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Exergetic and Economic Evaluation of CO2
Liquefaction Processes
Feng Chen and Tatiana Morosuk *


Citation: Chen, F.; Morosuk, T.
Exergetic and Economic Evaluation of
CO2Liquefaction Processes. Energies
2021,14, 7174. https://doi.org/
10.3390/en14217174
Academic Editor: Muhammad
Abdul Qyyum
Received: 20 September 2021
Accepted: 19 October 2021
Published: 1 November 2021
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Copyright: © 2021 by the authors.
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Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Institute for Energy Engineering, Technische Universität Berlin, 10587 Berlin, Germany;
[email protected]
*Correspondence: tetyana.mor[email protected]
Abstract:
The transport of CO
2
, as a part of the carbon capture and storage chain, has received in-
creased attention in the last decade. This paper aims to evaluate the most promising CO
2
liquefaction
processes that can be used for port-to-port and port–offshore CO
2
ship transportation. The energetic,
exergetic, and economic analyses are applied. The liquefaction pressure has been set to 15 bar
(liquefaction temperature
−
30
◦
C), which corresponds to the design of the existing CO
2
carriers. The
three-stage vapor-compression process has been selected among closed systems (with propane-R290,
ammonia-R717, and R134a as the working fluid) and the precooled Linde–Hampson process—as the
open system (with R717). The three-stage vapor-compression process R290 shows the lowest energy
consumption, and the CO
2
liquefaction cost 21.3 USD/tCO
2
. Although the power consumption of
precooled Linde–Hampson process is 3.1% higher than the vapor-compression process with R209,
the lowest
total capital expenditures are notable. The CO
2
liquefaction cost of precooled Linde–
Hampson process is 21.13 USD/tCO
2
. The exergetic efficiency of the three-stage vapor-compression
process with R290 is 66.6%, while the precooled Linde–Hampson process is 64.8%.
Keywords:
carbon dioxide; liquefaction; CO
2
ship transportation; exergy analysis; economic analysis
1. Introduction
The CO
2
emission from the combustion of fossil fuels represented the most signif-
icant contributor to global warming, i.e., almost 80% of the total GWP [
1
]. Addition-
ally,
the upward
trend of worldwide fossil fuels consumption as primary energy has not
stopped [
2
]. The possibility that fossil fuels will remain dominant in power generation in
the following years is high. Therefore, the feasible methods to mitigate the CO
2
emission
from fossil fuel combustion have been suggested: improving the efficiency of the system [
3
];
implementing renewable energy sources [4]; and carbon capture and storage (CCS) [5].
The CCS chain consists of three main parts [6,7]: carbon capture, transportation, and
storage or utilization. Figure 1shows alternative options along the CCS chain. Many efforts
have been made to develop efficient and economically effective carbon capture processes.
Except for being stored, CO
2
can be utilized in industrial conversion processes [
8
]. The
power-to-X options [
9
] give a new perspective for realizing the concepts of decarbonization
in conjunction with demand response management and large implementation of renewable
energy sources.
Geological CO
2
storage, which was proposed in the early 1990s, is the most technically
feasible final step in the CCS chain. The two most ordinary geological storage methods
are [9]:
•
Saline aquifer storage. The CO
2
is injected into the saline aquifers without considering
the potentially harmful effects for water sources (drinking water);
•
Enhanced oil recovery. To reach the maximal economic oil recovery through the
injection of CO2into the oil fields.
Energies 2021,14, 7174. https://doi.org/10.3390/en14217174 https://www.mdpi.com/journal/energies
Energies 2021,14, 7174 2 of 13
Energies2021,14,xFORPEERREVIEW2of13
Enhancedoilrecovery.Toreachthemaximaleconomicoilrecoverythroughthein‐
jectionofCO2intotheoilfields.
Figure1.CCSchain.AlternativeoptionsanditsTechnologyReadinessLevel(adaptedfrom[7]).
AsthelocationofCO2storageisdistributed,thetransportationinfrastructureshould
bedevelopedtoconnectthecaptureandstorageinfrastructures.Theavailabletechnolo‐
giesarepipelinesandships(Figure2).Thepipelinesareusedunderthecircumstanceof
large‐scaleCO2andshorttransportdistance.PurifiedCO2shouldbecompressedabove
criticalpressure(>73.8bar)toensuretransportationinasinglegasphase.Formarine
transport,thedensityofCO2ismaximizedthroughliquefaction.Thepressureformarine
transportationisslightlyabovethetriplepoint(≥5.2bar);however,CO2solidification
shouldbeavoided(duetospontaneousformationofdryiceincaseofdroppingthepres‐
sureduringtheloading/unloading).Therefore,forshiptransportation,therecommended
temperatureandpressureofCO2areintherangebetween−30and−50°Cthatcorre‐
spondsto6to15bar.CO2shiptransportationisavailableonasmallscale,makingiteco‐
nomicallynoncompetitivetopipelinetransportation.Atthesametime,theadvantageis
thattheinitialinvestmentiscomparativelylow,anditprovideshigherflexibilityinterms
ofdistance,clientdemand,andregulatoryapprovalissues[7].Thelargescaleofmarine
transportationofCO2willhaveapotentialinthefutureonlyunderseveralconditions;
oneofthemistheenergeticallyefficientandeconomicallyfeasibleCO2liquefactionpro‐
cess.Recently,theInternationalEnergyAgencyreportedthemarketpotentialforCO2‐
derivedproductsandservices[7].ThelistofindustrialparticipantsincludesAirProducts
andChemical,Inc.,AirLiquide,LindeAG,andothercryogeniccompanies.Forexample,
“FullvaluechainCCSinoneservice”isofferedbyAkerCarbonCapturecompany(Nor‐
way)[10].
Figure2.CO2transportationcost(adaptedfrom[7]).
AverydetailedstudyinthefieldofCCSchainisprovided,forexample,in[6,7,10];
however,theinformationaboutCO2liquefactionprocessesisnotprovided.
Figure 1. CCS chain. Alternative options and its Technology Readiness Level (adapted from [7]).
As the location of CO
2
storage is distributed, the transportation infrastructure should
be developed to connect the capture and storage infrastructures. The available technologies
are pipelines and ships (Figure 2). The pipelines are used under the circumstance of large-
scale CO
2
and short transport distance. Purified CO
2
should be compressed above critical
pressure (>73.8 bar) to ensure transportation in a single gas phase. For marine transport,
the density
of CO
2
is maximized through liquefaction. The pressure for marine transporta-
tion is slightly above the triple point (
≥
5.2 bar); however, CO
2
solidification should be
avoided (due to spontaneous formation of dry ice in case of dropping the pressure during
the loading/unloading). Therefore, for ship transportation, the recommended temperature
and pressure of CO
2
are in the range between
−
30 and
−
50
◦
C that corresponds to 6 to
15 bar. CO
2
ship transportation is available on a small scale, making it economically non-
competitive to pipeline transportation. At the same time, the advantage is that the initial
investment is comparatively low, and it provides higher flexibility in terms of distance,
client demand, and regulatory approval issues [
7
]. The large scale of marine transportation
of CO
2
will have a potential in the future only under several conditions; one of them is
the energetically efficient and economically feasible CO
2
liquefaction process. Recently,
the International Energy Agency reported the market potential for CO2-derived products
and services [
7
]. The list of industrial participants includes Air Products and Chemical,
Inc., Air Liquide, Linde AG, and other cryogenic companies. For example, “Full value
chain CCS in one service” is offered by Aker Carbon Capture Company (Norway) [10].
Energies2021,14,xFORPEERREVIEW2of13
Enhancedoilrecovery.Toreachthemaximaleconomicoilrecoverythroughthein‐
jectionofCO2intotheoilfields.
Figure1.CCSchain.AlternativeoptionsanditsTechnologyReadinessLevel(adaptedfrom[7]).
AsthelocationofCO2storageisdistributed,thetransportationinfrastructureshould
bedevelopedtoconnectthecaptureandstorageinfrastructures.Theavailabletechnolo‐
giesarepipelinesandships(Figure2).Thepipelinesareusedunderthecircumstanceof
large‐scaleCO2andshorttransportdistance.PurifiedCO2shouldbecompressedabove
criticalpressure(>73.8bar)toensuretransportationinasinglegasphase.Formarine
transport,thedensityofCO2ismaximizedthroughliquefaction.Thepressureformarine
transportationisslightlyabovethetriplepoint(≥5.2bar);however,CO2solidification
shouldbeavoided(duetospontaneousformationofdryiceincaseofdroppingthepres‐
sureduringtheloading/unloading).Therefore,forshiptransportation,therecommended
temperatureandpressureofCO2areintherangebetween−30and−50°Cthatcorre‐
spondsto6to15bar.CO2shiptransportationisavailableonasmallscale,makingiteco‐
nomicallynoncompetitivetopipelinetransportation.Atthesametime,theadvantageis
thattheinitialinvestmentiscomparativelylow,anditprovideshigherflexibilityinterms
ofdistance,clientdemand,andregulatoryapprovalissues[7].Thelargescaleofmarine
transportationofCO2willhaveapotentialinthefutureonlyunderseveralconditions;
oneofthemistheenergeticallyefficientandeconomicallyfeasibleCO2liquefactionpro‐
cess.Recently,theInternationalEnergyAgencyreportedthemarketpotentialforCO2‐
derivedproductsandservices[7].ThelistofindustrialparticipantsincludesAirProducts
andChemical,Inc.,AirLiquide,LindeAG,andothercryogeniccompanies.Forexample,
“FullvaluechainCCSinoneservice”isofferedbyAkerCarbonCapturecompany(Nor‐
way)[10].
Figure2.CO2transportationcost(adaptedfrom[7]).
AverydetailedstudyinthefieldofCCSchainisprovided,forexample,in[6,7,10];
however,theinformationaboutCO2liquefactionprocessesisnotprovided.
Figure 2. CO2transportation cost (adapted from [7]).
A very detailed study in the field of CCS chain is provided, for example, in [
6
,
7
,
10
];
however, the information about CO2liquefaction processes is not provided.
To demonstrate the scientific novelty of the authors’ research, i.e., the feasibility study
of the CO
2
liquefaction processes, the approach of the bibliometric analysis (using the
Scopus database available in July 2021) was selected.
Energies 2021,14, 7174 3 of 13
The bibliometric analysis started with the keyword “carbon dioxide” and resulted
in 500+ thousand research publications since 1876. Only 12% of those publications were
assigned to the energy field. The collection of the keywords that appeared in energy-related
publications in the field of “carbon dioxide” during the time period 1921–2021 is shown in
Figure 3a. The software VOSviewer was used for the identification of the links among the
selected keywords [11].
Energies2021,14,xFORPEERREVIEW3of13
Todemonstratethescientificnoveltyoftheauthors’research,i.e.,thefeasibility
studyoftheCO2liquefactionprocesses,theapproachofthebibliometricanalysis(using
theScopusdatabaseavailableinJuly2021)wasselected.
Thebibliometricanalysisstartedwiththekeyword“carbondioxide”andresultedin
500+thousandresearchpublicationssince1876.Only12%ofthosepublicationswereas‐
signedtotheenergyfield.Thecollectionofthekeywordsthatappearedinenergy‐related
publicationsinthefieldof“carbondioxide”duringthetimeperiod1921–2021isshown
inFigure3a.ThesoftwareVOSviewerwasusedfortheidentificationofthelinksamong
theselectedkeywords[11].
(a)
(b)
Figure3.Co‐occurrenceandlinksamongthekeywords(byVOSviewer):(a)keyword“carbondi‐
oxide”,timeperiod1921–2021,and(b)filter“refrigeration”,timeperiod2000–2021.
Figure 3.
Co-occurrence and links among the keywords (by VOSviewer): (
a
) keyword “carbon
dioxide”, time period 1921–2021, and (b) filter “refrigeration”, time period 2000–2021.
The research clusters are forming the areas of research: investigation of the properties
of CO
2
(including mixtures), heat transfer characteristics and equipment, development in
Energies 2021,14, 7174 4 of 13
the schematics, application of CO
2
as the working fluid for power and refrigeration systems,
and the environmental impact of CO
2
, etc. For example, the review and perspectives for
the application of supercritical CO
2
thermodynamic cycles for power generation have been
reported in the pioneering paper by Angelino [
12
]. The perspectives of CO
2
application for
refrigeration systems as primary and secondary working fluid have been highlighted by
Lorentzen [
13
]. R744 is the international nomenclature of CO
2
for refrigeration applications.
To describe the state-of-the-art in the field of authors’ research, only publications
limited by the keyword “refrigeration” (=“cryogenics”) were considered. As a result,
430 papers published over two decades formed the collection of the keywords shown
in Figure 3b.
The review paper [
14
] perfectly described the progress in CO
2
refrigeration systems
during the 20th century. However, the keyword “liquefaction” did not appear in this
publication. This keyword did not form the cluster in Figure 1b (due to a relatively small
number of publications).
The following papers, published during the last decade, demonstrate state-of-the-art
in the field of large-scale CO
2
liquefaction for “port to port” or “port to offshore” trans-
portation. The publications related to liquefaction CO
2
as a process within refrigeration
systems and small-scale applications are not considered here.
Two types of CO
2
liquefaction processes were simulated with ASPEN HYSYS, and
evaluated in [
15
]: conventional cascade refrigeration system (R744/R717) and single-
refrigerant (R717) liquefaction cycle (similar to the nitrogen-based liquefied natural gas
system). The reported thermodynamically optimal liquefaction pressure is 50 bar. The
single-refrigerant cycle has 5% less power consumption. The irreversibilities were evalu-
ated using Second Law efficiency; the value of 70% is reported for the single-refrigerant
cycle. An economic analysis was not applied.
Effect of impurities (O
2
, N
2
, Ar, H
2
, CO, H
2
S, and CH
4
) within CO
2
stream on op-
eration conditions of liquefaction process, materials for equipment, storage system, and
transportation is reported in [
16
]. Suitable pressure and temperature for CO
2
streams with
very high purity are reported as 6 bar and −57 ◦C.
An extended study on impurities is reported in [
17
]. Different CCS technologies were
evaluated where the liquefaction pressure varied between 7 and 70 bar. For pure CO
2
,
the specific
cost of the liquefaction process is between 17.7 (7 bar) and
15.1 (70 bar) EUR/tCO2
.
For amine-based post-combustion technology, the limit of CO
2
purity is reported as
99.94–99.86%
, the specific cost of liquefaction process is 18.0 (7 bar)–15.4 (70 bar) EUR/tCO
2
.
The liquefaction of CO
2
(99.81–97.98%) after membrane-based post-combustion is calcu-
lated as 20.10 (7 bar)–15.5 (70 bar) EUR/tCO
2
. Rectisol-based pre-combustion technology
results in 99.33–98.42% purity and 18.90 (7 bar)–15.10 (70 bar) EUR/tCO
2
. Regardless of
CCS technology, the lower specific cost is associated with high pressure.
The CO
2
liquefaction under supercritical pressures 80–240 bar was evaluated in [
18
].
The electrical energy demand is directly proportional to the pressure and was found to be
between 1.9 kWh/tCO2and 7.8 kWh/tCO2.
The maximum CO
2
liquefaction pressure of 220 bar was fixed for the evaluation of
four liquefaction cycles in [
19
]. The qualitative evaluation was applied to the following
processes: gas compression of CO
2
(four-stage compression process) as base case; super-
critical compression and pumping (four- and six-stage compression processes); subcritical
compression and pumping (four- and six-stage compression processes), and so-called
“refrigerated compression” (four-stage compression). The environmental temperature is
assumed to be lower than critical. No quantitative data for liquefaction processes are
available.
The evaluation of an entire CCS block has been performed in [
20
]; only relative
values are reported. The CO
2
liquefaction system is based on a four-stage compression
process. The goal was to achieve the maximum liquid yield. Economic analysis showed
that the CO
2
liquefaction cost could be reduced from approximately 10.5 USD/tCO
2
to
9.9–10.0 USD/tCO2
. The condensation temperature is assumed to be equal to
+10 ◦C
(sea-
Energies 2021,14, 7174 5 of 13
water is the cooling media). Such operation conditions make the cost of CO
2
liquefaction
incomparable low.
Authors of [
21
] applied the cryogenic liquefaction cycles for CO
2
liquefaction. Four
systems were evaluated: Linde–Hampson; Linde dual-pressure system; precooled Linde–
Hampson system; and closed system. Sensitivity analysis was conducted to investigate
the influence of parameters and selected systems on the life cycle cost. For the liquefaction
pressure of 6 bar, the Linde–Hampson system and the Linde dual-pressure system are more
economically effective, however the liquid yield is reduced.
A ship-based CCS chain with different CO
2
liquefaction pressures was evaluated
economically in [
22
]. The goal of this research is to determine the optimal liquefaction
pressure. Seven liquefaction pressures were suggested in order to cover the range between
the triple point (5.18 bar/
−
56.6
◦
C) and the critical point (73.8 bar/31.1
◦
C). CCS chain was
divided into five modules: a liquefaction system, storage tanks, a CO
2
carrier, storage tanks
in the intermediate terminal, and a pumping system. The optimal liquefaction pressure is
15 bar (−27 ◦C).
For the first time, the boil-off CO
2
re-liquefaction processes were addressed in [
23
].
Pressures between 7 and 20 bar were considered (for different designs of the CO
2
ships). As
only energy-related characteristics are relevant for ship application, the following results
are reported: the CO
2
re-liquefaction fraction is between 0.524 (7 bar) and 0.997 (20 bar), and
specific power consumption is between 187.8 kW/(tCO
2
/h) for 7 bar and 260.0 kW/(t/hr)
for 20 bar.
“Heat-pump-assisted CO
2
compression configurations” (the term used by authors) are
examined in [
24
]. The CO
2
liquefaction pressure has been set to 57 bar. The performance is
quantified in terms of net power consumption. The optimization using a genetic algorithm
was applied and allowed for an 8% electric power saving and achieving 68% exergetic
efficiency. In total, 44% of irreversibilities are associated with compressors, and 34% with
intercooler and condenser (i.e., exergy transfer to the environment).
Four CO
2
liquefaction systems are compared in terms of energy, exergy, and economic
performance in [
25
]. Exergoeconomic analysis was also performed. The authors proposed
the integration of an absorption refrigeration system in order to increase the thermodynamic
performance (exergetic efficiency is higher than 85%) and decrease the life cycle costs (for
more than 20%). The conclusions are based on the exergoeconomic factors. The obtained
results, unfortunately, cannot be used as references for this paper, as some initial data and
assumptions for analysis are not available.
The reported findings have an overview of research on the CO
2
liquefaction processes.
The exergy analysis was not applied often. The most promising CO
2
liquefaction processes
reported in the above-mentioned publications were selected. This paper focuses on the
evaluation of the ship-based CO
2
liquefaction systems with the help of exergy-based
methods.
2. CO2Liquefaction Systems: Description and Modeling
Based on evaluated publications, the performance of the vapor-compression lique-
faction process is the highest among all the closed liquefaction processes. Therefore, this
process was selected as the closed system, and three working fluids were evaluated: R290,
R7177, and R134a. For the open system, the precooled Linde–Hampson liquefaction
process showed promising energetic and economic performance. Thus, the precooled
Linde–Hampson liquefaction process with R717 as the working fluid was selected as an
alternative to the open system.
The following assumptions were made for the simulation and evaluation of the CO
2
liquefaction systems:
•
Large-scale CCS is assumed to be installed for a 500 MW pulverized coal-fired power
plant, with results of 395 tCO2/h.
•
The CO
2
stream usually exits the CCS block under pressure 1.2–3.5 bar. The authors
assumed the average value of 2 bar.
Energies 2021,14, 7174 6 of 13
•
Different kinds of CCS methods [
17
] provide the CO
2
stream with purity higher than
98%. For simplification, pure CO2is assumed to be liquefied.
•
The optimal liquefaction pressure of the ship-based CO
2
liquefaction process has been
reported as 15 bar. The authors assumed this value for simulation.
•
The systems were simulated under steady-state conditions, assuming the adiabatic
operation conditions for all components. The pressure drop in all heat exchanges is
neglected.
•Heat exchanger for liquefaction process: minimal temperature difference is 3K.
•The outlet temperature for interstate coolers and condensers has been set to 30 ◦C.
•
Compressors: maximum pressure ratio is 3, the isentropic efficiency is 0.85, and
electrical efficiency is 0.95.
The flow diagram of the vapor-compression liquefaction process is shown in
Figure 4
.
The captured CO
2
(stream 1) is compressed up to 15 bar (stream 5) by a two-stage compres-
sion process (CMP1 and CMP2) with interstate cooling and liquefied in the heat exchanger
(HEAT). Stream 6 is liquid CO
2
under conditions for ship transportation. In the refrigerant
cycle, stream 14–15 is used to remove the latent heat of the CO
2
during liquefaction. Af-
ter, the three-stage compression process (stream 15–stream 7) with incomplete interstage
cooling is used. Note, for R290 and R134a, only incomplete interstage cooling allows,
while for R717 both, complete and incomplete are technically possible. For realizing the
interstage cooling and achieving stream 14, three J-T valves in series (VAL1–VAL3) with
two corresponding separators (SEP1 and SEP2) are implemented. Table 1shows the simu-
lation result of the three-stage vapor-compression CO
2
liquefaction process with different
working fluids.
Energies2021,14,xFORPEERREVIEW6of13
Large‐scaleCCSisassumedtobeinstalledfora500MWpulverizedcoal‐firedpower
plant,withresultsof395tCO2/h.
TheCO2streamusuallyexitstheCCSblockunderpressure1.2–3.5bar.Theauthors
assumedtheaveragevalueof2bar.
DifferentkindsofCCSmethods[17]providetheCO2streamwithpurityhigherthan
98%.Forsimplification,pureCO2isassumedtobeliquefied.
Theoptimalliquefactionpressureoftheship‐basedCO2liquefactionprocesshasbeen
reportedas15bar.Theauthorsassumedthisvalueforsimulation.
Thesystemsweresimulatedundersteady‐stateconditions,assumingtheadiabatic
operationconditionsforallcomponents.Thepressuredropinallheatexchangesis
neglected.
Heatexchangerforliquefactionprocess:minimaltemperaturedifferenceis3K.
Theoutlettemperatureforinterstatecoolersandcondensershasbeensetto30°C.
Compressors:maximumpressureratiois3,theisentropicefficiencyis0.85,andelec‐
tricalefficiencyis0.95.
Theflowdiagramofthevapor‐compressionliquefactionprocessisshowninFigure
4.ThecapturedCO2(stream1)iscompressedupto15bar(stream5)byatwo‐stagecom‐
pressionprocess(CMP1andCMP2)withinterstatecoolingandliquefiedintheheatex‐
changer(HEAT).Stream6isliquidCO2underconditionsforshiptransportation.Inthe
refrigerantcycle,stream14–15isusedtoremovethelatentheatoftheCO2duringlique‐
faction.After,thethree‐stagecompressionprocess(stream15–stream7)withincomplete
interstagecoolingisused.Note,forR290andR134a,onlyincompleteinterstagecooling
allows,whileforR717both,completeandincompletearetechnicallypossible.Forrealiz‐
ingtheinterstagecoolingandachievingstream14,threeJ‐Tvalvesinseries(VAL1–VAL3)
withtwocorrespondingseparators(SEP1andSEP2)areimplemented.Table1showsthe
simulationresultofthethree‐stagevapor‐compressionCO2liquefactionprocesswithdif‐
ferentworkingfluids.
Figure4.Three‐stagevapor‐compressionCO2liquefactionprocess.
Table1.Thesimulationresultofthree‐stagevapor‐compressionCO2liquefactionprocess(Figure4).
CO2
Parameters/States123456
Temperature(°C)301153011630−28
Pressure(bar)2.005.485.4815.0015.0015.00
Specificenthalpy(kJ/kg)−8939−8863−8942−886−8951−9311
Specificexergy(kJ/kg)3710492157145208
Massflowsrate(kg/s)109.72109.72109.72109.72109.72109.72
R290
Parameters/States7891011121314
Temperature(°C)26543066−14−14−31
Pressure(bar)5.7410.8110.81 5.745.743.053.051.62
Specificenthalpy(kJ/kg)−2388−2350−2725−2725−2790−2790−2840−2840
Specificexergy(kJ/kg)91124110106110107113111
Figure 4. Three-stage vapor-compression CO2liquefaction process.
Table 1. The simulation result of three-stage vapor-compression CO2liquefaction process (Figure 4).
CO2
Parameters/States 1 2 3 4 5 6
Temperature (◦C) 30 115 30 116 30 −28
Pressure (bar) 2.00 5.48 5.48 15.00 15.00 15.00
Specific enthalpy (kJ/kg) −8939 −8863 −8942 −886 −8951 −9311
Specific exergy (kJ/kg) 37 104 92 157 145 208
Mass flows rate (kg/s) 109.72 109.72 109.72 109.72 109.72 109.72
R290
Parameters/States 7 8 9 10 11 12 13 14
Temperature (◦C) 26 54 30 6 6 −14 −14 −31
Pressure (bar) 5.74 10.81 10.81 5.74 5.74 3.05 3.05 1.62
Specific enthalpy (kJ/kg) −2388 −2350 −2725 −2725 −2790 −2790 −2840 −2840
Specific exergy (kJ/kg) 91 124 110 106 110 107 113 111
Mass flows rate (kg/s) 123.08 123.08 123.08 123.08 101.60 101.60 88.69 88.69
Parameters/States 15 16 17 18 19 20 21 22
Temperature (◦C) 15 41 30 −14 25 51 30 6
Pressure (bar) 1.62 3.05 3.05 3.05 3.05 5.74 5.74 5.74
Specific enthalpy (kJ/kg) −2395 −2355 −2373 −2446 −2382 −2342 −2381 −2422
Specific exergy (kJ/kg) 25 60 59 62 59 94 97 92
Mass flows rate (kg/s) 88.69 88.69 88.69 12.91 101.60 101.60 101.60 21.47
Energies 2021,14, 7174 7 of 13
Table 1. Cont.
R717
Parameters/States 7 8 9 10 11 12 13 14
Temperature (◦C) 28 98 30 6 6 −14 −14 −35
Pressure (bar) 5.31 11.58 11.58 5.31 5.31 2.44 2.44 0.94
Specific enthalpy (kJ/kg) −2707 −2567 −3913 −3913 −4030 −4030 −4124 −4124
Mass flows rate (kg/s) 33.00 33.00 33.00 33.00 30.00 30.00 28.00 28.00
Parameters/States 15 16 17 18 19 20 21 22
Temperature (◦C) 27 111 30 −14 27 96 30 6
Pressure (bar) 0.94 2.44 2.44 2.44 2.44 5.31 5.31 5.31
Specific enthalpy (kJ/kg) −2695 −2514 −2693 −2785 −2699 −2555 −2702 −2754
Mass flows rate (kg/s) 27.61 27.61 27.61 2.07 29.68 29.68 29.68 3.01
R134a
Parameters/States 7 8 9 10 11 12 13 14
Temperature (◦C) 26 55 30 6 6 −14 −14 −31
Pressure (bar) 3.63 7.69 7.69 3.63 3.63 1.71 1.71 0.81
Specific enthalpy (kJ/kg) −8784 −8764 −8964 −8964 −8998 −8998 −9024 −9024
Mass flows rate (kg/s) 234.02 234.02 234.02 234.02 193.59 193.59 169.07 169.07
Parameters/States 15 16 17 18 19 20 21 22
Temperature (◦C) 12.27 38.40 30.00 −13.91 24.63 51.86 30.00 6.18
Pressure (bar) 0.81 1.71 1.71 1.71 1.71 3.63 3.63 3.63
Specific enthalpy (kJ/kg) −8791 −8770 −8778 −8814 −8782 −8761 −8780 −8801
Mass flows rate (kg/s) 169.07 169.07 169.07 24.52 193.59 193.59 193.59 40.43
The flow diagram of the precooled Linde–Hampson liquefaction process is shown in
Figure 5. The captured CO
2
(stream 1) goes through the two-stage compression process
with interstage cooling. Stream 5 is mixed with return stream 13, and stream 6 is further
compressed up to 25 bar (stream 7). After cooling and liquefaction (stream 9), CO
2
is
then expanded in J-T valve down to the target pressure and separated. Stream 11 is the
product stream. For the refrigerant cycle, ammonia (R717) is selected as the working fluid
as suggested in [
21
]. The ammonia stream (stream 14) is compressed by the two-stage
compression process in order to achieve the condensation pressure. Stream 18 is then
expanded. Stream 19–14 (R717) together with “return” CO
2
stream 12–13 formed so-called
“cold composite curve” within 3-flow heat exchanger (HEAT) in order to liquefy the stream
of CO2, i.e., “hot composite curve”.
Energies2021,14,xFORPEERREVIEW8of13
Figure5.PrecooledLinde–HampsonCO2liquefactionprocess.
3.Evaluation:Tools,Results,andDiscussion
3.1.EnergyAnalysis
Aftersimulation,theenergybalancesareappliedtoallsystems’components.Asa
result,thetotalenergysupply(tot
W
)andtherequiredcoolingdutyforthesimulatedsys‐
temsaregiveninFigure6.
Figure6.Comparisonbasedonenergyanalysis.
Theonlyvariablethatdescribesthatenergeticperformanceoftheevaluatedrefrig‐
erationsystemisthecoefficientofperformance(COP),astheinversethermodynamiccy‐
clesareinvolved

tot
out
CO
in
COCO
W
hhm
energypliedsup
effectpositive
COP
222
(1)
Thepositiveeffectis40.82MW.Therefore,theCOPvaluesare:1.35(VCR290),1.29
(VCR717),1.35(VCR134a),and1.31(L‐HR717).
TheCOPvaluecannotbeappliedforliquefactionasa“stand‐alone”process(process
5–6inFigure4andprocess8–9inFigure5).Theentiresystemforcompressionandlique‐
factionoftheCO2streammustbeconsidered.NotethattheconceptofCOPofCarnot
cycleisnotmeaningfultoapplytotheevaluatedsystemsinordertomakeconclusions
regardingtheirreversibilities(includingcalculationofthesecondlawefficiency).
Figure 5. Precooled Linde–Hampson CO2liquefaction process.
3. Evaluation: Tools, Results, and Discussion
3.1. Energy Analysis
After simulation, the energy balances are applied to all systems’ components. As
a result, the total energy supply (
.
Wtot
) and the required cooling duty for the simulated
systems are given in Figure 6.
Energies 2021,14, 7174 8 of 13
Energies2021,14,xFORPEERREVIEW8of13
Figure5.PrecooledLinde–HampsonCO2liquefactionprocess.
3.Evaluation:Tools,Results,andDiscussion
3.1.EnergyAnalysis
Aftersimulation,theenergybalancesareappliedtoallsystems’components.Asa
result,thetotalenergysupply(tot
W
)andtherequiredcoolingdutyforthesimulatedsys‐
temsaregiveninFigure6.
Figure6.Comparisonbasedonenergyanalysis.
Theonlyvariablethatdescribesthatenergeticperformanceoftheevaluatedrefrig‐
erationsystemisthecoefficientofperformance(COP),astheinversethermodynamiccy‐
clesareinvolved

tot
out
CO
in
COCO
W
hhm
energypliedsup
effectpositive
COP
222
(1)
Thepositiveeffectis40.82MW.Therefore,theCOPvaluesare:1.35(VCR290),1.29
(VCR717),1.35(VCR134a),and1.31(L‐HR717).
TheCOPvaluecannotbeappliedforliquefactionasa“stand‐alone”process(process
5–6inFigure4andprocess8–9inFigure5).Theentiresystemforcompressionandlique‐
factionoftheCO2streammustbeconsidered.NotethattheconceptofCOPofCarnot
cycleisnotmeaningfultoapplytotheevaluatedsystemsinordertomakeconclusions
regardingtheirreversibilities(includingcalculationofthesecondlawefficiency).
Figure 6. Comparison based on energy analysis.
The only variable that describes that energetic performance of the evaluated refrigera-
tion system is the coefficient of performance (COP), as the inverse thermodynamic cycles
are involved
COP =positive e f f ect
sup plied energy =
.
mCO2hin
CO2−hout
CO2
.
Wtot
(1)
The positive effect is 40.82 MW. Therefore, the COP values are: 1.35 (VC R290), 1.29
(VC R717), 1.35 (VC R134a), and 1.31 (L-H R717).
The COP value cannot be applied for liquefaction as a “stand-alone” process (process
5–6 in Figure 4and process 8–9 in Figure 5). The entire system for compression and
liquefaction of the CO
2
stream must be considered. Note that the concept of COP of Carnot
cycle is not meaningful to apply to the evaluated systems in order to make conclusions
regarding the irreversibilities (including calculation of the second law efficiency).
The vapor-compression processes with R290 demonstrates the highest energetic per-
formance, therefore has been further evaluated using the exergetic analysis. The vapor-
compression process with R717 is less efficient; however, the same working fluid used for
precooled Linde–Hampson process is comparable to VC R290 (Figure 6). The cooling duty
required for any of the systems with R717 is slightly higher.
3.2. Exergetic Analysis
The exergetic analysis was applied to VC R290 and L-H R717 systems. The reference
conditions have been set to 20
◦
C and 1.013 bar. The only physical exergy was calculated,
and results are given in Tables 1and 2for corresponding systems. The exergy balances are
written using the approach “exergy of fuel/exergy of product” [26].
Note that within the exergy balance for the overall system
.
EF,tot =.
EP,tot +∑
k
.
ED,k+.
EL,tot (2)
the term
.
EL,tot
is vanished, as all coolers and condenser within each evaluated system are
assigned as dissipative components.
Energies 2021,14, 7174 9 of 13
Table 2. The simulation result of the precooled Linde–Hampson CO2liquefaction process (Figure 5).
CO2
Parameters/States 1 2 3 4 5 6 7
Temperature (◦C) 30 115 30 116 30 30 73
Pressure (bar) 2.00 5.48 5.48 15.00 15.00 15.00 25.00
Specific enthalpy (kJ/kg) −8939 −8864 −8942 −8869 −8952 −8952 −8919
Specific exergy (kJ/kg) 37 104 92 157 145 145 174
Mass flows rate (kg/s) 109.72 109.72 109.72 109.72 109.72 124.52 124.52
Parameters/States 8 9 10 11 12 13
Temperature (◦C) 30 −12 −28 −28 −28 27
Pressure (bar) 25.00 25.00 15.00 15.00 15.00 15.00
Specific enthalpy (kJ/kg) −8962 −9275 −9275 −9311 −9006 −8954
Specific exergy (kJ/kg) 170 204 201 208 149 145
Mass flows rate (kg/s) 124.52 124.52 124.52 109.72 14.80 14.80
R717
Parameters/States 14 15 16 17 18 19
Temperature (◦C) 19 88 30 102 30 −15
Pressure (bar) 2.37 5.24 5.24 11.58 11.58 2.37
Specific enthalpy (kJ/kg) −2715 −2572 −2702 −2558 −3913 −3913
Specific exergy (kJ/kg) 120 245 230 357 296 275
Mass flows rate (kg/s) 31.84 31.84 31.84 31.84 31.84 31.84
The exergetic efficiency of the overall system is
•vapor-compression
εVC =
.
EP,tot
.
EF,tot
=.
E6−
.
E1
.
Wtot
(3)
•precooled Linde–Hampson
εL−H=
.
EP,tot
.
EF,tot
=.
E11 −
.
E1
.
Wtot
(4)
Table 3summarizes some results from the exergetic analysis. Figure 7shows the
distribution of the exergy destruction among the system components.
Table 3. The result of exergy analysis of the system.
Fuel, .
EP,tot(MW)Product, .
EP,tot(MW)Destruction,
∑
k
.
ED,k(MW)
Exergetic
Efficiency, ε(%)
VC (R290) 34.34 22.88 11.46 66.6
L-H (R717) 35.28 22.88 12.40 64.8
In the three-stage vapor-compression process, 41% of the total exergy destruction is
associated with dissipative components (in yellow, Figure 7a), and 9% of the total exergy
destruction with J-T valves and mixing units. For precooled Linde–Hampson process,
45% of
the total exergy destruction is associated with dissipative components (in yellow,
Figure 7b), and 8% of the total exergy destruction with J-T valves.
The obtained results are comparable to the ones reported in [
24
]. The options for ther-
modynamic improvement of both systems should definitely include an increase in the isen-
tropic efficiency of compressors. The application of the advanced exergy
analysis [27]
will
not bring benefit for the evaluation of the system due to the large number of
(a) dissipative
components, and (b) components with a high percentage of the unavoidable exergy de-
struction (J-T valves and mixing units).
Energies 2021,14, 7174 10 of 13
Figure 7.
Exergy destruction of components: (
a
) vapor-compression process with R 290; (
b
) precooled
Linde–Hampson process with R717.
3.3. Economic Analysis
As the simulation was performed in Aspen Plus, the most convenient method is to
ascertain the equipment cost data directly from Aspen Process Economic Analyzer
®
in US
dollars for January 2019. The obtained data were adjusted to March 2021 using cost indices.
The assumptions used for the economic analysis:
•Project life—25 years;
•Construction time—2 years;
•Interest rate—7.5%;
•Operating hours per year—8000;
•Electricity cost—0.173 USD/kWh;
•Cooling water cost—0.029 USD/kWh.
The relative results obtained from the economic analysis are given in Figure 8. To
report the absolute numbers is not meaningful, as these numbers are linked to the capac-
ity of CCS block within a power plant and the corresponding CO
2
liquefaction system.
However, the specific cost of the entire liquefaction process is essential (Figure 9). The
conclusions obtained from economic analysis do not contradict the energetic analysis: the
most effective systems are VC R290 (21.30 USD/tCO2) and L-H R717 (21.13 USD/tCO2).
Energies 2021,14, 7174 11 of 13
Energies2021,14,xFORPEERREVIEW11of13
Theobtainedresultsarecomparabletotheonesreportedin[24].Theoptionsforther‐
modynamicimprovementofbothsystemsshoulddefinitelyincludeanincreaseinthe
isentropicefficiencyofcompressors.Theapplicationoftheadvancedexergyanalysis[27]
willnotbringbenefitfortheevaluationofthesystemduetothelargenumberof(a)dis‐
sipativecomponents,and(b)componentswithahighpercentageoftheunavoidableex‐
ergydestruction(J‐Tvalvesandmixingunits).
3.3.EconomicAnalysis
AsthesimulationwasperformedinAspenPlus,themostconvenientmethodisto
ascertaintheequipmentcostdatadirectlyfromAspenProcessEconomicAnalyzer®®in
USdollarsforJanuary2019.TheobtaineddatawereadjustedtoMarch2021usingcost
indices.
Theassumptionsusedfortheeconomicanalysis:
Projectlife—25years;
Constructiontime—2years;
Interestrate—7.5%;
Operatinghoursperyear—8000;
Electricitycost—0.173USD/kWh;
Coolingwatercost—0.029USD/kWh.
TherelativeresultsobtainedfromtheeconomicanalysisaregiveninFigure8.To
reporttheabsolutenumbersisnotmeaningful,asthesenumbersarelinkedtothecapacity
ofCCSblockwithinapowerplantandthecorrespondingCO2liquefactionsystem.How‐
ever,thespecificcostoftheentireliquefactionprocessisessential(Figure9).Theconclu‐
sionsobtainedfromeconomicanalysisdonotcontradicttheenergeticanalysis:themost
effectivesystemsareVCR290(21.30USD/tCO2)andL‐HR717(21.13USD/tCO2).
Theexergoeconomicanalysis[26]wasnotappliedtotheevaluatedsystems.Based
ontheauthors’experience[28],thecostofexergydestructionwilldominatewithinthe
majorityofcomponents.Theonlystructure‐parametricoptimizationshouldbeusedin
ordertoimproveboth,VCandL‐H,systems.
Figure8.Relativeresultsobtainedfromtheeconomicanalysis(VCR290isassumedtobeareference
case,100%).
Figure 8.
Relative results obtained from the economic analysis (VC R290 is assumed to be a reference
case, 100%).
Energies2021,14,xFORPEERREVIEW12of13
Figure9.SpecificCO2liquefactioncost(March2021).
4.Conclusions
Thispaperreportstheresultsofanexergeticandeconomicinvestigationofthree
vapor‐compression(closedsystem)andoneprecooledLinde–Hampsonprocesses.All
systemsareevaluatedforpotentialusefortheship‐basedCO2liquefactionprocesses.The
liquefactionpressureofCO2hasbeensetto15bartofitthedesignoftheavailableCO2
carriers.
Afterdeterminingthemostenergy‐efficientandeconomicallyfeasibleworkingfluid
forthethree‐stagevapor‐compressionprocess,i.e.,R290,theexergeticanalysiswasper‐
formed.Additionally,theexergeticanalysiswasappliedtoprecooledLinde–Hampson
process(onlyR717astheworkingfluidwasconsidered).
Thevapor‐compressionprocesswithR290hasfinallybeentestifiedtohavethebest
energeticandeconomicperformance.ThepowerconsumptionofprecooledLinde–
Hampsonprocessis3.1%higher,andthecostoftheliquefactionprocessishigheraswell.
Theobtainedresultscannotbedirectlycomparedtotheresultsreportedbyothers
duetodifferent(a)boundaryconditions,(b)approachesforconductingtheexergeticanal‐
ysis,and(c)scalingforeconomicanalysis.
Multi‐objectiveoptimizationisthenextresearchstep.
AuthorContributions:Conceptualization,F.C.andT.M.;methodology,T.M.;software,F.C.;vali‐
dation,F.C.;formalanalysis,F.C.;investigation,F.C.andT.M.;resources,F.C.andT.M.;datacura‐
tion,F.C.andT.M.;writing—originaldraftpreparation,F.C.;writing—reviewandediting,T.M.;
visualization,F.C.andT.M.;supervision,T.M.Allauthorshavereadandagreedtothepublished
versionofthemanuscript.
Funding:Thisresearchreceivednoexternalfunding.
ConflictsofInterest:TheauthorsdeclarenoconflictofInterest.
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Figure 9. Specific CO2liquefaction cost (March 2021).
The exergoeconomic analysis [
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on the authors’ experience [
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majority of components. The only structure-parametric optimization should be used in
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4. Conclusions
This paper reports the results of an exergetic and economic investigation of three
vapor-compression (closed system) and one precooled Linde–Hampson processes. All
systems are evaluated for potential use for the ship-based CO
2
liquefaction processes. The
liquefaction pressure of CO
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has been set to 15 bar to fit the design of the available CO
2
carriers.
After determining the most energy-efficient and economically feasible working fluid
for the three-stage vapor-compression process, i.e., R290, the exergetic analysis was per-
formed. Additionally, the exergetic analysis was applied to precooled Linde–Hampson
process (only R717 as the working fluid was considered).
The vapor-compression process with R290 has finally been testified to have the best en-
ergetic and economic performance. The power consumption of precooled Linde–Hampson
process is 3.1% higher, and the cost of the liquefaction process is higher as well.
The obtained results cannot be directly compared to the results reported by others due
to different (a) boundary conditions, (b) approaches for conducting the exergetic analysis,
and (c) scaling for economic analysis.
Multi-objective optimization is the next research step.
Energies 2021,14, 7174 12 of 13
Author Contributions:
Conceptualization, F.C. and T.M.; methodology, T.M.; software, F.C.; valida-
tion, F.C.; formal analysis, F.C.; investigation, F.C. and T.M.; resources, F.C. and T.M.; data curation,
F.C. and T.M.; writing—original draft preparation, F.C.; writing—review and editing, T.M.; visualiza-
tion, F.C. and T.M.; supervision, T.M. All authors have read and agreed to the published version of
the manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflict of Interest.
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