Thermoeconomic analysis of recuperative sub- and transcritical organic Rankine cycle systems

Thermoeconomic analysis of recuperative sub- and transcritical organic Rankine cycle systems

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IV IV International International Seminar Seminar on on ORC ORC Power Power Systems, Systems, ORC2017 ORC2017 IV International Seminar on ORC Power Systems, 13-15 September 2017, Milano, Italy 13-15 September 2017, Milano, Italy ORC2017 13-15 September 2017, Milano, Italy

a a a

Thermoeconomic analysis of recuperative suband transcritical Thermoeconomic analysis of recuperative suband transcritical Thermoeconomic analysis of recuperative suband transcritical The 15th International Symposiumcycle on District Heating and Cooling organic Rankine systems organic organic Rankine Rankine cycle cycle systems systems a b b a,∗ Oyeniyi A. Oyewunmi Steven Lecompte De Paepe b , Michel b , Christos N. Markidesa,∗ Assessing theaa,, feasibility of using the heat demand-outdoor Oyeniyi A. Oyewunmi Steven Lecompte De Paepe b , Michel b , Christos N. Markidesa,∗ Oyeniyi A. Oyewunmi , Steven Lecompte , Michel De Paepe , Christos N. Markides Clean Energy Processes (CEP) Laboratory, Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom Clean Energy Processes (CEP) Laboratory, Department Engineering,district Imperial College London,demand London SW7 2AZ,forecast United Kingdom temperature function for aofof Chemical long-term heat Department of Flow, Heat and Combustion Mechanics,Imperial Ghent University, Gent, Belgium Clean Energy Processes (CEP) Laboratory, Department Chemical Engineering, College London, London SW7 2AZ, United Kingdom Department of Flow, Heat and Combustion Mechanics, Ghent University, Gent, Belgium b b b Department

of Flow, Heat and Combustion Mechanics, Ghent University, Gent, Belgium

I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc Abstract a IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Abstract b Abstract Recherche &ofInnovation, 291 Avenue Dreyfous 78520for Limay, France recovery and power genThere is significant interest inVeolia the deployment organic Rankine cycle (ORC)Daniel, technology waste-heat c There is significant interestSystèmes in the deployment ofet organic Rankine cycle (ORC) technology for waste-heat recovery and power genDépartement Énergétiques Environnement IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France erationisinsignificant industrial settings.in This study considers ORC Rankine systems optimized fortechnology maximum for power generation using a case study of There the deployment of organic cycle (ORC) waste-heat recovery and power generation in industrialinterest settings. This study considers ORC systems optimized for maximum power generation using a case study of C as the heat source, covering over 35 working fluids andusing also considering the an exhaust flue-gas stream at aThis temperature of 380 ◦◦ORC eration in industrial settings. study considers systems optimized for maximum power generation a case study of an exhaust flue-gas stream at a temperature of 380 ◦ C as the heat source, covering over 35 working fluids and also considering the option of featuring recuperator. Systems based transcritical found to deliver higher fluids power outputs subcritical as the heat cycles source,are covering over 35 working also than considering the an exhaust flue-gas aastream at a temperature of 380on option of featuring recuperator. Systems based onCtranscritical cycles are found to deliver higher powerand outputs than subcritical ones, with optimal evaporation pressures are on 4–5 times the critical pressures andpower light hydrocarbons, and 1–2 option of featuring a recuperator. Systemsthat based cycles are found of to refrigerants deliver higher than subcritical ones, with optimal evaporation pressures that are 4–5transcritical times the critical pressures of refrigerants and light outputs hydrocarbons, and 1–2 Abstract times with thoseoptimal of siloxanes and heavy hydrocarbons. Fortimes maximum powerpressures production, a recuperator is light necessary for ORC and systems ones, evaporation pressures that are 4–5 the critical of refrigerants and hydrocarbons, 1–2 times those of siloxanes and heavy hydrocarbons. For maximum power production, a recuperator is necessary for ORC systems with constraints imposedand on their evaporation and condensation pressures. This includes, for example, limiting the minimum contimes those of siloxanes heavy hydrocarbons. For maximum power production, a recuperator is necessary for ORC systems with constraints onare their evaporation and condensation pressures. This of includes, foreffective example, solutions limiting the conDistrict heatingimposed networks commonly addressed in the literature as one the most forminimum decreasing the densation pressure to atmospheric pressure to prevent sub-atmospheric operation of this component, as is the case employing with constraints imposed on their evaporation and condensation pressures. This includes, for example, limiting thewhen minimum condensation pressure to atmospheric pressure to prevent sub-atmospheric operation this component, is the case when employing greenhouse gas emissions from the building sector. These systems require highofinvestments whichasare returned through the heat heavy hydrocarbon siloxane working For scenarios where such operating constraints are as relaxed, the optimal cycles do densation pressure toand atmospheric pressurefluids. to prevent sub-atmospheric operation of this component, is the case when employing heavy hydrocarbon siloxane working fluids. For where such operating constraints are relaxed, the optimal do sales. Duea to the and changed conditions andscenarios building renovation policies, heat power demand in with the this future couldcycles decrease, not feature recuperator, withclimate some systems showing more than threesuch times the generated than component, albeit heavy hydrocarbon and siloxane working fluids. For scenarios where operating constraints are relaxed, the optimal cycles do not feature athe recuperator, with some systems showing more than three times the generated power than with this component, albeit prolonging investment return period. at higher investment costs.with some systems showing more than three times the generated power than with this component, albeit not feature a recuperator, atThe higher investment costs. main scope of this paper is by to assess theLtd. feasibility of using the heat demand – outdoor temperature function for heat demand c higher  2017 The Authors. Published Elsevier at investment costs. cforecast.  2017 The Authors. Published by Elsevier Ltd. © 2017 The Authors. Published by Elsevier Ltd. The district of Alvalade, located in Lisbon (Portugal), used as aSeminar case study. ThePower district is consisted of 665 Peer-review under responsibility of the scientific committee of the IVwas International on ORC Systems. c  2017 The under Authors. Published by Elsevier Ltd. committee Peer-review responsibility of ofofthe IV Seminar on Power Systems. Peer-review under responsibility ofthe thescientific scientific committee the IVInternational International Seminar(low, onORC ORC Powerhigh) Systems. buildings that vary in both construction period and typology. Three weather scenarios medium, and three district Peer-review under responsibility of the scientific committee of the IV International Seminar on ORC Power Systems. Heat Recovery; Organic Rankine Cycle; Recuperator; Regenerator; Power Generation; Optimization. Keywords: renovation Waste scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were Keywords: Waste Heat Recovery; Organic Rankine Cycle; Recuperator; Regenerator; Power Generation; Optimization. compared with from a dynamic heat demand previously developed validatedOptimization. by the authors. Wasteresults Heat Recovery; Organic Rankine Cycle;model, Recuperator; Regenerator; Powerand Generation; Keywords: The results showed that when only weather change is considered, the margin of error could be acceptable for some applications 1. Introduction 1. Introduction error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation 1.(theIntroduction The of waste heat and sources of or heat, as or heat, scenarios, up to 59.5% (depending on the weather and renovation scenarios combination considered). The use usethe of error wastevalue heatincreased and of of alternative alternative sources of lowlowor medium-grade medium-grade heat, such such as geothermal geothermal or solar solar heat, The use of waste heat and of alternative sources of lowor medium-grade heat, such as geothermal or solar heat, can play a key role in decreasing the current dependence and consumption rates of fossil fuels, increasing security Theplay valuea of increased on average within the range of 3.8% uprates to 8% decade, corresponds to the can keyslope rolecoefficient in decreasing the current dependence and consumption of per fossil fuels,that increasing security can play in a key role in decreasing themedium-grade current dependence consumption rates of heating, fossil increasing security and decreasing emissions. Lowand heat can be recovered provide or converted useful decrease the number of heating hours of 22-139h during theand heating season to (depending on the fuels, combination of into weather and and decreasing emissions. Low- and medium-grade heat can be recovered to provide heating, or converted into useful and decreasing emissions. Lowandthe medium-grade heat[1]. can benumber recovered to provide heating, ordecade converted intofor useful renovation scenarios considered). On other of hand, function intercept increased for 7.8-12.7% perthat (depending onthe the power such as electricity, or a combination the two A of technologies exist are suitable power such as electricity, or a combination of the two [1]. A number of technologies exist that are suitable for the coupledsuch scenarios). The values couldofpower bethe used to[1]. modify theorganic function parameters for thethat scenarios considered, and power assuch electricity, or asuggested combination two A the number of technologies exist are suitable for difthe conversion of lower-grade heat to useful including Rankine cycle (ORC), which employs conversion of such lower-grade heatestimations. to useful power including the organic Rankine cycle (ORC), which employs difimprove theof accuracy of heat demand conversion such lower-grade heat to mixtures, useful power the organic Rankine cycle (ORC), [2–5]. which A employs different organic working fluids and their suchincluding as hydrocarbons, refrigerants, or siloxanes significant

ferent organic working fluids and their mixtures, such as hydrocarbons, refrigerants, or siloxanes [2–5]. A significant ferent organic working fluidsdevelopment and their mixtures, such as hydrocarbons, refrigerants,inordifferent siloxanes [2–5]. A significant effort has been placed on and effort hasThe been placedPublished on the the development and improvement improvement of of ORC ORC power power systems systems in different applications applications including including © 2017 Authors. byheat Elsevier Ltd. effort has been placedrenewable on the development and improvement of ORCconversion, power systems in different applications including waste-heat recovery, (geothermal, biogas/biomass) and solar-thermal power [6–9]. waste-heat renewableofheat (geothermal, biogas/biomass) solar-thermal power [6–9].and Peer-reviewrecovery, under responsibility the Scientific Committee of The 15thconversion, Internationaland Symposium on District Heating waste-heat recovery, renewable heatis (geothermal, biogas/biomass) conversion, andThe solar-thermal power [6–9].systems The uptake of ORC technology being handicapped by long payback periods. power output of ORC The uptake of ORC technology is being handicapped by long payback periods. The power output of ORC systems Cooling. The uptakebe of ORC technology is being handicapped by long payback periods. The powerthe output of ORC systems can can however however be enhanced enhanced by by employing employing aa recuperator, recuperator, aa heat heat exchanger exchanger used used to to preheat preheat the working working fluid fluid before before can however be enhanced by employing a recuperator, a heat exchanger used to preheat the working fluid before Keywords: Heat demand; Forecast; Climate change ∗ ∗ ∗

Corresponding author. Tel.: +44 (0)20 759 41601. Corresponding author. Tel.: +44 (0)20 759 41601. E-mail address:author. [email protected] Corresponding Tel.: +44 (0)20 759 41601. E-mail address: [email protected] E-mail address: [email protected] c 2017 1876-6102  The Authors. Published by Elsevier Ltd. 1876-6102 2017The TheAuthors. Authors.Published Publishedby byElsevier ElsevierLtd. Ltd. c©2017 1876-6102 Peer-review under responsibility of the scientific committee of theThe IV International Seminar on ORC Power Systems. c 1876-6102  2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee 15th International Symposium District Heating and Cooling. Peer-review under responsibility of the scientific committee of of the IV International Seminar on ORC on Power Systems. Peer-review under responsibility of the scientific committee of the IV International Seminar on ORC Power Systems. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the IV International Seminar on ORC Power Systems. 10.1016/j.egypro.2017.09.187

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evaporation using recovered heat from the working fluid after expansion. This can reduce the amount of thermal energy extracted from the heat-source stream, which increases the system’s thermal efficiency. Furthermore, this decreases the heat-source stream’s temperature drop within the evaporator, and thereby may in some cases relax the evaporator pinch limitations depending on where the pinch point is found inside this heat exchanger. This, in turn, may allow the ORC system to operate with higher working-fluid flowrates (until the pinch conditions are re-established), thus enabling a further increase in efficiency and power output, for the same heat-source conditions. However, a number of questions remain unanswered regarding the introduction of a recuperator, which is an additional component that leads inevitably to higher system complexity and cost. While its addition ensures an improvement in thermal efficiency, its effect on the optimal exergy efficiency and power output are still under discussion [10,11]. The roles of the working fluid (dry, isentropic, wet) and cycle architecture (subcritical, transcritical) on the decision to include a recuperator remain unexplored. For the cases where a recuperator may indeed be beneficial, the effectiveness of the heat exchanger is also important, and the additional costs associated need to be considered. In this work we explore the benefits and drawbacks of using recuperators in ORC systems with the aid of thermodynamic cycle analysis. The aforementioned working fluids and cycle architectures are optimized for maximum net-power generation, with particular consideration given to the heat-source characteristics and the condenser boundary conditions (cooling rates, exit temperatures). While cycles with no recuperation typically give higher exergy efficiencies, there exist cases where a combination of factors (working fluids, boundary conditions) result in recuperative cycles being optimal; we therefore extend our analysis to include the economic considerations of such cases. 2. ORC system models 2.1. External boundary conditions and working-fluid selection In this paper, the heat source is a flue gas from an industrial cement kiln, with a flowrate of 185 kg/s at 380 ◦ C. The heat sink is taken as cooling water at 25 ◦ C, with a maximum temperature increase of 30 ◦ C. Over 35 pure working fluids (see Table 1), spanning the classes of alkanes and their isomers, refrigerants, siloxanes and aromatic hydrocarbons (benzene and toluene) are considered. These working fluids, chosen to span a wide range of critical temperatures and in combination with the high heat-source temperature, are suitable for both subcritical and transcritical ORC systems. They vary in degree of ‘dryness’ from the very dry siloxanes and heavy hydrocarbons to the wet refrigerants such as R152a, and also including isentropic fluids such as R124 and R1234yf. The isentropic efficiencies of the pump and expander are 85% and 75% respectively while the heat exchangers’ minimum temperature difference (∆T min ) is 10 ◦ C. Table 1: Critical properties of selected ORC working fluids.

Working fluids’ class

Working fluids

Critical temperature (T crit , ◦ C)

Critical pressure (Pcrit , bar)

Light alkanes and alkene

Propane, butane, isobutane, pentane, hexane, isohexane, heptane, propylene. R113, R114, R115, R12, R123, R1233zd, R1234yf, R1234ze, R124, R125, R134a, R141b, R142b, R143a, R152a, R218, R227ea, R245fa, RC318. Octane, nonane, decane, D4, D5, MM, MDM, MD2M, benzene, toluene, water

96.7, 152.0, 134.7, 196.6, 234.7, 224.6, 267, 91.1.

42.5, 38.0, 36.3, 33.7, 30.3, 30.4, 27.4, 45.6.

214.1, 145.7, 80.0, 112.0, 183.7, 165.6, 94.7, 109.4, 122.3, 66.0, 101.1, 204.4, 137.1, 72.7, 113.3, 71.9, 101.8, 154, 115.2.

33.9, 32.6, 31.3, 41.4, 36.6, 35.7, 33.8, 36.3, 36.2, 36.2, 40.6, 42.1, 40.6, 37.6, 45.2, 26.4, 29.3, 36.5, 27.8.

296.2, 321.4, 344.6, 346.1, 245.5, 290.9, 288.9, 318.6, 373.9.

25.0, 22.8, 21.0, 13.3, 11.6, 19.4, 14.2, 12.3, 49.1, 41.3, 220.6.

Refrigerants

Heavy alkanes, siloxanes, aromatics and water

313.3, 326.3,

2.2. ORC thermodynamic model The thermodynamic model of simple subcritical ORCs is well described in literature. This consists of an energy balance across each component of the cycle. The model used here is also capable of analysing superheated and recuperated ORC systems. In recuperated cycles, the recuperator is modelled based on the amount of heat recoverable from the working fluid exiting the expander with a dimensionless parameter called the recuperative fraction (θrecup ): θrecup =

h4 − h4r T 4 − T 4r . ≈ h4 − h(T2 +∆Tmin , Pcond ) T 4 − (T 2 + ∆T min )

(1)

At θrecup = 0, the recuperative cycle reverts to the basic cycle with no recuperation, and when θrecup = 1, the maximum possible amount of heat is exchanged between the working fluid exiting the expander and that exiting the pump.

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2.3. Optimization algorithm An optimization algorithm in MATLAB is employed to find the maximum net-power output of the aforementioned waste-heat recovery ORC systems, which necessitates an objective function and constraints to be defined: maximize

Pevap , Pcond , θSH , θrecup , m ˙ wf

subject to:

˙ net = W ˙ exp − W ˙ pump } {W ◦

∆T i ≥ ∆T min (10 C) ∀ i

(2) (3)

T dew (Pcond ) ≤ T 4

(4)

Pevap ≤ 0.95Pcrit or Pevap ≥ 1.05Pcrit

(6)

0 ≤ θSH , θrecup ≤ 1 Pcond ≥ 1 bar(a) .

(5) (7)

Eq. 3 is applied separately to each discretized segment of the evaporator, condenser and recuperator, ensuring that the pinch conditions in these heat exchangers are satisfied. The temperature at the expander outlet, T 4 , has to be higher than or equal to the dew point temperature at the condensation pressure (Eq. 4) in order to prevent liquid droplet formation in the expander. In addition, both the degree of superheating and the recuperative fraction must be between zero and unity (Eq. 5). In Eq. 6, a switch is established between the subcritical cycles, and the supercritical vapour generation of transcritical cycles. The factors 0.95 and 1.05 are chosen arbitrarily to exclude the critical region and to prevent numerical instabilities with the equation of state and the optimizer; factors of 0.90 and 1.12 have also been used by other authors [12]. Finally, the (absolute) condensation pressure is constrained to be equal to or larger than 1 bar (ambient pressure), see Eq. 7, to avoid sub-atmospheric pressures in the cycle and expensive solutions to mitigate air ingress [7]. The effect of this constraint on the cycle design is also investigated in this work. 2.4. Component sizing and cost evaluation For the purpose of comparing the cost implications and benefits of the derived system designs, the installation costs are calculated using the earlier derived optimal solutions. The cost of the individual system components are calculated based on their sizes, and summed together. This gives an indication of the installation cost (other engineering costs not considered will be similar), which is weighted by the net power output to derive the specific investment cost (SIC). The heat exchangers (shell and tube) are sized with their UA-values, and costed using the ‘C-value’ method and the ESDU 92013 chart [13], where C is the ratio of the heat duty to the log-mean temperature difference. Heat exchangers involving multiple working-fluid phases, such as the evaporator and condensed, are divided into distinct segments (of constant heat capacity) and each segment is sized and costed accordingly. The pressure effects on the heat exchanger costs are accounted for by multiplying the base costs with a pressure factor defined as [14]: F P = 0.9803 + 0.018(P/100) + 0.0017(P/100)2 , where P is in psig.

(8)

The expanders are sized based on their power output and their costs are calculated for pressure discharge and vacuum discharge units respectively as [14]: 0.81 0.81 ˙ exp ˙ exp Cexp = 672.2W and Cexp = 1509W .

(9)

The centrifugal pump and accompanying motor are costed based on their head and power requirement as in Ref. [14]. All equipment costs are brought to 2016 figures using the CEPCI (500 for year 2006, 314 for 1982 for the C-value method, and 556.8 for year 2016). 3. Results and discussion We start by presenting and comparing the optimal net power output for the subcritical and transcritical ORC systems, with respect to their levels of recuperation. Finally, the effect of the condenser boundary condition is discussed. 3.1. Output from subcritical and transcritical cycles Simulations were performed to investigate the effect of the evaporation pressure (Pevap ) on the maximal net-power ˙ net , while employing the selected pure working-fluids from Table 1 in subcritical and transcritical ORCs. output, W These results are presented Fig. 1 (with the exception of a few refrigerants so as not to overload the figure), which shows plots of the power output as a function of the reduced evaporation pressure (Pevap,r = Pevap /Pcrit ). The subcritical cycles (Pevap,r < 1) are those to the left of the vertical dotted lines while the transcritical cycles (Pevap,r > 1) are to the right. As expected, the transcritical cycles deliver a higher power output than the subcritical cycles with the optimal net-power generally increasing with the evaporation pressure, irrespective of the working fluid.

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12

12

10

10

10

8

8

6

Propane Butane Isobutan Pentane Hexane ihexane Heptane Propylen

4 2 0 0.1

0.2

0.5

1

Pevap,r [−]

2

5

R113 R115 R12 R123 R124 R134a R142b R227ea RC318

6 4 2

10

0 0.1

0.2

0.5

1

Pevap,r [−]

2

5

10

˙ net [MW] W

12

˙ net [MW] W

˙ net [MW] W

There is, however, a limit to this increase in power output, at a supercritical evaporation pressure (Pevap,r > 1), after which the power output declines. This is a result of the dependency of the power output on the expansion pressure ratio (specifically, the enthalpy change) and the working-fluid mass flowrate, and also to a lesser extent on the required pumping power. At higher Pevap , there is always a large pressure ratio and hence a large enthalpy change during the expansion process. However, a higher Pevap brings the working-fluid’s evaporation temperature-profile ‘closer’ to that of the heat source, thereby reducing the maximum possible working-fluid mass flowrate before the evaporator pinch conditions are met. Furthermore, a higher evaporation pressure requires a higher pumping power. The decrease in the working fluid flowrate and increase in the pumping power eventually counterbalance the increased specific work output, leading to the observed optimal evaporation pressure at the maximum net-power output.

8 6

Octane Nonane Decane D4 D5 MM MDM MD2M Benzene Toluene

4 2 0 0.1

0.2

0.5

1

2

5

10

Pevap,r [−]

Fig. 1: Optimal net power output from subcritical (Pevap,r < 1) and transcritical (Pevap,r > 1) ORCs as a function of the (reduced) evaporation pressure, Pevap,r = Pevap /Pcrit with light hydrocarbon (left), refrigerant (middle) and heavy hydrocarbon/siloxane (right) working fluids.

This maximum power output generally occurs at Pevap,r values between 4.0 and 5.0 for the refrigerants and lighter hydrocarbons considered here, having similar profiles from Fig. 1. The heavier hydrocarbons and siloxanes have a different profile, with the power output increasing more gently with increasing Pevap,r , and peaking at Pevap,r values between 1.1 and 2.0. This could be a result of the condensation pressures of these working fluids which fall on the limit of atmospheric pressure from the constraint in Eq. 7. At this pressure, these fluids condense at high temperatures (60 ◦ C – 210 ◦ C), much higher than the heat sink temperatures, thereby limiting the power output. The refrigerants and the lighter hydrocarbons are condensed at the lowest temperature possible and are not limited by this constraint. The observed maxima in the net power outputs in Fig. 1 provides valuable insight into the design and economics of high-pressure ORC systems; higher Pevap do not always guarantee higher power outputs. Moreover, the purchase costs of high-pressure components/equipment are usually higher than those of low-pressure ones. Thus, ORC systems being designed to operate at higher Pevap , beyond the identified maxima, will have higher SICs due to their higher capital costs and lower net power production. Therefore, it may be beneficial from both the thermodynamic and economic perspectives to limit the operating pressure in ORC evaporators to the limits identified above. 3.2. Optimization of recuperative subcritical and transcritical ORC systems We now proceed to consider the employment of recuperators in subcritical and transcritical ORC systems. Simulations were performed aimed at maximizing the net power output of these systems, based on Eqs. 3 to 7. The optimum net power outputs from both the subcritical and transcritical cycles based on the chosen working fluids are presented in Fig. 2, while the recuperative fractions of the cycles are presented in Tables 2 and 3 respectively. 3.2.1. Optimal cycle design conditions For most of the working fluids considered here, the resulting optimal cycles were superheated to various degrees, ranging from 0.4 to 0.8 (1.0 for the transcritical cycles); the wet fluids such as propane, R143a and R152a need to be superheated before expansion to achieve a reasonably superheated vapour after the expansion process due to the constraint in Eq. 4. The exception to this were the heavy hydrocarbons (including benzene and toluene) and the siloxanes, which are very dry fluids and as such did not require any amount of superheat before the expander to achieve a superheated vapour after expansion.In the subcritical cycles, the optimal cycles generally feature evaporation at the Pevap,r limit of 0.95 for most of the working fluids, due to the high temperature of the heat source. The single exception was the cycle with D5, operating at a reduced evaporation pressure of 0.61, due to the close proximity of its critical temperature to the heat source temperature. Without the imposed limit, it may be expected that most optimal (subcritical) cycles will involve evaporation at the respective critical pressures of the fluids, i.e., Pevap,r = 1.

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5

It is also interesting to note the performance of the working fluids across the working fluid classes. With the ˙ net increases from propane till hexane but decreases beyond this up to decane (see Fig. 2). This is due to the alkanes, W lighter alkanes (propane to pentane) being condensed at the lowest possible temperature/pressure because they are not constrained by Eq. 7. The heavier alkanes on the other hand are all condensed at atmospheric pressure. This, with the fact that the critical pressures of the alkanes decrease with molecular complexity, reduces the pressure difference (and ˙ net from hexane to decane. This the specific enthalpy change) during expansion, thereby leading to a reduction in W trend is also noticeable with the siloxanes and between benzene and toluene, which are all condensed at atmospheric ˙ net between propane and hexane is reduced as each pressure. However, in the transcritical cycles, the disparity in W of the working fluids are no longer constrained to a Pevap,r of 0.95; they are now able to evaporate at higher pressures (with the optimal Pevap,r ranging from 6.5 for propane to 2.2 for hexane), thereby maximizing their power potential. 12 Subcritical Transcritical

˙ net [MW] W

10 8 6 4 2

Pr

op B ane u Is ta ob ne Pe uta nt n H an ex e ih a n e e H xan ep e t O ane ct N an on e D an P r eca e op ne yl e R n 11 R 3 11 R 4 11 5 R 12 R R 12 12 3 R 33z 12 d R 34 12 yf 34 z R e 12 R 4 1 R 25 13 R 4a 14 R 1b 14 R 2b 14 R 3a 15 2 R a R 218 22 R 7ea 24 R 5 fa C 31 8 D 4 D 5 M M M M DM B D 2M en To zen lu e e W ne at er

0

Fig. 2: Optimal net power output from subcritical and transcritical ORCs with working fluids from Table 1. Table 2: Recuperative fraction of subcritical ORCs at optimal net power output. Fluids with θrecup  0

Fluids with 0 < θrecup < 1

Fluids with θrecup  1

Pentane, decane, R113, R123, R141b, water.

Propane (0.84), propylene (0.70), R115 (0.66), R12 (0.95), R1234yf (0.87), R125 (0.37), R134a (0.90), R143a (0.45), R218 (0.64), benzene (0.21), toluene (0.23).

Butane, isobutane, hexane, isohexane, heptane, octane, nonane, R114, R1233zd, R1234ze, R124, R142b, R152a, R227ea, R245fa, RC318, D4, D5, MM, MDM, MD2M.

Table 3: Recuperative fraction of transcritical ORCs at optimal net power output. Fluids with θrecup  0

Fluids with 0 < θrecup < 1

Fluids with θrecup  1

Propane, butane, isobutane, pentane, propylene, R113, R114, R12, R123, R1233zd, R1234ze, R124, R134a, R141b, R142b, R143a, R152a, R245fa.

Isohexane (0.80), benzene (0.01), toluene (0.06).

Hexane, heptane, octane, nonane, decane, R115, R1234yf, R125, R218, R227ea, RC318, D4, D5, MM, MDM, MD2M.

3.2.2. Degree of recuperation Only a few of the working fluids have optimal subcritical cycles requiring no recuperation (θrecup  0, see Table 2). These fluids, with the exception of decane, are fluids with only a slight degree of dryness whereas other very dry fluids like the siloxanes require a great deal of recuperation. Also, the isentropic fluids such as R125 and to some extent benzene and toluene require low levels of recuperation. In contrast, all the wet fluids, such as propane, R12 and R152a require very large recuperative fractions since they are usually superheated, ensuring that vapour exits the expander. Similarly, all the working fluids condensing at atmospheric pressure, required high recuperative fractions. On comparing the recuperative fractions of the transcritical cycles (Table 3) with those of the subcritical cycles (Table 2), it can be seen that a higher number of working fluids now have optimal cycles which feature very little recuperation (θrecup  0). However, the optimal cycles with very dry working fluids and those condensing at atmospheric pressure remain with large recuperative fractions. Working fluids such as butane, R114 and R245fa, which required large amounts of recuperation in subcritical cycles, now require no recuperation when applied to transcritical cycles. Thus, it may be concluded that the restriction on their evaporation pressures (to Pevap,r = 0.95) in subcritical

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cycles, led to the optimizer resorting to recuperation in order to maximize the net power output. When this restriction is relaxed in transcritical cycles and the working fluids are being evaporated at much higher pressures, there is no longer the need for recuperation. Rather, the power is maximized by evaporating at higher pressures. 3.2.3. Economic indications The corresponding specific investment costs are presented in Fig. 3. The SIC is seen to have an inverse relationship with the net power output; systems with lower power output generally have higher SIC and vice versa. This is evident (in comparison to Fig. 2) in subcritical systems with R115, R125, R143a, R218, D5 or MD2M as working fluids; their low power outputs is seen to result in high SICs. A few exceptions to this general trend include the transcritical systems with propane, propylene, R12, R1234ze, R134a or R143a; they feature evaporators and recuperators operating at very high pressures (> 230 bar) and hence are much more expensive than the systems operating at lower pressures. Thus, although these systems deliver high power outputs, their SICs are nevertheless high. The inverse relationship is also evident within working fluid classes. For the alkanes, the SIC is seen to decrease from propane to hexane and then increase to decane, mirroring the trend in power output within the family. In the same vein, the SIC increases from D4 to D5 and from MM to MD2M, since the power output decreases from D4 to D5 and from MM to MD2M. However, this relationship between the SIC and the net power output does not follow through when a direct comparison is made between transcritical ORC systems and subcritical systems. Although a transcritical system delivers higher power output than a subcritical systems on the same working fluid (see Fig. 2), the transcritical systems are more expensive (higher SIC) as in Fig. 3. While subcritical systems are limited to a maximum evaporation pressure ratio of 0.95 (e.g., corresponding to Pevap = 32 bar for pentane), there is no such limit on the transcritical systems. The optimal evaporation pressure ratio varies between 1.1 and 8.5 in transcritical systems (e.g., corresponding to Pevap = 149 bar for pentane and higher for some refrigerants). Such high pressures require that the evaporators and recuperators are more expensive, hence the higher system cost and SIC of the transcritical systems. 700

SIC [£/kW]

600

Subcritical Transcritical

500 400 300 200 100

Pr

op B ane u Is ta ob ne Pe uta nt n H an ex e ih a n e e H xan ep e t O ane c N tan on e D ane P r eca op ne yl e R n 11 R 3 11 R 4 11 5 R 12 R R 12 12 3 R 33z 12 d R 34 12 yf 34 z R e 12 R 4 1 R 25 13 R 4a 14 R 1b 14 R 2b 14 R 3a 15 2 R a R 218 22 R 7ea 24 R 5 fa C 31 8 D 4 D 5 M M M M DM B D 2M en To zen lu e e W ne at er

0

Fig. 3: Specific investment cost of optimal subcritical and transcritical ORC systems with working fluids from Table 1.

3.3. Effect of condenser boundary conditions The cycles with working fluids having high critical temperatures (heavy hydrocarbons and siloxanes) were generally condensed at atmospheric pressure (Eq. 7). Their power output was clearly restrained, especially when compared to cycles with lighter working fluids in the same family. Beyond this, they were observed to feature high recuperative fractions. For these fluids, it is important to investigate their performance without this lower condensation pressure limit. The results from these simulations are presented in Fig. 4 (power and SIC) and in Table 4 (θrecup ). As expected, the condensation pressures after optimization were all below atmospheric, ranging from 0.0020 bar(a) to 0.76 bar(a). On comparing the recuperative fractions of the optimal cycles (Table 4) with those of the previous subcritical (Table 2) and transcritical (Table 3) cycles, it can be seen that a large number of the working fluids that earlier had large recuperative fractions, now have optimal cycles which feature very little recuperation (θrecup  0). These fluids include the alkanes from hexane till decane, benzene and toluene, D4 and MD2M; it is evident that relaxing the constraint in Eq. 7 resulted in optimal cycles without recuperation. A similar reversal was observed in Section 3.2.2, when the Pevap,r limit of 0.95 (for subcritical cycles) was relaxed to enable transition into transcritical cycles. Thus, it can be concluded that adding constraints on the operating range may result in recuperators being deployed for increased power output. When these constraints are relaxed, the optimal cycles usually feature no recuperation.

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Table 4: Recuperative fraction of subcritical and transcritical ORC systems at optimal net power output with working fluids condensing below atmospheric pressure (1 bar(a)). Cycle type

Fluids with θrecup  0

Fluids with θrecup  0

Subcritical

Hexane, isohexane, heptane, octane, nonane, decane, MD2M, benzene, toluene, water. Hexane, isohexane, heptane, octane, nonane, decane, D4, benzene, toluene.

D4 (0.68), D5 (0.90), MM (1.00), MDM (1.00). D5 (0.70), MM (1.00), MDM (1.00), MD2M (1.00).

700

10

600

Subcritical Transcritical

4

400 300 200 100

0

0 D5 MM MD MD M B e 2M nz e To ne lu e n Wa e ter

2

D5 MM MD MD M B e 2M nz e To ne lu e n Wa e ter

6

Subcritical Transcritical

500

He xa ih e n e xa He ne p ta O c ne ta No ne na D e ne can e D4

8

SIC [£/kW]

12

He xa ih e n e xa He ne p ta O c ne ta No ne na D e ne can e D4

˙ net [MW] W

Transcritical

Fig. 4: Optimal net power output (left) and specific investment cost (right) of subcritical and transcritical ORC systems with working fluids condensing below atmospheric pressure, i.e., 1 bar(a).

By allowing theses working fluids to condense below atmospheric pressure, the power output from the cycles can be greatly increased. The power output from the cycles with these fluids (in Fig. 4) can be compared with their counterparts in Fig. 2. The cycles with condensation below the atmospheric pressure are seen to deliver a higher power output than those with condensation at atmospheric pressure. Working fluids such as hexane and benzene are shown to show a slight improvement in their power outputs, up to 18% while the other, much drier working fluids, show much larger improvements, ranging between 200% and 350% in the cases of decane, D5 and MD2M. It should be noted that these increases in power output come at the expense of more expensive condensers and expanders as alluded to in Section 2.3, thus it should be expected that these systems will definitely be more expensive (in terms of their investment costs) than their counterparts featuring condensation at (or above) 1 bar. It may however be expected that the large increases in power output could justify the added investment in sub-atmospheric units, thereby making these systems with sub-atmospheric condensation cheaper (in terms of their SIC). Also, additional cost savings may be expected as these systems have been shown here to be optimal without requiring a recuperator. These expectations are however unfounded as the SIC of the systems with sub-atmospheric condensation (Fig. 4) are generally higher (from 10% to 60% and higher in transcritical systems) than those of the simpler systems (in Fig. 3). Only sub-atmospheric systems with D5 and MD2M as working fluids are cheaper (in terms of the SIC) than the corresponding simpler systems. A number of factors contribute directly to this. In the first instance, vacuum expanders are required here and these are more expensive (at similar power ratings) than the simpler expanders; also, these systems deliver higher power outputs, making the expanders even more expensive. In addition, since the condensation now takes place at the lowest possible pressures without restraint, the condensation temperatures are very low. This reduces the (log-mean) temperature difference between the working fluid and the heat sink, thereby increasing the UA-value (= Q˙ out /∆T LM ) of the condenser. For example, in the subcritical system with MDM condensing at 1 bar and 152 ◦ C, the ∆T LM is 113 ◦ C. When this restriction is relaxed, the working fluid condenses at 63 ◦ C, with a ∆T LM of 21 ◦ C, increasing the UA-value by at least a factor of 5. The UA-values of the condensers are further increased as a result of the larger amounts of heat being rejected. These make the condensers in the sub-atmospheric systems more expensive, and combined with the higher costs of the expanders, leads to higher overall system costs. The increase in overall system cost is thus seen to nullify the gains in power output derived from the expansion of the working fluids to sub-atmospheric temperatures, hence the higher specific investment costs.

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4. Conclusions We have presented results of optimized subcritical and transcritical ORC systems, while featuring the option of adding the recuperator, in order to improve the efficiency and power output of these systems, with the objective of maximizing their net power output. A range of working fluids have been considered, ranging from hydrocarbons and refrigerants to siloxanes and aromatic compounds, and encompassing various degrees of dryness. The ORC systems have been generally observed to deliver their maximum net power outputs at reduced evaporation pressure (Pevap,r = Pevap /Pcrit ) values between 4.0 and 5.0 for the refrigerants and between 1.1 and 2.0 for the heavier hydrocarbons and siloxanes. Beyond these, the power output has been found to decrease. Thus, it is suggested that higher Pevap will not guarantee higher power outputs, but will, however, result in more expensive evaporators and expanders and in turn result in higher specific investment costs (SIC, in £/$/e per kW). It may be concluded that it is beneficial from a thermo-economic perspective to limit the operating pressure in ORC evaporators to the above limits. It has also been found that most of the optimal subcritical cycles require large degrees of recuperation because of the limits imposed on the evaporation pressure in order to keep these cycles at subcritical conditions (due to the high heat-source temperature). In transcritical cycles, where this limit is relaxed, there is a reduced dependence on recuperation with the working fluids delivering higher power outputs at elevated evaporation pressures. In addition, restrictions imposed on the minimum condensation pressure (to be at or above atmospheric pressure) for economic reasons, lead to subcritical and transcritical cycles with dry working fluids (with high critical temperatures), such as the heavier hydrocarbons and the siloxanes, requiring significant recuperation (large recuperators). However, the relaxation of this constraint (with sub-atmospheric condensation) has been found to allow optimal cycles without recuperation, with considerably higher net power output system-designs. It can thus be concluded that such operational constraints may result in recuperators (with the accompanying additional costs) being required to maximize the power output from ORC systems. 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