# Material Balances Calculation Involving Purge Process

Bleeding off a portion of the recycle stream is important in a production process to avoid the accumulation of undesirable material. For instance, if inert components from a reactor feed are not separated from the recycling stream in the separation units, they would build up in the recycle stream until they made up the whole stream. To keep the inert level within reasonable level, some of the stream would need to be purged. Normally, a continuous purge would be employed. Assuming steady-state circumstances:

Loss of inert in the purge = Rate of feed of inerts into the system

The concentration of any component in the purge stream will be the same as that in the recycle stream at the point where the purge is taken off. Consequently, the relationship shown below can be used to calculate the necessary purge rate:

[Feed stream flowrate] × [Feed stream inert concentration] =

[Purge stream flowrate] × [Specified (desired) recycle inert concentration]

Let’s see example below.

In the production of ammonia from hydrogen and nitrogen, the conversion based on either raw material, is limited to 15%. The ammonia produced is condensed from the reactor product stream and the unreacted material recycled. If the feed contains 0.2% argon (from the nitrogen separation process), calculate the purge rate required to hold the argon in the recycle stream below 5.0%. Percentages are by volume.

Solution

Process diagram:

Basis = 100 mols feed. Purge rate will be expressed as mols per 100 mol feed.

Volume percentage are taken as equivalent to mol percent.

Let purge rate per 100 mol feed be F.

Based on equation above:

[Feed stream flowrate] × [Feed stream inert concentration] =

[Purge stream flowrate] × [Specified (desired) recycle inert concentration]

100 × 0.2% = F × 5%

F = 4 mol

Therefore, purge required is 4 mol per 100 mol feed.

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