Techno-economic evaluation of a multi effect distillation system driven by low-temperature waste heat from exhaust flue gases

Desalination 460 (2019) 64–80

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Techno-economic evaluation of a multi effect distillation system driven by low-temperature waste heat from exhaust flue gases

T

Sina Goodarzia, Ebrahim Jahanshahi Javarana, , Mohammad Rahnamab, Mohamadreza Ahmadic ⁎

a

Department of Energy, Institute of Science and High Technology and Environmental Sciences, Graduate University of Advanced Technology, Kerman, Iran Mechanical Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran c Golgohar Iron Ore and Steel Research Institute, Golgohar Mining and Industrial Company, Sirjan, Iran b

ARTICLE INFO

ABSTRACT

Keywords: Waste heat recovery Heat exchanger LCOW MED distillation Payback period

In this study, technical and economical evaluation of a multi effect distillation (MED) system is presented which utilizes the vapor produced from waste heat of exhaust flue gases. In order to recover the waste heat of flue gases, a shell and tube heat exchanger was designed with the Polytetrafluoroethylene (PTFE) material in order to resist corrosion as a result of sulfuric acid formation. Recoverable energy, which is obtained from experimental data, serves as the source of energy required to produce water vapor. Due to high fluctuations in the amount of vapor produced, an auxiliary boiler is employed for its compensation. The vapor which has been produced by the heat exchanger and/or auxiliary boiler, is used as the motive steam in the MED distillation. Economic analysis of MED distillation system driven by low-temperature waste heat is carried out and system payback period based on natural gas saving is obtained. Finally, waste-heat-driven MED distillation system is compared to a conventional MED on the basis of the levelized cost of water (LCOW) at different electrical and natural gas tariffs as well as the real interest rates. Economic evaluation shows that the LCOW is about 1.13–2.9 $/m3.

1. Introduction

surface, the large heat exchange surfaces required for heat transfer, scaling/deposition on the outer surface of the heat exchanger tubes, and the limited use of the low temperature heat [6]. Various methods for estimating the amount of the industrial waste heat within a region have been discussed by Brueckner et al. [7]; they were categorized based on the study scale, data collection, and the chosen approach. Also, to quantify this waste heat, it should be classified as theoretical, technical, or economic potentials. In the theoretical potential, the maximum recoverable energy with respect to the ambient temperature is found, while in the technical one, the feasible recoverable energy is obtained. In addition, the economic one deals with determining the rate of return, energy cost, and the payback period. A review of waste heat recovery technologies available to convert the low grade waste heat to useful forms has been presented by Shu et al. [8]. The technologies discussed included turbine, refrigeration, Rankine cycle, and desalination and combined cycle systems using more than two of these waste heat recovery technologies. In a study presented by Rakib et al. [9], the energy and cost saving potential of waste-heat utilization in common waste heat sources of textile industries including hot exhaust from onsite electricity generators, stenter exhaust and dyed waste water in Bangladesh were

Considering growth in global population along with higher standards of living, freshwater scarcity is one of the greatest challenges facing contemporary humans. Water desalination is a key technology to resolve this problem due to the huge amount of available salt water at seas. Desalination plants are generally categorized as thermal and membrane technologies [1], among which, low temperature multi-effect distillation (LT-MED) and reverse osmosis attracted more attentions [2,3]. The most important parameter in evaluation of a desalination plant is its energy consumption. The main advantage of LT-MED systems is that low grade heat from industrial processes can be utilized as a promising heat source [4]. In fact top brine temperature of this MED distillation is < 70 °C which makes them attractive the market of seawater desalination in recent years. The main focus of research studies in this area are on the thermodynamic and thermo-economic study of combined desalination, as well as new system integration approach with waste heat or renewable sources [5]. Waste heat resources can be classified by the temperature range as low, medium and high temperatures [6]. Most of the industrial waste heat is in the low temperature range. Low temperature heat recovery involves at least four challenges: corrosion of the heat exchanger

⁎

Corresponding author. E-mail address: [email protected] (E. Jahanshahi Javaran).

https://doi.org/10.1016/j.desal.2019.03.005 Received 28 September 2018; Received in revised form 10 December 2018; Accepted 12 March 2019 Available online 20 March 2019 0011-9164/ © 2019 Elsevier B.V. All rights reserved.

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estimated. In this study, energy savings, cost information and payback period were determined. Waste heat can be recovered using heat exchangers. Thakar et al. [10] designed a counter flow shell and tube heat exchanger to recover waste heat from exhaust gas of a diesel engine. The diesel engine with incorporation of heat exchanger showed improved performance with a considerable amount of primary fuel saving. A critical parameter in the heat exchanger design is surface area through which heat transfer occurs. Teke et al. [11] proposed a new model to determine the type and area of the most suitable heat exchanger for maximum waste heat recovery by considering economic parameters of present worth factor, unit area cost of the heat exchanger and life-time. The proposed model was validated in a case study and its appropriateness was verified. Performance evaluation of preheater and the evaporator heat exchangers made from a number of tubing materials in a desalination system and utilizing the low temperature waste heat of the exhaust flue gases was done by El-Dessouky and Ettouney [12]. Their results indicated that the heat transfer area of the PTFE pre-heaters and the evaporator was 2 to 4 times larger than that of the metal heat exchangers because of the low thermal conductivity of polymers. However, the lowest cost was obtained for the PTFE heat exchanger due to its much lower cost of the material. Usually, the temperature and flow rate of the industrial waste heat fluctuate in a certain range due to the variation of upstream industrial process [13–15]. An overview on the challenges of thermal power fluctuations in waste heat, the related issues affecting the recovery power systems and the available solutions for the problem were presented by Jiménez-Arreola et al. [15]. Different measures to compensate the fluctuations of different waste heat sources as well as the economic considerations required for the waste heat to power systems operating under fluctuating sources were reviewed. The waste heat utilization of exhaust gas of an internal combustion engine of low capacity for desalination was experimentally studied by employing a submerged horizontal tube straight pass evaporator and a condensing unit [16] without affecting the performance of the engine. It was found that the overall efficiency of the system is enhanced and thermal pollution was also considerably reduced by utilizing the heat energy in the condenser water in addition to the waste exhaust gas heat energy. Two novel sensible heat driven desalination processes, namely boosted MED distillation and flash boosted MED distillation were modeled by Rahimi et al. [17]. The boosted MED distillation contains a booster unit which is an evaporator in which the heat source fluid is employed to evaporate more feed water. The product vapor is then flown to an appropriate effect of the MED distillation and leads to supplementary distillate production. In the flash boosted MED distillation, the MED distillation effects operate in couple with a series of flashing boxes. It was shown that two novel desalination systems are more thermally efficient than conventional MED distillation and causes higher production rates than conventional MED distillation. As mentioned before, low grade heat recovery is on prime importance because it is available in nearly all industries. A study was conducted by Xuea et al. [18] on a LT-MED distillation utilizing lowgrade heat of a thermal power generating unit. Three different scenarios that use flue gas to evaporate seawater are proposed. In the first scenario, the flue gas used as the heat source of the first effect of the LTMED distillation system. In contrast, in the second scenario, a portion of circulating seawater of the condenser of steam turbine flows parallel into each effect as feed brine. In the third scenario, the extracted steam from the turbine used as the heat source of the first effect and the feed water is sent into MED distillation effects. Economic analysis revealed that reduction the amount of extracted steam from the turbine can remarkably reduce water production cost. A parametric study and economic evaluation of a MED distillation integrated with reciprocating internal combustion engine was carried

out by Salimi and Amidpour [19]. In this integrated system, the exhaust flue gas of the engine is used for steam production o be used as the heat source of the first effect of MED distillation. Economic analyses of the combined system was performed by the annualized cost of system method. It was determined that at higher market prices for fresh water of about > 7 US$ per cubic meter, the increase in number of effects is more significant to decrease of payback period. A LT-MED system powered by the cooling water of a diesel power generator set was introduced by Zhang e al. [20]. After driving the thermodynamic and heat transfer mathematical modeling of the system, a four-effect system was designed, built, installed and tested. Operationally, the evaporation temperature of each effect was linearly proportional to the heat load of the diesel engine. In was shown that by increasing the heat load of the diesel power generator set from 300 kW to 530 kW, the rate of fresh water production increases from 1.26 m3/h to 2.30 m3/h. A micro cogeneration unit comprising of a Stirling engine coupled with a single effect thermal desalination plant was investigated for the simultaneous production of fresh water and electricity [21]. Firstly, thermodynamic theories and numerical analysis were carried out to define the final prototype configuration. Then, an experimental test phase was carried out to evaluate the actual plant performance. The apparatus exhibited a very good response to varying thermal power input thus confirming the opportunity to feed the desalination plant also with different forms of waste heat. Thermodynamic and economic analysis of the integration of Organic Rankine cycle (ORC) and MED with waste-heat recovery system to produce electricity and distillate water at two different configurations, hybrid serial cascade and cascade configuration were carried out by Baccioli et al. [22] at steady state conditions. The aim of the work was to define the most viable cogenerative architecture from the thermodynamic and economic points of view for MED-ORC coupling in medium temperature waste heat recovery context, from those processes which can provide heat at medium temperature. Following a thorough literature survey done by authors, no previous published work was found in which waste heat has been used for water desalination using MED and its economic viability by considering thermal power fluctuations present in the waste heat from industrial processes. This paper aims to provide the economic viability of water desalination by a MED system driven by low temperature vapor produced using a PTFE shell and tube heat exchanger utilizing waste heat from outlet flue gases of a plant [23] by considering limiting conditions of the sulfuric acid dew point and design temperatures and reveals its technical and economical aspects; a subject which was not found in previous published works. In addition, to the best of authors' knowledge, there has been no published work on the economic comparison of a waste heat driven MED distillation system and a conventional one at various natural gas and electricity costs as well as interest rates. In this study, these systems are compared with each other based on the levelized cost of water. The methodological approach presented in this study aims to give the industrialists, researchers and better management of industries, guidelines for design of vapor production and multieffect distillation systems utilizing industrial waste heat considering fluctuations of exhaust waste heat. 2. Methodology The process flow diagram of the proposed system under consideration is depicted at Fig. 1 schematically. This system includes a shell and tube heat exchanger, an auxiliary boiler and a MED distillation unit. In the proposed heat exchanger, the exhaust flue gases come from an iron ore Pelletizing Plant whose characteristics were discussed in Ref. [23]. These gases flow through the tubes while pure water on the shell side is sprayed over them. Product vapor is directed to the first effect of MED distillation unit. Saline water sprays on MED distillation tube bundles and evaporates the steam generated in the first effect 65

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Fig. 1. The process flow diagram of the proposed system.

flows to the next effect and the same phenomenon taken place at subsequent effects. Desalinated water produced in each effect, is collected as distillate. Due to fluctuations in the daily-averaged mass flow rate and temperature of flue gases leaving energy in each duct changes resulting in variation in vapor production by the heat exchanger. Therefore, an auxiliary boiler is considered to mitigate the fluctuations of vapor entering the MED distillation system. To achieve the economic comparison of a waste heat driven MED distillation system and a conventional one at various natural gas and electricity costs as well as interest rates, the amount of desalinated water production should be determined. To this end, after the experimental data treatment and waste heat recovery estimation at Section 2.1, details of the selection of material, design and simulation of the heat exchanger for waste heat recovery and vapor production are discussed at Section 2.2. Then, the amount of distillate water is calculated with the mathematical modeling presented at Section 2.3. Finally, the levelized cost of water and payback period as well as the desired economic comparison is made by the aid of materials presented at Section 2.4. To achieve the objective mentioned above, a FORTRAN code based on the solution strategy as seen in Section 2.5 is developed.

calibration certification to the Golgohar company. The aforementioned procedure justifies that the measured date are realizable. Furthermore, composition of exhaust flue gases at each duct were measured by Testo 350 and Testo 454 measuring instruments, respectively. The composition of flue gases was measured three times in the period under consideration. One of the standard methods for doing the uncertainty analysis, is performing various measurements and using them to calculate the standard deviation and average. The average of three different measurements in the period under investigation at full load operating conditions was used in the calculation. Although there was a small difference between the measurements in the order of 2%, the average of these measurements was used in calculations. The extracted instantly data from the Golgohar pelletizing plant control room were converted to the three-hour data by a FORTRAN code. In addition, in the written computer program, the volumetric flow rate of flue gases is calculated by using power consumption and fan characteristic curve. Detailed description of the pelletizing plant and waste heat estimation from exhaust gases has been discussed in Ref. [23]. Waste heat input data consisting of temperature and mass flow rate of exhaust flue gases, were obtained from preceding measurements. Figs. 2 and 3 show monthly variation of daily-averaged flue gases temperature and mass flow rate at three ducts outlet, respectively. Also, in Table 1 mole percentage of flue gas components at three ducts is seen.

2.1. Input data and waste heat potential evaluation 2.1.1. Experimental data and the statistical treatment The experimental data in this study are temperatures and composition of exhaust flue gases coming from three ducts (called as G5.036, G5.037 and G5.042 ducts) as well as electro motors power consumption for a time interval of 5 months, starting on 21 of March 2015 Golgohar pelletizing plant in Iran [23]. The measured temperatures and power consumptions by the corresponding sensors are instantly (every second) sent to the control room, resulting in a large volume of the recorded data. To carry out an affordable analysis, data were averaged in every three-hour time interval resulting in eight data on each day from which the daily-averaged values were obtained. The sensors measuring flue gas temperatures are thermocouple of type K. In addition, there are a power meter and a sensor for each electromotor. There is an inspection unit in the pelletizing plant that revisits the sensors weekly and sends a report to the calibration unit. By observing non-calibration in the thermocouples, they are replaced by new ones. Regarding the electromotors, the difference between the energy measured by the power meter and that by the sensor in a period shows the un-calibration of the sensor or the failure of the power meter. It should be noted that the power meter is calibrated on a yearly basis and sensors are checked at the same time and replaced by new ones if it is required. Moreover, the iron ore plant has an overhaul each year. During the overhaul, all measuring devices are checked and calibrated. Iranian environmental protection organization (IEPO) has some Trusted Labs. All measurement tools used in these labs must have the calibration certificate from IEPO. The Golgohar company has contracts with some of these labs for the required measurement in the plant. These labs must present

Fig. 2. Monthly variation of daily-averaged flue gases temperature at three ducts outlet. 66

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point (TDP) temperature, as calculated from Eq. (1), the average temperature of the flue gas components, and the design temperature in the three ducts. Two cases can be considered for estimation of recoverable energy; these include cooling down the flue gases to a temperature above (case I) or below (case II) the sulfuric acid dew point temperature. Regarding these cases, the recoverable energy can be found by the following equations:

E = mFlue gas × Cp, Flue gas × (TFlue gas

TDP )

(2)

E = mFlue gas × Cp, Flue gas × (TFlue gas

TDesign)

(3)

TDesign is designed temperature of the plant [27,28] which is the minimum allowable temperature of flue gases during plant operation. 2.2. Heat exchanger design A heat exchanger (HX) is required to recover waste heat of flue gases and transfer it to another fluid. Details of the design and selection of materials used in the heat exchanger are discussed as follows. Among various types of heat exchangers, shell and tube heat exchanger is the most widely used in industries which cover a wide range of operating temperatures and pressures. This is due to its higher efficiency, relatively simple manufacturing process, and low cost of shell and tube heat exchangers. Fig. 4 shows a schematic view of the proposed HX in which pure water returning from the MED distillation unit is sprayed on the tube bundle and a low temperature vapor at 70 °C is produced. The feed (shell) side of the heat exchanger is subject to sub atmospheric pressure. To this end, a vacuum pump is used to maintain the pressure of the heat exchanger at 31.19 kPa in order to have the desired vapor. This produced vapor is the feed vapor to the MED distillation unit. The pure water accumulated at the bottom of the shell is continuously pumped to the nozzles. There are some issues that should be considered in the design/selection of a shell and tube heat exchanger, such as tube and shell materials, flow arrangement, evaporation mechanism, overall heat transfer coefficient, pressure drop, fan power consumption and economical aspects. It is assumed that the heat exchanger is well insulated and hence the heat losses to the environment can be ignored. Also, the shell temperature is low and close to the ambient temperature, which reduces the rate of heat transfer to the surrounding.

Fig. 3. Variation of daily-averaged mass flow rate of flue gases versus month. Table 1 Mole percentage of flue gas components at three ducts. Duct number Gas component (mole %)

N2 O2 H2O CO2 SO2

G5.036

G5.037

G5.042

75.3 18.8 5.45 0.36 0.09

77.7 15.5 5.74 0.52 0.54

76.7 18.96 4.19 0.12 0.03

2.1.2. Waste heat recovery estimation The amount of recoverable waste heat depends on the temperature at which the flue gases are cooled down. Due to the existence of pyrite (FeS2) in the content of green pellets, SO2 and SO3 can be formed in the induration process of pellets. As the temperature of exhaust flue gases is reduced during the heat recovery process, gas temperature may reach the dew point of the sulfuric acid, leading to droplet formation which, in turn, results in the corrosion of the metals used in the heat exchanger. Estimation of the dew point of sulfuric acid has been discussed by authors [24,25]. The one used in this study was based on the work of Verhoff and Banchero [26]. They provided a formula for estimation of dew point temperature (TDP) of sulfuric acid as:

TDP = 1000/[2.276

0.02943 × ln(PH2 o)

2.2.1. Material selection As discussed before, the temperature of flue gases may fall below dew point temperature of sulphuric acid. Therefore, a corrosive resistance material should be used for that part of the shell and tube heat exchanger that is in contact with the hot stream of flue gases. Levy et al. [29] evaluated the corrosive behavior of a wide range of materials under various sulfuric acid concentrations. Their results showed that PTFE had the best performance in the high acid conditions. Also, the polymer materials showed no significant signs of surface degradation over the entire acid concentration range. Table 3 [30] shows the thermal and mechanical properties of PTFE used in the heat exchangers.

0.0858 × ln(Pso3) (1)

+ 0.0062 × ln(Pso3) ln(PH2 O )]

It should be mentioned that different components exist in flue gases, such as SO3, SO2, HCl, HBr and NO2. These gases have different dew points when subject to water vapor. However, the maximum dew point temperature belongs to SO2/SO3. Therefore, the minimum possible temperature achievable in the process of cooling down the flue gases is that of SO3 dew point. Water vapor content and SO3 concentration are two important factors affecting the dew point temperature. Table 2 shows the values of these parameters as well as the sulfuric acid dew

2.2.2. Heat exchanger surface area The total outside surface area (A) of the tubes of heat exchange is calculated as [31]:

Table 2 Flue gas components and acid sulfuric dew point in the three ducts. Duct name

Duct G5.036

Duct G5.037

Duct G5.042

H2O volume % SO2 (PPM) SO3 (PPM) TDP sulfuric acid (°C) Ave temperature (°C) Design temperature (°C)

5.7 ± 0.6 1000 ± 100 15 138 133 133

6 ± 0.9 6000 ± 900 70 156 203 134

5 ± 0.5 400 ± 60 45 150 152 128

A=

E U LMTD

(4)

where, E , LMTD and U are the recoverable heat transfer rate, the logarithmic mean temperature difference and the overall heat transfer coefficient, respectively. Details of the logarithmic mean temperature difference, overall heat 67

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Fig. 4. Schematic representation of the proposed heat exchanger. Table 3 Thermal and mechanical properties of PTFE [30]. Thermal conductivity (W/m·K) Corrosion per year (mm/year) Water absorption, 24 h (%) Melting point (°C) Max operating temperature (°C) Density (kg/m3)

•

0.27 0–0.002 < 0.03 330 260–290 2170

Detailed mathematical modeling of the MED is observed in Table 4. 2.4. Economic analysis The aim of the economic analysis of the MED distillation driven by low-temperature waste heat from exhaust flue gases is to find the LCOW (the unit price of water over the lifetime of the project) and payback period of the project. The economic analysis encompasses HX, auxiliary boiler and MED distillation costs including the capital costs (CC), the operation and maintenance costs (OMC) [34], as well as benefits obtained by reducing the natural gas consumption of the MED distillation due to usage of waste heat over its lifetime. The capital recovery factor (CRF) is used to convert the capital costs to the annualized costs and can be written as follows [34]:

transfer coefficient and fan power required to overcome the pressure drop inside the tubes are presented in Appendix A. Finally, the total tube length can be obtained, as follows:

Ltot =

A do

(5)

Finally, the shell diameter can be expressed as [31,32]:

Ds = 0.637

CL CTP

A (PT /d o )2do Ltube

ambient temperature, which reduces the rate of heat transfer to the surrounding. The temperature difference in each effect is assumed to be the same.

1/2

(6)

CRF (i, n) =

where, the tube count constant (CTP) and the tube layout constant (CL) for the one-pass and triangular pitch are 0.93 and 0.87, respectively. PT/do is the pitch ratio assumed to be 1.3.

i . (1 + i) n (1 + i)n 1

(27)

where, “i” is the annual real interest rate and “n” is the life time of the project which is considered to be 20 years. The annualized costs are achieved by multiplying the CRF by capital costs of the system as follows:

2.3. MED distillation A parallel-cross feed MED distillation [33] consists of a series of effects, condenser and flashing boxes is schematically depicted in Fig. 5. To perform the thermodynamic modeling of the MED distillation plant, the following assumptions are considered:

CCannual = CC × CRF (i, n)

(28)

Then, the LCOW is determined by the following equation [34]:

LCOW =

• MED distillation operates in the range 70% up to 100% of maximum capacity. • There is no salt in the produced distillate. • The brine salinity of the desalination system is assumed to be 72 g/L. • Heat losses from all the components of the LT-MED are negligible. In

(CCHX + CCAB + CCMED ) × CRF(i, n) + OMC AWP

(29)

where, CCHX, CCAB and CCMED are the capital costs of the heat exchanger, auxiliary boiler and MED distillation, respectively. Also, AWP is the annual fresh water production (m3/y). In order to find the payback period, it is necessary to determine the gas consumption reduction of the MED distillation operating independent of waste heat recovery system. In other words, to produce

reality, the temperature of the low temperature stage is close to the

68

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Fig. 5. Schematic representation of a parallel-cross feed MED distillation system. Table 4 Detailed mathematical modeling parallel-cross MED distillation. Mathematical model

T=

T1 n

Description

Tn 1

T1 = Ts − ΔT Ti+1 = Ti − ΔT Tvi = Ti − BPEi BPE = A × XB + B × XB2 + C × XB3

A = 0.08325 + 0.0001883 × T + 0.00000402 × T2 B = 0.0007625 + 0.0000902 × T 0.00000052 × T2 C = 0.0001522 0.000003 × T 0.00000003 × T2 B1 = F − D1 Bi = F + Bi−1 − Di X1 =

Xi =

F (Xf ) B1 Xf . Fi + Xi 1 . Bi 1 Bi

D1. λ1 = Ms. λs − F1. Cp. (T1 − Tf) Tf = TN − ΔTcond Bi 1 × Cp × (Tci 1 Ti ) i Tv T Di = Di 1 × Cp × i 1 i i

di =

Ti′ =

Ti + NEAi Ti = Tvi + NEAi

NEAi =

Tci 1 Tvi Tvi

Di . i = (Di 1. i 1 + di 1. i Fi. Cp. (Ti Tf ) + Bi 1. Cp. (Ti

1 1

+ Di 1. Ti )

i 1)

Md = ∑i=1nDi + ∑i=2ndi

GOR =

(7)

Temperature of effect 1 Temperature of effects 2 to n Temperature of vapor Boiling point elevation

(8) (9) (10) (11)

Mass balance of effect 1 Mass balances of effect 2 to n Salinity balance of effect 1

(12) (13) (14)

Salinity balance of effect 2 to n

(15)

Energy balance of effect 1 Temperature of falling film Mass flow rate of vapor flashed off from the brine

(16) (17) (18)

Mass flow rate of vapor flashed off from the distillate

(19)

Temperature of vapor formed by flashing off from brine Temperature of vapor formed by flashing

(20) (21)

Non-equilibrium allowance

(23)

Energy balances of effect 2 to n

(24)

Total distillate product Gain output ratio

(25) (26)

Non-equilibrium allowance

33 × (Ti 1 Ti )0.55 Tvi

NEAi = 0.33 ×

Temperature difference between consecutive effects

Md Ms

the same amount of vapor required to operate the MED distillation, by a traditional system (boiler), the natural gas should be burned. On the other hand, an auxiliary boiler should be used to mitigate the fluctuations of vapor entering the MED distillation system when operating with the waste heat. Considering burner and boiler efficiencies as ηBurner and ηBoiler, and the Iran natural gas tariff, the annual natural gas consumption saving, which is considered as the benefit, can be calculated by:

A1 ($) =

E LHV ×

Burner

×

× Natural Gas Tariff Boiler

(22)

find the payback period of the project [35] as follows:

NPV = Net Present Benefit –Net Present Cost NPV = A1 (P / A1 , i%, n)–A2 (P / A2 , i%, n)–CCHX & AB

(31)

where, A2 is the annual operating cost including the electromotor and auxiliary boiler electrical energy consumption costs. Also, CCHX&AB is the capital cost of the heat exchanger and auxiliary boiler. In Eq. (31) (1 + i)n 1 (P / A, i%, n) = i (1 + i)n . In what follows, capital and operating costs of HX, AB and MED distillation are explained.

(30)

In this study, the Net Present Value (NPV) method was employed to 69

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additive, maintenance and spares, and insurance costs. 2.5. Solution algorithm In this study a FORTRAN code was developed to solve the set of equations. The solution strategy could be briefly described as follows: 1. The volumetric flow rate of flue gases is calculated by using power consumption data and fans characteristic curves. 2. The amount of the recoverable energy is estimated based on Eqs. (1) & (2), Tables 1 & 2 considering sulfuric acid dew point temperature. 3. The total outside surface area and length of the tubes of heat exchange is determined with the aid of the amount of the recoverable energy in step 2, Eqs. (4) & (5), Appendix A., Tables 3, 6 and 7. 4. The levelized cost of water and payback period are calculated using Eqs. (29) and (31) with the aid of Tales 4, 8–11 and Eqs. (32) & (34). 3. Results and discussion In the present study, two waste heat recovery potentials, namely, technical and economical ones [7], were considered in detail. Following the design and simulation of the heat exchanger, the results of a conventional MED unit is described. Then the economic evaluation of waste recovery driven MED distillation including the payback period and LCOW at two scenarios are presented.

Fig. 6. Time history of the recoverable waste heat with respect to the sulfuric acid dew point temperature limitation at the duct G5.037.

2.4.1. HX and auxiliary boiler cost analysis Heat exchanger costs are categorized as capital and operating and maintenance costs. In the HX cost analysis, the following assumptions are considered:

3.1. Technical potential The amount of recoverable waste heat depends on the minimum possible temperature achieved in the process of cooling down the flue gases, which is the dew point of sulfuric acid, as mentioned before. It is desirable that the temperature would not be lower than sulfuric acid dew point temperature (case I) in operating conditions because of the corrosion effects. Based on this limitation, Table 2 and Eq. (2), it is observed that the amount of the recoverable energy in G5.036 and G5.042 ducts are relatively low when the flue gases are at a temperature near the dew point of sulfuric acid. On the other hand, as is observed in Fig. 6, the excess temperature of flue gases in G5.037 duct is remarkable as compared to the dew point of sulfuric acid. The amount of the recoverable waste heat from flue gases in the G5.037 duct is shown in Fig. 6. Fluctuations of the recoverable energy are observed in this figure which are accompanied with the small period of nearly zero values for the waste heat. However, due to the low recoverable waste heat from three ducts, cooling down to the sulfuric acid dew point temperature could not be a good scenario in the waste heat recovery. Cooling the flue gases down to a temperature below that of the dew point temperature of sulfuric acid (case II) makes higher waste heat to recover but a corrosion resistant heat exchanger is required to be designed with viable economic analysis. Based on the operation instructions of the equipment of the pelletizing plant [27], the flue gas temperature at each duct must be above 134 °C; therefore, it could be considered as the minimum temperature in all calculations. It should be noted that dew point temperature of Sulfuric acid at operating conditions in the plant is above 134 °C (see Table 2). Therefore, cooling down the flue gas temperature to a temperature below 134 °C results in formation of sulfuric acid droplets; hence, a corrosion-resistance material should be selected for the components of the heat exchanger. Fig. 7 shows the recoverable waste heat with respect to the design temperature (Table 2 and Eq. (3)).

1. The water pump and its energy consumption costs can be ignored. 2. The repair and maintenance costs of the PTFE heat exchanger can be ignored due to the fact that the one-pass PTFE HX is corrosion resistant [30]. Capital costs (CCHX) include the cost of the PTFE heat exchanger (CCPTFE HX) and fan (electromotor, fan and variable-frequency drive) (CCFan), as follows:

CCHX = CCPTFE HX + CCFan

(32)

The cost of the PTFE heat exchanger (CCHX) includes the tube material cost and the manufacturing and installation costs. Due to the variable volumetric flow rate of flue gases, pressure drop and electromotor energy consumption are variable. In the design process, the fan is selected based on the maximum energy consumption and hence, a variable-frequency drive should be used to adjust the required power. According to the assumptions considered, the operating and maintenance costs (OMCHX) is only due to the electromotor electrical energy consumption as follows:

CEL = Power (in KW ) ×

8760 hrs $ × E lectricity Cost Unit year KWhr

(33)

The auxiliary boiler cost includes the capital cost (CCAB) and operating costs (OMCAB). The operating costs cover the annual cost of natural gas consumption and electricity (Eq. (33)). 2.4.2. MED distillation cost In order to perform the cost analysis, the capital as well as operating and maintenance cost must be considered. For conventional MED distillation plants, the capital cost can be approximated based on the GWI/ IDA database [36]. For the capacity range of 100 to 10,000 m3/day, this results in the following cost function.

CCMED = 3018.8 ×

0.9795

3.2. Heat exchanger design and simulation

(34)

The minimum inner tubes diameter of a shell and tube heat exchanger to prevent fouling formation is 1 in. [37]; in fact, the more the inner diameter of tubes, the more the materials required for manufacturing the heat exchanger. Meanwhile, the flue gas pressure inside

where ψ is the total production rate of a conventional MEDdistillation plant in m3/day. Annual operating and maintenance expenses were assumed to be comprised of electrical (Eq. (33)), labor, chemical 70

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Table 5 Number of tubes required for the heat exchanger based on different tube diameters. Inner diameter Inch 1 1 2 2

Thickness (mm)

mm

¼ ¾ ¼ ¾

31.75 44.45 57.15 69.85

3.52 4.94 6.35 7.76

Outer diameter (mm) 38.79 54.33 69.85 85.37

Number of tubes (Nt) 18,112 9240 5590 3742

Table 6 The average values of viscosity, thermal conductivity, and Pr number in the duct G5.037. Kmix (W/m·K) 0.038

μmix (kg/m·s) −5

2.6 × 10

Prmix 0.724

ducts was about the ambient pressure. On the other hand, the minimum tube lengths of the heat exchanger should not be < 8 ft. [37]. On the other hand, the standard inner diameters of the tubes of heat exchanger are 1 ¼, 1 ¾, 2 ¼ and 2 ¾ in. [37], for which tube thickness and outer diameter are available. Due to the dependency of flue gas density on temperature (Fig. 2) and composition (Table 1), the daily variation of the flue gas density was determined. Using known mass flow rate (Fig. 3) and density, volumetric flow rate of flue gases could be calculated. Fig. 8 shows average daily volume flow rate during the period under consideration. As is observed from this figure, maximum volumetric flow rate is 1.56 × 10+6 m3/hr (430 m3/s). According to the Ref. [38], the maximum allowable flue gas velocity inside tubes is 30 m/s. By considering the maximum volumetric flow rate and the inner diameter, the number of tubes could be determined. Table 5 shows the number of tubes required for the heat exchanger based on different standard tubes diameters. Thermal conductivity and viscosity of flue gases could be obtained from Appendix A.1, respectively. Due to the fact that viscosity and thermal conductivity dependence on the temperature of flue gases is

negligible, these properties are obtained at the standard temperature, as shown in Table 6. Please note that these values are related to the flue gases of the G5.037 duct. The inner side heat transfer coefficient of flue gases is obtained from Appendix A.1 by using Reynolds (Appendix A.1) and Prandtl numbers. It is clear that lower falling film temperature required less surface area for the tubes. In most industrial applications, some vapor with a temperature > 70 °C is required [39,40]. Owing to the fact that the flue gas temperature at the exit of the heat exchanger should not be less than the design temperature of 134 °C, using a falling film temperature of 70 °C, the logarithmic mean temperature difference is calculated from Appendix A.2 Results are shown in Fig. 9. The falling film heat transfer coefficient is obtained using known values of Reynolds and Prandtl numbers. Constant specific heat and thermal conductivity of the falling film are considered for the saturated water at 70 °C. Table 7 shows the falling film heat transfer coefficient for Pr = 2.56 and Re = 400, as obtained by Appendix A.1. Meanwhile, the thermal resistance of the heat transfer process was obtained from Appendix A.1 by using the data mentioned in Tables 1 and 6. The variable nature of temperature and mass flow rate of flue gases, and the resulting volumetric flow rate and Reynolds number yielded a variable inner-side heat transfer coefficient. The overall heat transfer coefficient could be obtained by using inner side heat transfer coefficient, characteristics of tubes, and the

Fig. 8. Variation of the daily-averaged volume flow rate of flue gases versus month.

Fig. 9. The monthly variation of LMTD in the duct G5.037.

Fig. 7. Monthly variation of the recoverable waste heat from the duct G5.037 with respect to the design temperature.

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Table 7 Falling film heat transfer coefficient. Cp, fallingfilm (kJ/kg K) Kfallingfilm (W/m·K) μfallingfilm (kg/m·s) Pr falling film Re falling film h falling film (W/m2 K)

4.19 0.66 404 × 10−6 2.56 400 5500

Fig. 11. Tube length obtained for different inner diameters.

Fig. 10. The monthly variation of the overall heat transfer coefficient for different inner diameters.

falling film coefficient. Fig. 10 shows the time history of the overall heat transfer coefficient of the four afore-mentioned inner diameters during the period under consideration. It is obvious from Fig. 10 that the overall heat transfer coefficient had a wide range of variations. It is worth mentioning that dominant thermal resistances to heat transfer from flue gases to water were the convective resistance of flue gases and the conductive resistance of tubes. Also, as can be observed in Fig. 10, using tubes with smaller inner diameters could increase the overall heat transfer coefficient. The length of each tube of the proposed heat exchanger is obtained using recoverable waste heat based on design temperature, logarithmic mean temperature difference (LMTD), and overall heat transfer coefficient (U). Fig. 11 depicts the tube length computed for the four standard tubes during the period under study. As mentioned previously, tube length should not be lower than 8 ft. Based on this fact, it could be observed that the diameter of tubes with 1 ¼ in diameters was not suitable because their length was higher than 8 ft. On the other hand, using tubes with large diameters could increase the cost of the heat exchanger. The lowest diameter of tubes with a length lower than 8 ft. was the one with 1 ¾ in. diameter, which was selected for the proposed heat exchanger. The number of tubes with the 3/4 in. diameter was obtained to be 9240, with the inner diameter of 1 ¾ in. and the length of 8 ft.; these were used for the simulation process. The shell diameter was obtained by using Eq. (6); it was 7.3 m. The required electrical energy of the fan to overcome the pressure loss inside the tubes was calculated by Appendix A.3. Fig. 12 displays the variation of the electrical energy required by the electro motor of the fan during the period under consideration. It is observed from this figure that the maximum power of the fans electromotor was about 30 kW. In this study, an electromotor with the rated power of 35 kW was selected for reliability issues. It should be noted that a variable-frequency drive (VFD) was used with the electromotor to control AC motor speed and torque by varying the motor

Fig. 12. Monthly variation of the electrical energy consumption of the fan.

input frequency and voltage at the times when the flue gas volume flow rate was reduced and accordingly, less electrical energy was required. By knowing the overall heat transfer coefficient, surface area of the heat exchanger and LMTD, the recoverable energy could be obtained from Eq. (4). By using enthalpy of vaporization for water at 70 °C, hfg = 2333 kJ/kg, the produced vapor was obtained from the relation m v = E / hfg . Fig. 13 shows variation of the produced vapor during the period under consideration. It was assumed that the amount of vapor for the rest of the year was similar to that shown in Fig. 13. 3.3. Basic design of a parallel cross MED distillation The aim of the present analysis is to design and install a parallelcross MED distillation system [41] operating at low temperature vapor produced by waste heat. Based on the inlet steam temperature (Ts) of 70 °C, the temperature in the last effect is obtained as 42 °C with the temperature difference between consecutive effects mentioned in Table 8. Maximum possible number of effects number is considered as 16. Using design and input data shown in Tables 8 and 4 (Eqs. (7) to (26)), the gain output ratio and amount of produced fresh water is obtained. It is clear that the amount of produced fresh water is 72

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Fig. 13. Time history of the produced vapor. Table 8 Design and input data of the MED distillation unit. Effect number range Vapor mass (ton/day) Vapor temperature (°C) Last effect temperature (°C) Film temperature (°C) Cooling water temperature (°C) The temperature difference between consecutive effects (°C) Water salinity

6–16 468.5 70 42 38 25 1.8–4.6 42,000

determined by multiplying the GOR and produced vapor. Fig. 14(a) and (b) demonstrates variation of GOR and maximum fresh water production at different effect numbers. The results shown in this figure used as the input data for the capital cost estimation of the MED distillation plant based on Eq. (34). The LCOW can be obtained by considering interest rate, natural gas and electricity costs. Table 9 [42–45] shows the range of these parameters. It should be noted that the LCOW is determined by the data in Table 10, Eq. (29) and natural gas and electricity costs. Annual cost is obtained using data mentioned in Table 10. Fig. 15 shows variation of LCOW versus effect number at different interest rates, natural gas and electricity cost at full load operation (468.5 ton/ day vapor at 70 °C) of a conventional MED distillation system with parallel-cross configuration. It is observed that increasing the number of effects reduces LCOW. Therefore, the most economical number of effects would be 16. Please note that increasing the number of effect does not change LCOW considerably for the case of low natural gas and electricity costs; its effect is more pronounced at higher rate of natural gas and electricity costs. The number of effects considered in the following discussion is 16 as mentioned before.

Fig. 14. Variation of a) GOR and b) maximum fresh water production, versus the effect number. Table 9 The range of affecting parameters [42–45]. Parameter

Range

Electricity cost Natural gas cost Interest rate (i)

0.02–0.3 $/kwhr 0.02–0.35 $/m3 2, 8 & 14%

Table 10 The annual cost of the MED distillation system.

3.4. Economic estimation It is generally accepted that MED systems should be operated above 70% of maximum capacity, a fact that almost all engineers and operators of the Combined Water and Power Plants experienced. In fact, their experimental observation revealed that performance and fresh water production encountered sudden reduction if maximum capacity reaches below this operation point. To compensate for the reduction in mass flow rate due to its

Electricity Worker Chemicals Maintenance Insurance Repair and switching

73

2 kwh/m3 0.1 $/m3 0.04 $/m3 0.25 $/m3 0.05% CC 1.5% CC

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Fig. 15. Variation of LCOW versus effect number at different interest rates, natural gas and electricity costs at full load operation (468.5 ton/day).

fluctuations in actual situations (see Fig. 13) such that it always maintains in the range of 70% to 100% of maximum capacity of 468.5 ton/day, an auxiliary boiler with capacity of 5 ton/h is considered in the present situation. There are two scenarios for operation of the auxiliary boiler. The first scenario is minimal usage of the auxiliary boiler capacity such that the entering vapor below 70% just exceeds this operation point. The second scenario is using the auxiliary boiler capacity as much as possible not only reach the entering vapor above 70%, but also to higher percentages up to the 100%. It should be noted that no exhaust flue gases are available during overhaul or shutdown mode and hence the MED distillation and auxiliary boiler are switched off during these periods. Fig. 16(a) and (b) show the monthly variation of the boiler vapor production at the first and second scenarios, respectively. By operating the auxiliary boiler at minimum and maximum scenarios, the mass flow rate of the vapor entering the MED distillation plant would be in the range 70% up to 100% of maximum capacity, as is observed in Fig. 17(a) and (b). The economics of the subsystems including heat exchanger, auxiliary boiler and MED system are presented is discussed next. Table 11 shows the cost of manufacturing of a PTFE heat exchanger [46]. The relative cost factor denotes the percentage of the underlying cost components of the HX relative to the material cost. The total capital cost of the fan, including electromotor, fan and variable-frequency drive and PTFE heat exchanger (based on Table 11), was 20,000 $ and 2,469,377$, respectively. Annual electrical energy consumption of fan is obtained from its average daily for five months' operations (Fig. 10) and multiplying by the number of days in a year. Based on the cost of electrical energy and annual electrical energy consumption, the cost of electricity consumed by the fan's electromotor is calculated (Eq. (33)). The total capital cost of the boiler is 55,000 $. Also, the annual natural gas consumption for minimum and maximum usage of the auxiliary boiler are 2,202,000 and 115,403 normal cubic meters, respectively. It should be mentioned that the annual gas consumption of the auxiliary boiler is obtained by considering ηBurner × ηBoiler = 0.8 and low heating value of the natural gas of 32 MJ/m3. It is of paramount important to the owners of the MED distillation plant to know the payback period of his/her investment in heat exchanger and auxiliary boiler. As mentioned before, the NPV method is employed to find the payback period (Eqs. (30)–(31)). The payback period depends on electrical and natural gas tariff as well as the real interest rate. Fig. 18 shows the discounted payback period of the waste heat recovery system versus interest rate. It can be seen that enhancing the

Fig. 16. Monthly variation of auxiliary boiler vapor production at a) the first scenario, b) the second scenario.

interest years could lead to increasing the number of years, balancing cost and benefit. This is due to the time value of money (benefit), which is reduced in the subsequent years of operation. It should be mentioned that, because of low electricity consumption, changing the electricity tariff has little effect on the payback period and therefore the value of 0.18 $/kWh is used in Fig. 18. It is concluded from this figure that payback period varies between 14 and 27 years even at low to moderate interest rates for a minimum natural gas tariff of 0.02 $/m3. Such payback periods are not desirable because at some interest rates, they even exceeds the life time of the projects and hence at this tariff, the waste heat recovery system is not economically feasible. Higher, tariff rates causes the payback period of the system to reduce to values below the life time of the system. It is observed payback period coincides the life time of the system with a tariff of 0.034 $/m3 and interest rate 14%. At natural gas tariff of 0.05 $/m3, the payback period is in the range about 4–8 years. At this tariff, the minimum attractive payback period (MAPBP) of the investor justify the investment. For instance, if the MAPBP is considered as six 74

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Fig. 18. Variation of the discounted payback period with the interest rate at different natural gas tariffs. Table 12 The simple payback period. Natural gas cost ($/m3) Simple payback period (year)

0.02 12.1

0.034 6.7

0.05 4.4

0.35 0.84

Table 13 Eight boundary cases to find LCOW for the waste heat driven MED distillation. Case no. Case Case Case Case Case Case Case Case

1 2 3 4 5 6 7 8

Scenario

Interest rate (i %)

70% 100% 70% 100% 70% 100% 70% 100%

2 2 2 2 14 14 14 14

Natural gas cost ($/m3) 0.02 0.02 0.35 0.35 0.02 0.02 0.35 0.35

Electricity cost ($/kWh) 0.02 0.02 0.3 0.3 0.02 0.02 0.3 0.3

Fig. 17. Monthly variation of vapor entering the MED distillation plant at a) the first scenario, b) the second scenario. Table 11 Capital cost of the unit length of the HX [46]. PTFE HX Material cost Manufacturing and installation cost Total cost

Relative cost factor

Cost/m ($/m)

1.00 0.37 1.37

80 29.6 109.6

years with interest rate between 2% to 9%, the investment is feasible. It is observed in Fig. 18 that at tariff 0.35 $/m3, the payback period is less than one year which shows that the project is economically feasible at all interest rates for this tariff. In addition, the simple payback period in the present economic analysis was obtained and shown in Table 12. One of the main goals of the present study is to find the LCOW at two scenarios. i.e. minimum and maximum usage of the auxiliary boiler, for a period of 20 years of the system operation at different natural gas and electricity cost as well as interest rates. To this end,

Fig. 19. The LCOW as well as all underlying costs at eight boundary cases.

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Fig. 20. Effect of natural gas cost on the LCOW, a) i = 2%, b) i = 8%, and c) 14%.

0.35 $/m3 (the highest natural gas price) the effect of natural gas price is more pronounced and scenario 70% is superior to the scenario 100%. Please note that the produced water for cases 4 and 8 (100%) are greater than that of cases 3 and 7 (70%), respectively. It is worth mentioning that, the case 2 with LCOW of 1.13 $/m3 is the best one among all cases. This is because in this case, the natural gas and electricity costs as well as interest rate are minimum and it is better to take advantage of the maximum capacity (100%) which is the one of this case. Fig. 19 illustrates just the effect of bonds values of the parameters which were explored on the LCOW. To clarify this issue in more detail, variation of natural gas cost on the LCOW is investigated at three interest rates and electricity costs in scenario 70% and 100% with results

eight cases are considered according to the bonds in Table 9. These cases are illustrated in Table 13. Fig. 19 displays the LCOW as well as all underlying costs for eight cases mentioned in Table 13. The capital cost in Fig. 17 includes the cost of HX, Auxiliary boiler and MED distillation, while the electricity costs of HX fan, Auxiliary boiler and MED distillation contribute to the electricity cost in this figure. As is observed in this figure, a pairwise comparison is made between scenarios of 70% and 100% (cases 1 & 2, cases 3 & 4, cases 5 & 6 and cases 7 & 8). It is observed that LCOW for scenario 100% is less than that of scenario 70% for all pairwise cases, except 3 & 4 and 7 & 8, for which the natural gas cost (the red columns) is the highest. In other words, at pairwise 3 & 4 and pairwise 7 & 8, at the natural gas cost of 76

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low cost of natural gas, the conventional system is superior to waste heat recovery system. However, waste heat recovery system is more economic than the conventional system for interest rate of 8% and natural gas price of 0.023 $/m3, while increasing interest rate the intersection of two systems in Fig. 21 moves to higher natural gas price for which the interest rate is 14% and the intersection is 0.031 $/m3. 4. Conclusions In the present study, techno-economic evaluation of a waste heat driven MED distillation system was performed. To this end, a PTFE heat exchanger which was corrosive resistant was designed to perform the heat recovery and produce the low temperature vapor. The number of tubes with the inner diameter of 1 ¾ in. and the length of 8 ft. was obtained to be 9240. The average amount of vapor for this heat exchanger is obtained as 336.11 ton/day. Economic analysis of conventional MED distillation system based on the LCOW indicator showed the optimum number of effects is 16. An auxiliary boiler was employed to compensate for the vapor reduction obtained from waste heat process. There were two scenarios for operation of the auxiliary boiler, minimum (70%) and maximum (100%) usage of the auxiliary boiler. Thereafter, the economical evaluation based on the NPV method at various natural gas tariff and the real interest rate was carried out, demonstrating that the discounted payback period at natural gas tariff 0.35 $/m3, is less than one year which shows that at this tariff the project is economically feasible at all interest rates. Then, the LCOW at two scenarios of 70% and 100% for a period of 20 years of the waste heat driven MED distillation system operation at different natural gas and electricity cost as well as interest rates. It was observed that at higher electricity and natural gas costs, scenario 70% is better than the scenario 100%. Finally, a comparison made between the LCOW of the waste heat driven MED distillation system and the conventional MED distillation system revealed that at interest rate 2%, waste heat recovery system is always economically better than the conventional system. Also, at interest rate 8% and 14%, at very low natural gas cost the conventional system is superior to waste heat recovery system.

Fig. 21. Comparison between waste heat driven MED distillation system and conventional MED distillation system.

shown in Fig. 20. It is observed that the intersection point of 70% and 100% scenarios is shifted to the higher natural gas cost with increasing interest rate. This is due to the fact that increasing the interest rate causes the contribution of annual capital cost to the LCOW dominates the contribution of natural gas cost. Also observed in this figure, by increasing the electricity cost, no tangible difference observed between those scenarios. This is because of domination of the cost of natural gas relative to that of electricity. Finally, a comparison is made between the LCOW of the waste heat driven MED distillation system and the conventional MED distillation system. Fig. 21 illustrates variation of LCOW versus natural gas cost for these systems at three interest rates (2%, 8% and 14%) considering electricity price of 0.18 $/kWh for scenario 100%. It is obvious that the slope of the curve for conventional system is more than that of waste heat recovery system for all interest rates. It is due to the fact that gas consumption in conventional systems is higher than waste heat recovery system. It is observed that waste heat recovery system is always economically better than the conventional system for the case of interest rate of 2%. In addition, at interest rates of 8% and 14% with very

Acknowledgment This work was financially supported by Golgohar Iron Ore and Steel Research Institute, Golgohar Mining and Industrial Company, Sirjan, Iran, with project No: 60907894/94-121.

Appendix A A.1. Overall heat transfer coefficient Overall heat transfer coefficient, which depends on both the tube side and shell side heat transfer coefficients and tube wall thermal conductivity, is calculated as [31]:

U=

1 1 ho

+

do ln(do / di) 2kw

+

1 hi

do di

(A.1)

where, di, do, ho, hi and kw are the inner and outer tube diameters, shell side and tube side heat transfer coefficients and the tube wall thermal conductivity, respectively. It should be noted that the effect of fouling resistances is ignored in Eq. (A.2). The wall thickness of a tube with the inner diameter di, the long term strength S at 82 °C (4.2 MPa), and the inside pressure P is calculated by [47]:

t=

di 2S P

1

(A.2)

Then, the outer diameter is calculated as follows: (A.3)

do = di + 2 × t

The shell side heat transfer coefficient (ho or hfalling) is the heat transfer coefficient of the falling film on the tube bundles. It is obtained using the experimental correlations given in ref. [48], as follows: 77

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NuTube,1 + j

Nu =

j

1 j

NuTube,2toj

2

0.25 3 + 0.008Re0.3 NuTube,1 = Re falling falling . Pr 2

0.25 3 NuTube,2toj = Re falling + 0.01Re0.3 falling . Pr

0.5

0.5

Nu kfalling

hfalling =

1/3 2 falling g

(A.4)

Here, j and νfalling are the row number of the tube bundles and the falling film kinematic viscosity. Also, Refalling can be calculated by:

4mfalling

Refalling =

µfalling Ltube Ni

(A.5)

where, Ni is the number of columns. Moreover, Prandtl number (Pr) for the falling film is given by:

Prfalling =

µfalling Cp, falling (A.6)

Kfalling

In this study, the triangular pitch is used for the tube arrangement. The tube side heat transfer coefficient (hi) can be obtained from the following correlation [49]:

ki 0.0677(Rei Pri (di/L))1.33 3.657 + 1 + 0.1Pri (Rei (di / L))0.3 di ki (fi/8)(Rei 1000)Pri d 1+ i di 1 + 12.7(fi/8)0.5 (Pri 0.67 1) L

hi =

0.027

µi ki Rei 0.8Pri 0.33 di µ wi

Rei < 2300

For 0.67

For

2300 < Rei < 10000

0.14

For

Rei > 10000

(A.7)

where, μi and μwi are the fluid viscosities computed at the bulk and wall temperatures. Also, fi is the Darcy friction factor, as follows [50]: (A.8)

2

fi = (1.82log10Rei 1.64)

The tube side Reynolds number (Rei) is given by:

4 × mi di µi Nt

Rei =

(A.9)

where, Nt is the number of tubes. It should be mentioned that due to the possibility of dust deposition inside the tubes, the one-pass heat exchanger should be used. In addition, Prandtl number inside the tubes is given by:

Pri =

µi Cp,i

(A.10)

Ki

To predict the thermal conductivity of flue gases, the following empirical formula, as proposed by Reid, can be used [51]. n

Xi Ki

Kmix =

n i=1

j=1

Xj

ij

(A.11)

Also, an approximate formula for the viscosity of gas mixtures, as derived by Sutherland, is employed [52]. n

Xi µi

µmix =

Xi +

i=1

n

j i

Xj

ij

(A.12)

where, xi is the mole fraction of each component in the flue gas mixture and ϕij is given by:

1+ ij

=

( ) .( ) Ci Cj

0.5

8 × 1+

Mi Mj

Mi Mj

0.25 2

0.5

(A.13)

Here, C denotes viscosities (μ) or thermal conductivity (K), and Mi is the molecular weight of each component.

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A.2. Logarithmic mean temperature difference equations The LMTD is written as [31]:

LMTD =

(Tinlet flue gas ln((Tinlet flue gas

Toutlet flue gas)

Tfalling film)/(Toutlet flue gas

(A.14)

Tfalling film ))

where, Tinletflue gas and Toutletflue gas are the inlet and outlet temperatures of flue gas. Also,Tfallingfilm is the temperature of the saturated water sprayed on the tubes bundle and depends on the pressure inside the shell (P < 1 bar). Lowering the pressure (below atmosphere) inside the shell results in increasing the LMTD; this, in turn, reduces the surface area and size of the heat exchanger. It should be mentioned that in some industrial applications, such as desalination plants, the low temperature saturated vapor is required. A.3. Pressure drop evaluation It is necessary to have insight regarding the pressure drop inside the tubes. To this end, the well-known formula of Darcy–Weisbach is used, as follows [32]:

Ptube = f ×

Ltube × di

×

Vi 2 2

(A.15)

For smooth circular tubes, the friction factor correlation (f) can be expressed as:

f = 0.046 × Re

0.25

(A.16)

3 × 10 4 < Rei < 106

For

It should be noted that placing heat exchanger in the duct increases the pressure loss of the flue gases, which may result in using a suction fan at the exit. The required fan power to overcome the pressure drop can be calculated by [46]:

mi × Cp, Mix × TMix , inlet × Wfan =

( ) Pout Pin

k 1 k

1 (A.17)

fan

where, TMix-inlet, k and Pin and Pout show the flue gas inlet temperature, specific heat ratio, and inlet and outlet pressures in the tubes, respectively. In addition, ηfan is the aspirator efficiency, which was assumed to be 80% in this study.

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