## Abstract

Air compressors, a key fluid power technology, play an essential role in industrial plants and office buildings, hospitals, and other types of facilities. The efficient use of the air compressor is crucial. By controlling unnecessary inefficiencies, high energy consumption can be reduced. This study aims to provide energy and exergy analysis on air compressors for different industries. Detailed case studies were also analyzed. The case study focuses on the energy and exergy analyses of the compressed air system of foundry industries. The results indicate that applying the six improvement recommendations yields significant amounts of energy and cost savings and significant improvements in the system's overall performance. The payback periods for different recommendations are economically feasible and worthwhile to use. The suggested improvement methods can provide cost savings with a low payback period.

## Introduction

Compressors are often mentioned as the fourth utility for an industry as it consumes a significant amount of energy. The compression process is very energy intensive due to the different irreversibility of the process [1,2] (see Fig. 1). Compressed air is fundamental for various manufacturing processes. Therefore, maximizing the compressor’s air efficiency is a priority in today’s industry to ensure more reliable product quality, increase productivity, and save energy [3].

Fig. 1
Fig. 1

The present researchers investigate the energy performance in different industries. During the investigation, the team discovers significant energy-saving opportunities, especially in waste management. The optimal use of energy resources, analysis and optimization of energy processes, mitigation of environmental pollutants, and sustainable energy is considered [426]. Efficient use of the equipment can ensure substantial energy savings. According to the US Department of Energy, compressed air systems consume 10% of the overall electricity and 16% of all motors energy consumed by the manufacturing industries of the United States [27]. However, only 10% of the facilities monitor the compressors’ energy consumption. Besides, the awareness of good practices for compressed air systems in the industry is only 9%. Using a variable frequency drive (VFD), eliminating leaks in the compressed air systems, and installing compressed air intake in the coolest location are the best practices that a facility can follow. Such energy-efficient practices can save up to 66% of the compressor energy consumption. [28].

Recently, researchers have focused on describing the energy efficiency measures such as air pressure, air consumption, power requirements, air quality, energy recovery, and maintenance for compressed air systems [2935] or even eliminating the compressor in some applications to solve compressor efficiency problems [36. Selim et al. provided detailed energy recommendations based on the industry category, including the compressed air system [37]. Meantime, Hasan et al. provided some of the challenges that the facilities are facing to implement those energy recommendations and how to overcome these challenges [38] Compressed air systems consist of two sections: the supply section (includes air filters, interstage and aftercooler stage, and receivers) and the demand section (includes regulators, piping network, dryers, moisture drain paths, lubrication path, pneumatic kit, and others) [39]. Figure 2 represents the effect of air leaks in the compressor system [31]. The dotted line in the figure predicts the exponential trend of the increased power lost with the increase of diameter. It also increases the maintenance costs.

Fig. 2
Fig. 2

Saidur et al. [40] reviewed the energy-saving opportunity for the compressed air system. This study described different energy-saving opportunities in the compressed air system (Fig. 3). The highest amount of energy loss happens due to leakage in the system. The researchers claimed that, during the energy investigation at a plant, different data should be recorded for analyzing the compressor's efficiency, such as mass flow rate of air, pressure, utility bills, load factor (LF), power factor, power rating, demand usage, efficiency at given load factor, operation hours, peak, and off-peak usage. The main problem with air leakage is the small size of a leak, which makes it hard to detect or to locate compared to heavy leaks that are easy to hear. Different methods were used to detect small air leaks, such as ultrasound technology and infrared thermography [41].

Fig. 3
Fig. 3

The industrial sector is the largest energy-consuming sector in the United States, with approximately 33% of the country's total energy consumption [42]. The average monthly energy consumption and cost per industry are relatively high [43]. Researchers found that these industries with food, machinery, fabricated metal product, and paper manufacturing use compressed air intensively [27] (e.g., 92% of the fabricated metal product industry use compressed air for production).

As described earlier, thorough research regarding compressed air systems has been conducted [4449]. However, a classification of the energy efficiency recommendations per industrial sector and the impact of these energy savings over the performance of the compressed air systems have not been thoroughly studied. This study focuses on energy and cost-saving opportunities for different industries based on the SIC code. A case study was also provided for better understanding and a more detailed approach that can be translated to other cases.

## Methodology

A database of 67 companies that were investigated is referenced in this study. A case study was discussed, which was completed in 2020. The companies were classified using the SIC code. The SIC code is composed of four digits. The first two digits represent the primary industry group, the third digit identifies the industry group, and the last digit specifies the industry. SIC codes from 20 to 39 (manufacturers), 14 (industrial sand), and wastewater treatment plants (code 49) were considered in this study.

The  Appendix represents the primary industry group per SIC code.

Among the factors for the energy savings related to the compressed air system, the following results are obtained: (a) use of adjustable frequency drive, (b) eliminate leaks in compressed air lines/valves, (c) install compressor air intakes in coolest locations, and (d) eliminate or reduce compressed air usage. For each proposed recommendation, the procedure to calculate the energy indicators is as follows:

• (a) Use adjustable frequency drive

The use of a variable speed drive (VSD) depends on the operating conditions of the compressor at different times. The load curve is a standard method to estimate the operating conditions of the compressor during a period. The following are the steps to determine whether it is feasible to install a variable frequency drive.

The power of the compressor is selected depending on the most critical conditions. This power can be calculated as a function of motor horsepower, MH, load factor, LF, and efficiency of the motor, η [50]. C1 was used as a unit conversion factor.
$Pd=MH×C1×LFη$
(1)
The percentage of power drawn from the compressor at different operating conditions can be estimated [50].
$Dkw=A1+(A2×Cap)+(A3×Cap2)+(A4×Cap3)$
(2)
where A1, A2, A3, and A4 are constants depending on the control system (VFD, throttled valve, and on–off) and Cap indicates the capacity. The value of these constants can be determined from the manual of Focus on Energy [50]. The polynomial describes the operating curve depending on the capacity (as a percentage of maximum flow) of the compressor.
The power consumed by the compressor can be estimated as a portion of the design power as shown in Eq. (3):
$CP=Dkw×(Pd100)$
(3)
The power consumed by the compressor, the percentage of time at specific capacity, and annual hours of operation indicate the annual energy usage of the system. The annual energy usage can be then estimated as follows:
$Ec=(∑nCPn×(Tn100))×H$
(4)

The annual energy savings (AES) can be calculated as the difference between the annual energy usage with the current control system and the energy usage when VFD is installed.

• (b) Eliminate leaks in compressed air lines/valves

The current energy consumption is calculated using compressor efficiency, η, power rating, P, annual operation hours, H, load factor, LF, and running factor, RF [50]:
$Ec=P×H×RF×LF×C1η$
(5)
The cost of the wasted air can be calculated by calculating the amount of energy is needed to replace the wasted air. The volumetric flow rate of wasted air was calculated as follows [50]:
$Vf=(Tin+460)×PleakPin×Ca×Cb×Cd×πD24CcTline+460$
(6)
Annual energy savings,
$AES=VfCFMBHP×C1×H×Nleaks×RFη$
(7)
• (c) Install compressor air intakes in coolest locations

The savings from operating at a lower intake air temperature depends on the power draw at high temperatures and low temperatures [50]. The fractional savings can be written in terms of temperature as follows:
$Fs=Ti−ToTi$
(8)
The following equation gives the monthly energy savings for air compressors with a reduction in compressor work,
$AESM=P×C1×H×LF×RF×Fs12×η$
(9)

For all the cases, the energy demand savings, demand reduction (DR (kW-month/year)), and annual cost savings (ACS) were calculated using the following equations.

The reduced energy usage will also result in a lower demand charge. DR can be calculated from AES, the number of months involved in the operation, M, and annual operating hours, H.
$DR=AES×MH$
(10)
The calculation of ACS involves the AES, DR, average electricity rate, REa, and demand rate, RD.
$ACS=AES×REa+DR×RD$
(11)
The payback period was calculated using the following equation:
$PaybackPeriod=ImplementationCostAnnualCostSavings$
(12)

### Exergy Analysis.

Energy analysis gives a great insight into the system's performance although the energy analysis alone does not consider the inefficiencies of the system. One way to evaluate such inefficiencies is to apply an exergy analysis of the system [51,52]. Equation (13) represents the formulation of exergy efficiency. The numerator considers the terms of the inlet, outlet, and ambient temperature and pressures, while the denominator is the energy consumption.
$ηexergy=m˙Cp(T0−Ti)+m˙Tambient(RlnPcomoressedP1−CplnToTi)Ep$
(13)
The total amount of useful work also depends on the operating the compressor loading and running factor (these factors change depending on the control method, such as load–unload, on–off, or VFD). Considering the running and loading factor, the exergy efficiency can be calculated as follows:
$ηexergy=(m˙Cp(T0−Ti)+m˙Tambient(RlnPcomoressedP1−CplnToTi))×RF×LFEp$
(14)

## Results and Discussions

### a) Use Adjustable Frequency Drive.

Running a compressor at the same speed all the time leads to higher energy consumption. Also, it reduces compressor efficiency by increasing wear and tear. Utilizing VSD/VSD can be a solution to this problem. The power varies as the third power of speed ratio, so small decreases in the speed will result in considerable energy savings.

From the data that the team has gained, it is observed that the iron and steel industries (3462) can save the highest electricity (310,000 kWh) and cost savings $20,000 (see Figs. 8 and 9). The payback period is about 0.6 on average, and the maximum is less than 2.5 years (Fig. 10). Fig. 8 Fig. 8 Fig. 9 Fig. 9 Fig. 10 Fig. 10 ### c) Ensure Cold Incoming Air to Compressor Intake. If the compressor’s inlet is indoors, the compressor rejects heat into the facility. As a result, the compressor has to compress hot air. Thermodynamically, this condition leads to more compressors work to compress the hot air as air expands at higher temperatures. The amount of work done by an air compressor is proportional to the temperature of the intake air. Therefore, less energy is needed to compress cool air than to compress hot air. Cooler air is denser and easier to compress. Compressing cooler outside air reduces compressor work, saving electricity and reducing operating costs (including maintenance). Depending on the season and location, outside air is often cooler than the air inside a compressor room. Normally the compressor takes the air from the outside during the heating season—when the outdoor temperature is colder than the indoor temperature—while for the cooling season, the compressor takes the air from the inside—when the outdoor temperature is hotter than the indoor temperature. The average electricity savings varies from 2200 kWh to 4,500,00 kWh (see Fig. 11), and the average payback period ranges from 0.1 to 5 years (see Fig. 12). Fig. 11 Fig. 11 Fig. 12 Fig. 12 ### d) Eliminate or Reduce Compressed Air Usage. A facility should always use its optimum compressor's discharge pressure and flow. Excessive pressure causes more air volume consumed by the system, which leads to more energy consumption and increases the demand. Figure 13 indicates that the average electricity savings vary from 3600 kWh/ year to 550,000 kWh/year. In terms of cost savings, it can save up to$35,000 (see Fig. 14). The excessive pressure can be reduced directly in the compressor screen. Hence, the payback period is immediate (for SIC code 2092, 3273, and 3679; see Fig. 15).

Fig. 13
Fig. 13
Fig. 14
Fig. 14
Fig. 15
Fig. 15

The pressure reduction should be made gradually by reducing the pressure in 7 kPa step by step. It is worth mentioning that the payback period of all recommendations is not immediate. For example, replacing the nozzles, piping, and so on. Another action to reduce the compressed air usage is to replace the air nozzles with engineered nozzles that use the Coanda effect to draw additional force to the outlet, reducing the compressed air usage. This replacement depends on the operating conditions. For this recommendation to be feasible, it was found that the nozzles have to be used more than 2000 h per year, and the duty cycle has to be higher than 20%. Otherwise, the payback period becomes too high.

### Total Savings With a Compressed Air System.

Table 1 represents the average power, electricity consumption, and cost savings of implementing the recommendations for 2015–2019. The average value of the energy savings was calculated by averaging the energy savings of each company within a single SIC code. The average savings related to compressor consumption were determined by dividing the electricity savings and total energy consumptions for the compressed air system. The average total compressor’s power rating ranges from 40 to 6500 HP. Some facilities use comparatively more compressed air in their operation, such as iron and steel forging facilities (SIC code 3462). Iron and forging facility often considers the largest end-use of electricity. The energy-efficient recommendations can save up to 588,329 kWh energy annually. This energy savings represents around $60,000, where the payback period is feasible as the payback period is less than 2 years for most cases. Table 1 Total savings with a compressed air system SIC codeAverage total compressor power (HP)Average of electricity savings (kWh)Average of cost savings ($)Average payback periodAverage energy savings related to compressor consumption (%)
1446100337,20717,2081.446.5
202213867,54651200.36.6
20484088096030.54.0
20927510,97213711.36.9
2099820155,49510,4750.82.5
242125049,81653540.88.9
265317512,56811680.41.4
273235085,94085400.24.6
2752540241,41913,3110.95.7
27597535,21130051.58.5
2821115089376191.50.3
285130017,60612120.71.3
289113092,64467380.113.0
3085150436,93434,8880.33.7
3089445278,96948970.214.0
31495520,71718793.311.8
3231450223,24811,0352.49.1
3261102101,01777722.116.0
32628086,66414,1010.519.7
32731009155961.00.04.2
331255525,99124261.02.1
332142517,87914880.21.6
332415063165480.61.6
336591361,37853461.61.1
344350088,92253084.44.6
344413515,57619230.53.2
346225045,55039831.26.8
3492254165,74911,0081.410.3
349922548,14534330.53.4
353280050,54240690.40.9%
353411072,19658061.315.0
3564100921212332.55.2
35778016,84413401.411.5
358531922,89532560.61.7
359910022,49917233.26.4
362415024,66223380.63.1
36254915,82813500.711.0
36792062487021.07.1
3714280297,75420,1610.821.0
39915023,59922670.212.9
39932340925261.67.7
49413075,37045703.633.3
4952935191,43711,1341.05.2
205137580,27563080.33.7
25217531052990.41.8
275218042,40934890.43.1
308916098154570.61.1
34626350588,32957,7310.82.6
3469550118,46977010.812.3
356820071,75563490.36.7
382420025,66322740.82.4
SIC codeAverage total compressor power (HP)Average of electricity savings (kWh)Average of cost savings ($)Average payback periodAverage energy savings related to compressor consumption (%) 1446100337,20717,2081.446.5 202213867,54651200.36.6 20484088096030.54.0 20927510,97213711.36.9 2099820155,49510,4750.82.5 242125049,81653540.88.9 265317512,56811680.41.4 273235085,94085400.24.6 2752540241,41913,3110.95.7 27597535,21130051.58.5 2821115089376191.50.3 285130017,60612120.71.3 289113092,64467380.113.0 3085150436,93434,8880.33.7 3089445278,96948970.214.0 31495520,71718793.311.8 3231450223,24811,0352.49.1 3261102101,01777722.116.0 32628086,66414,1010.519.7 32731009155961.00.04.2 331255525,99124261.02.1 332142517,87914880.21.6 332415063165480.61.6 336591361,37853461.61.1 344350088,92253084.44.6 344413515,57619230.53.2 346225045,55039831.26.8 3492254165,74911,0081.410.3 349922548,14534330.53.4 353280050,54240690.40.9% 353411072,19658061.315.0 3564100921212332.55.2 35778016,84413401.411.5 358531922,89532560.61.7 359910022,49917233.26.4 362415024,66223380.63.1 36254915,82813500.711.0 36792062487021.07.1 3714280297,75420,1610.821.0 39915023,59922670.212.9 39932340925261.67.7 49413075,37045703.633.3 4952935191,43711,1341.05.2 205137580,27563080.33.7 25217531052990.41.8 275218042,40934890.43.1 308916098154570.61.1 34626350588,32957,7310.82.6 3469550118,46977010.812.3 356820071,75563490.36.7 382420025,66322740.82.4 ### Case Study. In early 2020, the research team conducted an energy assessment study in one of the industries. The SIC for this company is 3321. The company uses eight reciprocating air compressors that are 50 years old. The total power of these compressors is 1908 HP. The operating conditions of all the compressors were logged using 8 four-channel Data-logger HOBO UX120 for 2 weeks. The operating conditions of each compressor are summarized in Table 2. Table 2 Compressed air system description Compressor no.Total package kWPower (HP)Running factorLoading factorFlowrate (m3/s)) 1167224.50.830.60.45 2167224.50.590.430.45 32102810.9970.4610.56 4210281000.56 5167224.50.8030.2850.45 6167224.50.9920.7950.45 7167224.50.60.3860.45 8167224.50.9920.7750.45 Compressor no.Total package kWPower (HP)Running factorLoading factorFlowrate (m3/s)) 1167224.50.830.60.45 2167224.50.590.430.45 32102810.9970.4610.56 4210281000.56 5167224.50.8030.2850.45 6167224.50.9920.7950.45 7167224.50.60.3860.45 8167224.50.9920.7750.45 The efficiency of the compressors was estimated at 72%. On average, the compressors are operating at 85% of the total production time. The bills and total motor capacity for a yearly period were collected and analyzed for this facility. The average price for electricity, demand, and gas are described in Table 3. Table 3 The average price of utilities  Electricity ($/kWh) 0.0442 Demand ($/kW) 6.61 Gas ($/MJ) 3967
 Electricity ($/kWh) 0.0442 Demand ($/kW) 6.61 Gas ($/MJ) 3967 The compressed air system represents approximately 12% of the total electricity consumed by motors. For the demand reduction calculations, a coincidence factor of 0.7 was considered. The coincidence factor is the ratio of the peak load of a system to the sum of peak loads of its components. The maximum coincidence factor can be 1, which indicates that all the individual components are peaking simultaneously. The air consumption for this system can be estimated using Eq. (5) as follows: $Ec=4,669,097kWh/year$ The exergy efficiency for the overall system is estimated using Eq. (13). Results show that the overall energy efficiency of the system is 33.9%. During the audit, several potential energy-saving opportunities were identified. The recommended actions for this case study were as follows: • Replace old compressors with energy-efficient substitutes • Eliminate of reducing compressed air usage • Lower compressed air set pressure • Install compressor air intakes in the coldest locations • Replace conventional coalescing filters with mist eliminators • Eliminate air leaks The energy savings, cost savings, and payback periods for each recommendation are summarized in Table 10. The payback period for the whole project is approximately 5 years. The following is the description of each of the recommendations. • (a) Replace the compressors with energy-efficient substitutes The measured maximum airflow for this facility is approximately 3.80 m3/s, with an average of 3.30 m3/s at a set pressure is 650 kPa. This analysis signifies a maximum standard capacity of 4.25 m3/s. These specifications can be achieved by installing four 450 HP centrifugal compressors or two 900 HP centrifugal compressors (total 1800 HP). Installing four 450 HP compressors offers more flexibility to the system and allows room for maintenance purposes by having a backup. Using an efficiency of 90% for the centrifugal compressors, the annual energy consumption of the new system can be estimated as follows: $Ep=1800×0.746×0.75×0.85×60000.9$ (15) $Ep=3,558,420kWh/year$ The energy savings can be estimated by subtracting the proposed energy consumption from the current energy consumption. Therefore, the annual energy savings can be estimated as follows: $AES=Ec−Ep$ (16) $AES=1,110,677kWh/year$ $DR=1718kW−month/year$ The cost of implementation includes purchasing the compressors, electrical components, and installation from the vendor. After contacting several vendors, the implementation cost of this recommendation is approximately$500,000. Using Eqs. (11) and (12), the annual cost savings and implementation are estimated as follows:
$ACS=59,393$
$Paybackperiod=8.40years$
$Overallexergyefficiency=40.4%$

The calculated savings are only considered from the energy standpoint. Considering that half and the oil-free air compressors have reduced maintenance due to the more straightforward design, the number of compressors is reduced by half. The savings from productivity are significant, and the payback period can be significantly reduced.

• (b)  Eliminate or reduce compressed air usage

During the audit, it was observed that the transport system requires a lower pressure (350 kPa) than the rest of the system. Therefore, it was suggested to separate the compressed air used for the transport process from the rest of the system. The recommended action is to install a new compressor with an operating pressure of 550 kPa, which is 85 kPa lower than the current consumption. This action will also reduce the pressure drop in the whole network, increasing the system's efficiency.

The energy savings come from the reduction in the operating pressure, which reduces the compressor load. The new load of the compressor can be calculated as follows:
$LFf=LFPc×Pf$
(17)
where LFf = final load on air compressor, Pc = current set up pressure, and Pf = proposed pressure.
The decrease in the compressor load gives a significant energy reduction. The annual energy savings can be calculated by subtracting the current energy consumption and the proposed energy consumption. The proposed energy consumption for each compressor under the new load condition can be found in Table 4. There is also a reduction in the on-peak demand because the compressors are operating most of the on-peak hours. Thus,
$AES=607,889kWh/year$
$DR=851kW−month/year$
$ACS=32,506$
Table 4

Load factor of each compressor after reducing the compressed air usage

10.52602,807
20.37304,529
30.4696,571
400
50.25280,046
60.69954,850
70.34284,580
80.67927,173
10.52602,807
20.37304,529
30.4696,571
400
50.25280,046
60.69954,850
70.34284,580
80.67927,173

The implementation of this recommendation requires the purchase and installation of the new compressor. It is also needed to remove the old compressor and separate the airlines from the transport. The flow rate for the transport system was measured to be 0.85 m3/s at 550 kPa. Thus, a 400 HP screw compressor can satisfy this demand. The cost of this recommendation is approximately $160,650. This analysis gives a payback period of 4.9 years. Table 5 represents the exergy efficiency of eight compressors after reducing the compressed air usage. • (c) Lower compressor pressure Table 5 Exergy efficiency of eight compressors after reducing the compressed air usage Compressor no.Exergy (%) 139.6 239.9 339.5 40 539.1 639.5 738.9 839.7 Compressor no.Exergy (%) 139.6 239.9 339.5 40 539.1 639.5 738.9 839.7 During the energy audit, it was found that the maximum pressure needed is approximately 345 kPa, while the set pressure is 650 kPa. For this reason, the proposed action is to reduce the pressure from 650 kPa to 550 kPa. The energy savings can be seen in a reduction in the load of the compressor. Such a reduction in the load can be calculated by applying Eq. (10) to all the compressors. Loads of each compressor under this reduced set pressure condition can be found in Table 6. The energy consumption (Eq. (5)) under this new load can be calculated using Eq. (5) for each compressor and summing all the energy consumptions (see Table 6). Table 7 represents the exergy after pressure reduction. Table 6 Final load factor after pressure reduction Compressor no.Final load factorEp (kWh/year) 10.55637,585 20.39320,990 30.43748,814 400 50.26291,248 60.731,010,203 70.36301,320 80.72996,365 Compressor no.Final load factorEp (kWh/year) 10.55637,585 20.39320,990 30.43748,814 400 50.26291,248 60.731,010,203 70.36301,320 80.72996,365 Table 7 Exergy after pressure reduction Compressor no.Exergy (%) 135.8 236.2 335.2 40 536 635.7 735.2 835.3 Compressor no.Exergy (%) 135.8 236.2 335.2 40 536 635.7 735.2 835.3 Therefore, $Ep=4,306,523.82kWh/year$ $AES=355,257kWh/year$ $DR=497.4kW−month/year$ The annual cost savings for this recommendation are estimated using Eqs. (10) and (11). Table 7 represents the exergy efficiency of the compressors after implementing pressure reduction. Exergy efficiency is around 35% for all compressors. The increase of the energy savings also increased the exergy of the machines. The implementation of this recommendation is zero because the only required action is to reduce the pressure from the settings. However, it is always recommended to gradually reduce the air pressure and check the system's performance carefully, for example, first, reduce the pressure by 14 kPa and check if all the equipment is working properly before making any further reductions to the desired pressure. • (d) Install compressor air intakes in coolest locations In this facility, the compressors are installed in four different rooms. The air intake for all the compressors was located inside the plant, which is, most of the time, warmer than the outside. The temperature for compressors 2, 5, and 7 was measured to be 295 K, while the temperature of the room that had compressors 1, 3, and 8 was measured as 307 K in January. The outside temperature (and the corresponding savings calculated using Eqs. (5) and (8)) can be found in Tables 8 and 9. The savings during the cooling season (summer) were neglected. However, the indoor temperature is probably hotter than the outside, and using outside air can save energy. Table 8 Monthly energy savings for compressors 2, 5, 7 MonthAverage temperature (K)Fractional savingsMonthly energy savings (kWh/year) January26510.098362 February2679.347740 March2737.266017 April2804.723912 May0 June0 July0 August0 September0 October2814.343597 November2746.795627 December2679.257666 Total42,921 kWh/year MonthAverage temperature (K)Fractional savingsMonthly energy savings (kWh/year) January26510.098362 February2679.347740 March2737.266017 April2804.723912 May0 June0 July0 August0 September0 October2814.343597 November2746.795627 December2679.257666 Total42,921 kWh/year Table 9 Monthly energy savings for compressors 1, 3, 6, 8 MonthAverage temperature (K)Fractional savingsMonthly energy savings (kWh/year) January26513.8342,251 February26713.114051 March27311.1233,972 April2808.6826,517 May0 June0 July0 August0 September0 October2818.3225,418 November27410.6732,597 December26713.0239,776 Total240,581 (kWh/year) MonthAverage temperature (K)Fractional savingsMonthly energy savings (kWh/year) January26513.8342,251 February26713.114051 March27311.1233,972 April2808.6826,517 May0 June0 July0 August0 September0 October2818.3225,418 November27410.6732,597 December26713.0239,776 Total240,581 (kWh/year) The total energy savings for this recommendation is the sum of the energy savings for all the compressors; the total monthly energy savings are as follows: $AES=283,502kWh/year$ $DR=397kW−month/year$ $ACS=15,160$ Implementing this recommendation requires installing ducting, elbows, and automatic dampers that open when the outside temperature is lower than the indoor temperature. As such, the cost of this recommendation is estimated at$6952 ($1738 for each room). Therefore, $Payback=0.4years$ $Exergyefficiency=35.2%$ • (e) Replace conventional coalescing filter for a mist eliminator The compressors’ outlet oil, solid particles, and water must be removed from the compressed air using filters [57]. Such filters produce a significant pressure drop because the flow is perturbed by several filters that trap the air impurities. As explained in prior sections, one of the best ways to reduce compressed air energy usage is to relieve pressure. Therefore, to reduce the pressure drop, the conventional coalescent filters can be replaced for mist eliminators. Coalescent filters operate under the coalescing effect, where the oil and water particles are trapped into the filter layers. The conventional filters use the pressure difference to create coalescence. The pressure drop of the coalescing filters varies from 14 to 70 kPa due to the nature of the filter. In contrast, mist eliminators use the diffusion effect to separate the oil and water particles, which leads to a pressure drop of approximately 3.5 kPa. The savings of replacing the conventional filters for mist eliminators manifest not only in the compressor's energy consumption but also in maintenance savings because the mist eliminators have a longer lifespan. Typically, the conventional coalescent filters must be replaced quarterly, while the mist eliminators can last up to 10 years before replacement. The pressure drop of 34.5 kPa was read in the differential pressure gauge installed in the filter. Considering that every 14 kPa pressure drop reduces the consumption by 1%, the expression that can determine the percentage of the energy, SP that can be saved is given as follows: $SP=PR×RS$ (18) where PR = pressure loss reduction (31 kPa) and RS = energy consumed for every additional increase in pressure (0.5% per kPa). Therefore, SP is approximately 2.25%. Thus, the annual energy savings can be calculated using Eq. (5) and multiplying by the SP. Hence, $AES=Ec×SP$ $AES=10,5055kWh/year$ $DR=147kW−month/year$ $ACS=5618$ The maintenance savings can be calculated by considering the number of filters that are replaced annually. Considering that 32 filters are replaced annually, with an average cost of$100, the annual maintenance savings (AMS) are as follows:
$AMS=3200$
Thus,
$ACS=8818$
The implementation of this recommendation requires purchasing and installing eight new filters. It is recommended that this recommendation is implemented when performing an oil change because the filters are replaced during such maintenance anyways. The price of each filter is estimated at $6000. However, incentives of 4$/HP are offered by a state program for projects replacing conventional coalescent filters with mist eliminators. There is 1908 HP installed in the facility, which gives approximately $7633 in incentives. Therefore, the implementation cost is$40,337.
$Payback=4.6years$

The payback period of this recommendation is less than the total lifespan for the mist eliminator filter. This signifies that replacing the filters is a feasible option.

• (f) Eliminate leaks in inert gas and compressed air lines/valves

When the compressed air system was audited, approximately 50 leaks were detected. The average diameter is about 0.00085 m. As such, the flow rate of the leaks can be estimated using Eq. (6) as follows:
$Vf=1.16CFM=0.0005475m3/s$
Air leaking represents air that is being compressed and wasted. The energy savings can be estimated using Eq. (7), the BHP/CFM was obtained from the nameplate as 4.2, and the average running factor for the compressed air system is 0.85.
$AES=1.164.2×0.746×6000×50×0.8572$
$AES=72,986kWh/year$
The demands savings and annual cost savings are estimated using Eqs. (10) and (11):
$DR=102.2kW−month/year$
$ACS=3902$

## Acknowledgment

US Department of Energy funded this project (Grant No. DE-EE0007716).

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request. The authors attest that all data for this study are included in the paper. Data provided by a third party listed in Acknowledgment. No data, models, or code were generated or used for this paper.

## Nomenclature

• D =

leak diameter (m)

•
• H =

annual operating hours (h)

•
• M =

number of months

•
• P =

power rating of the compressor (HP)

•
• R =

ideal gas constant (287 J/kg K)

•
• T =

percentage of time at specific capacity (%)

•
• $m˙$ =

mass flow rate (kg/s)

•
• C1 =

conversion factor (1 kW = 0.746 HP)

•
• Ca =

isentropic sonic volumetric flow constant (28.37 ft/s-°R0.5)

•
• Cb =

conversion constant (60 s/min)

•
• Cc =

conversion constant (144 in2/ft2)

•
• Cd =

coefficient of discharge for square-edged orifice (0.8)

•
• Cp =

specific heat at constant pressure (J/kg · K)

•
• DkW =

percentage of design power in kW (%)

•
• Ec =

current energy consumption (kWh/year)

•
• Fs =

fractional saving (%)

•
• Pd =

power at design conditions (kW)

•
• Pin =

inlet (atmospheric) pressure (101352.9 Pa)

•
• Pcompressed =

compressed air pressure (pa)

•
• Pleak =

line pressure at leak (Pa)

•
• REa =

average electricity rate (\$)

•
• Tin =

temperature of the air at the compressor inlet (K)

•
• Tambient =

ambient temperature (K)

•
• Tline =

average line temperature (K)

•
• Ti =

inside temperature (K)

•
• T0 =

outside temperature (K)

•
• Vf =

volumetric flow rate of free air (m3/s)

### Greek Symbols

• η =

compressor efficiency (%)

•
• ηexergy =

exergy (%)

### Appendix

Industries per SIC code are presented as Table 11.

Table 11

Industries per SIC code

SIC code (first two digits)Primary industry groupNumber of industries
14Industrial sand1
20Food and kindred products7
24Lumber and wood products, except furniture1
25Furniture and fixtures1
26Paper and allied products1
27Printing, publishing, and allied industries5
28Chemicals and allied products4
30Rubber and miscellaneous plastic products5
31Leather and leather products1
32Stone, clay, glass, and concrete products4
33Primary metal industries6
34Fabricated metal products, except machinery, and transport equipment10
35Industrial and commercial machinery and computer equipment6
36Electronic, electrical equipment and components, except computer equipment4
37Transportation equipment1
38Measuring, analyzing, and controlling instruments; Photographic, medical, and optical goods; watches and clocks1
39Miscellaneous manufacturing industries3
49Electric, gas and sanitary services6
Total number of companies67
SIC code (first two digits)Primary industry groupNumber of industries
14Industrial sand1
20Food and kindred products7
24Lumber and wood products, except furniture1
25Furniture and fixtures1
26Paper and allied products1
27Printing, publishing, and allied industries5
28Chemicals and allied products4
30Rubber and miscellaneous plastic products5
31Leather and leather products1
32Stone, clay, glass, and concrete products4
33Primary metal industries6
34Fabricated metal products, except machinery, and transport equipment10
35Industrial and commercial machinery and computer equipment6
36Electronic, electrical equipment and components, except computer equipment4
37Transportation equipment1
38Measuring, analyzing, and controlling instruments; Photographic, medical, and optical goods; watches and clocks1
39Miscellaneous manufacturing industries3
49Electric, gas and sanitary services6
Total number of companies67

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