Question

Problem #1: Haber-Bosch process. The Haber-Bosch process is an equilibrium-limited catalyzed reaction that converts nitrogen (N2) and hydrogen (H2) into ammonia (NH3). The process won Haber a Nobel Prize since it provided a way to produce fertilizer for millions of people at the beginning of the 20th century. However, this process typically has very low single pass conversion due to a low equilibrium at the prevailing temperature and therefore a recycle stream is required to achieve a high overall conversion. This process is typically conducted at 200 atm and 400 C. N2 + 3 H2 = 2 NH3 The fresh feed contains 23.3 mol% N2, 70 mol% H2, and 6.7 mol% inert gas. This stream combines with a recycle stream, and enters a reactor. The input stream to the reactor, N2 and H2, is in stoichiometric ratio. After the reaction, the product (NH3) is totally separated from the unreacted gas mixture in a condenser. The product goes in one stream, and the unreacted reactants are recycled. In order to rid the inert gas, a purge is included on the recycle. The single pass conversion of N2 to product is 13%. We want an overall conversion of 93% for N2. Use a basis of 100 mol/s for the fresh feed. (we suggest that you do these calculations in excel to allow you to make changes in the overall conversion for parts c, d, and e

a. Draw and label the diagram.

b. Fill in the SPICE table around the reactor.

c. Calculate the recycle ratio and mole fraction of inerts in the waste stream for an overall conversion of 93%.

d. Calculate the recycle ratio and mole fraction of inerts in the waste stream for an overall conversion of 90%.

e. Calculate the recycle ratio and mole fraction of inerts in the waste stream for an overall conversion of 98%.

f. What will happen to the reactor residence time (V/?̇ 2 – the time that the gas spends in the reactor) for an increase of R? Assume that the volume of the reactor remains the same.

g. What are the tradeoffs for a high conversion? Why would it cost more money?

(SPICE stands for species, initial, change, exit)

Answer 1

The inert in the fresh feed is completely removed through purge stream. The definitions of single pass and overall conversion is given below. Using the reaction stoichiometry, the balance is applied as shown below.