Modelling the power production of single and multiple extraction steam turbines

doi:10.1016/j.ces.2010.01.016

Chemical Engineering Science

Volume 65, Issue 9, 1 May 2010, Pages 2811-2820

https://doi.org/10.1016/j.ces.2010.01.016 Get rights and content

Abstract

A thermodynamic model for the prediction of the operating performance of back pressure steam turbines with single and multiple extractions is presented. The approach takes the advantage of previous models reported in the literature and incorporates some improvements that allow for the prediction of the shaft work under changes in the operating conditions such as steam flow rate and pressure of each of the extractions. Simulation under changed operating conditions is conducted through the use of expressions that correlate the temperature and enthalpy of the steam as a function of the extraction pressure. The model incorporates the calculation of the isentropic efficiencies of each stage. The validity of the model is demonstrated by comparing the results with those of commercial turbines reported in the open literature.

Introduction

There are two aspects related to the thermal integration of steams turbines into background processes. One is the targeting of power ahead of design that commonly is carried out using approximate thermodynamic models and the second is the actual selection of the turbine that will do the job of simultaneously producing heat and power to satisfy the needs of the process. In this context, targeting and selection are issues that are closely related. This relation was rightly appreciated by Mavromatis and Kokossis (1998) who developed an approach known as the hardware model for steam turbines. This model is a novel tool for targeting the cogeneration potential in a process, since it is based on typical turbine performance data. However, in the process of reconciling targeting and selection, there is still a need to test the theoretical model against true equipment performance, particularly in sight of the need to predict power production under a range of mass flow rates and extraction pressures.

Cogeneration targets in process integration have been approached in various ways that go from the use of the graphical determination to the more elaborate models. The potential for cogeneration in a process can be approximated by representing the Grand Composite Curve (Linnhoff et al., 1982) in terms of the Carnot factor; this gives rise to the Exergy Grand Composite Curve (Dhole and Linnhoff, 1993). For large industrial complexes, a tool known as Total Site Composite Curve has been developed and this can be represented in terms of the Carnot factor as well (Klemes et al., 1997). The exergy model is based on the fact that for any heat transfer process, the area enclosed between a hot source and a cold sink is proportional to the exergy loss; however, if an ideal thermal engine (Carnot cycle) is placed in between, power will be generated. When the various steam levels that supply heat to a process are plotted on the Exergy Grand Composite Curve, the total area enclosed between these levels is related to the potential for shaft work production (Fig. 1, Fig. 2). This model provides an easy and straightforward method to target for shaft work potential; however, a real steam turbine (Rankine cycle) exhibits a different performance and predictions based on the Carnot cycle are not accurate.

In an attempt to eliminate the limitations of the ideal models based on exergy calculations, Raissi (1994) proposed a method to predict the shaft work production from single pass out turbines. The most important feature of this work is that the power output is assumed to be proportional to the mass flow rate and the difference of saturation temperatures between inlet and outlet conditions. This model does not incorporate the consideration of the variation of the thermal efficiency with turbine size or with the operating load. The work by Mavromatis and Kokossis (1998) overcomes these limitations; it is based on the assumption that the performance of a steam turbine is described by a linear relationship known as Willans line; with this approximation the relations between turbine size and efficiency and even the variation of turbine efficiency with load are readily incorporated. Later, Varbanov et al. (2004) proposed a slight modification to this model that consists in the determination of the power output as a function of coefficients which in turn are calculated from linear equations that depend on the saturation temperature difference between inlet and outlet conditions.

This work presents a modified thermodynamic model for the prediction of the thermal performance of back pressure steam turbines with single and multiple extractions. The model makes use of some of the advantages of the turbine hardware model (Mavromatis and Kokossis, 1998). The nominal power production of commercially available steam turbines is used to validate the reliability of this model.

Section snippets

Modified thermodynamic model

From an energy balance, the power output (W) of a single extraction back pressure steam turbine can be determined from: $W = m (h_{1} - h_{2})$ where m is the steam mass flow rate; h₁ and h₂ are the specific enthalpies at inlet and outlet conditions respectively. The enthalpy change (h₁−h₂) can be calculated using the expression for the isentropic efficiency: $η_{iso} = \frac{h_{1} - h_{2}}{h_{1} - h_{2 iso}}$ where, h₂_iso is the outlet specific enthalpy of the steam considering isentropic conditions. Combining Eqs. (1), (2) we obtain: $\frac{W}{η_{iso}} = m Δ h$

Model validation

The power output that is obtained from the application of the theoretical model using operating data from commercial steam turbines is compared to the actual nominal power output. Two other models reported in the literature are also solved to compare their accuracy. These models are the ones presented by Mavromatis and Kokossis (1998) and Varbanov et al. (2004). Table 2 shows the performance parameters of three commercial turbines. The details of the results obtained using the three models are

Model for multiple extraction turbines

In cogeneration schemes with multiple extractions, the process itself dictates the operating variables such as: the number of extractions, the pressure of the extractions, and the mass flow rate of each extraction. This is, the process determines the number of steam levels and the minimum temperature at which they must be available and this is also in direct connection with the maximum power output that can be generated. The number of extractions can be as big as eight (Cotton, 1993), however

Validation of the multiple extraction turbine model

Performance data of multiple extraction steam turbines are taken from the open literature and shown in Table 4. The model by Mavromatis and Kokossis (1998) and Varbanov et al. (2004) are again used to compare with the new model. From the results shown in Table 5, it can be seen that the prediction using the new model exhibits the lowest deviations from the nominal power output.

Performance prediction under changed operating conditions

The shaft work produced by a turbine with N extractions is given by (Shapiro and Moran, 2004): $W = (h_{1} - h_{2 r}) \sum_{k = 1}^{N} m_{k} + \sum_{j = 2}^{N} {[\sum_{k = j}^{N} m_{k}] (h_{(k) r} - h_{(k + 1) r})}$ where h₁ is the specific enthalpy of the steam fed to the turbine; h₂_r is the specific enthalpy of the first extraction; h₍_k₎_r and h₍_k₊₁₎_r are the specific enthalpies at the inlet and outlet of extraction “k” and m_k is the steam mass flow rate in each of the expansion stages. The values of m_k are determined as a function of the heat load required by the

Conclusions

The thermodynamic model presented in this paper aims at reconciling two important aspects related to the design of cogeneration systems using steam turbines and its thermal integration into background processes. These two aspects are: targeting the power production ahead of design and the selection of the actual turbine to be implemented. A targeting model must be accurate enough to predict the performance of a given turbine. This accuracy can be validated by comparing the results of the

Notation

Cp	specific heat capacity, kJ/kg °C
h₁	specific enthalpy of steam at inlet conditions, kJ/kg
h₂	specific enthalpy of steam at first extraction, kJ/kg
h₂_iso	isentropic specific enthalpy of steam at first extraction, kJ/kg
h₂_r	actual specific enthalpy of steam at first extraction, kJ/kg
h_HP	specific enthalpy of steam at high pressure, kJ/kg
h_HPsat	specific enthalpy of saturated steam at high pressure, kJ/kg
h_LP	specific enthalpy of steam at low pressure, kJ/kg
h_LPsat	specific enthalpy of saturated steam at low

Acknowledgments

The authors would like to thank the financial support from the Mexican Council of Science and Technology, CONACYT, and by the Mexican Council for Science and Technology of the State of Guanajuato, CONCYTEG.

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Modelling the power production of single and multiple extraction steam turbines

Abstract

Introduction

Section snippets

Modified thermodynamic model

Model validation

Model for multiple extraction turbines

Validation of the multiple extraction turbine model

Performance prediction under changed operating conditions

Conclusions

Notation

Acknowledgments

Applied Thermal Engineering

Chemical Engineering Science

Trans IChemE Part A

A Thermodynamic approach to the design and synthesis of plant utility systems

Ind. Engng Chem Res

Total site targets for fuel, co-generation, emissions and cooling

Comput Chem Engng