Biomethane liquefaction: A systematic comparative analysis of refrigeration technologies

Applied Thermal Engineering 158 (2019) 113815

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Research Paper

Biomethane liquefaction: A systematic comparative analysis of refrigeration technologies Federico Capraa,b, Francesco Maglia,b, Manuele Gattia,b, a b

T

⁎

Politecnico di Milano, Department of Energy, Via Lambruschini 4, 20156 Milan, Italy Laboratorio Energia e Ambiente Piacenza (LEAP), Via Nino Bixio 27/C, 29121 Piacenza, Italy

HIGHLIGHTS

refrigeration schemes compared for 4.6 t /day biomethane liquefaction plant. • Five configuration selected with process modelling and optimization: RC-MR. • Best with Mixed Refrigerant (RC-MR) electric consumption of 3061 kJ /kg . • Rankine with Mixed Refrigerant (RC-MR) biomethane liquefaction cost of 6.3 €/GJ • Rankine • Sensitivity analysis on CAPEX, Price of Electricity, Plant size, cost of liquid N . CH4

el

CH4

LHV.

2

ARTICLE INFO

ABSTRACT

Keywords: Biogas Liquid biomethane Bio-LNG Refrigeration cycles Process design &optimization Techno-economic analysis

This work presents a comparative technical and economic analysis of alternative refrigeration technologies for the production of liquefied biomethane (a liquid biofuel also known as bio-LNG). These processes are designed for biogas plants (size: 1–10 tCH4/day), where they can be installed downstream of the biogas upgrading step, to bring biomethane (essentially pure CH4) from the gaseous to the liquid phase, at −152 °C and 2 bar. Five technologies are considered: liquid nitrogen vaporization (benchmark); reverse Rankine cycle with mixed refrigerant; reverse Brayton cycle; Claude cycle; reverse Stirling cycle. The energetic and economic analyses are carried out, under a consistent methodology (reference production capacity of 4.6 tCH4/day), based on Aspen Plus process modelling and simulation for the calculation of the heat and mass balances, linked with ad-hoc Matlab algorithms for equipment sizing and cost estimation, and adopting the PGS-COM numerical optimizer for the selection of the optimal process conditions. The Rankine cycle with mixed-refrigerant turns out to be the best option, with an electric consumption of 3061 kJ/kgCH4, and a levelized biomethane liquefaction cost of 6.3 €/GJLHV. However, for liquid nitrogen supply costs lower than 66 €/tN2, liquid nitrogen vaporization, the least capital-intensive option, becomes the favourite solution. Finally, sensitivity analysis on the key variables is carried out to give a broader perspective to the technoeconomic assessment.

1. Introduction and scope In the years to come, renewable biofuels, particularly bioethanol, biodiesel and biomethane are expected to play a significant role among the mitigation strategies for the containment of pollutants (especially PM, SOx and NOx) and greenhouse gas (GHG) emissions from the transport sector [1]. The most common pathway for biomethane production involves the anaerobic digestion of organic biomass in suitable

digesters to produce biogas, a gaseous mixture whose main components are CH4 and CO2, then purified to biomethane by means of an upgrading process. Biomethane (BM) is a gaseous mixture primarily composed of methane (95–97 %mol), which can replace natural gas as a fuel in all of its applications: power generation, space and process heating, transport and fuel for chemical reforming. Biomethane, when further refined to practically pure methane (99.9 %mol) and properly cooled at cryogenic conditions, i.e. in the

⁎ Corresponding author at: Politecnico di Milano, Department of Energy, Via Lambruschini 4, 20156 Milan, Italy. Laboratorio Energia e Ambiente Piacenza (LEAP), via Nino Bixio 27/c, 29121 Piacenza, Italy. E-mail address: [email protected] (M. Gatti).

https://doi.org/10.1016/j.applthermaleng.2019.113815 Received 10 January 2019; Received in revised form 18 April 2019; Accepted 22 May 2019 Available online 23 May 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature ASU Bz BAHX BC BM BoP Bio-CNG C CC ccf COMP CNG cp eLBM EC EM EXP ESDU finst Fp ftex GHG heq H H/D HRS HX IC LBM LHV LNG

N rotational speed specific speed Ns number of stages Nst m mass flow rate O&M operation and maintenance p pressure qw cooling water volumetric flow rate Qz heat transfer rate RC-MR rankine cycle with mixed refrigerant RC-MR-5K RC-MR with higher minimum temperature difference Ref reference S size Sf scale factor SEP phase separator SM stirling machine SMR single mixed refrigerant SMRC single mixed refrigerant cycle t metric ton tex turboexpander T temperature TIC Total Installed Cost TPC total plant cost V rotational speed Vz active heat transfer volume VAL throttling valve Wel Electric Power β pressure ratio γ global volumetric heat transfer coefficient Tpp pinch point temperature difference Tm, z zonal mean logarithmic temperature difference λ thermal conductivity η dynamic viscosity

air separation unit volumetric heat transfer coefficient brazed aluminium plate-fin heat exchanger Brayton cycle biomethane balance of plant compressed biomethane cost claude cycle carrying charge factor compressor compressed natural gas specific heat capacity specific energy consumption equipment cost electric driver expander Engineering Sciences Data Unit installation factor pressure factor cost reduction factor for turboexpander greenhouse gas equivalent yearly hours ideal enthalpy drop height to diameter ratio heat rejection system heat exchanger Installed Cost liquefied biomethane lower heating value liquefied natural gas

temperature range between −162 and −124 °C for pressures spanning between 1 and 10 bar, is liquefied (Liquid Biomethane is often called LBM or bio-LNG) and can therefore be used as a drop-in alternative of Liquefied Natural Gas (LNG). As a consequence of its liquid phase, LBM features a volumetric energy density of 21 MJ/l at atmospheric pressure (corresponding to a density of 0.42 kg/l). This is around 60% the energy density of diesel fuel, but nearly 600 times greater than gaseous BM density under normal conditions and 2–3 times higher than Compressed Biomethane (bio-CNG) or Compressed Natural Gas (CNG) one. The high energy density of LBM entails two major advantages:

gaseous and liquid form. According to this scenario, LBM and CBM (Compressed Biomethane) are expected to provide a crucial contribution to the achievement of the Italian target of renewables penetration in transport (10% on the total primary energy consumption of the sector) by 2020 [7]. The present work was conducted in the framework of GoBioM [8], a research project, funded by the Emilia-Romagna region (through the POR FESR 2014–2020 program), focused on the optimization of the biomethane value chain by developing technologies for biogas upgrading and small-scale biomethane liquefaction. This paper aims at carrying out a consistent techno-economic comparison among four technologies suitable for biomethane liquefaction, while benchmarking them against the state-of-the-art process for this application, i.e. refrigeration via liquid nitrogen evaporation. The four most promising refrigeration cycles layouts and refrigerants are selected based on a combination of literature review and engineering design criteria. The nominal design and operating conditions of each technology are identified, through detailed process modelling, simulation and numerical optimization, in order to determine the minimum cost for liquefaction (in terms of Euro per GJ of LBM). The reference scenario for this study is an existing biogas plant, with a size representative of the Italian context, i.e. agricultural biogas for the production of 999 kW of electricity [9], which can be retrofitted to LBM production, provided that upgrading and liquefaction plants are installed. Therefore, it is assumed that upgraded biomethane is available at the battery limits of the liquefaction process. The paper is organised as follows: Section 2 illustrates an updated literature review and a short overview of currently available small/ micro-scale LNG liquefaction technologies; Section 3 presents the reference biomethane production plant and the process schemes selected;

i. it makes LBM distribution more economical than that of gaseous BM, especially for the limited quantities typical of biomethane production plants; ii. it makes LBM suitable for the use in the heavy transport sector (e.g. heavy trucks and ships). In case of application of LBM in dual fuel vehicles, GHG emission savings compared to diesel may reach up to 49% depending on the biomass origin [2], whereas the first estimates concerning full LBM trucks report a GHG emissions (on a tank-to-wheel basis) reduction of more than 90% [3]. Moreover, besides its decarbonization potential, LBM shares with LNG several environmental benefits over diesel fuel in terms of pollutant emission reduction: − 92% NOx, − 99% SO2 and − 98–99% particulate matter [4]. In Italy, the interest towards LBM has increased significantly not only because the Italian Decree Dlgs 257/2016 [5] envisages the construction of up to 800 LNG/LBM refuelling stations along the country by 2030, but also because the most recent Italian Decree DM 2/3/2018 [6] supports, through incentives, biomethane production both in the 2

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F. Capra, et al.

Section 4 explains the methodology adopted, the techno-economic framework and the modelling assumptions; Section 5 discusses the results with a sensitivity analysis; Section 6 reports the conclusions; the Appendix describes the details for plant components design, sizing and costing.

the size of biomethane liquefaction plants is significantly smaller, ranging between 0.001 and 0.01 Mt/y. Fig. 1 reports a possible classification of the available biomethane liquefaction technologies, based on the type of source used for cooling, on the thermodynamic cycle adopted and on the refrigerant type. This classification is coherent with the broader one presented by [11] and based on (i) the methods for refrigerant pressure variation (J-T valve or expander), and (ii) on the variability of flow-rate during operation (steady state or periodic systems), followed by further distinction based on the cycle type and refrigerant composition. However, according to the specific purposes of biomethane liquefaction, which requires cryogenic temperatures and small sizes, the number of viable technologies for this type of application can be limited to the following categories, where options such as cascades (normally considered for LNG plants) are excluded to limit the system complexity and capital costs:

2. Literature review and status of small-scale LNG liquefaction technologies The liquefaction process of BM is conceptually similar to that of NG, but with two main differences: i. the fluid composition. NG is a mixture of methane, ethane, propane and heavier hydrocarbons (with molar percentages up to 15–20% [10]): hence NG condensation occurs at variable temperature (glide), whereas BM liquefaction takes place at nearly constant temperature (almost pure methane); ii. the typical plant size. The existing fossil NG liquefaction trains have an average nominal capacity of 3.5 Mt/y [10]. On the other hand, Cooling source type

Cooling effect

Expansion in a turbine

• Reverse Brayton cycles: The cooling duty is produced by the expan-

sion of a gaseous refrigerant through a turbine without

Cycle type

Closed

Refrigerant

• Nitrogen • Methane • ...

Reverse Brayton cycle (with regenerator)

Basic layout LBM

BM

Refrigerant

BM

Steady state systems

Refrigeration cycle (mechanical cooling)

Open

Linde cycle

Biomethane LBM

Joule-Thomson throttling Closed

Reverse Rankine cycle (with regenerator)

Open

Open Claude cycle

• Methane • Ethylene • Mixed refrigerant • ...

BM

Refrigerant

LBM

BM

Joule-Thomson throttling + Expansion in a turbine

LBM

Periodic systems

Closed

Cryogenic coolant (cryogenic cooling)

Biomethane

• Methane • ...

Closed Claude cycle

Refrigerant

BM

Refrigerant Piston-type expansion

Closed

LBM

BM

• Helium • ...

Reverse Stirling cycle

LBM Latent heat of vaporization at low temperature

• Liquid Nitrogen • ...

Cryogenic liquid vaporization

Vaporized refrigerant BM

Liquid refrigerant tank LBM

Fig. 1. Classification of the available liquefaction technologies for biomethane, in terms of (i) cooling source type, (ii) cooling effect, (iii) cycle type, (iv) refrigerant composition, (v) cycle layout. 3

Smart-MP LNG. Nitrogen recycling plant with single expansion turbine and booster Smart-HP LNG. Nitrogen recycling plant with double expansion turbine and booster Smart INT-LNG. Integrated plant with combined production of LNG and liquid nitrogen StarLiteLNG. Nitrogen Brayton cycle with a compander, composed of 3 intercooled compression stages and single expansion turbine StarLNG. Nitrogen Brayton cycle with double expansion turbine Turbo-Brayton. Nitrogen Brayton cycle Nitrogen Brayton cycle with double expander, with nitrogen produced from air on-site Optimised Dual Nitrogen Expander Cycle Nitrogen Brayton cycle with double expander C100N. Nitrogen cycle EXP N2. Nitrogen Brayton cycle EXP C1. Methane (Boil-Off Gas) Brayton cycle LNG-NCS. Nitrogen refrigeration cycle system NewMR. Single Mixed Refrigerant (SMR) Rankine cycle with water-glycol pre-cooler Single Mixed Refrigerant (SMR) Rankine cycle PRICO®. Single Mixed Refrigerant (SMR) Rankine cycle IPSMR®. Integrated Pre-cooled Single Mixed Refrigerant (SMR) Rankine cycle IPSMR®+. IPSMR with additional pre-cooling with core-in-kettle exchangers PCMR. Pre-Cooled Mixed Refrigeration SCMR. Single Cycle Mixed Refrigeration StarLNG. Single Mixed Refrigerant (SMR) Rankine cycle with Plate-Fin Heat Exchanger (PFHE), based on the LIMUM® products StarLNG. Single Mixed Refrigerant (SMR) Rankine cycle with Coil-Wound Heat Exchanger (CWHE), based on the LIMUM® products Combined process for biogas upgrading and liquefaction. Cooling duty for liquefaction provided by refrigeration integrated cascade Cryobox. Linde cycle with pre-cooling ECO-μLNG. Linde cycle with pre-cooling Linde cycle with turbocompressor StirLNG. Stirling cryocooler Smart-LIN LNG. Micro capacity plant where the liquid nitrogen is brought to the plant with road tankers LNG-E-LIN. Combined system of natural gas liquefaction and nitrogen evaporation

Brayton cycle

4

1600–3000 0.6–18.5

Linde CryoPur

12–16 4–16 0.5–2 0.15–7 2–25 12–24

< 100 4.8–43.2 30–500 < 4100 13 165 40–6000 40–6000 24–144 10–25 25–100 > 176 400 725 40–6000 40–6000 100–1600

Linde Air Liquide Wärtsilä Kanfa Aragon Air Liquide Chart GE Oil & Gas GE Oil & Gas Cryotec Wärtsilä GTI Black & Veatch Chart Chart GE Oil & Gas GE Oil & Gas Linde

Galileo Ecospray Ecomotive Solutions Stirling Cryogenics SIAD Macchine Impianti Cryotec

25–60 60–110 25–110 20–200

Size, tLBM/d

SIAD Macchine Impianti SIAD Macchine Impianti SIAD Macchine Impianti Cryostar/Linde

Technology provider

* CryoPur technology integrates the biogas upgrading, polishing and liquefaction steps, hence the consumption is referred to the whole process.

Stirling machine Liquid nitrogen vaporization

Linde cycle

Rankine cycle

Commercial name (if available) and main features of the process

Technology

Table 1 Commercial technologies for biomethane liquefaction. Size data are reported both in t/d and kt/year (1 t = 1000 kg).

4.2–5.6 1.4–5.6 0.2–0.7 0.05–2.5 0.7–8.8 4.2–8.4

0.2–6.5

560–1050

< 35 1.7–15.1 10.5–175 < 1435 4.6 57.8 14–2100 14–2100 8.4–50.4 3.5–8.8 8.8–35 > 61.6 140 254 14–2100 14–2100 35–560

8.8–21 21–38.5 8.8–38.5 7–70

Size, ktLBM/y

*

0.31–1.45 0–0.07

0.75–0.84

1.4–1.77

0.48

> 0.70

0.67

0.87–0.98 > 0.35

0.6–1.1

0.78

Electricity consumption, kWh/ kgLBM

[29,30] [31,32] [33] [34] [17] [24]

[28]

[19]

[19] [20] [19] [21] [22] [19] [23] [23] [24] [25] [26] [27] [19] [19] [23] [23] [19]

[17] [17] [17] [18]

Refs.

F. Capra, et al.

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10.8 Rankine cycle with mixed refrigerant + glycol precooling

2014

•

•

• •

condensation. The most suitable working fluid for these Brayton cycles is nitrogen or the biomethane to liquefy itself. Reverse Brayton cycles are typically proposed with 1 or 2 expanders [12]. Joule-Thomson cycles: Reverse Rankine and Linde cycles. The cooling effect is produced by throttling a liquid refrigerant through a JouleThomson valve (isenthalpic lamination). The working fluid is compressed in the vapour phase from the evaporation to the condensation pressure where it is cooled and condensed to subcooled liquid at constant pressure, then is throttled via the J-T valve and finally evaporated to provide the refrigeration effect. For small-scale cryogenic applications, the most common Rankine cycles configurations employ a regenerative single cycle loop (whereas cascades are preferred for larger scale plants), where a mixture of refrigerants is adopted as a working fluid. These processes are typically referred to as Single Mixed Refrigerant (SMR). In several large-scale applications (Mt of LNG per year), an initial pre-cooling stage is employed and cascades of Rankine cycles are installed. As reported by Van Nguyen et al. [13], processes involving cascades of Reverse Rankine cycles, such as the propane pre-cooled mixed refrigerant system (C3MR) or similar are widely employed in large-scale LNG plants, but are not suitable for small-scale applications as a consequence of their high equipment count and capital cost. Claude cycles combine the two cooling effects proper of Reverse Brayton and Joule-Thomson cycles. Claude cycles may be open or closed-circuit: in the former case biomethane is directly used as refrigerant. In this cycle, the working fluid is compressed, cooled by an after-cooler and split in two streams, one is expanded in a turbine, while the other is throttled through a valve. The two-phase mixture produced by throttling is fed to a phase separator: the liquid leaves the cycle as LBM, while the vapour is recycled back to the regenerator and compressor. The same cycle can be used in a closed form where a suitable refrigerant, different than biomethane, can be adopted. Claude cycles are nowadays widely used in large cryogenic liquefiers for air separation or similar purposes [11], whereas their application for small-scale plants is much more limited because of the higher plant complexity compared to Rankine or Brayton refrigerators. Stirling machines. The cooling duty is provided by a working fluid (typically helium) which undergoes a reverse Stirling cycle which was first introduced for small-scale nitrogen liquefiers [11]. Liquid nitrogen vaporization. The cooling duty is provided by the evaporation of liquid nitrogen, produced outside the battery limits of the biomethane production plant (typically by means of an Air Separation Unit) and supplied via cryogenic tanks.

Several available configurations have been already investigated when applied to natural gas liquefaction, which is usually characterized by a larger size and slightly different behaviour of the gas to be liquefied: Baccioli et al. [12] compared the performance of a liquefaction plant integrated with cryogenic upgrading against a sequential biogas upgrading and biomethane liquefaction configuration. The considered plant size is 3.5 t/d and the selected refrigeration technology is a dual expander Brayton cycle. Biomethane is compressed to 50 bar before being liquefied. The pinch analysis is used to optimise the energy balance. An energy consumption close to 2750 kJ/kg is reported for liquefaction, without economic analysis. Van Nguyen et al. [13] compared and optimized three technologies for the liquefaction of natural gas from the grid: (i) a single mixed refrigerant Rankine cycle (SMRC), (ii) a single expander Brayton cycle, (iii) a dual expander Brayton cycle. The SMRC achieves the lowest specific energy consumption, 45% less than the Brayton cycle. Ancona et al. [14] proposed an open Linde cycle integrated with a chiller to liquefy grid gas available at medium pressure (30 bar). This cycle is able to liquefy grid gas with a specific consumption of 1871 kJ/ kgNG. An improved solution based on the substitution of the throttling

Oslo, Norway

Landfill gas Landfill gas Landfill gas Anaerobic digestion of vegetable waste products from grain trade and food production Anaerobic digestion of household food waste Trabuco Canyon, California, USA Albury, United Kingdom Livermore, California, USA Lidköping, Sweden

3.78

2.98 4.13 7 4.2 8.5 11.8 20 12 Rankine cycle with mixed refrigerant Rankine cycle with mixed refrigerant Rankine cycle with mixed refrigerant Nitrogen Brayton cycle

2006 2008 2009 2011

Size, kt/y LBM Size, t/d LBM Liquefaction technology Biogas source Location

Table 2 List of existing LBM production plants in the world.

Year of inauguration

F. Capra, et al.

5

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valve with an expander is also proposed, which is claimed to achieve an energy consumption of 1425 kJ/kgNG. However, this improved solution entails that the expander is working well within the two phase region. The technical feasibility of such solution is still to be explored, so all the expanders in the present work are assumed to operate in the vapour region only. Cao et al. [15] investigated the sensitivity of the reverse Rankine cycle to the composition of the mixed refrigerant working fluid: SMR Rankine cycle is robust and can achieve reasonable efficiency even if the refrigerant composition moves away from the optimal one. In [16] the design and testing of a small scale natural gas liquefier is described. The liquefier is based on a mixed-refrigerant cycle with precooling. A consumption between 2738 kJ/kgNG and 3397 kJ/kgNG is claimed, while an investment cost of 1000 $/(tNG/y) is expected for the liquefier, which would escalate to a total plant cost of 1.4 M€ for a 4.6 t/d plant. A list of commercial technologies proposed by vendors for very small scale LNG production is reported in Table 1, while some details about the existing LBM production facilities are reported in Table 2. Also a number of prototypes, specifically tailored for the small scale application, is being tested, such as the technology presented by GRAF [35], for which no commercial application has been reported yet.

Table 3 Typical specifications for biomethane liquefaction.

Feedstock Anaerobic Digestion

Raw Biogas Pre-treatment

Possible issue

CO2 H2O H2S

50 ppm 0.1–1 ppm 1–4 ppm

Solidification on cold surfaces Solidification on cold surfaces Corrosion

(i) (ii) (iii) (iv) (v)

a reverse Brayton cycle (BC) a reverse Rankine cycle with mixed refrigerant (RC-MR) an open Claude cycle (CC) a reverse Stirling machine (SM) a process based on Liquid Nitrogen vaporization (LN2).

Biomethane condensation pressure is a free variable of the optimization for Brayton, Rankine and Claude cycles; for these options, the trade-off between higher biomethane compression power and lower cooling duty requirements can be exploited by carrying out biomethane condensation at a higher pressure (optimized case by case) than the delivery one (set at 2 bar for all).

As shown in Fig. 2, the LBM production chain starts with the anaerobic digestion of organic compounds, followed by pre-treatment of raw biogas to remove contaminants, then the upgrading process separates most of the carbon dioxide, to obtain gaseous biomethane. Biomethane is further polished and sent to the liquefaction section, where it is cooled below the saturation temperature to finally obtain LBM. The biomethane stream prior to liquefaction has to satisfy the technical specifications reported in Table 3; for this reason, the liquefaction process can be conceptually decoupled from the upstream biomethane production and purification sections, and it can be assumed that the biomethane entering the liquefaction section is 100% CH4. Even though anaerobic digestion, pre-treatment, upgrading and polishing are not analysed in this work, it must be noticed that they account for a significant fraction of the overall energy efficiency of the LBM production chain. Fig. 3 reports the typical consumption of the processes operating upstream to liquefaction, scaled on the primary energy content of the liquid biomethane produced (data are for the reference biogas plant of this paper, with details in Table 4): the expenditure of primary energy for anaerobic digestion is within 6–7% of the output, whereas the other energy intensive process is biogas upgrading, which accounts for 7–13% of the primary energy contained in the purified biomethane, depending on the efficiency of the upgrading technique selected (i.e. water scrubbing or membranes). Last but not least, there is the consumption of the refrigeration technology, which is estimated at the end of this paper. As showed by Bortoluzzi et al. [9], the most common size for existing agricultural biogas-to-electricity plants in the Italian scenario is 999 kWel, on average corresponding to a biogas flow rate of 537 Nm3/h which is assumed as the reference in this work. The upgrading and polishing sections lead to the production of 268.7 Nm3/h, or 4.6 t/d, of H2S and other contaminants Pre-treated Raw Biogas Biogas

Typical limit value

gaseous biomethane (100% CH4) suitable for liquefaction (see Table 4). The inlet and outlet biomethane conditions assumed for the liquefaction section are reported in Table 5. A delivery pressure of 2 bar is chosen since it is a common value for LNG tanks. In particular, the liquefied biomethane is produced as a saturated liquid at 2 bar(a), hence at a temperature of −152.5 °C. The five candidate technologies for the BM liquefaction section are:

3. Basis of design and liquefaction processes configuration

Digestate

Component

3.1. Brayton cycle (BC) The process layout of the Brayton cycle is shown in Fig. 4. The refrigerant, pure nitrogen, follows this loop: stream #5 is compressed to the maximum pressure of the cycle, then pre-cooled and expanded (EXP) to generate the cooling duty required for biomethane cooling (i.e. de-superheating, liquefaction and final throttling to 2 bar), which takes place in the heat exchanger HX-2 (#3 to #4). The refrigerant cooling is achieved by means of an after-cooler and the recuperative heat exchanger HX-1, performing regeneration between the low- and highpressure refrigerant streams. The refrigerant is compressed by an electrically-driven booster compressor (COMP-1) followed by a compressor (COMP-2) mechanically balanced with the expander EXP. The advantage is that refrigerant is non-flammable; on the other hand, the typical defects of a Brayton cycle are envisaged: the cooling duty is provided by the sensible warming of a gaseous stream which reflects into a higher refrigerant mass flow rate and, hence, increased capital costs compared to the case of a phase-changing refrigerant; in the Brayton cycle the coupling of the cooling and heating curves with the hot sink and cold source (T-Q profiles) is more difficult and therefore larger thermodynamic irreversibilities will inevitably occur. The key process conditions for the cycle design and optimisation are: minimum pressure p ; • Refrigerant Refrigerant inlet temperature T ; • 5

5

CO2

CO 2, H2O Gaseous Biomethane

Upgrading

N2 and other noncondensable gases

High purity Biomethane

Polishing

Liquefaction

Liquid Biomethane

Fig. 2. LBM production chain. The focus of this paper is on the last process (enclosed in the red box). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 6

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E of biomass not converted into biogas (% of organic fraction of biomass converted to biogas varies with feedstock)

Ebiogas Ebiomass

EAnaerobic

E

Digestion (digesters heating and electricity cons) 6 ÷ 7%

E CH4 slip from biogas upgrading

Ebiomethane

101 ÷ 110% (depending on % CH4 slip in upgrading)

Ebiomethane

Primary Energy content of the biofuel produced

ELBM refrigeration

polishing

7 ÷ 13% (depending on the upgrading technology)

<1%

biomethane

100% 100% (negligible CH4 (negligible CH4 losses) losses)

100%

EBiogas Upgrading

H2S removal and biogas drying

E liquid biomethane (LBM)

E high purity

Primary Energy consumed in the various processes of the biomethane liquefaction chain

Analyzed in this research (depends on refrigeration technology efficiency)

<1%

Fig. 3. Overall primary energy efficiency of the LBM production chain. Figures are scaled with respect to the primary energy content of the LBM produced. The flow diagram above reports the primary energy content of the energy carrier in output at the various steps described in Fig. 2. The flow diagram in grey reports the primary energy consumed by each step (reference data taken from [8]). This study analyses the consumption of the liquefaction step. Note: in this diagram, the conversion factor between primary energy and electricity is 0.4 (1 kWh of primary energy produces 0.4 kWh of electricity).

3.2. Rankine cycle with mixed refrigerant (RC-MR)

Table 4 Summary of size data for the plant investigated. Capacity of the biogas production section (expressed as Equivalent electric power from biogas), kWel Biogas flow rate, Nm3/h Biomethane flow rate, Nm3/h Biomethane flow rate, t/d Biomethane molar composition

The reverse Rankine cycle considered, shown in Fig. 5, is similar to the PRICO process patented by Black & Veatch [27]. The refrigerant is a mixture of nitrogen and light hydrocarbons: methane, ethane, propane and iso-butane. The mixed refrigerant stream #6 is compressed and precooled in the heat exchanger HX-1. Next, its vapour phase (#15) – mostly composed of the lighter, more volatile fluids – is further precooled by HX-2 and then expanded through the throttling valve VAL-2, to generate cryogenic refrigeration (provided by the cold refrigerant #17) for biomethane condensation. Afterwards, stream #18 is warmed in HX-2, to pre-cool both the gaseous biomethane (#3 to #4) and the high-pressure refrigerant (#15 to #16), and the same happens in HX-1, for the first refrigerant pre-cooling stage. At last, stream #20 is recycled at the inlet of the first compression stage in COMP-1. The mixed refrigerant compression is divided into two stages for intercooling purposes. The liquid phase produced by SEP-2 in #12, mainly composed of the heavier hydrocarbons of the refrigerant mixture, is throttled through VAL-1 to provide additional auto-refrigeration duty which is exploited during gaseous biomethane pre-cooling in HX-2. As suggested by the patent US9574822B2 [27], the refrigerant composition can be tailored in order to reach very low mean temperature differences in the main heat exchanger. On the other hand, as a drawback, the composition of the refrigerant must be kept under strict control to avoid operational issues. The thirteen considered decision variables for the optimization problem are:

999 537 268.7 4.6 100% CH4

Table 5 Inlet and outlet conditions assumed for the liquefaction section.

Mass flow rate, t/d Composition Pressure, bar(a) Temperature, °C

Inlet gaseous biomethane

Outlet liquefied biomethane

4.6 100% CH4 1.01325 25

4.6 100% CH4 2 −152.5

maximum pressure p ; • Refrigerant • Refrigerant mass flow rate m ; • Biomethane condensation pressure, p . 9

5

2

Gaseous Biomethane inlet 1

EM COMP-3 2 12 5

6

7

8

9

3

HX-2

liquefaction pressure p ; • Biomethane outlet pressure p ; • COMP-1 outlet pressure p ; • COMP-2 • HX-1 hot refrigerant outlet temperature T ; • VAL-1 outlet pressure p (which is set equal to VAL-2 outlet pressure, p ); • HX-2 hot refrigerant outlet temperature T ; • HX-2 heavy cold refrigerant outlet temperature T ; in refrigerant x ; • NCH fraction in refrigerant x ; • C H fraction fraction in refrigerant x ; •

Liquefied Biomethane outlet

2

8

10

4 10

11

11

13

HX-1

17

EM

16

COMP-1

COMP-2

14

EXP

2

Fig. 4. Process layout of the Brayton cycle (BC). Biomethane streams are in green.

N2,6

4

2

7

CH4,6

6

C2 H6 6

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Gaseous Biomethane inlet 1

Liquefied Biomethane outlet

EM COMP-3

2

HX-2

3

HX-3

4

5

14 19

20 6

7

9

8

10

11 HX-1

EM

16 VAL-2

SEP 12

EM

17

18 15

13 VAL-1

COMP-2

COMP-1

Fig. 5. Rankine cycle with mixed refrigerant (RC-MR) process layout. Biomethane streams are in green.

in refrigerant x • Ci-CHH fraction fraction in refrigerant x • Refrigerant mass flow rate m . • 3

pressure p ; • Maximum • HX-1 pinch point temperature difference • HX-2 pinch point temperature difference • Split fraction to EXP m /m ; • EXP outlet pressure p .

C3 H8,6 ;

8

4

10

8

i C4 H10,6 ;

6

10

Tpp, HX 1; Tpp, HX 2 ;

9

11

3.3. Claude cycle (CC)

It should be noted that the optimizer can eventually simplify this Claude cycle to a Linde cycle: in case p11 is made equal to p8, the expander EXP is by-passed and we have a Linde cycle.

The Linde cycle-based layout adopted in this work is an open Claude cycle (Fig. 6): it uses biomethane itself as the working fluid. The gaseous biomethane is compressed by COMP-1, followed by an after-cooler and then fed to the main cycle in #3. Here, further inter-cooled compression and pre-cooling via the recuperative heat exchanger HX-1 occurs. Afterwards, stream #9 is split into two branches. Stream #12 is pre-cooled with a second recuperative heat exchanger (HX-2), expanded through a throttling valve (VAL) and sent to the phase separator SEP, where the produced LBM is collected as the liquid phase and leaves the cycle as a product. The other branch of the splitter, stream #10, is expanded in EXP to provide mechanical power while cooling down, and is then mixed with the saturated vapour stream #16 leaving the SEP: stream #17 carries out pressurised biomethane (recuperative) precooling in HX-2 and HX-1, and it is eventually recycled in COMP-2. The main cycle compression is performed by means of an electrically-driven booster compressor (COMP-2) followed by a second compressor (COMP-3) mounted on the same shaft of the expander EXP. The Claude cycle combines some of the features of the Brayton cycle, where a turbine provides the cooling duty while extracting mechanical power, with the typical characteristics of Joule-Thompson cycles, where cooling duty is produced by a throttling valve. On the other hand, both the Claude and the Brayton cycle require more machinery than the Rankine cycle, thus they are expected to be more capital intensive. The five design variables for the optimization are:

Gaseous Biomethane inlet 1

The reverse Stirling cycle, in its ideal version, consists of four transformations carried out into a piston-cylinder system [36]: (i) an isothermal compression at ambient temperature where heat is transferred to the surroundings, (ii) regenerative cooling at constant volume, with heat transfer to a solid regenerator, (iii) isothermal expansion to provide the requested cooling duty to the surroundings (i.e. condensation heat removed from methane), (iv) regenerative heating at constant volume, with heat transfer from the solid regenerator to the working fluid. Stirling cryocoolers are small and compact machines, typical for applications that require a few watts of refrigeration at cryogenic temperatures down to 70–80 K and less [11]. Thus, the main disadvantage is the difficulty in the scale-up from W to hundredth-kW range, which leads to the use of several units in parallel to achieve higher sizes and prevents scale economies to be exploited. Moreover, on the long-term continuous operation they may be less maintainable than classical reverse-Rankine or Brayton cycle [37]. The conceptual integration of a Stirling machine in a biomethane liquefaction process is shown in Fig. 7; consistently with other technologies, an initial compression of the biomethane inlet stream is considered in order to reach

HX-1

19

3

2

3.4. Stirling machine (SM)

4

5

6

7

8

18

HX-2

9 12

17

10

EM

14

SEP

VAL 15

EM COMP-1

1 16 6

13

COMP-2

COM P-3

EXP

11

Fig. 6. Claude cycle (CC) process layout. Biomethane streams are in green.

8

Liquefied Biomethane outlet

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Table 7 Assumptions for liquid nitrogen vaporization (LN2) economic assessment. Cost installation factor represents the average value for process vessels reported by [41]. Parameter

Value 3

Purchased cost of a LN2 tank (60 m capacity), k€ Cost Installation factor, –

135 2.5

Fig. 7. Stirling machine (SM) process layout. Biomethane streams are in green.

of LN2 consumed per kg of LBM, which is practically set by the heat of vaporization of biomethane. The LN2 consumption is assumed equal to 2.5 kgLN2/kgBM, as reported by a gas producer in [42]. Sizing and economics assumptions are reported in Table 7. The cost of the LN2 tank is assumed equal to that of a LNG tank of the same capacity [43]. Two items sum up to determine the cost of LN2: (i) original bulk price and (ii) transport cost. The original bulk price is reported to vary between 80 $/t (68 €/t) [44] and 187 €/t [45], while the transportation cost is 1.5 €/km [46] if bulk truck delivery is considered. In order to determine the typical LN2 cost range considered in the sensitivity analysis (Section 5), a supply distance of 200 km is assumed, to be covered with a truck with a 48 m3 capacity. The LN2 tank is sized in order to guarantee 72 h of continuous operation.

Table 6 Assumptions for Stirling Machine (SM) economic assessment. The cost installation factor has been taken from [41]. Parameter

Value

Biomethane flow rate treated by a single machine (at 2 bar), t/d Stirling Machine specific electric consumption, kJ/kgLBM Purchased cost (of a single machine), k€ Cost Installation factor, –

2.66 4466 627 2

the design LBM outlet pressure. However, differently from the other refrigeration cycles investigated in this work, this layout has not been optimized because, in the field of methane liquefaction, this technology, although attractive, features a very limited number of applications and ad hoc components and designs are often employed, so that, to date, there is one specialized company offering this line of machines for commercial applications [38]. Therefore, instead of modelling the cycle and its components, the energy consumption is estimated by considering the Stirling machine as a black-box system with the efficiency retrieved from the literature. In particular, the performance and sizing data have been interpolated from a vendor datasheet [39], while cost data have been declared by the same vendor [40]. The main assumptions for the calculation are reported in Table 6.

4. Methodology The optimization problem considered for each cycle is the search of operating conditions that minimize the biomethane liquefaction cost. Process simulations are performed via Aspen Plus v9.1 [47], adopting the equation of state GERG 2008 [48] which ensures a very high accuracy [13] for the calculation of thermodynamic properties of the fluids considered in this paper (i.e. biomethane, pure refrigerants and hydrocarbon-based mixed refrigerant mixtures). The numerical approach for the optimization is of the black-box type: the Matlab [49] optimizer is blind towards the constitutive equations of the Aspen Plus v9.1 [47] process model, which is used as an input–output tool: at an upper level the optimizer sets the decision variables and computes the objective functions, while at a lower level heat and mass balances are solved in Aspen Plus, while sizing and costing functions are written ad hoc in Matlab. The process constraint taken for the optimization is the minimum pinch point temperature difference, which must be higher than 1 K in the cold box heat exchangers, i.e. the typical minimum value for cryogenic heat exchangers (see the sizing procedure, ESDU, described in Appendix), whereas a temperature approach of 10 K is selected for inter-coolers. The PGS-COM [50] algorithm is selected for optimization. The stopping criteria is the maximum number of feasible function evaluations carried out without any observed objective function improvement (meaning that at least a local maximum has been selected), which is set to 1000. The specific biomethane liquefaction cost (CLBM ) is the key economic indicator and is selected as objective function (see Eq. (1)): the levelized biomethane liquefaction cost accounts for both the capital expenditure (in terms of Total Plant Cost, TPC ) and operative costs (O& Ms and Cost of electricity).

3.5. Liquid nitrogen vaporization (LN2) The heat exchange with liquid nitrogen, during which LN2 is vaporized on one side while biomethane is liquefied on the other, is the operationally simplest and less capital-intensive option, since it basically involves the installation of a liquid nitrogen tank and a heat exchanger (see Fig. 8). Apart from biomethane compression to 2 bar, this scheme has no additional electricity consumption. Differently from other electric-driven based refrigeration cycles, in this case the cooling duty production is shifted to a large-scale centralized Air Separation Unit (ASU), located out of the battery limits of the biomethane production plant. By the way, a continuous liquid nitrogen supply has to be guaranteed, in the form of LN2 tanks. In this case process optimization is not carried out, since the process consists of a heat exchanger only, where the only variable is the amount

Gaseous Biomethane inlet LN2 tank

CLBM , /GJ =

EM COMP

(TPC· ccf + O &M + Cel ) (heq· mLBM ·LHVLBM )

(1)

where ccf is the capital carrying charge used to annualize the Total Plant Cost, Cel is the cost of electricity, heq is the number of yearly equivalent operating hours, mLBM the mass flow rate of liquefied biomethane produced and LHV is the fuel lower heating value (equal to 50 MJ/kg for methane). The values of these parameters are reported in Table 8.

Liquefied Biomethane outlet

Fig. 8. Liquid nitrogen vaporization (LN2). Biomethane streams are in green. 9

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parameter incorporates all the information on the financial structure of the investment (i.e. interest rate for debt and nominal return for equity, debt/equity ratio, inflation rate, etc.) and represents the fraction of the capital investment to be charged annually in order to recover the investment while obtaining the desired return on capital. More details on the equipment selection, performance and indirect cost functions are reported in the Appendix.

Table 8 Economic assumptions. Number of workforce needed

1

Fixed personnel cost, k€/y Price of electricity cel, /MWh Carrying Charge Factor (ccf), % Equivalent hours h eq , h/y

60 159.2 15 8400

Plant lifetime, y

20

5. Results and discussion Tables 9–11 summarize the decision variables ranges spanned during the analysis and the optimal values identified through optimization. Fig. 9 depicts the T-Q diagrams of the cold box of the refrigeration techniques analysed, where the thermal integration between hot and cold streams of the cycles is highlighted. The better integrated cycle is RC-MR, which is therefore the most efficient option as showed by the energy consumption figures of Table 12 (excluding LN2 that has nearzero electricity consumption, since it uses a cryogenic liquid as cold carrier). Since the high thermal integration of RC-MR and the low minimum temperature differences (1 °C) can make the RC-MR cycle complex to operate, also a less ‘aggressive’ case with higher pinch point temperature differences has been assessed (T-Q curves in Fig. 9 and performances in Table 12). Among the refrigeration cycle-based technologies, the RC-MR achieves an optimized electricity consumption of 3061 kJ/kg, followed by the CC (+37%), the BC (+41%) and the SM (+44%). In case a less tightly integrated cold box is required for operability purposes of the RC-MR cycle (case named RC-MR-5K), the minimum temperature difference is increased from 1 to 5 K (by increasing the refrigerant mass flow rate by 20% and reducing T16 to −141 °C), and the electricity consumption becomes 3499 kJ/kg (RC-MR-5K is 14% less efficient than RC-MR), still the lowest among the refrigeration options investigated. This confirms the superiority of Rankine cycles in terms of energy efficiency for biomethane liquefaction. More details on the compressors/ expanders design for the optimal cycle configurations are reported in the Appendix. Table 12 highlights also the Total Plant Cost and the specific cost of biomethane liquefaction for each technology. The Rankine cycle achieves the minimum cost for LBM production starting from gaseous biomethane, featuring an optimal value of 6.29 €/GJ (corresponding to 0.315 €/kg of LBM). The break-even cost of Liquid Nitrogen for the LN2 technology is 66.3 €/tN2: it means that below this purchase N2 cost, liquid Nitrogen is the lowest cost option for LBM production. The levelized cost of LBM production of the other technologies increases, with respect to the RC-MR cycle ones, by: +43% for the Brayton cycle, +49% for the Claude cycle, +124% for the Stirling machine. In case of less aggressive thermal integration, the Rankine cycle still remains the best one with a cost of 6.83 €/GJ (cost increase of +9%). The Total Plant Cost is broken-down to highlight the contribution of the major equipment units in Fig. 10. The most expensive category for the RC-MR, BC and CC cycles is the machinery (compressors and, where included, expanders) covering more than 50% of the TPC. On the other hand, the liquid nitrogen system features a different cost structure, since it features capital costs lower than refrigeration cycles and involve

Another useful performance metric is the specific energy consumption (defined in Eq. (2)), which incorporates the energy intensity of the technologies and is directly related to operating costs

eLBM , kJ / kg =

Wel mLBM

(2)

The factorial methodology is adopted for capital costs evaluation: following the procedure outlined in the Appendix section. The size and purchase cost (EC) of the major equipment units of the liquefaction plant are evaluated, while the other direct, installation and indirect costs are lumped into the installation multiplication factors ( finst , i ) which have been taken from [41], where not differently specified. Apart for cold box heat exchangers (e.g. see the Appendix), the Equipment cost is calculated with the well-known power law rule (Eq. (3)), where Sref,i and ECref,i are the reference size and cost, sfi is the scale factor, whereas Si and ECi are the actual size and cost of the equipment. The product between the Equipment Cost and the Multiplication factor (finst , i ) gives the Installed Cost (ICi) of the equipment unit i (Eq. (4)). The Total Installed Cost (TIC) is then derived according to Eq. (5). All costs are expressed in December 2016 € currency. For the less representative units, such as valves, piping, etc., sizing is not carried out, while their cost is considered within the Balance of Plant (BoP) contribution, which is assumed to be 20% of the Total Installed Cost, coherently with the typical percentages reported by [41] for feasibility studies. In Eq. (6), the Total Plant Cost (TPC or CAPEX), which reflects the overnight cost of capital, is derived. Operating & Maintenance costs are calculated according to the assumptions highlighted in Table 8 The cost for electricity consumption is calculated according to Eq. (8). The 2016 average Italian electricity price for the 2.000–20.000 MWh/y consumption range is assumed, according to ARERA [51].

ECi = ECref , i·

Si

sfi

Sref , i

(3)

ICi = ECi·finst , i

(4)

TIC =

(5)

i

(ICi )

TPC = TIC + BoP

(6)

O&M , k / y= (6\% TPC + fixed personnel cost)·(1 + 0.3)

(7)

Cel, k / y= Wel·heq· cel

(8)

According to the well-known EPRI methodology [52] for cost assessment, a Carrying Charge Factor of 15% has been selected. This

Table 9 Optimal decision variables for BC case study. Stream numbers are referred to Fig. 4. Variable

Symbol

Lower bound

Upper bound

Optimal design value

Refrigerant minimum pressure, bar Refrigerant pre-cooling temperature, °C Refrigerant maximum pressure, bar Refrigerant mass flow rate, kg/s Biomethane pressure, bar

p5 T5 p9 m5 p2

1 −10 10 0.50 2

40 30 65 5.00 50

6 26.3 58.5 0.681 12.1

10

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Table 10 Optimal decision variables for RC-MR case study. Stream numbers are referred to Fig. 5. Variable

Symbol

Lower bound

Upper bound

Optimal design value

COMP-1 outlet pressure, bar COMP-2 outlet pressure, bar HX-1 hot refrigerant outlet temperature, °C VAL-1 outlet pressure, bar HX-2 hot refrigerant outlet temperature, °C HX-2 heavy cold refrigerant outlet temperature, °C N2 fraction in refrigerant, %mol CH4 fraction in refrigerant, %mol C2H6 fraction in refrigerant, %mol

p8 p10 T11 p13 T16 T14 x N2,6 x CH4,6 x C2 H6 6 x C3 H8,6

5 11 22 1 −160 10 0 5 5

10 35 32 3 −130 30 25 50 50

6.9 28.6 28.1 1.03 −136.7 10.7 0.3 42.3 20.8

0 0.1 2

50 1.5 50

36.6 0.363 6.3

C3H8 fraction in refrigerant, %mol

i-C4H10 fraction in refrigerant, %mol Refrigerant mass flow rate, kg/s Biomethane pressure, bar

0

xi C4 H10,6 m6 p2

50

0

Table 11 Optimal decision variables for CC case study. Stream numbers are referred to Fig. 6. Variable

Symbol

Maximum pressure, bar HX-1 pinch point temperature difference, K

p8 Tpp,HX

1

Split fraction to EXP, – EXP outlet pressure, bar

Tpp,HX

2

m10/ m9 p11

HX-2 pinch point temperature difference, K

Lower bound

Upper bound

Optimal design value

15.0 1.0

90.0 20

72.8 7.1

0.100 2.0

0.750 10

0.694 4.9

1.00

35.0

21.2

Fig. 9. Temperature-Heat Duty (T-Q) curves for the cold-box heat exchangers of the optimal cycle configurations. Liquid nitrogen and Stirling are not reported since a black-box approach has been followed for them, based on literature data. 11

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Table 12 Key performance indicators for each technology.

Specific electricity consumption, kJ/kg TPC, M€ LBM cost, €/GJLHV

LBM

RC-MR

RC-MR-5K

LN2

BC

CC

SM

3061 0.89 6.29

3499 0.93 6.83

10 0.69 6.29

4311 1.50 9.01

4184 1.61 9.35

4409 3.17 14.08

the LN2 tank as the most expensive item. Finally, the Stirling machines are affected by a more expensive capital cost due to the higher complexity and disadvantageous scale economies (i.e. need to purchase multiple fixed size modules). The levelized cost represented in Fig. 11 reflects the contribution of: annualized total plant cost (i.e. capital expenditure spread over the entire life of the plant with the ccf), cost forelectricity, cost for the liquid nitrogen supply (for the LN2 option only), and O&M costs. For the RC-MR, BC and CC options, the operating cost is the largest cost-source, confirming that the optimization of energy efficiency is crucial also from an economic perspective; for the LN2 option the same consideration applies but replacing the electricity with liquid nitrogen as the most expensive factor of production. In case the battery limits of this technique include also the energy consumption for liquid nitrogen

production, according to the overview conducted by [53] on the energy efficiency of real Air Separation Units (ASU), the actual electricity consumption for LN2 separation and liquefaction starting from ambient air, would be 0.64 kWh/kg of LN2 (corresponding to a second law efficiency of the process of around 30%). Since 2.5 kg of LN2 are required to produce 1 kg of LBM, the electricity consumption would be 5760 kJ/ kg of LBM, hence 88% higher than the electricity consumption of the RC-MR cycle. This reflects directly into the cost for liquid nitrogen purchase. The selection of the leading technology between the Rankine mixed refrigerant and liquid nitrogen is hugely dependent on the price at which liquid nitrogen is available. For this reason, a sensitivity analysis on the LN2 price is performed in the followings. 5.1. Sensitivity analysis In order to give a broader perspective to the techno-economic assessment results, while addressing the intrinsic uncertainty of the factorial cost methodology, a sensitivity analysis against four types of variables has been carried out:

• CAPEX. The capital cost estimate is expected to have the accuracy

Fig. 10. Total plant cost breakdown for the different liquefaction technologies.

•

•

Fig. 11. Breakdown of the contribution to BM liquefaction cost for the different liquefaction technologies. 12

range of a feasibility study hence between −30% and +50% as reported by [54]. Therefore, the sensitivity on the capital cost, shown in Fig. 12a) considers this range of variability; it highlights that the impact on the biomethane liquefaction cost is noticeable (and larger for the cycles with higher CAPEX estimates, e.g. Stirling, Claude and Brayton) but would not change the ranking among the cycle options, since even with an increase of the CAPEX of Rankine by 50% this option would remain less expensive in terms of €/GJLBM than Brayton or Claude (even if their CAPEX is reduced by 30%), as a consequence of the significantly higher efficiency of the mixed refrigerant Rankine cycle. Nonetheless, the break-even cost of LN2 will increase from 66 to 84 €/tLN2 in case the Rankine CAPEX goes up by 50% (Rankine LBM cost becomes 7.15 €/GJLBM). Price of Electricity. Also the price of electricity is expected to vary mainly depending on exogenous variables (e.g. plant location, electricity mix, price of gas, oil, economic growth indicators, etc.). For this reason, the sensitivity on the PoE (Fig. 12b) considers a possible excursion of the price of ± 20% around the central value, where 20% was the variation of the electricity prices in the last 10 years for non-household consumers in the EU-28 (source Eurostat, [55]). A ± 20% of the Price of Electricity leads to a maximum LBM cost variation of ± 9% for Rankine, ± 8% for Brayton and Claude, and ± 6% for Stirling, whereas has practically no direct impact on the liquid nitrogen vaporization case, where the electricity consumption is limited to biomethane compression only. Plant size. In this case the comparison focuses on the plant capacity, i.e. by varying the biomethane flow rate, and has been limited to the two outperforming options (continuous curves of Fig. 13): LN2 and RC-MR. Fig. 13 illustrates that the lower capital-intensity of LN2 (smaller capital expenditure than RC-MR) is advantageous at the lower sizes. On the other hand, for plant sizes larger than 4.6 tLBM/ day, the RC-MR achieves lower LBM costs than LN2 for two reasons: first, the economies of scale provide a noticeable specific CAPEX reduction for the refrigeration cycle, secondly, because the increased flow rate allows a more efficient design of the turbomachines (according to the Balje’s diagram).

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Fig. 12. Sensitivity of the cost of biomethane liquefaction to: (a) capital cost estimate (−30% + 50% variability around the central estimate); (b) Price of Electricity ( ± 20% variation considered).

• Liquid nitrogen supply price. A parametric analysis on the price of

this study, further investigation of the plant dynamics, start-up and operations is worth performing in the future, following an approach similar to the one of [57] or [56]: looking forward to the identification of suitable control strategies which might also suggest different, more stable, designs capable to operate under disturbances (e.g. change of ambient temperature, of flow rate of biomethane or leakage of mixed refrigerant charge from the circuit, etc.).

LN2, based on three scenarios (blue curves in Fig. 13) is conducted: the reference case (continuous line) refers to the “break-even value” of 66.3 €/t, whereas the extreme cases are the minimum and maximum LN2 price found in the literature, respectively equal to 76.8 €/t [44] and 196.2 €/t [45], all including transport. Considering this possible excursion of the LN2 price, the break-even plant size is below 4.6 t/day of LBM, meaning that only for very small plant sizes and LN2 prices in the low range region, LN2 is more convenient than RC-MR.

6. Conclusions This work presents the techno-economic comparison of different refrigeration technologies for biomethane liquefaction. The cycle configurations are defined after a bibliographic review, whereas the selection of operating conditions, the calculation of energy performance, the sizing of major equipment and the preliminary costing are based on detailed process modelling and numerical optimization. The analysis leads to the following main conclusions:

It is important to notice that the operability of the steady-state optimal cycle designs found in this research is not guaranteed a priori, since, as reported in the literature, there are sets of refrigeration cycle conditions which are attainable according to mass and energy balance analysis but not in practical operation, because the plant turns out to be poorly controllable or difficult to operate [56]. Lack of controllability is a known issue for very complex refrigeration cycles, entailing multiple recycle loops and including very tightly matched multi-stream heat exchangers, whereas it is less frequent but still possible for the simpler cycle configurations considered in this paper [57]. Hence, in view of confirming the technical and economic findings of

• The five short-listed technologies deemed suitable for biomethane

liquefaction are: (a) liquid nitrogen vaporization; (b) reverse Rankine cycle with mixed refrigerant; (c) reverse Brayton cycle with gaseous nitrogen; (d) Claude open cycle with biomethane itself as

Fig. 13. Sensitivity analysis to LBM production cost varying the size of the plant for three different scenarios of LN2 prices (Break-even price for 4.6 tLBM/day size; Literature Min; Literature Max). Circles represent the evaluated points at five different sizes, whereas connecting piecewise lines represents the trend. 13

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refrigerant; (e) reverse Stirling cycle with helium as refrigerant.

upper bound relates to the Stirling case) of the primary energy content of the produced LBM. From the point of view of the entire value LBM production chain, the overall expenditure of primary energy for anaerobic digestion, pre-treatment, biogas upgrading, polishing and liquefaction ranges between 30 and 40% of the produced LBM energy content, depending on the efficiency of the upgrading technique selected (i.e. water scrubbing or membranes) and on the refrigeration technology. This means that the Energy Return on Energy Investment for liquid biomethane plants is positive, i.e. between 2.7 and 3.3, though not so high compared to other decarbonized fuels production pathways. The Energy Return on Energy Investment for compressed biomethane CBM is slightly higher (i.e. between 3.6 and 4), however its sector of application is limited to low range light vehicles.

• The refrigeration technology attaining the highest energy efficiency, • • •

•

after process optimization, is the reverse Rankine cycle, with mixed refrigerant and two throttling levels, featuring regenerative precooling. This option reports a specific consumption of 3061 kJ/ kgLBM for a reference LBM production capacity of 4.6 tLBM/day. Rankine cycle with mixed refrigerant turns out to be the best option also according to the economic indicators, provided that liquid nitrogen supply costs more than 66.3 €/tN2. Below that threshold, liquid nitrogen is preferable because it is less capital intensive. The levelized biomethane liquefaction cost equals 6.3 €/GJLHV for the most profitable option (RC-MR). According to this economic indicator, the merit order is (from the most to the least attractive): RC-MR and LN2 (for liquid nitrogen price equal to 66.3 €/tN2); Brayton Cycle; Claude Cycle; Stirling cycle. Sensitivity on CAPEX shows that, despite a sensible change in absolute costs, the ranking among the cycle options is not going to change (hence RC-MR remains the best one). Sensitivity on the plant size highlights that, above 4–5 tLBM/day, the Rankine cycle is more convenient than liquid nitrogen vaporization even for the minimum LN2 cost reported in the literature (75 €/tN2). The higher the size, the more convenient becomes the Rankine cycle. The primary energy consumption for BM liquefaction varies between 14% and 20% (the first figure refers to Rankine-MR while the

Acknowledgements This study is part of the “GoBioM” research project (CUP: E82F16001020007) which has been funded by the Emilia-Romagna Region via the POR-FESR 2014–2020 program. Prof. Emanuele Martelli (Politecnico di Milano) is also acknowledged for making available to the authors his PGS-COM algorithm for numerical optimization purposes.

Appendix A In this section the methodology and the assumptions adopted for machinery, heat exchangers and other major components design and performance and cost evaluation is detailed. A.1. Compressors For compressor selection and design, preliminary performance estimate can be conducted with Baljé’s diagram [60]. A commercial flowsheeting software (Aspen Plus® v.9.1) is used to simulate the overall heat and mass balances, while the selection and design of the compressors is carried out by an ad-hoc Matlab routine. Each compression train is followed by an after-cooler(inter-cooling temperature equal to 28 °C). For each compression train, a matrix of possible compressor configurations is defined, based on compressor type and number of stages, as reported in Table A-2. The possible compressor configurations considered in the analysis are: (i) rotating centrifugal compressors with one, two, or three stages, (ii) reciprocating compressors with one or two stages, (iii) screw compressors with one or two stages. In order to reduce the compression power, an intercooler is considered after each stage. The optimal rotating speed of the compressor train is also determined, and cases are considered in which (i) the compression train is coupled to a synchronous electric motor or (ii) its rotating speed is optimized and a gearbox is included. For each function evaluation (i.e. set of decision variables), the optimal compression train configuration is selected with the following strategy:

• At a higher level the entire process is simulated with a fixed compressor efficiency. The output of this step are the design conditions of compressor: inlet mass flow rate, temperature, pressure of the working fluid, as well as the compression ratio. • Every possible compression train configuration is simulated in Matlab and the electric consumption (and heat rejected by the intercoolers and after-coolers) is computed. The specific speed (NS ) of each compressor stage is calculated according to Eq. A(1).

NS =

N · V1 3

(A1)

4 Had

where the corresponding dimensions are: N [rpm], V1 [ft3/s], Had [ft]. If the obtained NS lies out of the range suggested for the considered compressor type, such configuration is discarded, otherwise the stage polytropic efficiency is assumed to be the best possible for the current NS (i.e. design lying on the Cordier’s line). Fluid properties are computed with the Refprop property package [61] linked with Matlab.

• The cost of each compression train configuration is calculated and the compressor configuration (e.g. reciprocating or screw or centrifugal) giving the minimum LBM production cost is selected.

The purchase cost of the compressors is based on the power law with the scale factors reported in Table A-1. The cost effect of the number of stages follows the relation proposed by [62]. The multiplication factors proposed by Ulrich [41] are used to estimate the installation cost of the compressors. The Installed Cost of compressor is therefore calculated as described by Eq. A(2).

ICCMP = ECref ·

Wel, CMP Wel, ref

sf

·

Nst Nstref

0.5

· finst , CMP

(A2)

Except for the turbo-expander case, compressors are moved by electric drivers. The electric efficiency of the drivers is calculated according to the 14

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Table A-1 Reference sizes and costs assumed for the calculation of the purchase cost of the major equipment units. Scaling parameter Compressor, centrifugal Compressor, reciprocating Compressor, screw Electric driver Expander, centripetal Brazed Aluminium Plate-Fin Heat Exchanger Heat rejection system Vertically-oriented tank (stainless steel, H/D = 3) Mist eliminator (stainless steel)

Reference size (S0)

El. Power, kW 100 El. Power, kW 100 El. Power, kW 100 El. Power, kW 100 El. Power, kW 100 Cost assessment according to ESDU 97,006 Water flow, l/s 10 Cross section area, m2 0.1 2 1 Area, m

Reference equipment cost (EC0), k€

Scale factor (sf)

Availability

Refs.

240 120 240 10 40

0.6 0.7 0.7 0.67 0.67

[58]

4.78 12.3 1.2

0.88 0.57 1

0.98 0.94 0.98 1 1 1 1 – –

[59] [58] [41] [41]

standard IEC/EN 60034-30-1:2014 for IE4 Super Premium efficiency motors [63]. The rotating speed of the machines is selected based on an economic criterion, considering either direct coupling with electric drivers working at 750, 1000, 1500, 3000 rpm, or the additional cost of a gearbox if the compressor is not synchronous with grid frequency. The installation factor isequal to 2 in case a gearbox is present, 1.5 otherwise. The gearbox, when applied, has an efficiency of 95% [41]. A.2. Turbo-expanders The expander included in Claude and Brayton processes is a centripetal turbine, mechanically balanced by a centrifugal compressor. The turbo-expander is sized to obtain the maximum efficiency of the overall machine, for given expander inlet conditions and discharge pressure, while the decision variables are:

• The pressure ratio of the compressor section • The turbo-expander rotational speed N [rpm] number of stages of the expander section N • The • The number of stages of the compression section N

CMP , tex

tex

st EXP , tex stCMP , tex

The main constraints are: 1. The specific speed must fall in the ranges reported in Table A-3. 2. The max peripheral speed of the machine has to be lower than 600 m/s [64]. 3. The maximum enthalpy drop per stage is limited accordingly to Table A-3. The cost of the expander is expressed in Eq. A(3), while the cost of the turbo-expander is assumed to be a fraction of the cost of the two machines (compressor and turbine) as expressed in Eq. A(4), since single case and shaft are adopted for both the machines (hence ftex is a factor lower than 1).

ICEXP = ECref ·

Wel Welref

sf

·

Nst Nstref

0.5

· finst , EXP

(A3) (A4)

ICtex = (ICcmp + ICexp)·ftex

Table A-2 Compression train possible configurations and design assumptions. Compressor type

Allowable number of stages

Rotating speed

Max pressure ratio of a single stage

Min NS [–]

Max NS [–]

Centrifugal Reciprocating Screw

1/2/3 1/2 1/2

Free (with gearbox), or coupled with synchronous electric motor at 750, 1000, 1500, 3000 rpm

3 8 8

17 0.029 2.15

151 3.3 263

A.3. Heat exchangers The heat exchangers of the refrigeration cycles, apart from inter- and aftercoolers, are integrated in a cold box, which is a multi-stream heat exchanger insulated to minimize the thermal losses. The cold box is a Brazed Aluminium Plate-Fin Heat Exchanger (BAHX) with fins of the serrated type, a common technology for cryogenic applications. The main advantages of BAHXs are: (i) high surface compactness, (ii) ability to handle multiple streams, (iii) operating temperature from cryogenic to 150 °C, (iv) low minimum pinch point temperature difference down to 1 K [65], (v) better thermal conductivity of aluminium compared to stainless steel [66], (vi) nearly ideal counter-current flow arrangement [67]. The main drawbacks of BAHXs are: (i) low maximum operating pressure compared to other technologies [59], (ii) slow thermal gradients required due to the poor mechanical resistance to thermal stress [66]. The design pressure drops are 1% of the inlet pressure, the maximum allowable pressure is 100 bar and the minimum achievable temperature difference is 1 K [59]. Thermal losses have been neglected. 15

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Table A-3 Turbo-expander design parameters.

Centrifugal compressor Centripetal expander

Min NS

Max NS

Max h [kJ/kg]

17 14.9

151 820

120* 600

* Value obtained from [64], assuming a load coefficient of 1.5 and a maximum peripheral speed of 400 m/s.

The cold box is designed, sized and costed according to ESDU 97006 [59]. Given the exchanged heat duty, inlet and outlet temperature of each stream, hot and cold side composite curves are calculated with Aspen Plus. The cumulative curve is then split into several zones (e.g. 50) such that both temperature profiles can be linearized. For each zone, an average volumetric heat transfer coefficient Bz is obtained from Eq. A(5).

Qz n Qi i=1 i

Bz =

(A5)

where Qz is the total heat transferred in the zone, n is the number of streams involved in the zone, Qi is the heat exchanged by the i -th stream and i is the local volumetric heat transfer coefficient of the i -th stream. Then, the active heat transfer volume Vz of each zone is calculated from Eq. A(6).

Vz =

Qz / Tm, z Bz

(A6)

where Tm, z is the zonal logarithmic mean temperature difference. The total volume of the heat exchanger is obtained by summing all the zonal active volumes Vz and including an additional 15% allowance for the headers and distributors. The cost is estimated from the cost per unit volume data presented in graphical form in ESDU 97006, multiplied by a suitable pressure factor Fp in case of pressures exceeding 25 bar. The global volumetric heat transfer coefficients have been assumed or calculated for each zone of the heat exchanger in accordance to ESDU 97006 [59]. For pure fluids the following assumptions are made:

• Liquid phase. value is provided by ESDU 97006. • Two-phase system (Vapour-Liquid). value is provided by ESDU 97006. • Vapour phase. The mass flux is assumed from ESDU 97006 depending on the gas pressure. For each heat exchangerzone, the following physical •

properties are retrieved from Refprop [61]: specific heat capacity cp , dynamic viscosity and thermal conductivity . The assumptions on the heat exchanger geometry and aluminium thermal conductivity (summarized in Table A-4) allow to apply the procedure for the calculation of the local volumetric heat transfer coefficient described in ESDU 97006. The value of for the whole temperature range is calculated as the average of the values obtained for each portion. Supercritical fluid. The procedure is identical to the one described for the vapour phase, but the value assumed for the mass flux is the one presented in ESDU 97006 for liquid streams.

MR for the mixture (i.e. the mixed refrigerant for the Rankine cycle) is then obtained as the average, weighted on the mass fractions of nitrogen and hydrocarbons and decreased by a penalty factor of 30%, as shown in Eq. A(7). Such penalty is suggested by Kedzierski et al. [68] to model the reduction in the heat transfer coefficient due to the presence of a mixture in place of a pure fluid.

MR

=[

N2·w N2

+

HC ·(1

(A7)

w N2)]·0.7

where w N2 is the nitrogen mass fraction. A.4. Heat rejection system In this work, for each proposed lay-out, a centralised cooling tower is sized to reject all the waste heat to the environment. The electric power consumption WHRS of the overall heat rejection system (fan, pumps of the cooling medium loops) is 2% of the thermal power rejected. The water flow rate qw (in l/s) is estimated from Eq. A(8), a correlation interpolated from vendor data, where WHRS is expressed in kW. The overall cost of the heat rejection system is predicted based on NETL data [58], as reported in Table A-1. (A8)

qw = 2.07· WHRS Table A-4 Heat exchanger parameters assumed for the calculation of

[66].

Parameter

Value

Type of fins Fin frequency, 1/m Fin thickness, m Plate gap/fin height, m Parting sheet thickness, mm Aluminium thermal conductivity, W/m·K

Serrated 708.7 2.032 ⋅ 10−4 6.35 ⋅ 10−3 1.5 130

16

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A.5. Vapor-liquid separators The internal volume of the flash drums performing liquid-vapour separation is calculated assuming equilibrium separation performances. A residence time of 5 min as half full holdup time is considered and a demister is included. The cost of separators is estimated from Ulrich data [41] (see Table A-1), considering a vertically-oriented tank with H/D ratio equal to 3 and a mist eliminator; both units are in stainless steel. Appendix B. Details on the optimal cycle configurations B.1. Brayton cycle (BC) The optimal design for the BC case study, together with the lower and upper bounds considered in the optimization problem, are reported in Table 9. The maximum pressure of nitrogen in the cycle is 58.4 bar. The Grand composite temperature-heat duty diagram for the reverse BC is reported in Fig. 9: the pinch point temperature difference is close to 1 K. The optimal biomethane liquefaction pressure is 12.1 bar, hence higher than the final pressure of 2 bar at which LBM is made available. The refrigerant fluid is pre-cooled down to −96 °C, before being expanded. Such solution allows reaching the minimum temperature of the cycle (−158 °C) with a single stage expander. The amount of heat exchanged by the two plate fin heat exchangers is significant (135 kW): of such thermal power, just 35% is used to liquefy the biomethane, while 65% is used for regenerative purposes to pre-cool Nitrogen. The detail of compressor and turbo-expander preliminary design is reported in Table B-1. COMP-1 is able to cover the needed compression ratio with a single stage, and with a satisfactory efficiency, according to Balje’s diagram. For what the turbo-expander is concerned, the mechanic power at the balanced shaft is 40 kW, and a trade-off between compressor and expander efficiency is reached. Table B-1 BC compressor design and costs detail. Compressor costs do include the cost of electric drivers. COMP-1

Turboexpander

Installed Cost, k€ Power, kW Machine type

623.5 189.3 (electric) Reciprocating

Number of stages

2

263.7 40 (mechanic) Centrifugal/centripetal COMP-2 1

EXP 1

Stage pressure ratio Isentropic efficiency

Stage 1

Stage 2

Stage 1

Stage 1

2.65 77%

2.65 77%

1.62 75%

9.4 81%

B.2. Rankine cycle with mixed refrigerant (RC-MR) The optimization results for the RC-MR cycle are reported in Table 10. The maximum pressure achieved (28.6 bar) is lower than the one obtained for the Brayton cycle. The throttling pressure is set to 1.03 bar. The composition of the mixed refrigerant envisages no propane (C3H8) and practically negligible nitrogen (0.3%), while the component with the highest concentration is methane (42.3%) trailed by isobutane (36.6%). After the L-V separator SEP-2, the heaviest components mainly condense in the liquid stream. Such stream (CH4 10.2%, C2H6 17.2%, isobutane 72.6%, 0.181 kg/s) is throttled in valve VAL-1: it reaches a temperature of −30 °C and is used to pre-cool the vapour stream leaving SEP-2. This latter stream shows a similar mass flow rate (0.182 kg/s) and it is richer in volatile components (N2 0.4%, CH4 59.5%, C2H6 22.8%, isobutane 17.3%). This scheme leads to the best heat integration among the refrigeration cycles, as can be observed from the tight matching between hot and cold curves in Fig. 9. The attained pinch point temperature difference is close to 1 K, and is located at three points (inlet point of stream 13 in HX-2, cold end of HX-2, cold end of HX-3). There are two major slope changes in the cold stream curve: the first one is due to the phase change of the mixed refrigerant which takes place across HX-1, while the second one is generated by the temperature reduction obtained by throttling valve VAL-1. Hence, the optimized composition of the mixed refrigerant ensures an excellent match of the cooling curves for the largest part of heat exchangers. This reflects on an efficient cooling power exploitation, with the drawback of an increased and, therefore, more expensive, heat exchanger area. However, if the cost allocation among the different components is observed, it appears clear that the impact of the cold box on the total cost is limited (less than 20% of the TPC) compared to the cost of compressors (around 60%). Hence, aggressive design of the heat exchangers (i.e. high efficiency and cost) is coherent. More details on the design of compression units can be found in Table B-2. Two single-staged reciprocating compressor are selected for the RC-MR lay-out, due to their reduced cost with respect to other compressor types and reasonable performances achieved. The machines are directly coupled to electric drivers. The preliminary design based on the Balje diagram Table B-2 RC-MR cycle compressor design and costs detail. Compressor costs do include the cost of electric drivers.

Installed Cost, k€ Electric Power, kW Specific installed cost, €/kW Compressor type Number of stages Isentropic efficiency

COMP-1

COMP-2

215.7 75.0 2876 Reciprocating 1 74%

176.7 56.3 3139 Reciprocating 1 73.7%

17

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highlight that it is possible to achieve satisfactory isentropic efficiencies (close to 74%) in the optimized design conditions. Due to the reduced size of the machines, the respective specific installed cost is considerable, since economies of scale are highly unfavourable. B.3. Claude cycle (CC) The optimal decision variables for the CC case study are reported in Table 11. Given the peculiar nature of the CC, in which the whole cooling effect is due to the Joule Thomson effect, large pressure differences are needed. In the optimal case, the maximum pressure of the cycle (out of COMP-3) is equal to 72.3 bar, largely exceeding the critical pressure of methane (46 bar). This acts on the shape of the hot profile of the cumulative T-Q diagram, as reported in Fig. 9, where the red curve follows a cubic trend typical of ipercritical isobars close to the critical point. The methane phase change happens in the throttling valve and in the subsequent separator two single phase streams are split. The throttling pressure is equal to the LBM delivery pressure (i.e. 2 bar). In the optimal configuration, the turboexpander has a pressure ratio of 1.8. The remaining pressure ratio (24.2) is obtained through the two-stage reciprocating compressor COMP-2. The design details are reported in Table B-3. The turboexpander has a very high cost, due to the large number of stages required (three). Also in this case, the pinch point temperature difference is close to 1 °C. Table B-3 CC machinery design and costs detail. COMP-2 cost include the cost of electric drivers. COMP-2

Turboexpander

Installed Cost, k€ Electric Power, kW Specific installed cost, €/kW Machine type

657.65 204.9 3210 Reciprocating

Number of stages

2

334.50 31.5 10,790 Centrifugal/centripetal COMP-3 2

EXP 3

Stage pressure ratio Isentropic efficiency

Stage 1

Stage 2

Stage 1

Stage 2

Stage 1

Stage 2

Stage 3

4.92 76%

4.92 76%

1.34 76.3%

1.34 71.5%

2.45 71.7%

2.45 77.3%

2.45 79.6%

B.4. Stirling cycle (SM) According to our analysis, the Stirling system is less competitive than other cycles, mainly due to the high purchase cost of the Stirling machines themselves, which is affected by a higher degree of uncertainty than the other technologies, because of the lower level of detail and the limited information available in the literature. However, it is interesting, to back-calculate the capital cost for which Stirling machine breaks-even with the RC-MR technology: to this purpose the specific investment cost of the Stirling machine should be nearly 100 k€/(tBM/d), against the value of 545 k €/(tBM/d) adopted in this work based on literature data [34].

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