Split fraction

The Important Sequence Model module does sensitivity studies and importance rankings for about a thousand highest frequency sequences. The analyst zooms to the most frequent plant damage category, to the most frequent sequences in that category, to the most important top event, to the most important split fraction, and to the most important cutsets. If sensitivity analysis is needed on the model as a whole, a menu option, "CLONE a Model," makes a copy of the model, c hange,s are made, and results compared. 

The procedure is based on the theory of recycle processes published by Nagiev (1964). The concept of split-fractions is used to set up the set of simultaneous equations that define the material balance for the process. This method has also been used by Rosen (1962) and is described in detail in the book by Henley and Rosen (1969). 

Uj i i = the fraction of the total flow of component k entering unit i that leaves in the outlet stream connected to the unit j the split-fraction coefficient , gi 0 lc = any fresh feed of component k into unit i flow from outside the system (from unit 0). 

The flow of any component from unit i to unit j will equal the flow into unit i multiplied by the split-fraction coefficient. 

The value of the split-fraction coefficient will depend on the nature of the unit and the inlet stream composition. 

For practical processes most of the split-fraction coefficients are zero and the matrix is... 

In general, the equations will be non-linear, as the split-fractions coefficients (a s) will be functions of the inlet flows, as well as the unit function. However, many of the coefficients will be fixed by the process constraints, and the remainder can usually be taken as independent of the inlet flows (A s) as a first approximation. 

The fresh feeds will be known from the process specification so if the split-fraction coefficients can be estimated, the equations can be solved to determine the flows of each component to each unit. Where the split-fractions are strongly dependent on the inlet flows, the values can be adjusted and the calculation repeated until a satisfactory convergence between the estimated values and those required by the calculated inlet flows is reached. 

In a chemical reactor, components in the inlet streams are consumed and new components, not necessarily in the inlet streams, are formed. The components formed cannot be shown as split-fractions of the inlet flows and must therefore be shown as pseudo fresh-feeds. 

A reactor is represented as two units (Figure 4.10). The split-fractions for the first unit are chosen to account for the loss of material by reaction. The second unit divides the reactor output between the streams connected to the other units. If the reactor has only one outlet stream (one connection to another unit), the second unit forming the reactor can be omitted. 

The procedure for setting up the equations and assigning suitable values to the split-fraction coefficients is best illustrated by considering a short problem the manufacture of acetone from isopropyl alcohol. 

Figure 4.12 is redrawn in Figure 4.13, showing the fresh feeds, split-fraction coefficients and component flows. Note that the fresh feed g2ok represents the acetone and hydrogen generated in the reactor. There are 5 units so there will be 5 simultaneous equations. The equations can be written out in matrix form (Figure 4.14) by inspection of Figure 4.13. The fresh feed vector contains three terms.

The values of the split-fraction coefficients will depend on the function of the processing unit and the constraints on the stream flow-rates and compositions. Listed below are suggested first trial values, and the basis for selecting the particular value for each component. 

Substitution of the values of the split-fraction coefficients for the other components will give the sets of equations for the component flows to each unit. The values of the split-fraction coefficients and fresh feeds are summarised in Table 4.2. 

Most proprietary spreadsheets include a routine for the inversion of matrices and the solution of sets of linear simultaneous equations. By using cell references, with cell copying and cell pointing, it is a simple procedure to set up the split fraction matrices... 

Once the spreadsheet has been set up it is easy to change the values of the split fractions and fresh feeds, and iterate until the design constraints for the problem are satisfied. 

Step 1 Set up the table of split-fractions and fresh feeds, Figure 4.15. 

Step 4 Copy the appropriate split-fractions and fresh feeds from the table of split-fractions and fresh feeds, Figure 4.15, into the component matrices, Figure 4.17. Copy the cell references, not the actual values. Using the cell references ensures that subsequent changes in the values in the primary table, Figure 4.15, will be copied automatically to the appropriate matrix. 

Step 9 Change the values of the appropriate split fractions, or fresh feeds, in the primary table, Figure 4.15, and observe the changes to the calculated values which will carry through the spread sheet automatically. Iterate on the values until the desired result is obtained. 

Table 4.3 shows the feed of each component and the total flow to each unit. The composition of any other stream of interest can be calculated from these values and the split-fraction coefficients. The compositions and flows should be checked for compliance with the process constraints, the split-fraction values adjusted, and the calculation repeated, as necessary, until a satisfactory fit is obtained. Some of the constraints to check in this example are discussed below. 

This should approximate to the azeotropic composition (9 per cent alcohol, 91 per cent water). The flow of any component in this stream is given by multiplying the feed to the column (X5k) by the split-fraction coefficient for the recycle stream (a 15/.). The calculated flows for each component are shown in Table 4.4. 

These compositions should be checked against the vapour-liquid equilibrium data for acetone-water and the values of the split-fraction coefficients adjusted, as necessary. 

Guide rules for estimating split-fraction coefficients... 

The split-fraction coefficients can be estimated by considering the function of the process unit, and by making use of any constraints on the stream flows and compositions that arise from considerations of product quality, safety, phase equilibria, other thermodynamic relationships and general process and mechanical design considerations. The procedure is similar to the techniques used for the manual calculation of material balances discussed in Section 4.3. 

Suggested techniques for use in estimating the split-fraction coefficients for some of the more common unit operations are given below. 

The split-fractions for the reactants can be calculated directly from the percentage conversion. The conversion may be dependent on the relative flows of the reactants (feed composition) and, if so, iteration may be necessary to determine values that satisfy the feed condition. 

For a unit that simply combines several inlet streams into one outlet stream, the split-fraction coefficients for each component will be equal to 1. = 1. 

If the unit simply divides the inlet stream into two or more outlet streams, each with the same composition as the inlet stream, then the split-fraction coefficient for each component will have the same value as the fractional division of the total stream. A purge stream is an example of this simple division of a process stream into two streams the main stream and the purge. For example, for a purge rate of 10 per cent the split-fraction coefficients for the purge stream would be 0.1. 

A distillation column divides the feed stream components between the top and bottom streams, and any side streams. The product compositions are often known they may be specified, or fixed by process constraints, such as product specifications, effluent limits or an azeotropic composition. For a particular stream, 5 , the split-fraction coefficient is given by ... 

The split-fraction coefficients are not very dependent on the feed composition, providing the reflux flow-rate is adjusted so that the ratio of reflux to feed flow is held constant Vela (1961), Hachmuth (1952). 

Then the split-fraction coefficients can be calculated from a material balance. 

Ctjik Split-fraction coefficient fraction of component k flowing from unit i to unit j —... 

Adjust the values chosen for the split-fractions and feeds, so the results meet the constraints,... 

Using the data given below, draw an information flow diagram of the process and calculate the process stream flow-rates and compositions for the production of 600 t/d ammonia. Use either the Nagiev split fraction method, with any suitable spreadsheet or manual calculations. 

Separation of toluene from the other components can be by solvent extraction or extractive distillation, just as described in the benzene chapter. The boiling points of benzene and toluene are far enough apart that the feed to separation unit of choice can be split (fractionated) rather easily into benzene concentrate and a toluene concentrate. Alternatively, the separation unit can be thought of as aromatics recovery unit. Then an aromatics concentrate stream is fed to the solvent extraction unit, and, the aromatics outturn can be split into benzene and toluene streams by fractionation. Both schemes are popular. 

Control is the manipulation of a degree of freedom (e.g., heater, cooler or exchanger load, stream split fraction) in order to make a process feasible and/or economically optimal in the steady state. In this chapter, control is used in a static sense only process dynamics are not considered. 

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