CO2 battery charging train: compression with heat to the TES, from the atmospheric dome to liquid storage

Lower limit in the input guards and the feasibility flag.

Unit multiplier in the CRF, the guards and the Customized switch.

Upper limit of a percentage in the input guards.

Converts a percentage (0-100) to a fraction.

Converts MW to kW (and kW to MW by division).

Converts tonnes to kilograms for the mass flow in kg/s.

Converts degrees Celsius to kelvin in the stage temperature rise.

1 kWh/t = 3,600 kJ / 1,000 kg = 3.6 kJ/kg; converts specific work and enthalpy differences to kWh/t.

Value of the technology_case select for the default case.

Value of the technology_case select for the three-stage case.

Value of the technology_case select for the five-stage case.

Default case: one compression section from 1 atm to the storage pressure, no cooling to ambient before the TES. This is what sends the heat to the TES hot, as the Energy Dome reference case does.

Stage count of the three-stage intercooled alternative. Yan's system (atmospheric holder, compression with heat-recovery coolers, condenser, liquid tank) intercools to ambient + 5 K, so its heat reaches the TES at about 146 °C only.

Stage count of the CCS-style case: more stages, closer to isothermal, lower work and a cooler discharge, so less useful heat for the TES.

Reference size of the scale law (the Energy Dome standard compressor frame). The Weiland law is written as a ratio to this size; the result is identical to the absolute correlation.

Suction pressure of the first stage.

Above this condensing temperature no liquid can form at any pressure; the condensation margin is measured against it. NIST gives 30.98 °C.

Upper guard on the storage pressure: the liquid store must stay subcritical. Also a benchmark for the condensing pressure.

Temperature the CO2 regains from the TES on discharge = compressor discharge temperature minus 5 K. Vendor statement, not a measured approach temperature.

Each intercooler returns the gas to ambient + 5 K before the next stage.

The CO2 condenses at ambient + 3 K against the dry coolers.

Electric-to-shaft efficiency of the drive motor. The motor losses are counted in the heat and losses output.

Universal gas constant for the ideal-gas compression work.

Molar mass of CO2; R/M = 0.18892 kJ/kg·K.

Numerator of the heat-capacity ratio k = Cp/Cv (1.282) used in the polytropic group (k-1)/k.

Denominator of the heat-capacity ratio. Taken at 1 atm and 50 °C, inside the stage temperature range; the real-gas departure of the last stage is discussed in scope_real_gas_crosscheck.

First point of the linear gas-enthalpy line at 1 atm.

Second point of the linear gas-enthalpy line; slope 0.85082 kJ/kg·K.

Low end of the mean Cp used for the uncooled case: Cp_mean = (h(450 °C) - h(20 °C)) / 430 K = 1.0111 kJ/kg·K, then k = Cp/(Cp - R) = 1.230.

High end of the mean Cp of the uncooled case, at the 450 °C compressor exit of Astolfi et al. 2022. Taken at 1 atm (ideal-gas part); the real-gas departure at 70 bar and high temperature is small and not modelled.

Upper end of the temperature span of the mean Cp (20-450 °C) for the uncooled case, and the published reference against which the computed discharge temperature is read.

Lower end of the mean-Cp span (about ambient + 5 K at the 15 °C default).

Temperature span of the linear gas-enthalpy line (0 to 50 °C).

Cubic term of the saturated-liquid enthalpy fit. Max error 0.6 kJ/kg on 0-28 °C (checked: 289.05 against NIST 289.62 at 28 °C, 249.05 against 249.26 at 18 °C).

Quadratic term of the saturated-liquid enthalpy fit.

Linear term of the saturated-liquid enthalpy fit.

Constant term of the saturated-liquid enthalpy fit (h at 0 °C).

Cubic term of the saturation-pressure fit. Max error 0.008 bar on 0-28 °C (34.846 against 34.851 at 0 °C, 54.649 against 54.651 at 18 °C, 68.910 against 68.918 at 28 °C).

Quadratic term of the saturation-pressure fit.

Linear term of the saturation-pressure fit.

Constant term of the saturation-pressure fit (psat at 0 °C).

Guard: a condensing temperature below 0 °C is outside the fitted range and is refused.

Guard: a condensing temperature above 28 °C is outside the fitted range and close to the critical point; it is refused. With the 3 K condenser pinch this caps the ambient at 25 °C.

Reference ambient of the load penalty: the compressor work is compared with the same train at 15 °C.

Coefficient of the integrally geared centrifugal compressor cost law. Transposed: the correlation is fitted on sCO2 compressors with an inlet at 65-90 bar, here the inlet is at 1 bar.

Scale exponent of the compressor cost on its shaft power: specific cost falls as size^(0.3992-1). Sourced to a DOE cost-data regression; evidence medium because the low-pressure CO2 duty is a transposition.

Coefficient of the drive-motor cost law.

Scale exponent of the motor cost.

Largest single motor the law covers. Above it the model uses parallel motor trains of equal size, as Energy Dome does with its double-compressor layout.

Installation on top of the bare equipment cost (Weiland's correlations are equipment costs).

Cost index of the Weiland base year.

Cost index of the 2023 reporting year.

Converts 2023 USD to 2023 EUR after CEPCI escalation.

Fixed O&M of the compression train per year. Girelli applies it to the whole plant; applied here to the compressor train.

Lower clamp of the scaled compressor specific CAPEX. Checked at the slider ends (3 and 135 MW): it never binds.

Upper clamp of the scaled compressor specific CAPEX. Checked at the slider ends: it never binds.

Benchmark for the condensing pressure at a cold site.

Benchmark for the condensing pressure at the 15 °C nominal ambient (T_cond 18 °C).

Benchmark at the hottest ambient the model accepts (25 °C, T_cond 28 °C): 1.1 bar below the 70 bar storage pressure.

Check point of the liquid enthalpy fit (fit gives 249.05).

Check point of the liquid enthalpy fit (fit gives 289.05).

Discharge side of the reference frame; not used by this charging calculator, given for chaining with the turbine calculator.

Whole-plant vendor claim, used only as a qualitative ceiling: see scope_vendor_claim_comparison.

Upper end of the vendor whole-plant claim.

Default charge power 24 MW = the Energy Dome standard compressor frame (24 MWe compressor, 18 MWe turbine, 200 MWh, 10 h). The chain contract range is 2.5-100 MW of discharge, about 3-135 MW of charge.

Default 10 h of charging per cycle: '24MW/10h' charging in the Energy Dome standard configuration. The chain contract range is 4-24 h.

Default 300 full cycles a year, the Girelli et al. 2025 case (section 5). The usage lever of the service cost.

Default isentropic efficiency 85 % (of the compression in the default case, of each stage in the intercooled cases): Girelli et al. 2025 Table 1 ('Compressor isentropic efficiency 85%') and Yan et al. 2023 Table 1 (0.85). Slider 80-90 %.

Default ambient 15 °C (Girelli et al. 2025, Table 1). The input binds to the site mean temperature; condensation feasibility must also be checked at the site's hot-season temperature. Slider 0-25 °C: above 25 °C the condensing temperature leaves the fitted NIST range and approaches the 31 °C critical point.

Default liquid storage pressure 70 bar: Energy Dome TMCES 2022 slide 4 (CO2 storage 'High (70 bar)', temperature 'CO2 = Ambient'). Slider 65-73 bar, below the 73.8 bar critical pressure.

Default discount rate 5 % and economic life 30 years (Girelli et al. 2025, section 4.2; Energy Dome TMCES 2024 slide 18 '30+ y'). The rate is real: all costs are constant 2023 EUR, nothing is escalated.

Compression work is computed with an ideal-gas polytropic model per stage (McCollum & Ogden 2006 stage equation with Z = 1): stage temperature rise = T_in (r^((k-1)/k) - 1) / eta_is, work = N cp dT. Uncooled default case: k = 1.230 from the NIST mean Cp between 20 and 450 °C at 1 atm (Cv = Cp - R). Intercooled cases: k = 1.282 from NIST Cp/Cv at 1 atm and 50 °C. Equal pressure ratio per stage.

Every stage, the first one included, takes its gas at ambient + 5 K. The first stage actually draws from the dome at about ambient, so the work is overstated by about 1.7 % at 15 °C: a conservative simplification.

First-law split for an ideal gas: enthalpy depends on temperature only, so all shaft work leaves as sensible heat when the gas is cooled back to the stage inlet temperature. Heat to TES = shaft power. The condenser and dry coolers reject h_gas(1 atm, T_in) - h_liq,sat(T_cond) from NIST. The balance W_sh + m h_in = m h_liq + Q_TES + Q_rej closes by construction. In the default case all of this heat leaves the compressor at about 436 °C; in the intercooled cases it is at 91-146 °C. How much the TES can store usefully is the TES calculator's question, not this one's.

Real-gas cross-check: McCollum & Ogden 2006 use per-stage Z and k (stage 5: Z = 0.845, k = 1.704). The research step ran their equation at N = 5, eta 85 %, T_in 20 °C and got 81.5 kWh/t of shaft work; this model gives 84.3 kWh/t at the same point (+3 %). The 81.5 is a computation with McCollum's equation, not a figure printed in the report.

Condensation feasibility is explicit: the CO2 condenses at ambient + 3 K against dry coolers. If the saturation pressure at that temperature exceeds the storage pressure, ambient condensation is impossible without a chiller or water cooling (not modelled, not costed) and the flag shows 1. At 70 bar this happens above about 26 °C ambient; at 65 bar above about 21.5 °C. The critical point (31 °C, 73.8 bar) is the absolute limit.

Scope exclusion: the dry coolers, the condenser and the TES are NOT in the CAPEX. Weiland's dry-cooler law (32.88 UA^0.75) needs a UA that would rest on an unsourced air-side temperature difference. The CAPEX is the compressor, its motor(s) and their installation only.

The Weiland integrally geared compressor law is fitted on sCO2 compressors with an inlet at 65-90 bar (uncertainty -39 %/+48 %). Here the inlet is at 1 bar, so the large low-pressure volumetric flow makes it a transposition: evidence medium-low. The Hendriks CCS compression law quoted by McCollum & Ogden 2006 gives about 1,450 USD(2005)/kW at 24 MW before escalation, an upper envelope that would exceed the vendor whole-plant claim per kW of compressor.

Qualitative comparison only: Energy Dome claims 225-250 USD/kWh for the whole plant (TMCES 2024, 2024 USD), about 45-50 M USD for 200 MWh, i.e. roughly 1,900-2,100 USD per kW of compressor. The modelled compressor train (2023 EUR) is roughly a fifth to a quarter of that. The currency years differ and no 2024 rate is cited, so no position is concluded beyond 'well below the whole-plant claim'.

Chain-contract anchor: IEEE Spectrum (E. Waltz, 21 Dec 2025) reports '2,000 tonnes of carbon dioxide' in the Sardinia dome and '20 MW over 10 hours' (200 MWh). The default case gives 201.7 t/h, i.e. about 2,017 t per 24 MW x 10 h charge (+0.8 %) at 119.0 kWh_e/t. This is an independent check: the 2,000 t enters no node. The intercooled cases give 2,622 t (three stages) and 2,797 t (five stages), 31-40 % above: the TES and discharge calculators should be chained to the default case.

Service cost = (annualised CAPEX + fixed O&M) / tonnes liquefied per year. It excludes the value of the charging electricity: the electricity is the inlet of the asset and the project prices it; counting it here would double count. No revenue, tax or subsidy. Constant 2023 EUR, real discount rate.

Corners of the input box (cases 1-3, efficiency 80-90 %, ambient 0-25 °C, storage pressure 65-73 bar): specific electricity 75.4-132.6 kWh_e/t (top end: uncooled case, 80 %, 25 °C, 73 bar); compressor exit 67-494 °C (above 450 °C the mean Cp is a short extrapolation); condenser heat 61.5-78.2 kWh_th/t; condensing pressure 37.7-68.9 bar. CAPEX 369-732 EUR/kW over 10-37 MW of charge power; below 10 MW it rises above the stored bound (about 824 EUR/kW at 3 MW), above 37 MW parallel motors bring it to about 260-370 EUR/kW. The service cost spans about 0.08-97 EUR/t over all corners of size, duration, cycles and finance; the stored bound covers the nominal case and the plotted sweeps.