Organic Rankine Cycle for Waste Heat Recovery in a Refinery

Article pubs.acs.org/IECR

Organic Rankine Cycle for Waste Heat Recovery in a Refinery Cheng-Liang Chen,* Po-Yi Li, and Si Nguyen Tien Le Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan, Republic of China ABSTRACT: Waste heat recovery is one of the most important development fields for the organic Rankine cycle (ORC), where a low boiling point organic fluid is used as a working medium. The ORC can be applied to heat and power plants or to industrial and farming processes. Some heat sources, like hot exhausts from furnaces, which contain particles or sulfide might harm pipes of an evaporator. It is suggested to introduce water or heat transfer oil as an intermediate medium for aiming at recovery of waste heat. In this paper, a mathematical model is represented for integrating ORC with the heat transfer fluid circulated as an intermediate fluid for recovering waste heat from the background process. An ORC-integrated superstructure considering all possible matches of heat-exchange between waste hot process streams, circulating heat transfer fluid, and ORC is proposed. The superstructure also takes into account the possibilities of several sets of ORC and circulating heat transfer fluid. Based on this superstructure, the model is designed and formulated as a mixed-integer nonlinear programming (MINLP) problem. A high-level modeling system, General Algebraic Modeling System (GAMS) is employed for the sake of solving this MINLP model. A case study of crude preheat train is investigated to demonstrate the novel application of the proposed model for industrial waste heat recovery. Economic analysis shows less than two payback years for the installation of ORC on a typical crude preheat train for waste heat recovery.

1. INTRODUCTION Heat and power, or energy in general, which are mostly generated from fossil fuels are mainly required in industrial processes. Over the previous decade, it has been seen that the costs of fossil fuels have shot up by four times although the prices of many industrial products remain relatively stable because of oversupply or worldwide stringent competition. Moreover, taking a quick look back over the last 200 years, the world population increased gradually from 1 to 2 billion during the 123 years between 1804 and 1927. But later from 1928 to 2012, it rocketed up to 7 billion and is predicted to reach 8 billion in 20241 which brings about the challenge of higher living standards. As global population increases and living standards improve, there is a greater need to consume more energy, almost over 75% of which is distributed from fossil fuels.2 The rapid growth in consumption of fossil fuels breaks the balances of the environment which is inherently established well for people and other lives. According to data recorded, due to human contributions, there was an alarming CO2 content increase exceeding the threshold of 400 ppm on May 9th, 2013, although for 650 000 years before this atmospheric CO2 has never been above 300 ppm.3 This meant that there were 15 billions of tons of CO2 per year or 4 billion tons of carbon per year emitted to the environment beyond the stability of the carbon cycle.4 Those significant numbers sent an urgent message to humans and have been showing the severe effects to the environment such as serious thermal, chemical, and particulate pollution happening in many big industrial cities.5 The growing energy demand is met with nonrenewable fossil fuel resources, which are attached to polluted emission and unbalancing of the carbon cycle, making them the single biggest driver of global warming and climate change. To face these urgent issues, one of the most important activities is to push the consumption of fossil fuels to the limit. Renewable and eco-friendly energy sources, solar, wind, biofuels for instance, have been approached to promote the use of cleaner © XXXX American Chemical Society

forms of energy; however, they are not economical to apply on the scale of industrial needs. Therefore, efforts to maximize energy utilization efficiency, in other words, waste energy recovery, especially in manufacturing plants are totally worthwhile to be pursued and implemented. Process integration (PI), defined as a holistic approach to process design, retrofitting, and operation which emphasizes the unity of the process for minimizing the consumption of resources such as heat, water, etc.,6 is one of the most widely used techniques for enhancing heat utilization within process units and streams. A large amount of research over the last two decades has focused on carrying out heat exchange between process streams that need to be heated and those that need to be cooled for reducing the demand of external hot and cooling utilities.7,8 Furman and Sahinidis9 provided a thorough review of the literature on heat-exchanger network synthesis (HENS) for heat recovery within a process. Chronological milestones and major discoveries in HENS were highlighted. This review also paid tribute to all those pioneers in the development of the insightbased pinch analysis and design methods and the superstructurebased mathematical optimization approaches. However, further recovery of waste heat from the low temperature range is seldom considered in industrial plants. For given hot and cold streams, we are going to maximize the heat recovery between the process streams. The “process pinch” is one important concept for process heat recovery. There is heat deficit above the process pinch, and there is heat surplus below the pinch temperature. This means that, above the process pinch, cooling utilities should not be used and use of hot utilities should be avoided below the Special Issue: Sustainable Manufacturing Received: September 10, 2015 Revised: January 25, 2016 Accepted: January 28, 2016

A

DOI: 10.1021/acs.iecr.5b03381 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

objective. This study is to recover the waste heat from a fixed background process, i.e. the background process configuration cannot be changed. Therefore, indirect recovery is preferred this our work. Furthermore, our objective is try to maximize the amount of waste heat that is able to convert to useful work through ORC. Thus, below the process pinch section is perfect to apply the ORC instead of above the pinch area which would increase the consumption of hot utilities. In the previous studies, the organic working fluid usually travels for a long distance around a plant and faces many heat sources of various high temperature levels. Actually, this is necessary because, in some plants, the inherent designs are compact and convenient somehow. Therefore, in the case of an ORC installed for improving the heat recovery, pipes of organic working fluid need to be constructed and weave their ways through a tangled net of pipes and units. Obviously, high temperature heat sources in this situation would be very dangerous because the flammable organic working fluid could burst into flames whenever it is hard to prevent. Hence, traveling of an organic working fluid with a long distance between pipes and units within a plant is not a smart choice. One suggestion could help overcome this challenge is employing another fluid that is safer and more stable than an organic working fluid. That is the concept of circulating a heat transfer fluid which alters the organic working fluid to run around to take heat from heat sources then transfer it to the organic working fluid operating only within a safe area for an ORC. On the other hand, another approach should be considered which is the use of more than one ORC. Each of ORC could be established at each heat source so that it can avoid the risk of fire or explosion caused by organic working fluids. Different cases of using one or more than one ORC integrated into the background process with a circulating fluid to recover low-grade waste heat are investigated. This article depicts a superstructure for heat exchanger network synthesis involving a combination of organic Rankine cycles for recovery of low-grade waste heat from the background processes through the heat transfer function of an intermediate medium called a circulating heat transfer fluid. A unified MINLP model is then developed for portraying the integration of hot and cold process streams with the aid of ORC for recovery of waste process heat. Investigation on a crude preheat train example from the literature8,17 is implemented to demonstrate the efficacy of the proposed superstructure and MINLP formulation for maximizing the recovery of low-grade waste heat through the concept of net power acquired from operation of the ORC. The payback year is analyzed to demonstrate the economics of applying the proposed ORC for recovery of waste heat from an industrial refinery.

pinch. Therefore, we should recover the waste heat only from below the pinch section. The waste heat is generally classified according to the temperature, such as, low-grade waste heat for stream temperature below 230 °C; medium-grade waste heat between 230 and 650 °C; high-grade waste heat for 650 °C or higher. A large portion of the heat created expensively is finally released to the environment due to lack of effective methods for recovery. It is reported that industrial low-grade waste heat accounts for nearly 50% or more of total heat input.10 Heat exhaustion causes considerable hardware costs and operating losses, such as fuel, electricity, water, etc., and also reinforces emission of green house gases (GHGs). Despite various efforts to maximize the efficiency of heat utilization in industrial processes, an effective method to recover the waste heat from low to medium temperature sources and transform it into useful mechanical work or electricity is an attractive alternative to reduce the total fuel consumption and also the thermal pollution. The organic Rankine cycle (ORC) is one of the feasible technologies to recover waste heat from low to medium temperature heat sources and to generate electricity. Instead of steam, a selected dry organic fluid such as n-pentane is used as a working medium in an organic Rankine cycle which circulates repeatedly to transform the low-grade heat into mechanical or electrical power. Many studies have been dedicated to developing power cycles from different temperature heat sources and working fluids and improving the efficiency of cycles. Several researchers have investigated the application and the performance of ORC. To name a few, Saleh et al.11 gave a thermodynamic screening of pure components as working fluids for ORC systems in geothermal power plants. Papadopoulos et al.12 studied the systematic methods for selection of optimal working fluids for ORC under various operating conditions. Papadopoulos et al.13 also proposed using the computer-aided molecular design method for selection of binary working fluid mixtures used in the ORC. Desai and Bandyopadhyay14 gave a thorough analysis on the application of ORC for heat recovery from typical background processes. Therein, the inlet/outlet targets of hot and cold process streams were given and the waste heat was limited from the heat surplus zone. The authors presented a feasible method for the integration of the ORC with the background process to generate mechanical work. Therefore, Desai and Bandyopadhyay’s work mentioned a direct waste heat recovery applied at below the pinch section. In their work, the background process was changed to adopt the ORC application. Valencia et al.15 proposed superstructure-based modeling and optimization for integration of ORC with industrial processes. The design objective was to minimize the overall capital and operating costs. The ORC-integrated process optimization problem was formulated as a mixed-integer nonlinear programming (MINLP) problem. Examples showed improvement over the previously reported methods due to the fact that the trade-off between the capital and operating costs as well as the sale of the produced electricity were considered simultaneously. However, the external hot utility in the examples was greater than the standalone heat exchanger network. Recently, Chen et al.16 proposed a modified superstructure and an MINLP formulation which restricted the waste heat recovery from the heat surplus zone. The resulting heat exchanger networks below the process pinch, however, are usually different from the original one. Therefore, it can be said that Valencia’s work was a direct waste heat recovery and their design objective was concerned about the cost and economic benefit obtained from application of ORC. The differences of the current study are the configuration and the

2. PROBLEM STATEMENT The concept of an organic Rankine cycle integrated into a background process can be declared as follows. There is a given set 0 = {i|1, ..., I } of waste hot process streams which will be cooled down from known supplied temperatures Ti,in to target values Ti,out; a set 4 = {m|1, ..., M } of dry organic working fluids are involved for recovery of low-grade waste heat; and a given set 9 = {r |1, ..., R } of circulating heat transfer fluid which is used as an intermediate medium to transfer heat between a background process and an integrated ORC. Besides, a set * = {c|1, ..., C} of available cooling utilities and the heat capacity flow rates of all streams and available utilities, FC, all are known. The concept of waste heat is considered as the residue of B


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Figure 1. (a) Typical waste hot stream where all residual heat is removed by a cooler. (b) ORC for directly recovering waste heat. (c) Superstructure of ORC assisted with recirculating hot fluid for waste heat recovery.

stream i plays a role of a hot stream and the circulating heat transfer fluid r is a cold stream, HEir is a heat exchanger between a waste hot process stream i and a circulating heat transfer fluid r; Cic is a cooler to bring the temperature of the waste hot process stream i to the final target temperature Ti,out by cooling utility c; rhir ∈ [0, 1] and rcir ∈ [0, 1] are split ratios of corresponding hot and cold streams attending transferring in the heat exchanger HEir, where the corresponding output temperatures of hot and cold streams are denoted as thir and tcir, respectively. The term ti is the intermediate temperature after mixing all of thir because of nonisothermal mixing of split streams, which is also the input temperature of the cooler Cic. Similarly, for heat exchange where circulating heat transfer fluid r is considered as a hot stream and the organic working fluid m is a cold stream, Erm is a heat exchanger between a circulating heat transfer fluid r and an organic working fluid m; rhrm ∈ [0, 1] and rcrm ∈ [0, 1] are split ratios of corresponding hot and cold streams coming transferring in the heat exchanger Erm. Adiabatic mixing is applied for all mixing of split streams. In this work, there are only hot streams from which waste heat is recovered. The hot streams could be split to be recovered by different circulating heat transfer fluids. In case of only one circulating fluid used, there is no stream splitting on hot streams. For the purpose of generalizing the supposed superstructure, splitting the mass flow in these streams is applied in this model.

total hot process streams heat after all possible exchangers with cold process streams that need to be taken out by cooling utilities. The ORC-integrated system is improved with circulated heat transfer fluids installed in the heat surplus zone, below the process pinch, to collect the waste heat from waste hot process streams. The recovered waste heat is then passed to the ORC, and the high-pressure vapor of organic working fluid is finally fed to a turbine to generate electricity or useful work. An ORCintegrated waste heat recovery problem is to create an optimum heat recovery configuration that can generate the maximum amount of net power from the recovered waste heat.

3. SUPERSTRUCTURE FOR INTEGRATION OF ORC WITH WASTE HOT STREAMS Figure 1a shows a typical waste hot process stream where the residue heat is removed by a cooler. Figure 1b depicts a direct integration of organic Rankine cycle for recovering the waste heat from the waste hot stream. In order to create the best configuration of the heat exchanger network (HEN) to maximize the recovered low-grade heat from the waste hot process streams by applying the circulating hot fluid as a heat transfer medium, a single stage superstructure which integrates the ORC and the circulating heat transfer fluid for waste heat recovering is proposed, as shown in Figure 1c. In an ORC-integrated superstructure, for heat exchange where a waste hot process C


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Therefore, only the waste hot process streams will be concerned in the following formulation. Equations 1 and 2 are the overall heat balance for the waste hot stream i and the circulating heat transfer fluid r. Let FCi denote the heat capacity flow rate of waste hot stream i,a term defined as a product of a given mass flow rate and the corresponding specific heat capacity of that stream, the overall heat balance for the waste hot stream i, FCi(Ti,in − Ti,out), equals the sum of the heat exchanged with circulating heat transfer fluid r, qir, and the external cold utilities c, qic. Similarly, the overall heat balance for the circulating heat transfer fluid r, f rCpr(tr,in − tr,out), where f r and Cpr refer to the mass flow rate and the heat capacity of the circulating fluid respectively, equals to the sum of all of the heat recovered from all waste hot stream i, and also equals the sum of all of the heat released to working fluid medium m.

The operating principle of an organic Rankine cycle is shown in four key processes, as shown in Figure 2. PVm denotes a pump

∑ qir + ∑ qic = FCi(Ti ,in − Ti ,out)

Figure 2. Organic Rankine cycle.

r∈9

Ppm

to compress a low-pressure requiring mechanical work organic working liquid into high-pressure liquid. Pressure level at this state is equal to the saturated pressure in the evaporator Erm where the high-pressure liquid will visit after the pump to be heated up and finally evaporate into a high-pressure organic working vapor. The amount of heat Qe taken from hot process streams then transferred through circulating heat transfer fluid to organic working fluid drives the evaporator. A turbine TCm is employed to expand the vapor from high pressure to a pressure level which equals the pressure of the low-pressure organic working liquid, simultaneously produce useful work Ptm. Finally, low-pressure organic working vapor, which usually lies in the superheated vapor region in case of dry fluids, is then condensed into saturated liquid by discharging extra low-grade thermal energy to external cooling utilities. Note, there are many heat exchangers existing in this supposed superstructure. In fact, there is no perfect heat exchanger of those the effectiveness is 100%. However, for the purpose of studying the waste heat recovery, the heat exchanger design is not going to be reached. Therefore, there is an assumption that the effectiveness of heat exchangers (e.g., evaporator, condenser, etc.) are considered as 1. It means it is emphasized first the amount of heat recovered from the background process that is transferred totally through the circulating fluid and second the power produced based on that amount of recovered waste heat. Furthermore, in this work, it tries not to change the background process. Instead, a circulating heat transfer fluid will be applied to run around absorbing waste heat and transfer to ORC for converting to useful work. Therefore, only waste hot streams are considered to recover heat. Note that the superstructure implies some assumptions. (1) The split flow of waste hot streams is allowed to go through more than one heat exchanger. This means that heat exchangers in parallel are possible. However, the superstructure does not consider heat exchangers in series. (2) Bypass is not allowed. (3) Adiabatic mixing is applied for all mixing of split streams.

∀i∈0 (1)

c∈*

∑ qir = ∑ i∈0

qrm = fr Cpr(tr ,in − tr ,out)

∀r∈9

m∈4

(2)

For reaching the final target temperatures for waste hot stream i, Ti,out, the waste hot stream i releases surplus heat qic to external cold utilities c ∈ * , eq 3 gives the total heat given to external cold utilities, FCi(ti − Ti,out).

∑ qic = FCi(ti − Ti,out)

∀i∈0 (3)

c∈*

Equations 4 and 5 respectively denote the quantity of heat transferred in heat exchanger qir and evaporator qrm. In these equations, rhir is the split ratio for waste hot stream i that exchanges heat with circulating fluid r and its output temperature is designated as thir. Similarly, rcir and tcir are the split ratio and output temperature for circulating fluid r, rhrm, and rcrm are the split ratios of circulating fluid r and working fluid m that exchanges heat with each other. Note that the split working fluid streams are assumed to be mixing isothermally for simplifying the formulation. qir = rhir FCi(Ti ,in − thir ) = rcirfr Cpr(tcir − tr ,out) ∀ i ∈ 0, r ∈ 9

(4)

qrm = rhrmfr Cpr(tr ,in − thrm) = rcrmfcme (Tme ,out − Tme ,in) e + λrm

∀ r ∈ 9, m ∈ 4

(5)

Also note that those split ratios at each specific location sum to one according to the mass balance, as shown in eqs 6−9.

∑ rhir = 1

∀i∈0 (6)

r∈9

∑ rcir = 1

∀r∈9 (7)

i∈0

4. MINLP FORMULATION AND SOLUTION STRATEGY This article aims at developing a feasible approach to maximize the recovery of low-grade waste heat via the integration of ORC and circulating heat transfer fluid with the background process. Thus, the heat integration between process hot and cold streams has been implemented, and the use of the ORC on recovering waste heat from the remaining waste hot streams can not increase the consumption of external hot utilities when compared with the stand-alone system without the involvement of the ORC.

∑

rhrm = 1

∀r∈9 (8)

m∈4

∑ rcrm = 1 r∈9

∀m∈4 (9)

Equation 10 shows the heat balance for working fluid m in the ORC over the evaporators, and eq 11 is the heat balance around the condensers. The total heat transferred from the waste hot D


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Industrial & Engineering Chemistry Research process streams to working fluid m, with heat capacity flow rate fcem, can increase the working fluid temperature from Tem,in to Tem,out and then evaporate the working fluid into high-pressure vapor, as shown in eq 10. Equation 11 shows similar mechanism around the condensers. Note that the heat involved in the balance of working fluid is composed of both sensible and latent heats, Λem and Λcm. The latter can be summed up from individual evaporators or condensers, as shown in eqs 12 and 13, where Lem and Lcm are the specific latent heats under operating conditions of evaporator and condenser. Note that L*m represents for the overall specific latent heat of a working fluid. λerm and λcmc stand for the specific latent heat of the working fluid that participates in heat transfer with the circulating fluid r at heat exchanger Erm and with the cooling utilities c at heat exchanger Cmc, respectively. The Peng−Robinson equation of state (PR-EOS) is adopted for calculating the specific latent heat and the enthalpy for the potential working fluids. The calculation details of the PR-EOS are depicted in the Appendix.

∑ qrm = fcme (Tme ,out − Tme ,in) + Λem

∑ λrme = fm Lme

=

∑

c λmc

=

fm Lmc

(19)

Tmt ,in = Tme ,out

∀m∈4

(20)

Tmc ,in = Tmt ,out

∀m∈4

(21)

∑ rhir thir

(22)

∀r∈9 (23)

∑

rhrmthrm

∀r∈9 (24)

m∈4

Equations 25−31 guarantee the decreasing temperature of waste hot process streams and the increasing temperature of cold streams when they flow through the heat exchanger networks. Similar assignments are also given for the working fluid.

(11)

∀i∈0

Ti ,in ≥ ti

tr ,in ≥ tr ,out

(13)

(14)

ΔHmc − Lmc Smc = f m c Tmc ,in − Tmc ,out Tm ,in − Tmc ,out (15)

(16)

Pmt = fm ΔHmt

∀m∈4

(17)

∀r∈9

(27)

Tmp ,out ≥ Tmp ,in

∀m∈4

(28)

Tme ,out

Tme ,in

∀m∈4

(29)

Tmt ,in ≥ Tmt ,out

∀m∈4

(30)

Tmc ,in

∀m∈4

(31)

≥

≥

Tmc ,out

ΔTmin ≤ dtirin ≤ Ti ,in − tcir + Γ(1 − zir )

Equation 16 gives the power Ppm required for compressing working fluid m from a saturated low-pressure liquid to evaporation pressure liquid. ΔHpm denotes change in enthalpy due to compression, which can be computed from the operating condition of the evaporator. Equation 17 is the generated power by high-pressure working fluid vapor going through the turbine. ∀m∈4

(26)

The temperature differences defined in eqs 32−39 ensure that the temperature difference is always positive and will be greater than the given minimum approaching temperature ΔTmin, when a certain match of heat exchange exists. The minimum approaching temperature ΔTmin sets the lower limit on the temperature difference that must exist between the hot and cold streams of every heat exchanger in the network for a reasonable sizing. A decrease in ΔTmin causes an increase in the heatexchange area. ΔTmin is chosen arbitrarily as 10 °C in the following study. In these equations, z* ∈ {0, 1} denotes a binary variable which represents the existence of a certain heat exchanger if its numerical value is one. Note that the corresponding constraint will be relaxed for a nonexistent heat exchanger where its binary variable has zero value.

ΔHme − Lme Sme = fm e e e Tm ,out − Tm ,in Tm ,out − Tme ,in

Pmp = fm ΔHmp

(25)

∀i∈0

ti ≥ Ti,out

∀m∈4

∀m∈4

∀i∈0

∑ rcirtcir

tr ,out =

(12)

∀m∈4

∀m∈4

=

i∈0

Equations 14 and 15 represent a simple method to determine the heat-capacity flow rates of the working fluid m in evaporator and condenser, fcem and fccm. Therein, f m is the mass flow rate of the organic working fluid m, ΔHem and ΔHcm are enthalpy changes in evaporator and condenser. For further details, ΔH*m is the total specific energy of the working fluid passing through evaporator/ condenser to raise the temperature from Tm,in * to Tm,out * then make a phase change isothermally at the same temperature T*m,out. The specific energy required to raise the temperature is denoted as S*m , namely the specific sensible heat. Similarly, the specific energy required for isothermal phase change is denoted as Lm*, namely the specific latent heat.

fcmc = fm

Tmp ,out

tr ,in =

∀m∈4

c∈*

fcme = fm

(18)

Tme ,in

r∈9

∀m∈4

r∈9

Λ cm

∀m∈4

ti =

(10)

c∈*

Λ em =

Tmp ,in = Tmc ,out

∀m∈4

r∈9

∑ qmc = fcmc (Tmc ,in − Tmc ,out) + Λcm

Equations 18−24 assign the known input and output stream temperatures, and those stream temperatures at various mixing points.

∀ i ∈ 0, r ∈ 9

(32)

ΔTmin ≤ dtirout ≤ thir − tr ,out + Γ(1 − zir ) ∀ i ∈ 0, r ∈ 9

(33)

in ΔTmin ≤ dtrm ≤ tr ,in − Tme ,out + Γ(1 − zrm)

∀ r ∈ 9, m ∈ 4 E

(34) DOI: 10.1021/acs.iecr.5b03381 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 3. Pinch point in (left) the evaporator and (right) the condenser.

Equation 42 is used to guarantee zero heat transfer rate for a nonexistent heat exchanger.

out ΔTmin ≤ dtrm ≤ thrm − Tme ,in + Γ(1 − zrm)

∀ r ∈ 9, m ∈ 4 ΔTmin ≤

in dtmc

≤

Tmc ,in

(35)

Q Lz ≤ q ≤ Q Uz * * * * ∈ {ir , rm , ic , mc| ∀ i ∈ 0, r ∈ 9, m ∈ 4, c ∈ *}

− Tc ,out + Γ(1 − zmc)

∀ m ∈ 4, c ∈ *

(36)

(42)

Furthermore, eq 43 can be added to guarantee at least one existent evaporator for each working fluid.

out ΔTmin ≤ dtmc ≤ Tmc ,out − Tc ,in + Γ(1 − zmc)

∀ m ∈ 4, c ∈ *

(37)

∑ zrm ≥ 1

ΔTmin ≤ dticin ≤ ti − Tc ,out + Γ(1 − zic) ∀ i ∈ 0, c ∈ * ΔTmin ≤ dticout ≤ Ti ,out − Tc ,in + Γ(1 − zic) (39)

Note that eqs 25−31 and 32−39 are possible to divide into two of the same overall meaning categories. However, it is not easy for each category to be represented by one generic equation. Further studies will consider this issue for simplification. The possible phase change in evaporator and condenser needs further attention. In the evaporator, the waste heat transferred to the high-pressure working fluid liquid will be used to increase its temperature until evaporation at the saturation temperature. In the condenser, the residue heat is released to the cooling water where the low-pressure working fluid vapor will decrease its temperature until its condensation at the saturation temperature. Two additional constraints are used to guarantee the temperatures inside the evaporator and condenser are greater than the minimum approaching temperature, such as shown in Figure 3 and eqs 40 and 41.

P0: max P net = x 0 ∈ Ω0

∀ r ∈ 9, m ∈ 4

∀ m ∈ 4, c ∈ *

(Pmt − Pmp)

m∈4

e c ⎧ zir , zrm , zic , zmc ; q , q , q , q ; λrm , λmc ; ⎫ ir rm ic mc ⎪ ⎪ ⎪ ⎪ Λ e , Λ c ; fm , f , fc e , fc c ; C ; P t , P p ; m m pr m m r m m ⎪ ⎪ ⎪ ⎪ x1 ≡ ⎨ rcir , rhrm , rcrm; ti , tr ,in , tr ,out ; thir , tcir , thrm ; ⎬ ⎪ ⎪ ⎪ dt in , dt out ; dt in , dt out , dt in , dt out , dt in , dt out ;⎪ ir ir rm rm ic ic mc mc ⎪ ⎪ ⎪ ⎪ ∀ i ∈ 0, r ∈ 9, m ∈ 4, c ∈ * ⎭ ⎩

(40)

e e c c e,sat ⎧ , Pmc,sat ; Lme , Lmc ;⎫ ⎪Tm ,out , Tm ,in ; Tm ,out , Tm ,in ; Pm ⎪ ⎬ x2 ≡ ⎨ ⎪ e ⎪ c e c t p ⎩ Sm , Sm; ΔHm , ΔHm; ΔHm , ΔHm; ∀ m ∈ 4 ⎭

⎡ fcmc (Tmc ,in − Tmc ,out) ⎤ ⎥ ΔTmin ≤ Tmc ,out − ⎢Tc ,out − FCc ⎦ ⎣ + Γ(1 − zmc)

∑

x 0 = x1 ∪ x2

⎡ rhrmfcme (Tme ,out − Tme ,in) ⎤ ⎥ − Tme ,out ΔTmin ≤ ⎢thrm + rhrmFCr ⎦ ⎣ + Γ(1 − zrm)

(43)

The ORC-integrated heat recovery problem can be formulated as the following mixed-integer nonlinear programming (MINLP) problem P0, where the design objective is to maximize the overall net power (Pnet) between power generation and consumption in the turbine (Ptm) and pump (Ppm). We proposed maximizing the overall net power, instead of maximizing the thermal efficiency, since the amount of recovered heat input into the ORC cycle is not fixed. The operating temperature and pressure will give significant influence on the total amount of waste heat recovered by the ORC cycle and also the power generation efficiency. The case study in next section will elucidate furthermore the numerical details.

(38)

∀ i ∈ 0, c ∈ *

∀m∈4

r∈9

Ω 0 = {x 0| eqs 1−43}

(41) F


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Industrial & Engineering Chemistry Research For a given set of waste hot streams, one can find the maximized net power by solving P0. However, one can find that under some operating conditions, such as the evaporator and condenser temperatures and pressures play crucial roles during the optimization. To simplify the convergent speed and to figure out the impacts of these crucial operating variables, one simplified solution strategy is adopt, such as shown in Figure 4.

heats at various states can then be found quite easily. Only those remaining variables in x1 will be solved for maximizing the net power. The problem P0 will be simplified into the following MINLP problem P1. P1: max P net = x1 ∈ Ω1

∑

(Pmt − Pmp)

m∈4

Ω1 = {x1| eqs 1−43}

5. PREHEAT TRAIN EXAMPLE AND DISCUSSION The proposed ORC-integrated model for waste heat recovery is demonstrated on a crude preheat train process adapted from the literature.8,17 After a complete process heat integration, the resulting six waste hot streams are worth for heat recovery, such as shown in Figure 5. To solve the MINLP problem P1, the General Algebraic Modeling System (GAMS)18 is used as the main solution environment on 1.00 GB RAM processor with BARON as the MINLP solver. This example involves six waste hot process streams along with cooling water as the cooling utilities. Given data for the problem, including the starting and targeting temperatures of the waste hot streams, their heat-capacity flow rates, the available utilities, etc. are listed in Table 1. The minimal approaching temperature Table 1. Data of Waste Hot Streamsa target T (deg C) H1 H2 H3 H4 H5 H6 CW

Figure 4. Proposed optimization flowsheet to maximize the net power from the ORC-integrated waste heat recovery system.

Instead of directly including all design variables in the optimization, the evaporator and condenser temperatures e c (Tm,out and Tm,out ) are optimized explicitly. The optimal operating temperatures are optimized in the outer loops, and those variables in x2 including operating pressure as well as those thermodynamic variables such as enthalpies and specific latent

fuel oil light naphtha gas oil reflux kerosene heavy naphtha

heat capacity flow rate (kW/K)

Tin

Tout

163.33 302.70 82.24 91.30 53.61 6.74

120 108 172 169 135 127 20

90 71 65 77 38 38 30

a Cpr = 2.16 (kJ/kg·K); ΔTmin = 10 °C; isentropic efficiency of turbine 0.8; isentropic efficiency of pump 0.65; working medium n-pentane.

Figure 5. Typical crude preheat train with six waste hot streams.8,17 G


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e Table 2. Effects of Evaporator Temperature on ORC Performance where Tcm,out = 30 °C (Pc,sat m = 0.821 bar) and Tm,in ≈ 30.1 °C (Working Fluid n-Pentane)

Tem,out ORC

no. of hot streams

one ORC

H5 H5 H5 H5 H5 H5 H5 H5 H5 H1−6 H1−6 H1−6 H1−4 H5,6 H1,4 others H3,4 others

two ORCs

Tcm,in

Pe,sat m

fm

wnet

bar

kg/s

kJ/kg

44.5 46.8 47.7 48.2 49.1 49.6 50.6 51.5 53.8 44.5 48.2 52.5 48.2 48.2 53.4 45.4 57.7 45.0

2.471 2.833 2.989 3.069 3.234 3.319 3.494 3.676 4.162 2.471 3.069 3.865 3.069 3.069 4.061 2.611 5.035 2.540

8.01 7.31 7.02 6.88 6.59 6.44 6.15 5.85 5.09 84.4 73.0 58.3 65.6 7.6 27.6 48.8 32.3 40.6

31.0 35.1 36.7 37.5 39.1 39.8 41.4 43.0 46.8 31.0 37.5 44.5 37.5 37.5 46.0 32.6 52.9 31.8

deg C 65 70 72 73 75 76 78 80 85 65 73 82 73 73 84 67 93 66

Wnet

Qe MW

0.248 0.257 0.258 0.258 0.258 0.256 0.255 0.252 0.238 2.617 2.736 2.592 2.460 0.286 1.270 1.590 1.710 1.290

ηORC %

3.100 3.113 3.014 2.963 2.859 2.807 2.699 2.587 2.294 35.27 31.46 25.95 27.70 3.27 12.10 20.50 15.00 17.10

8.0 8.2 8.5 8.7 9.0 9.1 9.4 9.7 10.4 7.4 8.7 10.0 8.9 8.7 10.5 7.8 11.4 7.5

Figure 6. Effects of evaporator temperature (condenser temperature is kept 30 °C) on (a) working fluid flow rate, (b) net power, (c) total heat transferred to the working fluid, and (d) outlet temperature of H5 (working fluid n-pentane) .

ΔTmin is taken as 10 °C in the following. Basically, working fluid is chosen based on the operating temperature of the ORC compared to the critical temperature of the working fluid. The operating temperature have to be lower than the critical temperature. Furthermore, in order to avoid harming turbines by liquid drops of working fluids condensed through expansion, the working fluid chosen should be a “dry” fluid, thus the ORC cycle can be operated with saturated vapor. Besides, there are some criteria considered such as the safety, the feasibility, etc. In

this case study, the supply temperature of the six waste hot streams ranges from 108 to 172 °C, and the target temperature spreads from 38 to 90 °C. Several dry working fluids can be used in this case study, such as n-butane, n-pentane, and hexane. However, the performance of these three working are found quite similar. Thus, only n-pentane will be illustrated in the following case study. Besides, it needs to employ a circulating heat transfer fluid. The heat transfer fluid or the circulating fluid should be kept in liquid phase under the operating condition, H


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Figure 7. Optimized configuration that can maximize the waste heat recovery from H5 where the evaporator and the condenser temperatures are 73 and 30 °C, respectively.

Figure 8. Optimized configuration that can maximize the waste heat recovery from H1−6 where the evaporator and the condenser temperatures are 73 and 30 °C, respectively.

high heat capacity, safe and feasible. However, our work is not going to focus on the most effective circulating fluid. It is believed that there is no significant impact from circulating fluid on the overall net power as soon as we assumed the waste heat is transferred perfectly from hot streams to the ORC. For example, Dowtherm A19 is one of synthetic organic fluids from DOWTHERM company that is a promising heat transfer fluid including indirect applications. It is used widely in many industries such as oil and gas, plastic processing, chemical processing, solar energy industries. Dowtherm A heat transfer fluid is a eutectic mixture of two very stable compounds, biphenyl (C12H10) and diphenyl oxide (C12H10O). The temperature range of Dowtherm A is suitable for our case study, from 15 to 400 °C in liquid phase. Another choice for circulating heat transfer fluid is Therminol products by Eastman Chemical company.20 Therminol provides a high performance and stability in systems with operating temperature from −115 to 400 °C. And many other suitable commercial heat transfer fluids could be chosen based on economic consideration. The solution procedure is based on the proposed optimization flowsheet, as shown in Figure 4. To simply the solution strategy, two design variables, the evaporator and condenser outlet temperatures, are determined out of the MINLP problem P1 where the relevant thermodynamic parameters of the ORC system can be calculated explicitly. After gaining the results from the MINLP model, it needs to check the results under different evaporator and condenser outlet temperatures to find the final optimized results. Before undertaking the whole preheat train example, the H5(kerosene) stream is used to investigate the impact of evaporator and condenser outlet temperatures on the ORC

performance, especially the overall net power. One can expect higher heat load if the condenser can be operated at lower pressure and temperature. In this study, the cooling water temperature is assumed to be 20 °C and the minimum approaching temperature is 10 °C, thus the lowest possible condenser outlet temperature will be 30 °C. Table 2 depicts some numerical results where Tcm,out is kept its lowest possible value, 30 °C, and Tem,out varies from 65 to 85 °C. As the evaporator temperature increases, the power generated by the turbine and thus the specific net power per unit working fluid flow rate also increase. However, the total heat transferred to the working fluid and thus the working fluid flow rate decrease. The total net power is a product of the working fluid flow rate and the specific net power. Even though the total net power is a weak function of the evaporator temperature within the range in between 70 and 80 °C, the conditions of Tcm,out = 30 °C and Tem,out = 73 °C give the maximum net power (Pnet = 0.258 MW). Further to Table 2, Figure 6 also shows some of these relations. Figure 7 illustrates the optimized configuration that can maximize the net power based on the recovered waste heat from H5. In the testing on single waste hot stream H5, the waste heat recovered from H5 is allowed to vary freely, as shown in Table 2. It is noted that the net power for a given amount of heat input into the cycle, i.e., the thermal efficiency in power generation, is 8.7% when Tem,out = 73 °C, which is much lower than 10.4%, the efficiency for Tem,out = 85 °C. However, the total heat recovered for the former case is 2.963 MW, which is much higher than 2.294 MW for the latter scenario. The resulting total net power for the former case, 0.258 MW is a little higher than that for latter scenario, 0.238 MW. These results and other data in Table 2 show that maximization of thermal efficiency will definitely result in different I


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Figure 9. Three configurations that use two sets of ORC to recover waste heat from H1−6.

recommendation, and maximizing the total net power should be more meaningful in this study.

When the waste heat of streams H1−6 is recovered simultaneously by using the proposed ORC model, Table 2 J


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net power. The last design can contribute 24 GWh per year. Note that the change of the process pinch leads to the change of the hot-stream inlet temperature in this model. Because the waste heat recovery is applied at below the pinch area, the hot-stream inlet temperature will increase when the process pinch increases, and vice versa. Therefore, it can be said that the study on the group of hot-stream temperature mentioned above reflects the impact of the process pinch point. Further detailed economic analysis is required for making a fair decision on the installation of the ORC system for recovering waste heat from the refinery process.

shows the effects of evaporator temperature on the ORC performance. The resulting net power is a weak function of the evaporator temperature, and Tcm,out = 30 °C and Tem,out = 73 °C give the maximum net power. Figure 8 illustrates the optimized operating condition that can maximize the net power generated from the recovered waste heat from H1−6. Therein, the total waste heat recovered is 31.48 MW (4.90, 7.98, 7.43, 7.98, 2.86, and 0.31 MW from H1−6), the generated net power is Pnet = 2.736 MW, and the overall efficiency is 8.7%. The yearly generated electricity is 22 GWh if the total operating period is 8040 h. For more details, Figure 8 is described as follows: There are six hot streams going to be recovered the waste heat. Each of hot stream will transfer heat with a circulating fluid that is split to meet the requirement of proper heat recovery. For example, there is 4.90 MW of heat from the hot stream H1 that will be taken by a part of the circulating fluid. This part of circulating fluid that participates in heat transfer with H1 is equal to 19.2% of the total flow rate of the circulating fluid used in this configuration. Since the H1 releases 4.90 MW of heat, its temperature decreases from 120 to 90 °C, and the heat transferred to a part of circulating fluid makes the temperature of this part increases from 71.6 to 110 °C. Every different part of circulating fluid transferring with each different hot stream has the same initial temperature that is 71.6 °C, but different final temperature because of the different amount of heat taken from different hot streams. After all splitting streams of the circulating fluid take the waste heat from hot streams, they are mixing together adiabatically to reach the temperature 119 °C. The circulating fluid then delivers all 31.5 MW heat taken from hot streams to the ORC working fluid to relax the temperature itself down to 71.6 °C before splitting to run around collecting waste heat again. The ORC working fluid receives 31.5 MW waste heat to vaporize into 73 °C vapor. This high-pressure vapor drives the turbine to produce 2.78 MW power and becomes a 48.2 °C lowpressure vapor. Then, this vapor is condensed to a 30 °C lowpressure liquid by transferring 28.7 MW heat to cooling utilities. The low-pressure liquid then is compressed by a pump driving by 0.04 MW power to become a 30.2°C high-pressure liquid. This high-pressure liquid is ready to evaporate by receiving heat 31.5 MW of heat from the circulating fluid, completing the organic Rankine cycle. All of variables will be solved by GAMS for each case of ORC working condition identified by (Tem,out; Tcm,out). One can note that the initial and final target temperatures of these six waste hot streams are quite different. It is possible to enhance the efficiency of the ORC-integrated heat recovery process if those hot streams can be grouped according to some characteristics and recovered by using different sets of ORC operated under different conditions. Figure 9 shows three possible configurations that uses two ORCs to recover waste heat from H1−6. In Figure 9a, H5 and H6 are allocated into one group due to their lower target temperatures. The resulting net powers from group 1 (H1−4) and group 2 (H5 plus H6) are 2.460 and 0.286 MW, with efficiencies 8.9% and 8.7%, respectively. Detailed numerical results are also shown in Table 2. In Figure 9b, H1 and H4 are categorized into one group due to their higher target temperatures. The resulting net powers from group 1 (H1 plus H4) and group 2 (remaining streams) are 1.270 and 1.590 MW, respectively. In Figure 9c, H3 and H4 (group 1) are recovered by one ORC due to their higher initial temperatures. The remaining streams are categorized into group 2. The resulting net powers from these two groups are 1.710 and 1.290 MW, respectively, which give the highest overall

6. ECONOMIC ANALYSIS Even though the thermoeconomic feasibility and the inherent tradeoffs of waste heat recovery using ORC has been well established for a variety of applications, a brief calculation on economic performance of the ORC which is integrated with a stand-alone HEN is shown in this work. This brief economic analysis is to show the feasibility of waste heat recovery using ORC, as well as to have a rationale for the selection of waste heat recovery configuration. However, note that it is not going to show the total economic performance of the whole system. HEN is not taken into account, instead, the attention is paid to the installation of ORC including capital costs of heat exchangers, turbines and pumps; operating costs, as well as the money-based benefits obtained. Also noted that the following economic analysis is based on several ideal assumptions, such as 100% heat exchanger effectiveness. The results of economic analysis need further consideration in practical application. The total capital cost (TCC) for implementing the ORC system on an existing HEN is calculated according to the following equation, based on the size of units:22 TCC =

⎧

⎫β ⎬ in out in out 1/3 ⎩ [dtir dtir (dtir + dtir )/2 + δ] ⎭ qir (1/hi + 1/hr )

⎪

∑ ∑ CV⎨

⎪

i∈0 r∈9

+

∑ i∈0

+

⎪

⎪

⎪

⎪

⎧ ⎫β q (1/hr + 1/hm) ⎬ CV⎨ in outrm in out 1/3 ⎩ [dtmrdtmr (dtmr + dtmr )/2 + δ] ⎭ m∈4

∑ ∑

⎪

⎪

⎪

⎪

⎧

576 394

∑

in

out

in

⎩ [dtmcdtmc (dtmc ⎪

⎫β ⎬ out + dtmc )/2 + δ]1/3 ⎭

qmc(1/hm + 1/hc )

⎪

∑ ∑ CV⎨ m∈4 c∈*

+

⎪

⎧ ⎫β qic(1/hi + 1/hc ) ⎬ ∑ CV⎨ in out in out 1/3 ⎩ [dtic dtic (dtic + dtic )/2 + δ] ⎭ c∈*

r∈9

+

⎪

⎪

⎪

{[C P0FBM]mturbine

m∈4

+ [C P0(1.89 + 1.35FPFM)]mpump }

(44)

where CV = 1650 is an area cost coefficient for a heat exchanger where the heat transfer is implemented between two streams; h is called out as a film heat transfer coefficient for each of hot or cold side of a heat exchanger; δ is a very small value to ensure the mathematically feasible meaning of the equation; the power of β = 0.65 is a parameter indicating the economy of scale, one of rules used for an estimate of the capital cost for a unit (usually it takes a value within 0.6 to 0.9). For cost estimate of pump and turbine, C0P is a purchased equipment free-on-board cost (i.e., equipment cost at a manufacture’s site) at base conditions, which depends on the power consumed or generated by pump or turbine, respectively. The following correlations are used for estimate of purchased equipment free-on-board cost21 K


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Table 3. Cost, Revenue, and Payback Years for Various ORC Designs in the Crude Preheat Train Example (Working Fluid nPentane) h

HX

pump

turbine

TCC

YR

PB

best scenario

(kW/m2·K)

($)

($)

($)

($)

($)

(y)

1ORC (H1−6) 1ORC (H1−5) 2ORC (H1−6) 1ORC (H1−6) 1ORC (H1−5) 2ORC (H1−6) 1ORC (H1−6) 1ORC (H1−5) 2ORC (H1−6)

1.0 1.0 1.0 0.1 0.1 0.1 10 10 10

1,393,000 1,366,000 1,519,000 6,222,000 6,100,000 6,785,000 312,000 306,000 340,000

88,000 87,000 137,000 88,000 87,000 137,000 88,000 87,000 137,000

1,792,000 1,788,000 3,051,000 1,792,000 1,788,000 3,051,000 1,792,000 1,788,000 3,051,000

3,273,000 3,241,000 4,707,000 8,102,000 7,975,000 9,973,000 2,191,000 2,181,000 3,528,000

2,200,000 2,179,000 2,412,000 2,200,000 2,179,000 2,412,000 2,189,000 2,168,000 2,360,000

1.49 1.49 1.95 3.68 3.66 4.13 1.00 1.01 1.49

⎧ 2.2476 + 1.4965log P t − 0.1618 for turbine 10 ⎪ ⎪ (log10P t)2 ⎪ log10 C P0 = ⎨ ⎪ 3.3892 + 0.0536log P p + 0.1538 for pump 10 ⎪ ⎪ (log P p)2 ⎩ 10

turbine and the power consumed by a pump within an ORC. The yearly revenue (YR) earned from an ORC is expressed according to the following equation: YR = C eH yP net

with the unit sale price of electricity C = 0.1 USD/kWh and yearly operating hours Hy = 8040. Subsequently, pay-back period (PB) is simply obtained by total capital cost divided by the income of net power, TCC/YR. There are two possibilities for application of ORC integrated with the background process which are investigated in this work. For each of possibility for application of ORC, there are several scenarios studied to find out the optimized operating condition that can maximize the net power produced from recovery of waste heat. Table 3 reveals the results of payback periods in cases of integrations of one ORC and two ORCs. Obviously, expenditure for installation of one ORC 3 273 000 USD for the background process is expected to be less than construction of two ORCs 4 707 000 USD. It is shown for the total capital cost, however, it would be incorrect if one expends double to build up two ORCs compared to one ORC. It is because of the differences of the capacities, namely heat transfer area for heat exchanger and power for pump and turbine, which decide the capital cost of equipment, instead of installing the same ORCs to get the waste heat recovery target. There are eight heat exchangers used for one ORC integrated into the background process, whereas ten heat exchangers are applied for the use of two ORCs. As mentioned above, due to the greater-than-3 pressure ratio criterion, 3.7 for one ORC and 3.1 and 6.1 for two ORCs, each of ORC is suggested employing two pumps for operation. It is also found reasonable for the yearly incomes. Note that the operating cost of units is implicitly included in term of the net power involved in the calculation of yearly income. Finally, the payback years predicted for each case, around 1.5−2 y, are acceptable. Based on calculation of capital cost of each component of an ORC including heat exchanger, pump and turbine, one can expect that there is a chance to reduce these component costs. It is easy to recognize that the heat transfer coefficient h could make some changes on heat exchanger capital cost due to relationship of which the larger heat transfer coefficient, the smaller heat transfer area. However, it is not simply linear. It is hard to go into detail because there are many other factors which should be taken in account to consider. Generally, heat transfer coefficient is recommended for further examination. Moreover, in case of integration of two ORCs, the pressure ratio of the ORC used for the group of four lower-temperature waste hot streams is almost 3. Hence, there is a chance of reduction in capital cost as well as

(45)

In terms of the capital cost estimate for turbine, beside purchased cost C0P, there is another factor FBM = 3.4, namely bare module factor, which is identified from a corresponding graph and an identification number that is typical for each type of turbine and assumption of carbon steel material.21 For cost estimate of turbine, it could be more simplistic compared to pump, due to only this factor needs to be dealt with. For cost estimate of pump, more parameters and factors need to be specified. Factor FP is pressure corrected factor which is available if a pump operates at pressure levels greater than 10 bar; otherwise it is 1 based on the following correlation21 ⎧0 for P e,sat ⎪ ≤ 10 bar ⎪ log10 FP = ⎨ e,sat for P e,sat ⎪− 0.3935 + 0.3957log10 P ⎪ − 0.0023(log P e,sat)2 ≤ 100 bar ⎩ 10

(47) e

(46)

Another factor for cost estimate of pump is FM = 1.6, material corrected factor which is also found from a corresponding graph and an identification number that is typical for each type of pump and assumption of carbon steel material.21 It has to be noticed that the number of pumps which will be mentioned soon later is necessary to be involved in capital cost. Finally, economic indicators or cost indices are required to convert purchased equipment cost into one that is accurate for the present time. It is considered as a time corrected factor. In this work, chemical engineering plant cost index (CEPCI 394 and 576 for 2001 and 2015, respectively) is referred to adjust for the effects of inflation through time. Operating cost of an ORC is simplified that only pumps are taken into account. As can be seen, there is only a pump is shown in an ORC operation principle figure. However, there could be more than one pump installed due to the level of pressure it need to be reached, particularly two pumps should be recommended if the pressure ratio is greater than three. In cost estimate, operating cost of a pump depends on the amount of power need to supply for operation of the pump. Similarly, an income obtained from an ORC is also calculated based on the amount of power that produces from the turbine. For convenience, net power is introduced as difference between the power generated by a L


Article

Industrial & Engineering Chemistry Research Appendix

operating cost of pump, then the pay-back period for this case changes a little to 1.94 y, if one decides to run this ORC with one pump, there could be more some possibilities of risk although. Furthermore, among six waste hot streams considered to recover waste heat, the amount of heat recovered from the 6th hot stream (H6) seems to be insignificant compared to other streams. Therefore, it is possible to think of ignoring this stream so that one can hope the total capital cost could be cut back while the target of waste heat recovery could still be satisfied. Thus, it is expected that the pay-back period in this case would be shorter. Although it could be a trivial difference in this scenario, one could find how it works in other situations when improvement is required in the concept of cost estimate.

Useful equations for calculating enthalpy and saturated pressure are given as follows. Coefficients for calculating these thermodynamic properties can be found in the literature.23 Enthalpy = Ideal gas enthalpy + Departure enthalpy H(Tc , Pc , t ) = ΔHIG + HDep

Ideal gas enthalpy

ΔHIG =

∫T

t

CpIG dT

ref

Departure enthalpy

7. CONCLUSION

H

The organic Rankine cycle (ORC) is found appealing to further recover a part of the residual energy in the hot process streams and transfer it into useful work when it is applied for a background process which is a stand-alone heat exchanger network (HEN) among given basic stream inlet and outlet information as well as operational limitations. This article aims at proposing a systematic procedure to design an ORC-integrated heat recovery system. A generic representation of a superstructure for heat exchanger network synthesis (HENS) between all of the waste hot streams with units of a crude preheat train is presented at first. This superstructure is then expanded to include organic Rankine cycles for recovering residual heat from the heat surplus zone below the process pinch through assistance of circulating heat transfer fluid so that it is called indirect ORCintegrated heat recovery. The waste heat is considered as the residue heat of total hot process streams after all of possibilities of process-to-process matches as well as external utilities. Thus, use of ORC on recovering waste heat from the remaining of waste hot streams will not increase the consumption of utilities compared to a stand-alone HEN without ORC. The ORCintegrated heat recovery problem can be formulated as a mixedinteger nonlinear programming (MINLP) problem (defined as P0) . A simplified solution strategy is depicted that the evaporator and condenser outlet temperatures of an ORC are optimized then all of operating pressures as well as those thermodynamic properties such as enthalpies and specific latent heats are found quickly. Subsequently, the problem becomes P1 with the design objective is to maximize the net power between the power generated and consumed through the turbine and pump while a number of variables for this problem are reduced due to those defined above. Several cases of ORC integration to the background process are investigated. The outlet temperature of the condenser is found that the lower it is, the more efficiently the ORC works. Hence, Tcm,out = 30 °C is chosen because the cooling utility temperature is assumed to be 20 °C and the minimum approaching temperature is 10 °C. It is shown that there is 2.736 MW of net power obtained at conditions of Tcm,out = 30 °C and Tem,out = 73 °C in case of one ORC integrated into the process. However, when two ORCs are applied with difference groups of waste hot streams, one is grouped due to their higher initial temperatures, the other one includes all remaining streams, the net power obtained is recorded of 3MW. Therefore, it is more informative that an economic analysis reveals 1.49 and 1.95 y of payback of the two foregoing cases for further consideration of selection on a proper ORC-involved waste heat recovery system.

Dep

t = Rt(Z − 1) +

( ddat ) − a ln⎡ Z + (1 + 2 2b

⎢ ⎣ Z + (1 −

2 )B ⎤ ⎥ 2 )B ⎦

Peng−Robinson EOS Z=

V aV − 2 V−b Rt(V + 2bV − b2)

or 0 = Z3 + (B − 1)Z2 + (A − 3B2 − 2B)Z + (B3 + B2 − AB)

where A=

aP Rt 2

a = 0.45724

B=

bP Rt

(RTc)2 α Pc

b = 0.0778

RTc Pc

2 ⎡ ⎛ ⎛ t ⎞0.5⎞⎤ ⎢ ⎥ α = 1 + κ ⎜⎜1 − ⎜ ⎟ ⎟⎟ ⎢ ⎝ Tc ⎠ ⎠⎥⎦ ⎝ ⎣

κ = 0.37464 + 1.54226ω − 0.26992ω 2 ⎡ ⎤ ⎛ P sat ⎞ ⎢ ⎥−1 ω = −log10⎜ ⎟ ⎢ ⎥ P ⎝ ⎠ c ⎣ Tr = 0.7 ⎦ Tr = reduced temperature −0.5⎡ ⎛ ⎛ t ⎞0.5⎞⎤ κR2Tc ⎛ t ⎞ ⎢ da = − 0.45724 1 + κ ⎜⎜1 − ⎜ ⎟ ⎟⎟⎥ ⎜ ⎟ dt Pc ⎝ Tc ⎠ ⎢⎣ ⎝ Tc ⎠ ⎠⎥⎦ ⎝

Antoine equation

■

⎛ D ⎞ 2 log10(P sat) = D1 − ⎜ ⎟ ⎝ T + D3 ⎠

AUTHOR INFORMATION

Corresponding Author

*Tel.: 886-2-33663039. Fax: 886-2-23623040. E-mail: CCL@ ntu.edu.tw. Notes

The authors declare no competing financial interest. M


Article


■

ACKNOWLEDGMENTS The authors thank the Ministry of Science of ROC for supporting this research under Grant NSC102-2221-E-002216-MY3.

■

■

Λcm = overall latent heat of organic working fluid m in condensers

REFERENCES

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NOMENCLATURE

Indices and Sets

c ∈ * = {1, ..., C}, cooling utility i ∈ 0 = {1, ..., I}, waste hot process stream m ∈ 4 = {1, ..., M}, working fluid in an ORC r ∈ 9 = {1, ..., R}, circulating fluid for heat transfer x* = set of unknown variables, * ∈ {0, 1, 2} Ω* = searching space, * ∈ {0, 1} Parameters Cpr = specific heat of circulating heat transfer fluid r FCi = heat capacity flow rate for waste hot stream i Lm* = specific latent heat of working fluid m in evaporator/ condenser (* ∈ {e, c}) P*m ,sat = saturated pressure in evaporator/condenser (* ∈ {e, c}) Ti,† = inlet/outlet († ∈ {in, out}) temperatures of waste hot stream i T*m,† = inlet/outlet († ∈ {in, out}) temperatures of working fluid m in * ∈ {e, c, t, p} Q† = lower and upper bounds († ∈ {L, U}) of heat load Γ = upper bound for temperature difference ΔH*m = specific enthalpy change of organic working fluid m around * ∈ {e, c, t, p} ΔTmin = minimum approach temperature difference Binary Variables z* = 1, * ∈ {ir, rm, ic, mc} denotes existence of a unit Positive Variables dt†* = * ∈ {ir, rm, ic, mc}, input and output († ∈ {in, out}) temperature difference at hot and cold exits of heat exchangers HEir, Erm, Cic, or Cmc f * = * ∈ {r, m}, mass flow rate of circulating fluid r and working fluid m fc*m = heat capacity flow rate of working fluid m in evaporator/ condenser (* ∈ {e, c}) q* = * ∈ {ir, rm, ic, mc}, heat load in heat exchanger HEir, evaporator Erm,condenser Cic or Cmc rhir, rcir = split ratio of hot waste stream i and cold circulating fluid r in heat exchanger HEir rhrm, rcrm = split ratio of hot circulating fluid r and cold working fluid m in evaporator Erm ti = temperature of waste hot stream i after implementation of heat recovery tr,† = input and output († ∈ {in, out}) temperatures of circulating heat transfer fluid r thir, tcir = temperature of waste hot stream i and cold circulating fluid r at exit of HEir thrm = temperature of hot circulating heat transfer fluid r at exit of evaporator Erm Ptm = power generated by turbine with organic working fluid m Ppm = power consumed by pump with organic working fluid m λerm = specific latent heat of organic working fluid m in evaporator Erm λcmc = specific latent heat of organic working fluid m in condenser Cmc Λem = overall latent heat of organic working fluid m in evaporators N


Organic Rankine Cycle for Waste Heat Recovery in a Refinery

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