Heat integration and utilities

Lesson 4 ended with an intuition: the ATJ plant needs about 10 MW of heat for its feed and reaction, but its exothermic reactors and quench give back nearly as much, so most of the purchased heat should be avoidable. This lesson tests that intuition with pinch analysis, the method CHE-446 taught on the ethyl acetate line, and then designs the utilities that remain. It is also where the carbon intensity of the product starts to be decided, because every megawatt of purchased heat carries emissions with it.

The stream data

Riya extracts the stream data from the balances of Lessons 4 to 6. Each hot stream needs cooling and each cold stream needs heating; each has a supply temperature, a target temperature and a duty. Streams that change phase are split into segments so that each can be treated as having a constant heat capacity flow rate. The feed vaporization, for example, is a cold stream of 5.0 MW between 110 and 145 °C, the range over which the hydrous ethanol and dilution water boil at the reactor feed pressure. The oligomerization reactor is a hot stream of 4.6 MW at 178 to 182 °C, the temperature at which its cooling water boils.

Two large streams deserve comment. The oligomerization loop circulates diluent and recycle gas that must be cooled to 40 °C to separate the liquid product and reheated to 180 °C to enter the reactors. That 6 to 7 MW is mostly exchanged between the loop's own outlet and inlet in a feed-effluent exchanger, as in any reactor loop. Pinch analysis treats it like any other pair of streams, but its size explains why the plant's total exchanger area will be larger than its utility duties suggest.

The problem table

The problem table algorithm finds the minimum utilities before any exchanger is designed. Hot stream temperatures are shifted down and cold stream temperatures up by half the minimum approach temperature ΔTmin, so that any hot stream can heat any cold stream in the same shifted interval. In each interval, the surplus or deficit of heat is the difference between the hot and cold heat capacity flow rates times the interval width. Cascading the surpluses from the top down, and adding just enough hot utility at the top to make every cascaded heat flow non-negative, gives the minimum hot utility; the heat left at the bottom is the minimum cooling. The pinch is where the cascaded heat flow is zero.

# Heat integration of the ATJ plant: problem table algorithm, then the high-temperature utility options
streams = [  # (name, supply C, target C, duty MW); hot streams cool, cold streams heat
    ('H1a dehydration effluent, gas', 350, 125, 1.66), ('H1b quench condensation', 125, 60, 4.00),
    ('H1c quench subcooling', 60, 40, 0.43), ('H2 oligomerization reactor heat', 182, 178, 4.63),
    ('H3 oligomerization effluent', 200, 40, 6.80), ('H4 hydrogenation product', 260, 60, 1.90),
    ('H5 jet column condenser', 200, 195, 0.90), ('H6 splitter condenser', 110, 105, 0.70),
    ('H7 stabilizer condenser', 60, 55, 0.80), ('H8 compressor intercoolers', 110, 40, 0.50),
    ('C1a feed preheat', 40, 110, 0.60), ('C1b feed vaporization', 110, 145, 5.00),
    ('C1c superheat to bed 1', 145, 450, 2.40), ('C2 interbed reheat', 350, 450, 2.00),
    ('C3 water stripper reboiler', 110, 115, 0.75), ('C4 jet column reboiler', 280, 290, 0.90),
    ('C5 stabilizer and splitter reboilers', 150, 185, 1.50), ('C6 hydrogenation feed', 40, 200, 0.66),
    ('C7 oligomerization loop reheat', 40, 180, 6.00)]
dTmin = 10.0
def problem_table(streams, dTmin):
    sh = []                                   # shifted temperatures: hot down, cold up by dTmin/2
    for n, ts, tt, q in streams:
        hot = ts > tt; s = -dTmin / 2 if hot else dTmin / 2
        sh.append((ts + s, tt + s, q / abs(tt - ts), hot))
    T = sorted({t for a, b, _, _ in sh for t in (a, b)}, reverse=True)
    cascade, heat = [0.0], 0.0
    for hi, lo in zip(T, T[1:]):
        net = 0.0
        for a, b, cp, hot in sh:
            top, bot = max(a, b), min(a, b)
            ov = max(0.0, min(hi, top) - max(lo, bot))
            net += cp * ov * (1 if hot else -1)
        heat += net; cascade.append(heat)
    QH = -min(cascade); QC = cascade[-1] + QH
    flows = [c + QH for c in cascade]
    pinch = T[flows.index(min(flows))]
    return QH, QC, pinch
hot_tot = sum(q for n, a, b, q in streams if a > b); cold_tot = sum(q for n, a, b, q in streams if a < b)
QH, QC, pinch = problem_table(streams, dTmin)
print(f"without integration: hot utility {cold_tot:.2f} MW, cooling {hot_tot:.2f} MW")
print(f"dTmin {dTmin:.0f} K: minimum hot utility {QH:.2f} MW, minimum cooling {QC:.2f} MW, pinch at {pinch:.0f} C shifted")
for d in (5, 20, 30):
    a, b, p = problem_table(streams, d)
    print(f"  dTmin {d:>2} K: hot {a:.2f}, cold {b:.2f} MW, pinch {p:.0f} C")
# The whole minimum hot utility lies above the pinch, at 255 to 450 C: no plant steam can supply it.
high = QH
GRID, GAS, FUELGAS = 400.0, 56.0 + 10.0, 59.0       # g CO2e per kWh; g per MJ natural gas incl. upstream; purge gas
hours = 8000; purge_MW = 0.6                        # ethylene, ethane and hydrogen purges burned as fuel
elec = high / 0.98 * hours * 1000                   # kWh/yr for an electric heater
fired_gas = max(0.0, high / 0.88 - purge_MW) * hours * 3600   # MJ/yr natural gas for a fired heater
print(f"electric heater: {elec/1e6:.1f} GWh/yr, {elec*GRID/1e9:.1f} kt CO2e/yr; cost {elec*0.075/1e6:.1f} million/yr at 0.075 per kWh")
print(f"fired heater on purge gas plus natural gas: {fired_gas/1e6:.0f} TJ/yr gas, {fired_gas*GAS/1e9:.1f} kt CO2e/yr "
      f"(plus {purge_MW*hours*3600*FUELGAS/1e9:.1f} kt biogenic from purge); cost {fired_gas/1000*3.5/1e6:.1f} million/yr at 3.50 per GJ")
ce, cf = elec * 0.075 / 1e6, fired_gas / 1000 * 3.5 / 1e6
ee, ef = elec * GRID / 1e9, fired_gas * GAS / 1e9
if ee < ef: print(f"electrifying costs {ce-cf:.1f} million/yr more and avoids {ef-ee:.1f} kt: {(ce-cf)/(ef-ee)*1000:.0f} per metric ton CO2e avoided")
else: print(f"electrifying costs {ce-cf:.1f} million/yr more and adds {ee-ef:.1f} kt CO2e/yr")

without integration: hot utility 19.81 MW, cooling 22.32 MW
dTmin 10 K: minimum hot utility 3.81 MW, minimum cooling 6.32 MW, pinch at 255 C shifted
  dTmin  5 K: hot 3.77, cold 6.28 MW, pinch 258 C
  dTmin 20 K: hot 4.56, cold 7.07 MW, pinch 120 C
  dTmin 30 K: hot 5.15, cold 7.66 MW, pinch 125 C
electric heater: 31.1 GWh/yr, 12.4 kt CO2e/yr; cost 2.3 million/yr at 0.075 per kWh
fired heater on purge gas plus natural gas: 107 TJ/yr gas, 7.1 kt CO2e/yr (plus 1.0 kt biogenic from purge); cost 0.4 million/yr at 3.50 per GJ
electrifying costs 2.0 million/yr more and adds 5.4 kt CO2e/yr

Without integration the plant would need about 19.8 MW of hot utility and 22.3 MW of cooling. With ΔTmin of 10 K, the targets fall to 3.8 MW of heating and 6.3 MW of cooling: a reduction of more than 80 % in purchased heat. The intuition was right. The pinch is at about 255 °C in shifted temperature, so all of the remaining hot utility is needed above it, at temperatures between about 255 and 450 °C, for the superheat to the first dehydration bed, the interbed reheats and the jet column reboiler. No steam the site can supply reaches that range.

The sensitivity to ΔTmin is unusual. Between 5 and 10 K the targets barely change, but at 20 K the hot utility rises to 4.6 MW and the pinch jumps to about 120 °C, where the quench condensation meets the feed vaporization. That jump says the plant has two near-pinches, and that the heat exchanged between the condensing quench gas and the boiling feed is tight. Riya keeps ΔTmin at 10 K for the high-temperature exchangers, where film coefficients of gases are poor and area is expensive, but checks that the quench-to-feed exchanger can be designed with a 10 K approach at reasonable area. Lesson 8 confirms it can, with a large plate exchanger.

Designing the heat exchanger network

Riya then designs a network that achieves close to the targets, following the pinch design rules: no heat transfer across the pinch, no hot utility below it, no cooling above it. Above the pinch, the dehydration effluent's gas cooling (350 to about 260 °C) partly superheats the feed, and the fired heater supplies the rest of the superheat and the reheats. Below the pinch, the key matches are:

• Oligomerization reactor steam to feed vaporization. The reactor raises steam at about 10 bar(g); the steam condenses in the feed vaporizer at 180 °C, boiling the hydrous ethanol and dilution water at 110 to 145 °C. This single match moves 4.6 MW and is the heart of the integration.
• Quench condensation to feed preheat and the water stripper reboiler. The bottom of the quench tower runs at about 120 °C; a pumped circuit of quench water carries heat to the feed preheater and the stripper reboiler.
• Hydrogenation product to the stabilizer and splitter reboilers, at 150 to 185 °C, and to the hydrogenation feed.
• Oligomerization loop feed-effluent exchange, as described above.
• The jet column condenser, at about 195 °C under vacuum, to the hydrogenation feed and part of the loop reheat.

What remains is cooling at low temperature: the last of the quench, the loop effluent below about 60 °C, the stabilizer condenser and the compressor intercoolers. These go to cooling water or air coolers. The network has more matches than the minimum the targets imply, because Riya splits two streams to avoid temperature crosses, and it uses about 4.0 MW of hot utility instead of the 3.8 MW target. Professor Marchetti's question is whether the last 0.2 MW is worth chasing. It is not: it would need two more exchangers to save about 50,000 dollars a year.

Steam balance

Integration creates a utility system as well as removing one. The oligomerization reactors raise about 8 t/h of 10 bar(g) steam, and the feed vaporizer condenses it. If the reactors are offline or at reduced rate, the vaporizer still needs heat. Riya therefore connects the ATJ steam system to the site's medium-pressure header in both directions: it can import steam during start-up or when oligomerization is down, and export small surpluses. The steam drum on each reactor is also the coolant system whose pressure sets the reactor's temperature, which Lesson 9 controls. A heat-integrated plant is more efficient and also more tightly coupled: an upset in one section travels to the others through the heat exchangers. Start-up needs particular thought, because the dehydration section must be running before the oligomerization reactors can make the steam that the dehydration section's feed vaporizer relies on.

The high-temperature heater

The 3.8 MW above the pinch must come from a heater. Two options are compared. A fired heater burns the plant's purge gases, about 0.6 MW of ethylene, ethane and hydrogen, together with natural gas. An electric heater uses electricity from the grid, and the purge gas goes to the site's boilers instead. The trade-off is cost against carbon, and the answer depends on the grid.

In Iowa, where the grid emits about 400 g CO₂e per kWh, the electric heater would emit about 12.4 kt CO₂e a year against 7.1 kt for the fired heater, and cost about 2 million dollars a year more. Electrification would raise both cost and emissions. The team chooses a fired heater and records that electrification would make sense only with a dedicated low-carbon supply, such as a power purchase agreement with a wind farm, which Iowa has in abundance.

The fired heater is a cylindrical vertical heater with a radiant section, where the reheat coils sit, and a convection section, where the superheat coil and an air preheater recover heat from the flue gas. Low-NOx burners keep it within the emission limits Lesson 11 will set.

Other utilities

The remaining utilities are sized from the network and the equipment list. Cooling of about 6.3 MW at a 11 K rise needs about 140 kg/s, roughly 500 m³/h, of cooling water from a new cell on the existing tower, which also loses about 2 % of its circulation to evaporation in summer. The electrical load is about 1.6 MW: the ethylene compressor, the recycle and hydrogen compressors, the vacuum system, pumps and air cooler fans. A hot oil circuit heated by the fired heater supplies the jet column reboiler. Nitrogen is needed for purging, blanketing and adsorbent regeneration, and instrument air for the control valves; both come from the site's systems. Riya lists every utility with its normal and peak demand and its cost, the data Lesson 12 needs for the operating cost.