Normal butane is catalytically isomerized to isobutene. A fresh feed stream containing pure n-butane at temperature T₁ [(°C) is mixed adiabatically with a recycle stream containing n-butane and isobutene, and the combined stream is fed to the reactor, where some but not all of the n-butane in the feed is converted. The reactor effluent is pumped to a distillation column. The overhead distillation product contains primarily isobutene and a small amount of n-butane. The bottoms product, which also contains both species, is the stream recycled to the reactor. The streams leaving the distillation column are at different temperatures.

(a) Determine the number of degrees of freedom associated with the feed mixer, the reactor, the distillation column, and the entire process. Include all unknown process stream temperatures and process unit heat duties in your analysis.

(b) Suppose a single-pass conversion of 35.0% is attained in the reactor, the overhead distillation column product contains 88.5 mole% isobutene, and the recycle stream contains 85.0 mole% n-butane, Calculate the overall conversion, the recycle ratio (mol recycle/mol fresh feed), and the gram-moles of overhead product produced per 100 mol fresh feed.

(c) Solve the problem of part (b) again, only this time do it as it might be done by a sequential modular simulation of the process. Take a basis of calculation of 100 mol fresh feed and choose r (mol recycle) as the tear stream variable. Begin by assuming n_г = 100mol and go through three successive substitution iterations (Appendix A.2). What is the percentage error in the third calculated value of n?

(d) Repeat part (c), only perform a Wegstein acceleration step (Appendix A.2) after the first two successive substitution iterations. What is the percentage error in the last calculated value of n?

(e) Set up a spreadsheet to do the calculations of parts (c) and (d), using Example 10.2-3 as a model. Proceed to convergence.