Compressor
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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%.
The compressor model can be inserted in a steam line that is part of a Flash Train.
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 | Required / Optional | Number of Connections | Description | |
Min | Max. | |||
In | Required | 1 | 1 | Input stream to compressor. |
Out | Required | 1 | 1 | Output stream from compressor. |
Behaviour when Model is OFF
If the user disables the unit, by un-ticking the On tick box, then the material will flow straight through the Compressor with NO change to either Temperature or Pressure.
So basically, the unit will be 'bypassed' without the user having to change any connections.
Model Theory
Equations
Isentropic Method
For an ideal gas:
- (1) [math]\displaystyle{ \mathrm{C_p = C_v + R} }[/math]
- where:
- [math]\displaystyle{ \mathrm{C_p} }[/math] = heat capacity at constant pressure on a per mole basis
- [math]\displaystyle{ \mathrm{C_v} }[/math] = heat capacity at constant volume on a per mole basis
- R = universal gas constant
The k value, the ratio of specific heats, can be calculated as follows:
- (2) [math]\displaystyle{ k = \cfrac{C_p}{C_p - R} }[/math]
For an ideal gas with constant heat capacities, which undergoes a mechanically reversible, adiabatic (or isentropic) process, the following equation applies:
- (3) [math]\displaystyle{ \cfrac{T_2}{T_1}=\left (\cfrac{P_2}{P_1}\right)^{((k-1)/k)} }[/math]
This can be rewritten as:
- (4) [math]\displaystyle{ T_{out} = T_{in} * \left (\cfrac{P_{out}}{P_{in}}\right)^{((k-1)/k)} }[/math]
- where:
- [math]\displaystyle{ \mathrm T_{out} }[/math] = outlet temperature
- [math]\displaystyle{ \mathrm P_{out} }[/math] = outlet pressure
- [math]\displaystyle{ \mathrm P_{in} }[/math] = inlet pressure
- [math]\displaystyle{ \mathrm T_{in} }[/math] = inlet temperature
Isentropic Full Method
For situations where Cp is not constant through the compression process, the isentropic full method may be used. This method assumes that compression process is isentropic (mechanically reversible and adiabatic) so that the entropy of the gas is constant throughout the process (the same as above), [math]\displaystyle{ S_{out} = S_{in} }[/math]. However, the final temperature is found by solving for a temperature where the entropy of the outlet stream at the outlet pressure matches the entropy of the inlet stream. This method is more accurate than the isentropic method above.
Isentropic Efficiency and Work
Thus given the inlet temperature and pressure and the outlet pressure, the outlet temperature can be calculated. The outlet temperature and pressure can be used to find the outlet enthalpy, [math]\displaystyle{ H_{out} }[/math]. The work required will be the enthalpy difference of the gas between the inlet and the outlet of the compressor. For a reversible, adiabatic process, this will be the minimum or ideal amount of work required for compression:
- (5) [math]\displaystyle{ W_{s} = {H_{out}}-{H_{in}} }[/math]
The adiabatic efficiency is used for the Isentropic and isentropic full methods and is defined as:
- (6) [math]\displaystyle{ \text{Adiabatic}\,\text{Efficiency}=\cfrac{{{W}_{s}}}{{{W}_{a}}} }[/math]
- where:
- [math]\displaystyle{ \mathrm W_{s} }[/math] = isentropic or ideal work
- [math]\displaystyle{ \mathrm W_{a} }[/math] = actual work required
The actual work includes fluid friction and other irreversible losses. When the efficiency is less than 100%, the final enthalpy is found by calculating the isentropic work, dividing it by the efficiency and adding it to the inlet enthalpy. This gives the outlet enthalpy. A temperature is then found that matches the outlet enthalpy at the given outlet pressure.
Polytropic Method
The polytropic or "small Stage" efficiency is sometimes used to compare the performance of compressors with multiple stages.
The polytropic exponent has the following form:
- (7) [math]\displaystyle{ \cfrac{n}{n-1} = \cfrac{k}{k-1} * \mathrm {Polytropic\ Efficiency} }[/math]
then
- (8) [math]\displaystyle{ T_{out} = T_{in} * \left (\cfrac{P_{out}}{P_{in}}\right)^{((n-1)/n)} }[/math]
When the polytropic efficiency is 100%, the polytropic method is equivalent to the isentropic method. As with the isentropic method, once the outlet temperature has been determined for the outlet pressure, then the outlet enthalpy can be found directly.
NB the polytropic efficiency is not equal to the adiabatic efficiency (except when the pressure ratio is one, i.e. zero pressure rise). For a given polytropic efficiency, the adiabatic efficiency will vary as a function of pressure ratio and decrease as the pressure ratio increases.
Compressor Power
For all methods the compressor power is the mass flow rate times the enthalpy change between the inlet and outlet:
- (9) [math]\displaystyle{ Compressor Power = mass flow * ({H_{out}}-{H_{in}}) }[/math]
The actual power required to run the compressor includes the mechanical drive efficiency to account for the efficiency of the motor, gearbox, belts, etc.
- (10) [math]\displaystyle{ \text{Compressor}\,\text{Drive}\,\text{Power}=\cfrac{\text{Compressor}\,\text{Power}}{\text{Mechanical}\,\text{Drive}\,\text{Efficiency}} }[/math]
Calculation Steps
Step 1) Determine the outlet pressure based on user specified value, boost or ratio.
Step 2) Select the calculation method.
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 selected method and efficiencies.
Step 4) Calculate the outlet enthalpy based on the outlet temperature and pressure.
Step 5) Calculate the Compressor Power and the drive power required using equations (9) and (10)
Assumptions, Limitations and comments
- This model assumes ideal gas behaviour.
- There are no chemical reactions or phase change occurring during compression.
- The isentropic and polytropic methods allow user entry of the specific heat ratio, k, which will override the calculated value. This may be used to approximate compression where there is significant heat transfer during the process.
- 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.
- 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
Summary of Data Sections
- Compressor tab - contains the main configuration information relating to the unit.
- Info tab - contains general settings for the unit and allows the user to include documentation about the unit and create Hyperlinks to external documents.
- Links tab, contains a summary table for all the input and output streams.
- Audit tab - contains summary information required for Mass and Energy balance. See Model Examples for enthalpy calculation Examples.
Compressor Page
Unit Type: Compressor - The first tab page in the access window will have this name.
Tag (Long/Short) | Input / Calc | Description/Calculated Variables / Options | |||
Tag | Display | This name tag may be modified with the change tag option. | |||
Condition | Display | OK if no errors/warnings, otherwise lists errors/warnings. | |||
ConditionCount | Display | The current number of errors/warnings. If condition is OK, returns 0. | |||
GeneralDescription / GenDesc | Display | This is an automatically generated description for the unit. If the user has entered text in the 'EqpDesc' field on the Info tab (see below), this will be displayed here. If this field is blank, then SysCAD will display the unit class ID. | |||
Requirements | |||||
On | Tickbox | If the unit is disabled, by un-ticking this box, then material flows straight through the unit, with no change to temperature or pressure. | |||
PressMethod | Fixed | The user specifies the outlet pressure from the Compressor. | |||
Boost | The user specifies the pressure boost of the compressor. | ||||
Ratio | The user specifies the ratio of the outlet pressure to the inlet pressure. | ||||
PressureReqd / P_Reqd | Input | Only visible if Fixed is chosen for the Pressure method. This sets the required pressure of the outlet (discharge) stream. | |||
PressBoostReqd / PBoostReqd | Input | Only visible if Boost is chosen for the Pressure method. The difference in pressure between the inlet and outlet streams. | |||
PressRatioReqd / PRatioReqd | Input | Only visible if Ratio is chosen for the Pressure method. The ratio of the outlet pressure to the inlet pressure. | |||
MaxPressRatio / MaxPRatio | Input | The maximum compression ratio that the Compressor can provide. If the required final pressure / inlet pressure > than this value, then SysCAD will restrict the final pressure so that the maximum pressure ratio is not exceeded. The unit will give the user an error message if this occurs. | |||
CalculationMethod / Method | Isentropic | The isentropic outlet temperature will be calculated using the pressure ratio, inlet temperature and the ratio of heat capacities (k). | |||
Isentropic Full | The outlet temperature will be calculated using the pressure ratio and finding an outlet temperature such that the outlet entropy at the outlet pressure matches the inlet entropy. | ||||
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 heat capacity ratio,k. If this is left unchecked, then the model will assume ideality and use equation (1) to calculate k based on Cp values in the species 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. | |||
Adiabatic.Efficiency / AdiabaticEff | Input | Only visible if Isentropic or Isentropic Full is chosen for the Calculation method. This efficiency is used to calculate the actual work required from the isentropic work. A lower efficiency will increase the work required. | |||
Polytropic.Efficiency / PolytropicEff | Input | Only visible if Polytropic is chosen for the Calculation method. | |||
Compressor.Efficiency / CompressorEff | Input | This is the mechanical efficiency of the compressor drive and gear box (if present) and is used to calculate the drive motor power required from the IdealPower. A lower efficiency will lead to a larger Power and a larger difference between Power and IdealPower. | |||
Results | |||||
MassFlow / Qm | Calc | The total mass of material flowing through the compressor. | |||
TemperatureIn / Ti | Calc | The temperature of material at the inlet of the compressor. | |||
TemperatureOut / To | Calc | The temperature of material at the outlet of the compressor. | |||
PressureIn / Pi | Calc | The actual pressure at the inlet of the compressor. | |||
PressChange / dP | Calc | The pressure change in the compressor. | |||
PressureOut / Po | Calc | The actual pressure at the outlet of the compressor. | |||
PressRatio / PRatio | Calc | The pressure ratio of the compressor = Pressure Out / Pressure In. | |||
DensityIn / Rhoi | Calc | The density of material at the inlet of the compressor. | |||
DensityOut / Rhoo | Calc | The density of material at the outlet of the compressor. | |||
VapourFracIn / Vfi | Calc | Vapour Mass Fraction at the inlet of the compressor. | |||
VapourFracOut / Vfo | Calc | Vapour Mass Fraction at the outlet of the compressor. | |||
IdealPower | Calc | This is the amount of power put into the fluid being compressed and is the enthalpy difference between the inlet and outlet streams per unit time. The lower the efficiency the more power required to achieve the same pressure. | |||
Power | Calc | The required compressor drive power for the given adiabatic and drive efficiencies. | |||
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: | Piping2.dll |
→ | Units/Links | → | Piping: Compressor | |
or | Group: | General |
→ | Units/Links | → | Piping: Compressor |
See Model Selection for more information on adding models to the configuration file.
Insert into Project
Insert Unit | → | Piping | → | Compressor |
See Insert Unit for general information on inserting units.