Recycle, bypass and purge

Lesson 4 found that the molecular sieve recovers only about 85 percent of the ethanol it receives in the product; the rest leaves in the regeneration stream. Sending that stream to a drain would waste millions of dollars of ethanol a year, so the plant returns it to the beer column, where the ethanol is recovered again. That return is a recycle. Kingfisher Bioenergy is also studying a small ammonia plant that would make fertilizer from hydrogen produced with renewable electricity, and its synthesis loop is the textbook example of recycle with a purge. Theo is asked to work out how recycle changes both processes. This lesson covers the three stream arrangements that make real plants efficient: recycle, bypass and purge.

Why processes recycle

A recycle stream returns material from a point downstream to a point upstream in the same process. Plants recycle for several reasons. Reactions rarely go to completion in one pass, so unreacted feed is separated from the product and sent back to the reactor. Separations are never perfect, so streams containing valuable product are returned for another try. Solvents, catalysts and heat carriers are expensive and are reused many times. Recycle can also dilute a feed to control temperature or moderate a fast reaction. The ethanol plant recycles backset to the slurry tank, regeneration ethanol to the beer column, evaporator condensate to the cook water, and carbon dioxide scrubber water to the fermenters.

The language matters. The fresh feed enters the process from outside. The process feed, or unit feed, is what actually enters the reactor or separator after the recycle has joined the fresh feed. The recycle ratio is the recycle flow divided by the fresh feed flow. In a loop with a high recycle ratio, the internal flows can be many times the plant's net throughput, and the equipment inside the loop must be sized for those internal flows.

A strategy for recycle problems

Recycle problems look harder than they are. The key is to choose boundaries in the right order. Usually the overall boundary, which crosses only the fresh feed, the products and any purge, has the fewest unknowns and should be solved first. The recycle stream never crosses the overall boundary, so it does not appear there at all. Then solve the mixing point, the reactor or the separator, whichever has zero degrees of freedom next.

The example shows the most important idea about recycle: the overall performance of a process depends on what leaves it, not on what happens in a single pass through one unit. A separator or reactor with modest single-pass performance can still give an excellent overall result if the unconverted or unrecovered material is recycled, provided there is a way out for everything that enters.

Overall and single-pass conversion

For a process with a reactor and a recycle, two conversions are defined. The single-pass conversion is the fraction of a reactant entering the reactor that reacts in one pass. The overall conversion is the fraction of the reactant in the fresh feed that reacts in the process as a whole. Lesson 6 covers reaction balances in full; here it is enough to see how recycle separates the two numbers.

If every bit of unreacted feed is separated and recycled, and nothing else leaves, the overall conversion approaches 100 percent regardless of the single-pass conversion. In practice, separations are imperfect and purges remove some reactant, so the overall conversion is high but not complete.

Purge streams

Recycle has a trap. Any substance that enters with the fresh feed and has no exit will build up in the loop without limit. Inert gases in a reactor feed, such as argon and methane in ammonia synthesis gas, are the classic case: they are not consumed by the reaction and are not condensed with the product, so they circulate with the recycle gas. Without a way out, their concentration rises until the reaction stops. The cure is a purge, a small stream bled from the recycle line. At steady state, the inert leaving in the purge must equal the inert entering in the fresh feed.

The purge removes valuable reactants too, because they have the same composition as the rest of the recycle. A small purge keeps losses low but lets the inert concentration rise, which dilutes the reactants and enlarges the loop. A large purge keeps the inert concentration low but wastes reactant. Choosing the purge fraction is an economic trade-off.

Solving loops by iteration

The ammonia loop could be solved by hand because each species gave a single linear equation. Larger problems, and any with nonlinear relations such as equilibrium, are solved by iteration. Choose a stream inside the loop, usually the recycle, as the tear stream; guess its flows; calculate around the loop to get a new value; and repeat until the guess and the result agree. This is called successive substitution. It is exactly what sequential modular simulators do, and it converges slowly when the recycle ratio is high, which is why simulators add acceleration methods.

# Recycle with purge: an ammonia synthesis loop solved by successive substitution
# N2 + 3 H2 -> 2 NH3. Fresh feed (mol/h): H2, N2 and argon as an inert.
fresh = {'H2': 74.70, 'N2': 24.90, 'Ar': 0.40}
X = 0.25            # single-pass conversion of N2 in the reactor
purge_frac = 0.08   # fraction of the separator gas that is purged

def loop(purge_frac, tol=1e-8):
    rec = {'H2': 0.0, 'N2': 0.0, 'Ar': 0.0}   # first guess: no recycle
    for it in range(1, 20000):
        feed = {k: fresh[k] + rec[k] for k in fresh}          # mixer
        xi = X * feed['N2']                                   # extent of reaction
        out = {'H2': feed['H2'] - 3 * xi, 'N2': feed['N2'] - xi, 'Ar': feed['Ar'], 'NH3': 2 * xi}
        gas = {k: out[k] for k in ('H2', 'N2', 'Ar')}         # separator: all NH3 condensed
        new = {k: (1 - purge_frac) * gas[k] for k in gas}     # splitter
        if max(abs(new[k] - rec[k]) for k in rec) < tol:
            return it, feed, out, gas, new
        rec = new
    raise RuntimeError('did not converge')

it, feed, out, gas, rec = loop(purge_frac)
nf = sum(feed.values())
print(f"Converged in {it} iterations")
print(f"Reactor feed {nf:.1f} mol/h; argon fraction {feed['Ar'] / nf:.4f}")
print(f"Recycle {sum(rec.values()):.1f} mol/h; recycle ratio {sum(rec.values()) / sum(fresh.values()):.2f}")
purge = {k: purge_frac * gas[k] for k in gas}
print(f"Ammonia product {out['NH3']:.2f} mol/h; purge {sum(purge.values()):.2f} mol/h")
overall = 1 - purge['N2'] / fresh['N2']
print(f"Overall N2 conversion {overall:.3f} versus single-pass {X:.2f}")
print("\npurge fraction  Ar in reactor feed  overall conversion  recycle ratio")
for p in (0.02, 0.05, 0.08, 0.12, 0.20):
    _, f, o, g, r = loop(p)
    print(f"{p:14.2f}{f['Ar'] / sum(f.values()):20.4f}{1 - p * g['N2'] / fresh['N2']:20.3f}{sum(r.values()) / 100:15.2f}")

Converged in 210 iterations
Reactor feed 326.3 mol/h; argon fraction 0.0153
Recycle 226.3 mol/h; recycle ratio 2.26
Ammonia product 40.16 mol/h; purge 19.68 mol/h
Overall N2 conversion 0.806 versus single-pass 0.25

purge fraction  Ar in reactor feed  overall conversion  recycle ratio
          0.02              0.0505               0.943           2.96
          0.05              0.0226               0.870           2.54
          0.08              0.0153               0.806           2.26
          0.12              0.0113               0.735           1.96
          0.20              0.0080               0.625           1.51

Bypass

A bypass sends part of a feed around a process unit and blends it back with the unit's outlet. It is used when a unit overshoots a target and only part of the stream needs treatment, when a unit has limited capacity, or to control a temperature or composition finely. The balance on a bypass is an ordinary splitter and mixer problem.