteady state process is the operation of a batch distillation column, which would exhibit a time-varying product composition. A transient model reduces to a steady state model when d/dt = 0. Most optimization problems treated in this book are based on steady state models. Optimization problems involving dynamic models usually pertain to optimal control or real-time optimization problems (see Chapter 16)... 

Figure E2.7 shows the process flow chart for a series of two distillation columns, with mass flows and splits defined by j, x2,..., 5. Write the material balances, and show that the process model comprises two independent variables and three degrees of freedom.

The equality constraints. The process model comprises the equality constraints. For a conventional distillation column we have the following typical relations ... 

Skogestad, S. Dynamic and Control of Distillation Columns—A Critical Survey. Modeling Identification Control 18 177-217 (1997). 

Changes in the hydraulic hold-up of liquid on the column plates is known to have a significant effect on the separating efficiency of batch distillation columns, and may be relatively easily incorporated into the batch simulation model. The hydraulic condition of the plates is represented in Fig. 3.52. 

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