Integrating working fluid design into the thermo-economic design of ORC processes using PC-SAFT

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

Integrating working fluid into thermo-economic design IntegratingThe working fluid design design intoonthe the thermo-economic 15th International Symposium District Heating and Cooling design of of ORC ORC processes processes using using PC-SAFT PC-SAFT a a b Assessing theaa,feasibility of using the heat demand-outdoor Johannes a , Matthias a , Madlen Hoppb , Johannes Schilling Schilling , Dominik Dominik Tillmanns Tillmanns , Matthias Lampe Lampe , Madlen Hopp , b a,∗ Joachim Bardow b , Andr´ temperature function for aGross long-term Joachim Gross , Andr´ee district Bardowa,∗heat demand forecast a Chair of Technical Thermodynamics, RWTH Aachen University, 52056 Aachen, Germany a Chair of Technical Thermodynamics, RWTH Aachen University, 52056 Aachen, Germany a,b,c a Process Engineering, a b c c of Thermodynamics and Thermal Stuttgart University, Pfaffenwaldring 9, 70569 Stuttgart, Germany Institute of Thermodynamics and Thermal Process Engineering, Stuttgart University, Pfaffenwaldring 9, 70569 Stuttgart, Germany

b Institute b Institute

I. Andrić

*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre

a

IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Abstract c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France Abstract

To exploit the full thermo-economic potential of an Organic Rankine Cycle (ORC), the process, equipment and working fluid To exploit the full thermo-economic potential of an Organic Rankine Cycle (ORC), the process, equipment and working fluid have to be optimized simultaneously. Today, working fluid selection and thermo-economic process optimization are commonly have to be optimized simultaneously. Today, working fluid thermo-economic optimization separated. This separation leads to suboptimal solutions if selection the prior and working fluid selectionprocess fails. In this work, are we commonly present an separated. This separation leads to suboptimal solutions if the prior working fluid selection fails. In this work, we present an Abstract approach for the integrated thermo-economic design of ORC process, equipment and working fluid using consistent thermodynamic approach the approach integratedisthermo-economic design of ORC process, equipment and working fluid using consistent thermodynamic modeling.forThe based on the Continuous-Molecular Targeting–Computer-aided Molecular Design (CoMT-CAMD) modeling. The approach is based on the Continuous-Molecular Targeting–Computer-aided Molecular Design (CoMT-CAMD) District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing approach. In CoMT-CAMD, the properties of the working fluid are modeled by the physically-based Perturbed-Chain Statisticalthe approach. InFluid CoMT-CAMD, the properties of the working fluid are modeled by the physically-based Perturbed-Chain Statistical greenhouse gas emissions from the building sector. These systems require high investments are returnedfluids through thethe heat Associating Theory (PC-SAFT) equation of state. A CAMD formulation allows the designwhich of novel working during Associating Fluid Theory (PC-SAFT) equation of state. A CAMD formulation allows the design of novel working fluids during the sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, process optimization. So far, CoMT-CAMD was limited to equilibrium thermodynamics. Some of the authors recently developed process optimization. Soproperties far,return CoMT-CAMD limited to equilibriumbased thermodynamics. Some and of the authors recently developed prolonging investment period. models for thethetransport viscosity was and thermal conductivity on entropy scaling PC-SAFT. The integration of models for the transport properties viscosity and thermal conductivity based on entropy scaling and PC-SAFT. The integration of The models main scope of designing this paperthe is to assess thewithin feasibility of using the heat demandIn–particular, outdoor temperature functionoffor demand these allows equipment the CoMT-CAMD approach. the heat exchanger theheat ORC can these models allows designing the equipment within the CoMT-CAMD approach. In particular, the heat exchanger of the ORC can district ofcorrelations Alvalade, located inphase, Lisbon (Portugal),and was used as a heat casetransfer. study. The district consistedsizing, of 665 beforecast. designedThe using detailed for single evaporation condensation Based on theisequipment bebuildings designed that usingvary detailed correlations for single phase, and condensation heat transfer. Based onhigh) the equipment sizing, in both construction period and evaporation typology. Three weather scenarios (low, optimization medium, and three district a thermo-economic objective function can be considered in the resulting mixed-integer nonlinear problem. Thereby, athe thermo-economic objective function can be considered in in thea single resulting mixed-integer optimization problem.values Thereby, renovation scenarios were developed (shallow, intermediate, deep). To estimate thenonlinear error, obtained heat demand were thermo-economically optimal working fluid is identified optimization problem jointly with the corresponding optimal the thermo-economically optimal working fluiddemand isisidentified infor a single optimization problem jointly with corresponding optimal compared results The from a dynamic heat model, previously developed and validated thethe authors. process and with equipment. resulting approach illustrated the design of a subcritical ORC forby waste heat recovery. We show process and equipment. The resulting approachchange is illustrated for the design of a subcritical ORCbe foracceptable waste heatfor recovery. We show Thetheresults showed that when only weather is considered, the margin error could some applications that predicted specific purchased-equipment costs are in good accordance withofreal ORC applications. that the predicted specific purchased-equipment costs are in good accordance with real ORC applications. error annual Published demand was lower than c(the  2017 TheinAuthors. by Elsevier Ltd.20% for all weather scenarios considered). However, after introducing renovation cscenarios,  2017 Authors. Published by Elsevier © 2017 The Thethe error value increased up to Ltd. 59.5% (depending onIV theInternational weather andSeminar renovation scenarios Peer-review under responsibility of the scientific committee of the on ORC Powercombination Systems. considered). Peer-review under responsibility of thescientific scientific committee the IV International Seminar onper ORC PowerSystems. Systems. Peer-review responsibility the committee ofofthe International on ORC Power The value under of slope coefficientof increased on average within theIV range of 3.8%Seminar up to 8% decade, that corresponds to the CoMT-CAMD, integrated design, fluid selection, economics, transport properties Keywords: decrease inCoMT-CAMD, the number integrated of heatingdesign, hoursfluid of 22-139h during thetransport heatingproperties season (depending on the combination of weather and selection, economics, Keywords: renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and the accuracy of heat demand estimations. 1.improve Introduction

1. Introduction (ORC) generate power from low temperature heat [1]. Low temperature heat ©Organic 2017 TheRankine Authors. Cycles Published by Elsevier Ltd.electrical Organic Rankine Cycles (ORC) generate electrical power from low temperature heat [1]. Low temperature heat can be obtained from renewableofheat waste heat. To ensure an economically efficient process, the ORC Peer-review under responsibility the sources ScientificorCommittee of The 15th International Symposium on District Heating and has can be obtained from renewable heat sources or waste heat. To ensure an economically efficient process, the ORC has toCooling. be tailored to its specific application. For this purpose, process, equipment and working fluid have to be optimized to be tailored to its specific application. For this purpose, process, equipment and working fluid have to be optimized simultaneously. simultaneously. Keywords: Heat demand; Forecast; Climate change ∗ Corresponding ∗ Corresponding

author. Tel.: +49-241-80-95381 ; fax: +49-241-80-92255. Tel.: +49-241-80-95381 ; fax: +49-241-80-92255. E-mail address:author. [email protected] E-mail address: [email protected] 1876-6102 2017The TheAuthors. Authors.Published PublishedbybyElsevier ElsevierLtd. Ltd. c ©2017 1876-6102  c 2017 1876-6102  The Authors. Published by Elsevier Ltd. of The 15th International Symposium on District Heating and Cooling. Peer-review under responsibility Scientific Committee Peer-review under responsibility of of thethe scientific committee of the IV International Seminar on ORC 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.2017.09.179

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Today, however, working fluid selection and thermo-economic process optimization are usually carried out separately following a two-stage approach [2]: In a first stage, working fluid candidates are preselected using heuristic guidelines. In a second stage, the preselected working fluids are assessed by individual thermo-economic process optimizations. However, if the preselection in the first stage fails, the two-stage approach leads to suboptimal solutions. Thus, several authors recommended to integrate the working fluid selection directly into the process optimization [2,3]. The resulting integrated design of process and working fluid leads to a challenging mixed-integer nonlinear program (MINLP) optimization problem [4], since discrete degrees of freedom are added to the process optimization. Systematic solution approaches based on equilibrium thermodynamics have been developed as recently reviewed by Linke et al. [5]. A two-stage design approach has been proposed for pure working fluids based on Computer-aided Molecular Design (CAMD) and a cubic equation of state (EoS) by Palma-Flores et al. [6]. In a first stage, a set of working fluid candidates is obtained based on a deterministic optimization before different process configurations are investigated for the working fluid candidates in a second stage. An approach for the integrated design of ORC process and mixture based on a process-level objective function and CAMD is presented by Papadopoulos et al. [7]. Mavrou et al. [8] showed a better process performance for mixtures identified using an integrated design approach. Bardow et al. [9] proposed an optimization-based targeting approach for the integrated design of processes and solvents using PC-SAFT [10], the so-called Continuous-Molecular Targeting (CoMT). Subsequently, the CoMT approach was applied for the design of ORC processes and working fluids [11] and extended by a CAMD formulation [12] to so-called CoMT-CAMD. In the so-called CoMT stage, the discrete pure component parameters describing a working fluid in PC-SAFT are relaxed to continuous variables transforming the MINLP into a nonlinear program (NLP). The result of the NLP is a hypothetical optimal working fluid, the so-called target. In a second stage, a seconddegree Taylor-approximation around the target is used to estimate the objective function value of real working fluids generated by CAMD. Recently, the CAMD formulation was directly linked to the process model and PC-SAFT allowing the authors to solve the integrated design problem in solely one stage [13]. The resulting 1-stage CoMT-CAMD approach solves the MINLP using outer-approximation extended by a relaxation strategy. Since an equilibrium fluid model is used, 1-stage CoMT-CAMD was limited to a thermodynamic objective function. However, the thermodynamic optimum may differs from a thermo-economic optimum [14]. To perform a thermoeconomic design, equipment sizing has to be integrated into the design of process and working fluid to quantify the investment costs. Sizing the equipment requires not only an equilibrium fluid model but also a model for transport properties to capture transport-related trade-offs. Previously, integrated thermo-economic design was mainly addressed in process engineering. Pereira et al. [15,16] proposed an approach for thermo-economic design of solvent and process for CO2 absorption based on the fluid model SAFT-VR. The approach is limited to the design of linear alkanes and heuristic equipment sizing, but shows the advantages of a thermo-economic design approach. The presented approach is extended by Burger et al. [17] for the design of linear alkyl ethers using a hierarchical method with shortcut models of the process and SAFT-γ Mie. Herein, the viscosity is calculated using a group contribution (GC) approach. A thermo-economic design approach has also recently been proposed by the same group combining an outer-approximation formulation with a physical-domain reduction [18]. A hybrid stochastic-deterministic design approach is presented by Zhou et al. [19] for thermo-economic design of solvents for Diels-alder reaction. Since no models for transport properties are considered, the equipment sizing is performed based on heuristics. This brief review shows that a lack of a model for transport properties enforces equipment sizing based on heuristic design correlations. In this work, we extend the 1-stage CoMT-CAMD approach for the thermo-economic design of ORC process, equipment and working fluid. For this propose, we integrate newly proposed models for the transport properties viscosity and thermal conductivity based on PC-SAFT [20,21] yielding a consistent model for both equilibrium and transport properties. Thereby, the equipment design of the heat exchanger can be performed based on detailed heat transfer correlations. The paper is structured as follows: In section 2, the framework of the extended 1-stage CoMT-CAMD approach is presented. The approach is applied for a thermo-economic design of an Organic Rankine Cycle in section 3. Conclusions are drawn in section 4. 2. 1-stage CoMT-CAMD for integrated thermo-economic design To allow for a thermo-economic design using the 1-stage CoMT-CAMD approach, the approach has to be extended by models for equipment design and cost correlations. For this purpose, a model for transport properties is required beside the equilibrium fluid model. In section 2.1, the problem formulation of extended 1-stage CoMT-CAMD for



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thermo-economic design is described. In section 2.2, the fluid model PC-SAFT is presented, which is used to model both equilibrium and transport properties. 2.1. Problem formulation The 1-stage CoMT-CAMD approach for integrated thermo-economic design takes place at 6 levels (see Figure 1): On the main level 1, the economics are calculated serving as the assessment criterion of the optimization. On 3 design levels, the design is performed for the equipment (level 2), the process (level 4) and the working fluid (level 6). These design levels are connected by 2 property levels for equilibrium properties (level 5) and transport properties (level 3).

Fig. 1. Illustration of the 6 levels of thermo-economic design (left) and the formulation of the corresponding MINLP optimization problem (right)

The integrated design problem can be formulated as an MINLP optimization problem (see problem (1)) [4]. The optimization problem consists of one objective function f to be optimized (e.g., specific investment cost). This objective function depends on process variables x (e.g., pressure levels), equilibrium properties θ (e.g., enthalpies) and transport properties κ (e.g., viscosities). The equipment design is composed of equality constraints g1 (e.g., heat transfer correlations) and inequality constraints g2 (e.g., limitations in the turbine). The process design in turn consists of equality constraints p1 (e.g., energy balances) and inequality constraints p2 (e.g., pressure limits). Both equilibrium properties θ and transport properties κ are calculated using the PC-SAFT equation of state. In PC-SAFT, a working fluid is characterized by a set of pure component parameters z. To allow for the design of the working fluid within the optimization, a CAMD formulation is employed. Within this CAMD formulation, a working fluid is described by a vector yS which contains the number of functional groups constituting the molecular structure of the working fluid. The pure component parameters z are calculated by the homosegmented GC approach of PC-SAFT [22] from the molecular structure yS of the working fluid. Additional equality constraints F1 and inequality constraints F2 ensure the design of structurally feasible molecular structures [23]. The resulting degrees of freedom are the continuous process variables x and the integer numbers of the functional groups yS of the molecular structure. The result of the MINLP is the thermo-economically optimal molecular structure of the working fluid jointly with the optimal process and equipment sizes. To ensure a stable computation of the demanding iterative calculations of PC-SAFT and the equipment design, PC-SAFT and the process model are performed in external functions serving as a black box for the optimization. These external functions prevent the use of global optimization solvers. Thus, we use the local MINLP solver DICOPT [24] to solve the integrated design problem. DICOPT initially solves a relaxation problem identical to the CoMT problem of the CoMT-CAMD approach and subsequently identifies a real molecular structure using an outer-approximation algorithm. However, the thermo-economic optimum of this modelbased approach relies on the accuracy of the underlying models. To account for short-comings in the models and possible local optima, we employ integer-cuts [25] to obtain a ranking of working fluid candidates. For this purpose,

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the MINLP is solved repeatedly, wherein the previous solutions are excluded from the design space. The obtained ranking has to be assessed subsequently by safety, environmental and legal criteria as well as all other aspects which are not sufficiently captured by the employed model. 2.2. Thermodynamic model PC-SAFT for equilibrium and transport properties Both equilibrium and transport properties of the working fluid are calculated using the thermodynamically consistent Perturbed-Chain Statistically Associating Fluid Theory (PC-SAFT) equation of state [10] extended by dipolar contributions [26]. In PC-SAFT, a molecule is characterized by a set of typically 3 to 7 pure component parameters. In this work, we consider non-associative working fluids without a quadrupolar moment, so we need 4 pure component parameters: the segment number m, the segment diameter σ, the segment dispersion energy /k and the dipole moment µ. The pure component parameters are calculated from the molecular structure yS using the homosegmented GC approach of Sauer et al. [22]. Since PC-SAFT is a model of the residual Helmholtz energy, absolute properties are obtained using the heat capacity of the ideal gas as a reference, which is calculated from the molecular structure by Joback’s GC approach [27]. The molar mass is also calculated from the molecular structure. The model for the transport properties is based on Rosenfeld’s entropy scaling [28]. Rosenfeld found a monovariable dependency between transport properties and the residual entropy. Based on this work, a GC approach for the calculation of the viscosity has been presented by L¨otgering-Lin and Gross [20] and for the thermal conductivity by Hopp and Gross [21]. In these approaches, the entropy scaling is formulated as a third-order polynomial in terms of the residual entropy calculated using PC-SAFT. Group contributions are fitted to measurement data of the viscosity and thermal conductivity. The errors of the proposed GC approach are largely under 10 % for the viscosity [20] and under 8 % for thermal conductivity [21]. The considered groups are limited to the current state of the new GC approach of the thermal conductivity which covers: CH3 , CH2 , CH and C for branched alkanes, CH2 and CH for 1-alkenes, CArom and CHArom for aromatics with alkyl side groups and CH O for aldehydes. Additionally, the small molecules Methane and Ethane are defined as separated groups. However, additional groups can easily be integrated into the design approach as soon as further data for the groups of the thermal conductivity is taken into account. 3. Case study: The design of a subcritical Organic Rankine Cycle The 1-stage CoMT-CAMD approach is applied to the design of an ORC for waste heat recovery. The general specifications of the ORC are given in section 3.1. The models used for the sizing of the heat exchanger and the rotating equipment are presented in section 3.2. The results are discussed in section 3.3. 3.1. Specifications of the Case Study To exemplify the presented 1-stage CoMT-CAMD approach, we consider a subcritical, non-regenerated ORC for waste heat recovery (see Figure 2). The waste heat is freely available and considered as a water mass flow at 120 ◦C (see Table 1). The cooling is enabled by cooling water at 15 ◦C. turbine

3

out TWH

2

4 condenser

Qpre

preheater

Qevap

1

b) TinWH

Pnet

PT

evaporator

TinWH

generator geargbox

G

3

in TCW +ΔTCW

in TCW

Qcond

TemperaturegT

a)

ΔTsh pcond 4

2 1

ΔTCW

in TCW

pump PP workinggfluidg+WF)

out TWH

pevap

Entropygs wastegheatg+WH)

coolinggwaterg+CW)

Fig. 2. Flowsheet (a) and qualitative temperature-entropy diagram (b) of the considered ORC



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To assess the ORC process, we consider the specific investment cost SIC as objective function given by: SIC =

TCI , Pnet

(2)

where TCI denotes the total capital investment of the process and Pnet the net power output. The total capital investment TCI is calculated as   TCI = f1 · PECRE,k + f2 · PECHE, j , (3) j∈J

k∈K

where PECRE,k denotes the purchased-equipment cost of the rotating equipment k and PECHE, j the purchased-equipment cost of the heat exchanger j. The purchased equipment costs PEC are multiplied by correction factors f1 = 3.7 and f2 = 3.1 to account for additional direct and indirect costs [29]. The correction factor of the heat exchanger f2 is lower, since the cost correlation used for the heat exchanger already includes costs for installation (see section 3.2). The net power output is calculated based on equilibrium thermodynamics: Pnet = ηG · (|PT | − |PP |) = ηG · m ˙ WF · (|h4 − h3 | − |h2 − h1 |),

(4)

where ηG denotes the generator efficiency and hi the enthalpy of state i. The continuous degrees of freedom of the process x are the mass flow rate of the working fluid m ˙ WF , the pressure p red red as well as the evaporator p expressed in reduced form p = levels of the condenser pred evap pcritical and the degree of cond superheating after the evaporator ∆T sh . Additionally, the number of turbine stages nSt of the axial turbine is considered as integer degree of freedom. The inequality constraints of the process p2 are the limitation on the absolute pressure levels (pmax , pmin ) as well red as reduced pressure levels (pred min , pmax ) and the steam quality at turbine outlet ϕmin (see Table 1). Furthermore, the minimal approach temperature in the heat exchanger is constrained to be positive to ensure feasible heat transfer. Pressure drops in the heat exchangers and pipes are neglected in this work. Based on the model of the considered axial turbine, we include 2 equipment constraints g2 to avoid high Mach numbers and large blade heights: a limitation of the volume ratio per turbine stage ΦSt and a limitation of the isentropic enthalpy drop per turbine stage ∆his,St [30]. We limit the maximal number of functional groups of the molecular structure to nmax = 25 leading to 2647 feasible molecular structures, which fulfill the CAMD constraints, and 55 binary degrees of freedom describing the molecular structure. Table 1. Specifications of the case study.

Parameter Temperature (WH) Flow rate (WH) Temperature (CW) Temperature rise (CW) Isentr. turbine efficiency Isentr. pump efficiency Generator efficiency Max. group number

Symbol

Value

Parameter

in T WH m ˙ WH in T CW ∆T CW ηs,T ηs,P ηG nmax

120 ◦C 20 kgs 15 ◦C 10 K 0.8 0.7 0.95 25

Min. absolute pressure Max. absolute pressure Min. reduced pressure Max. reduced pressure Min. steam quality Max. stage volume ratio Max. isentr. stage enthalpy drop

Symbol

Value

pmin pmax pred min pred max ϕmin ΦSt,max ∆his,St,max

1 bar 50 bar 0.01 0.8 0.95 4 65 kJ kg−1

3.2. Equipment design The heat exchangers are modeled as shell and tube heat exchanger in counter-flow without shell baffles. The purchased-equipment cost PECHE, j are calculated depending on heat exchanger area. We use a cost correlation from Hall et al. [31] for stainless steel, which already includes the costs for installation. The Chemical Engineering Plant Cost Index (CEPCI) is used to account for inflation. The inner and outer diameters of the tubes are fixed to di = 16 mm and do = 20 mm, respectively. The number of tubes is found from the mass flow rate and a maximal allowed velocity in the tubes. The diameter of the shell in turn is found from the mass flow rate and a maximal allowed velocity in the

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shell. The maximal velocities are set to cmax,l = 1.5 ms for liquids and cmax,v = 20 ms for vapors [32]. The heat exchanger areas are calculated using heat transfer correlations for single phase, evaporation and condensation. In these correlations, the heat transfer is described based on dimensionless parameters such as Nusselt or Reynolds number, which in turn strongly depends on the transport properties. We assume that the working fluid is on the shell side and the water for heating and cooling on the tube side. For the heat transfer in the preheater and on the side of the heating and cooling water, we consider a correlation for single-phase forced convection [33]. In the evaporator, a local heat transfer correlation for flow boiling [34] is used, while we use a heat-transfer correlation for filmwise condensation in the condenser [32]. The heat transfer correlations for flow boiling and flimwise condensation depend on the steam quality ϕ. Thus, we discretize the evaporator and the condenser in the steam quality ϕ to calculate partial areas of the heat exchanger, which are summed subsequently. Additionally, the heat transfer correlation for flow boiling depends on the heat exchanger area itself so that we use an iterative calculation for the evaporator area. The purchased-equipment cost of the rotating equipment PECRE,k are calculated based on Astolfi et al. [30]. While the purchased-equipment cost of the pump, generator and gearbox are simply predicted based on the power input, we consider a cost correlation for the axial turbine depending on the number of turbine stages nStages and the last stage size parameter SP. This correlation captures a more detailed trade-off between the fluid properties and the purchasedequipment cost of the turbine. However, the correlation is used in an extended range of the equipment sizes compared to the original reference, so inaccuracies can occur. 3.3. Results We use the presented 1-stage CoMT-CAMD approach for the integrated thermo-economic design of the ORC considering the specific investment cost SIC as objective function. The MINLP solver DICOPT initially relaxes the e . This target problem to identify a hypothetical optimal working fluid leading to a target value of SIC = 2915 kW serves as a lower bound of the optimization. A ranking of 5 real working fluids is identified using 1-stage CoMTCAMD with integer-cuts (see Table 2). In this case study, only short alkanes and alkenes are identified. The best real e , which is 13.3 % higher than the target. Here, the major part working fluid is propene with a value of SIC = 3303 kW of the purchased-equipment cost is constituted by the cost for the rotation equipment with 60 %. The main costs are the purchased-equipment cost of the axial turbine. Jointly with the equipment sizes, a thermo-economically optimal approach temperature is identified as a result of the optimization: For propene, the optimal approach temperature is ∆T = 2.79 K in the evaporator and preheater and ∆T = 4.74 K in the condenser. The computation of the presented ranking of 5 working fluids requires 1.33 h using 1 Intel-Xeon CPU with 3.0 GHz and 64 GB RAM. To demonstrate the importance of an integrated thermo-economic design, we also perform a thermodynamic optimization of the considered ORC using the net power output Pnet as objective function. Since there is no trade-off between the net power output and the approach temperature in the heat exchanger, we define a minimal approach temperature of ∆T min = 2 K for the thermodynamic design. The 1-stage CoMT-CAMD approach identifies a thermodynamic target e ). We identify propane as the thermodynamically optimal real working with a value of Pnet = 619 kW (SIC = 8426 kW e fluid with Pnet = 488 kW (SIC = 5121 kW ). Beside the optimal identified molecular structure, the operating point of the thermodynamic optimum strongly differs from the thermo-economic optimum showing the significance of an integrated thermo-economic design of process, working fluid and equipment. In order to validate the results, we compare the results to data from scientific publications and ORC manufacturers collected by Quoilin et al. [3]. To ensure a fair comparison, we chose the specific purchased-equipment cost as validation criterion, since the correction factors f1 and f2 in equation (3) vary in literature. The specific purchased-equipment cost of the Top 5 identified working fluids show good agreement with the reference data (see Figure 3). Additionally, the working fluids are identified in a range of low specific purchased-equipment cost compared to the reference data showing the potential of a thermo-economic optimization with 1-stage CoMT-CAMD. The potential of the approach can be improved in further studies by consideration of additional functional groups and more detailed models of the process. 4. Conclusions In this work, we present an approach for the integrated thermo-economic design of ORC processes, working fluid and equipment. For this purpose, we linked a CAMD formulation directly to a thermo-economic model of an ORC process, which allows for the design of novel and promising working fluids. The PC-SAFT equation of state is



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Table 2. The Target and the top 5 molecular structures identified by the 1-stage CoMT-CAMD approach and the corresponding specific investment cost SIC. Additionally, the net power output Pnet , total capital investment TCI as well as the purchased-equipment cost of the rotating equipment PECRE and heat exchanger PECHE are shown as a result of the optimization.

Rank

Target Propene Propane 1-Butene Isobutane n-Butane

SIC /

e kW

2915 3303 3474 4546 4573 4874 specific€purchased-equipment€cost€€/€€€€/€kW

1 2 3 4 5

Name

Pnet / kW

TCI / 106 e

PECRE / 106 e

PECHE / 106 e

456 417 411 389 387 378

1.33 1.38 1.43 1.77 1.77 1.84

0.22 0.23 0.25 0.34 0.35 0.38

0.16 0.17 0.17 0.15 0.16 0.16

8000 7000 6000 5000 4000 3000 2000 1000 0 10

100 1000 net€power€output€/€kW

10000

Fig. 3. Comparison of the specific purchased-equipment cost of the Top 5 working fluids identified with 1-stage CoMT-CAMD (squares) with data for ORCs for waste heat recovery from scientific publications and manufactures (circles) [3].

used to obtain a thermodynamically consistent model for both equilibrium and transport properties. Thereby, the economic consequences of changing the molecule are captured within the resulting design approach, which is called 1-stage CoMT-CAMD. The consistent model for equilibrium and transport properties enables a detailed sizing of the equipment and, thus, a thermo-economic assessment of the process during the integrated design. The heat exchangers are designed using detailed heat transfer correlations for single phase, evaporation and condensation heat transfer. The resulting approach identifies the thermo-economically optimal working fluid and the corresponding optimal process and equipment sizes in one single optimization. We successfully apply the presented 1-stage CoMT-CAMD approach for the design of a subcritical Organic Rankine Cycle for waste heat recovery. The approach identifies the most promising working fluids, which minimize the specific investment cost. We show the significance of a thermo-economic design by comparing the thermo-economic results to the results of an integrated thermodynamic design. The identified working fluids and the corresponding specific purchased-equipment cost show a good accordance to real ORC processes. Acknowledgements We thank the Deutsche Forschungsgemeinschaft (DFG) for funding this work (BA2884/4-1). References [1] Colonna, P., Casati, E., Trapp, C., Mathijssen, T., Larjola, J., Turunen-Saaresti, T., et al. Organic Rankine Cycle Power Systems: From the Concept to Current Technology, Applications, and an Outlook to the Future. J Eng Gas Turbines Power 2015;137(10):100801. [2] Bao, J., Zhao, L.. A review of working fluid and expander selections for organic Rankine cycle. Renew Sust Energ Rev 2013;24:325–342.

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