Available online at www.sciencedirect.com

Energy Procedia 00 (2017) 000–000www.elsevier.com/locate/procedia

IV International Seminar on ORC Power Systems, ORC201713-15 September 2017, Milano, Italy

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

Johannes Schillinga, Dominik Tillmannsa, Matthias Lampea, Madlen Hoppb,Joachim Grossb, Andre Bardowa,∗

aChair of Technical Thermodynamics, RWTH Aachen University, 52056 Aachen, GermanybInstitute of Thermodynamics and Thermal Process Engineering, Stuttgart University, Pfaffenwaldring 9, 70569 Stuttgart, Germany

Abstract

To exploit the full thermo-economic potential of an Organic Rankine Cycle (ORC), the process, equipment and working fluidhave to be optimized simultaneously. Today, working fluid selection and thermo-economic process optimization are commonlyseparated. This separation leads to suboptimal solutions if the prior working fluid selection fails. In this work, we present anapproach for the integrated thermo-economic design of ORC process, equipment and working fluid using consistent thermodynamicmodeling. The approach is based on the Continuous-Molecular Targeting–Computer-aided Molecular Design (CoMT-CAMD)approach. In CoMT-CAMD, the properties of the working fluid are modeled by the physically-based Perturbed-Chain StatisticalAssociating Fluid Theory (PC-SAFT) equation of state. A CAMD formulation allows the design of novel working fluids during theprocess optimization. So far, CoMT-CAMD was limited to equilibrium thermodynamics. Some of the authors recently developedmodels for the transport properties viscosity and thermal conductivity based on entropy scaling and PC-SAFT. The integration ofthese models allows designing the equipment within the CoMT-CAMD approach. In particular, the heat exchanger of the ORC canbe designed using detailed correlations for single phase, evaporation and condensation heat transfer. Based on the equipment sizing,a thermo-economic objective function can be considered in the resulting mixed-integer nonlinear optimization problem. Thereby,the thermo-economically optimal working fluid is identified in a single optimization problem jointly with the corresponding optimalprocess and equipment. The resulting approach is illustrated for the design of a subcritical ORC for waste heat recovery. We showthat the predicted specific purchased-equipment costs are in good accordance with real ORC applications.c© 2017 The Authors. Published by Elsevier Ltd.Peer-review under responsibility of the scientific committee of the IV International Seminar on ORC Power Systems.

Keywords: CoMT-CAMD, integrated design, fluid selection, economics, transport properties

1. Introduction

Organic Rankine Cycles (ORC) generate electrical power from low temperature heat [1]. Low temperature heatcan be obtained from renewable heat sources or waste heat. To ensure an economically efficient process, the ORC hasto be tailored to its specific application. For this purpose, process, equipment and working fluid have to be optimizedsimultaneously.

∗Corresponding author. Tel.: +49-241-80-95381 ; fax: +49-241-80-92255.E-mail address: andre.bardow@ltt.rwth-aachen.de

1876-6102 c© 2017 The Authors. Published by Elsevier Ltd.Peer-review under responsibility of the scientific committee of the IV International Seminar on ORC Power Systems.

2 J. Schilling et al. / Energy Procedia 00 (2017) 000–000

Today, however, working fluid selection and thermo-economic process optimization are usually carried out separatelyfollowing 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. System-atic solution approaches based on equilibrium thermodynamics have been developed as recently reviewed by Linke etal. [5]. A two-stage design approach has been proposed for pure working fluids based on Computer-aided MolecularDesign (CAMD) and a cubic equation of state (EoS) by Palma-Flores et al. [6]. In a first stage, a set of working fluidcandidates is obtained based on a deterministic optimization before different process configurations are investigatedfor the working fluid candidates in a second stage. An approach for the integrated design of ORC process and mixturebased 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 sol-vents using PC-SAFT [10], the so-called Continuous-Molecular Targeting (CoMT). Subsequently, the CoMT ap-proach 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 describinga 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 second-degree Taylor-approximation around the target is used to estimate the objective function value of real working fluidsgenerated by CAMD. Recently, the CAMD formulation was directly linked to the process model and PC-SAFT allow-ing the authors to solve the integrated design problem in solely one stage [13]. The resulting 1-stage CoMT-CAMDapproach solves the MINLP using outer-approximation extended by a relaxation strategy. Since an equilibrium fluidmodel 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 thermo-economic design, equipment sizing has to be integrated into the design of process and working fluid to quantify theinvestment costs. Sizing the equipment requires not only an equilibrium fluid model but also a model for trans-port properties to capture transport-related trade-offs. Previously, integrated thermo-economic design was mainlyaddressed in process engineering. Pereira et al. [15,16] proposed an approach for thermo-economic design of solventand process for CO2 absorption based on the fluid model SAFT-VR. The approach is limited to the design of linearalkanes and heuristic equipment sizing, but shows the advantages of a thermo-economic design approach. The pre-sented approach is extended by Burger et al. [17] for the design of linear alkyl ethers using a hierarchical methodwith 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 combiningan outer-approximation formulation with a physical-domain reduction [18]. A hybrid stochastic-deterministic designapproach is presented by Zhou et al. [19] for thermo-economic design of solvents for Diels-alder reaction. Since nomodels 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 heuristicdesign correlations. In this work, we extend the 1-stage CoMT-CAMD approach for the thermo-economic design ofORC process, equipment and working fluid. For this propose, we integrate newly proposed models for the transportproperties viscosity and thermal conductivity based on PC-SAFT [20,21] yielding a consistent model for both equi-librium and transport properties. Thereby, the equipment design of the heat exchanger can be performed based ondetailed heat transfer correlations. The paper is structured as follows: In section 2, the framework of the extended1-stage CoMT-CAMD approach is presented. The approach is applied for a thermo-economic design of an OrganicRankine 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 extendedby models for equipment design and cost correlations. For this purpose, a model for transport properties is requiredbeside the equilibrium fluid model. In section 2.1, the problem formulation of extended 1-stage CoMT-CAMD for

J. Schilling et al. / Energy Procedia 00 (2017) 000–000 3

thermo-economic design is described. In section 2.2, the fluid model PC-SAFT is presented, which is used to modelboth 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 designlevels, the design is performed for the equipment (level 2), the process (level 4) and the working fluid (level 6). Thesedesign 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]. Theoptimization problem consists of one objective function f to be optimized (e.g., specific investment cost). Thisobjective 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., heattransfer correlations) and inequality constraints g2 (e.g., limitations in the turbine). The process design in turn consistsof equality constraints p1 (e.g., energy balances) and inequality constraints p2 (e.g., pressure limits). Both equilibriumproperties θ and transport properties κ are calculated using the PC-SAFT equation of state. In PC-SAFT, a workingfluid is characterized by a set of pure component parameters z. To allow for the design of the working fluid withinthe optimization, a CAMD formulation is employed. Within this CAMD formulation, a working fluid is described bya 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 themolecular structure yS of the working fluid. Additional equality constraints F1 and inequality constraints F2 ensurethe design of structurally feasible molecular structures [23]. The resulting degrees of freedom are the continuousprocess 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 withthe optimal process and equipment sizes. To ensure a stable computation of the demanding iterative calculations ofPC-SAFT and the equipment design, PC-SAFT and the process model are performed in external functions servingas 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 arelaxation problem identical to the CoMT problem of the CoMT-CAMD approach and subsequently identifies a realmolecular structure using an outer-approximation algorithm. However, the thermo-economic optimum of this model-based approach relies on the accuracy of the underlying models. To account for short-comings in the models andpossible local optima, we employ integer-cuts [25] to obtain a ranking of working fluid candidates. For this purpose,

4 J. Schilling et al. / Energy Procedia 00 (2017) 000–000

the MINLP is solved repeatedly, wherein the previous solutions are excluded from the design space. The obtainedranking has to be assessed subsequently by safety, environmental and legal criteria as well as all other aspects whichare 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 con-sistent Perturbed-Chain Statistically Associating Fluid Theory (PC-SAFT) equation of state [10] extended by dipolarcontributions [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 compo-nent parameters: the segment number m, the segment diameter σ, the segment dispersion energy ε/k and the dipolemoment µ. The pure component parameters are calculated from the molecular structure yS using the homosegmentedGC approach of Sauer et al. [22]. Since PC-SAFT is a model of the residual Helmholtz energy, absolute propertiesare obtained using the heat capacity of the ideal gas as a reference, which is calculated from the molecular structureby 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 monovariabledependency between transport properties and the residual entropy. Based on this work, a GC approach for the calcu-lation of the viscosity has been presented by Lotgering-Lin and Gross [20] and for the thermal conductivity by Hoppand Gross [21]. In these approaches, the entropy scaling is formulated as a third-order polynomial in terms of theresidual entropy calculated using PC-SAFT. Group contributions are fitted to measurement data of the viscosity andthermal conductivity. The errors of the proposed GC approach are largely under 10 % for the viscosity [20] and under8 % for thermal conductivity [21]. The considered groups are limited to the current state of the new GC approachof 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 groupscan easily be integrated into the design approach as soon as further data for the groups of the thermal conductivity istaken 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 generalspecifications of the ORC are given in section 3.1. The models used for the sizing of the heat exchanger and therotating 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 forwaste 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.

PP

PT

Qevap

Qpre

2

3

4

1

a) b)

Qcond Tem

pera

ture

gT

Entropygs

3

4

12

pevap

pcond

ΔTsh

TWH

TWH

TCW

preh

eat

erev

apor

ator

cond

ense

r

pump

turbine

G

generatorgeargbox

workinggfluidg+WF) wastegheatg+WH) coolinggwaterg+CW)

Pnet

in

out

in

TWHin

TWHout TCW

in

ΔTCW

+ΔTCWTCWin

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

J. Schilling et al. / Energy Procedia 00 (2017) 000–000 5

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

SIC =TCIPnet

, (2)

where TCI denotes the total capital investment of the process and Pnet the net power output. The total capital invest-ment TCI is calculated as

TCI = f1 ·∑k∈K

PECRE,k + f2 ·∑j∈J

PECHE, j, (3)

where PECRE,k denotes the purchased-equipment cost of the rotating equipment k and PECHE, j the purchased-equipmentcost of the heat exchanger j. The purchased equipment costs PEC are multiplied by correction factors f1 = 3.7 andf2 = 3.1 to account for additional direct and indirect costs [29]. The correction factor of the heat exchanger f2 islower, 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 · mWF · (|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 mWF, the pressurelevels of the condenser pred

cond as well as the evaporator predevap expressed in reduced form pred =

ppcritical

and the degree ofsuperheating after the evaporator ∆Tsh. Additionally, the number of turbine stages nSt of the axial turbine is consideredas integer degree of freedom.The inequality constraints of the process p2 are the limitation on the absolute pressure levels (pmax, pmin) as wellas reduced pressure levels (pred

min, predmax) 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 consideredaxial turbine, we include 2 equipment constraints g2 to avoid high Mach numbers and large blade heights: a limitationof 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 feasiblemolecular structures, which fulfill the CAMD constraints, and 55 binary degrees of freedom describing the molecularstructure.Table 1. Specifications of the case study.

Parameter Symbol Value Parameter Symbol Value

Temperature (WH) T inWH 120 ◦C Min. absolute pressure pmin 1 bar

Flow rate (WH) mWH 20 kgs Max. absolute pressure pmax 50 bar

Temperature (CW) T inCW 15 ◦C Min. reduced pressure pred

min 0.01Temperature rise (CW) ∆TCW 10 K Max. reduced pressure pred

max 0.8Isentr. turbine efficiency ηs,T 0.8 Min. steam quality ϕmin 0.95Isentr. pump efficiency ηs,P 0.7 Max. stage volume ratio ΦSt,max 4Generator efficiency ηG 0.95 Max. isentr. stage enthalpy drop ∆his,St,max 65 kJ kg−1

Max. group number nmax 25

3.2. Equipment design

The heat exchangers are modeled as shell and tube heat exchanger in counter-flow without shell baffles. Thepurchased-equipment cost PECHE, j are calculated depending on heat exchanger area. We use a cost correlation fromHall et al. [31] for stainless steel, which already includes the costs for installation. The Chemical Engineering PlantCost Index (CEPCI) is used to account for inflation. The inner and outer diameters of the tubes are fixed to di = 16 mmand do = 20 mm, respectively. The number of tubes is found from the mass flow rate and a maximal allowed velocityin the tubes. The diameter of the shell in turn is found from the mass flow rate and a maximal allowed velocity in theshell. The maximal velocities are set to cmax,l = 1.5 m

s for liquids and cmax,v = 20 ms for vapors [32].

6 J. Schilling et al. / Energy Procedia 00 (2017) 000–000

The heat exchanger areas are calculated using heat transfer correlations for single phase, evaporation and conden-sation. In these correlations, the heat transfer is described based on dimensionless parameters such as Nusselt orReynolds number, which in turn strongly depends on the transport properties. We assume that the working fluid ison the shell side and the water for heating and cooling on the tube side. For the heat transfer in the preheater and onthe side of the heating and cooling water, we consider a correlation for single-phase forced convection [33]. In theevaporator, a local heat transfer correlation for flow boiling [34] is used, while we use a heat-transfer correlation forfilmwise condensation in the condenser [32]. The heat transfer correlations for flow boiling and flimwise condensationdepend on the steam quality ϕ. Thus, we discretize the evaporator and the condenser in the steam quality ϕ to calculatepartial areas of the heat exchanger, which are summed subsequently. Additionally, the heat transfer correlation forflow 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]. Whilethe purchased-equipment cost of the pump, generator and gearbox are simply predicted based on the power input, weconsider a cost correlation for the axial turbine depending on the number of turbine stages nStages and the last stagesize parameter SP. This correlation captures a more detailed trade-off between the fluid properties and the purchased-equipment cost of the turbine. However, the correlation is used in an extended range of the equipment sizes comparedto 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 ORCconsidering the specific investment cost SIC as objective function. The MINLP solver DICOPT initially relaxes theproblem to identify a hypothetical optimal working fluid leading to a target value of SIC = 2915 e

kW . This targetserves as a lower bound of the optimization. A ranking of 5 real working fluids is identified using 1-stage CoMT-CAMD with integer-cuts (see Table 2). In this case study, only short alkanes and alkenes are identified. The best realworking fluid is propene with a value of SIC = 3303 e

kW , which is 13.3 % higher than the target. Here, the major partof the purchased-equipment cost is constituted by the cost for the rotation equipment with 60 %. The main costs arethe purchased-equipment cost of the axial turbine. Jointly with the equipment sizes, a thermo-economically optimalapproach 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 presentedranking 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 optimiza-tion of the considered ORC using the net power output Pnet as objective function. Since there is no trade-off betweenthe net power output and the approach temperature in the heat exchanger, we define a minimal approach temperatureof ∆Tmin = 2 K for the thermodynamic design. The 1-stage CoMT-CAMD approach identifies a thermodynamic targetwith a value of Pnet = 619 kW (SIC = 8426 e

kW ). We identify propane as the thermodynamically optimal real workingfluid with Pnet = 488 kW (SIC = 5121 e

kW ). Beside the optimal identified molecular structure, the operating pointof the thermodynamic optimum strongly differs from the thermo-economic optimum showing the significance of anintegrated thermo-economic design of process, working fluid and equipment.

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

Rank Name SIC / ekW Pnet / kW TCI / 106e PECRE / 106e PECHE / 106e

- Target 2915 456 1.33 0.22 0.161 Propene 3303 417 1.38 0.23 0.172 Propane 3474 411 1.43 0.25 0.173 1-Butene 4546 389 1.77 0.34 0.154 Isobutane 4573 387 1.77 0.35 0.165 n-Butane 4874 378 1.84 0.38 0.16

J. Schilling et al. / Energy Procedia 00 (2017) 000–000 7

In order to validate the results, we compare the results to data from scientific publications and ORC manufacturers col-lected by Quoilin et al. [3]. To ensure a fair comparison, we chose the specific purchased-equipment cost as validationcriterion, since the correction factors f1 and f2 in equation (3) vary in literature. The specific purchased-equipmentcost 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 datashowing the potential of a thermo-economic optimization with 1-stage CoMT-CAMD. The potential of the approachcan be improved in further studies by consideration of additional functional groups and more detailed models of theprocess.

10 100 1000 10000net€power€output€/€kW

1000

0

2000

3000

4000

5000

6000

7000

8000sp

ecifi

c€pu

rcha

sed-

equi

pmen

t€cos

t€€/€€

€€/€k

W

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

4. Conclusions

In this work, we present an approach for the integrated thermo-economic design of ORC processes, working fluidand equipment. For this purpose, we linked a CAMD formulation directly to a thermo-economic model of an ORCprocess, which allows for the design of novel and promising working fluids. The PC-SAFT equation of state isused to obtain a thermodynamically consistent model for both equilibrium and transport properties. Thereby, theeconomic consequences of changing the molecule are captured within the resulting design approach, which is called1-stage CoMT-CAMD. The consistent model for equilibrium and transport properties enables a detailed sizing of theequipment and, thus, a thermo-economic assessment of the process during the integrated design. The heat exchangersare designed using detailed heat transfer correlations for single phase, evaporation and condensation heat transfer. Theresulting approach identifies the thermo-economically optimal working fluid and the corresponding optimal processand equipment sizes in one single optimization.We successfully apply the presented 1-stage CoMT-CAMD approach for the design of a subcritical Organic RankineCycle for waste heat recovery. The approach identifies the most promising working fluids, which minimize the specificinvestment cost. We show the significance of a thermo-economic design by comparing the thermo-economic resultsto the results of an integrated thermodynamic design. The identified working fluids and the corresponding specificpurchased-equipment cost show a good accordance to real ORC processes.

AcknowledgementsWe thank the Deutsche Forschungsgemeinschaft (DFG) for funding this work (BA2884/4-1).

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