The fresh feed to an ammonia production process contains nitrogen (N2) and hydrogen (H2) in stoichiometric proportion, along with an inert gas (I). The feed is combined with a recycle stream containing the same three species, and the combined stream is fed to a reactor in which a low single pass conversion of nitrogen is achieved. The reactor effluent flows to a condenser. A liquid stream containing essentially all of the ammonia formed in the reactor and a gas stream containing all of the inerts and the unreacted nitrogen and hydrogen leave the condenser. The gas stream is split into two fractions: one is removed from the process as a purge stream, and the other is the recycle stream combined with the fresh feed.
a. Let xI0 be the mole fraction of inerts in the fresh feed, fsp the single pass conversion of nitrogen in the reactor and yp the fraction of the gas leaving the condenser that is purged (mol purged/ mol total). Taking a basis of 1 mol fresh feed, draw and fully label a process flowchart, incorporating xI0, fsp, and yp in the labeling. Then, assuming that the values of these three variables are given, write a set of equations for the total moles fed to the reactor (nA), the moles of ammonia produced (np), and the overall nitrogen conversion (fov). Each equation should involve only one unknown variable, which should be circled.
b. Solve the equations of part a for xI0=0.01, fsp=0.20, yp=0.10.