The High Cost of Compressed Air and Typical Cost Savings Using the AeroValve Solution WHITE PAPER THE HIGH COST OF COMPRESSED AIR AND TYPICAL COST SAVINGS USING THE AEROVALVE SOLUTION BY: Lowell Jones, Ph.D. Lead Engineer, AeroValve LLC Michael Goldfarb, Ph.D. CTO, AeroValve LLC FEBRUARY 6, 2014 Copyright 2014 AeroValve LLC Page 1 of 8 The High Cost of Compressed Air and Typical Cost Savings Using the AeroValve Solution Page 2 of 8 TABLE OF CONTENTS 1 INTRODUCTION ............................................................................. 3 2 COST OF COMPRESSED AIR ....................................................... 3 2.1 Formula Derivation .................................................................................... 3 2.2 Sample Calculation ..................................................................................... 6 2.3 Experimental Verification ......................................................................... 7 3 AEROVALVE TECHNOLOGY...................................................... 8 3.1 Energy-Saving Valve Technology ............................................................. 8 3.2 Cost-Savings Case Studies ......................................................................... 8 Copyright 2014 AeroValve LLC The High Cost of Compressed Air and Typical Cost Savings Using the AeroValve Solution 1 Page 3 of 8 INTRODUCTION While pneumatic technology provides a clean, high-power, low-cost means of implementing factory automation, the compressed air costs associated with pneumatic systems are notoriously high, often accounting for up to 30% or more of the power costs at a plant. In the U.S. alone it has been estimated that the energy used to compress air exceeds a half quadrillion BTUs per year.1 AeroValve LLC has developed an innovative directional control valve technology that provides a plug-and-play replacement for a standard directional control valve that will typically save 25% of compressed air costs, without compromising system function. The intent of this white paper is to illustrate cost savings provided by AeroValve technology in a typical pneumatic actuation application. 2 COST OF COMPRESSED AIR 2.1 Formula Derivation One of the primary contributors to the high cost of compressed air is the relative low efficiencies of compressed air systems, which are typically characterized by efficiencies from electrical input power to compressed air outlet power of 10% to 14%. These costs are not always wellunderstood, and as such the authors use this section to derive and explain the electricity costs associated with operation of a compressed-air system. In assessing the costs associated with a pneumatic system or component, it is most convenient to compute costs as a function of the compressor outlet air flow. The relation between the electrical input power to a compressor and the pneumatic power that can be utilized at the output of the compressor is show in Eqn (1): π· ! = π ! π ! π·! (1) where: π·! = Power out (available pneumatic power) π·π = Power in (electric power supplied to compressor) π! = Motor efficiency from electrical power input to rotational mechanical shaft power output (typically between 85% and 95%) π! = Compressor efficiency from rotational mechanical shaft power input to constant pressure outlet air power (typically between 10% and 18% for positive displacement compressors) Note that the available pneumatic power assumes that the pneumatic component utilizing this power will not extract heat as work from the compressed air. Alternately stated, the temperature of the compressed air, when used by the pneumatic component, is not significantly higher than the ambient temperature of the system. In other words, following compression, the pneumatic 1 Talbott, Compressed Air Systems: A Guidebook on Energy and Cost Savings, 1993, p. 1. Copyright 2014 AeroValve LLC The High Cost of Compressed Air and Typical Cost Savings Using the AeroValve Solution Page 4 of 8 component performs work in the same manner as does a hydraulic component. This is consistent with the manner in which pneumatic components perform work in an automation environment. Given this assumption, the power that can be utilized from constant pressure and volumetric flow is: π·! = (π! β π! )π! (2) where: π! = Absolute pressure at the output of the compressor π! = Absolute pressure at the inlet of the compressor π! = Volumetric flow rate at the output of the compressor Defining output gage pressure as π! β‘ (π! β π! ), Eqn (2) can also be written as2: !πΎ! !" = π! !!! !" (3) where: πΎ! = Work output π£! = Volume output Assuming steady-state conditions, both sides of Eqn. (3) can be integrated to result in: πΎ! = π! π£! (4) Likewise, both sides of Eqn (1) can be integrated to provide a relationship between input energy and output work: πΎ! = π! π! π¬! (5) Combining Eqns (4) and (5) and solving for input energy results in: ! ! π¬! = ! ! !! ! ! (6) Now to introduce cost to the analysis the following relationship is used: πΆπ¬ ! πͺ = (!!!) 2 Van Wylen and Sonntag, Fundamentals of Classical Thermodynamics, 1986, p. 98. Copyright 2014 AeroValve LLC (7) The High Cost of Compressed Air and Typical Cost Savings Using the AeroValve Solution where: Page 5 of 8 πͺ = Cost of running the compressor system ($) πΌ = Cost of electrical power ($/J) π½ = Unitless cost factor of running the compressor system (typically 0.2 < π½ < 0.3) The π½ cost factor is site-specific and typically includes: maintenance, capital depreciation, watercooling costs, and other overhead associated with the system. Substituting Eqn (7) into Eqn (6) and solving for cost results in: πͺπ = ! !"! !! ! !! (!!!) (8) or as a cost specific to volume: πͺ! = ! !"! ! !! (!!!) (9) where πͺ! is the cost per volume of compressed air in its compressed or outlet state. To put this cost equation into more commonly used units, a conversion factor must be applied: πͺ! = 0.0543 ! where: !"! ! !! (!!!) (10) πΌ is in $/kW-hr π! is in psi πͺ! is in $/MCF (1 MCF = 1000 cubic feet) This cost calculation being in the compressed state is a critical distinction instead of it being relative to the compressorβs inlet air. Although computing the cost of air relative to the outlet flow is most direct, it also requires knowledge of the outlet pressure for a given application. In order to remove dependence on the outlet pressure, the cost can instead be transformed, using the ideal gas law, to an equivalent volume of air at the inlet (i.e., at standard conditions). To determine the cost of compressed air relative to the inlet flow, simply apply the ideal gas law. For a given mass of gas and ignoring temperature effects, the ideal gas law simplifies to: π! π£! = π! π£! (11) or π£! = Copyright 2014 AeroValve LLC !! !! !! (12) The High Cost of Compressed Air and Typical Cost Savings Using the AeroValve Solution Page 6 of 8 Substituting Eqn (12) into Eqn (8), dividing by π£! to give the cost of compressed air per inlet volume, and applying the unit conversion factor: πͺ! = 0.0543 ! !"! !! (13) ! !! (!!!) !! or more simply: ! πͺ! = ! ! πͺ! (14) ! 2.2 Sample Calculation This calculation is intended to provide an estimate of the average cost of compressed air in a typical U.S. industrial setting using real-world data. Assumptions for this scenario include standard inlet conditions (14.7 psia and 20°C) and an outlet pressure of 90 psig. The remaining average input variables were gathered from various sources that are sited by each value below: π! = 90%3 π! = 15%4 πΌ = $0.07/kW-hr5 π½ = 24%6 Using Eqns (10) and (14) the cost per MCF of air at the inlet and outlet is shown in Table 1 below: Table 1: Sample Calculation Results Cost of air at inlet conditions (standard) Cost of air at outlet (90 psig) 3 $0.47/MCF $3.33/MCF Efficiency is often stated as an overall system value of between 10% and 15%. Compressor motors have efficiencies ranging from 85% to 95%, resulting in a combined efficiency range for the remaining compressor components of 11% to 18%: http://www1.eere.energy.gov/manufacturing/tech_assistance/pdfs/compressed_air1.pdf http://www.ceati.com/freepublications/7017A_guide_web.pdf http://www.deq.state.ms.us/mdeq.nsf/pdf/OPC_CompressedAirEnergySavingsProjects/$File/Co mpressedAirEnergySavingsProjects.pdf?OpenElement 4 Ibid. Mid-point of range used. 5 http://www.eia.gov/electricity/data.cfm#sales 6 http://www.ceati.com/freepublications/7017A_guide_web.pdf Copyright 2014 AeroValve LLC The High Cost of Compressed Air and Typical Cost Savings Using the AeroValve Solution Page 7 of 8 Again, it is important to note that published data for the cost of compressed air ranges from $0.18/MCF to $0.66/MCF.7 This range is the cost for the inlet flow. The outlet flow cost is typically 7x-8x higher due to the same mass of air being compressed into a smaller volume. 2.3 Experimental Verification A simple test to illustrate and verify this cost analysis was designed and carried out at AeroValveβs laboratory. A power meter was used to measure the total energy delivered to a 2 HP reciprocating air compressor while it supplied 90 psig air to a 5-port/3-position valve cycling a double-acting cylinder. The total calculated displaced volume per cylinder stroke was 5.7 cubic inches. After 5,000 cycles of cylinder actuation, the energy consumed by the compressor was measured as 1.58 kW-hr. The total volume of compressed air displaced was: !!! ! !! ! 5.7 !"#$%& × !"#$ !!! × ! !"#$%&! ! !"!#$ × 5000 ππ¦ππππ = 33 ππ‘ ! Again, assuming $0.07/kW-hr as the cost of power, the volumetric specific cost of the compressed (outlet) air is: 1.58 ππβπ × 0.07 $ !"!! × ! !! !! × ! !""" !! ! ! !"# = $π. ππ/π΄πͺπ or at standard (inlet) conditions using Eqn (14): $".!" !"# × !".! (!"!!".!) = $π. ππ/π΄πͺπ While this value is in close agreement with the theoretical outlet value from Table 1, note that it does not include a π½ cost factor which, if included, would increase the $/MCF further. This discrepancy is likely due to the small 2 HP laboratory compressor having a somewhat lower efficiency than what was assumed for the industrial compressor of the sample calculation. 7 Talbott, Compressed Air Systems: A Guidebook on Energy and Cost Savings, 1993, p. 200. http://www.nfpa.com/events/pdf/2013-fpsc/021-langro.pdf http://www1.eere.energy.gov/manufacturing/tech_assistance/pdfs/compressed_air1.pdf http://www.ceati.com/freepublications/7017A_guide_web.pdf http://www.deq.state.ms.us/mdeq.nsf/pdf/OPC_CompressedAirEnergySavingsProjects/$File/Co mpressedAirEnergySavingsProjects.pdf?OpenElement Copyright 2014 AeroValve LLC The High Cost of Compressed Air and Typical Cost Savings Using the AeroValve Solution 3 Page 8 of 8 AEROVALVE TECHNOLOGY 3.1 Energy-Saving Valve Technology AeroValveβs patented solenoid valve technology is an elegant, no-hassle solution to cost reduction. Designs that are plug-n-play replacements for standard off-the-shelf valves typically recycle 25% of the compressed air used in pneumatic actuator applications, without compromising actuator function. This translates directly to significant cost savings, due to reduced electricity costs as a result of reduced compressed air usage, in addition to reduced compressor maintenance costs. The technology can be applied to the majority of popular 5-port/3-position and 5-port/2-position valve lines with negligible cost difference for a truly plug-n-play cost-savings replacement option. 3.2 Cost-Savings Case Studies The following case studies share the same parameters used for the sample calculation in section 2.2. Additionally, all case studies assume 2-shift operation, cycling 60 times per minute, and airline lengths of 20 feet. Table 2 below gives a variety of typical cylinders used in industrial environments and the respective annual cost-savings that can be expected by employing AeroValve technology. Table 2: Case Study Results Bore Size (in) 0.75 1 2 4 Stroke (in) 2 3 4 6 Line OD (in) 0.25 0.25 0.375 0.5 Annual Cost Savings per Valve $120 $134 $318 $1,039 Clearly, the annual savings gained by employing this technology would pay for any difference in valve cost in short order. To review other case studies and use an on-line cost-savings calculator visit AeroValveβs website at http://aerovalve.com. Copyright 2014 AeroValve LLC
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