FeCl3-Promoted [3 + 2] Annulations of Î³-Butyrolactone Fused

CHERD-2861; No. of Pages 13

ARTICLE IN PRESS chemical engineering research and design x x x ( 2 0 1 7 ) xxx–xxx

Contents lists available at ScienceDirect

Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd

Synthesis cooling water system with air coolers Jiaze Ma a , Yufei Wang a,∗ , Xiao Feng b , Dongmei Xu c a

State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, China School of Chemical Engineering & Technology, Xi’an Jiaotong University, Xi’an 710049, China c College of Chemical and Environmental Engineering, Shandong University of Science and Technology, Qingdao 266590, China b

a r t i c l e

i n f o

a b s t r a c t

Article history:

Adding air coolers to cooling water system is an effective way to reduce heat load and the

Received 19 July 2017

cost of cooling water system. It is also an effective method to prevent fouling and save

Received in revised form 13 October

water in the region where water is scarce. There is a trade-off between air cooler system

2017

and cooling water system. When heat load of air cooler is high, cooling tower consumes

Accepted 16 October 2017

less fresh water, but the cost of air cooler can be high. Conventionally, the two systems are

Available online xxx

optimized separately. This paper presents an optimization model for synthesizing cooling water system with air coolers. The water coolers, air coolers, pumping scheme and cooling

Keywords:

tower are simultaneously optimized. Each hot stream can be cooled down by air cooler

Cooling water system

to certain degree and then cooled down by water cooler to target temperature. Or it can be

Air cooler

cooled down by the air cooler or water cooler exclusively. The model is formulated as mixed-

Cooler network

integer nonlinear programming (MINLP) problem. The objective is to formulate the cooling water system with the minimizing total annual cost. The case is optimized under two cities

MINLP

with different prices of water and electricity. Results show that optimization model yields 29.4% and 13.1% TAC reduction. Results also indicate that it is particularly necessary to add air coolers to cooling water system in region where water is scarce and electricity price is low. © 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

1.

Introduction

Water cooling and air cooling are among the two most common meth-

water system by minimizing water flowrate. Because water cooling consumes fresh water and produces waste water, the system has certain impact on local environment. Panjeshahi et al. (2009) optimized

ods that are employed to reject industrial waste heat to environment. Because water has suitable thermal properties and non-harmful chem-

cooling water system that involved environmental considerations as well as energy conservation. However, all the models previously men-

ical composition, cooling water system by far, has been widely used

tioned mainly focus on minimizing water flowrate. In order to achieve

and thoroughly studied. The pioneer work conducted by Kim and Smith (2001) introduced mathematic model that emphasizes interac-

the heat exchanging service, more contact areas are required. Later, Ponce-Ortega et al. (2007) proposed an MINLP model that considered the capital cost of coolers and cooling water cost simultaneously. In their work, stage-wise cooler network was proposed. The objective

tion between cooling tower and cooler network. Cooling water is reused in mixed parallel/series cooler arrangement, and cooling tower has better performance owning to low cooling water flow rate and high water return temperature. To reduce complexity and improve flexibility of cooler network, Feng et al. (2005) proposed a cooling water network

was minimizing the total cost and this model was more economical than other model previously mentioned. Few years later, they studied the detailed design of cooling tower, the optimization of cooling tower

with an intermediate main that is easy to control and operate. Introducing intermediate mains allows water to be reused which in turn

was based on MINLP model (Serna-González et al., 2010) and rigorous poppe model (Rubio-Castro et al., 2011). For optimizing cooling tower,

leads to increase of tower efficiency. Research conducted by Castro

Singh and Das (2017) optimized performance parameters and energy consumption of cooling tower simultaneously. Xie et al. (2017a,b) con-

et al. (2000) also focuses on reducing the operational cost of cooling

ducted experimental investigation as well as numerical analysis on ∗

Corresponding author. E-mail addresses: [email protected], [email protected] (Y. Wang). https://doi.org/10.1016/j.cherd.2017.10.020 0263-8762/© 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Please cite this article in press as: Ma, J., et al., https://doi.org/10.1016/j.cherd.2017.10.020

Synthesis cooling water system with air coolers. Chem. Eng. Res. Des. (2017),


2


Nomenclature a,b,c,ca Af Ara (i) Arw (i) cp Cfpump Cpump di dtin (i)

Constants of cooler capital cost Annualized factor Exchanger area of air cooler i Exchanger area of water cooler i Specific heat capacity of cooling water Fixed charge for pump Pressure cost coefficient for pumps Internal tube diameter Temperature approach between hot stream outlet temperature and cold stream inlet temperature in water cooler dtout (i) Temperature approach between hot stream inlet temperature and cold stream outlet temperature in water cooler dtain (i) Temperature approach between hot stream outlet temperature and air inlet temperature in air cooler dtaout (i) Temperature approach between hot stream inlet temperature and air outlet temperature in air cooler e Unit cost of electricity Factor of friction f fa Air capacity flowrate rate Mass flowrate of fresh cooling water in cooler fw(i) E–i fin(i) Mass flowrate of cooling water in cooler E–i Air mass velocity G Maximum air mass velocity Gmax gc Gravitational constant Annual operational time h h(i) Film transfer coefficient of hot stream i hw Film transfer coefficient of cooling water Film transfer coefficient of air ha Conductivity of cooling water kt Parameter used in relating physical properties Kt(i) to pressure drop Nb Number of bundles OCfan-tower Operational cost of cooling tower fan OCpump Pump operational cost CCpump Pump capital cost pfan-cooler Fan power consumption Cooler E–i tube pressure drop pt (i) pair Pressure drop of air cooler’s fan Total pressure drop of cooler network ptotal Heat load of air cooler i qa (i) qw (i) Heat load of water cooler i Tambient Air inlet temperature of air cooler i Taout Air outlet temperature of air cooler i Thaout (i) Hot stream outlet temperature of air cooler i Thin (i) Hot stream inlet temperature of air cooler i Thout (i) Hot stream outlet temperature of water cooler i Tmin Minimum temperature difference Temperature of fresh cooling water Tfw VF Face velocity of air cooler VNF Actual face velocity of air cooler w Fresh water price Zi,j Whether cooler E–i send the outlet cooling water to cooler E–j

Greek letter Viscosity correction factor ˚t t Cooling water viscosity Pump efficiency pump fan-cooler Cooler’s fan efficiency Density of cooling water Exponent for the pump cost function

heat transfer of wet cooling tower. Both of cooling tower and cooler network should be optimized simultaneously because of intrinsic interaction between them. Later, the simultaneously optimized model was proposed by Ponce-Ortega et al. (2010). In this work, they optimized pump, cooler network, and cooling tower all together, the most optimal configuration was presented. Although they proposed effective model to optimize cooling water system, the stage-wise cooler network they employed involved too many mixers and splitters, which leads to high complexity of system. In comparison with stage-wise network, seriesparallel cooler network is more practical and flexible. Series-parallel network was employed in many research works (Ma et al., 2017; Sun et al., 2015). And it turns out the series-parallel network is an effective configuration to increase the water reuse and decrease the total annual cost of system. All the literatures cited above are grassroots design problem. Retrofitting the existed cooling water system also has the great significance in industry, and many scholars studied the retrofitting problem. As mentioned before, when coolers are arranged in series configuration, cooling water is reused, which leads to the increase of tower performance. But coolers cannot be arranged arbitrarily. The problem that which pair of coolers should be arranged in series has to be addressed. Wang et al. (2014) have proposed the two-step method to convert parallel configuration into series-parallel structure without adding more contact area. Retrofitting parallel cooler network into series-parallel network will reduce water flowrate. However, because coolers are in series connection, the pressure drop will increase, which requires more pumping energy to transport cooling water. To cope with pressure drop effects, many optimization model of cooling water network considering pressure drop were proposed (Kim and Smith, 2003; Gololo and Majozi, 2013). Except converting cooler network into series arrangement, other researchers proposed optimization model that considering piping cost (Reddy et al., 2013), or adds new cooler to ˜ system (Picón-Núnez et al., 2012). Cooling water system has been studied for a long period of time. Another common cooling method, the air cooling, has also been studied by many scholars. Doodman et al. (2009) proposed optimized model for designing air cooler. Detailed design of air cooler is quite complex, so they employed global sensitivity analysis and harmony search algorithm to optimized the air cooler. Manassaldi et al. (2014) proposed disjunctive mathematical model for the optimal design of air cooler, which minimize the heat transfer area as well as the fan power consumption. Kashani et al. (2013) addressed conflict between temperature approach and the total annual cost by employing non-dominated sorting genetic-algorithm. Their work presented proper procedure for selecting and designing air cooler. Other researchers studied the environmental effects on air cooler, like the freezing of air cooler (Chen et al., 2016; Wang et al., 2017), or the impact of ambient air temperature (Fahmy and Nabih, 2016) or the fouling effects (Kuruneru et al., 2016). Air cooling and water cooling have been studied over a long period of time due to their extraordinary cooling capacity. However, no researchers have ever combined both cooling mechanisms in a single system to obtain the optimal matches between air cooling and water cooling. Air heat capacity (1.004 kJ/(kg K)) is only a quarter of water heat capacity (4.183 kJ/(kg K)). Cooling down a same hot stream, the air mass flowrate of air cooler is four more times than the water mass flowrate of the water cooler. The film transfer coefficient heat capacity of air are lower than the coefficients of water, air cooler always has




ARTICLE IN PRESS 3

chemical engineering research and design x x x ( 2 0 1 7 ) xxx–xxx

higher contact area than water cooler, which leads to high investment cost. Although cooling water has physical properties that are suitable to remove waste heat, cooling tower consumes a large amount of water and produces waste water constantly. Water cooling is very expensive in the region where water is scarce, because of the high cost of treating waste water and consuming fresh water. Therefore, this paper proposed a two stage cooling mechanism where hot stream is first cooled down by air cooler to certain degree, and water cooler cools down the hot stream to the target temperature. Fig. 1 is employed to show the coupling structure of air and water coolers. The two stages cooling mechanism allows system to select cooling methods automatically. Each hot stream can be cooled down by air or water exclusively, or it can be cooled down by both of them. Thaout (i) is the outlet temperature of hot stream of air cooler. It is also the

3.

Model formulation

3.1.

Air cooler formulation

In Eq. (1), qa (i) represents heat load of air cooler that is used to cool down the hot stream i. Thin (i) and Thaout (i) are inlet and outlet temperature of hot stream i of the air cooler, fh(i) is heat capacity flowrate of hot stream. Tambient and Taout (i) are inlet and outlet air temperature of air cooler. fa(i) is air heat capacity flowrate. qa(i) = (Thin(i) − Thaout(i)) · fh(i) = (Taout(i) − Tambient) · fa(i) · (1)

break-point between air and water cooling. The break-point indicates the heat load distribution of air and water cooling of a hot stream. For each hot stream that was cooled by both of air and water cooler, there is an optimal heat load distribution between air cooler and water cooler. Air cooler consumes electricity and cooling tower consumes electricity as well as fresh water. With the fixed heat loads of hot streams, if the heat load of air cooler is high, the water and electricity consumption of cooling water is low as well as capital cost of water coolers. On opposite, if the heat load of water cooling is high, the electricity consumption of air cooler is low as well as capital cost of air coolers. To obtain the optimal distribution and the break-points of hot streams, the cost of air cooling and cooling tower, as well as other cost were optimized simultaneously. One industrial case has been optimized under two conditions where fresh water and electricity prices are different. And different heat load distributions of air and water cooling were presented. Final analysis indicated whether it is necessary to employ coupling structure. The circumstances have been identified where employing coupling structure are particularly necessary.

2.

Problem statement

Given a set of hot streams, corresponding cooling configuration is optimized. The cooling system involves air coolers and water coolers. The proposed model allows system to select optimal cooling methods based on the properties of the hot streams. The hot streams can be cooled down by air cooler at first, and then cooled down by water cooler in second stage. The hot streams can also be cooled down by air or water exclusively. Air cooler capital cost, operational cost, and water cooler capital cost, cooling tower cost as well as pumping cost were optimized simultaneously. The objective is to formulate the most optimal structure that satisfies the required heat exchanging service with the minimum total annual cost. The optimal heat load distributions among air and water cooling were obtained. The optimal temperature break-points of air and water cooling were identified. To explore the implication of coupling structure in different industrial situations, one case was optimized under different circumstances with different water and electricity prices. MINLP model was employed to solve the problem, and optimal design was based on several assumptions:

In Eqs. (2) and (3), dtain and dtaout represent temperature approaches on both sides of air cooler, and temperature approaches are supposed to be larger than minimum temperature difference of air cooler. Eq. (4) is employed to show air cooler contact area, h(i) and ha are film transfer coefficients of both side of cooler. Thin (i) − Taout (i) = dtain ≥ T min

(2)

Thaout (i) − Tambient = dtaout ≥ T min

(3)

Ara (i) =

dtain (i) · dtaout (i) ·


(4)

2

Ambient temperature influences face velocity of air cooler, VF and VNF are face velocity and actual face velocity of air cooler (Briggs and Young, 1963). NF = F ·

293 273 + Tambient

(5)

Outside film heat transfer coefficient of air cooler depends on actual face velocity. 0.718 ha = 218.9 · NF

(6)

Air cooler fan pressure drop is related to air mass flowrate, number of bundles. Eqs. (7)–(9) are employed to calculate fan pressure drop. G represent mass velocity rate, Gmax is the maximum mass velocity when the air flows through the narrow part of air cooler. Nb is number of bundles in air cooler, f is friction factor. G = F · air

(7)

Gmax = 2G

(8)

pair = 9.8 · ffriction

1. The specific heat capacities and film transfer coefficients of hot and cold streams are constant. 2. The water coolers are 1–1 counter current shell and tube exchangers. 3. Each hot stream corresponds to one air cooler and one water cooler.

1 1 1/3 · h(i) + ha dtain (i)+dtaout (i)

qa (i)

Nb · G2max 2g

(9)

The energy consumed by cooler fan depends on pressure drop, volumetric flowrate of air, and fan efficiency. In Eq. (10), Pfan-cooler is cooler fan power consumption. Pfan−cooler =

pair · Vair fan−cooler

(10)



4


Fig. 1 – Air and water coolers coupling structure.

Fig. 2 – Inlet and outlet streams details of each water cooler unit.

3.2.

Series-parallel water cooler superstructure model

In order to reduce total water flowrate and increase cooling tower performance, cooling water should be reused between different coolers when it is necessary. Fig. 2 is employed to show the inlet and outlet streams of each cooler unit. In the series-parallel structure, the coolers inlet cooling water stream is either fresh cooling water from cooling tower, or the used cooling water from other cooler. The outlet cooling water sends to either cooling tower or other cooler for reusing. There are some constraints to illustrate the relationships between inlet and outlet streams. In Eq. (11), the binary variable Z(i,j) represents whether cooler E–i sends the outlet cooling water to cooler E–j. When Z(i,j) value is 1, there is a connection between cooler E–i and cooler E–j. Each cooler, for example cooler E–i, could only send the outlet cooling water to only one cooler, or send the cooling water back to cooling tower directly. n

Besides, coolers cannot reuse their own outlet cooling water. Eq. (13) shows this relationship that when i is equal to j, the value of Z(i,j) is 0.

Zi.,j = 0, i = j.

To define inlet temperature and mass flowrate of each cooler, Eqs. (14) and (15) are employed.

⎡ Tin (i) = Tfw · ⎣1 −

(11)

n

⎤ Zj,i ⎦ +

j=1

⎡ fin (i) = fw (i) · ⎣1 −

Zi,j ≤ 1

(13)

n j=1

n

(Zj,i · Tout (j))

(14)

j=1

⎤ Zj,i ⎦ +

n

(Zj,i · fw (j))

(15)

j=1

j=1

On the other hand, each cooler, for example cooler E–j, can only accept the used cooling water from only one cooler, or receive the fresh cooling water from cooling tower. This relationship is represented in Eq. (12). n

Zi,j ≤ 1

(12)

i=1

The intention of introducing above constrains is to simplify cooler network. If one cooler connects with multiple coolers, more splitters and mixers are required. A very complex structure is not desired in practical industry. Please cite this article in press as: Ma, J., et al., https://doi.org/10.1016/j.cherd.2017.10.020

In Eqs. (14) and (15), fw (i) represents mass flowrate of fresh cooling water in cooler E–i, fin(i) is mass flowrate of cooling water in cooler E–i. Tin (i) and Tout (i) are inlet and outlet temperature of cooler E–i respectively. Tfw is temperature of fresh cooling water. When there is no used water sent to cooler E–i, the inlet cooling water stream is from cooling tower and the inlet cooling water temperature is equal to fresh water temperature. When cooler E–i receives the used water from other cooler E–j, the cooler E–i cannot receive the fresh water and the inlet water temperature is outlet water temperature of E–j. When cooler E–i does not receive water from other cooler, it consumes fresh water. However, when cooler E–i receives the used cooling water from other cooler E–j, it should not consume fresh water and the flowrate of cooler E–i is equal to the flowrate of E–j.


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The total mass flowrate of cooling water is the sum of all the fresh water mass flowrates sent from cooling tower to coolers.

ft =

n

fw (i)

(16)

i=1

Eq. (17) expresses the relationship between heat load and inlet and outlet temperatures and cooling water flowrate in cooler E–i. qw (i) = (Thaout (i) − Thout (i)) · fh(i) = (Twout (i) − Twin (i)) · cp · fin (i) (17)

The calculation of exchanger area is expressed in Eq. (18), the Chen approximation for logarithmic mean of temperature is used (Chen, 1987). dtin (i) is temperature approach between hot stream outlet temperature and cold stream inlet temperature. dtout (i) is temperature approach between hot stream inlet temperature and cold stream outlet temperature. h(i) denotes film transfer coefficient of hot stream i. hw is film transfer coefficient of cooling water. Arw (i) =

1 1 1/3 · h(i) + hw dtin (i)+dtout (i)

qw (i) dtin (i) · dtout (i) ·

(18)

2

Temperature approaches between cold and hot streams are supposed to be larger than the minimum temperature approach difference. The cooling water outlet temperature should be larger than the inlet temperature. Those constraints are represented in Eqs. (19)–(21). Each Hot stream may be cooled down by air cooler to certain degree, therefore the hot stream outlet temperature in air cooler equals to inlet temperature of water cooler. Thaout (i) denotes hot stream inlet temperature of water cooler and Thout (i) is hot stream target temperature. dtin (i) = Thout (i) − Tin (i) ≥ T min

(19)

dtout (i) = Thaout (i) − Tout (i) ≥ T min

(20)

Tout (i) ≥ Tin (i)

n

(Zj,i · pt(j)) +

j=1

3.3.

n

(Zi,j · pt(j))

(24)

j=1

Cooling tower formulation

There are many factors influence the performance and cost of cooling tower, including local air wet bulb temperature, air humidity, and atmospheric pressure, air flowrate, water flowrate and inlet and outlet temperature etc. To formulate the cooling tower, the following definitions are necessary: First, operational cost of cooling tower consists of fan cost, make-up cooling water cost, water chemical treatment cost and blowdown treatment cost. During the working process, minerals and impurities accumulate at bottom of cooling tower, therefore a part of cooling water has to be blowdown and keep the cooling tower working properly. Also, part of cooling water will evaporate during working process. To keep the fixed water flowrate, equivalent makeup water should be added to system. OCtower = OCfan−tower + 110ft + w · h · Mmakeup + 1138Bblowdown (25)

In Eq. (25), OCfan-tower is tower fan operational cost. ft is total flowrate of cooling water. Mmakeup is flowrate of makeup water. Bblowdown is flowrate of water blowdown. w, h are price of fresh water and annual operation time (Panjeshahi et al., 2009). OCfan−tower =

e · h · Cfactor · Fair−tower fan−tower

(26)

(22)

The constant Kt is related to cooling water viscosity t , viscosity correction factor ˚t , tube internal diameter di , tube external diameter dt , density of water , conductivity kt , and specific heat capacity cpt . ϕt4.5 · dt 0.5 · 11/6 2.5

7/3 · fin(i) · t · kt

According to Evans (1979), 1 kW is required to draft each 18216.44 m3 /h of air, the power consumption of tower fan can be deduced. In Eq. (26), Cfactor is fan factor, Fair-tower is air mass flowrate of cooling tower, fan-tower is fan efficiency. The air flowrate in the cooling tower is related to amount of water evaporation Evop , inlet air humidity win and outlet air humidity wout . Fair =

pt (i) = Kt(i) · Ar(i) · ht3.5

0.023

ptotal ≥ pt(i) +

(21)

The tube side pressure drops among coolers are treated as optimized variables. Pressure drop is related to the constant Kt , contact area, and film transfer coefficient. Normally, cooling water flows along the tube side and hot streams flow along the shell side. In this paper, only the tube side pressure drop is considered and Eqs. (22)–(24) are employed to show tube side pressure drop formulation (Soltani and Shafiei, 2011).

Kt(i) =

When two coolers are in series, the pressure drop of this branch is the sum of pressure drops of two coolers. For example, when cooler i connects with cooler j, pressure drop of this branch is sum of pressure drop of cooler i and cooler j. Because of the series-parallel structure, total pressure drop of cooler network is the largest pressure drop among the different branches. When cooling system is in balance, the pressure drops of branch pipelines are the same, they all equal to total pressure drop. Eq. (24) is employed to calculate system total pressure drop.

7/6 · Cpt

·

di dt


(23)

Evop wout − win

(27)

When part of cooling water evaporated, the rest of cooling water is cooled down. The amount of water evaporation is related to cooling tower range and water flowrate. Range is difference between cooling water inlet and outlet temperature. In Eq. (29), Tcin and Tcout are cooling tower inlet and outlet temperature. Evop = 0.00153 · ft · Range

(28)


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Range = Tcin − Tcout

(29)

Besides, the amount of blowdown water and makeup water are related to evaporation and cycle of concentration. Bblowdown =

Evop c − 1

Mmakeup = Evop ·

(30)

c c − 1

(31)

Cooling tower inlet air humidity is local air humidity. Outlet air humidity depends on vapor pressure. Wout =

MW w Ps · MW air Pa − Ps

Table 1 – Hot stream data. Stream

Tin (◦ C)

Tout (◦ C)

Fcp (kW/◦ C)

h (w/m2 ◦ C)

1 2 3 4 5 6 7 8 9 10

150 80 105 185 90 135 75 150 195 80

85 55 40 65 55 65 50 85 50 65

200 150 60 100 80 120 100 65 90 55

854 1743 720 1352 750 785 542 782 121 974

(32) ·(Tcout − Twb )−0.9924 + (0.022Twb + 0.39)2.447

In Eq. (32), MWw and MWair are water and air molecular weight, Ps and Pa are vapor pressure and local atmospheric pressure. Vapor pressure is a function of mean temperature Tmean in cooling tower (Kim and Smith, 2003). LnPs = 23.1 −

Tmean

4.

4111 Tmean + 237.7

(34)

Besides, the capital cost of cooling tower is determined by many factors. Eq. (35) is capital cost of cooling tower. In Eq. (36), Approach is temperature difference between cooling tower outlet temperature and air wet bulb temperature Twb .

)

(35)

Approach = Tcout − Twb

(36)

The relationship between cooling tower inlet and outlet temperature is expressed as Eq. (37). Qtower is total heat load of cooling tower which equals to sum of heat loads of all water coolers, cp is heat capacity of cooling water. Tcout =

Qtower + Tcin cp · ft

(37)

When tower outlet cooling tower mixed with makeup water, the mixed cooling water temperature is obtained as Eq. (38). Tfw and Tmakeup are temperature of mixed cooling water and makeup water.

Tfw =

Tcout · ft − Mmakeup + Tmakeup · Mmakeup ft

(38)

The objective is to minimize the total annual cost of system. Total annual cost includes capital and operational cost of cooling tower, air coolers, pumps and the water coolers.

TAC = Af · Cf pump + Cpump

·e · h + Af

n

Solution technique employed

ft · p

[a + b · Arw c (i)] + Af

i=1

+e · h · Pfan−cooler + 746.74ft

n

+

ft · p · pump

[ca · Ara c (i)]

i=1 0.79

· (Tcin − Tcout )0.57


In this paper, the MINLP model is employed and model was implemented in the software GAMS, solvers DICOPT is used to solve the MINLP problem. No global optimal solution was ensured by using DICOPT in this work. Although the obtained result was a local optimum, it was in the vicinity of the global optimum. Therefore, the obtained result was used to obtain physical insights of this work.

5.

CCtower = Af · (746.74ft0.79 · Range0.57 · Approach−0.9924 + 2.447

(39)

(33)

Tcout + Tcin = 2

(0.022Twb + 0.39)

+OCfan−tower + 110ft + w · h · Mmakeup + 1138Bblowdown

Case study

To verify the effectiveness of proposed model, a case study taken from a refinery in Xi’an is employed. The case study involved ten hot streams. This industrial case was optimized under two different circumstances. The hot stream data is shown in Table 1. Physical and economic parameters of case study are presented in Tables 2 and 3 respectively. To reduce the calculation difficulty, the minimum approach temperature difference (Tmin ) is specified as 10 ◦ C. This is an empirical value and it is common in most of current cooling systems. We yield less optimal configuration with the fixed value of Tmin . However the obtained structure can still be used to analyze physical insights of this work.

5.1.

Cooling water system in Xi’an

To illustrate the necessity of coupling air coolers with cooling water system, the base case is optimized without air coolers. Then we optimized same case with employing of a set of air coolers and compared corresponding data with base case data. The price of electricity and fresh water in Xi’an are known. Fig. 3 is employed to show the configuration of base case. There are 4 pairs of coolers are in series connection. And Fig. 4 is the optimized configuration with air coolers. Except stream 2 and stream 10, all hot streams are cooled down by both air cooler and water cooler. Table 4 is employed to compare data of optimized configurations. For configuration with air coolers, the total water flowrate is 203.7 kg/s, which is less than half of the flowrate in base case (446.1 kg/s). With less cooling water in system, cooling tower cost reduced correspondingly. Although installing and running a set of air coolers requires $ 284,285 extra cost, $




7

Fig. 3 – Cooling water system without air cooler in Xi’an.

550,756 reduction on cooling tower cost and $ 109,854 reduction on water coolers capital cost can be yielded. Cooling tower operational cost has occupies near 75% of total annual cost, and when installing new air coolers to existing cooling water system, we can save $ 509,952 on cooling tower operational cost. Therefore, even for an existed cooling water system, it is still economical to install air coolers to save cost. The proposed model is also suitable for retrofitting problem. The pressure drop of cooling water system increased from 8976 Pa to 23,871 Pa, after introducing air coolers to system. Although the total water flowrate decreased owning to the installing of air coolers, the total pump cost still increased $ 2049. But the reduction on cooling tower cost and water cooler capital cost


are much higher than the increase of pumping cost. Finally, introducing air cooler to system leads to 29.4% reduction on the total annual cost. The outlet hot stream temperatures of air coolers (breakpoints of air and water cooler) range from 66.3 ◦ C to 113.7 ◦ C. It can be found that the break-points between air cooling and water cooling varied significantly. For the hot stream H8, the hot stream was cooled down by the air cooler to 113.7 ◦ C at first. Then the hot stream was cooled down by water cooler to the target temperature 85 ◦ C. However, for the hot stream H7, the hot stream was cooled down by air cooler to 66.3 ◦ C, and then cooled down by water cooler to target temperature 50.0 ◦ C. The break-points of stream H8 is significantly



8


Fig. 4 – Cooling water system with air coolers in Xi’an.

higher than the break-point of stream H7. The wide variations between the break-points of different streams are mainly due to the interactions between hot streams and cooling water network. When a hot stream is cooled down by air cooler to a certain degree, a water cooler is required to cool down the stream to target temperature. Since water coolers are in seriesparallel arrangements, the outlet hot streams from air coolers can be cooled down by the fresh water or used cooling water from another cooler. Fig. 5 shows the distribution of the break-points of eight hot streams. For the left sector, the four hot streams were cooled down by fresh cooling water. For the right sector, the rest of four streams were cooled down by the used cooling water. It


is found that when a hot stream is cooled down by the used cooling water, the break-point of that stream is higher than 95.7 ◦ C. When a hot stream is cooled down by fresh water, the break point is lower than 95.3 ◦ C. For example, the break-point of hot stream H7 is 66.3 ◦ C. If the stream is cooled down by used cooling water with temperature over 30 ◦ C, the temperature difference of water cooler is quite low and more contact areas are required. However, the used water can be used to cool down the stream with high break-point. For example, the break-point of stream H8 is 113.7 ◦ C, and this stream can be cooled down by used water. Although this stream is cooled down by the used cooling water, the water cooler still keeps a high temperature difference. Air coolers and water cooler


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Fig. 5 – Distribution of the break-points of air and water cooling.

Table 4 – Comparison of heat load distribution and economic data in Xi’an.

Table 2 – Physical parameters of case study. Items

Data

Minimum approach temperature difference Tmin Maximum allowable outlet temperature of cooler Tmax Make-up water temperature Tmakeup Ambient temperature Tambient Wet bulb temperature Twb Cooling water specific heat capacity Cpt Air specific heat capacity Cpa Air saturated humidity at wet bulb temperature Atmospheric pressure Water cooler film heat transfer coefficient hw Density of cooling water ␳ Viscosity of cooling water ␮t Air cooler face velocity Air cooler friction factor Air cooler number of bundles Viscosity correction factor t Conductivity kt Tube internal diameter Di Cycle of concentration ␲

10 ◦ C

55 ◦ C 23 ◦ C 25 ◦ C 12 ◦ C 4.18 kJ/(kg ◦ C) 1.004 kJ/(kg ◦ C) 0.011 kgw/kga 101,325 Pa 2.5 kW/(m2 ◦ C) 995 kg/m3 1 × 10−3 kg/m s 3 m/s 0.95 4 1.05 0.6 w/m ◦ C 15.4 mm 4

Table 3 – Economic parameters of case study. Items Water cooler capital cost($) Air cooler capital cost Pump capital cost($) Plan lifetime Xi’an electricity price Nanchang electricity price Xi’an fresh water price Nanchang fresh water price Pump efficiency Air cooler fan efficiency Cooling tower fan efficiency Plant operation time Interest rate Annualized factor

Cost data

Remarks

11000 + 260A

A in m2

4778A0.525 8600 + 7310 (Mp/␳)0.2 5 years 0.083 $/kwh 0.096 $/kwh

A in m2 p in Pa, ␳ in kg/m3 , M = kg/s

0.843 $/t 0.344 $/t 70% 70% 75% 2.88 × 107 s/y 15% 0.298

network were optimized simultaneously. To keep the optimal temperature difference of each water cooler unit, the breakpoints of streams varied according to the water network. In other word, the break-point of a stream depends on whether the inlet cooling water of their water coolers is fresh water or used water. Please cite this article in press as: Ma, J., et al., https://doi.org/10.1016/j.cherd.2017.10.020

Capital cost of water coolers ($) Capital cost of air coolers ($) Operational cost of air coolers ($) Operational cost of cooling tower ($) Capital cost of cooling tower ($) Fresh water consumption cost ($) Heat load of air coolers (kw) Heat load of cooling tower (kw) Operational cost of pumps ($) Capital cost of pumps ($) Total annual cost($)

5.2.

Cooling system in Xi’an without air coolers

Cooling system in Xi’an with air coolers

229,410

119,556

0

178,073

0

106,212

939,910

429,958

88,515

47,711

764,769

349,608

0

34,954

64,450

29,496

3286

4803

13,682 1,274,805

14,214 900,530

Cooling water system in Nanchang

City Nanchang and city Xi’an have different electricity and water price. The intention of conducting second case study is to optimize same case with different electricity and fresh water price, and discuss the performance of air coolers in different situations. Different from Xi’an where water is extremely scarce, Nanchang has relatively plentiful water resource. The fresh water price in Nanchang is much lower than price in Xi’an. Fig. 6 is the optimized configuration of base case, the hot streams were cooled down by cooling water exclusively. Fig. 7 is the configuration with air coolers. As showed in Fig. 7, there are seven air coolers in the system. Different from Xi’an case, hot stream H7 in this case does not require air cooler to exchange heat. Table 5 listed comparison of heat load distributions and economic data. After introducing air coolers to system, the pressure drop of cooling water system increased from 7215 Pa to 15,481 Pa. Although the total water flowrate decreased owning to the installing of air coolers, the total pump cost still increased $ 2696. Cooling tower cost reduced significantly with introducing of air coolers. Although introducing air coolers needs $ 215,364 extra cost, $ 243,320 reduction on cooling tower cost and $ 85,938 reduction on water cooler cost can be obtained. The total annual cost decrease 13.1% which indicates the proposed model is still effective even in the region where water reservoir is relatively plentiful. The outlet hot stream temperatures of air coolers (break-points of air and water cooling) range from 79.9 ◦ C to 129.5 ◦ C. Same as case1, the break-points of hot streams varied. Same pattern can be observed in this case: for the hot stream H1, H4, H6, H8, they were cooled down by



10


Fig. 6 – Cooling water system without air cooler in Nanchang.

used cooling water, and their break-points are higher than 106.8 ◦ C. For hot stream H3, H5, H9, they were cooled down by fresh water, and their break-points are below 103.1 ◦ C. The interaction between air coolers and cooling water network causes the variation of break-points of hot streams. Therefore, using simultaneous optimization model yields the optimal break-points of each hot stream and optimal distributions of heat loads. After optimized same industrial case under different circumstances of two cities, we found that two configurations have different heat load distributions among air cooler and water cooler. Fig. 8 is comparison of heat load distribution in


two cities. In Xi’an, air coolers occupied more than half of total heat load. This is because the water price in Xi’an is much higher than water price in Nanchang. The cooling mechanism of cooling tower is to evaporate part of cooling water to cool down rest of water. Fresh water has to be added to system constantly because of the continuous evaporation and blow down. For city like Xi’an where fresh water is expensive, the air cooling is more economical. In Nanchang, air cooler only occupies 40% of total heat load which is lower than Xi’an air cooling heat load. This is because water cooling is more desirable in Nanchang where water is cheap. And running cost of air cooler in Nanchang is expensive because of high electricity




11

Fig. 7 – Cooling water system with air cooler in Nanchang.

price. In comparison with the heat load distribution in Xi’an, water cooling occupies more heat load because of low water price and high electricity price. The water and electricity price ratio in both cities are presented in Fig. 8. Xi’an price ratio is 10.15, Nanchang price ratio is 3.58. When water to electricity price ratio is relatively high, air cooling is more desirable and economical than water cooling. For the city where price ratio is low, water cooling should occupy majority of the total heat load. Fig. 9 displays the boundaries of temperature break-points of air and water cooling. When Xi’an case was optimized with the parameter of Nanchang, the boundaries shifted toward left


side, which indicates that the hot streams should be cooled down to a lower degree in place like Xi’an than place like Nanchang. For Xi’an case, the configuration with air coolers saved 29.4% TAC. For Nanchang case, the configuration with air coolers saved 13.1% TAC. Xi’an case has a higher reduction on TAC than Nanchang case, which indicates that for city where water is scarce and electricity is cheap, air cooling is an economical choice. The heat load of air cooling should be higher than the heat load of water cooling. And it is particularly necessary to employ coupling structure to achieve cooling service, in the region where water is scarce and electricity is relatively cheap.


ARTICLE IN PRESS


12


Fig. 8 – Comparison of heat load distributions in two cities.

Fig. 9 – Temperature boundaries of air and water cooling.

Table 5 – Comparison of heat load distribution and economic data in Nanchang.

Capital cost of water coolers ($) Capital cost of air coolers ($) Operational cost of air coolers ($) Operational cost of cooling tower ($) Capital cost of cooling tower ($) Fresh water consumption cost ($) Heat load of air coolers (kw) Heat load of cooling tower (kw) Operational cost of pumps ($) Capital cost of pumps ($) Total annual cost($)

6.

Cooling system in Nanchang without air coolers

Cooling system in Nanchang with air coolers

226,251

140,313

0

141,921

0

73,443

516,394

303,457

89,430

59,047

312,076

186,255

0

25,872

64,450

38,578

2906

4593

13,101 848,085

14,110 736,887

Conclusion

Acknowledgements Financial support from the National Natural Science Foundation of China under Grant No. 21576286, SINOPEC under Grant No. 315020, and Science Foundation of China University of Petroleum, Beijing (No. 2462017BJB03) is gratefully acknowledged.

References

In this paper, we present a cooling system coupled air and water. The proposed model allows system to select cooling method automatically. After introducing air coolers to cooling Please cite this article in press as: Ma, J., et al., https://doi.org/10.1016/j.cherd.2017.10.020

water system, the total annual cost for cooling service reduced significantly as a result of optimal distribution of heat load. We also found that different fresh water prices and electricity prices exert great influence on the configuration. For the region where water is scarce and electricity is not expensive, it is particularly necessary to employ air coolers to reduce heat load of cooling water system. Besides, the proposed model can help engineers obtain optimal temperature break-points between air and water cooling. The temperature break-points depends on following factors: whether the hot stream is cooled down by fresh water or used cooling water, the properties of hot stream, interaction between air cooler and cooling water network, local water price and electricity price. Given a set of hot streams, when temperature is higher than upper bound of break-point, water cooling is not ideal. When temperature is lower than lower bound of break-point, air cooling is not economical.

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