Steam turbines modeling

In order to derive the part-load equations, consideration should be given to how the full-load performance depends on the steam pressure drop. Peterson and Mann10 present curves of the overall efficiency of industrial steam turbines at maximum load. The form of such curves is illustrated in Figure 23.11a. Each curve represents data for many steam turbines at fullload. Performance curves of this form can be used to derive the steam turbine model. Another interpretation... 

Steam turbine performance is modeled using a standard steam flow versus horsepower map and valve position versus steam flow. The turbine inlet valve(s) is positioned by the governor system to maintain constant speed (or another parameter when synchronized). 

Aerothermal analysis This pertains to a detailed thermodynamie analysis of the full power plant and individual eomponents. Models are ereated of individual eomponents, ineluding the gas turbine, steam turbine heat exehangers, and distillation towers. Both the algorithmie and statistieal approaehes are used. Data is presented in a variety of performanee maps, bar eharts, summary eharts, and baseline plots. 

Figure 23.10a illustrates the relationship between turbine efficiency and mass flow through the turbine. Because hMECH his, the major contribution to the nonlinear trend of the overall efficiency with part-load is from the isentropic efficiency his A turbine model needs to capture this behavior. It should also be noted that there will be an efficiency associated with an electricity generating set coupled to the steam turbine (typically 95 to 98%). 

Figure 23.11 Modeling steam turbines at maximum load. (From Varbanov PS, Doyle S and Smith R, 2004, Trans IChemE, 82A 561, reproduced by permission of the Institution of Chemical Engineers.)...

Equations 23.6, 23.17 and 23.18 provide a complete model for steam turbines. 

Equation 23.25 has the same basic form as the linear Willans Line Equation used to model steam turbines. The basic assumption behind the use of Equation 23.25 is that the gas turbine would need to have a control system that would maintain a fixed fuel-to-air ratio and steam-to-air ratio at part-load. 

The gas turbine performance at part-load follows the same basic form as that for steam turbines illustrated in Figure 23.10, with the mass flowrate defined in terms of the mass flowrate of fuel. Thus, the part-load gas turbine performance can be modeled as4,9 ... 

Steam turbines are used to convert part of the energy of the steam into power and can be configured in different ways. Steam turbines can be divided into two basic classes back-pressure turbines and condensing turbines. The efficiency of the turbine and its power output depend on the flowrate of steam to the turbine. The performance characteristics can be modeled by a simple linear relationship over a reasonable range of operation. 

Site composite curves can be used to represent the site heating and cooling requirements thermodynamically. This allows the analysis of thermal loads and levels on site. Using the models for steam turbines and gas turbines allows cogeneration targets for the site to be established. Steam levels can be optimized to minimize fuel consumption or maximize cogeneration. A cost trade-off needs to be carried out in order to establish the optimum trade-off between fuel requirements and cogeneration. 

A steam turbine is operating between inlet steam of 40 barg and 420°C and outlet steam of 5 barg. Using the Willans Line Model with parameters from Table 23.1 for large turbines and intercept ratio of 0.05, calculate the power production for a turbine at full load with a flowrate of steam of 10 kg s-1. 

The third step is to model the components of the conceptual plant. For example, a steam turbine may be modeled as an adiabatic process with 85% isentropic efficiency. 

An interesting application of this approach in another field has been described by Keller (K2). In the design of steam turbines rather complicated heat-balance calculations are required. While each particular installation is different, and therefore requires a different mathematical model, the components of each turbine are always similar. A large-scale computer program was developed, therefore, which would through suitable instructions combine the calculations required for each component into an over-all heat balance for the turbine. 

It is important to have the correct set of variables specified as independent and dependent to meet the modeling objectives. For monitoring objectives observed conditions, including the aforementioned independent variables (FICs, TICs, etc.) and many of the "normally" (for simulation and optimization cases) dependent variables (FIs, TIs, etc.) are specified as independent, while numerous equipment performance parameters are specified as dependent. These equipment performance parameters include heat exchanger heat transfer coefficients, heterogeneous catalyst "activities" (representing the relative number of active sites), distillation column efficiencies, and similar parameters for compressors, gas and steam turbines, resistance-to-flow parameters (indicated by pressure drops), as well as many others. These equipment performance parameters are independent in simulation and optimization model executions. 

The problems encountered on the simple liquid system described above are met once again in accentuated form for example in the modelling of a steam turbine with several stages, as described in Chapters 15... 

In modeling a gas turbine in the context of steam and power system, the purpose is to know the fuel consumption (gfuei) for a given net power output (Wnet) and fuel efficiency. It is also important to know the exhaust mass flow (mex) and temperature (Tex), which determine the integration opportunity with steam turbine cycle. Gas turbine performance curves are provided by manufatcturer. As an example for ilustration, the key parameters are described by the following equations (Manninen and Zhu, 1999) ... 

The purpose is to develop a steam balance for operational supervision as well as for identification of improvement opportunities in the steam system. Models for boilers, turbines, deaerators (DAs), letdown valves, desuperheaters, and steam flash tanks are discussed in the previous chapter. Historian and distributed control system (DCS) data will be coimected to steam balance so that the steam balance is capable of dynamically balancing the steam and power demands due to process variations, units on or off, and weather change. 

Application Remarks You do not need to feel intimidated with the set of equations above. You will find the task simple when you follow the top-down approach to establish steam balances from boilers to each steam header, to steam turbines and letdown valves, and to deaerator and blowdown flash drum. The top-down approach for steam balance is discussed in detail in Chapter 16. During the process of setting up the steam balances, you could apply some of the equations above for modeling the equipment and subsystems. The steam balances can be conducted readily in a spreadsheet environment. 

---