Properties of Steam – What is Steam

A pressurizer is a component of a pressurized water reactor. Pressure in the primary circuit of PWRs is maintained by a pressurizer, a separate vessel connected to the primary circuit (hot leg), and partially filled with water heated to the saturation temperature (boiling point) for the desired pressure by submerged electrical heaters. The temperature in the pressurizer can be maintained at 350 °C (662 °F), which gives a subcooling margin (the difference between the pressurizer temperature and the highest temperature in the reactor core) of 30 °C. Subcooling margin is a very important safety parameter of PWRs since the boiling in the reactor core must be excluded. The basic design of the pressurized water reactor includes such a requirement that the coolant (water) in the reactor coolant system must not boil. To achieve this, the coolant in the reactor coolant system is maintained at a pressure sufficiently high that boiling does not occur at the coolant temperatures experienced while the plant is operating or in an analyzed transient.

Functions

Pressure in the pressurizer is controlled by varying the temperature of the coolant in the pressurizer. For these purposes, two systems are installed. Water spray system and electrical heaters system. The volume of the pressurizer (tens of cubic meters) is filled with water on saturation parameters and steam. The water spray system (relatively cool water – from the cold leg) can decrease the pressure in the vessel by condensing the steam on water droplets sprayed in the vessel. On the other hand, the submerged electrical heaters are designed to increase the pressure by evaporating the water in the vessel. Water pressure in a closed system tracks water temperature directly; as the temperature rises, the pressure goes up.

Steam generators are heat exchangers that convert feedwater into steam from heat produced in a nuclear reactor core. The steam produced drives the turbine. They are used in most nuclear power plants, but there are many types according to the reactor type.

The hot primary coolant (water 330°C; 626°F; 16MPa) is pumped into the steam generator through the primary inlet. High pressure of primary coolant is used to keep the water in the liquid state. Boiling of the primary coolant shall not occur. The liquid water flows through hundreds or thousands of tubes (usually 1.9 cm in diameter) inside the steam generator. The feedwater (secondary circuit) is heated from ~260°C 500°F to the boiling point of that fluid (280°C; 536°F; 6,5MPa). Heat is transferred through the walls of these tubes to the lower pressure secondary coolant located on the secondary side of the exchanger where the coolant evaporates to pressurized steam (saturated steam 280°C; 536°F; 6,5 MPa). The pressurized steam leaves the steam generator through a steam outlet and continues to the steam turbine. Heat transfer is accomplished without mixing the two fluids to prevent the secondary coolant from becoming radioactive. The primary coolant leaves (water 295°C; 563°F; 16MPa) the steam generator through the primary outlet and continues through a cold leg to a reactor coolant pump and then into the reactor.

As seen from the phase diagram of water, in the two-phase regions (e.g.,, on the border of vapor/liquid phases), specifying temperature alone will set the pressure, and specifying pressure will set the temperature.

• The saturation vapor curve is the curve separating the two-phase state and the superheated vapor state in the T-s diagram.
• The saturated liquid curve is the curve separating the subcooled liquid state and the two-phase state in the T-s diagram.

If water exists as a liquid at the saturation temperature and pressure with a quality of x = 0, it is called a saturated liquid state (single-phase). If the liquid temperature is lower than the saturation temperature for the existing pressure, it is called a subcooled liquid or a compressed liquid. The term subcooling refers to a liquid existing at a temperature below its normal boiling point.  For example, water normally boils at 100°C (at atmospheric pressure); at room temperature 20°C, the water is termed “subcooled”. Analogically the subcooling is also defined in nuclear engineering but for another purpose.

For example, the temperature in the pressurizer can be maintained at 350 °C (662 °F), which gives a subcooling margin (the difference between the pressurizer temperature and the highest temperature in the reactor core) of 30 °C. Subcooling margin is a very important safety parameter of PWRs since the boiling in the reactor core must be excluded.

Wet steam is characterized by the vapor quality, which ranges from zero to unity – open interval (0,1). When the vapor quality is equal to 0, it is referred to as the saturated liquid state (single-phase). On the other hand, when the vapor quality is equal to 1, it is referred to as the saturated vapor state or dry steam (single-phase). Between these two states, we talk about vapor-liquid mixture or wet steam (two-phase mixture). At constant pressure, the addition of energy does not change the mixture’s temperature, but the vapor quality and specific volume change. In the case of dry steam (100% quality), it contains 100% of the latent heat available at that pressure. Saturated liquid water, with no latent heat and therefore 0% quality, will only contain sensible heat.

Typically most nuclear power plants operate multi-stage condensing steam turbines. In these turbines, the high-pressure stage receives steam (this steam is nearly saturated steam – x = 0.995 – point C at the figure) from a steam generator and exhausts it to a moisture separator-reheater (point D). The steam must be reheated to avoid damages caused to the steam turbine blades by low-quality steam. The reheater heats the steam (point D), and then the steam is directed to the low-pressure stage of the steam turbine, where it expands (point E to F). The exhausted steam is well below atmospheric pressure and is in a partially condensed state (point F), typically of a quality near 90%.

Specific Enthalpy of Wet Steam

The specific enthalpy of saturated liquid water (x=0) and dry steam (x=1) can be picked from steam tables. In the case of wet steam, the actual enthalpy can be calculated with the vapor quality, x, and the specific enthalpies of saturated liquid water and dry steam:

h_wet = h_s x + (1 – x ) h_l              

where

h_wet = enthalpy of wet steam (J/kg)

h_s = enthalpy of “dry” steam (J/kg)

h_l = enthalpy of saturated liquid water (J/kg)

As can be seen, wet steam will always have lower enthalpy than dry steam.

Specific Entropy of Wet Steam

Similarly, the specific entropy of saturated liquid water (x=0) and dry steam (x=1) can be picked from steam tables. In the case of wet steam, the actual entropy can be calculated with the vapor quality, x, and the specific entropies of saturated liquid water and dry steam:

s_wet = s_s x + (1 – x ) s_l              

where

s_wet = entropy of wet steam (J/kg K)

s_s = entropy of “dry” steam (J/kg K)

s_l = entropy of saturated liquid water (J/kg K)

Specific Volume of Wet Steam

Similarly, the specific volume of saturated liquid water (x=0) and dry steam (x=1) can be picked from steam tables. In the case of wet steam, the actual specific volume can be calculated with the vapor quality, x, and the specific volumes of saturated liquid water and dry steam:

v_wet = v_s x + (1 – x ) v_l              

where

v_wet = specific volume of wet steam (m³/kg)

v_s = specific volume of “dry” steam (m³/kg)

v_l = specific volume of saturated liquid water (m³/kg)

Example:

A high-pressure steam turbine stage operates at a steady state with inlet conditions of  6 MPa, t = 275.6°C, x = 1 (point C). Steam leaves this turbine stage at a pressure of 1.15 MPa, 186°C, and x = 0.87 (point D). Calculate the enthalpy difference between these two states.

The enthalpy for the state C can be picked directly from steam tables, whereas the enthalpy for the state D must be calculated using vapor quality:

h_{1, wet} = 2785 kJ/kg

h_{2, wet} = h_2,s x + (1 – x ) h_2,l  = 2782 . 0.87 + (1 – 0.87) . 790 = 2420 + 103 = 2523 kJ/kg

Δh = 262 kJ/kg

Dry steam, or saturated steam,  is characterized by vapor quality, which is equal to unity. When the vapor quality is equal to 0, it is referred to as the saturated liquid state (single-phase). On the other hand, when the vapor quality is equal to 1, it is referred to as the saturated vapor state or dry steam (single-phase). Between these two states, we talk about vapor-liquid mixture or wet steam (two-phase mixture). At constant pressure, the addition of energy does not change the mixture’s temperature, but the vapor quality and specific volume change. In the case of dry steam (100% quality), it contains 100% of the latent heat available at that pressure. Saturated liquid water, with no latent heat and therefore 0% quality, will only contain sensible heat.

Typically most nuclear power plants operate multi-stage condensing steam turbines. In these turbines, the high-pressure stage receives steam (this steam is nearly saturated steam – x = 0.995 – point C at the figure) from a steam generator and exhausts it to a moisture separator-reheater (point D). The steam must be reheated to avoid damages caused to the steam turbine blades by low-quality steam. The reheater heats the steam (point D), and then the steam is directed to the low-pressure stage of the steam turbine, where it expands (point E to F). The exhausted steam is well below atmospheric pressure and is in a partially condensed state (point F), typically of a quality near 90%.

As seen from the phase diagram of water, in the two-phase regions (e.g.,, on the border of vapor/liquid phases), specifying temperature alone will set the pressure, and specifying pressure will set the temperature.

• The saturation vapor curve is the curve separating the two-phase state and the superheated vapor state in the T-s diagram.
• The saturated liquid curve is the curve separating the subcooled liquid state and the two-phase state in the T-s diagram.

If steam exists entirely as vapor at saturation temperature, it is called saturated vapor, saturated steam, or dry steam. The dry saturated vapor is characterized by the vapor quality, which is equal to unity. Superheated vapor or superheated steam is a vapor at a temperature higher than its boiling point at the absolute pressure where the temperature is measured. The pressure and temperature of superheated vapor are independent properties since the temperature may increase while the pressure remains constant. The substances we call gases are highly superheated vapors.

The process of superheating water vapor in the T-s diagram is provided in the figure between state E and the saturation vapor curve. As can be seen, also wet steam turbines use superheated steam, especially at the inlet of low-pressure stages. The enthalpy must be obtained from the superheated steam tables to evaluate the cycle thermal efficiency.

The superheating process is the only way to increase the peak temperature of the Rankine cycle (and to increase efficiency) without increasing the boiler pressure. This requires another type of heat exchanger called a superheater, which produces superheated steam.

In the superheater, further heating at fixed pressure results in increases in both temperature and specific volume. The process of superheating in the T-s diagram is provided in the figure between state E and the saturation vapor curve.

Typically most nuclear power plants operate multi-stage condensing steam turbines. In these turbines, the high-pressure stage receives steam (this steam is nearly saturated steam – x = 0.995 – point C at the figure) from a steam generator and exhausts it to a moisture separator-reheater (point D). The steam must be reheated or superheated to avoid damages caused to the blades of the steam turbine by low-quality steam. High content of water droplets can cause rapid impingement and erosion of the blades, which occurs when condensed water is blasted onto the blades. To prevent this, condensate drains are installed in the steam piping leading to the turbine. The reheater heats the steam (point D), and then the steam is directed to the low-pressure stage of the steam turbine, where it expands (point E to F). The exhausted steam is well below atmospheric pressure and is in a partially condensed state (point F), typically of a quality near 90%.

Calculate heat required to evaporate 1 kg of water at the atmospheric pressure (p = 1.0133 bar) and at the temperature of 100°C.

Solution:

Since these parameters correspond to the saturated liquid state, only latent heat of 1 kg of water vaporization is required. From steam tables, the latent heat of vaporization is L = 2257 kJ/kg. Therefore the heat required is equal to:

ΔH = 2257 kJ

Note that the initial specific enthalpy h₁ = 419 kJ/kg, whereas the final specific enthalpy will be h₂ = 2676 kJ/kg. The specific enthalpy of low-pressure dry steam is very similar to the specific enthalpy of high-pressure dry steam, despite having different temperatures.

Calculate heat required to evaporate 1 kg of feedwater at the pressure of 6 MPa (p = 60 bar) and at the temperature of 275.6°C (saturation temperature).

Solution:

Since these parameters correspond to the saturated liquid state, only latent heat of 1 kg of water vaporization is required. From steam tables, the latent heat of vaporization is L = 1571 kJ/kg. Therefore the heat required is equal to:

ΔH = 1571 kJ

Note that the initial specific enthalpy h₁ = 1214 kJ/kg, whereas the final specific enthalpy will be h₂ = 2785 kJ/kg. The specific enthalpy of low-pressure dry steam is very similar to the specific enthalpy of high-pressure dry steam, despite having different temperatures.

Calculate the amount of primary coolant, which is required to evaporate 1 kg of feedwater in a typical steam generator. Assume that there are no energy losses. This is only an idealized example.

Balance of the primary circuit

The hot primary coolant (water 330°C; 626°F; 16MPa) is pumped into the steam generator through the primary inlet. The primary coolant leaves (water 295°C; 563°F; 16MPa) the steam generator through the primary outlet.

h_{I, inlet} = 1516 kJ/kg

=> Δh_I = -206 kJ/kg

h_{I, outlet} = 1310 kJ/kg

Balance of the feedwater

The feedwater (water 230°C; 446°F; 6,5MPa) is pumped into the steam generator through the feedwater inlet. The feedwater (secondary circuit) is heated from ~230°C 446°F to the boiling point of that fluid (280°C; 536°F; 6,5MPa). Feedwater is then evaporated, and the pressurized steam (saturated steam 280°C; 536°F; 6,5 MPa) leaves the steam generator through the steam outlet and continues to the steam turbine.

h_{II, inlet} = 991 kJ/kg

=> Δh_II = 1789 kJ/kg

h_{II, outlet} = 2780 kJ/kg

Balance of the steam generator

Since the difference in specific enthalpies is less for primary coolant than for feedwater, it is obvious that the amount of primary coolant will be higher than 1kg. To produce of 1 kg of saturated steam from feedwater, about 1789/206 x 1 kg =  8.68 kg of primary coolant is required.

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