This operation models steam expansion and electricity generation in a steam turbine (either of the straight-flow or extraction type) coupled to an electric generator.
● Power Generation in a Straight Flow Steam Turbine-Generator Procedure
● Power Generation in an Extraction Steam Turbine-Generator Procedure
If the equipment that hosts this operation is a straight flow steam turbine-generator, the user must set the exhaust pressure and the program will calculate the isentropic efficiency (if it’s not set by the user), shaft power, exhaust temperature and electric power.
If the equipment that hosts this operation is an extraction turbine-generator, the overall expansion may be broken into intermediate expansions. The user may optionally specify up to three intermediate expansions (one for each extraction port, covering the range between the input port or the last used extraction port and the selected extraction port) and extract steam through the corresponding extraction ports. By default, another expansion will be added automatically to cover the range between the input port (if no intermediate expansion is specified by the user) or the last used extraction port (if at least one intermediate expansion is specified by the user) and the outlet port. Hence, the total number of intermediate expansions can be up to four.
To specify an intermediate expansion, the user must check the “Include Expansion?” option for the corresponding extraction port through the “Oper. Cond’s” tab. If this is the first specified expansion, it will cover the range between the inlet port and the selected extraction port. If this is the second or third specified expansion, it will cover the range between the last used extraction port and the selected extraction port for this expansion. For example:
● If the “Include Expansion?” option for the first extraction stream is checked, the program will simulate the expansion of steam between the input port and the first extraction port.
● If the “Include Expansion?” option for the second extraction stream is checked, the program will simulate the expansion of steam from the previous port to the second extraction port. If the “Include Expansion?” option for the first extraction stream is not checked, the previous port is the input port. If the “Include Expansion?” option for the first extraction stream is checked, the previous port is the first extraction port.
For each expansion, the user must set the final pressure and the percentage of total feed flow that must be extracted, and the program will calculate the isentropic efficiency (if this is not set by the user), shaft power and final temperature. In addition, the program will calculate the total electric power produced by all expansions.
Steam turbines convert the thermal energy of steam into mechanical energy. Steam jets of high pressure deliver kinetic energy to a series of impellers and thereby the steam cools down and expands to low pressure. This physical situation falls between the isentropic and isothermal extremes. To calculate the power output supplied at the shaft of the steam turbine for each expansion, the following equations are used:
|
|
|
|
where:
● F is the mass flow rate of steam,
● h1 is the specific enthalpy of steam at the expansion’s intake conditions,
● h2 is the specific enthalpy of steam at the expansion’s delivery conditions,
● h2s is the specific enthalpy of steam for isentropic expansion,
● Wi is the theoretical power output for isentropic expansion,
● εi is the isentropic efficiency of the expansion,
● ε0 is the condensate-free value of isentropic efficiency,
● x is the fraction of condensate at the expansion’s delivery conditions, and
● f is the fraction of additional thermodynamic/mechanical efficiency losses that may exist between the turbine rotor and shaft (e.g., due to turbulence and friction), which are not accounted for by the value of ε0.
The following specification options are available for specifying the expansion model that is used for the calculation of theoretical power output and outlet temperature for each expansion:
a) Analytical Isentropic Expansion Model
b) Built-In Steam Calculator
By default, option (a) is selected. If option (a) is selected, the following analytical expression of the overall mechanical energy balance is used to calculate the theoretical power output of isentropic expansion of a gas, for each expansion:
|
|
where:
● F is the gas mass flow rate,
● m is a polytropic coefficient, which for isentropic expansion is equal to the specific heat ratio of gas (average value for steam = 1.3),
● v1 is the specific volume of gas at the expansion’s intake conditions,
● p1 is the pressure of gas at the expansion’s intake conditions, and
● p2 is the pressure of gas at the expansion’s delivery conditions.
If option (b) is selected, the thermodynamic properties of steam are calculated based on a built-in steam calculator. More specifically, the specific enthalpies h1 and h2s, as well as the temperature and quality of steam at the end of the expansion, are calculated based on the built-in steam calculator. Then, the theoretical power output of isentropic expansion is calculated as h1-h2s.
The total shaft power is calculated as the sum of the shaft power values over all expansions.
The following specification options are available for specifying the isentropic efficiency per expansion:
a) Set by User
b) Calculated Based On Condensate-Free Isentropic Efficiency
If option (a) is selected, the isentropic efficiency for each expansion may be specified directly. If option (b) is selected, the user may choose between the following two options for the calculation of the condensate-free isentropic efficiency:
a) Built-In
b) Set By User
If option (a) is selected, the condensate-free efficiency with respect to shaft power will be estimated using a built-in model. The model is based on efficiency vs. power data provided by Ulrich (1984), which were fitted to a quadratic curve. The model is valid in the range 100 kW – 1.5 MW. The isentropic efficiency for each expansion is then corrected for condensate and mechanical losses according to eq. (A.361). The fraction of condensate at delivery conditions for each expansion, is estimated by solving the system of eq. (A.360) and eq. (A.361) iteratively until the assumed condensate value matches the calculated condensate value at delivery enthalpy-pressure conditions.
If option (b) is selected, the user may edit the parameters of the quadratic curve. Then, the condensate-free isentropic efficiency and the corrected isentropic efficiency for each expansion are calculated similarly to option (a).
The enthalpy of steam at the end of each expansion is calculated by subtracting the shaft power produced during that expansion from the enthalpy at the start of that expansion.
The enthalpy of steam at the start of each subsequent expansion is calculated by subtracting the enthalpy of extracted steam (if any) from the available enthalpy at the end of each preceding expansion.
The temperature, as well as physical state of gas at exhaust conditions, is estimated by performing a p-h flash based on the pressure and enthalpy of gas at exhaust conditions, and the procedure’s default physical state calculation options.
The user may choose between two turbine types:
a) Back Pressure
b) Condensing
By default, option (a) is selected. If option (b) is selected, it is assumed that the turbine exhaust is directed to an implicit steam surface condenser. A steam surface condenser can be used to expand steam to sub-atmospheric pressures, and thereby increase the power output of the turbine. In that case, the equipment resource that hosts the operation is in fact a condensing turbine and the outlet stream returned by the model is the condensate that exits from the condenser.
If a condensing turbine is selected, the user must also specify the properties of the cooling agent and the operating temperature of the condenser. The operating pressure of the condenser is assumed equal to the outlet pressure of the turbine exhaust. Based on these, the model will calculate the cooling duty and cooling load of the condenser.
The following specification options are available for specifying the operating temperature of the condenser:
a) Set by User
b) Saturation Temperature
By default, option (b) is selected. If option (b) is selected, the operating temperature of the condenser is set equal to the saturation temperature of steam at the outlet pressure. If the built-in steam calculator option is selected, then the saturation temperature of steam is calculated based on the built-in steam calculator. If the analytical isentropic expansion model is selected, then the saturation temperature of gas is set equal to the minimum boiling point of gas at the outlet pressure. If option (a) is selected, the user may specify a lower temperature than the steam’s saturation temperature in order to simulate subcooling of steam.
To calculate the cooling duty of the condenser, the following equation is used:
|
|
where:
● Q is the cooling duty of the condenser,
● hin,c is the specific enthalpy of steam at intake conditions to the condenser,
● hout,c is the specific enthalpy of condensate at the operating conditions in the condenser, and
● εc is the heat transfer efficiency in the condenser.
Note that if the built-in steam calculator option is selected, the specific enthalpies of steam and condensate are calculated based on the built-in steam calculator. The pressure and temperature of condensate are set equal to the pressure and saturation temperature of steam at turbine exhaust conditions.
The cooling load (mass flow rate of cooling agent) is calculated by dividing the cooling duty by the mass-to-energy factor of the selected cooling agent.
A power generator is coupled to the turbine shaft to convert shaft power into electricity. To calculate the total electric power produced by the turbine, the following equation is used:
|
|
where εG is the efficiency of conversion of shaft power to electric power.
The user must specify the efficiency of conversion of shaft power into electric power of the power generator, and based on this, the program will calculate the total electric power produced by the turbine using the above equation.
In Design mode, if the calculated shaft power exceeds the maximum shaft power of the turbine, the program assumes multiple units operating in parallel with a total power output equal to the calculated power. If the equipment size option is in Rating Mode, the user specifies the rated power and the number of units. If the calculated power output per unit exceeds the rated power, a warning message is displayed advising the user to increase the rated power or number of units, or reduce the mass flow rate of the feed stream.
1. Ulrich, G.D. (1984). A Guide to Chemical Engineering Process Design and Economics, John Wiley & Sons, pp. 84-93.
2. Dixon, S.L. (1998). Fluid Mechanics and Themodynamics of Turbomachinery, Butterworth-Heinemann, pp. 30-31.
3. Boyce, M.P. (2006). Gas Turbine Engineering Handbook, 3rd edition, Elsevier, pp. 110-122.
4. Peters, M.S. and K.D. Timmerhaus, (1991). Plant Design and Economics for Chemical Engineers, 4th edition, McGraw-Hill, pp. 523-525.
5. Loh, H.P. and Lyons J. (2002). “Process Equipment Cost Estimation”, Final Report, DOE/NETL-2002/1169.
● If the built-in steam calculator is selected, and the equipment is in Design Mode, the following constraints must be satisfied with respect to inlet temperature and inlet/outlet pressure:
a) The inlet temperature must be in the range 0-2000°C (273.15 K - 2273.15 K).
b) The inlet pressure must be in the range 611.657 Pa (triple point) - 100 MPa (1000 bar).
c) If the inlet temperature is >800°C, then the inlet pressure must be <= 10 MPa.
● If the built-in steam calculator is selected, and the equipment is in Rating Mode, the following constraints must be satisfied with respect to inlet temperature and inlet/outlet pressure:
a) The inlet temperature must be in the range 0-800°C (273.15 K - 1073.15 K).
b) The inlet pressure must be in the range 611.657 Pa (triple point) - 100 MPa (1000 bar).
● The built-in isentropic efficiency curve is valid for power output in the range 100 W - 1.5 MW.
● The following constraints apply to the parameters of a custom efficiency curve:
a) Parameter ‘a’ of the isentropic efficiency curve must be <=0.
b) If parameter ‘c’ of the isentropic efficiency curve is zero, then the corresponding parameter ‘b’ cannot be equal to 1.
c) If parameter ‘c’ of the isentropic efficiency curve is not zero, then the discriminant of the second-degree polynomial that represents the isentropic efficiency curve must be greater than zero.
If the host equipment is a straight-flow steam turbine-generator, the interface of this operation has the following tabs:
● Oper. Cond’s, see Power Generation in a Straight Flow Steam Turbine-Generator: Oper. Conds Tab
● Expansion Data, see Power Generation in a Gas Expander-Generator: Expansion Data Tab
● Labor, etc, see Operations Dialog: Labor etc. Tab
● Description, see Operations Dialog: Description Tab
● Batch Sheet, see Operations Dialog: Batch Sheet Tab
● Scheduling, see Operations Dialog: Scheduling Tab
If the host equipment is an extraction steam turbine-generator, the interface of this operation has the following tabs:
● Oper. Cond’s, see Power Generation in an Extraction Steam Turbine-Generator: Oper. Conds Tab
● Expansion Data, see Power Generation in an Extraction Steam Turbine-Generator: Expansion Data Tab
● Labor, etc, see Operations Dialog: Labor etc. Tab
● Description, see Operations Dialog: Description Tab
● Batch Sheet, see Operations Dialog: Batch Sheet Tab
● Scheduling, see Operations Dialog: Scheduling Tab
