- Email: [email protected]
Integrated thermo-economic design of ORC process, working fluid and equipment using PC-SAFT
Antonio Espuña, Moisès Graells and Luis Puigjaner (Editors), Proceedings of the 27th European Symposium on Computer Aided Process Engineering – ESCAPE 27 October 1st - 5th , 2017, Barcelona, Spain © 2017 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/B978-0-444-63965-3.50301-9
Integrated thermo-economic design of ORC process, working fluid and equipment using PC-SAFT Johannes Schillinga , Dominik Tillmannsa , Matthias Lampea , Madlen Hoppb , Joachim Grossb and André Bardowa* a Chair
of Technical Thermodynamics, RWTH Aachen University, 52056 Aachen, Germany b Institute of Thermodynamics and Thermal Process Engineering, Stuttgart University, Pfaffenwaldring 9, 70569 Stuttgart, Germany [email protected]
Abstract Organic Rankine Cycles (ORCs) generate electrical power from low-temperature heat. To exploit the full potential of a heat source, the cycle has to be tailored to the specific application. In this work, we present an approach for the integrated thermo-economic design of ORC process, working fluid and equipment based on a single thermodynamic model. The approach is based on the Continuous-Molecular Targeting–Computer-aided Molecular Design (CoMT-CAMD) approach. Herein, the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state is used as a thermodynamic model. So far, CoMT-CAMD was limited to equilibrium thermodynamics. However, novel PCSAFT-based models for transport properties using entropy scaling enable the integration of rigorous equipment design into the CoMT-CAMD approach. By solving the resulting mixed-integer nonlinear optimization problem, the presented approach allows the integrated design of economically optimal ORCs. Keywords: CoMT-CAMD, transport properties, integrated design, PC-SAFT, economics
1. Introduction Electrical power can be generated from low-temperature heat using Organic Rankine Cycles (ORC). To obtain a thermo-economically optimal process, the working fluid selection of the ORC has to be integrated with the process and equipment design (Linke et al., 2015). This integration leads to a challenging mixed-integer nonlinear program MINLP (Gani, 2004). Thus, systematic solution approaches have been developed as recently reviewed for ORCs by Linke et al. (2015). In our previous work, we proposed the Continuous-Molecular Targeting–Computer-aided Molecular Design (CoMT-CAMD) approach for the integrated design of solvents for CO2 capture (Bardow et al., 2010) and working fluids for ORCs (Lampe et al., 2015). Herein, the Perturbed-Chain Statistically Associating Fluid Theory (PC-SAFT) (Gross and Sadowski, 2001) is used as thermodynamic model of the fluid. In the CoMT stage, the discrete pure component parameters describing a working fluid in PC-SAFT are relaxed to identify a hypothetical optimal working fluid, the so-called target. In a following stage, real fluids are identified using CAMD and a Taylor-approximation of the objective function around the target. Recently, we directly linked the CoMT problem to the CAMD formulation allowing us to solve the MINLP in one stage in the resulting 1-stage CoMT-CAMD
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approach (Schilling et al., 2017). Since solely an equilibrium model is employed for the fluid, only thermodynamic objective functions can be considered. However, the thermodynamic optimum may differ from a thermo-economic optimum, which requires the design of the equipment to quantify the investment costs. Equipment design requires a model for transport properties to capture all transport-related trade-offs. An approach for thermo-economic design of solvent and process has been proposed by Pereira et al. (2011) for CO2 absorption. The approach employs a heuristic equipment sizing and shows already the advantages of an integrated thermo-economic design. The same group extended their work by a hierarchical approach using shortcut models (Burger et al., 2015) and recently by a physical domain reduction (Gopinath et al., 2016). In this work, we integrate rigorous methods for equipment sizing into 1-stage CoMTCAMD enabling the integrated thermo-economic design of ORC process, equipment and working fluid. For this purpose, we integrate PC-SAFT-based models for transport properties yielding a thermodynamically consistent model for both equilibrium and transport properties. The transport properties allow for a detailed sizing of the equipment and, thus, for a thermo-economic assessment of the process.
2. Framework for integrated thermo-economic design The integrated thermo-economic design of process, equipment and working fluid takes place at 6 levels (Figure 1): the economics serving as assessment criterion are given at the main level 1. On 3 design levels, the design is performed for the equipment (level 2), the process (level 4) and the working fluid (level 6). The design levels are linked by 2 fluid-property levels for transport properties (level 3) and equilibrium properties (level 5).
Figure 1: Schematic illustration (left) and problem formulation (right) of the presented 1-stage CoMT-CAMD approach for integrated thermo-economic design. 2.1. Problem Formulation The integrated design problem can be formulated as an MINLP as given in problem (1) based on Gani (2004). In this problem, a thermo-economic objective function f (e.g., net
Integrated thermo-economic design of ORC process, working fluid and equipment using PC-SAFT
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present value) is optimized, which depends on process variables x (e.g., pressure levels), equilibrium properties θ (e.g., enthalpy) and transport properties κ (e.g., viscosity) of the working fluid. The equipment model encompasses equality constraints g1 (e.g., heat transfer correlations) and inequality constraints g2 (e.g., velocity limits). The process model is characterized by equality constraints p1 (e.g., energy balances) and inequality constraints p2 (e.g., pressure limits). The PC-SAFT equation of state is used to calculate both the equilibrium properties θ and transport properties κ in each liquid and vapor state of the process. In PC-SAFT, each working fluid is characterized by a set of pure component parameters z. The design of the working fluid is enabled by a CAMD formulation, wherein the working fluid is described by a vector yS , which contains the number of functional groups representing the molecular structure of the working fluid. The CAMD formulation and PC-SAFT are linked using the homosegmented group contribution (GC) approach of PC-SAFT (Sauer et al., 2014), which calculates the pure component parameters z from the molecular structure yS . Structural feasibility of the molecule is ensured by additional equality constraints F1 and inequality constraints F2 (Struebing et al., 2011). The presented MINLP problem is solved in 1-stage CoMT-CAMD and yields the optimal combination of the molecular structure of the working fluid and the corresponding process and equipment sizes. The MINLP is solved using the MINLP solver DICOPT (Grossmann et al., 2002), which combines an outer-approximation formulation with a relaxation strategy similar to the CoMT problem in the CoMT-CAMD approach. To account for possible local optima as well as shortcomings in the GC approach, we use integer-cuts (Grossmann and Kravanja, 1995) to obtain a ranking of working fluid candidates. 2.2. Equilibrium and transport properties based on PC-SAFT and CAMD The Perturbed-Chain Statistically Associating Fluid Theory (PC-SAFT) (Gross and Sadowski, 2001) is used as a consistent thermodynamic fluid model to model both equilibrium and transport properties. A detailed description of the modeling for the equilibrium properties θ in 1-stage CoMT-CAMD is given in Schilling et al. (2017). The calculation of the transport properties κ is based on Rosenfeld’s entropy scaling (Rosenfeld, 1977), who found a monovariable dependency between transport properties and the residual entropy. Based on the work of Rosenfeld, Lötgering-Lin and Gross (2015) present a GC approach for the viscosity and Hopp and Gross (2016) for the thermal conductivity using PC-SAFT-based entropy scaling. The functional groups employed in this work are the current state of the newly developed GC approach of the thermal conductivity, i.e., 9 groups for branched alkanes, 1-alkenes, aldehydes and aromatics. Additional groups can easily be considered as soon as new data is available.
3. Case study for design of Organic Rankine Cycles The presented 1-stage CoMT-CAMD approach for integrated thermo-economic design is applied to the design of an ORC for waste heat recovery. For this purpose, the sizing is performed for the rotating equipment and all heat exchangers with three heat transfer types accounting for the different heat transfer mechanisms. 3.1. Specification of the ORC case study We consider a small-size ORC, which utilizes low-temperature waste heat (WH) available as water at 150 ◦C and cooling water (CW) as heat sink (see Table 1). The heat input is performed in two heat exchangers: a preheater and an evaporator (see Figure 2).
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Qevap
Qpre out WH
T
2
3
G condenser
in
TWH
preheater evaporator
turbine
4
1
pump PP working fluid (WF)
T
out CW
T
in CW
Qcond
b)
pevap in
TWH Temperature T
a)
3 Tsh pcond
Tout WH
4
2 1
out TCW
in TCW
Entropy s waste heat (WH)
cooling water (CW)
Figure 2: (a) Flowsheet and (b) temperature-entropy diagram of an ORC process. We consider the net present value NPV of the ORC as objective function calculated as f = NPV = −TCI + (τ · eel · Pnet − coc · TCI) · PVAF,
(2)
e where τ = 7,500 ha denotes the annual operating hours, eel = 0.12 kW h the earnings from electricity and PVAF = 8.1 a the present value annuity factor. The annual maintenance costs are estimated as share coc = 0.02 of the total capital investment TCI. The total capital investment TCI is calculated as sum of the purchased-equipment cost PEC multiplied by correction factors for additional direct and indirect costs (Pierobon et al., 2013). The net power output Pnet is calculated from the process model. The continuous degrees of freedom of the process x are the mass flow rate of the working fluid m˙ WF , the reduced operating pressure levels of the condenser pred cond and the evaporator pred evap and the degree of superheating at turbine inlet ΔTsh . The process inequality constraints p2 are constraints on the minimal and maximal pressure levels and the steam quality at turbine outlet (Table 1). Furthermore, the minimal approach temperature is constrained to be positive to ensure feasible heat transfer. Table 1: Specifications of the case study. Parameter Symbol Value Parameter Symbol Value kg Flow rate (WH) m˙ WH 10 s Flow rate (CW) m˙ CW 175 kg s in in Temp. (WH) TWH 150 ◦C Temp. (CW) TCW 15 ◦C 0.8 Min. pressure pmin 1 bar Isentr. turb. efficiency ηs,T 0.75 Max. pressure pmax 50 bar Isentr. pump efficiency ηs,P 0.98 Min. steam quality ϕmin 0.95 Generator efficiency ηG
3.2. Equipment design The purchased-equipment cost of the turbine, pump, generator and gear box are calculated based on Astolfi et al. (2014). The number of turbine stages nStages is considered as an integer variable. Additionally, two turbine design constraints g2 on the isentropic enthalpy drop and the volume ratio per turbine stage are considered to avoid high Mach numbers and large blade heights (Astolfi et al., 2014). The heat exchangers are modeled as shell and tube heat exchanger in counter-flow without shell baffles. The purchasedequipment cost are calculated based on the heat exchanger areas (Hall et al., 1990). The heat exchanger areas are calculated based on heat transfer correlations. In the preheater and for the side of the waste heat and cooling water, a heat transfer correlation for single
Integrated thermo-economic design of ORC process, working fluid and equipment using PC-SAFT
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phase forced convection is assumed (Verein Deutscher Ingenieure, 2010). The evaporator is modeled using a correlation for flow boiling from Gungor and Winterton (1986). Since this local correlation depends on the steam quality ϕ and the heat exchanger area itself, a discretization in the steam quality ϕ is performed and solved by iterative calculations. In the condenser, we assume a correlation for filmwise condensation (Verein Deutscher Ingenieure, 2010), which also requires a discretization in the steam quality ϕ. 3.3. Results The presented 1-stage CoMT-CAMD approach is applied to the integrated thermo-economic design of the described ORC. Initially, a target value of NPV = 2.1 · 106 e is obtained in the relaxed CoMT problem. Integer-cuts are used to obtain a ranking of 5 promising real working fluids (Table 2). The optimal real working fluid is propene with NPV = 1.8 · 106 e, which is 13.0 % lower than the target value. For propene, the optimization identifies an optimal approach temperature of ΔT = 4.2 K in both the preheater and the evaporator and ΔT = 6.1 K in the condenser. The result of 1-stage CoMT-CAMD shows a good agreement to manufacture data collected by Quoilin et al. (2013). Table 2: The target and the top 5 identified molecular structures as well as the corresponding net present value NPV , net power output Pnet and total capital investment TCI. Rank Name NPV / 106 e Pnet / kW TCI / 106 e Target 2.07 538 1.60 1 Propene 1.80 489 1.52 2 Propane 1.62 469 1.55 3 But-1-ene 0.91 405 1.76 4 Isobutane 0.89 406 1.79 5 n-Butane 0.74 389 1.81 In comparison, a thermodynamic design of the ORC is performed considering the net power output Pnet as objective function. Since no trade-off exists between the net power output and the minimal approach temperature, a minimal approach temperature of ΔTmin = 2 K is assumed. The target value of the thermodynamic design is Pnet = 634 kW (NPV = −1.5 · 106 e). The thermodynamically optimal real working fluid is propane with Pnet = 589 kW (NPV = 0.55 · 106 e). The operating point and the resulting equipment design strongly differ from the thermo-economic optimum showing the significance of an integrated thermo-economic design.
4. Conclusion In this work, we integrate newly proposed models for transport properties based on PCSAFT into the 1-stage CoMT-CAMD approach. Thereby, we enable the integrated design of process, equipment and working fluid and thus a thermo-economic design of the process. The PC-SAFT equation of state is used as thermodynamically consistent model for both equilibrium and transport properties. The transport properties allow us to consider detailed correlations for sizing of the equipment during the optimization. The thermoeconomically optimal working fluid and the corresponding process are identified in one single optimization. The 1-stage CoMT-CAMD approach is successfully applied to the design of an ORC using detailed heat transfer correlations for the sizing of the heat exchangers. We identify the working fluids which maximize the net present value of the process. We show that a thermodynamic design results in an operating point with low net present value emphasizing the importance of a thermo-economic design.
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Acknowledgements We thank the Deutsche Forschungsgemeinschaft for funding this work (BA2884/4-1).
References Astolfi, M., Romano, M. C., Bombarda, P., Macchi, E., 2014. Binary ORC (Organic Rankine Cycles) power plants for the exploitation of medium–low temperature geothermal sources – Part B: Techno-economic optimization. Energy 66, 435–46. Bardow, A., Steur, K., Gross, J., 2010. Continuous-Molecular Targeting for Integrated Solvent and Process Design. Ind. Eng. Chem. Res. 49 (6), 2834–40. Burger, J., Papaioannou, V., Gopinath, S., Jackson, G., Galindo, A., Adjiman, C. S., 2015. A hierarchical method to integrated solvent and process design of physical CO2 absorption using the SAFT-γ Mie approach. AIChE J. 61 (10), 3249–69. Gani, R., 2004. Chemical product design: Challenges and opportunities. Comput. Chem. Eng. 28 (12), 2441–57. Gopinath, S., Jackson, G., Galindo, A., Adjiman, C. S., 2016. Outer approximation algorithm with physical domain reduction for computer-aided molecular and separation process design. AIChE J. 62 (9), 3484–504. Gross, J., Sadowski, G., 2001. Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res. 40 (4), 1244–60. Grossmann, I. E., Kravanja, Z., 1995. Mixed-integer nonlinear programming techniques for process systems engineering. Comput. Chem. Eng. 19, 189–204. Grossmann, I. E., Viswanathan, J., Vecchietti, A., Raman, R., Kalvelagen, E., 2002. GAMS/DICOPT: A discrete continuous optimization package. GAMS Corporation Inc. Gungor, K. E., Winterton, R., 1986. A general correlation for flow boiling in tubes and annuli. Int. J. Heat Mass Transfer 29 (3), 351–8. Hall, S. G., Ahmad, S., Smith, R., 1990. Capital cost targets for heat exchanger networks comprising mixed materials of construction, pressure ratings and exchanger types. Comput. Chem. Eng. 14 (3), 319–35. Hopp, M., Gross, J., 2016. Group-contribution method for thermal conductivity using PC-SAFT and entropy scaling. In: Proceedings of PPEPPD 2016. Porto, Portugal, 2016. Lampe, M., Stavrou, M., Schilling, J., Sauer, E., Gross, J., Bardow, A., 2015. Computer-aided molecular design in the continuous-molecular targeting framework using group-contribution PC-SAFT. Comput. Chem. Eng. 81, 278–87. Linke, P., Papadopoulos, A., Seferlis, P., 2015. Systematic Methods for Working Fluid Selection and the Design, Integration and Control of Organic Rankine Cycles–A Review. Energies 8 (6), 4755–801. Lötgering-Lin, O., Gross, J., 2015. Group Contribution Method for Viscosities Based on Entropy Scaling Using the Perturbed-Chain Polar Statistical Associating Fluid Theory. Ind. Eng. Chem. Res. 54 (32), 7942–52. Pereira, F. E., Keskes, E., Galindo, A., Jackson, G., Adjiman, C. S., 2011. Integrated solvent and process design using a SAFT-VR thermodynamic description: High-pressure separation of carbon dioxide and methane. Comput. Chem. Eng. 35 (3), 474–91. Pierobon, L., Nguyen, T.-V., Larsen, U., Haglind, F., Elmegaard, B., 2013. Multi-objective optimization of Organic Rankine Cycles for waste heat recovery: Application in an offshore platform. Energy 58, 538–49. Quoilin, S., van Broek, M. D., Declaye, S., Dewallef, P., Lemort, V., 2013. Techno-economic survey of Organic Rankine Cycle (ORC) systems. Renew. Sust. Energ. Rev. 22, 168–86. Rosenfeld, Y., 1977. Relation between the transport coefficients and the internal entropy of simple systems. Physical Review A 15 (6), 2545–9. Sauer, E., Stavrou, M., Gross, J., 2014. Comparison between a Homo- and a Heterosegmented Group Contribution Approach Based on the Perturbed-Chain Polar Statistical Associating Fluid Theory Equation of State. Ind. Eng. Chem. Res. 53 (38), 14854–64. Schilling, J., Lampe, M., Gross, J., Bardow, A., 2017. 1-stage CoMT-CAMD: An approach for integrated design of ORC process and working fluid using PC-SAFT. Chem. Eng. Sci. 159, 217–30. Struebing, H., Adjiman, C. S., and Galindo, A., 2011. Optimal solvent design for reactions using computeraided molecular design. URL http://www.minlp.org/library/problem/mod/index.php?lib=MINLP&i=180&pi=-137 Verein Deutscher Ingenieure, 2010. VDI heat atlas, 2nd Edition. Springer reference. Springer, Heidelberg.
Integrated thermo-economic design of ORC process, working fluid and equipment using PC-SAFT Johannes Schillinga , Dominik Tillmannsa , Matthias Lampea , Madlen Hoppb , Joachim Grossb and André Bardowa* a Chair
of Technical Thermodynamics, RWTH Aachen University, 52056 Aachen, Germany b Institute of Thermodynamics and Thermal Process Engineering, Stuttgart University, Pfaffenwaldring 9, 70569 Stuttgart, Germany [email protected]
Abstract Organic Rankine Cycles (ORCs) generate electrical power from low-temperature heat. To exploit the full potential of a heat source, the cycle has to be tailored to the specific application. In this work, we present an approach for the integrated thermo-economic design of ORC process, working fluid and equipment based on a single thermodynamic model. The approach is based on the Continuous-Molecular Targeting–Computer-aided Molecular Design (CoMT-CAMD) approach. Herein, the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state is used as a thermodynamic model. So far, CoMT-CAMD was limited to equilibrium thermodynamics. However, novel PCSAFT-based models for transport properties using entropy scaling enable the integration of rigorous equipment design into the CoMT-CAMD approach. By solving the resulting mixed-integer nonlinear optimization problem, the presented approach allows the integrated design of economically optimal ORCs. Keywords: CoMT-CAMD, transport properties, integrated design, PC-SAFT, economics
1. Introduction Electrical power can be generated from low-temperature heat using Organic Rankine Cycles (ORC). To obtain a thermo-economically optimal process, the working fluid selection of the ORC has to be integrated with the process and equipment design (Linke et al., 2015). This integration leads to a challenging mixed-integer nonlinear program MINLP (Gani, 2004). Thus, systematic solution approaches have been developed as recently reviewed for ORCs by Linke et al. (2015). In our previous work, we proposed the Continuous-Molecular Targeting–Computer-aided Molecular Design (CoMT-CAMD) approach for the integrated design of solvents for CO2 capture (Bardow et al., 2010) and working fluids for ORCs (Lampe et al., 2015). Herein, the Perturbed-Chain Statistically Associating Fluid Theory (PC-SAFT) (Gross and Sadowski, 2001) is used as thermodynamic model of the fluid. In the CoMT stage, the discrete pure component parameters describing a working fluid in PC-SAFT are relaxed to identify a hypothetical optimal working fluid, the so-called target. In a following stage, real fluids are identified using CAMD and a Taylor-approximation of the objective function around the target. Recently, we directly linked the CoMT problem to the CAMD formulation allowing us to solve the MINLP in one stage in the resulting 1-stage CoMT-CAMD
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approach (Schilling et al., 2017). Since solely an equilibrium model is employed for the fluid, only thermodynamic objective functions can be considered. However, the thermodynamic optimum may differ from a thermo-economic optimum, which requires the design of the equipment to quantify the investment costs. Equipment design requires a model for transport properties to capture all transport-related trade-offs. An approach for thermo-economic design of solvent and process has been proposed by Pereira et al. (2011) for CO2 absorption. The approach employs a heuristic equipment sizing and shows already the advantages of an integrated thermo-economic design. The same group extended their work by a hierarchical approach using shortcut models (Burger et al., 2015) and recently by a physical domain reduction (Gopinath et al., 2016). In this work, we integrate rigorous methods for equipment sizing into 1-stage CoMTCAMD enabling the integrated thermo-economic design of ORC process, equipment and working fluid. For this purpose, we integrate PC-SAFT-based models for transport properties yielding a thermodynamically consistent model for both equilibrium and transport properties. The transport properties allow for a detailed sizing of the equipment and, thus, for a thermo-economic assessment of the process.
2. Framework for integrated thermo-economic design The integrated thermo-economic design of process, equipment and working fluid takes place at 6 levels (Figure 1): the economics serving as assessment criterion are given at the main level 1. On 3 design levels, the design is performed for the equipment (level 2), the process (level 4) and the working fluid (level 6). The design levels are linked by 2 fluid-property levels for transport properties (level 3) and equilibrium properties (level 5).
Figure 1: Schematic illustration (left) and problem formulation (right) of the presented 1-stage CoMT-CAMD approach for integrated thermo-economic design. 2.1. Problem Formulation The integrated design problem can be formulated as an MINLP as given in problem (1) based on Gani (2004). In this problem, a thermo-economic objective function f (e.g., net
Integrated thermo-economic design of ORC process, working fluid and equipment using PC-SAFT
1797
present value) is optimized, which depends on process variables x (e.g., pressure levels), equilibrium properties θ (e.g., enthalpy) and transport properties κ (e.g., viscosity) of the working fluid. The equipment model encompasses equality constraints g1 (e.g., heat transfer correlations) and inequality constraints g2 (e.g., velocity limits). The process model is characterized by equality constraints p1 (e.g., energy balances) and inequality constraints p2 (e.g., pressure limits). The PC-SAFT equation of state is used to calculate both the equilibrium properties θ and transport properties κ in each liquid and vapor state of the process. In PC-SAFT, each working fluid is characterized by a set of pure component parameters z. The design of the working fluid is enabled by a CAMD formulation, wherein the working fluid is described by a vector yS , which contains the number of functional groups representing the molecular structure of the working fluid. The CAMD formulation and PC-SAFT are linked using the homosegmented group contribution (GC) approach of PC-SAFT (Sauer et al., 2014), which calculates the pure component parameters z from the molecular structure yS . Structural feasibility of the molecule is ensured by additional equality constraints F1 and inequality constraints F2 (Struebing et al., 2011). The presented MINLP problem is solved in 1-stage CoMT-CAMD and yields the optimal combination of the molecular structure of the working fluid and the corresponding process and equipment sizes. The MINLP is solved using the MINLP solver DICOPT (Grossmann et al., 2002), which combines an outer-approximation formulation with a relaxation strategy similar to the CoMT problem in the CoMT-CAMD approach. To account for possible local optima as well as shortcomings in the GC approach, we use integer-cuts (Grossmann and Kravanja, 1995) to obtain a ranking of working fluid candidates. 2.2. Equilibrium and transport properties based on PC-SAFT and CAMD The Perturbed-Chain Statistically Associating Fluid Theory (PC-SAFT) (Gross and Sadowski, 2001) is used as a consistent thermodynamic fluid model to model both equilibrium and transport properties. A detailed description of the modeling for the equilibrium properties θ in 1-stage CoMT-CAMD is given in Schilling et al. (2017). The calculation of the transport properties κ is based on Rosenfeld’s entropy scaling (Rosenfeld, 1977), who found a monovariable dependency between transport properties and the residual entropy. Based on the work of Rosenfeld, Lötgering-Lin and Gross (2015) present a GC approach for the viscosity and Hopp and Gross (2016) for the thermal conductivity using PC-SAFT-based entropy scaling. The functional groups employed in this work are the current state of the newly developed GC approach of the thermal conductivity, i.e., 9 groups for branched alkanes, 1-alkenes, aldehydes and aromatics. Additional groups can easily be considered as soon as new data is available.
3. Case study for design of Organic Rankine Cycles The presented 1-stage CoMT-CAMD approach for integrated thermo-economic design is applied to the design of an ORC for waste heat recovery. For this purpose, the sizing is performed for the rotating equipment and all heat exchangers with three heat transfer types accounting for the different heat transfer mechanisms. 3.1. Specification of the ORC case study We consider a small-size ORC, which utilizes low-temperature waste heat (WH) available as water at 150 ◦C and cooling water (CW) as heat sink (see Table 1). The heat input is performed in two heat exchangers: a preheater and an evaporator (see Figure 2).
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Qevap
Qpre out WH
T
2
3
G condenser
in
TWH
preheater evaporator
turbine
4
1
pump PP working fluid (WF)
T
out CW
T
in CW
Qcond
b)
pevap in
TWH Temperature T
a)
3 Tsh pcond
Tout WH
4
2 1
out TCW
in TCW
Entropy s waste heat (WH)
cooling water (CW)
Figure 2: (a) Flowsheet and (b) temperature-entropy diagram of an ORC process. We consider the net present value NPV of the ORC as objective function calculated as f = NPV = −TCI + (τ · eel · Pnet − coc · TCI) · PVAF,
(2)
e where τ = 7,500 ha denotes the annual operating hours, eel = 0.12 kW h the earnings from electricity and PVAF = 8.1 a the present value annuity factor. The annual maintenance costs are estimated as share coc = 0.02 of the total capital investment TCI. The total capital investment TCI is calculated as sum of the purchased-equipment cost PEC multiplied by correction factors for additional direct and indirect costs (Pierobon et al., 2013). The net power output Pnet is calculated from the process model. The continuous degrees of freedom of the process x are the mass flow rate of the working fluid m˙ WF , the reduced operating pressure levels of the condenser pred cond and the evaporator pred evap and the degree of superheating at turbine inlet ΔTsh . The process inequality constraints p2 are constraints on the minimal and maximal pressure levels and the steam quality at turbine outlet (Table 1). Furthermore, the minimal approach temperature is constrained to be positive to ensure feasible heat transfer. Table 1: Specifications of the case study. Parameter Symbol Value Parameter Symbol Value kg Flow rate (WH) m˙ WH 10 s Flow rate (CW) m˙ CW 175 kg s in in Temp. (WH) TWH 150 ◦C Temp. (CW) TCW 15 ◦C 0.8 Min. pressure pmin 1 bar Isentr. turb. efficiency ηs,T 0.75 Max. pressure pmax 50 bar Isentr. pump efficiency ηs,P 0.98 Min. steam quality ϕmin 0.95 Generator efficiency ηG
3.2. Equipment design The purchased-equipment cost of the turbine, pump, generator and gear box are calculated based on Astolfi et al. (2014). The number of turbine stages nStages is considered as an integer variable. Additionally, two turbine design constraints g2 on the isentropic enthalpy drop and the volume ratio per turbine stage are considered to avoid high Mach numbers and large blade heights (Astolfi et al., 2014). The heat exchangers are modeled as shell and tube heat exchanger in counter-flow without shell baffles. The purchasedequipment cost are calculated based on the heat exchanger areas (Hall et al., 1990). The heat exchanger areas are calculated based on heat transfer correlations. In the preheater and for the side of the waste heat and cooling water, a heat transfer correlation for single
Integrated thermo-economic design of ORC process, working fluid and equipment using PC-SAFT
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phase forced convection is assumed (Verein Deutscher Ingenieure, 2010). The evaporator is modeled using a correlation for flow boiling from Gungor and Winterton (1986). Since this local correlation depends on the steam quality ϕ and the heat exchanger area itself, a discretization in the steam quality ϕ is performed and solved by iterative calculations. In the condenser, we assume a correlation for filmwise condensation (Verein Deutscher Ingenieure, 2010), which also requires a discretization in the steam quality ϕ. 3.3. Results The presented 1-stage CoMT-CAMD approach is applied to the integrated thermo-economic design of the described ORC. Initially, a target value of NPV = 2.1 · 106 e is obtained in the relaxed CoMT problem. Integer-cuts are used to obtain a ranking of 5 promising real working fluids (Table 2). The optimal real working fluid is propene with NPV = 1.8 · 106 e, which is 13.0 % lower than the target value. For propene, the optimization identifies an optimal approach temperature of ΔT = 4.2 K in both the preheater and the evaporator and ΔT = 6.1 K in the condenser. The result of 1-stage CoMT-CAMD shows a good agreement to manufacture data collected by Quoilin et al. (2013). Table 2: The target and the top 5 identified molecular structures as well as the corresponding net present value NPV , net power output Pnet and total capital investment TCI. Rank Name NPV / 106 e Pnet / kW TCI / 106 e Target 2.07 538 1.60 1 Propene 1.80 489 1.52 2 Propane 1.62 469 1.55 3 But-1-ene 0.91 405 1.76 4 Isobutane 0.89 406 1.79 5 n-Butane 0.74 389 1.81 In comparison, a thermodynamic design of the ORC is performed considering the net power output Pnet as objective function. Since no trade-off exists between the net power output and the minimal approach temperature, a minimal approach temperature of ΔTmin = 2 K is assumed. The target value of the thermodynamic design is Pnet = 634 kW (NPV = −1.5 · 106 e). The thermodynamically optimal real working fluid is propane with Pnet = 589 kW (NPV = 0.55 · 106 e). The operating point and the resulting equipment design strongly differ from the thermo-economic optimum showing the significance of an integrated thermo-economic design.
4. Conclusion In this work, we integrate newly proposed models for transport properties based on PCSAFT into the 1-stage CoMT-CAMD approach. Thereby, we enable the integrated design of process, equipment and working fluid and thus a thermo-economic design of the process. The PC-SAFT equation of state is used as thermodynamically consistent model for both equilibrium and transport properties. The transport properties allow us to consider detailed correlations for sizing of the equipment during the optimization. The thermoeconomically optimal working fluid and the corresponding process are identified in one single optimization. The 1-stage CoMT-CAMD approach is successfully applied to the design of an ORC using detailed heat transfer correlations for the sizing of the heat exchangers. We identify the working fluids which maximize the net present value of the process. We show that a thermodynamic design results in an operating point with low net present value emphasizing the importance of a thermo-economic design.
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Acknowledgements We thank the Deutsche Forschungsgemeinschaft for funding this work (BA2884/4-1).
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