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Cascade refrigeration, solved as coupled loops

Propylene, ethylene and methane loops in series to −150 °C, each colder loop condensing against the next-warmer one's evaporator.

Three genuinely coupled closed refrigerant loopsEach loop condenses against the next one's evaporatorFrom the ChemSep casebook (Refrigeration_3-Stage-150C)
Propylene compressor
Propylene JT valve
Propylene condenser
Ethylene compressor
Ethylene JT valve
Cascade exchanger 1
Methane compressor
Methane JT valve
Cascade exchanger 2
Cold-end evaporator

The actual dark-mode canvas: three closed refrigerant loops in series, each one rejecting its condensing duty into the evaporator of the loop above it, reaching −150 °C at the cold end.

The loops are coupled, so the duties compound

Cold-end duty propagates upward: every watt lifted at −150 °C has to be rejected by the methane loop into the ethylene loop, and again into the propylene loop. Solving all three together is what makes the compressor powers real rather than three independent textbook cycles added up.

hin=hout(isenthalpic JT expansion in every loop)h_{in} = h_{out} \quad \text{(isenthalpic JT expansion in every loop)}
Qcond,k=Qevap,k1(the cascade coupling — one loop’s condenser is the next one’s load)Q_{\text{cond},\,k} = Q_{\text{evap},\,k-1} \quad \text{(the cascade coupling — one loop's condenser is the next one's load)}
COP=QcoldkWcomp,k(paid for by every stage, not just the cold one)\mathrm{COP} = \frac{Q_{\text{cold}}}{\sum_k W_{\text{comp},k}} \quad \text{(paid for by every stage, not just the cold one)}

Unit ops shipped for this vertical

Compressor

Polytropic compression to pipeline/process pressure.

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Throttle valve

Isenthalpic Joule-Thomson expansion — the same relation cryogenic JT liquefaction relies on.

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Heater / cooler

Duty- or outlet-condition-specified energy-balance stage.

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Heat exchanger

Two-stream counter-current exchanger — the crude/residue preheat that pays for a CDU's fired duty.

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Live plant integration

Stream each stage's suction and discharge pressure plus the cascade-exchanger approaches from the plant's OPC-UA server into this flowsheet's twin comparison — a warm approach in one exchanger loads every compressor above it, which is exactly what a whole-cascade solve shows and a single-loop calculation cannot.

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