Rigorous Methods fo r the Simulation of Multistaged Separations

solution of the nonequilibrium model when compared with the equilibrium stage model (there are 5nc+1 equations per stage on the nonequilibrium model and

2nc+^ equations per stage on the equilibrium stage). One of the suggested alternatives is the "stage lumping", where the column is divided in sections, each representing more than one real tray. Every section is then modelled by a set of 5nc+^ equations and variables. As expected, the accuracy of the predicted compositions decreased as the number of sections employed was decreased. In order to improve the quality of the results obtained using this "lumping" technique the bulk vapour composition must be evaluated using the following expression

(2.55)

where n is the number of "lumped" trays.

The application of the nonequilibrium method into industrial-scale distillation and absorption columns is presented by Taylor et al. (1992). Due to the good agreement between experimental and predicted values and, based on their experience with this new methodology, they recommend its use for the following classes of problems:

• packed columns;

• strongly nonideal systems;

• columns with sharp profiles or containing a maximum; • columns with multiple feeds and/or sidestreams; • columns with unknown efficiencies.

2 .4 - Se l e c t io n o f t h e Me t h o d t o Use

After ensuring that the problem is well defined it is necessary to select which method is more suitable for the system to be analysed and for the output to be produced.

Chapter 2 - Rigorous Methods fo r the Simulation o f Multistaged Separations 46 necessary to feed more information in order to initialise the solution procedure. It is also necessary to check if the selected method of solution is able to deal with the kind of specifications to be imposed.

Some very useful guidelines on which method to choose are presented by King (1980). Haas (1992) also presents a very good discussion of the subject and a decision diagram to help in the selection (see Figure 2.4).

2 .5 - Mo d e l s fo r Pa c k e d Co lu m n s

Nowadays the application of packed-bed separation columns has increased in the field of distillation. Unfortunately the modelling work of packed-bed separation processes presented in the open literature is much less than that for staged systems.

The packed column is a non-linear distributed parameter system that needs to be significantly simplified (without losing important information) before any kind of analysis can be performed.

Frequently the engineer that deals with the design of a packed column introduces some simplifying assumptions like the Height of a Transfer Unit (HTU) or the Height Equivalent to a Theoretical Plate (HETR) causing a reduction on the accuracy of the results.

Holland and co-workers [Holland (1975), McDaniel (1968, 1969), McDaniel et al. (1970), Bassyoni (1969)] opted to divide the packed column into increments or discrete mass transfer sections. Such increments are then considered as stages in a tray column. With this approach any of the previously presented methods to deal with tray columns can be used to simulate the packed column.

In their technique the temperatures of the vapour and liquid streams leaving a section are considered to be equal; the errors caused by the introduction of this

Tall Short Homotopy Relaxation Complex Short Tall Boiling range Global Newton Highly nonideal Short

or tall _{Distillation Distillation Distillation}

Distillation Nonequilibrium Ideal or mildly nonideal Moderately nonideal Absorber/ stripper Absorber/ stripper Simple or complex Narrow boiling Middle boiling Wide boiling Boston or Russell inside-out How ' ideal?. Boston inside-out (bubble point) Russell inside-out (Sum-rates) Russell inside-out (2N-Newton) Russell inside-out (2N-Newton) Boston or Russell inside-out Boston or Russell inside-out (2N-Newton) Boston or Russeii inside-out (2N-Newton) Chemical absorption reactive mass transfer dependent Simple: Few feeds, Few sidedraws, Heat exchangers •'! bo 2 g I

I

Chapter 2 - Rigorous Methods fo r the Simulation o f Multistaged Separations_______ ^

approximation are absorbed in the vaporisation efficiencies that are employed to correct the composition of the exit streams from departures to equilibrium.

Unfortunately these vaporisation efficiencies are not easily computed in advance and therefore they used some field tests in order to estimate these parameters that were then used in further simulations.

Another approach to model the packed column is to write differential mass and energy balances for a small element of packing and to solve them by a numerical integration scheme.

Some researchers have been working attempting to solve the differential equations produced when the two-film concept of mass transfer is applied.

Treybal (1969) presented a solution procedure that for the first time also included the mass and heat transfer resistances of the liquid phase. His procedure was only able to deal with simple three component systems, with only one component being transferred.

This methodology was extended by Feintuch and Treybal (1978) to multicomponent systems. For a specified absorption separation one should guess the conditions of one of the exit streams. Based on the guessed exit stream and with a specified number of packing height increments, a complex iterative procedure, with several levels of nested loops, is used. Kelly et al.

(1984) employed this methodology to model the absorption of acid gases in methanol. They made some alterations to the solution algorithm to improve the convergence characteristics of the systems they studied.

von Rosenberg and Hadi (1980) replaced the differential equations by finite difference equations that are then solved using a tridiagonal matrix algorithm. The problem with the finite difference technique is the large number of segments needed to approximate the continuous system.

Chapter 2 - Rigorous Methods fo r the Simulation of Multistaged Separations 49