Transcritical CO₂ supermarket pack, cycle to issued report
An illustrative transcritical CO₂ booster pack for a Brisbane supermarket — 117 kW medium temperature at −8 °C and 31 kW low temperature at −30 °C — carried through Kelvin from heat load to issued report. Every figure below is Kelvin’s own calculation — its engine run on the brief — and none is typed in.
Published by Sentoro Technologies.
An illustrative design brief
This is a representative brief written to show the method, not a customer’s project, and every figure must be verified by a qualified professional before it’s relied on for a real one.
- Medium temperature
- 117.1 kWat −8 °C
- Low temperature
- 30.9 kWat −30 °C
- Design ambient
- 31.0 °CBrisbane
- Gas cooler
- 86.3 bartranscritical
- COP
- 1.76at design
- Charge
- 175 kgpipework and receiver
- Energy
- 457 MWh/yrupper bound
1The brief
A medium supermarket: about 2,500 m² of sales floor, with dairy, meat, produce and freezer coolrooms behind it. One transcritical CO₂ booster pack serves every case and coolroom. What follows is the whole brief as it is entered in Kelvin; everything after it is Kelvin’s calculation.
Design inputs
| Reading | Value |
|---|---|
| SiteIts summer design dry bulb is just above CO₂'s critical temperature, so the pack runs transcritical at design — the case a CO₂ design in a warm Australian city has to answer. | Brisbane |
| Refrigerant and systemTranscritical CO₂ booster: LT compressors discharge into MT suction; one gas cooler; flash gas to MT suction through a bypass valve. | R-744 booster |
| MT evaporatingSuperheat 7 K at the evaporator exit | −8°C |
| LT evaporatingSuperheat 10 K at the evaporator exit | −30°C |
| Gas cooler approachGas cooler exit above the design ambient | 3K |
| Compressor isentropic efficiencyOne figure for every stage, as Kelvin's cycle takes it | 0.68 |
| Liquid receiver40 % liquid at design | 300L |
Display cases
| Case | Group | Duty |
|---|---|---|
| Dairy multideck, 24 m | MT | 34kW |
| Meat multideck, 12 m | MT | 18kW |
| Produce multideck, 15 m | MT | 20kW |
| Ready-meals multideck, 10 m | MT | 12kW |
| Deli serve-over, 8 m | MT | 8kW |
| Drinks multideck, 10 m | MT | 14kW |
| Glass-door freezers, 20 doors | LT | 16kW |
| Island freezers, 10 m | LT | 10kW |
Kelvin has no display-case load model: a case’s duty is entered from its maker’s data at the suction temperature. These duties are illustrative, not any maker’s.
The store, as the brief draws it
Point at a run or an evaporator to read it; tap to keep it. Zoom with the buttons (or Ctrl or ⌘ and the wheel), then drag the plan to move around it.
Coolrooms
| Room | Size (m) | Room (°C) | Product (kg/day) | Entering (°C) |
|---|---|---|---|---|
| Dairy coolroomMT · 1 door | 8 × 5 × 3.2 | 2 | 1,500 | 8 |
| Meat coolroomMT · 1 door | 6 × 4 × 3.2 | 0 | 800 | 5 |
| Produce coolroomMT · 1 door | 8 × 6 × 3.2 | 4 | 2,000 | 22 |
| Freezer roomLT · 1 door | 8 × 6 × 3.2 | −20 | 1,000 | −15 |
Three walls face the sales floor at 24 °C, one the dock; the ceiling is under the roof, in a void taken at 40 °C. Everything else is the Heat Load station’s default for the room’s preset.
2Heat load
Kelvin’s heat load engine sizes each coolroom: transmission through its six surfaces, infiltration through its door, the product brought down to room temperature, and what people and lights add — then takes the larger of holding and pull-down, adds a safety margin and spreads the day’s load over the hours the plant runs. The cases add their entered duties. Each group’s total is the duty the cycle is solved for.
Coolroom loads, by component
Each bar is a room’s loads over the day. The tick is its design load: the governing of holding and pull-down, plus a 10 % margin, spread over the hours the plant runs (16–18 h a day) — so a bar doesn’t sum to its tick.
Coolroom loads
| Room | Transmission | Infiltration | Product | Internal | Design |
|---|---|---|---|---|---|
| Dairy coolroomChiller (MT), 2 °C · pulldown governs · 16 h/day | 1.06 | 0.39 | 0.39 | 0.17 | 3.32 |
| Meat coolroomCool Store, 0 °C · pulldown governs · 16 h/day | 0.78 | 0.44 | 0.17 | 0.14 | 2.53 |
| Produce coolroomChiller (MT), 4 °C · pulldown governs · 16 h/day | 1.11 | 0.34 | 1.57 | 0.18 | 5.28 |
| Freezer roomFreezer (LT), −20 °C · pulldown governs · 18 h/day | 1.53 | 1.43 | 0.12 | 0.23 | 4.86 |
Design load: the governing of holding and pull-down, plus a 10 % margin, scaled from 24 hours to the plant’s running hours. Infiltration by the doorway method.
Coolroom plans
Design load 3.32 kW, pulldown governing. Point at a wall, the door or the unit to read its part of the load; tap to keep it.
Each group’s duty, unit by unit
Duty by suction group
| Unit | Group | Duty |
|---|---|---|
| Dairy coolroomHeat load engine | MT | 3.32kW |
| Meat coolroomHeat load engine | MT | 2.53kW |
| Produce coolroomHeat load engine | MT | 5.28kW |
| Freezer roomHeat load engine | LT | 4.86kW |
| Dairy multideck, 24 mEntered | MT | 34.00kW |
| Meat multideck, 12 mEntered | MT | 18.00kW |
| Produce multideck, 15 mEntered | MT | 20.00kW |
| Ready-meals multideck, 10 mEntered | MT | 12.00kW |
| Deli serve-over, 8 mEntered | MT | 8.00kW |
| Drinks multideck, 10 mEntered | MT | 14.00kW |
| Glass-door freezers, 20 doorsEntered | LT | 16.00kW |
| Island freezers, 10 mEntered | LT | 10.00kW |
| MT total | at −8 °C | 117.13kW |
| LT total | at −30 °C | 30.86kW |
3Why CO₂
R-744 is carbon dioxide: a global warming potential of 1 — it is the gas every other GWP is measured against (IPCC) — no ozone depletion (it is in none of the Montreal Protocol’s annexes), and safety class A1, lower toxicity and no flame propagation (ISO 817 and ASHRAE 34). For a supermarket, where this pack holds 175 kg in its pipework and receiver alone and a leak goes into a building full of people, that combination is the reason to accept what CO₂ asks in return.
What it asks is pressure, and a low critical point. CO₂’s critical point is 30.98 °C at 7,377.3 kPa (CoolProp, on the R-744 page). Above it there is no condensing: the gas cooler cools a supercritical fluid, and its pressure is set for efficiency rather than by a condensing temperature. In Brisbane, the design ambient of 31.0 °C is already above the critical temperature, so this pack runs transcritical at design — the case that decides whether CO₂ works in a warm climate, and the one this example follows through.
The booster arrangement keeps it to one refrigerant and one gas cooler: the LT compressors lift the freezer suction to the MT suction pressure, and the MT (high-pressure) compressors take everything to the gas cooler.
R-744: saturation pressure and the critical point
4Design conditions
The cycle is solved at Brisbane’s summer design dry bulb, 31.0 °C: the ASHRAE 0.4 % annual cooling design dry bulb for Brisbane (ASHRAE 2013), as published in AIRAH Ecolibrium, June 2015, Table 2, the figure Kelvin's Brisbane climate profile is built from. The gas cooler’s exit is that plus the 3 K approach, 34.0 °C.
Brisbane, month by month
Each Navy Ink point is a month’s design high, not its mean. The pen line is the gas cooler exit each month's cycle is solved to, the dry bulb plus the approach: it is the exit, not the air, that has to be below the critical temperature for the pack to condense, and Kelvin keeps the head above the critical pressure a little below it too, where condensing would cost more work (the square points). The tick on the scale is the design ambient the cycle is solved at, 31.0 °C. The dashed line is the refrigerant's critical temperature (CoolProp).
Brisbane, month by month
| Month | Design (°C) | Runs |
|---|---|---|
| Jan | 30.5 | Transcritical |
| Feb | 30.3 | Transcritical |
| Mar | 28.5 | Transcritical |
| Apr | 25.5 | Subcritical, condensing at 28.5 °C |
| May | 22.2 | Subcritical, condensing at 25.2 °C |
| Jun | 19.0 | Subcritical, condensing at 22.0 °C |
| Jul | 18.2 | Subcritical, condensing at 21.2 °C |
| Aug | 19.3 | Subcritical, condensing at 22.3 °C |
| Sep | 22.3 | Subcritical, condensing at 25.3 °C |
| Oct | 25.5 | Subcritical, condensing at 28.5 °C |
| Nov | 27.7 | Transcritical, in the transition band (gas cooler exit 30.7 °C) |
| Dec | 29.9 | Transcritical |
Kelvin’s monthly design-high dry bulbs for Brisbane: the ASHRAE annual design dry bulb, brought down slightly to a monthly design high, with the Bureau of Meteorology’s monthly shape scaled to meet it. Each is a month’s design high, not its mean. How the pack runs in each month is the energy analysis’s own solution (section 9).
5The cycle
Kelvin solves the booster at the design ambient: the LT stage from −30 °C to MT suction, the HP stage from MT suction to the gas cooler, the high-pressure valve down to the receiver, and the receiver’s flash gas bypassed to MT suction. The numbered points below are its state points, drawn on R-744’s pressure–enthalpy diagram; point anywhere on it to read the state there.
The cycle on R-744's P–h diagram
Point anywhere on the diagram to read the state there
- Pressure
- —
- Temperature
- —
- Specific enthalpy
- —
- Specific entropy
- —
- Density
- —
- Specific volume
- —
- Saturation
- —
- Superheat or subcooling
- —
The cycle’s points and lines are Kelvin’s design results; the dome, isotherms and the readout under the diagram are R-744’s public diagram, computed with CoolProp — one of the refrigerant pressure–temperature tables and P–h diagrams. Dashed: the flash gas, separated in the receiver and throttled through the bypass valve to MT suction.
State points
| Point | P (kPa) | T (°C) | h (kJ/kg) | Flow (kg/s) |
|---|---|---|---|---|
| 1ltLT evaporator exit (superheated vapour) | 1,427.7 | −20.0 | 447.8 | 0.130 |
| 2ltLT booster discharge → MT suction | 2,802.7 | 38.6 | 492.0 | 0.130 |
| 1mtMT evaporator exit (superheated vapour) | 2,802.7 | −1.0 | 444.7 | 0.500 |
| 3HP suction (MT + LT + flash vapour) | 2,802.7 | −1.6 | 443.8 | 1.059 |
| 4HP compressor discharge (supercritical) | 8,633.4 | 102.0 | 517.6 | 1.059 |
| 5Gas cooler exit | 8,633.4 | 34.0 | 298.6 | 1.059 |
| 6HPV exit → receiver (isenthalpic, two-phase) | 3,890.0 | 4.2 | 298.6 | 1.059 |
| 7Receiver saturated liquid → both EV inlets | 3,890.0 | 4.2 | 210.5 | 0.630 |
| 8Flash vapour → FGBV into MT suction line | 3,890.0 | 4.2 | 428.1 | 0.429 |
Enthalpy on the IIR datum, as on R-744’s page. Flow is the mass flow through the point.
Pressures, power and COP
| Reading | Value |
|---|---|
| Gas cooler pressureOptimum head pressure, Liao et al. (2000) | 8,633.4 kPa86.3 bar |
| Receiver (flash tank)Held by the high-pressure valve | 3,890.0 kPa4.21 °C saturated |
| MT suctionHP compressors, pressure ratio 3.08 | 2,802.7 kPa−8 °C |
| LT suctionLT compressors, pressure ratio 1.96 | 1,427.7 kPa−30 °C |
| Shaft powerLT 5.74 kW · HP 78.14 kW | 83.88kW |
| Gas cooler heatDuty 147.99 kW plus shaft power 83.88 kW | 231.87kW |
| COPRefrigeration duty over shaft power; the Carnot COP between the same temperatures is 5.55 | 1.764 |
Mass flows
| Reading | Value |
|---|---|
| LT stageThrough the LT evaporators and compressors | 0.1301kg/s |
| MT evaporatorsThrough the MT evaporators | 0.5002kg/s |
| Flash gasFrom the receiver through the bypass valve | 0.4288kg/s |
| HP stageAll three, through the HP compressors and gas cooler | 1.0590kg/s |
Gas cooler approach temperature
The approach is how close the gas cooler brings the CO₂ to the air: exit temperature less ambient. Above the critical point the optimum head pressure follows the exit temperature, so every kelvin of approach raises the pressure the HP compressors work against. Kelvin re-solves the same pack at each approach:
COP and head pressure against approach
The pack at other approaches
| Approach (K) | Exit (°C) | Gas cooler (bar) | Shaft power (kW) | COP |
|---|---|---|---|---|
| 2 | 33.0 | 83.4 | 80.33 | 1.84 |
| 3 | 34.0 | 86.3 | 83.88 | 1.76 |
| 4 | 35.0 | 89.2 | 87.64 | 1.69 |
| 5 | 36.0 | 92.1 | 91.05 | 1.63 |
| 6 | 37.0 | 95.0 | 94.62 | 1.56 |
The brief’s approach in bold. Duty unchanged; head pressure by Liao et al. (2000).
6Pipe layout and sizing
One suction and one liquid header per group runs from the pack, back of house first: the coolrooms, then the cases on the sales floor. Kelvin splits the layout into 47 segments, gives each the mass flow of everything downstream of it, and sizes it to Kelvin’s default velocity band for its line — suction 4–12 m/s, liquid 0.5–1.5 m/s, discharge 10–18 m/s. It reports each path’s pressure drop as the saturation temperature it costs the evaporator at its end.
Pipe layout
Point at a run or an evaporator to read it; tap to keep it. Zoom with the buttons (or Ctrl or ⌘ and the wheel), then drag the plan to move around it. Each run's size is in its tooltip, or on the plan with “Sizes on the plan”.
The governing paths — the ones that lose the most (point at a row to find it on the plan):
MT suction to Ready-meals multideck, 10 m
| Segment | Size | Length (m) | Velocity (m/s) | ΔP (kPa) | ΔTsat (K) |
|---|---|---|---|---|---|
| Header0.500 kg/s | 1 5/8" | 4.0 | 6.12 | 2.4 | 0.03 |
| Header0.486 kg/s | 1 5/8" | 6.0 | 5.95 | 3.4 | 0.04 |
| Header0.475 kg/s | 1 5/8" | 6.0 | 5.81 | 3.3 | 0.04 |
| Header0.453 kg/s | 1 3/8" | 18.0 | 7.85 | 21.1 | 0.27 |
| Header0.308 kg/s | 1 3/8" | 10.0 | 5.33 | 5.7 | 0.07 |
| Header0.231 kg/s | 1 1/8" | 12.0 | 6.09 | 11.2 | 0.14 |
| Header0.145 kg/s | 7/8" | 8.0 | 6.53 | 11.7 | 0.15 |
| Branch0.051 kg/s | 1/2" | 12.0 | 7.69 | 48.9 | 0.63 |
Path total: 107.5 kPa, 1.39 K of saturation temperature, so the ready-meals multideck, 10 m’s evaporator sees that much below the pack’s suction.
LT suction to Island freezers, 10 m
| Segment | Size | Length (m) | Velocity (m/s) | ΔP (kPa) | ΔTsat (K) |
|---|---|---|---|---|---|
| Header0.130 kg/s | 1 1/8" | 5.0 | 7.05 | 3.2 | 0.07 |
| Header0.110 kg/s | 1 1/8" | 22.0 | 5.94 | 10.3 | 0.22 |
| Branch0.042 kg/s | 3/4" | 20.0 | 5.41 | 13.3 | 0.28 |
Path total: 26.8 kPa, 0.56 K of saturation temperature, so the island freezers, 10 m’s evaporator sees that much below the pack’s suction.
Velocity bands’ source, as Kelvin states it: ASHRAE Handbook—Refrigeration Ch.1 velocity practice (suction 4.5–20, discharge 10–18, liquid 0.5–1.25 m/s).
The pack's own lines, and the liquid header
| Reading | Value |
|---|---|
| LT discharge to MT suction4.0 m, 14.1 kPa, 0.130 kg/s | 3/4"10.5 m/s |
| HP discharge to the gas cooler12.0 m, 104.5 kPa, 1.059 kg/s — both groups and the flash gas | 1 1/8"12.9 m/s |
| Gas cooler outlet to the high-pressure valve12.0 m, 0.8 kPa, 1.059 kg/s | 2 1/8"0.81 m/s |
| MT liquid header, first run4.0 m, 0.5 kPa, 0.500 kg/s | 1 3/8"0.69 m/s |
The pack’s own lines aren’t drawn on the plan above, as the Pipe Layout station doesn’t draw them: they are listed here, as its ledger lists them.
What this section leaves out, and why
Tube pressure ratings. These are bore sizes on Kelvin’s default ACR tube. CO₂’s pressures — the gas cooler’s, and the whole system’s standing idle on a hot day — are beyond what ordinary refrigeration tube is made for, and a CO₂ pack is piped in tube rated for them. Kelvin judges a tube’s rating once the standstill temperatures are entered; this example leaves them blank, as the Pipe Layout station starts.
Flash in the liquid lines. The receiver’s liquid is saturated, so any drop in a liquid line flashes some of it: Kelvin flags 12 of the 12 liquid paths, the largest losing 0.40 K.
7Equipment duties
What each piece of plant has to do, from the cycle — the duties a selection is made against, brand-neutral. Kelvin checks a selection against these once a maker’s model is entered from its datasheet; this example enters none. Kelvin doesn’t size the high-pressure or bypass valves: their duties are listed for the valve maker’s selection.
The pack, part by part
Plant
| Reading | Value |
|---|---|
| LT compressors0.1301 kg/s, 13.6 m³/h swept, 14.3 → 28.0 bar, 5.74 kW shaft, discharge 38.6 °C | 30.86kW |
| HP compressorsPlus the LT discharge and flash gas: 1.0590 kg/s, 57.6 m³/h swept, 28.0 → 86.3 bar, 78.14 kW shaft, discharge 102.0 °C | 117.13kW MT |
| Gas cooler102.0 → 34.0 °C at 86.3 bar, in 31.0 °C air | 231.87kW |
| High-pressure valve86.3 → 38.9 bar | 1.0590kg/s |
| Liquid receiverAt 38.9 bar, 4.2 °C | 300L |
| Flash gas bypass valve38.9 → 28.0 bar | 0.4288kg/s |
Evaporators and expansion valves
| Unit | Duty (kW) | Evaporating (°C) | Flow (kg/s) |
|---|---|---|---|
| Dairy coolroom | 3.32 | −8 | 0.0142 |
| Meat coolroom | 2.53 | −8 | 0.0108 |
| Produce coolroom | 5.28 | −8 | 0.0225 |
| Freezer room | 4.86 | −30 | 0.0205 |
| Dairy multideck, 24 m | 34.00 | −8 | 0.1452 |
| Meat multideck, 12 m | 18.00 | −8 | 0.0769 |
| Produce multideck, 15 m | 20.00 | −8 | 0.0854 |
| Ready-meals multideck, 10 m | 12.00 | −8 | 0.0512 |
| Deli serve-over, 8 m | 8.00 | −8 | 0.0342 |
| Drinks multideck, 10 m | 14.00 | −8 | 0.0598 |
| Glass-door freezers, 20 doors | 16.00 | −30 | 0.0674 |
| Island freezers, 10 m | 10.00 | −30 | 0.0421 |
Each expansion valve is fed liquid from the receiver at 38.9 bar, 4.2 °C.
8Refrigerant charge
Kelvin works out the charge in every pipe it sized from the bore, the length and the density in that line, and the receiver’s from its volume and liquid level.
Where the charge is
Charge
| Reading | Value |
|---|---|
| Liquid lines | 59.9kg |
| Suction lines | 5.4kg |
| Discharge linesThe LT and HP discharges | 1.04kg |
| Pipework47 lines, 168 L | 66.4kg |
| Receiver300 L at 40 % liquid | 108.1kg |
| Pipework and receiver | 174.5kg |
Not in this total: the evaporator coils, the cases and the gas cooler, whose charge Kelvin takes from each maker’s data (it has no coil volume model) — none is entered here.
9Energy and running cost
Kelvin re-solves the pack for each month at that month’s design dry bulb — transcritical in the warm months, condensing below CO₂’s critical point in the cool ones — and runs it 18 hours a day at design duty, with motors at 92 % and a tariff of $0.25/kWh. Compressor energy only: no fans, lighting or heaters.
An upper bound
Upper bound at design-high ambients: every hour of each month is run at that month's design dry bulb, not its mean, so expected consumption is lower.
Monthly energy
Month by month
| Month | Ambient (°C) | COP | Power (kW) | Energy (kWh) | Cost (AUD) |
|---|---|---|---|---|---|
| Jantranscritical | 30.5 | 1.80 | 89.3 | 49,838 | 12,460 |
| Febtranscritical | 30.3 | 1.82 | 88.6 | 44,648 | 11,162 |
| Martranscritical | 28.5 | 1.96 | 81.9 | 45,691 | 11,423 |
| Aprsubcritical | 25.5 | 2.27 | 71.0 | 38,335 | 9,584 |
| Maysubcritical | 22.2 | 2.73 | 59.0 | 32,927 | 8,232 |
| Junsubcritical | 19.0 | 3.18 | 50.7 | 27,353 | 6,838 |
| Julsubcritical | 18.2 | 3.29 | 48.8 | 27,249 | 6,812 |
| Augsubcritical | 19.3 | 3.13 | 51.4 | 28,664 | 7,166 |
| Sepsubcritical | 22.3 | 2.71 | 59.3 | 32,024 | 8,006 |
| Octsubcritical | 25.5 | 2.27 | 71.0 | 39,613 | 9,903 |
| Novtranscritical | 27.7 | 2.04 | 78.8 | 42,573 | 10,643 |
| Dectranscritical | 29.9 | 1.85 | 86.9 | 48,509 | 12,127 |
| Year | mean COP | 2.42 | 457,423 | 114,356 |
Power is electrical input: shaft power over the motor efficiency.
Running cost
| Reading | Value |
|---|---|
| Energy, a yearFrom the months above | 114,356AUD |
| Refrigerant top-up, a year17.5 kg at 10 % of the charge a year, $10.00/kg | 175AUD |
| A year | 114,530AUD |
| Over 10 yearsUndiscounted | 1,145,304AUD |
10The issued report
In Kelvin each stage above is a station with its own record, and each record issues as a PDF report with its inputs, results and sources — the documents a design is issued with. For this pack:
The chain, and what each station issues
What Kelvin issues
| Report | Sections |
|---|---|
| Cycle report | Input parameters · Cycle state points · System schematic · Engineering checks |
| Heat load report | Room schedule · Suction group totals |
| Pipe layout report | Floor plan · Pipe schedule · Sizing checks · Evaporator performance |
| Equipment schedule | Compressors · Condenser / gas cooler · Evaporators · Expansion valves · Liquid receiver · Oil separator |
| Refrigerant charge report | Charge split · Pipe charge breakdown · Receiver and oil · Liquid line pressure drop |
| Energy report | Analysis inputs · Monthly energy · Monthly breakdown |
| Running cost report | Inputs and assumptions · Running cost · Pipework BOM |
Put your own pack through Kelvin
Kelvin’s Free plan includes the refrigerant library, P–h diagrams, single-stage cycles and draft reports. Paid plans carry a system on through pipework, equipment, charge, energy and cost to issued reports.
Verify before relying on these figures
Kelvin’s calculations are design aids based on published methods and standard thermodynamic and hydraulic models. Every figure on this page must be verified by a qualified professional before it’s relied on, and a real design checked against AS/NZS 5149 and the equipment makers’ data.