Supplementary Backward Equations v(p,T) for the Critical and Supercritical Regions (Region 3) of the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
H.-J. Kretzschmar ◽  
A. H. Harvey ◽  
K. Knobloch ◽  
R. Mareš ◽  
K. Miyagawa ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
Critical Point ◽  
International Association ◽  
Computing Time ◽  
Computer Time ◽  
Singular Behavior ◽  
Steam Power ◽  
Power Cycles ◽  
Independent Variables ◽  
Iterative Procedures

When steam power cycles are modeled, thermodynamic properties as functions of pressure and temperature are required in the critical and supercritical regions (region 3 of IAPWS-IF97). With IAPWS-IF97, such calculations require cumbersome iterative calculations, because temperature and volume are the independent variables in the formulation for this region. In order to reduce the computing time, the International Association for the Properties of Water and Steam (IAPWS) adopted a set of backward equations for volume as a function of pressure and temperature in region 3. The necessary numerical consistency is achieved by dividing the region into 20 subregions, plus auxiliary subregions near the critical point in which the consistency requirements are relaxed due to the singular behavior at the critical point. In this work, we provide complete documentation of these equations, along with a discussion of their numerical consistency and the savings in computer time. The numerical consistency of these equations should be sufficient for most applications in heat-cycle, boiler, and steam-turbine calculations; if even higher consistency is required, the equations may be used to generate guesses for iterative procedures.

Supplementary Backward Equations p(h,s) for the Critical and Supercritical Regions (Region 3), and Equations for the Two-Phase Region and Region Boundaries of the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam

2007 ◽  
Vol 129 (4) ◽  
pp. 1125-1137 ◽  
Author(s):  
H.-J. Kretzschmar ◽  
J. R. Cooper ◽  
J. S. Gallagher ◽  
A. H. Harvey ◽  
K. Knobloch ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
Steam Turbine ◽  
International Association ◽  
Computing Time ◽  
Phase Region ◽  
Specific Enthalpy ◽  
Two Phase ◽  
Steam Power ◽  
Power Cycles ◽  
Backward Equation

When steam power cycles are modeled, thermodynamic properties as functions of enthalpy and entropy are required in the critical and supercritical regions (region 3 of IAPWS-IF97). With IAPWS-IF97, these calculations require cumbersome two-dimensional iteration of temperature T and specific volume v from specific enthalpy h and specific entropy s. While these calculations are not frequently required, the computing time can be significant. Therefore, the International Association for the Properties of Water and Steam (IAPWS) adopted backward equations for p(h,s) in region 3. For calculating properties as a function of h and s in the part of the two-phase region that is important for steam-turbine calculations, a backward equation Tsat(h,s) is provided. In order to avoid time-consuming iteration in determining the region for given values of h and s, equations for the region boundaries were developed. The numerical consistency of the equations documented here is sufficient for most applications in heat-cycle, boiler, and steam-turbine calculations.

Supplementary Backward Equations T(p,h), v(p,h), and T(p,s), v(p,s) for the Critical and Supercritical Regions (Region 3) of the Industrial Formulation IAPWS-IF97 for Water and Steam

2006 ◽  
Vol 129 (1) ◽  
pp. 294-303 ◽  
Author(s):  
H.-J. Kretzschmar ◽  
J. R. Cooper ◽  
A. Dittmann ◽  
D. G. Friend ◽  
J. S. Gallagher ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
Specific Volume ◽  
International Association ◽  
Computing Time ◽  
Saturation Pressure ◽  
Two Dimensional ◽  
Steam Power ◽  
Power Cycles ◽  
Computational Speed ◽  
Boundary Equations

In modeling advanced steam power cycles, thermodynamic properties as functions of pressure and enthalpy (p,h) or pressure and entropy (p,s) are required in the critical and supercritical regions (region 3 of IAPWS-IF97). With IAPWS-IF97, these calculations require cumbersome two-dimensional iteration of temperature T and specific volume v from (p,h) or (p,s). While these calculations in region 3 are not frequently required, the computing time can be significant. Therefore, the International Association for the Properties of Water and Steam (IAPWS) adopted backward equations for T(p,h), v(p,h), T(p,s), and v(p,s) in region 3, along with boundary equations for the saturation pressure as a function of enthalpy, p3sat(h), and of entropy, p3sat(s). Using the new equations, two-dimensional iteration can be avoided. The numerical consistency of temperature and specific volume obtained in this way is sufficient for most uses. This paper summarizes the need and the requirements for these equations and gives complete numerical information. In addition, numerical consistency and computational speed are discussed.

Supplementary Backward Equations for Pressure as a Function of Enthalpy and Entropy p(h,s) to the Industrial Formulation IAPWS-IF97 for Water and Steam

2004 ◽  
Vol 128 (3) ◽  
pp. 702-713 ◽  
Author(s):  
H.-J. Kretzschmar ◽  
J. R. Cooper ◽  
A. Dittmann ◽  
D. G. Friend ◽  
J. S. Gallagher ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
International Association ◽  
Computing Time ◽  
Liquid Region ◽  
Two Dimensional ◽  
Power Cycles ◽  
Enthalpy And Entropy ◽  
Basic Equations ◽  
Time Required ◽  
Fundamental Equations

In modeling steam power cycles, thermodynamic properties as functions of the variables enthalpy and entropy are required in the liquid and the vapor regions. It is difficult to perform these calculations with IAPWS-IF97, because they require two-dimensional iterations calculated from the IAPWS-IF97 fundamental equations. While these calculations are not frequently required, the relatively large computing time required for two-dimensional iteration can be significant in process modeling. Therefore, the International Association for the Properties of Water and Steam (IAPWS) adopted backward equations for pressure as a function of enthalpy and entropy p(h,s) as a supplement to the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam (IAPWS-IF97) in 2001. These p(h,s) equations are valid in the liquid region 1 and the vapor region 2. With pressure p, temperature T(h,s) can be calculated from the IAPWS-IF97 backward equations T(p,h). By using the p(h,s) equations, the two dimensional iterations of the IAPWS-IF97 basic equations can be avoided. The numerical consistency of pressure and temperature obtained in this way is sufficient for most heat cycle calculations. This paper summarizes the need and the requirements for the p(h,s) equations and gives complete numerical information about the equations. Moreover, the achieved quality of the equations and their use in the calculation of the backward function T(h,s) is presented. The three aspects, numerical consistency with the IAPWS-IF97 basic equations, consistency along subregion boundaries, and computational speed important for industrial use are discussed.

Assessment of the Computing Time for the IAPWS-IF97 Equations

2006 ◽  
Vol 129 (3) ◽  
pp. 885-887 ◽  
Author(s):  
Kiyoshi Miyagawa
Keyword(s):  
Thermodynamic Properties ◽  
Simple Structure ◽  
Computer Systems ◽  
Computing Time ◽  
Ordinary Water ◽  
Independent Variables ◽  
Modern Computer ◽  
Water Substance

Computing times of equations based on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam (IAPWS-IF97) were tested. Modern computer systems are optimized for “simple” computational operations, which favors the simple structure of IAPWS-IF97. Provision of “backward equations,” which are approximation of inverse equations, is one of the features of IAPWS-IF97. The backward equations showed much shorter computing times than iterative routines, which had been used to calculate with several independent variables. IAPWS-IF97 is faster than the equations of IAPWS Formulation 1995 for the Thermodynamic properties of Ordinary Water Substance for General and Scientific Use (IAPWS-95) by factors 70 to 200 times.

A Rational Equation of State for Water and Water Vapor in the Critical Region

1964 ◽  
Vol 86 (3) ◽  
pp. 320-326 ◽  
Author(s):  
E. S. Nowak
Keyword(s):  
Water Vapor ◽  
Equation Of State ◽  
Thermodynamic Properties ◽  
Specific Heat ◽  
Critical Point ◽  
Critical Region ◽  
Constant Pressure ◽  
Parametric Equation ◽  
Enthalpy And Entropy ◽  
Specific Volumes

A parametric equation of state was derived for water and water vapor in the critical region from experimental P-V-T data. It is valid in that part of the critical region encompassed by pressures from 3000 to 4000 psia, specific volumes from 0.0400 to 0.1100 ft3/lb, and temperatures from 698 to 752 deg F. The equation of state satisfies all of the known conditions at the critical point. It also satisfies the conditions along certain of the boundaries which probably separate “supercritical liquid” from “supercritical vapor.” The equation of state, though quite simple in form, is probably superior to any equation heretofore derived for water and water vapor in the critical region. Specifically, the deviations between the measured and computed values of pressure in the large majority of the cases were within three parts in one thousand. This coincides approximately with the overall uncertainty in P-V-T measurements. In view of these factors, the author recommends that the equation be used to derive values for such thermodynamic properties as specific heat at constant pressure, enthalpy, and entropy in the critical region.

scholarly journals Comparison of Li2CO3-Na2CO3-K2CO3, KCl-MgCl2 and NaNO3-KNO3 as heat transfer fluid for different sCO2 and steam power cycles in CSP tower plant under different DNI conditions

2021 ◽  
Vol 13 (4) ◽  
pp. 168781402110119
Author(s):  
Kamran Mahboob ◽  
Awais A Khan ◽  
Muhammad Adeel Khan ◽  
Jawad Sarwar ◽  
Tauseef A Khan
Keyword(s):  
Heat Transfer ◽  
Power Plant ◽  
Rankine Cycle ◽  
Capacity Factor ◽  
Solar Thermal ◽  
Heat Transfer Fluid ◽  
Incident Power ◽  
Steam Power ◽  
Power Cycles ◽  
Plant Configuration

This work presents the characteristics of a solar thermal tower power plant in two different places (Seville and Dubai) using three different HTFs (NaNO3-KNO3, KCl-MgCl2 and Li2CO3-Na2CO3-K2CO3) and three different power cycles (Rankine, sCO2 Recompression and sCO2 Partial cooling cycles). An indirect configuration is considered for the Gemasolar power plant. Detailed modelling is carried out for the conversion of incident power on the heliostat to the output electricity. Optimization of the cycle is carried out to determine the most promising cycle configuration for efficiency. The results showed that for the Gemasolar power plant configuration, the performance of the KCl-MgCl2 based plant was poorest amongst all. NaNO3-KNO3 based plant has shown good performance with the Rankine cycle but plant having Li2CO3-Na2CO3-K2CO3 as HTF was best for all three cycles. Partial cooling was the best performing cycle at both locations with all three HTFs. Placing the Seville Plant in Dubai has improved the efficiency from 23.56% to 24.33%, a capacity factor improvement of 21 and 52 GW additional power is generated. The optimization of the plant in Dubai has shown further improvements. The efficiency is improved, the Capacity factor is increased by 31.2 and 77.8 GW of additional electricity is produced.

Water Production from Exhaust Gases of Steam Power Plants

1979 ◽  
Vol 101 (4) ◽  
pp. 677-679
Author(s):  
N. Papageorgiou
Keyword(s):  
Natural Gas ◽  
Power Plants ◽  
Water Production ◽  
Economic Aspects ◽  
Steam Generators ◽  
Steam Power ◽  
Power Cycles ◽  
Exhaust Gases ◽  
Steam Power Plants ◽  
Nontraditional Method

An attractive and nontraditional method for water production is presented in this paper. The proposed method is to condense the exhaust gases of the natural gas fired steam generators of power plants. In order to achieve this, it is necessary that modification of the convectional steam power cycles be accomplished without sacrificing the efficiency of the power plants. An investigation and modification of the power cycles is proposed. Economic aspects are also considered.

Computation of Thermodynamic Properties of Carbon Dioxide in the Range 0–750 Deg C

1970 ◽  
Vol 92 (3) ◽  
pp. 301-309 ◽  
Author(s):  
G. Angelino ◽  
E. Macchi
Keyword(s):  
Carbon Dioxide ◽  
Thermal Properties ◽  
High Temperature ◽  
Thermodynamic Properties ◽  
Thermodynamic Functions ◽  
Critical Region ◽  
Density Measurement ◽  
Working Fluid ◽  
Power Cycles ◽  
Wide Range

The computation of power cycles employing carbon dioxide as working fluid and extending down to the critical region requires the knowledge of the thermodynamic properties of CO2 within a wide range of pressures and temperatures. Available data are recognized to be insufficient or insufficiently accurate chiefly in the vicinity of the critical dome. Newly published density and specific heat measurements are employed to compute thermodynamic functions at temperatures between 0 and 50 deg C, where the need of better data is more urgent. Methods for the computation of thermal properties from density measurement in the low and in the high temperature range are presented and discussed. Results are reported of the computation of entropy and enthalpy of CO2 in the range 150–750 deg C and 40–600 atm. The probable precision of the tables is inferred from an error analysis based on the generation, by means of a computer program of a set of pseudoexperimental points which, treated as actual measurements, yield useful information about the accuracy of the calculation procedure.

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