Problem 3.7.1

 

An ammonia synthesis reactor gives a conversion of 22 percent when gases a stoichiometric ratio of 3 moles of hydrogen to one mole of nitrogen is maintained at the reactor inlet.  The product gas is cooled in a series of chillers before passing through a separator, where liquid ammonia is withdrawn.  Five percent of the separator off gas is purged while 95 percent is recycled to the ammonia reactor.  Nitrogen is derived from air during the reforming process where hydrogen is produced.  After reforming, the gases are sent to different reactors that remove any carbon monoxide, carbon dioxide and methane.  Fresh air contains 78.006 percent nitrogen and 0.994 percent argon.  Find the composition of gas stream at different stages of the synthesis process. 

 

Solution: 

 

Assume 100 moles of nitrogen are fed to the reactor.  This corresponds to Point 1 in the block diagram.  We know that the at this point, hydrogen to nitrogen is maintained at 3 to 1.  Hence 300 moles of hydrogen are entering the reactor.

 

The ammonia reactor has a conversion of 22 percent, so 22 moles of nitrogen, 66 moles of hydrogen are consumed and 44 moles of ammonia are produced.  The composition of the gas at the reactor inlet, Point 2, is nitrogen 78 moles, ammonia 44 moles, and hydrogen 234 moles.

 

This gas passes through a series of chillers, thus condensing the ammonia vapors in the process and enters the ammonia separator.  Liquid ammonia is withdrawn from the bottom of the separator referred as Point 3 and its quantity is 44 moles.

 

The separator off-gas has lost liquid ammonia, the rest of the components being the same as entering the separator.  Given the information that only five percent of the off-gases are purged, nitrogen in the purge stream is 0.05 time 78 equal 3.9 moles.  Similarly, amount of hydrogen being purged can be found to be 0.05 time 234 equal 11.7 moles.

 

We know that 95 percent of the off-gases are being recycled.  Amount of nitrogen in the recycle stream is 0.95 time 78 equal 74.1 moles.  Similarly, hydrogen amount is 0.95 time 234 equal 222.3 moles. 

 

Now, we can calculate the amount of fresh feed, as the combined feed going to the reactor contains 100 moles of nitrogen, and stoichiometric value of hydrogen (300 moles).  Nitrogen entering from the fresh feed is 100 minus 74.1 equal 25.9 moles.  Similarly, hydrogen quantity entering with the fresh feed is 300 minus 222.3 equal 77.7 moles.  Please note that argon to nitrogen ratio in the feed is 0.994 to 78.006.  Multiplying this value with 25.9 (amount of nitrogen in the fresh feed) gives argon quantity as 0.33 moles.

 

At steady state, amount of argon entering the system is equal to the amount leaving through purge stream.  Hence, amount of argon at Point 5 is 0.33 moles.

 

Amount of argon in the recycle stream is 0.95 over 0.05 or 19 times more than the purge stream.  This amount of argon is calculated to be 0.33 time 19 or 6.271 moles.

 

The last missing value is amount of argon in the separator off-gas (Point 4).  This value is calculated as 6.271 plus 0.33 or 6.601 moles.

 

Now, we have all the quantities required at Points 1 through 7.