Analysis of the effect of seasonal climate changes on cooling tower efficiency, and strategies for reducing cooling tower power consumption

Accepted Manuscript Analysis of the Effect of Seasonal Climate Changes on Cooling Tower Efficiency, and Strategies for Reducing Cooling Tower Power Consumption Ricardo F.F. Pontes, Willian M. Yamauchi, Evelin K.G. Silva PII: DOI: Article Number: Reference:

S1359-4311(18)36325-7 https://doi.org/10.1016/j.applthermaleng.2019.114148 114148 ATE 114148

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

16 October 2018 2 July 2019 17 July 2019

Please cite this article as: R.F.F. Pontes, W.M. Yamauchi, E.K.G. Silva, Analysis of the Effect of Seasonal Climate Changes on Cooling Tower Efficiency, and Strategies for Reducing Cooling Tower Power Consumption, Applied Thermal Engineering (2019), doi: https://doi.org/10.1016/j.applthermaleng.2019.114148

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Analysis of the Effect of Seasonal Climate Changes on Cooling Tower Efficiency, and Strategies for Reducing Cooling Tower Power Consumption Ricardo F. F. Pontes1,†, Willian M. Yamauchi1, Evelin K. G. Silva1 1 – Chemical Engineering Department, Universidade Federal de São Paulo, R. Arthur Ridel, 275, 09972-270, Diadema, SP, Brazil

ABSTRACT Cooling towers are widely used in chemical industries to cool water with ambient air that is susceptible to weather changes not only during the day, but also during the year, resulting in challenges to cooling towers design and operation.

In the design phase, the difficulties to

determine the cooling tower capacity arise not only from the uncertainty of cooling water consumption but also from ambient temperature variations, which have a direct impact on the volume of cooling tower fill and fan power. Wide temperature variations can result in cooling towers that excessively cool water during significant portion of the year. Moreover, an oversized cooling tower brings challenges to the plant operation, since the cooling tower turndown must be high to account for the colder days. The mathematical model of cooling tower operation that is composed by mass and energy balances, and by cooling tower characteristic equations can be simulated to design cooling towers, and forecast their performances in four Brazilian cities (Manaus, Salvador, São Paulo and Porto Alegre). Analyzing the results enables the calculation of the cooling tower slack, and the required turndown during the year in these four cities. This work proposes strategies for cooling tower fan operation to reduce the slack, and estimates the electrical energy cost reduction if such strategies are implemented.

†Corresponding author.

1

Keywords: Cooling tower, mathematical modeling, process analysis, process design, energy conservation

1. INTRODUCTION Despite not being part of the production process core, plant utilities often impact on the plant capital and operating costs [1-3]. One of the main utilities systems is the cooling water system consisting of cooling towers, cooling water pumps, supply and return cooling water piping, and cooling water consumers [1, 4] such as heat exchangers that require cold fluid to cool process fluids. Cooling water production demands considerably high electrical energy consumption, for motors of both cooling tower fans and pumps. Several efforts have been made to reduce costs associated to cooling water systems by either optimizing cooling water system mathematical models or conducting pinch analysis. Cortinovis et al. [1], Deziani et al. [2], Kim et al. [3], and Castro et al. [4] minimize cooling tower operating costs by manipulating ambient air flow rate through the cooling tower and cooling water blowdown. Deziani et al. [2] propose a method for reducing cooling water evaporation and, consequently, make-up water consumption by using air to air heat exchangers. Kim et al. [3], Ponce-Ortega et al. [5], Gololo and Majozi [6], Gololo and Majozi [7], and Dakwala et al. [8] minimize cooling water flow rate by re-arranging the heat exchangers network in order to reuse cooling water. Castro et al. [4], Chang et al. [9] and Viljonen et al. [10] study the influence of variable weather conditions on operating costs of a cooling tower installed in the city of Porto Alegre, but this work does not address how to reduce operating costs in these varying weather conditions. Zheng et al. [11], Panjeshahi et al. [12], and Rubio-Castro et al. [13] present similar method, but aim to minimize total (operating and cooling) costs of cooling water system.

Serna-González et al. [14] optimize total costs by re-arranging the heat

exchangers network, and by determining the cooling tower fill that is used. Sun et al. 2

[15] optimize the whole cooling water system, including cooling tower and cooling water pumps network. Cooling towers can be either natural or mechanical draft, in which the latter use fans to induce air flow through the cooling tower [16]. Mechanical draft cooling towers occupy significant less space than natural draft ones. However, fans require electrical energy and, therefore, higher operating costs. Naturally, cooling tower performance relies on ambient air temperature, which means that cooling tower has to be designed for the hottest days of the year. Many times, over the year, actual ambient temperature is less than the design ambient temperature, and consequently electrical energy consumption can be excessive if fans turndown is not high enough. In subtropical areas, this problem is aggravated during winter months when ambient temperatures can be 20 oC lower than the considered design air temperature. During colder days, if the ambient air flow rate is not reduced, the cooling tower cools water below the design supply temperature. This can upset processes that require cooling water.

In this case, cooling tower fans should operate with reduced speed and,

consequently, power consumption. This speed reduction can be achieved by the use of variable frequency drives (VFD). Chang et al. [9] devised a control strategy based on the installation of VFDs in cooling tower fans achieving a 38% reduction in energy consumption, as a result of the cubic relationship between motor power and speed. However, many times to reduce capital costs, new cooling towers projects and plants with existing cooling towers do not contemplate the acquisition and the installation of VFDs, and a viable solution is to operate one or more fans intermittently bringing operational challenges. In addition several existing cooling towers do not operate with VFDs and for the installation of multiple VFDs for a multiple cell cooling tower, with multiple fans and motors, the existing motor control center (MCC) would need multiple appropriate spare buckets, and that is highly unlikely. Therefore, the installation of VFDs on existing motors would require a new MCC or the reform of the existing MCC, both costly alternatives. 3

This paper aims to model cooling towers design and operation in different cities with particular annual weather variations. Using historical data for ambient air temperature, the performed simulations yield values for supply cooling water temperature, required air flow rate and fan motor power consumption as function of ambient air temperature. This work presents strategies for fan operation according to the number of cells with installed VFDs, as well as an estimate of operating costs reduction.

2. COOLING TOWER MATHEMATICAL MODEL The following assumptions are considered for modeling the cooling tower [6, 13, 17, 18]: A1. Steady state operation A2. Negligible heat loss through cooling tower wall A3. Negligible change of water flow rate due to evaporation along the tower; water flow rate in cooling water circuit is kept constant by use of make-up water A4. Constant air and water specific heats along the tower A5. Constant overall mass transfer coefficients along the tower Hence, the energy balance for a cooling tower can be written as: L.Cp.(T1 – T2) = G.(h2 – h1)

(1)

where L is the cooling water flow rate (kg.h-1) Cp is the specific heat for water (kcal.kg-1.oC-1) T1 is the cooling water return temperature (oC) T2 is the cooling water supply temperature (oC) 4

G is the air flow rate (kg/h) h1 is the enthalpy of ambient air (kcal.kg-1) h2 is the enthalpy of the outgoing air (kcal.kg-1) The air enthalpy h is calculated as a function of a temperature t, and of water vapor to dry air ratio u [19]: (2)

h = 1.006.t + u.(1.84.t + 2501)

The difference between cooling water return and supply temperatures is known as the cooling water system range. Normally, cooling water return temperature is limited to 45 oC to avoid calcium salts precipitation [20]. Cooling water supply temperature can be set at 30 oC to assure a difference of more than 5 oC between supply cooling water and ambient air temperatures. For many cooling water systems, it is not recommended to lower the supply temperature, since that can cool process fluids to lower temperatures than designed. Properties such as viscosity and solutes solubility can be drastically altered, as well as the physical state. The difference between the cooling water supply and ambient air temperatures is known as cooling water system approach. The higher the approach is, the higher the driving force for mass and heat transfer is and, therefore, the lower the volume of the cooling tower fill is. Considering Assumptions A1 to A5, the cooling tower characteristic equation derived from Merkel’s model is given by [17, 18, 21]: K.a.Z L'

T2 dT

(3)

= Cp.∫T1hsat – h

where K.a is the volumetric air mass transfer coefficient (kg.h-1.m-3) L’ is the cooling water mass flux (kg.m-2.h-1) hsat is the enthalpy of saturated air (kcal.kg-1) 5

There are more rigorous methods for cooling tower thermal evaluation than Merkel’s method, but these require the knowledge of model parameter values that may be difficult to estimate [18, 21]. To evaluate the operating costs of a cooling tower, the mathematical model based on Merkel’s method, which is simple and widely used [22], is used. The water volumetric flux Q’ can be obtained by equation (4). In the Appendix, it is described how this equation is derived. Q’ = 14.9 – 0.967.T2 – 0.696.t1 + 3.58.10-2.T 22 + 2.46.10-2.t 12 – 2.10.10-4.T 23 – – 6.47.10-4. t 13 + 7.07.10-3.T2.t1

(4)

where Q’ is the cooling water volumetric flux (m3.m-2.h-1) t1 is the ambient air wet bulb temperature (oC) The water mass flux can be obtained by: L' = Q '.H2O

(5)

where H2O is the water density (kg.m-3) The cooling tower dimensions are calculated by: A = Z =

L

(6)

L' L' .K.a

( ) K.a.Z L'

(7)

where A is the sectional area of the cooling tower (m2) Fan efficiency varies according to design air flow, fan model and fan manufacturer. For the purpose of this work, these variations are not considered. The following assumption is made for cooling tower fan power: 6

A6. Fan efficiency does not depend on air flow rate, and is constant

Therefore, the following equation applies [23]: PF =

( 1 + u).G

(8)

10728.ρmix

where PF is the fan power (kW)

mix is the humid air density at atmospheric pressure (kg.m-3) Considering the ideal gas law, the humid air density is calculated by the following equations:

mix =

( 1 + u).(vap.air)

(9)

vap + air

air =

683.1 1.8.t2 + 492

(10)

vap =

426.9 u.(1.8.t2 + 492)

(11)

where air is the dry air density at atmospheric pressure (kg.m-3)

vap is the water vapor density at atmospheric pressure (kg.m-3)

3. ANALYSIS OF CLIMATE VARIATION IMPACT Brazil has a considerably large distance of about 4,400 km from its northernmost to southernmost points. As a result, climate variation differs considerably in various cities nationwide. For this study, four major Brazilian cities are considered and listed on Table 1. Table 1 – Brazilian cities considered for analysis on climate variation 7

City

Parallel

Elevation above sea level (m)

Manaus

3o06’S

92

Salvador

12o58’S

8

São Paulo

23o34’S

760

Porto Alegre

30o02’S

10

Figure 1 shows yearly variations of average daily wet and dry bulb temperatures (WBT and DBT respectively) in these four cities from 1987 to 2017 [24]. As expected, Porto Alegre is the city with the highest variations, followed by São Paulo that shows considerable variations too. Salvador and Manaus present the lowest variations. For Manaus, during 156 days, practically more than half year, DBT is about 27 °C and in 199 days WBT is about 23 °C.

8

200 Manaus Salvador São Paulo Porto Alegre

Days / Year

150

100

50

0 13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

Dry Bulb Temperature (oC) 200 Manaus Salvador São Paulo Porto Alegre

Days / Year

150

100

50

0 10

11

12

13

14

15

16

17

18

Wet Bulb Temperature

19

20

21

22

23

24

(oC)

Figure 1 – Average daily temperatures yearly distribution for Manaus, Salvador, São Paulo and Porto Alegre For calculating cooling water system approach, the considered design WBT (t1d) for each city is the 95th percentile of all wet bulb temperatures during the last 30 years. The cooling water supply temperature is set at 30 oC to ensure that the approach is above 5 oC for all four cities. Figure 2 shows how the approach varies during the year in all four cities. 9

200

Manaus

180

Salvador

160

São Paulo Porto Alegre

Days / year

140 120 100 80 60 40 20 0 6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Approach (oC)

Figure 2 – Yearly approach distribution for Manaus, Salvador, São Paulo and Porto Alegre As case study, this paper considers a paper mill that demands a cooling water flow rate of 5,500 m3/h, and a design supply temperature (T2d) and a return temperature (T1d) of, respectively, 30 and 45 oC. The cooling water demand is the sum of several individual consumers’ demands. These consumers mostly consist of heat exchangers used to cool process fluids such as black liquor or fiber suspensions. Table 2 presents design WBT, dimensions for cooling towers, design air flow rate (Gd) and design fan power (PFd) if the mill was to be located in each of the four cities. Table 2 – Cooling tower characteristics for evaluated cities (T1d = 45 oC, T2d = 30 oC) City

t1d (oC)

Gd (ton/h)

PFd (kW)

Zp (m)

Ap (m2)

Manaus Salvador São Paulo Porto Alegre

24 24 21 22

4.52x103 4.52x103 3.92x103 4.10x103

209.1 209.1 180.5 188.8

7.13 7.13 6.77 6.86

781 781 692 717

10

The analysis of Figure 2 shows how often cooling towers operate under design point. In Porto Alegre, for instance, during 157 days in the year, the cooling tower operates with an approach higher than 10 oC. As for Manaus, which has the lowest yearly WBT variation, only in 109 days in the year the approach would be equal or higher than 8 °C. Using the cooling tower dimensions and design fan power calculated in Table 2, equations (4) is solved for T2 for different values of t1, actual WBT, and consequently the approach. Figure 3 shows how T2 varies during the year in all four cities. 200 Manaus Salvador São Paulo

150

Days / Year

Porto Alegre

100

50

0 29.5 - 30.0

29.0 - 29.4

28.5 - 28.9

28.0 - 28.4

27.5 - 27.9

27.0 - 27.4

26.5 - 26.9

26.0 - 26.4

25.5 - 25.9

T2 (oC)

Figure 3 – Actual cooling water supply temperature variation during the year for Manaus, Salvador, São Paulo and Porto Alegre

4. STRATEGIES FOR REDUCING COOLING TOWER ENERGY CONSUMPTION 4.1. Cooling tower slack

11

During colder days, if a cooling tower operates with the design air flow rate, the water is cooled below 30 oC, and in other to reach this value, it is necessary to use a reduced air flow rate (Gred,t1) calculated as a function of the ambient WBT. The cooling tower fan slack (St1) is defined as:

St1 =

Gd Gred,t1

(12)

- 1

Figure 4 shows the histogram of cooling tower fan slack for the four cities. For Manaus, the fan slack is below 0.10 for more than 250 days of the year, whereas for Porto Alegre this value is above 0.20 for 60% of the year. The reduction on energy consumption is proportional to the slack and is calculated according to the implemented strategy to achieve this reduction, either by operating a fan intermittently or by using one or more VFDs.

200 Manaus Salvador São Paulo

150

Days / Year

Porto Alegre

100

50

0 0.00 - 0.04 0.05 - 0.09 0.10 - 0.14 0.15 - 0.19 0.20 - 0.24 0.25 - 0.29 0.30 - 0.34 0.35 - 0.39 0.40 - 0.44 0.45 - 0.49 Fan Slack

Figure 4 – Fan slack for Manaus, Salvador, São Paulo and Porto Alegre 4.2. Assumptions for cooling towers with multiple cells 12

Industries usually divide cooling towers in multiple cells, each one with a single fan, to achieve operational flexibility allowing to turn off one or more fans during colder days. Figure 5 shows a schematic design for a cooling tower divided into n cells.

Cooling water return

Li T1

Li T1

Li T1

G t2

Ambient air

Outgoing air

G t1 Cell 1 Li T2i

Cell 2 Li T2i

Cell n Li T2i

Cooling Tower Basin

Cooling water supply

L T2

Figure 5 – Schematic design for a cooling tower divided into n cells To attain this reduction in energy consumption, it is necessary to decrease the fan power, either by reducing speed of a single fan, or by turning off one or more fans when using multiple fans, or even by adopting a combination of both strategies. If all cell fans are on, the cooling water supply temperature (T2) is calculated in the same manner as it is calculated for a one cell cooling tower. When one or more cell fans are off, then the following assumptions are made to calculate T2. 13

Considering that a cooling tower cell is an individual cooling tower: A7. Cell i cooling water flow rate, Li (i = 1…n), is obtained by dividing the overall cooling water flow rate by the number of cells A8. Cell i sectional area, Ai, is obtained by dividing the overall sectional area by the number of cells A9. All cells have the same height, Z A10. Design air flow rate (Gdi) for cell i is obtained by dividing the overall design air flow rate by the number of cells A11. Design fan power (PFdi) for cell i is obtained by dividing the overall design fan power by the number of cells The cooling tower basin that collects water cooled by all cells is a homogeneous tank and, consequently, the temperature is uniform throughout the basin. It is reasonable to consider that due to the turbulence and mixing caused by the effects of water falling from cells and water being pumped out of the basin. Therefore: A12. Cooling tower supply temperature is obtained by averaging water outgoing temperatures, T2i (i = 1…n), of all individual cells. T2i values are calculated according to the operation of each cell fan The following equations are valid for Assumptions A7 to A12: L

(13)

Li = n . A

(14)

Ai = n . Gdi =

Gd

PFdi =

n

(15)

.

PFd n

(16)

. 14

1

n

(17)

T2 = n.∑i T2i 4.3. Strategies for reducing cooling tower power consumption

To reduce the cooling tower slack, the T2 value must be kept at a setpoint of 30 oC. This can be done by either reducing the fan speed or by operating one fan intermittently, since turning a fan off most likely results in a T2 value above the setpoint. For a cell i with VFD-operated fan, the reduction of the fan speed alters the air flow rate going through that cell (Gi) as shown by the following equation [10]:

ri =

( ) =( ) si

Gi

sdi

Gdi

(18)

where ri is the ratio of the reduced speed of the fan in relation to the design speed si is the speed of the fan sdi is the design speed of the fan In cell i with VFD, power consumption (PFi) is calculated by [24]: PFi = PFdi.r3i

(19)

VFDs can considerably reduce the operating frequency of the motor. However, low frequencies can cause the motor to overheat due to poor ventilation. Chang et al. [9] established the value of 30 Hz for the minimum frequency for a motor to operate. Considering that the alternate current in Brazil is at 60 Hz, this work adopts the following constraint: (20)

ri ≥ 0.5

15

If the value of t1 is very low, the VFD-operated motor reaches the lower established limit; and this requires one fan to operate intermittently to maintain T2 at the setpoint. If cell i fan is on, T2i is calculated by solving the equation (1) for known values of t1 and of Gi, the air flow rate through cell i. The value of the individual power consumed (PFi) for that cell is the same of PFdi if the fan is continuously on and no speed reduction exists. For a cell with the fan off, the following assumption is made: A13. There is no cooling and the cell outgoing water temperature is the same of the return cooling water temperature as there is no air flow rate through the cell, since the fan is off In this case: (21)

T2i = T2off = T1

For a cell with intermittent use of the fan, the following assumption can be made: A14. T2i is the weighted average of the outgoing water temperature when the fan is on and off Therefore: (22)

T2i = fp.T2d + (1 - fp).T2off

where fp is the fraction of time that the fan is on for a cell operating intermittently T2d is the outgoing water temperature when the fan operates at design speed (oC) A value of fp of 1.0 means that the fan is always on, while a value of 0.0 means that the fan is always off. 16

The average consumed power (PFi) by the fan of a cell operating intermittently is calculated by: (23)

PFi = fp.PFdi

4.4. Cooling tower operating parameters as a function of ambient air temperature The proposed strategies are applied to the case study cooling tower, which is composed by three cells. Varying the number of cells operating with VFDs (nv) from 0 to 3; the values of ri,t1 and fp,t1 are calculated as a function of t1 for the four cities to maintain T2 at the setpoint of 30 oC. If the cell has no VFD, only the value of fp,t1 needs to be calculated by solving equation (17). If the cooling tower operates with at least one VFD, fp,t1 is calculated as a function of ri,t1. The calculated values of ri,t1 and fp,t1 minimize the following objective function: n

(24)

min PF = ∑i = 1PFi

Minimization of equation (24) is done using GAMS / CONOPT [25]. The optimal solutions are shown of Figure 6. For cooling towers with two or three VFDs installed, the optimal solutions show that all fans with VFD operate at the same speed.

17

1.00

1.00

1.00

rt1 s(nv=1) (nv = 1)

0.90

0.90

0.80

0.90

rt1 fp,t1

0.80

rt1 fp,t1

Manaus

0.70

0.60

Salvador

0.70

rt1 s(nv=2) (nv = 2)

0.60

0.80

0.50

0.50 24

23

22

t1 (oC)

21

24

r

23

22

(nv = 3)

0.70

20

19

1.00

1.00

0.90

0.80

f (nv = 0)

0.60

21

t1 (oC)

t1 s(nv=3)

p,t1 fp(nv=0)

0.80

rt1 fp,t1

rt1 fp,t1

0.60

0.70 0.50 24

0.60

23 f22 p,t1 21 fp(nv=1)

0.40

Porto Alegre

(nv = 1)

São Paulo

0.20

0.50 21

20

19

18

17

t1

16

15

14

22

13

21

20

19

18

17

16

15

14

13

12

11

10

t1 (oC)

(oC)

Figure 6 – Operating parameters (ri,t1 and fpi,t1) as a function of ambient wet bulb air temperature (t1) and number of installed VFDs (nv) for Manaus, Salvador, São Paulo and Porto Alegre For Manaus, if there is at least one fan operating with a VFD, there is no need to operate intermittently a cell during the year. Since the other three cities present larger ambient temperature variations, for a cooling tower with a single VFD (nv =1) during the coldest days, the cooling tower operates with one cell at reduced speed and another intermittently. The results show that the solutions calculated are not bound by constraint (20), as the value of si,t1 reaches a minimum value of 0.54. Values of fp,t1 close to 0.0 and 1.0 should be avoided since in practice it means that the fan motors will turn on and off in short time intervals. Electrical motor manufacturers [26] do not recommend this procedure. Therefore, for these operating parameters, it is recommended to alternate the fan that operates intermittently.

18

Figure 7 shows the results for the cooling tower total fan power (PF,t1) as a function of t1 and nv for the four cities. The use of at least one VFD yields a significant power consumption reduction, especially in the coldest days. In Porto Alegre, when t1 reaches 10 oC, the value of PF,t1 for nv =1 is about 20% lower than the one for nv = 0, and if nv = 3, then this reduction reaches 56%. In Manaus, however, this reduction is lower, but on the coldest days, a cooling tower with three VFDs can be about 30% more economical than one with no VFD installed. Notably, there is significant reduction in a cooling tower with two VFDs compared to one with one VFD in São Paulo and Porto Alegre. This can be explained by the fact that for colder temperatures, a cooling tower with one VFD operates with one fan intermittently.

250

250

Salvador

1.00

Manaus

fp(nv=0) nv = 0

200

PF (kW)

PF (kW)

200 0.90

150

150

nv = 1 s(nv=1)

0.80 24

23

22

21

100

rt1…

100

24

23

22

21

20

19

t1 (oC)

t1 (oC) 200

200

0.70

nv = 2 s(nv=2) 150

PF (kW)

PF (kW)

150 0.60

100

100

São Paulo

nv = 3 s(nv=3)

0.50 24 50 21

20

19

18

17

16

15

14

23

22 21 t1 (oC)

13

Porto Alegre 50 22

t1 (oC)

21

20

19

18

17

16

15

14

13

12

11

10

t1 (oC)

Figure 7 – Total fan power as a function of ambient wet bulb air temperature (t1) and number of installed VFDs (nv) for Manaus, Salvador, São Paulo and Porto Alegre 4.5. Calculation of cost reduction

19

The cooling tower annual expenditure without turning any fan off, 8760 hours of operation, TE (BRL.year-1) is defined as: (25)

TE = 8760.PFd.EC

where EC is the electrical energy cost (BRL.kW-1) The reduced annual expenditure, RE (BRL.year-1), is given by:

n t1d RE = 24.EC.∑i = 1∑t1 = t1minPFi,t1.FDt1

(26)

where t1,min is the minimum wet bulb temperature recorded for a city (oC) FD,t1 is the number of days in a year for which the t1 value is recorded The annual expenditure reduction ES is defined as: (25)

ES = TE - RE

Considering the energy cost in Brazil to be 158.53 BRL.MWh-1 [27], Table 3 presents the values for ES for each for the 4 cities as a function of nv. Table 3 – Electrical energy cost reduction with intermittent fan operation as a function of the number of VFDs installed

20

City

nv

TE (BRL.year-1)

RE (BRL.year-1)

ES (BRL.year-1)

ES / TE

281,119

9,263

3.19%

253,182

37,200

12.81%

247,507

42,875

14.77%

3

245,442

44,940

15.48%

0

276,048

14,333

4.94%

247,331

43,051

14.83%

2

235,120

55,262

19.03%

3

229,993

60,389

20.80%

0

231,966

30,225

10.41%

196,562

65,629

22.60%

2

171,187

91,004

31.34%

3

157,787

104,404

35.95%

0

231,966

30,225

10.41%

19,656

65,629

22.60%

2

171,187

91,004

31.34%

3

157,787

104,404

35.95%

0 1 Manaus

2

290,382

1 Salvador

290,382

1 São Paulo

250,664

1 Porto Alegre

262,191

In all four cities, the use of one VFD increases significantly the annual reduction in energy consumption compared to a cooling tower with no VFD installed. However, the use of additional VFDs only yields a significant reduction if the air temperature varies considerably during the year. In Manaus, the annual reduction in energy consumption is almost quadrupled when one VFD is installed. But for cooling towers with two to three VFDs installed, the difference in annual reduction is about 5%, while this reduction is 20% for cooling towers with one to three VFDs installed. In Porto Alegre, a cooling 21

tower with three VFDs installed yields an annual reduction of 15% compared to one with two VFDs installed and 60% to one VFD installed.

5. CONCLUSIONS This paper addresses the analysis of yearly climate changes in the design and operation of cooling towers. Historical meteorological records are used to determine the design wet bulb air temperature to be used in cooling tower design equations, yielding cooling tower’s dimensions, required air flow rate, and fan power. Since the design of the cooling tower has to consider the most critical situations, the hottest days of the year, most of the year the cooling tower operates overdesigned, with excessive power consumption. Four Brazilian cities are used as study cases: Manaus, Salvador, São Paulo and Porto Alegre. Manaus, located close to the Equator, presented the lowest yearly ambient temperature variation and, therefore, for more than half of a year the fan slack was below 0.10. On the other hand, Porto Alegre, a subtropical city, presented a considerably wide range of ambient temperatures during the year, with fan slack reaching as high as 0.44 on colder days. The results for Porto Alegre show the need to set strategies that reduce cooling towers operating costs. To reduce fan motor power consumption, either a variable frequency driver is installed, or the fan is operated intermittently.

This work establishes a

methodology to estimate the annual reduction in electrical energy consumption for each considered strategy. This methodology can be applied in either cooling tower projects, either to design a new one or to retrofit an existing one, to determine how many VFDs should be installed to reduce the annual energy consumption to a target value. The use of at least one VFD yields significant reduction in energy consumption compared to cooling towers with no VFD installed. In Manaus, for a cooling tower with three cells, the use of two VFDs presented similar annual reduction values to a similar tower with three VFDs 22

installed. However, for the other three cities, the use of VFDs in all three cells present a significant annual reduction compared to cooling towers with fewer VFDs installed.

ACKNOWLEDGEMENTS The authors acknowledge the financial support from FAPESP, Brazil (grant 2017/181456).

APPENDIX Water volumetric flux as a function of water and air temperatures Figure 12-8c in Maloney [28] provides a chart for sizing counterflow induced-draft cooling towers for different water and air temperature values. For a return cooling water temperature (T1) of 45 oC, several points in this chart were extracted for polynomial interpolation and are given in Table A1. Table A1 – Water volumetric flux (Q’) for different values of supply cooling water temperature (T2) and ambient air temperature (t1), and T1 = 45 oC [28] T2 (oC)

t1 (oC) 19.4 20.0 18.3 20.0 22.8 22.8 22.8 21.1 21.1 19.4 26.7

Q’ (m3.m-2.h-1) 14.2 12.8 12.8 15.6 19.4 17.8 15.3 16.9 15.0 15.0 25.3

3.06 3.67 3.06 3.06 3.06 3.67 4.28 3.06 3.67 3.06 3.06 23

26.7 26.7 26.7 26.7 29.4 29.4 29.4 32.2 23.9 23.9 23.9 23.3 23.3 23.1 21.7 17.8 19.2

23.9 22.5 20.6 16.1 25.3 22.5 18.3 25.3 21.1 19.4 16.9 13.3 16.1 12.8 12.8 11.9 14.2

3.67 4.28 4.89 6.11 4.89 6.11 7.33 7.33 3.06 3.67 4.28 4.89 4.28 4.89 4.28 3.67 3.36

This proposed polynomial by this work to correlate the data from Table A1 is: Q' = a0 + a1.T2 + a2.t1 + a3.T22 + a4.t21 + a5.T32 + a6.t31 + a7.T2 .t1

(A1)

where an are the polynomial coefficients for equation (A1) (n = 0 to 7) Using SciLab v6.0.1 with the sub-routine LEASTSQ [29], the optimal values obtained for the polynomial coefficients are given in Table A2. The calculated value for R2 is 0.9934. Table A2 – Optimal values for polynomial coefficients an obtained by sub-routine LEASTSQ in SciLab v6.0.1 Coefficient a0 a1 a2 a3 a4 a5 a6

Optimal value

Unit m3.m-2.h-1 m3.m-2.h-1.ºC-1 m3.m-2.h-1.ºC-1 m3.m-2.h-1.ºC-2 m3.m-2.h-1.ºC-2 m3.m-2.h-1.ºC-3 m3.m-2.h-1.ºC-3

14.9 -9.67.10-1 -6.96.10-1 3.58.10-2 2.46.10-2 -2.10.10-4 -6.47.10-4 24

7.07.10-3

a7

m3.m-2.h-1.ºC-2

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Highlights   

Cooling towers installed in subtropical cities have large values of fan slack Intermittent use of fans and installation of VFDs (Variable frequency drives) can reduce the cooling tower energy consumption Proposed methodology for the design or retrofit of cooling towers

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