Compressor

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Contents 1 General Description 1.1 Diagram 2 Inputs and Outputs 3 Model Theory 3.1 Assumptions, Limitations and comments 4 Data Sections 4.1 Requirements 4.2 Results 5 Adding this Model to a Project

General Description

The compressor model can be used to increase the pressure of streams which consist mostly of gases. The user will receive a warning if the fraction of vapours in the feed is less than 99%.

Diagram

The diagram shows the default drawing of the Compressor, with the required connecting streams. The unit will not operate unless all of the above streams are connected.

The physical location of the connections is not important, the user may connect the streams to any position on the drawing.

Inputs and Outputs

Input / Output	No. of Connections		Description
	Min	Max.
In	1	1	Input stream to compressor.
Out	1	1	Output stream from compressor.

Model Theory

Equations

For an ideal gas:

(1) C_p = C_v + R

where:

C_p = heat capacity at constant pressure on a per mole basis

C_v = heat capacity at constant volume on a per mole basis

R = universal gas constant

Then K, the ratio of specific heats, can be calculated as follows:

(2)

For an ideal gas with constant heat capacities, which undergoes a mechanically reversible, adiabatic (or isentropic) process, the following equation applies:

(3)

This can be rewritten as:

(4)

where:

T_out = outlet temperature

P_out = outlet pressure

P_in = inlet pressure

T_in = inlet temperature

Thus given the inlet temperature and pressure and the outlet pressure, the outlet temperature can be calculated.

The adiabatic efficiency is used for the Isentropic method and is defined as:

(5)

where:

dT_i = calculated temperature change for isentropic process

dT_a = actual temperature change

The polytropic exponent has the following form:

(6)

then

(7)

For all cases,

(8) Ideal Power = Rate of Enthalpy Out - Rate of Enthalpy In

(9)

Calculation Steps

Step 1) Determine the outlet pressure based on user specified value, boost or ratio.

Step 2) If the user has specified a value for K, use this value in the calculations, otherwise calculate K as the ratio of Cp to Cv using equation (2).

Step 3) Calculate the outlet temperature based on the outlet pressure:

a) for the Isentropic method: use equation (4).

b) for Polytropic method: use equations (6) and (7).

Step 4) Calculate the outlet enthalpy based on the outlet temperature and pressure.

Step 5) Calculate the Power using equations (8) and (9)

Assumptions, Limitations and comments

1. This model assumes that the gases behave as ideal gases.
2. The feed stream should contain only gases. Small amounts of liquids and solids will have little affect. The outlet temperature and pressure are determined by the gases present in the stream only. Any liquids or solids in the inlet will be assumed to exit the compressor at this new temperature and pressure. When the power is calculated using the enthalpy difference between the inlet and outlet, this will include any solids or liquids in the stream. Thus the presence of solids and liquids will usually lead to an increase in power requirements.
3. Note: If the stream contains no gases, then the model will produce unrealistic results.

References

1. Bloch H.P. A Practical guide to Compressor Technology, McGraw-Hill 1996

2. Perry et al Perry's Chemical Engineers' Handbook 6^th Edition, McGraw-Hill 1984

Data Sections

The default access window consists of four sections,

1. The first tab has the same name as the model tag, contains the main configuration information relating to the unit.
2. The section, Info, fully described in Info Tab Page Section.
3. The section, Links, only visible in SysCAD 9.2, contains a summary table for all the input and output streams. See Links Table.
4. The last section is the Audit. See Model Examples for enthalpy calculation Examples.

Tag / Symbol	Input / Calc	Description/Calculated Variables / Options
Common First Data Section
Requirements
PressMethod	List	Off - This switches off the compressor. The inlet will equal the outlet with no changes in temperature or pressure and zero power used.
		Fixed - The user can specify (fix) the outlet pressure.
		Boost - The user can specify a boost to the pressure compared to the inlet pressure.
		Ratio - The user can specify the ratio of the outlet pressure to the inlet pressure.
OutletPressRqd / PRqd	Input	Only visible if Fixed is chosen for the Pressure method. The pressure of the outlet (discharge) stream.
PressBoostRqd / PBoost	Input	Only visible if Boost is chosen for the Pressure method. The difference in pressure between the inlet and outlet streams.
PressRatioRqd / PRatioRqd	Input	Only visible if Ratio is chosen for the Pressure method. The ratio of the outlet pressure to the inlet pressure.
CalculationMethod / Method	List	Isentropic - The isentropic outlet temperature will be calculated using the pressure ratio, inlet temperature and the ratio of heat capacities (K).
		Polytropic - The outlet temperature will be calculated using the pressure ratio, inlet temperature, ratio of heat capacities (K) and the polytropic efficiency.
SpecifyK	Tickbox	This allows the user to specify the value of K, the ratio of heat capacities. If this is left unchecked, then the model will assume ideality and use equation (1) to calculate K based on Cp values in the specie database.
K	Input	Only visible if SpecifyK option is selected. This is the user specified value of k, the ratio of specific heats of the gas in the feed stream.
AdiabaticEff	Input	Only visible if Isentropic is chosen for the Calculation method. This efficiency is used to alter the calculated isentropic temperature change. A lower efficiency will lead to a larger temperature change.
PolytropicEff	Input	Only visible if Polytropic is chosen for the Calculation method.
CompressorEff	Input	This efficiency is used to calculate the Power from the IdealPower. A lower efficiency will lead to a larger Power and a larger difference between Power and IdealPower.
Results
Mass_Flow / Qm	Calc	The total mass flow through the unit.
TemperatureIn / Ti	Calc	The inlet temperature.
TemperatureOut / To	Calc	The outlet temperature.
PressIn / Pi	Calc	The inlet pressure.
Press_Change / dP	Calc	The outlet pressure.
PressOut / Po	Calc	The outlet pressure.
PressRatio / PRatio	Calc	The outlet pressure.
VapourFracIn / Vfi	Calc	The fraction of vapours in the inlet stream.
VapourFracOut / Vfo	Calc	The fraction of vapours in the outlet stream.
IdealPower	Calc	The calculated difference in enthalpy between the inlet and outlet streams per unit time.
Power	Calc	The ideal power, adjusted by the compressor efficiency. The lower the efficiency the more power required.
Gas.MWT	Calc	The weighted average of the molecular weights of the vapours in the inlet stream.
Gas.Cp	Calc	The weighted average of the heat capacities at constant pressure (Cp) of the vapours in the inlet stream.
Gas.Cv	Calc	The heat capacity at constant volume (Cv) of the vapours in the inlet stream. This is calculated using the heat capacity at constant pressure (Cp).
Gas.K	Calc	The ratio of the Gas Cp to the Gas Cv, i.e. the K value.

Adding this Model to a Project

Insert into Configuration file

Sort either by DLL or Group.

	DLL:	Basic1.dll	→	Units/Links	→	Process Piping: Compressor
or	Group:	General	→	Units/Links	→	Process Piping: Compressor

See Project Configuration for more information on adding models to the configuration file.

Insert into Project

Insert Unit

→

Process

→

Piping

→

Compressor

See Insert Unit for general information on inserting units.