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Simultaneous heat integration and techno-economic optimization of Organic Rankine Cycle (ORC) for multiple waste heat stream recovery Haoshui Yu a, John Eason b, Lorenz T. Biegler b, *, Xiao Feng c a

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 c School of Chemical Engineering & Technology, Xi'an Jiaotong University, Xi'an, 710049, China b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 6 August 2016 Received in revised form 2 December 2016 Accepted 16 December 2016

In the past decades, the Organic Rankine Cycle (ORC) has become a promising technology for low and medium temperature energy utilization. In reﬁneries, there are usually multiple waste heat streams to be recovered. From a safety and controllability perspective, using an intermedium (hot water) to recover waste heat before releasing heat to the ORC system is more favorable than direct integration. The mass ﬂowrate of the intermediate hot water stream determines the amount of waste heat recovered and the ﬁnal hot water temperature affects the thermal efﬁciency of ORC. Both, in turn, exert great inﬂuence on the power output. Therefore, the hot water mass ﬂowrate is a critical decision variable for the optimal design of the system. This study develops a model for techno-economic optimization of an ORC with simultaneous heat recovery and capital cost optimization. The ORC is modeled using rigorous thermodynamics with the concept of state points. The task of waste heat recovery using the hot water intermedium is modeled using the Duran-Grossmann model for simultaneous heat integration and process optimization. The combined model determines the optimal design of an ORC that recovers multiple waste heat streams in a large scale background process using an intermediate heat transfer stream. In particular, the model determines the optimal heat recovery approach temperature (HRAT), the utility load of the background process, and the optimal operating conditions of the ORC simultaneously. The effectiveness of this method is demonstrated with a case study that uses a reﬁnery as the background process. Sensitivity of the optimal solution to the parameters (electricity price, utility cost) is quantiﬁed in this paper. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Organic Rankine Cycle Waste heat recovery Heat integration Duran-Grossmann model Process optimization

1. Introduction In recent decades, as energy prices ﬂuctuate and environmental pollution become more severe, efﬁcient energy utilization has received widespread attention. In particular, the Organic Rankine Cycle (ORC) has become a promising technology for waste heat recovery due to its simplicity, feasibility, and reliability [1]. The ORC converts low-temperature heat into power and can be applied to many ﬁelds as solar thermal energy [2], geothermal energy [3], engine waste heat [4], biomass [5], and industrial waste heat [6]. Recently, Yari et al. [7] compared the trilateral Rankine cycle, Kalina cycle and organic Rankine cycle from the viewpoint of thermodynamic and exergoeconomics. They found that ORC is the most advantageous among the three options from the point of economics.

* Corresponding author. E-mail address: [email protected] (L.T. Biegler). http://dx.doi.org/10.1016/j.energy.2016.12.061 0360-5442/© 2016 Elsevier Ltd. All rights reserved.

Parametric optimization and exergetic analyses were performed for lı et al. [8]. Deeboth subcritical ORC and supercritical ORC by Yag thayat et al. [9] proposed a dimensionless term, Figure of Merit (FOM), to investigate the performance of ORC system for low temperature waste heat recovery with mixture working ﬂuids. For waste heat recovery in an industrial process, there are usually multiple waste heat streams. The design of an appropriate ORC will depend on the properties of the background process (i.e. waste heat streams). The decision of which streams to recover and what order to recover them exerts a large inﬂuence on the ORC system performance. Desai et al. [10] proposed a methodology for integration and optimization of an ORC considering the background process. Utilizing pinch technology, the operating conditions of the ORC are determined manually and the heat exchanger network is derived with a heuristic method. Based on this work, Chen et al. [11] proposed a two-step method to optimize the ORC and synthesize the heat exchanger network. In the ﬁrst step, a stand-alone heat exchanger network is synthesized to minimize the hot utility.

H. Yu et al. / Energy 119 (2017) 322e333

In the second step, they incorporate the ORC into the heat surplus zone below the pinch point and maximize the power output. However, their work only samples ORC design parameters (e.g. evaporation temperature) at several speciﬁed values. Moreover, rigorous thermodynamic models for the ORC were not incorporated. It is also important to consider the trade-off in capital cost and operating cost while designing an ORC for the purpose of recovering multiple waste heat streams. Li et al. [12] optimized a twostage serial ORC system to maximize the ratio of net power output to total thermal conductance. Alternatively, Yang and Yeh [13] maximized the ratio of net power output to total heat exchanger area of an ORC for ocean thermal energy conversion. Yari et al. [7] performed exergo-economic optimization of an ORC to minimize speciﬁc investment cost. However, these works only consider heat exchanger costs; they do not consider the capital cost of the turbine, pump, and condenser. More detailed economic models are desirable to get a reliable measure of the ORC's beneﬁt. In this paper, multiple waste heat streams are recovered by an intermediate hot water stream (for safety and practicality considerations). The hot water can be regarded as a cold stream in the heat exchanger network and as the heat source in ORC system. Along with the Duran-Grossmann model for heat integration, the model proposed in this paper includes rigorous thermodynamic models of the ORC and equipment cost correlations. This model can help engineers customize an economically optimal ORC to a

323

background process, by considering heat integration and ORC design optimization simultaneously. 2. Problem deﬁnition There are huge amounts of waste heat in the chemical and oil reﬁning industries. So customizing an ORC to a waste heat redundant process is very attractive for industry in order to save cold utility and generate power. From the view of safety, control, and operability, using an intermediate hot water stream to transfer waste heat to the working ﬂuid may be more practical. The ORC system analyzed in this work is represented in Fig. 1. The hot water stream enters the background process to recover waste heat; this is represented by the left hand side of Fig. 1, with the composite curves (CC) given by the lower left graphic describing the heat exchange occurring within the box outlined in the upper left. This hot water stream then releases the recovered heat to the organic working ﬂuid in an ORC system, also represented by the T-S diagram in the lower right graphic of Fig. 1. The mass ﬂowrate of hot water exerts great inﬂuence on the utility load of the heat exchanger network, the amount of waste heat recovered, the pump work consumed by the hot water pump, and the temperature of hot water at the outlet of the heat exchanger network. The hot water outlet temperature and its heat exchange behavior in the ORC in turn affects the ORC system thermal efﬁciency. The capital cost of ORC components interacts strongly with the operating conditions.

Fig. 1. The ﬂowsheet and the graphical interpretation of the problem.

H. Yu et al. / Energy 119 (2017) 322e333

Therefore, optimization of the ORC system and heat integration of the chemical process should be considered simultaneously. In most cases, efforts to increase the thermodynamic efﬁciency of the system usually increase the overall capital cost of the system, so thermodynamic optimization alone may lead to impractical results. In this paper, a techno-economic objective is considered. The design of an ORC that simultaneously considers process heat integration while optimizing for thermodynamic and techno-economic performance of an ORC has not been addressed in the open literature. The problem solved in the present work can be formulated as follows: for a given set of process streams and utilities, design a waste heat recovery system (using a hot water stream) and an ORC to convert waste heat to power. The mass ﬂowrate and temperature proﬁle of the hot water stream is a key design variable, since the temperature and ﬂowrate of the hot water stream have tight interactions with the ORC system. In the following section, the mathematical model for waste heat recovery and ORC design optimization is presented. 3. Model description The proposed model consists of the Duran-Grossmann heat integration model, a rigorous thermodynamic model of an ORC, and an equipment cost model. This model considers the operating cost, capital cost and the revenue from power output simultaneously.

determined by the largest heating deﬁcit of all the process streams through inequality (3): p

ZH ðxÞ QHU

Once the hot utility is determined, the cold utility can be derived from energy balance as shown in Equation (4).

QCU ¼ UðxÞ þ QHU where UðxÞ ¼

Min OBJ ¼ FðxÞ þ CHU QHU þ CCU QCU

gðxÞ 0

i2H

(1a) QSIAðxÞp ¼

X

h n o FCPj max 0; Tjout ðT p HRATÞ

j2C

oi n max 0; Tjin ðT p HRATÞ

(1b)

The heat deﬁcit above the pinch for each pinch candidate is expressed as follows: p

ZH ðxÞ ¼ QSIAðxÞp QSOAðxÞp

(2)

where x are the process variables. The minimum hot utility is

P j2C

FCPj ðTjout Tjin Þ.

(5)

where x is the scalar argument and ε is a small constant, typically between 103 and 106. The optimization and heat integration problem (6) can then be written as follows,

The problem of heat integration to minimize the consumption of utility has been widely investigated in the past decades. Pinch technology is a very popular tool for heat integration [14] that has been applied to diverse problems in energy system design, water network design, and hydrogen network design [15]. However, an important limitation of pinch technology is that the ﬂowrates and temperatures of streams must be ﬁxed. Instead, a simultaneous optimization can lead to more proﬁtable schemes than a sequential strategy in which heat integration and optimization of the ORC system are performed separately. In this work, the Duran-Grossman model [16] is applied to automatically consider heat integration during ORC optimization. The model is based on the pinch method, but ﬁxed temperature intervals are not required to determine the energy target. Instead, the stream inlet temperatures serve both as optimization variables and pinch candidates, since pinch points are always associated with inlet temperatures of streams. For each pinch candidate, the heat load of hot streams above the pinch candidates (QSOA) and the heat load of cold streams above pinch candidates (QSIA) are calculated by Equation (1a,b).

h n o i FCPi max 0; Tiin T p max 0; Tiout T p

FCPi ðTiin Tiout Þ

9 8 0 1 > > = 1 < 1 2 B C max 0; x z @x þ x2 þ ε A > > 2 ; :

s:t: hðxÞ ¼ 0

X

P i2H

(4)

Because nonlinear programming (NLP) algorithms require continuous derivatives for the constraints, the max operator in Equations (1) and (2) should be smoothed, e.g., by the following function [17]:

3.1. Duran-Grossmann model

QSOAðxÞp ¼

(3)

=

324

(6)

p

ZH ðxÞ QHU

UðxÞ þ QHU QCU ¼ 0 QHU 0; QCU 0 where h(x) ¼ 0 represents the mass balance and heat balance equations and Equations (1)e(2), g(x) 0 are speciﬁcation constraints of the process, and F(x) is the economic performance indicator for the process. In this paper F(x) includes the equipment cost, operating cost, and the revenue from power generation of the ORC system; these will be discussed in detail in section 3.4. The above model can determine the optimal process operating conditions and heat integration simultaneously.

3.2. ORC thermodynamic model To facilitate formulation of the ORC model, we consider the ORC from Fig. 1. The ORC stream for the working ﬂuid contains seven different state points, which are also mapped onto the T-S diagram in Fig. 2. At state point 1 the condensed working ﬂuid is pumped as a liquid to a higher pressure at point 2. Then, it is heated in the evaporator by the hot water stream that interacts with the background process. The evaporator generally contains three heat transfer sections, the subcooled section (point 2 to point 3), twophase section (point 3 to point 4), and superheated section (point 4 to point 5). Note that state points 4 and 5 may coincide if superheating is not preferred in the evaporator. From state point 5 the working ﬂuid is expanded by the turbine to state point 6, and cooled in the condenser to saturated vapor (point 7) in the superheated section and then to saturated liquid (point 1) in the twophase section.

H. Yu et al. / Energy 119 (2017) 322e333

325

f "ðZV Þ ¼ 6ZV þ 2ðB 1Þ 0

(9)

is used to determine the vapor phase root ZV. This constraint is applied to state points 4, 5, 6 and 7 as shown in Fig. 2. The third constraint (non-positive second derivative):

f "ðZL Þ ¼ 6ZL þ 2ðB 1Þ 0

(10)

is used to determine the liquid phase root ZL. This constraint applies to state points 1, 2, and 3 shown in Fig. 2. Equations 8e10 guarantee that the correct root of the cubic equation is used at all of the corresponding state points. The relationship between saturated vapor pressure and evaporation temperature is given by the Extended Antoine equation as shown in Equation (11):

ln P ¼ C1 þ

Equation of State and Physical Properties For each of the working ﬂuid phase conditions at the seven points in Fig. 2, thermodynamic properties are calculated using the PengRobinson (PR) equation of state. The form of the PR equation for pure components is given as follows:

2

Z þ ðB 1ÞZ þ A 2B 3B

2

Z þ B þ B AB ¼ 0 3

2

H Hid ¼ H ex

(12)

ZT Hid ¼

CPid dT

(13)

T0

(7)

where Z is the compressibility factor, A and B are parameters related to the critical properties, temperature, and pressure of the working ﬂuid. Detailed information about the PR equation, the coefﬁcients A, B and the resulting thermodynamic properties are given in the Appendix. For each state point in the model, corresponding thermodynamic property variables are deﬁned. Then, the equations in this section will specify the appropriate values for each property using the PR equation. For example, Equation (7) is written for each of the seven state points in order to ensure that the compressibility factors corresponding to each state point are all roots of the PR equation. The cubic PR equation has up to three real roots, which need to be determined appropriately during the optimization process. Kamath et al. [18] proposed an equation-based strategy to map roots to phases for cubic equation of state. The liquid root corresponds to the smallest real root and the vapor root corresponds to the largest one. Moreover, the ﬁrst derivative with respect to Z must be positive to avoid the non-physical middle root. The sign of the second derivative determines the phase. A non-negative second derivative denotes the vapor phase, and a non-positive second derivative denotes the liquid phase. As a result, the following three inequalities should be incorporated into our model. The ﬁrst constraint:

0 f ðZÞ ¼ 3Z 2 þ 2ðB 1ÞZ þ A 2B 3B2 0

(11)

where C1-C7 are constants related to the working ﬂuid. Once the correct root of the PR equation is identiﬁed, the necessary thermodynamic properties can be calculated using explicit analytical expressions for departure functions [19]. The following equations are used to calculate the thermodynamic properties for each state point.

Fig. 2. T-S diagram of ORC system.

3

C2 þ C4 T þ C5 ln T þ C6 T C7 T þ C3

(8)

excludes the meaningless middle root. This constraint is applied to all the state points shown in Fig. 2. The second constraint (nonnegative second derivative):

2 2 C3 =T C5 =T þ C4 sinhðC3 =TÞ coshðC5 =TÞ

CPid ¼ C1 þ C2 *

(14)

where C1-C5 are constants retrieved from Aspen Plus v7.3. From the integral, the ideal gas enthalpy is given by:

coshðC3 =TÞ coshðC3 =T0 Þ Hid ¼ C1 ðT T0 Þ þ C2 C3 sinhðC3 =TÞ sinhðC3 =T0 Þ sinhðC5 =TÞ sinhðC5 =T0 Þ C4 C5 coshðC5 =TÞ coshðC5 =T0 Þ

(15)

and the departure function for enthalpy is given as:

Hex ¼ RTc ðT=Tc ÞðZ 1Þ 2:078ð1 þ kÞa0:5 lnððZ þ 2:414BÞ=ðZ 0:414BÞÞ

(16)

Organic working ﬂuid pump model Between state points 1 and 2 in Fig. 2, the power consumed by the working ﬂuid pump can be calculated by Equation (17):

Wwf ;p ¼

M,mwf

r

ðP2 P1 Þ

(17)

where M is the molecular weight of the organic working ﬂuid, r is the mass density of the organic working ﬂuid, and mwf is the molar ﬂowrate of organic working ﬂuid.

H. Yu et al. / Energy 119 (2017) 322e333

Hot water pump model

Wt ¼ mwf ðh5 h6 Þ

To circulate the hot water between the reﬁnery and ORC power station, a hot water pump must be installed. The power consumed by the pump is proportional to the mass ﬂowrate of hot water and the pressure drop, which depends on the distance between reﬁnery and the ORC power station, the pipe parameters, and the properties of hot water. Since detailed pumping costs require additional design information, including pipe diameter, pipe material, distance, and mass ﬂowrate, we adopt the simpliﬁed method proposed by Reddy et al. [20] as shown in Equation (18), which relates the pressure drop DP over 100 m pumping distance to the heat capacity ﬂowrate of hot water (FCp), with no heat loss in the pipes.

DP ¼ 0:0023FCp þ 9:0925

(18)

In this study, the distance between the ORC power station and reﬁnery is assumed to be 100 m. The pump work consumed by the hot water pump is calculated by Equation (19).

Whw;p ¼

FCp 0:0023FCp2 9:0925FCp ,DP ¼ þ r,Cp r,Cp r,Cp

(19)

As the organic working ﬂuid is heated from subcooled liquid phase to saturated vapor or even superheated vapor (from state points 2 to 5 in Fig. 2), the evaporator is modeled using three subunits: the preheating, two-phase, and superheating sections. The energy balance for the superheated, two-phase, subcooled sections and overall evaporator are shown as follows:

Qeva;sup ¼ mwf ðh5 h4 Þ ¼ mhw CP Tout;hw;hen T4P

(20)

Qeva;twp ¼ mwf ðh4 h3 Þ ¼ mhw CP ðT4P T3P Þ

(21)

Qeva;sub ¼ mwf ðh3 h2 Þ ¼ mhw CP T3P Tout;hw;orc

(22)

Qeva;over ¼ mwf ðh5 h2 Þ ¼ mhw CP Tin;hw;orc Tout;hw;orc

(23)

Note that the hot water temperature at the inlet of evaporator in ORC is equal to the hot water temperature at the outlet of the heat exchanger network; the temperature hot water at the outlet of ORC is equal to the hot water temperature at the inlet of the heat exchanger network. So the following constraints are incorporated in the model.

Tout;hw;orc ¼ Tin;hw;hen

(24)

Tin;hw;orc ¼ Tout;hw;hen

(25)

Turbine model The expansion of the working ﬂuid through the turbine is modeled as adiabatic, so the pressure and temperature satisfy Equation (26):

P5 g1=g P6

The net power output is given by the difference between power output of the turbine and the power consumption of the working ﬂuid and hot water pumps as given in Equation (28):

Wnet ¼ Wt Wwfp Whwp

(28)

Condenser model The condenser model, between state points 6, 7 and 1, is also divided into two parts, namely the superheated region and the two phase region. Equations (29) and (30) are the energy balance equations for the condenser.

Qcon;sup ¼ mwf ðh6 h7 Þ ¼ mcw CP Tout;cw;orc T7P

(29)

Qcon;twp ¼ mwf ðh7 h1 Þ ¼ mcw CP T7P Tin;cw;orc

(30)

3.3. Cost correlations

Evaporator model

T5 ¼ T6

(27)

(26)

where g is the heat capacity ratio of working ﬂuid. The power output of the turbine is given by Equation (27):

Many researchers only consider heat exchanger cost for the purpose economic optimization [21] and use the speciﬁc area per unit power output as the objective function. However, the minimization of speciﬁc area does not necessarily lead to the optimal design. In this paper, the cost of each component of ORC is considered for the techno-economic optimization. The correlations in Ref. [22] are adopted in this paper for capital costs of the ORC components. Heat exchanger model The heat exchangers are the most important components in ORC system. The capital cost of heat exchanger may have signiﬁcant inﬂuence on the system design. The heat exchanger area can be calculated by Equations (31) and (32).

A¼

Q U$DTlm

DTlm ¼

(31)

Dt1 Dt2 lnðDt1=Dt2Þ

(32)

To avoid numerical problems when the approach temperatures of both sides of the exchanger are equal, the Chen approximation for the DTlm is used as shown in Equation (33) [23].

DTlm z Dt1$Dt2$

Dt1 þ Dt2

1 3 =

326

2

(33)

In this paper, the evaporator and condenser are assumed to be countercurrent shell & tube heat exchangers. As the evaporator and condenser are divided into 3 and 2 regions, respectively for modeling purposes, the total area of the evaporator and condenser is the sum of the regions as shown in Equations (34) and (35).

Aeva;total ¼ Aeva;sub þ Aeva;twp þ Aeva;sup

(34)

Acon;total ¼ Acon;sup þ Acon;twp

(35)

The heat exchanger cost is given by Equation (36), which is also

H. Yu et al. / Energy 119 (2017) 322e333

adopted from Ref. [22].

COSThe ¼ 190 þ 310,A

(36)

Pump model The pump cost is different for the organic working ﬂuid pump and hot water pump. The capital cost for the organic working ﬂuid pump is given by Equation (37):

COSTwfp ¼ 900,

Wwfp 0:25 300

(37)

The capital cost for the hot water pump is given by Equation (38):

Whwp 0:25 COSThwp ¼ 500, 300

(38)

327

The annualized factor AF is assumed as 0.18/year, which is about the factor obtained by assuming 3% interest rate for a 6 year project The number of annual operating hours (AOH) is 8000 h/year The electricity price (Pr) is 0.10 $/(kW$h) The annual pumping and loss cost of cooling water in the ORC condenser is assumed as 50 $/(kW/ C) The hot and cold utility costs are 100 $/(kW$year) and 20 $/(kW$year) respectively The heat transfer coefﬁcients U between hot water and organic working ﬂuid are assumed as 150 W/(m2∙ C), 300 W/(m2∙ C) and 50 W/(m2∙ C) for the subcooled, two phase and superheated regions respectively [26]. The model to determine the optimal conﬁguration of the system can be formulated as the following problem P1, where x1 denotes the set of variables to be optimized and c(x1) represents the feasible search space deﬁned by the constraints. P1: Min OBJ ¼ FðxÞ þ CHU QHU þ CCU QCU þ Corc;cw FCpcw X þ AF COSTi Profit i

Turbine model The turbine cost can vary signiﬁcantly for cases with the same power output but different volume ratios and volume ﬂowrates [24]. In this paper, the turbine cost is proportional to the turbine size, which depends on the outlet volume ﬂowrate of the turbine. The turbine cost is calculated according to Equation (39), also taken from Ref. [22].

COSTtur ¼ 1:5,ð225 þ 170,Voutlet Þ Voutlet

(39)

. ¼ mwf Z6 RT P6

(40)

3.4. Objective function Commonly used objective functions in the open literature includes net present value (NPV) [3], speciﬁc investment cost [22], and levelized cost of electricity [25]. When the background process and the ORC are optimized simultaneously, the utility cost of the background process makes up a large part of the total cost of the system. In this paper, total annual cost of the whole system excluding the heat exchanger network investment cost is adopted as the objective function of the optimal design problem. The objective function OBJ takes into account the utility cost, operating cost, and the equipment cost of the ORC components as well as the proﬁt from power generation as shown in Equation (41).

OBJ ¼ CHU QHU þ CCU QCU þ Corc;cw FCpcw þ AF,

X

COSTi Profit

i

(41) As the cooling water in the ORC is circulated, the cost of cooling water consists of pump work consumption and losses. The cost of cooling water is proportional to heat capacity ﬂowrate as shown the third term in the objective function. The proﬁt of the system is the product of electricity price (Pr), net power output, and the annual operating hours (AOH) given by Equation (42).

Profit ¼ AOH,Pr,Wnet For this study, the following parameters are ﬁxed:

(42)

9 8 < Duran Grosssmann model Eqs:ð1Þ ð6Þ = s:t: cðx1 Þ ¼ x1 Thermodynamic model Eqs:ð7Þ ð17Þ ; : Equipment cost model Eqs:ð18Þ ð40Þ

3.5. Determination of the optimal HRAT In the objective function of P1, the cost of the heat exchanger network is not considered. The cost of the heat exchanger network is related to the Heat Recovery Approach Temperature (HRAT), which also has great impact on the utility consumption and the amount of waste heat recovered by hot water. So it is necessary to consider the effect of HRAT on the design of the whole system. Because HRAT is a constant in the Duran-Grossmann model, we should solve P1 for various HRATs and then compute the sum of OBJ and the annualized cost of the heat exchanger network (TAChen ), denoted as (OBJ þ TAChen). The cost of heat exchanger network can be estimated via the Bath formula, which can predict the area requirement of heat exchange network based on the composite curves [27]. The minimum area target based on enthalpy intervals deﬁned by the “kink” points is presented in Equation (43):

Amin ¼

intervals X k

X qn 1 streams DTlmk n hn

(43)

The cost of the heat exchanger network is calculated via Equation (44) adopted by Aspen Energy Analyzer [28]. In this paper, the heat transfer coefﬁcients of any process stream matches are set as 0.1 kW/(m2∙ C), a conservative estimate for hydrocarbon water pairings.

i h TAChen ¼ AF$ 10000 þ 800ðAmin Þ0:7

(44)

Once TAChen and optimal OBJ of P1 are obtained at various HRATs, the HRAT featuring the minimum (OBJ þ TAChen) is the optimal HRAT. Then the heat exchanger network under the optimal HRAT can be derived via pinch design principles or mathematical programming methods. The optimal scheme featuring minimal overall total annual cost is obtained. It should be noted that a positive (OBJ þ TAChen) does not mean that the ORC system is not

328

H. Yu et al. / Energy 119 (2017) 322e333

proﬁtable. Even though ORC is not adopted in the system, the background process still needs a heat exchanger network. So when an ORC is adopted to recover the waste heat in the process, the inﬂuence of HRAT on the system performance should be considered.

4. Case study 4.1. Optimization with N-butane (R600) as working ﬂuid The proposed model for simultaneous process optimization of ORC and heat integration is applied to part of a reﬁnery as the background process. This case is taken from Ref. [29], in which the system is designed via pinch technology from the perspective of efﬁcient energy utilization. The process stream data for the background process are listed in Table 1 with 6 hot streams and 6 cold streams. The proposed model can be used to determine the optimal hot water ﬂowrate, ORC operating conditions and HRAT, which leads to the minimum overall annual cost of the system (OBJ þ TAChen). When HRAT is set to 10 C, the corresponding minimum hot and cold utilities are 2950 kW and 17200 kW. There is considerable waste heat in this system, which can be utilized by an ORC. Here R600 is designated as the working ﬂuid because the waste heat temperature lies in the range of 120e200 C where R600 performs well [30]. To determine the optimal HRAT, the model proposed in this paper P1 is solved for various HRATs. The model P1 is implemented in General Algebraic Modeling System (GAMS) with CONOPT 3 [31]

as the NLP solver. The model has 524 variables and 522 constraints and solves in 0.03 CPUs on a desktop computer. The results for various HRATs are listed in Table 2. Fig. 3 illustrates the effect of HRAT on the total annual cost of the system. The blue line (OBJ) represents the objective function of P1; the green line represents the annualized cost of heat exchanger network (TAChen ), and the red line represents (OBJ þ TAChen). Tradeoffs between OBJ and TAChen are observed as HRAT increases. When HRAT becomes small, more process heat can be recovered and more waste heat can be extracted from the background process. Thus less utilities are needed, so more power can be generated by ORCs and this leads to lower OBJ but higher TAChen. With increasing HRAT, OBJ increases linearly and TAChen decreases. As seen from Fig. 3, the optimal HRAT is about 7 C. Moreover, if waste heat is not recovered via ORC, the heat exchanger network area with HRAT at 7 C is about 31829 m2, the corresponding hot and cold utilities are 2410 kW and 16660 kW, respectively, and the corresponding total annual cost (TAChen) is 803211 $/year. When an ORC is customized to this system, the

Table 1 Background process stream data for the case study. Stream

Supply temperature ( C)

Target temperature ( C)

Heat capacity ﬂowrate (kW/ C)

Heat load (kW)

H1 H2 H3 H4 H5 H6 C1 C2 C3 C4 C5 C6

300 170 350 120 70 120 70 40 90 160 30 123

40 80 100 40 40 70 300 120 300 185 50 124

40 70 70 65 220 160 30 50 70 270 315 1100

10400 6300 17500 5200 6600 8000 6900 4000 14700 6750 6300 1100

Fig. 3. Effect of HRAT on the system performance.

Table 2 Optimization results for various HRATs. HRAT ( C)

OBJ ($/year)

HU (kW)

CU (kW)

Amin (m2)

TAChen ($/year)

OBJ þ TAChen ($/year)

Power (kW)

2 3 4 5 6 7 8 9 10 11 12 13 14 15

3608 29883 63168 96245 129108 161753 194175 226366 258317 288969 319171 348926 378234 407097

1510 1690 1870 2050 2230 2410 2590 2770 2950 3060 3170 3280 3390 3500

4064 4354 4642 4926 5207 5484 5756 6023 6284 6654 7023 7391 7758 8124

174670 132160 107830 91878 80546 72044 65416 60098 55732 51728 48377 45526 43069 40928

749606 617021 535381 478835 436861 404197 377923 356260 338042 320954 306346 293677 282566 272729

745998 646904 598549 575080 565969 565950 572098 582626 596359 609923 625517 642603 660800 679826

1044 1024 1004 985 966 947 929 911 893 860 827 795 763 732

Italics font means the optimal condition of the system. The bold font means the total annual cost of the system under the optimal operating conditions.

H. Yu et al. / Energy 119 (2017) 322e333

329

Table 3 The optimal operating conditions using the optimal HRAT ¼ 7 C. Variable

Optimal value

Variable

Optimal value

hot utility (kW) cold utility (kW) net power output (kW) thermal efﬁciency hot water heat capacity ﬂowrate (kW/ C) cooling water heat capacity ﬂowrate (kW/ C) cooling water outlet temperature ( C) area of evaporator (m2)

2410 5510 947 8.47% 247.7 1617 31.3 3579

evaporation temperature ( C) condensation temperature ( C) turbine inlet temperature ( C) turbine outlet temperature ( C) hot water temperature inlet of heat exchanger network ( C) hot water temperature outlet of heat exchanger network ( C) working ﬂuid molar ﬂowrate (mol/s) area of condenser (m2)

82.8 38.5 105.6 349.5 77 122 417.5 4257

minimum (OBJ þ TAChen) is 565950 $/year as shown in Table 2. It can be seen that overall gain of customizing an ORC to the system is 237261 $/year. The detailed results at optimal HRAT (7 C) are listed in Table 3. It can be seen that the hot water inlet temperature of heat exchanger network is 77 C, which means that it is not economic to recover waste heat below 84 C (77 C þ 7 C). This reveals that it is not worthwhile to recover all the recoverable waste heat to generate power. The maximum net power output of the previous paper [29] using the same case study is only 761.3 kW. The net power output is increased by about 24.3%. However, that work didn't consider the effect of HRAT on the system design, and the heat exchanger network had been given. While that method is suitable for the problem to customize an ORC to an existing heat exchanger network, the method proposed in this paper maximizes performance for the green ﬁeld design of the whole system including the heat recovery approach temperature of background process heat exchanger network, hot water mass ﬂowrate, and operating conditions of ORC system. The composite curve and grand composite curves of the system with and without the hot water under optimal conditions are shown in Fig. 4. If an ORC is not considered to recover waste heat, the hot utility and cold utility of the system (shown with the red and blue lines) are 2410 kW and 16660 kW respectively and the pinch point occurs at 167/160 C. After hot water is used to recover waste heat in the process, the hot utility remains the same and the cold utility (green line in Fig. 4) reduces to 5510 kW. Two more pinches are formed at 120/113 C and 97/90 C because hot water is heated from 77 C to 122 C by the background hot process streams. It is clear that after the hot water is introduced to the system, the (red and green) composite curves are much closer to each other

below 167/160 C, as 11150 kW of waste heat is recovered by hot water. Within the temperature range of hot water, the hot composite curve and cold composite curve are nearly parallel. Since the hot water ﬂowrate and temperatures have been determined, the corresponding heat exchanger network can now be derived via pinch design principles or from the expanded transshipment model [32]. One of the many possible conﬁgurations of the system is shown in Fig. 5. 4.2. Comparison of different working ﬂuids Working ﬂuid is a crucial factor that inﬂuences the performance of the ORC system. Thermodynamic properties are key factors to consider for working ﬂuid selection. In addition, environmental effects, safety, stability and the cost of working ﬂuids also should be considered [33]. Yu et al. [34] proposed a new pinch based method for simultaneous selection of working ﬂuid and operating conditions for sensible waste heat sources. The results showed that the working ﬂuid whose critical temperature is slightly lower than the waste heat inlet temperature is likely to be the optimal working ﬂuid when power output is the screening criterion. Toffolo et al. [35] screened optimal working ﬂuid based on multiple criteria, thermodynamic performance, economic performance and offdesign behavior. In this paper, the performance of different working ﬂuids is investigated to consider the effect of working ﬂuid on the system design. Molina-Thierry and Flores-Tlacuahuac [36] also proposed a method for simultaneous optimal design of ORC and mixture working ﬂuids. We intend to extend our model to mixture working ﬂuids as well in future work. In this paper, several promising working ﬂuids identiﬁed by Yu et al. [30] and Hung et al. [37] are applied to case study in Section 4.1. The critical properties and

Fig. 4. Composite curve and GCC including/excluding hot water.

330

H. Yu et al. / Energy 119 (2017) 322e333

Fig. 5. Heat exchanger network conﬁguration.

minimization in Ref. [30] because a rigorous techno-economic optimization is performed here. Other screening criteria may select a different working ﬂuid for this application. For the technoeconomic optimization, the results listed in Table 5 show that R600a has the best performance among the four working ﬂuids. The corresponding optimal operating conditions are listed in Table 6. R600a can generate more power compared with other working ﬂuids. In this case, the working ﬂuid is about 25 C superheated at the inlet of the turbine. This contradicts the common assumption that superheating is not desirable for organic Rankine cycles, since superheating cannot increase the thermal efﬁciency much for dry working ﬂuids [38]. Instead, superheating performs better in this case because the temperature-enthalpy proﬁle of working ﬂuid matches better with that of hot water under superheating

constants for the Extended Antoine equation and ideal gas heat capacity of the investigated working ﬂuids are listed in Table 4. For different working ﬂuids, the optimal operating conditions and HRAT can be determined via the same procedures as illustrated by the case study in section 4.1. The optimal results for each working ﬂuid are listed in Table 5. While there is a huge difference in performance among these working ﬂuids, the optimal HRATs are only slightly different among the working ﬂuids. Note that OBJ denotes the sum of total annual operating cost and annualized ORC capital cost minus the proﬁt from electricity; a negative OBJ means the revenue from power generation outweighs the sum of total annual operating cost and annualized ORC capital cost. Moreover, OBJ is strongly related to the price of electricity. The sensitivity analysis section will show the effects of electricity price on the OBJ. We observe that R600 does not rank as highly as with the energy

Table 4 Working ﬂuids considered in this paper. Working ﬂuid

Tc ( C)

Pc (bar)

Extended Antoine equation C1

C2

C3

C4

C5

C6

C7

C1

C2

C3

C4

C5

R227ea R600a R600 R245fa

101.68 134.65 151.97 154.05

29.12 36.40 37.96 36.40

48.26 96.917 54.83 61.27

4278 5039.9 4363.2 5494.5

0 0 0 0

0 0 0 0

5.698 15.01 7.046 7.457

1.08E-16 0.022725 9.45E-6 5.877E-17

6 1 2 6

100.1 76.394 80.154 97.947

147.46 168.02 162.42 163.59

1073.6 826.54 841.49 2009.8

101.21 102.85 105.75 166.01

573.16 2483.1 2476.1 846.71

Ideal gas heat capacity constants

Table 5 Optimal results for the four investigated working ﬂuids. Working ﬂuid

Optimal HRAT ( C)

OBJ ($/year)

HU (kW)

CU (kW)

Amin (m2)

TAChen ($/year)

OBJ þ TAChen ($/year)

Power (kW)

R227ea R600a R600 R245fa

7 6 7 6

193850 170991 161753 81823

2410 2230 2410 2230

3804 4143 5484 4634

70523 84936 72044 82883

398234 453320 404197 445655

625244 282329 565950 363832

1098 1490 947 1280

H. Yu et al. / Energy 119 (2017) 322e333

331

Table 6 Optimal operating conditions for R600a with HRAT ¼ 6 C. Variable

Optimal value

Variable

Optimal value

hot utility (kW) cold utility (kW) net power output (kW) thermal efﬁciency hot water heat capacity ﬂowrate (kW/ C) cooling water heat capacity ﬂowrate (kW/ C) cooling water outlet temperature ( C) area of evaporator (m2)

2230 4143 1490 12% 243.3 1999 30.3 4688

evaporation temperature ( C) condensation temperature ( C) turbine inlet temperature ( C) turbine outlet temperature ( C) hot water temperature inlet of heat exchanger network ( C) hot water temperature outlet of heat exchanger network ( C) working ﬂuid molar ﬂowrate (mol/s) area of condenser (m2)

83.2 36.5 107.8 76.3 68.8 123.4 493 5200

Table 7 Inﬂuence of electricity price on the system performance. Pr ($/kW$h)

Optimal HRAT ( C)

OBJ ($/year)

HU (kW)

CU (kW)

Amin (m2)

TAChen ($/year)

OBJ þ TAChen ($/year)

Power (kW)

0.08 0.09 0.10 0.11 0.12

6 6 6 5 5

57521 54135 170991 332794 729536

2230 2230 2230 2050 8930

4755 4420 4142 3639 4100

82390 83764 84936 98262 85294

443807 448951 453320 501793 454650

501328 394816 282329 168998 274887

1359 1430 1490 1566 3029

Table 8 Inﬂuence of cold utility price on the system performance. Cold utility cost ($/kW$year)

Optimal HRAT ( C)

OBJ ($/year)

HU (kW)

CU (kW)

Amin (m2)

TAChen ($/year)

OBJ þ TAChen ($/year)

Power (kW)

16 18 20 22 24

6 6 6 6 7

187949 179372 170991 162800 115601

2230 2230 2230 2230 2410

4337 4239 4142 4048 4221

84110 84525 84936 85344 76592

450243 451790 453320 454836 421806

262294 272417 282329 292036 306205

1476 1483 1490 1496 1476

conditions. Therefore, more heat can be released to the organic working ﬂuid. Even though the thermal efﬁciency is not increased much by superheating, the power output still increases, because superheating can lead to higher recovery of waste heat.

which demonstrates that the cold utility cost has little effect on the optimal ORC operating conditions.

5. Sensitivity analysis

A model for simultaneous heat integration and optimization of ORC system with hot water as the intermedium for recovery of multiple waste heat streams is proposed in this paper. The model considers the interaction between the background process heat integration, thermodynamic and economic optimization of the ORC system simultaneously. The model was applied to a case study from a reﬁnery. Compared with the previous work that only considered the optimization of standalone ORC system, the net power output is increased by about 24.3%. This method is especially applicable for conceptual design of the combined background and ORC system. Moreover, the effects of the price of electricity and cold utility cost have been investigated in this study. The results show that electricity price has strong inﬂuence on the system. As expected, more power is generated in response to increasing electricity price; the total annual cost decreases and the optimal HRAT tends to be smaller. On the other hand, the cost of cold utility has little inﬂuence on the optimal system design. The rigorous heat transfer behavior in the evaporator and condenser is not investigated, and the heat transfer coefﬁcient is assumed at ﬁxed values in this paper. In future work, a more detailed heat transfer coefﬁcient model and organic working ﬂuid mixtures will be considered to further improve system performance.

The price of electricity and utility are important parameters for the system performance. In this section, the inﬂuence of electricity and cold utility price on the optimal conﬁguration of the system is brieﬂy discussed. As R600a shows the best performance in Section 4.2, it is selected as the working ﬂuid in the sensitivity analysis. The price of electricity and cold utility will be allowed to ﬂuctuate within þ20% and 20%. In the base case above, the electricity and cold utility price are 0.1 $/kW$h and 20$/(kW$year). The optimal results within the electricity price ﬂuctuation range are listed in Table 7. As the electricity price increases from 0.08 to 0.12 $/kW$h, the optimal HRAT remains almost the same, but (OBJ þ TAChen) decreases from 501328 to 274887. The higher price of electricity makes the system more proﬁtable, but hot utility increases to 8930 kW, which is much higher than the hot utility in other cases. Note that (OBJ þ TAChen) < 0 implies that the revenue from power generation exceeds the sum of total operating cost, annualized ORC capital cost and annualized heat exchanger cost of the system. This also demonstrates that when the electricity price reaches 0.12 $/kW$h, it is worth consuming more hot utility to heat hot water, in order to generate more power. With the given parameters and cost correlations in this paper, the electricity price is limited to 0.12$/ kW$h. If the price of electricity were higher than 0.12$/kW$h, then hot utility could also be used to generate power directly. The results under different cold utility costs are listed in Table 8. As the cold utility cost increases, the sum of OBJ and TAChen increases gradually but the power output shows only a tiny deviation,

6. Conclusion and future work

Acknowledgements Financial support from the National Natural Science Foundation of China under Grant No. 21576286, SINOPEC under Grant No.

332

H. Yu et al. / Energy 119 (2017) 322e333

313109 is gratefully acknowledged.

k

Appendix

M m

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

V aV

P¼ V b RT V 2 þ 2bV b2 where

a ¼ 0:45724

ðRTc Þ2 a Pc

RTc Pc i2 h a ¼ 1 þ k 1 ðT=Tc Þ0:5

ORC Pr QSOA QSIA q TAC T0 V Z

r g

b ¼ 0:0778

temperature intervals in the back ground heat exchanger network molecular weight of organic working ﬂuid molar ﬂowrate of working ﬂuid or mass ﬂowrate of hot water organic Rankine cycle electricity price heat load of hot streams above the pinch candidates heat load of cold streams above the pinch candidates heat load of stream total annual cost reference temperature volume compressibility factor density of organic working ﬂuid heat capacity ratio

Subscripts

k ¼ 0:37464 þ 1:54226u 0:26992u

2

Tc and Pc are the critical pressure and temperature. u is acentric factor. Compressibility factor Z ¼ PV=RT, then the Peng-Robinson equation can be written in the following form

Z 3 þ ðB 1ÞZ 2 þ A 2B 3B2 Z þ B3 þ B2 AB ¼ 0 where

A¼

aP ðRTÞ2

and B ¼

bP RT

The enthalpy can be calculated via departure function

HðT; PÞ HðT; PÞid ¼ HðT; PÞex HðT; PÞid ¼

ZT CPid dT T0

2 2 C3 =T C5 =T þ C4 CPid ¼ C1 þ C2 * sinhðC3 =TÞ coshðC5 =TÞ ex HðT; PÞ ¼ RTC ðT=TC ÞðZ 1Þ 2:078ð1 þ kÞa0:5 lnððZ þ 2:414BÞ=ðZ 0:414BÞÞ where CPid denotes the heat capacity of ideal gas, C1 to C5 are con-

stants retrieved from Aspen Plus®. HðT; PÞex denotes the excess enthalpy, which can be calculated based on compressibility factor Z. Nomenclature A AF AOH CU C COST Cp FCp H HRAT HU h i j

heat exchanger area annualized factor annual operating hours cold utility cold stream set capital cost of components in the system speciﬁc heat capacity heat capacity ﬂowrate enthalpy/hot stream set heat recovery approach temperature hot utility heat transfer coefﬁcient, enthalpy hot streams/components in ORC system cold streams

c con cw cwp eva he hen hw hwp L lm n outlet sub sup tur twp V wf wfp

critical point condenser cooling water cooling water pump evaporator heat exchanger heat exchanger network hot water hot water pump liquid phase logarithmic mean stream outlet of turbine subcooled section superheated section turbine two-phase section vapor phase working ﬂuid working ﬂuid pump

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