Section 3.7.2.1: Process Case Study Assignments

Preliminary Exercise

Set up the material balance equations in matrix-vector form and write them out.

Using the `typical' values given for the parameters, solve using one of the solvers with which you were supplied.

Linear Process Modelling Exercise

The above method of describing a process is not very convenient, and the output obtained from the material balance calculation is not related to the way in which an engineer would think about the plant, i.e. in terms of streams and component flows.

You are required to produce a program (or spreadsheet if you are not working with Fortran) in which you need specify only the three process parameters of conversion, recovery and purge fraction. the program should be designed so that these can easily be set by the user.

This program should also produce a process-oriented output rather than a list of values. It is suggested that this should be a table of streams and component flowrates, e.g. with a column for each component and a row for each of the six streams (or vice-versa), all suitably labelled.

Partially Linear Process Model

1. It is required to present the results in terms of total component flows and mol fraction compositions. The latter are of course calculated from the ratio of one component flow to the total flow. This involves a nonlinear equation; however, this nonlinear subset constitutes a `tail' of the equation set and can also be calculated directly, i.e. without iteration.

Adapt your model to calculate this information.

2. To maintain reactor performance it is necessary to ensure that no more than 1% of C is present in the reactor inlet stream. This is done by adjusting the purge to maintain that value.

The set of equations now becomes nonlinear because P is now an unknown equations like the following occur:
x13 - P x10 = 0

Because there is an additional unknown another equation is needed. This is provided by the mol fraction specification at the reactor inlet:
x3 / (x1 + x2 + x3) - 0.01 = 0

(As written this is also nonlinear, although unlike the preceding equation, it may be rearranged to linear form if required.)

However, if we regard P as a tear variable we may guess a value for it and see if the mol fraction specification equations is satisfied. This is in effect iteration on a single variable and so may be handled as was, e.g. the bubble point calculation. The whole linear equation solution procedure is `nested' within this iteration.

Adapt your model as necessary to find the required purge rate at 0.8 fractional conversion and 0.1 fractional recovery of C in the column overheads. If you are using bisection you will appreciate that P must lie between 0.0 and 1.0. However, a value of zero will cause a `divide by zero' in the linear solver, so use a small positive value instead.

Return to Case Study Index

Return to Section 3 Index

Course Organiser
Last Modified 2/9/00