Ammonia Reactor Design

For our Introduction to Process Analysis class, we were tasked with optimizing an ammonia reactor based off of the Haber-Bosch process, given specific parameters.  This was our first insight into the concepts of thermodynamics, and chemical reaction engineering.  Our task was to find the optimal volume of the plug flow reactor and condensing temperature in order to maximize profit of the production of ammonia.


With a growing population, the demand for food production is on the rise.  In order to accomodate for this growth, improvements in agricultural usage must be made, in addition to dietary alterations.  Industrial food supply chain is one of the biggest consumers of fossil fuels and producers of greenhouse gas, which poses a challenge for designing a reactor that can increase yield and minimize emissions.  The Haber–Bosch process, designed by Fritz Haber and Carl Bosch, operates via a plug flow reactor paired with a condensation and recycle process.  Currently, this process is the main process of ammonia production from atmospheric air.  Ammonia is created from a mixture of nitrogen and hydrogen following the chemical equation: 

At steady-state, atmospheric air feeds into a recycle stream and enters the plug flow reactor and is promoted via an iron catalyst.  The gas-phase reaction occurs inside the reactor and sends the products to a heat exchanger to isolate ammonia from unconverted gas products.  The gases travel to the top of the condenser where the stream splits into a purge and recycle stream.

Design Parameters

Mole Fraction at Fresh Feed "F"

Reaction Rate:​

Antione's Constants of Ammonia:

A = 7.36050

B = 926.132

C = 240.17

PFR Reactor Conditions:

Temperature : 900ºF

Pressure  : 300 bar

β : 0.00140

k1 :  1.20 lbmol/cubic ft. hr

K : .00467

Single-Pass Conversion : .20

Other Considerations:

Recycle Ratio : 4

Production Capacity : 100,000 ton/year

Reactor Pricing : $200,000 ft/year

Energy Cost : $0.0002 1/Btu

Cp = 17.74 Btu / lbmol K

Our Approach

In order to start solving for the contents at each interval, assumptions need to be made:

  • Ideal gas assumption was used since we had not learned equations of state.

  • Atmospheric heat transfer is neglected 

  • Assumed 100mol/hr basis at the fresh feed "F" inlet in order to calculate the amount of moles at the feed.

  • Argon is identified as a tie component since it does not participate in the reaction.

  • At steady state, no argon accumulates, therefore the amount of argon in the fresh feed is equal to the amount of argon leaving the system in the purge stream.

  • The fresh feed contains a stoichiometric ratio of hydrogen to nitrogen in 3:1 ratio, that is maintained in the same ratio in all the streams in the system. 

The mixture of ammonia vapor and the non-condensable gases leaving the condenser, CV, splits and a small amount leaves in a purge stream P  . The balance of ammonia, nitrogen, hydrogen, and argon is returned to the recycle stream R. Therefore, streams CG, R, and P  have the same molar compositions.  Performing mole balances on stream junctions

CG, RF, and the reactor allowed us to represent the molar composition of each stream in terms of molar fraction of nitrogen, y.  Additionally, Raoult's Law was utilized in order to isolate the ratio of vapor and liquid contents in the condenser to a single variable, z.  At this point, a system of equations was generated to find the molar compositions of each stream that was dependent on condenser temperature, :

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At this point, solving for a maximum yield of ammonia would intuitively come from the lowest condensing temperature possible; however, this would be very cost and energy intensive.  Solving for the cost of production required solving for the dimensions of the reactor, and heat of the reactor.  We solved for heat of the reactor using Newton's Law of Cooling (given). 





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We utilized MATLAB in order to iteratively solve for the cheapest operating conditions at given temperatures.  MATLAB package trapz was utilized in order to implement trapezoidal approximation methods.

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We estimated that operating the reactor at 280K would cost $242M annually, which would require a PFR volume of 143 cubic feet to produce 100,000 tons of ammonia per year.  Deviation of the temperature by 5K will cause a fluctuation in operating costs by less than 1%; however, the operating conditions do raise some environmental concerns.  According to this process, 1,460 tons of ammonia is emitted into the atmosphere.  Ammonia exposure is a health hazard; 25ppm in 10 hours can prove to be fatal.  Routine maintenance or monitoring of leaks would be necessary.  We would recommend scrubbing water-soluble ammonia into this purge stream in order to reduce environmental concerns before flaring the excess gases.