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# Basic steps to compressor unit calculation and selection

With over two hundred years existence reciprocating (piston) compressors have been widely used for hundred years only. Application may be both household-oriented, such as pneumatic tools supplied by compressed air and professional, such as industrial machines supplied by compressed gas, and release of heavy-duty refrigeration units. Data sheets may help to pre-select the compressor unit, which is meant for practical use. Data sheets play a pivotal role in designing and calculating the proper compressor unit, tools, pneumatic equipment and associated power.

Compressors are commonly used in industry to transfer various media and are essentially mechanical devices to compress working medium in gas form. There are a wide variety of compressors, thus, proper selection and calculation of compressors is required to best fit with industry-associated application requirements.

Generally, compression of working medium is processed in compressor either with the use of rotating blades or in cylinders through pistons. Compressors with rotating blades are used for flows with large volume rates and low discharge pressure, while piston compressors are destined for high pressure. There are a lot of operating conditions to consider, including current standards and practices. Thus, selection of compressor is an important process with many aspects to consider.

To select the proper compressor the actual purpose will need to be discerned as well as design values, such as pressure, temperature, flow rate and type of compressor.

Data on gas, required flow rate, suction pressure and temperature and discharge pressure are key values for compressor selection.

Selection of compressors shall rest upon general principles of thermodynamics applied to gas compression theory, comparison of several compressor types, calculation and selection theory and compressor calculation formula to visualize the calculation theory.

## Selection of compressor units. Types of compressor units

The basics steps for selecting a compressor unit.

The term “compressor” means a unit to be utilized for increasing pressure of compressible medium via decreasing the specific volume of medium passing through compressor. Level of inlet and outlet pressure shall vary from deep vacuum to surplus pressure depending on operational needs. This is one of conditions to match type and configuration of compressor. Compressors are separated usually in two large subgroups: dynamic and positive-displacement. Various types of compressors may be selected for one particular application to best fit with structural specifics.

## Properties of working medium. Gas compression

Compressor may compress different gases. Gas thermodynamic or compressible gas mixture properties must be furnished to a vendor to properly configure the compressor unit. Full content, common name and chemical formula of gas are required for calculating the compressor unit. Data sheets of compressor units shall clearly indicate the gas testing data with each component name, molecular weight, boiling point and etc. listed. This data are very important for identification of correct compressor values. Ratio between general gas values (pressure, temperature and volume) is called gas equation.

The simplest gas equation is the ideal gas equation.

P · V = R · T

where:
P — pressure,
V — molecular weight,
R — gas constant,
T —temperature.

This equation applies to gas only, temperature of which is higher than critical temperature and pressure is way lower than critical pressure. The air shall abide by this law under atmospheric conditions.

Real gas differs from ideal gas by the factor called compressibility (“Z”). The term “compressibility” is used in thermodynamics to explain deviations of thermodynamic properties of real gasses from properties of ideal gasses.

P · V = Z · R · T

“Z” value – functional relation of gas content, its pressure and temperature.

## Compression process

Compression ratio (R) – is the pressure ratio at discharge to suction pressure:

R = Pd/Ps (where Pd and Ps are absolute).
One stage compressor has only one R value.
Two stage compressors have 3 R values.

R = overall compression ratio
R1 = first stage compression ratio
R2 = second stage compression ratio.

R = Pd/Ps

R1 = Pi/P

R2 = Pd/Pi

Ps – suction pressure
Pd – discharge pressure
Pi – pressure between stages

While compressing the air in compressor unit, molecular weight becomes lower to result in less spacing between molecules. Since quantity of gas molecules is increased in fixed volume, its weight and density of fixed volume also increase. Growth of density results in pressure increase.

The vertical line from point 1 to point 2 indicates an isentropic compression process to require minimal compression from Р1 to Р2 on figure below. Actual compression process follows from point 1 up and right facing rising entropy to end up at point 2 on isobar for Р2.

Compressor operations are focused on gas pressure and temperature to be increased and heat to be removed from compressor. In most cases it is required to increase the gas pressure with least capacity values. If the compression process is adiabatic, no heat is transmitted between compressor and environment to result in less operation during isentropic compression. This assumes no losses in compressor, which indeed is unachievable; however, it may be used for indicative compression performance index. Isentropic compression performance index is identified as operational compression during isentropic process divided by actual operations used for gas compression. Compression performance index is often indicated as isentropic performance index.

However, it is possible to make a compressor with over 100% isentropic performance indexes. Operations in reversible isothermal process are less than in isentropic process. Gas temperature in reversible isothermal process is maintained with reversible heat transmission during compression at suction temperature. This process shall have no losses. However, consumed capacity is almost always more than isentropic capacity; thus, isentropic performance index is used for compressor classification.

Two types of compressors - displacement and dynamics- currently present differ in principles of working medium compression. Displacement compressors compress gas to detain significant gas volumes in closed environment with subsequent decrease of volume. Compression starts when certain amount of gas enters the process chamber of the unit with subsequent decrease of inner volume of the process chamber.

Dynamic compressor type is used to compress gas by means of mechanically-operated blades or impeller to transfer speed and pressure of gas. Larger impeller diameter, larger molecular weight of gas or higher rotations will produce more pressure. Usually displacement compressors are selected for fewer amounts of gas and larger pressure values. Dynamic compressors are selected for larger amounts of gas and lower pressure values.

## Basics steps to compressor selection to include

1. Calculate compression ratio.
2. Select whether one stage or multiple stage compressor needed.
3. Discharge temperature calculation.
4. Identify volumes required.
5. Identify operational volumes required.
6. Select compressor model.
7. Identify minimal rotation torque of selected compressor.
8. Select actual rotation torque.
9. Calculate actual operational volume.
10. Calculate capacity required.
11. Select suitable configurations.
12. Select proper compressor.

## Data sheet of compressor equipment

Most important data sheets of compressor equipment are emphasized below:

• Outlet pressure in atm and bars. Most popular household compressors produce from 6 to 8 bars pressure; industrial compression units may produce 25 bars pressure. Pressure means that any given model of compressor may produce pressure internally and discharge the air mass into a sealed cavity. Pressure index is calculated by class and capacity of compression unit. The use of extra-high pressure compressors for household needs is not necessary. A small unit with up to 10 bars operational pressure will be sufficient. Large industrial facilities may not always operate at such values; in this case more powerful compression machines or units shall be used. Operational pressure of compressor is an average between maximum producible pressure to stop the discharge process and minimum pressure in the system to start-up the compressor. Normally, the pressure differential is 2 bars between stop and start-up the compressor. Given this index all compressors are divided into compression machines of low, medium and high pressure. Not all compressors have sufficient capacity to compress the air while producing high pressure; as a matter of fact only heavy-duty piston units may reach 30 atm pressure index. Screw-type compressor versions may not operate at such high indexes;
Inlet / outlet pressure. Least inlet gas flow shall be indicated in data sheet of compressor units. This is required to ensure the compressor capacity.
Pressure may be absolute or surplus. Relative note shall be made in the data sheet as well as units of indicated pressure.
• Inlet temperature. Volume flow rate, pressure requirements and required power may affect the inlet temperature. Thus, maximum inlet temperature shall be also specified.
• Discharge temperature. Discharge temperature (Td) depends on inlet temperature, compression index, gas specific heat and compression performance indicator. This temperature is important for mechanical design of compressor, selection of compression stage, calculations of cooler and pipelines.
• Suction capacity or air discharge (amount of induced or forced air at outlet). Regularly, first value is stated by manufacturers of compressor equipment in technical passports, because running compressors lose capacity at discharge due to air loss and suction capacity is always a bit higher. Compressor capacity is volume of compressed air flow upon a particular given time and is expressed in m3/hour or l/min. Various compressor types vary in capacity to specify particular application of compressor equipment. Amount of inlet air consumed upon a particular given time prior to compression is also considered a unit capacity. Otherwise this parameter is called the air flow rate. The reality is that there is a difference between two parameters. So one shall rely on outlet capacity. When selecting the proper compressor about 30% oversized capacity shall be taking into account;
• Motor power is measured in kW. Motor may be diesel, turbine or electric. Motor power is one of the core parameters to ensure compressor to manage air discharge. The higher the capacity the more power is consumed. Failure to calculate the power correctly may result in power consumption without effect. Usually, heavy-duty motors are installed in high power units requiring this particular drive;
• Compressor weight and overall dimensions. These values may vary from typical small size units easy to transport and operate in a garage to heavy-duty ones to require more space for installation. Big facilities do not pay serious attention to weight and dimensions, since the equipment is fixed and installed in a separate engine room. Dimensions and weight of compression unit always refer to its capabilities.
Alternatively, household compressor is quite compact, so most dimensions refer to receivers of 50, 100, 200 liters and more. Optionally, compressors with rotating blades may be used to constantly discharge air without the need for receivers. Sure, with no receivers installed weight and dimensions of compressors are significantly less making the unit easily relocatable;
• Air receiver is also an important parameter to enable idle operations. Air receivers are tanks designed for collecting compressed air. Receiver volume enables continuous off-line operations of pneumatics. It serves to energy saving. Another advantage is that compressor unit may discharge air with given pressure parameters.
• Corrosiveness of transferred gas. Composition of corrosive gas shall be identified for all operating conditions. It is important because of cracks coming from corrosion under pressure in high-strength material.
• Liquid in gas flow. Liquid in gas shall be avoided. Otherwise, it may cause malfunction of compressor. Separator shall be installed to dewater working medium; electrical tracing and insulation of inlet port shall be made when outside temperature is below gas dew point or hydrocarbon components heavier than ethane are compressed.

In some industries, like nutrition sector, no contaminants are allowed in compressed air. In this case, when selecting compression unit, power parameters shall be less preferential than design features. Data sheets of compressors shall comply with compressed air purity requirements with unit compression to be processed without any lubricating oils applied to working surface.

## Design particulars of compressor equipment

Design particulars of compressor are as follows:

1. Type of drive. ICE or electric motor;
2. Stage numbers for air compression. This parameter is justified and important for selection of piston compressors to enable gas compression in several cylinders in stages;
3. Cooling system (oil, air and water).
4. Mobility. Compressors to be fixed on special foundation or on trailer for ease of transportation;
5. Part element arrangement. All constituents of compressor unit may be frame or receiver mounted;
6. Receiver installation: vertical or horizontal.

Mains supply should be also noted, because of the lack of electrical supply points with 380 V at some tire shops. In some cases even power supply of 220 V may be unstable.

Selection of compressor is closely related to preliminary calculation of above technical data. Before calculating compressor particulars certain subtle details shall be highlighted. Air mass to be transferred by compressor is constant depending directly on compressor design specifics. However, it is common practice to identify capacity with volumetric and not mass values. This often leads to failure in calculations and as a result to errors in manufacturing calculation.

This is due to air to be compressed like all gases. As a result one and the same air mass fills different volume to depend on pressure and temperature values. Precise relation between these values may be explained with a complex power dependence or polytrophic equation. Compressor unit fills the receiver to increase in pressure and lose volumetric displacement. Thus, volumetric supply of compressor is variable. What value shall be specified in data sheets of compressor units then?

As per industry standards and codes compressor capacity is calculated with air volume at outlet following to recalculation of physical conditions in the process of suction. Usually, physical conditions at inlet of compressor are typical for regular operations: temperature is 20 °С, pressure - 1 bar. As per industry standards and codes deviation of actual values of compressor unit ±5% is allowed from those specified in technical passports.

Also values of compressed air consumers shall be recalculated to correspond to compressor unit characteristics. For example, rated flow amounts to 100 l/min, thus, pneumatic tool consumes the air volume per minute that would amount to 100 l at normal conditions.

Foreign manufacturers are not familiar with Russian industrial standards and codes, thus, their capacity calculations vary to result in calculation errors. Data from technical passports of their compressor units are based on theoretical capacity (suction capacity).

Theoretical capacity of compressor is defined by geometric measurement of air in the working area during one suction period. Then this volume is multiplied by the number of periods (cycles) per time unit. This theoretical capacity is higher than actual capacity of compressor unit. Theoretical and actual capacity difference is compensated by the capacity factor (Cf) to depend on suction conditions and compressor unit design specifics (valve losses: suction and discharge, amount of volume not completely displaced) to enable decreasing the volumetric efficiency (piston compressor). Capacity factor of industrial design compressors amounts from 0.6 to 0.8.

Difference in theoretical and actual compressor calculations at inlet and outlet may reach a significant value. When indicated in the data sheet theoretical capacity of compressor unit shall be recalculated for capacity at outlet, thus, to decrease the value by 30-40%.

## Designing a compressor

Compressor data sheet shall by all means indicate maximum allowable operating pressure. In line with maximum allowable temperature values these data shall be used by manufacturers to design the body and main parts of compressor to withstand maximum allowable operating pressure and temperature. For centrifugal and reciprocating compressors maximum allowable operating pressure is computed with adding maximum inlet pressure to maximum differential pressure to take place in compressor at more complex set of conditions. For piston cylinders and compressors with rotating blades body maximum allowable operating pressure shall be higher than nominal discharge pressure by 10% or 25 psi depending on which value is higher.

Maximum allowable temperature shall be maximum discharge temperature for centrifugal and reciprocating compressors during operations to include some deviation values. Maximum allowable temperature for cylinders of piston compressors and body of rotating blades compressors shall be higher than nominal discharge temperature.

## Pipeline flanges and nominal value

End-to-end dimensions, nominal flange value and type shall be clearly stated in data sheets for all compressor inlets and outlets. Shaft seal and piston rod also shall be clearly stated in data sheets.

## Oil lubrication system and lubricating oil

Primary system function is uninterruptable supply of pure and cooling lubricating fluid to bearings and seal, gears and drives of compressor. Due to its importance calculation of these systems shall be clearly indicated in data sheets.

## Materials

Gases under compression may help selecting the compressor materials; in particular, it pertains to contact elements. For example, while compressing H2S, sulfide cracking of high-strength materials may occur. Materials suitable for operations are considered to be thermally treated and yield point lower than 90000 psi.

## Process compression stages

Compression ratio (R) is the ratio of discharge pressure (Р2) to suction pressure (Р1) in compressor, Р2/Р1. When compression to higher pressures is required, compressor calculation assumes several compression stages; in some cases coolers are required to remove heat between compression stages. Additional compression stages are required e.g.:

• To reduce temperature at the end of each compression stage applying interim cooling up to allowable level to ensure proper compressor operations.
• To reduce temperature at inlet compression stage to drop the flow required for reaching the set compression ratio.
• To ensure differential pressure limits of various compressor types, e.g. axial load limits in centrifugal compressors, stress limit of rod in piston compressors, axial load in compressors with rotating blades.
• To reduce power consumption compressor drive due to interim coolers operation between stages and to maintain safe temperature limits.

## Choosing a one-stage or multiple-stage compressor

The choice of proper number of compression stages is largely based on the compression ratio.

Discharge temperature and operational mode are also considered when identifying the proper number of compression stages.

R value # stages
1-3 Single-stage
3-5 Normally single-stage, occasionally two-stage
5-7 Normally two-stage, occasionally single-stage
7-10 Two-stage
10-15 Normally two-stage, occasionally three-stage
15+ Three-stage

Comparison of a single-stage and two-stage compressor both installed to do the same application (same capacity, gas and pressures):

Single-Stage Two-Stage
Discharge Temperature higher lower
Initial cost lower higher
Overall System Complexity lower Higher

As with many engineering decisions, a suitable compromise between initial cost and operating / maintenance costs must be found.

1. At first, all air consumers Q must be calculated, l/min.
Air consumed by all consumers shall be summed up. This is made based on technical passport characteristics to get Q ratio (l/min) as the air volume to be consumed by pneumatics. This ratio is close to maximum parameter, should a large number of consumers is involved. It may be reduced by load coefficient, since not all consumers are involved at the same time in operations. The goal is to introduce corrections for reduction to be at sole discretion of compressor unit owner to ensure sufficient air volume in pneumatics.

2. Next parameter for calculation is compressor capacity A (l/min).
Lots of miscalculations lie in false identification of A parameter and understanding of compressor capacity. All compressor manufacturers indicate maximum inlet air consumption in technical passports or catalogues. This parameter may not be applied as outlet compressor capacity since this parameter does not include compressor performance and design specifics. In this regard calculation of compressor capacity shall be as follows:

A = Q · (β/η)

where
Q – total air volume to be consumed by all consumers of pneumatic system to be measured in l/min;
β – coefficient to count for design specifics of compressor unit by manufacturer;
η – performance index of compressor unit.
β and η values (for reference) are for compressor operations within working pressures from 6 to 8 bars are given below.

Compressor design b h
Semiprofessional compressors 1,7 0,55
Professional compressors 1,5 0,65
Heavy-duty compressors 1,3 0,75
Rotary compressors 1 1

3. Last but not least value for compressor selection is the volume of receiver V (l). Manufacturers recommend following range A when selecting the volume of receiver:

V = (1/2 ÷ 1/8)·A

Selecting proper receiver and volume value ensure pressure compensation and leveling to result in pneumatic system to be more flexible towards load bearing.

4. When choosing pressures for compressor the rule to follow is that pressure produced by compressor must be higher than pressure to be operated by consumers of compressed air. Any compressor pumps the air up to maximum operating pressure Рmax., and then shuts off. Subsequently, compressor starts when pressure dropped to Рmin. Difference between max. and min. pressures of compressor amounts to 2 bars.

5. To proceed further with compressor selection it is important to determine the actual application: to decide how and what is the purpose of using the compressor. It is important to determine time span for continuous operations, maximum volume of compressed air, operating pressure and other technical parameters as stated above.

Type of compressor: this is a core parameter for above characteristics to depend on. To have total required power calculated one can conclude that in case a compressor is needed for a spray unit or any other pneumatic tool with slight operating pressure values is required, the best option will be a piston compressor. When it comes to high capacities and several air consumers, one should contemplate rotary or scroll compressor units. Length to which the medium would be supplied, i.e. compressed air should also be noted.

6. Compressor characteristics, especially, capacity values are affected by elevation above sea level, ambient temperature and atmospheric pressure. The higher the elevation is the lower the temperature and ambient pressures are. This should be noted when operating an air compressor under such conditions because these conditions affect capacity values of compressor and nominal consumption of compressed air. Thus, should the compressor be operated at high altitudes, output characteristics would differ from those specified in technical passport in certain manner.

In fact, the air is discharged at heights to result in deterioration of cooling of electric motor of air compressor and its heat-affected parts. Motor to operate under nominal characteristics at maximum elevation above sea level of 1000 m and maximum temperature of 40°С (see table below to indicate values of various motors under certain elevation and temperature parameters). Some types of compressors are equipped with electric motors with typical capacity losses at high elevation. Lower capacity should be supplied to compressor shaft accordingly.

Type of motor: Capacity drop in % per 1000 meters Capacity drop in % per each 10 °С of temperature rise
Atmospheric 12 3,6
Supercharged 8 5,4

## Algorithm for choosing an air compressor based on capacity and pressure values. Scheme of compressor selection

Proper type of compressor may be selected based on general initial data following the scheme below.

Below compressor characteristics are based on compressor type:

Type of compressor: Maximum values:
Piston Q = from 2 to 5 m3/min
РН = from 0.3 to 200 Mn/m2 (laboratory study indicated up to 7000 Mn/m2)
n = from 60 to 1000 rpm
N = max. 5500 kW
Rotary Q = from 0.5 to 300 m3/min
РН = from 0.3 to 1.5 Mn/m2
n = from 300 to 3000 rpm
N = max. 1100 kW
Centrifugal Q = from 10 to 2000 m3/min
РН = from 0.2 to 1.2 Mn/m2
n = from 1500 to 10000 (max. 30000) rmp
N = max. 4400 kW (for sky-borne - 10 000 kW and above)
Reciprocating Q = from 100 to 20000 m3/min
РН = from 0.2 to 0.6 Mn/m2
n = from 2500 to 20000 rpm
N = max. 4400 kW (for sky-borne max. 70000 kW)

One has to be precisely accurate when choosing an air compressor; otherwise, time saved during preliminary calculations may result in pre-calculation errors and subsequently, selection of improper type of compressor not being able to accomplish the job.

## Example of a piston compressor selection

Reciprocating (piston) compressor is a positive displacement compressor. When selecting a compressor, basic parameters such as discharge pressure, suction temperature, mode of operation and gas composition and required capacity should be identified first. Selection should be also focused on relative humidity of performance index, cost and reliability. Compressors may have similar piston functioning, when applied for different use. For instance, long-stroke compressors tend to be slower than short-stroke compressors in functioning. In general, short-stroke compressors are light-weight and have less allowable loads values.

Compressor speed and length of stroke depend on power required. Light-weight, high-speed short-stroke compressors require less power when applied. At the same time, long-stroke, low-speed compressors require more power when applied. Heavy-duty compressors are connected directly to drive gear, where applicable. Consequently, speed parameters of drive gear may also affect compressor selection.

Next, the number of stages should be selected. Allowable discharge temperature, piston compression ratio and performance index are key factors to be noted. If estimated discharge temperature is too high using one stage, more stage would be assumed. Isentropic discharge temperature may be pre-selected; but if certain number of stages would result in a deadlock, discharge temperature should be more precisely computed. Similar compression ratio is expected to be used for all stages, when roughly calculated. Virtually, it is always recommended to select higher compression ratio for low pressure stages to decrease more critical high pressure stages.

All applications, where multiple stages are required for operations, intercoolers should be used. In this case increasing the number of stages would result in higher performance index of compressor unit. Due to intercoolers the compression process is deemed to be close to isothermal compression resulting in less power to be consumed.

If working medium is condensed in intercooler, liquid must be separated from gas, whereas compressed gas mass to discharge is reduced to result in less power consumption. However, by adding stages the number of valves, intermediate piping and coolers is increased. When using multiple stages, pressure losses in valves and piping would reduce advantages of intercoolers and efficiency.

Cost of compressor is rising with increased number of stages due to the need for coolers, valves, piping and additional cylinders.

Cylinders should be selected for each stage upon selection of the number of stages. To select proper cylinder opening it is required to know inlet conditions, capacity, speed and length of stroke. It is required to correctly select nominal pressure values for cylinder for safe operations, to consider loads, losses and power.

Also unbalancing force, to be supplied from compressor to frame, potential vibrations to result in crankshaft and drive gear damage, and level of noise must be considered; compressor position, performance index and cost must be optimized.