Process integration and superstructure optimization of Organic Rankine Cycles (ORCs) with heat exchanger network synthesis

Accepted Manuscript Title: Process Integration and Superstructure Optimization of Organic Rankine Cycles (ORCs) with Heat Exchanger Network Synthesis Author: Haoshui Yu John Eason Lorenz T. Biegler Xiao Feng PII: DOI: Reference:

S0098-1354(17)30212-0 http://dx.doi.org/doi:10.1016/j.compchemeng.2017.05.013 CACE 5815

To appear in:

Computers and Chemical Engineering

Received date: Revised date: Accepted date:

26-9-2016 14-5-2017 15-5-2017

Please cite this article as: Yu, H., Eason, J., Biegler, L. T., and Feng, X.,Process Integration and Superstructure Optimization of Organic Rankine Cycles (ORCs) with Heat Exchanger Network Synthesis, Computers and Chemical Engineering (2017), http://dx.doi.org/10.1016/j.compchemeng.2017.05.013 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Process Integration and Superstructure Optimization of Organic Rankine Cycles (ORCs) with Heat Exchanger Network Synthesis

State Key Laboratory of Heavy Oil Processing, New Energy Institute, China University of Petroleum, Beijing, 102249, China

Chemical Engineering Department, Carnegie Mellon University, Pittsburgh, PA 15213, United States School of Chemical Engineering & Technology, Xi'an Jiaotong University, Xi'an 710049, China

an

3

us

2

cr

1

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Haoshui Yu1, John Eason2, Lorenz T. Biegler∗2, Xiao Feng3

Abstract: Low and medium temperature energy utilization is one way to alleviate the energy crisis and

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environmental pollution problems. In the past decades, Organic Rankine Cycles (ORCs) have become a very promising technology for low and medium temperature energy utilization. When an ORC is used to recover waste heat in chemical plants, heat integration between the ORC and the process streams should be performed to save

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more utilities and generate more power. This study aims to integrate an ORC into a background process to generate

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maximum electricity without increasing the hot utility usage. We propose a two-step method to integrate an ORC to

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a background process, optimally considering the modifications of the ORC to increase the thermal efficiency and heat recovered by the working fluid simultaneously. The first step is to determine the configuration (turbine bleeding, regeneration, superheating) and operating conditions (working fluid flowrate, evaporation and condensation temperatures, turbine bleed ratio, degree of superheat, bleeding pressure). The second step is to synthesize the heat exchanger network by minimizing the number of heat exchangers that keep the hot utility unchanged. A well-studied example from the literature is solved to demonstrate the effectiveness of the proposed model for industrial waste heat recovery. The net power output in this paper is improved by 13% compared with the best known previous literature design for this system. The proposed method is also useful for quickly screening working fluids while considering integration potential. Screening of several working fluids revealed that using R601 (n-pentane) in place of the original working fluid (n-hexane) can increase the power output of the example system by an additional 14%.

∗

Corresponding author: [email protected]

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Key words: Organic Rankine cycle, optimization, process integration, Duran-Grossmann model, heat exchanger network synthesis

1. Introduction

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The Organic Rankine Cycle (ORC) is a promising technology to convert low temperature heat into electricity. An ORC is a simple Rankine cycle similar to the steam Rankine cycle used in

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conventional power plants, but an ORC uses organic compounds instead of water in order to achieve a better efficiency at low temperature levels. Therefore, an ORC can convert medium or

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low temperature heat into power efficiently with a proper working fluid (Yu et al., 2015). The basic organic Rankine cycle consists of only four components, namely the evaporator, turbine, condenser, and pump. Fig.1 shows both the process equipment configuration and the

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corresponding thermodynamic process in a T-S diagram. In the evaporator, there are three sections, namely I-preheating (2-3), II-evaporating (3-4) and III-superheating (4-5). When using

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a dry working fluid, superheating does not significantly increase the thermal efficiency of the ORC but leads to larger heat transfer area (Mago et al., 2008). However, if superheating results

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in more heat recovered due to a better match between organic working fluid and waste heat temperatures, superheating may be favored in order to increase the power output. Other

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modifications such as turbine bleeding and regeneration, which increase the thermal efficiency,

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are considered in this paper and will be discussed in detail later. Turbine

6

T

Heat source

5 4

3

5

III

4

Evaporator

II

7

Cooling water

6

2

3

Condenser

I

2

1

7

1

S

Pump

Fig. 1 The flowsheet and T-S diagram of a basic ORC

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ORCs are widely used to generate power from solar energy (Freeman et al., 2015; Pei et al., 2010; Wang et al., 2010), geothermal energy (Fu et al., 2013; Liu et al., 2015; Walraven et al., 2015), engine waste heat recovery (Saidur et al., 2012; Vaja & Gambarotta, 2010; Wang et al., 2012), biomass energy (Al-Sulaiman et al., 2011; Drescher & Brüggemann, 2007), and industrial

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waste heat (Chen et al., 2016; Kotowicz et al., 2015; Vatani et al., 2013; Yu et al., 2016a). However, waste heat recovery in the process industry, e.g. from chemical plants or refineries,

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differs from other application areas because multiple waste heat sources usually need to be recovered. So the integration between an ORC and process streams should be considered while

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designing an ORC system.

Process integration technology considers the system as a whole and includes two branches,

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namely pinch technology and mathematical programming. Pinch technology has the advantage of intuitiveness, simplicity and clarity (Liu et al., 2014). Most of the previous work (Desai & Bandyopadhyay, 2009; Guo et al., 2014) used pinch technology to integrate the ORC to the

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system. However, this method has difficulty with many degrees of freedom, as when process design is considered simultaneously with heat integration. To get satisfactory results, the

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integration based on pinch technology should be performed under various operating conditions. On the other hand, mathematical programming can automate this process with many degrees of

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freedom of the system (Klemeš & Kravanja, 2013). In this paper, we will combine concepts from

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pinch technology and mathematical programming. Pinch technology can tell us the potential for integration and suggest possible process modifications to get better integration. Then we can formulate a corresponding mathematical model to get an accurate optimal solution. The optimal solution can then be analyzed from a pinch technology perspective, in order to understand the physical meaning of the results and to confirm the quality of the solution. Desai and Bandyopadhyay (2009) proposed a method based on pinch technology to optimally customize an ORC into a chemical process to recover surplus waste heat. This is a very early (and highly cited) paper, focusing on the integration of an ORC with a background process. As this method is based on pinch technology, the operating conditions of the ORC cannot be optimized automatically. They integrate the ORC under various sample conditions into the background process and then determine the optimal configuration of the ORC based on the comparison of different operating conditions. The grand composite curve (GCC) is used as a tool to determine the maximum working fluid flowrate, while integrating an ORC into the heat

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surplus zone. The heat exchanger network is derived via heuristic rules. This method cannot consider many degrees of freedom simultaneously and relies on manual trial-and-error optimization. However, the results may be far away from the optimal solution. Based on their work, Chen et al. (2014) proposed a new method based on mathematical programming to

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simultaneously optimize the ORC and synthesize the heat exchanger network. This method consists of two steps. In the first step, they use a stage-wise superstructure to synthesize the heat

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exchanger network above the pinch point, which minimizes the external utility consumption. In the second step, an ORC is incorporated below the pinch point to maximize the power output.

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However, turbine bleeding, regeneration, and superheating are not considered in their model. They also optimized their model under various operating conditions, since a rigorous

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thermodynamic model of the ORC is not incorporated in their model. Yu et al. (2016a) proposed to use hot water as an intermediate to recover multiple waste heat streams and integrated an ORC into a background process based on pinch technology. None of these studies considered other

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configurations (e.g., with a superstructure including turbine bleeding, regeneration and superheating) along with simultaneously considering a rigorous thermodynamic model. Thus

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their studies rely on improvements by trial-and-error.

To maximize the net power output for a given system, one may: (1) increase the thermal

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efficiency of ORC, which generally means higher evaporating temperature, and (2) increase the

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amount of waste heat recovered, which generally means tighter integration of the organic working fluid with process streams. However, in most cases, these two goals are conflicting. The pinch design method cannot handle this trade off problem very well, so in this work we propose a mathematical programming model to optimally integrate an ORC into a background process, maximizing the net power output of the ORC. In this study, we propose a new two-step method to integrate and optimize an ORC into a background process. This method incorporates rigorous thermodynamic models, a superstructure considering many modifications of the basic ORC (turbine bleeding, regeneration and superheating), the Duran-Grossmann model (Duran & Grossmann, 1986) to determine the operating conditions (mass flowrate, evaporating temperature, condensation temperature, bleeding ratio if bleeding is favored, degree of superheating if superheating is favored) of the ORC while performing heat integration, and an expanded transshipment model (Papoulias & Grossmann, 1983) to derive the heat exchanger network involving the ORC. In the first step, the

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configuration and operating conditions of the ORC are determined. Once these key variables are determined, the heat exchanger network can be derived from the expanded transshipment model (Papoulias & Grossmann, 1983) in the second step. The next section presents the problem statement for the design and integration of ORCs. The

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third section provides a detailed optimization formulation and solution strategy. A comprehensive case study is presented in the fourth section to demonstrate our approach. The

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last section concludes the paper along with directions for future work.

2. Problem statement

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Starting from the basic ORC design, several modifications are introduced to improve the thermal efficiency. As the outlet stream of the turbine lies in the superheated region, the temperature of

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the organic working fluid is higher than the temperature of the stream at the outlet of the pump. The outlet stream of the turbine can be used to heat the outlet stream of the pump. So a

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regenerator can be added using the basic ORC to increase the thermal efficiency of the ORC. To increase the thermal efficiency of an ORC further, turbine bleeding is proposed by Desai and Bandyopadhyay (2009). Turbine bleeding refers to extracting a portion of the working fluid at an

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intermediate pressure from the turbine. Then this high pressure and temperature stream mixes

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with the low pressure and temperature organic working fluid. As the temperature of the working fluid at the inlet of the evaporator is increased, the thermal efficiency is increased via turbine

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bleeding. The flowsheet and T-S diagram of an ORC with regeneration and turbine bleeding are shown in Fig. 2.

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Turbine 8

T

6

Heat source

7

6

3

Mixer 2

4 1

3

Pump II

Regenerator

5 4 3

9

2

8

9

Cooling water

1

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Condenser

1

2 Pump I

7

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5

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Evaporator

S

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Fig. 2 ORC incorporating turbine bleeding and regenerator proposed by Desai and Bandyopadhyay (2009)

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As shown in Fig. 2, state point 4 should be a saturated liquid, so the turbine bleeding may be fully specified by the pressure at this point. Turbine bleeding can increase the thermal efficiency

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of the ORC system, but the non-isothermal mixing in the mixer may lead to significant exergy

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loss and reduced opportunities for integration with the process streams. Regeneration assumes that heat exchange will occur between the superheated stream (8-9) and the subcooled stream (2-

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3) as shown in Fig. 2. By relaxing this assumption and allowing these heat exchange tasks to integrate elsewhere, a more tightly integrated system may be found with a larger power output. Although regeneration and turbine bleeding can increase the thermal efficiency of a standalone ORC, the aim is to maximize the net power output instead of maximizing the thermal efficiency. Desai and Bandyopadhyay found that when the process waste heat streams must be cooled to ambient temperature, regeneration leads to the rejection of more heat by the process to the cold utility compared with the basic cycle and the net power output remains the same (Desai & Bandyopadhyay, 2009). So the configuration of the ORC depends on the background process. Turbine bleeding extracts a new hot stream from the turbine, which normally mixes with the condensed working fluid. However, we could instead allow this extracted stream to Integrate With Cold Streams (IWCS) in the process. Thus the turbine bleeding becomes more flexible because it is not necessary to enforce a saturated state like the state point 4 in Fig. 2. The superheated working fluid at the outlet of turbine does not necessarily preheat the ORC stream

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(from state point 2-3), instead it could also Integrate With Cold Streams (IWCS). The high pressure working fluid can also Integrate With Hot Streams (IWHS), either before or after mixing with the turbine bleed stream. Thus, the streams of the ORC can be modeled as process streams for the purpose of heat integration. This ORC configuration has more degrees of

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freedom, which may result in better integration opportunities and higher net power output. Considering all the above opportunities to fully integrate the ORC with the background process,

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a superstructure of an ORC that considers turbine bleeding, regeneration and superheating is proposed in this paper as shown in Fig. 3. Compared to the ORC shown in Fig. 2, the

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superstructure of an ORC in Fig. 3 shows more flexibility and integration opportunities, which

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may lead to more net power output.

Fig. 3 Proposed ORC Superstructure

The problems to be solved in this paper can be stated as follows. Consider the set I = {i 1,..., I } of hot process streams to be cooled from their supply temperatures to target temperatures, and a set J = { j 1,..., J } of cold process streams to be heated to their target temperatures. The heat capacity

flowrates of both hot process streams and cold process steams are given. There is abundant waste heat below the pinch of the process, which is recovered by an ORC to generate power. The

Page 7 of 35

objective is to maximize the net power output of the system without increasing the hot utility consumption, and to derive a heat exchanger network configuration involving the ORC. To maximize the power output, many configurations such as turbine bleeding, regeneration and superheating are considered simultaneously in this paper. To fully integrate an ORC with process

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streams, the mass flowrate of the organic working fluid, configuration and operating conditions of the ORC are free variables. The streams of the ORC can be regarded as process streams for

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the sake of performing the heat integration between the ORC and process streams. As the configuration and operating conditions of the ORC are variables, classical pinch technology

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cannot deal with this kind of heat integration problem other than by trial and error adjustment of operating conditions, as in previous work (Chen et al., 2014; Desai & Bandyopadhyay, 2009).

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This problem is broken into two sub-problems. The first problem seeks the flowrate of working fluid, the bleeding pressure and bleeding ratio (if turbine bleeding is favored), degree of superheating (if superheating is favored) and the other operating conditions of the ORC. Once

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the organic working fluid flowrate and operating conditions of the ORC are determined, the

3. Model formulation

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second problem considers the design of the heat exchanger network.

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The ORC system analyzed in this work is represented by the flowsheet in Fig. 3. When the ORC is integrated with the process streams, the configuration and operating conditions should be

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determined. To optimally customize an ORC into a background process, a two-stage method is proposed in this paper. In the first stage, heat integration of the ORC with process streams and optimization of the ORC is performed simultaneously. The objective is to determine the configuration and operating conditions of an ORC with maximum net power output. In the second stage, a heat exchanger network can be synthesized via the expanded transshipment model (Papoulias & Grossmann, 1983). In this stage, the ORC related streams are regarded as process streams and some ORC streams are divided into several streams to accommodate isothermal phase transition. The objective of the expanded transshipment model is to minimize the number of matches between streams without increasing the consumption of hot utility. Based on the results from the expanded transshipment model, the heat exchanger network can then be derived.

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3.1 Model to determine the ORC configuration and operating conditions In the first stage, the purpose is to determine the optimal configuration and operating conditions featuring maximum net power output. Decisions related to configuration are whether turbine bleeding and superheating can be adopted for a specific background process. The decision

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variables related to the operating conditions are evaporation temperature, degree of superheat, molar flowrate of working fluids, turbine bleeding pressure, turbine bleeding ratio, and

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condensation temperature. A rigorous thermodynamic model to calculate the thermodynamic properties of ORC at each state point should be used. Additionally, a model for heat integration

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that deals with variable stream parameters is necessary. 3.1.1 Rigorous thermodynamic model of ORC

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To overcome the limitations of pinch technology while integrating a variable ORC into a background system, Chen et al. (2014) proposed a two-stage mathematical model. However,

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rigorous thermodynamic models were not incorporated, superheating was not considered in their model, and operating conditions were determined by trial and error. To determine the optimal solution, a rigorous thermodynamic model must be incorporated in the ORC model. To facilitate

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the formulation of the model, the state point set SP = {1, 2,3,...11} is defined to refer to the

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thermodynamic state at different points in the cycle, shown in Fig. 4. There are eleven state points in the ORC system proposed in this paper. However, state points 4 and 5 may coincide if

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non-superheating is preferable, and the turbine bleeding steam (from 8 to 3) may not exist if turbine bleeding cannot increase the net power output. The state point set SP = {1, 2,3,...11} can be classified into two subsets, namely liquid state points LSP = {1,2,3,10,11} and gas state points

GSP = {4,5,6,7,8,9} . The Peng-Robinson (PR) equation of state is used for thermodynamic properties.

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Fig. 4 T-S diagram of an ORC with superstructure

equation is as follows:

∀sp ∈ SP

(1)

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Z 3 + (B −1)Z 2 + ( A − 2B − 3B2 )Z + (B3 + B2 − AB) = 0

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Detailed information about the PR equation can be found in the Appendix. The form of the PR

where Z is the compressibility factor, and A and B are parameters related to critical properties

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and temperature and pressure of the substance. As the PR equation is a cubic equation, there are

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up to three real roots for the equation. Kamath et al. (2010) proposed an equation-based strategy to map roots to phases for cubic equations of state. The liquid root corresponds to the smallest

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real root and the vapor root corresponds to the largest one. The first derivative with respect to Z must be positive to avoid the nonphysical middle root. The sign of the second derivative may be used to determine the phase. A nonnegative second derivative denotes the vapor phase, and a non-positive second derivative denotes the liquid phase. The following three equations use the first derivative to exclude the middle root of the cubic equation, and use the second derivative to specify the corresponding phase of the root.

f ' ( Z sp ) = 3Z sp 2 + 2( B − 1) Z sp + ( A − 2 B − 3B 2 ) ≥ 0 ∀sp ∈ SP

(2)

f '' (Z sp ) = 6Zsp + 2( B − 1) ≥ 0

∀sp ∈ GSP (vapor phase root)

(3)

f '' ( Z sp ) = 6 Z sp + 2( B − 1) ≤ 0 ∀sp ∈ LSP (liquid phase root)

(4)

Embedding these three inequality constraints into the optimization model (see P1 below) allows the precise root of each state point to be calculated with the temperature and pressure at the corresponding state.

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Once the correct root of the PR equation is identified, the necessary thermodynamic properties can be calculated using explicit analytical expressions for departure functions (Reid et al., 1987). The following equations are used to calculate the thermodynamic properties: H − H id = H ex

S − Sid = S ex C5T05 H = ∫ C dT = ((T / T0 )5 − 1) + ... + C1T0 (T / T0 − 1) T0 5 id

T

id P

V R CVid C5T0 4 S =∫ dT + ∫ dV = ((T / T0 ) 4 − 1) + ... + C1 ln(T / T0 ) T0 T V0 V 4 T

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id

cr

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(5)

0.45724 R 2T S (T , P ) = R ln(( Z − B ) P0 / P ) − 2 2b P

Tc κ ln(( Z + 2.414 B ) / ( Z − 0.414 B ))) PcT

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ex

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H ex = RTC ((T / TC )( Z − 1) − 2.078(1 + κ )α 0.5 ln(( Z + 2.414 B ) / ( Z − 0.414 B )))

CPid = C1 + C2T + C3T 2 + C4T 3 + C5T 4

(6) (7) (8) (9) (10) (11)

C1-C5 are species-related constants for the ideal gas heat capacity calculation.

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The relationship between vapor pressure and evaporation temperature is given by the Antoine

C2 T + C3

(12)

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ln P = C1 +

te

equation:

where C1-C3 are the Antoine constants for the working fluid. The enthalpy should be calculated for each state point, and the entropy should be calculated just for the state points related to the turbine. As long as the thermodynamic properties of the working fluid can be calculated via the PR equation, the equation-based model of the ORC system can be built as follows.

• Pump of organic working fluid

There are two organic working fluid pumps in the proposed superstructure of the ORC system. The pump work can be calculated via the following equations: W pump I =

M ⋅ m LP

ρ

( P2 − P1 )

(13)

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W pump II =

M ⋅ m HP

ρ

( P11 − P10 )

(14)

where M is the molecular weight of the organic working fluid, mLP and m HP are the molar

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flowrates of the working fluid at low and high pressure levels, respectively, and ρ is the density of the working fluid. • Turbine

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The turbine is modeled with a fixed isentropic efficiency. To use this model in an equation oriented environment, we introduce shadow (i.e., hypothetical) state points at the turbine outlets

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to represent isentropic expansion. Fig. 5 illustrates the shadow streams and real streams of a turbine to incorporate turbine bleeding. The entropy of the shadow streams is set to the inlet

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entropy using Eqs. (15) and (16), and the pressure is set to match the true outlet pressure using Eqs. (17) and (18). With these two degrees of freedom specified, the enthalpy of the shadow

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stream is also implicitly specified by the thermodynamic model above. The isentropic efficiency Eqs. (19) and (20) therefore provide the enthalpy of the exit stream, which in turn gives the work

S5 = S8, shadow

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P6, shadow = P6

te

S5 = S6, shadow

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output using Eqs. (21) and (22).

(15) (16) (17)

P8,shadow = P8

(18)

H 6 − H 5 = ηis ⋅ ( H 6, shadow − H 5 )

(19)

H 8 − H 5 = ηis ⋅ ( H 8, shadow − H 5 )

(20)

Wtur ,ble = m ⋅ ( H 8 − H 5 )

(21)

Wtur ,con = m ⋅ ( H 6 − H 5 )

(22)

The net power output of the ORC system is shown as follows: Wnet = Wtur ,ble + Wtur , con − W pump I − W pump II

(23)

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Fig. 5 Shadow streams and real streams of a turbine with turbine bleeding

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• Degree of superheating constraint

Since an overly large degree of superheating may increase the capital cost for heat exchangers,

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the degree of superheating should lie within a reasonable range. In this paper, the degree of superheating is set as less than 20 °C.

(24)

M

T5 − T4 ≤ 20

The evaporator(s) and condenser(s) in the ORC can be regarded as heat exchangers, but the matches of heat exchangers are unknown. We allow for possible nonconventional matches; for

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example, the turbine bleed stream can integrate with cold process streams. Only the enthalpy at

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each state point of the ORC needs to be calculated via the cubic equation of state. The optimization will automatically take the working fluid flowrate to the maximum allowable value

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to increase work output (until the pinch point(s) prevent further progress). The duty of the evaporator(s) and condenser(s) will depend on the heat integration with process streams.

3.1.2 Duran-Grossmann model to determine ORC operating conditions Heat integration of process streams to minimize the consumption of utility has been widely researched in the past decades. Pinch technology is one of the most important tools for heat integration (Linhoff et al., 1982). The transportation model (Cerda et al., 1983) and transshipment model (Papoulias & Grossmann, 1983) are also effective for heat integration to determine the minimum hot utility and cold utility. However, an important limitation of these methods is that the flowrates and temperatures of streams must be fixed due to the requirement of temperature intervals. The Duran-Grossmann model (Duran & Grossmann, 1986) provides a powerful alternative method to solve the problem considering process optimization and heat integration simultaneously.

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The pinch-based Duran-Grossmann model needs information about the heat capacity of every stream involved in the heat integration. However, when the streams undergo an isothermal phase transition, the model will encounter numerical problems in dealing with the infinite heat capacity flowrate of the stream. For ORC streams involving phase change, we decompose the streams into

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separate sub-streams for liquid, two-phase, and vapor as appropriate. These sub-streams are separately considered for the heat integration with corresponding inlet and outlet temperatures

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and associated heat loads. Based on the T-S diagram of the superstructure of an ORC shown in Fig. 4, the streams in an ORC can be decomposed into the sub-streams listed in Table 1. These

Table 1. Decomposed streams in the ORC State points

Inlet temperature

ORCC1

2→3

T2

ORCC2

3→4

T3

ORCC3

4→5

T4

ORCC4

11→3

ORCH1

6→7

ORCH2

7→1

ORCH3

8→9

ORCH4

9→10

Heat load m(H3-H2)

T4

m(H4-H3)

T5

m(H5-H4)

T11

T3

m(H3-H11)

T6

T7

m(H6-H7)

T7

T1

m(H7-H1)

T8

T9

m(H8-H9)

T9

T10

m(H9-H10)

M

T3

d

te

Outlet temperature

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Stream

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sub-streams make it easier to represent the heat capacities for use in the Duran-Grossmann model.

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The heat load of each ORC sub-stream can be calculated with the enthalpy difference of the starting state point and ending state point of the corresponding ORC stream. Then the heat capacity flowrate can be obtained as long as the temperature change and the heat load are known. Note that for the isothermal phase change streams ORCC2, ORCH2 and ORCH4, the temperature changes are assumed to be 0.1°C to avoid infinite heat capacity flowrate. Once the inlet and outlet temperatures and heat capacity flowrates of the working fluid are initialized, the Duran-Grossmann model can be applied to the heat integration of process streams and ORC streams. The set of hot streams from the ORC is defined as ORCI = {ORCH1,...ORCH 4} and the set of cold streams from the ORC is defined as ORCJ = {ORCC1,...ORCC 4} . In the DuranGrossmann model, the inlet temperatures of streams are considered as pinch candidates. The set of pinch candidates is defined as PC = {Ts,in s ∈ I ∪ J ∪ ORCI ∪ ORCJ } .

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The criterion to determine the correct pinch among all the pinch candidates is to select the one that guarantees the feasible heat transfer between hot and cold streams (Duran & Grossmann, 1986). For each pinch candidate, the heat load of cold streams and hot streams above pinch can be calculated, and then the hot utility can be calculated by the heat loads of cold streams and hot

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streams above each pinch candidate. Then the one with the largest hot utility load among the candidate set corresponds to the correct pinch point.

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The heat content of one stream above each pinch candidate depends on whether the stream is entirely above the pinch candidate, whether it crosses the pinch, or whether it is entirely below

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the pinch (Biegler et al., 1997). To incorporate all three cases in one explicit algebraic equation and facilitate the modeling, the following equations for cold stream and hot stream are derived.

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The heat load of hot streams (QSOA) and the heat load of cold streams above the pinch candidates (QSIA) are calculated by the following two equations:

∑

FCpi max {0, Ti in − T p } − max {0, Ti out − T p } ∀p ∈ PC

(25)

∑

FCp j  max {0, T jout − (T p − ∆T )} − max {0, T jin − (T p − ∆T )} ∀p ∈ PC

(26)

i∈I UORCI

QSIA( x) p =

d

j∈J UORCJ

M

QSOA( x) p =

Y p ( x) = QSIA( x) p − QSOA( x) p ∀p ∈ PC

(27)

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te

The heat deficit for each pinch candidate is then expressed as follows:

(28)

The actual minimum hot utility is determined by the largest heating deficit of all the pinch candidates through the following inequality: Y p ( x ) ≤ QHU ∀p ∈ PC

Once the hot utility is determined, the cold utility can be derived from a heat balance as shown in Eqs. (29) and (30).

QCU = Ω( x) + QHU Ω( x) =

∑

i∈I U ORCI

FCpi (Ti in − Ti out ) −

(29)

∑

j∈ J U ORCJ

FCp j (T jout − T jin )

(30)

Because nonlinear programming (NLP) algorithms require derivative information for the constraints, the max operators in Eqs. (25) and (26) should be smoothed. In this paper, the max operator is smoothed by the following function (Balakrishna & Biegler, 1992):

Page 15 of 35

1 ( x + x2 + ε ) (31) 2 ε is a small constant, typically between 10-3 and 10-6. However, Dowling et al. (2015) have max {0, x} ≈

observed that with very small values for ε , CONOPT has a tendency to prematurely terminate at infeasible or non-optimal points if the initial points are far from an optimum. Therefore the

ip t

optimization model is solved by repeatedly shrinking ε by an order of magnitude, from 0.1 to 0.00001.

cr

With the above information built into this model, the optimal configuration (whether to

us

incorporate turbine bleeding and superheating) and operating conditions (evaporating and condensation temperature, degree of superheat, turbine bleed ratio) can be determined based on

an

the formulation to perform heat integration.

3.1.3 Objective function

M

The goal of the first stage model is to determine the configuration and operating conditions of the ORC featuring maximum net power output. However, if the objective is just to maximize the net power output, the objective may be unbounded, because the net power output can be infinity at

d

the cost of infinite hot utility. To keep the hot utility consumption the same as the original energy

te

target without incorporating an ORC, a penalty term for hot utility is incorporated into the objective function. The objective function is formulated to maximize the revenue from power

Ac ce p

output minus the hot utility cost, as shown in Problem P1. The price of electricity is taken as 0.1$/kWh and the annual operating time is 8000h/year, so the coefficient of the electricity term becomes 800$/(year·kW). The cost of hot utility is taken as 100$/(year·kW). As a result, the objective is essentially to maximize the net power output of the system. With all of this information compiled into the model, the optimal configuration (whether incorporating turbine bleeding and superheating) and operating conditions (evaporation and condensation temperature, degree of superheat) can be determined. Then the first step model can be expressed as problem P1 as follows: P1: max obj1 = 800Wnet − 100 HU s.t. Rigorous thermodynamic model Duran-Grossmann model

Eqs. (1)-(24) Eqs. (25)-(31)

Page 16 of 35

3.2 Model to determine the heat exchanger network structure Problem P1 can determine the optimal configuration and operating conditions of the ORC. But the actual heat exchanger network synthesis problem still remains. Heat exchanger network synthesis (HENS) has been extensively studied in the field of process systems engineering.

ip t

Methods for heat exchanger network synthesis can be broadly classified into two categories, pinch methods (Linnhoff & Hindmarsh, 1983) and mathematical programming (Cerda et al.,

cr

1983; Cerda & Westerberg, 1983). Both of these methods are widely used in process system design and retrofit, and minimizing the number of heat exchangers is a key step in the heat

us

exchanger network structure determination. Problem P1 tends to tightly integrate the ORC with the background process so that multiple pinch points occur. This behavior is clearly shown in the

an

case study below. To simplify the final heat exchanger network structure, minimization of the number of heat exchangers is selected as the objective function in this section. The MILP expanded transshipment model (Papoulias & Grossmann, 1983) is adopted to synthesize the heat

M

exchanger network due to its effectiveness on large and tight heat integration problems. Binary variables yijq are introduced to represent the existence of matches between hot stream i

d

and cold stream j. As the minimum hot utility has been determined via P1, the expanded

te

transshipment model that minimizes the matches between streams can be applied directly. If the hot utility and cold utility are regarded as hot and cold streams as well, the expanded

Ac ce p

transshipment model can be formulated as Problem P2. P 2 : min obj2 =

∑∑

yijq

∑Q

=QikH

i∈ H q j∈C q

s.t . Rik − Ri , k −1 +

j∈C k

ijk

∀i ∈ H

∑Q

=Q Cjk

∀j ∈ C

∑Q

≤ QijU yijq

∀j ∈ C ∀k ∈ K

j∈C k

k∈K

ijk

ijk

Rik , Qijk ≥ 0

∀k ∈ K

∀k ∈ K

yijq ∈ {0,1}

where K is the index set for all the temperature intervals; QikH and QCjk are the heat contents of hot stream i and cold stream j in temperature interval k; Rik is the heat residual of temperature interval k, Qijk is the heat exchanged between hot stream i and cold stream j in temperature interval k. QijU is the upper bound of heat exchanged between hot stream i and cold stream j.

Page 17 of 35

With the results of P2, the binary variables indicating the matches between hot stream and cold streams, and the corresponding heat loads are determined and they allow the heat exchanger network involving an ORC to be derived. In this study, we derive the final networks using guidelines from pinch technology (Linhoff et al., 1982).

to a background process, which has not been explored in previous works.

ip t

The two-stage method proposed in this paper considers the following factors to integrate an ORC

Rigorous thermodynamic properties are calculated via a cubic equation of state.

•

The superstructure of an ORC incorporates turbine bleeding, regeneration, and

cr

•

•

us

superheating.

An ORC can be fully integrated with the process streams to maximize the net power

•

an

output.

The Duran-Grossmann model is applied to optimize an ORC superstructure while considering heat integration simultaneously.

M

GAMS 24.1.3 (Brooke et al., 1988) is used to formulate the models. The NLP problem P1 was solved with CONOPT (Drud, 1994) as the solver. For the MILP problem P2, CPLEX/GAMS

d

(www.gams.com) is selected as the solver.

te

In the next section, our methodology is applied to a well-studied case in order to compare to previous work and to demonstrate the benefits of this methodology.

Ac ce p

4. Case study

To illustrate the effectiveness of the method proposed in this paper, a literature example adapted from the work of Desai and Bandyopadhyay (2009) and Chen et al. (2014) is solved via the method. The process stream data are listed in Table 2. There are 3 hot streams and 4 cold streams in this process.

Table 2. Process stream data for the case study Stream

Supply temperature(°C)

Target temperature(°C)

FCp (kW/°C)

Duty (kW)

H1 H2 H3 C1 C2 C3 C4

353 347 255 224 116 53 40

313 246 80 340 303 113 293

9.802 2.931 6.161 7.179 0.641 7.627 1.690

392.1 296.0 1078.2 832.8 119.8 457.6 427.6

Page 18 of 35

In order to use the same basis for comparison with previous studies, the assumptions adopted in Desai and Bandyopadhyay (2009) are used in this paper as follows. • The heat recovery approach temperature (HRAT) is 20 °C

ip t

• The working fluid is n-hexane • The turbine isentropic efficiency is 0.8

cr

• The minimum condensation temperature of ORC is 50 °C

The thermodynamic parameters of n-hexane used in the thermodynamic model are obtained from

us

Aspen Plus V8.8 (Aspen Plus, 2013).

When heat integration is performed for the process streams without considering the ORC, the

an

corresponding hot and cold utility targets are 244.1 kW and 172.6 kW with HRAT fixed at 20 °C. The pinch point corresponds to 244 °C for hot streams and 224 °C for cold streams. The results for P1 are listed in Table 3. A comparison with the results from the other two papers

M

is listed in Table 4.

As the work from Desai and Bandyopadhyay (2009) is based on pinch technology, their method

d

cannot handle many degrees of freedom well. The analysis based on pinch technology indicates

te

that turbine bleeding may be favored in this specific case because the GCC below the pinch has a pocket, as shown in Fig. 10. Based on the method of Desai and Bandyopadhyay (2009), we know

Ac ce p

that stretching the working fluid T-H curve into the pocket will increase the heat recovery. There are two ways to make the organic working fluid T-H curve stretch into the pocket, namely turbine bleeding and higher condensation temperature. As their method does not simultaneously optimize these degrees of freedom, a result is only obtained through trial and error (e.g., one parameter at a time). The reported results in their paper are listed in Table 4. The maximum power output design in their work does not incorporate turbine bleeding, but the condensation temperature is high, which makes the organic working fluid T-H curve extend into the pocket below the pinch point (see Fig. 10). The best design considering turbine bleeding is also listed in Table 4. The net power output is less than the design that considers increasing the condensation temperature only.

Table 3. The results for optimal solution of P1with n-hexane as the working fluid Variable

Optimal value

Variable

Optimal value

Page 19 of 35

hot utility (kW)

244.1

evaporation temperature (°C)

cold utility (kW)

117.7

degree of super heat (°C)

net power output (kW)

54.8

bleeding pressure (bar)

1.66

thermal efficiency (%) total working fluid molar flowrate (mol/s) bleeding working fluid molar flowrate (mol/s) pump I work consumption(kW)

14.8

157.6 85.4

0.165

bleeding stream temperature (°C) bleeding condensation temperature (°C) lower pressure condensation temperature (°C) lower condensation pressure(bar)

pump II work consumption (kW)

0.149

waste heat recovered (kW)

a

0.54 369.9

(Desai & Bandyopadhyay, 2009)

an

The design with turbine bleeding 244.1 131.5 41.1 196.5 na/50 not reported 0.54 219.7

d

M

The design with maximum power 244.1 129.8 42.7 224 80 0.67 337.7

(Chen et al., 2014) 244.1 124.3 48.28 180 77 0.77 394.48

This study 244.1 117.7 54.84 178.7 85.44/50a 0.49 20 0.53 369.9

te

hot utility (kW) cold utility (kW) net power output (kW) evaporation temperature(°C) condensation temperature(°C) turbine bleeding ratio degree of superheat(°C) working fluid flowrate (kg/s) waste heat recovered (kW)

us

Table 4. Comparison with previous work Items

50

cr

3.623

20

ip t

7.333

178.7

: turbine bleeding is adopted, so there are two condensation temperatures

Ac ce p

As shown in Table 4, all the results show the same hot utility, which is the basis of comparison among the three works. The same case is also studied by Hipólito-Valencia et al. (2013) using an economic objective function that considers the capital cost, operating cost and revenue from power. The power output is 98.22 kW at the cost of 297.13 kW hot utility consumption. So the results of that work are not listed in Table 4. Desai and Bandyopadhyay (2009) report a design with maximum net power output of 42.7 kW and a design considering turbine bleeding with net power output of 41.1 kW. In Chen et al.’s (2014) paper, the net power output is 48.28 kW. By using the method proposed in this paper, the maximum power output is improved to 54.84 kW. This gives an increase of 28% and 13% respectively compared with the work of Desai and Bandyopadhyay (2009) and Chen et al. (2014). These two papers do not consider turbine bleeding and superheating simultaneously in their methods. Our results suggest that turbine bleeding and superheating is favored for these specific process streams. Superheating is favored because the working fluid profile can more closely

Page 20 of 35

match the waste heat profile. This specific case study is relatively small (only one hot stream below pinch) and the integration opportunity is limited. However, optimization problem P1 can fully integrate the ORC into the background process and show a remarkable improvement on the power output. If this method is applied to a larger background process, the merits of this method

ip t

will be more obvious compared to the other two studies.

Once the configuration and operating conditions are determined by P1, all the streams in the

cr

system are known. The next step is to synthesize the heat exchanger network via P2. Based on the results from P1, the stream data including ORC sub-streams are listed in Table 5. Then P2

us

should be solved to synthesize the heat exchanger network involving an ORC. Based on the results of P2, we can derive a heat exchanger network as shown in Fig. 7. Compared with the

an

heat exchanger networks from Desai and Bandyopadhyay (2009) and Chen et al. (2014) as shown in Figs. 5 and 6, respectively, there are three heat exchangers between the hot stream and the organic working fluid. As there is only one hot stream below the original process pinch point

M

I, the working fluid has to exchange heat directly with H3. The three heat exchanger design

te

d

avoids non-isothermal mixing of working fluid.

Ac ce p

Table 5. Stream data including ORC sub-streams Stream

Supply temperature(°C)

Target temperature(°C)

FCp (kW/°C)

Duty (kW)

H1 H2 H3 C1 C2 C3 C4 ORCH1 ORCH2 ORCH3 ORCH4 ORCC1 ORCC2 ORCC3 ORCC4

353 347 255 224 116 53 40 136.6 50 157.6 85.4 50.6 178.6 178.7 85.6

313 246 80 340 303 113 293 50 49.9 85.4 85.3 178.6 178.7 198.6 178.6

9.802 2.931 6.161 7.179 0.641 7.627 1.690 0.631 1114 0.661 1013.6 0.88 1405.8 1.6 0.9

392.1 296 1078.2 832.8 119.8 457.6 427.6 54.6 111.4 47.7 101.3 112.6 140.5 32.9 83.7

Page 21 of 35

Fig. 6 is the heat exchanger network for the design with the maximum net power output reported by Desai and Bandyopadhyay (2009). In this design, the condensation temperature is 80 °C and the condensation stream of ORC is used to heat cold stream 3 and cold stream 4. The cooling

ip t

utility load is 129.8 kW. Fig. 7 is the heat exchanger network from the study of Chen et al. (2014). The condensation temperature is 77 °C and the cold utility load is reduced to 124.7 kW.

cr

Our results show a condensation temperature at 85.44 °C and the cold utility load at just 117.7 kW, with the condensation streams from turbine heating C3 and C4 in sequence. No regenerators

us

are needed between the outlet stream of the turbine and the outlet stream of the organic working fluid pump. This demonstrates that the superheated stream may not necessarily preheat the

an

organic working fluid. If the regenerators exist, the heat exchanger network would be much more complicated. The superstructure proposed in this paper as shown in Fig. 3 allows for more integration opportunities for the system. The heat exchanger network in Fig. 8 shows that the

M

turbine bleeding stream is completely used to heat cold process streams and no cooling water is needed for the turbine bleeding stream condensation. To avoid non-isothermal mixing, three

d

evaporators are needed in our case. It is clear that the system becomes tighter and more efficient in energy utilization. The results will be analyzed below through pinch technology to obtain

Ac ce p

te

more useful information on the ORC system design.

Page 22 of 35

M

an

us

cr

ip t

Fig. 6 The heat exchanger network and ORC configuration of Desai and Bandyopadhyay (2009)

Ac ce p

te

d

Fig. 7 The optimal heat exchanger network structure from Chen et al. (2014)

Fig. 8 Heat exchanger network based on expanded transshipment model in this study

Page 23 of 35

After the optimal results are obtained from the mathematical model, the results may be analyzed through pinch curves to gain more understanding of the physical meaning of the results. Fig. 9 contains the pinch curves of the original process streams and the optimized process streams including ORC streams. The integration of the ORC does not change anything above the original

ip t

process pinch (Pinch point I) as shown in Fig. 9, but it exerts great influence on the pinch curve below the pinch. Three more pinch points are formed below the original process pinch.

cr

Fig. 10 contains the GCC plots from our method and Desai and Bandyopadhyay (2009). In Fig. 10(b) there are three pinch points. The first pinch point is the original process pinch point, which

us

minimizes the hot utility requirement of the overall process. With the increase of flowrate of the working fluid, the second pinch point occurs at the evaporation temperature. Then the third pinch

an

point corresponds to the condensation stream of the ORC transferring heat to the cold streams. In their paper, they concluded that if all three pinch points exist simultaneously, the maximum shaft work output from ORC is achieved and net power output cannot be increased any further. Our

M

result, shown in the GCC plot in Fig. 10(a) has 4 pinch points. Pinch point I and pinch point II are the original process pinch point and the pinch point corresponding to the evaporation

d

temperature, respectively. Pinch point III is the pinch point formed between the turbine bleeding stream and the cold streams. Pinch point IV is the pinch point between the lower pressure turbine

te

outlet stream and cold stream 4. These four pinch points correspond to the process pinch point,

Ac ce p

the evaporation stream, the high pressure condenser, and low pressure condenser. From the pinch curve shown in Fig. 9, it is clear how each pinch point forms. Moreover, the pinch curves below pinch point I are closer compared to the original ones, since the ORC has transformed some of the surplus heat to power, and this indicates higher efficiency from an energy utilization perspective.

Page 24 of 35

ip t cr us

Ac ce p

(a)

te

d

M

an

Fig. 9 Pinch curves of original process and optimized process incorporating ORC streams

(b)

Fig. 10 (a) GCC based on our method and (b) GCC of the design with maximum power output from Desai and Bandyopadhyay (2009)

A key advantage of the presented method in this paper is the ability to quickly screen working fluids while considering process integration. Desai and Bandyopadhyay (2009) also tried changing the working fluid for the example process and found that benzene offered improved performance. The results of optimization problem P1 using benzene are listed in Table 6. The results are similar to the original working fluid n-hexane. However, the condensation pressure at 50 °C is obtained under vacuum conditions at only 0.361 bar, which is not desirable in practice. The power output increases to 57.4 kW compared to 54.8 kW with n-hexane, but considering the saturated vapor pressure of benzene is relatively low compared to other low critical temperature organic compounds, the vacuum operation seems to be an unavoidable problem. Therefore, benzene is not a good choice for this case study.

Page 25 of 35

Table 6. The results for optimal solution of P1 with benzene as the working fluid Variable

Optimal value

Variable

Optimal value

hot utility (kW)

244.1

evaporation temperature (°C)

cold utility (kW)

115.1

degree of superheat (°C)

net power output (kW)

57.4

bleeding pressure (bar)

thermal efficiency (%) total working fluid molar flowrate (mol/s) bleeding working fluid molar flowrate (mol/s) pump I work consumption (kW)

18.88

128.5 85.43

0.095

bleeding temperature (°C) bleeding condensation temperature (°C) lower pressure condensation temperature (°C) lower condensation pressure (bar)

pump II work consumption (kW)

0.086

waste heat recovered (kW)

304.1

ip t

20

cr

6.984

174.71

us

3.446

1.189

50 0.361

an

A previous study (Yu et al., 2015) found that a working fluid with a critical temperature slightly below the maximum possible evaporation temperature is likely to result in high power output,

M

because the close integration with waste heat profiles allows more heat to be extracted from the system. Since the pinch temperature corresponding to hot streams is 244 °C and the heat

d

recovery approach temperature is 20 °C, the maximum possible evaporation temperature of the ORC is 224 °C. The critical temperature of n-hexane is 234 °C, so we predict that a working

te

fluid whose critical temperature is lower than 224 °C may perform better. We selected R601 (npentane) with critical temperature 196.55 °C as an alternative working fluid to resolve the

Ac ce p

problem.

The results of solving P1 using n-pentane are listed in Table 7. It is clear that the net power output and the waste heat recovery increase significantly. The lower condensation temperature is 80 °C and the turbine bleeding condensation temperature is 108.4 °C. These high condensation temperatures allow more condensation heat to be used to heat the cold process streams, which in turn allows more heat from hot streams to be transferred to the organic working fluid. However, high condensation temperature does decrease thermal efficiency to 13.9%, but the higher recovery of waste heat and the tight integration of the system offsets this to provide higher power output. Detailed ORC sub-stream data under the optimal conditions with R601 as the working fluid is listed in Table 8. Based on the stream data, the corresponding heat exchanger network can be derived from the expanded transshipment model. Since the heat exchanger network is similar to the case with n-hexane, it is not presented here.

Page 26 of 35

This case study indicates that the trade-off between thermal efficiency and waste heat recovery can be exploited by the optimization tools used in this work. Moreover, the optimization formulation is robust enough to screen different working fluids. For the initial case, where nhexane is used as the working fluid, the power output is increased by 13.6% compared with the

ip t

best known published design for this system. If a new working fluid R601 (n-pentane) is used, the power output can be increased by 28.6% (to 62.1 kW) compared to the best known published

cr

result. As R601 (n-pentane) has a more appropriate critical temperature for the waste heat temperatures in this case study, R601 performs better. This result reinforces the importance of

us

considering the working fluid selection when integrating an ORC to a background process. Table 7. The results for optimal solution of P1 with R601 (n-pentane) as the working fluid Optimal value

Variable

Optimal value

an

Variable

244.1

evaporation temperature (°C)

195.3

cold utility (kW)

108.3

degree of superheat (°C)

20.0

net power output (kW)

62.1

bleeding pressure (bar)

7.12

thermal efficiency (%) total working fluid molar flowrate (mol/s) bleeding working fluid molar flowrate (mol/s) pump I work consumption (kW)

13.9

bleeding temperature (°C) bleeding condensation temperature (°C) lower pressure condensation temperature (°C) lower condensation pressure (bar)

165.7 108.4

waste heat recovered (kW)

446.3

11.8

M

hot utility (kW)

d

3.37

te

0.31

Ac ce p

pump II work consumption (kW)

0.274

80 3.68

Table 8. Stream data including ORC sub-streams with R601 as the working fluid Stream

Supply temperature(°C)

Target temperature(°C)

FCp (kW/°C)

Duty (kW)

H1 H2 H3 C1 C2 C3 C4

353 347 255 224 116 53 40

313 246 80 340 303 113 293

9.802 2.931 6.161 7.179 0.641 7.627 1.690

392.1 296 1078.2 832.8 119.8 457.6 427.6

Page 27 of 35

80 79.9 108.4 108.3 195.3 195.4 215.3 195.3

1.284 1954.576 0.550 704.214 2.209 297.729 4.033 0.957

84.6 195.5 31.5 70.42 253.3 29.8 80.26 82.95

ip t

145.9 80 165.68 108.4 80.2 195.3 195.4 108.6

cr

ORCH1 ORCH2 ORCH3 ORCH4 ORCC1 ORCC2 ORCC3 ORCC4

5. Conclusions

us

We propose a novel two-stage methodology to optimally integrate an ORC into a background process. A superstructure of an ORC system with many possible configurations, including

an

regeneration, turbine bleeding and superheating, is formulated to fully integrate the ORC into the background process. Compared with previous work, the superstructure of an ORC leads to a significant improvement on the configuration of an ORC, which may result in better integration

M

with the process. Moreover, this method incorporates rigorous thermodynamic and heat integration models and optimizes the system automatically under various operating conditions,

d

instead of by trial and error. In the first stage, an NLP is solved to determine the configuration and operating conditions of the ORC with heat integration. In the second stage, an expanded

te

MILP transshipment model is solved to synthesize the heat exchanger network. The method is

Ac ce p

robust enough to determine the optimal configuration and integration opportunities of the system. The effectiveness of this method is verified through a well-studied case. The net power output shows significant increases over recent case studies. For this case study, turbine bleeding and superheating are adopted because they can lead to better integration of the ORC streams with the process streams. The results show that four pinches are developed simultaneously. The hot composite curve and the cold composite curve are much closer, which indicates more effective heat integration. Even though the composite curves are very tight and there are four pinch points, the expanded transshipment model can help us to derive the final heat exchanger networks. The method also has the advantage of easily screening different working fluids. A new working fluid, R601 (n-pentane), is applied to this case study, substantially increasing power output. R601 is more suitable for this background process. Rigorous thermodynamic equations in the model make it possible to automatically optimize ORC conditions, so our proposed method avoids

Page 28 of 35

having to determine the ORC conditions by trial and error. This method is especially suitable for customizing an ORC into a large background process to fully explore the integration opportunity. Finally, while we do not consider capital cost in this study, our optimization model can be extended directly to deal with additional costs related to network piping, as well as composite

ip t

curves with variable approach temperatures that trade off recovered energy with equipment costs. Such an approach can be found in Yu et al. (2017), which performs a techno-economic

cr

optimization of ORCs, and optimizes pipe costing models, heat recovery approach temperature (HRAT), utility loads of the background process, and ORC operating conditions simultaneously.

us

Appendix.

an

Peng-Robinson equation The Peng-Robinson equation of state is used in this paper.

RT a − 2 V − b (V + 2bV − b2 )

M

P=

where

d

RTc Pc

Ac ce p

b = 0.0778

( RTc )2 α Pc

te

a = 0.45724

α = 1 + κ (1 − (T / Tc )0.5 ) 

2

κ = 0.37464 +1.54226ω − 0.26992ω2

Tc and Pc are the critical pressure and temperature and ω is the acentric factor. Using the compressibility factor Z = PV / RT , the Peng-Robinson equation can be written in the following form:

Z 3 + ( B − 1) Z 2 + ( A − 2 B − 3 B 2 ) Z + ( B 3 + B 2 − AB ) = 0 where

A=

aP

( RT )

2

and B =

bP RT

The enthalpy and entropy can be calculated via departure functions as in Eqs. (5)-(10).

Page 29 of 35

Acknowledgements Financial support from the National Natural Science Foundation of China under Grant No. 21576286, SINOPEC under Grant No.313109 and China Scholarship Council are gratefully

ip t

acknowledged.

Nomenclature cold utility

FCp

heat capacity flowrate

GCC

grand composite curve

GSP

gas state point set

H

enthalpy

I

the set of hot process streams

i

hot process streams

i’

hot ORC sub-streams

HRAT

heat recovery approach temperature

HU

hot utility

IWCS

Integrate With Cold Streams

IWHS

Integrate With Hot Streams

J

the set of cold streams

j

cold streams

K

temperature interval set

LSP M

us

an

M

d

te

Ac ce p

k

cr

CU

temperature intervals in the back ground heat exchanger network

liquid state point set molecular weight

MILP

mixed integer linear programming

m

molar flowrate

NLP

nonlinear programming

ORC

organic Rankine cycle

ORCC

cold streams from organic Rankine cycle

ORCH

hot streams from organic Rankine cycle

ORCI

the set of hot streams of organic Rankine cycle

ORCJ

the set of cold streams of organic Rankine cycle

P

pressure

Page 30 of 35

PC

pinch candidate set

PR

Peng-Robinson

Qijk

the heat exchanged between hot stream i and cold stream j in temperature interval k the upper bound of heat exchanged between hot stream i and cold stream j

QikC

the heat content of hot stream j in temperature interval k

QikH

the heat content of hot stream i in temperature interval k

QSOA

heat load of hot streams above the pinch candidates

QSIA

heat load of cold streams above the pinch candidates

Rik

the heat residual of temperature interval k

S

entropy

s

stream in the Duran-Grossman Model for heat integration

SP

state point set of ORC

sp

state point of ORC

T

temperature

Y

heat deficit

Z

compressibility factor

∆T

minimum heat transfer approach temperature

con HP LP tur

us

an

M

d

te

bleeding

Ac ce p

Subscripts ble

cr

ip t

QijU

condenser

high pressure low pressure turbine

Superscripts ex

excess

id

ideal state

p

pinch candidate

References Al-Sulaiman FA., Hamdullahpur F., Dincer I. Greenhouse gas emission and exergy assessments of an integrated organic Rankine cycle with a biomass combustor for combined cooling, heating and power production. Applied Thermal Engineering 2011; 31: 439-446.

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Aspen Plus, Version 8.8. 2013. Cambridge: Aspen Technology, 2013 http://www.aspentech.com Balakrishna S., Biegler LT. Targeting strategies for the synthesis and energy integration of nonisothermal reactor networks. Industrial & Engineering Chemistry Research 1992; 31: 2152-64.

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Biegler LT., Grossmann IE., Westerberg AW. Systematic methods for chemical process design. Upper Saddle River, NJ, USA: Prentice-Hall;1997. Brooke A., Kendrick D., Meeraus A., Raman R. GAMS - A User's Guide 1988, Washington DC http://www.gams.com

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Cerda J., Westerberg AW., Mason D., Linnhoff B. Minimum utility usage in heat exchanger network synthesis A transportation problem. Chemical Engineering Science 1983; 38: 373-87.

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Cerda J., Westerberg AW. Synthesizing heat exchanger networks having restricted stream/stream matches using transportation problem formulations. Chemical Engineering Science 1983; 38: 1723-40.

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Chen CL., Chang FY., Chao TH., Chen HC., Lee JY. Heat-exchanger network synthesis involving Organic Rankine Cycle for waste heat recovery. Industrial & Engineering Chemistry Research 2014; 53: 16924-36.

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Chen CL., Li PY., Le SNT. Organic Rankine cycle for waste heat recovery in a refinery. Industrial & Engineering Chemistry Research 2016; 55(12): 3262-75.

d

Chen Y., Grossmann IE., Miller DC. Computational strategies for large-scale MILP transshipment models for heat exchanger network synthesis. Computers & Chemical Engineering 2015; 82: 68-83.

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- Organic Rankine Cycles (ORCs) generate power from waste heat in chemical processes. - We develop a novel synthesis and integration strategy based on Duran-Grossmann (DG).

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- Superstructure optimization includes detailed thermodynamics within DG approach.

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- Compared to previous studies, significant increases in generated power are shown.

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