Download Steam - Nuclear Community

Revision 1
December 2014
Steam
Student Guide
GENERAL DISTRIBUTION
GENERAL DISTRIBUTION: Copyright © 2014 by the National Academy for Nuclear Training. Not for sale
or for commercial use. This document may be used or reproduced by Academy members and participants.
Not for public distribution, delivery to, or reproduction by any third party without the prior agreement of the
Academy. All other rights reserved.
NOTICE: This information was prepared in connection with work sponsored by the Institute of Nuclear Power
Operations (INPO). Neither INPO, INPO members, INPO participants, nor any person acting on behalf of them
(a) makes any warranty or representation, expressed or implied, with respect to the accuracy, completeness, or
usefulness of the information contained in this document, or that the use of any information, apparatus, method,
or process disclosed in this document may not infringe on privately owned rights, or (b) assumes any liabilities
with respect to the use of, or for damages resulting from the use of any information, apparatus, method, or
process disclosed in this document.
ii
Table of Contents
INTRODUCTION................................................................................................................... 2
TLO 1 THERMODYNAMIC PROPERTIES OF STEAM .............................................................. 3
Overview ....................................................................................................................... 3
ELO 1.1 Steam Terms ................................................................................................... 4
ELO 1.2 Phase Changes .............................................................................................. 14
ELO 1.3 Property Diagrams ........................................................................................ 21
ELO 1.4 Steam Tables and Mollier Diagrams ............................................................ 30
TLO 1 Summary .......................................................................................................... 46
STEAM SUMMARY ............................................................................................................ 50
iii
This page is intentionally blank.
iv
Steam
Revision History
Revision
Date
Version
Number
Purpose for Revision
Performed
By
11/5/2014
0
New Module
OGF Team
12/11/2014
1
Added signature of OGF
Working Group Chair
OGF Team
Rev 1
1
Introduction
It is necessary to transmit the thermal energy released during the fission
process through a complex network of plant systems that
thermodynamically connect the reactor core to the main turbine generator.
Each of these systems uses water in one state or another as the working
fluid. The reactor coolant system (RCS) uses subcooled water to transfer
the fission heat to the steam generators (SGs), while the pressurizer portion
of the RCS operates at saturated conditions.
The secondary side of the SGs produce dry saturated or superheated steam
for use in the high-pressure main turbine, then superheat the steam for use
in the low-pressure turbines. The exhausted steam condenses to a
subcooled liquid in the condenser, then the condensate/feedwater heaters
reheat it and it travels on its way back to the SGs to start the cycle again.
This cycle uses water in many states and phases to carry out energy transfer
from the reactor core to the main turbine.
Understanding these energy conversions requires studying the interplay of
three significant thermal sciences ( heat transfer, thermodynamics, and fluid
flow) as they relate to the normal and abnormal operation of the plant. This
course will review the nature and behavior of water as they relate to the
various energy-conversion processes.
Thermodynamic Properties of Steam Importance
Water is the most commonly used working fluid in thermodynamic cycles
because it is abundant and has a high specific heat capacity and critical
temperature. Water can exist in various states, which makes it useful as
both a liquid and vapor for various thermodynamic processes.
Steam is water in its vapor form and, since it is easy to convert water into
steam, power generation uses water as the standard working fluid and for
heat removal. Due to steam’s high heat capacity, a relatively small mass of
steam can store and transport a large amount of thermal energy. Steam’s
large heat capacity allows the use of smaller equipment to deliver or convert
the thermal energy to a required power output.
Substances exist as either solids or fluids in nature. A solid is a substance
that has a definite volume and shape and resists forces that tend to alter
these properties. A fluid is a substance that flows, has no fixed shape, and
yields easily to external pressure. Fluid is a broad classification that
includes liquids, vapors, and gases. The relatively free movement of its
molecules within a nearly constant volume characterizes a liquid.
Gases and vapors do not have an independent shape or volume, but have a
tendency to expand freely to fill any available space (regardless of the
quantity of the substance). Gases and vapors are essentially equivalent and
differ only in context; both can be converted into liquids by raising their
pressure and/or decreasing their temperature. Gases, however, are in the
low-density form at "normal" temperatures and pressures (e.g. 14.7 psig and
2
Rev 1
68°F), whereas "vapors" are typically in the liquid form under these
conditions; higher temperatures would convert these substances to gaseous
form.
Because steam vapor is so important to thermodynamic processes, reliable
and accurate tests have established many of its properties. Mollier diagrams
and steam tables provide properties in graphical and tabulated forms,
respectively.
The operator must be proficient in the use of steam tables and the Mollier
diagram to determine the specific properties of the working fluid at any
location in the primary or secondary system.
Objectives
At the completion of this training session, the trainee will demonstrate
mastery of this topic by passing a written exam with a grade of 80 percent
or higher on the following Terminal Learning Objective (TLO):
1. Use Mollier diagrams and steam tables to determine properties of a
fluid.
TLO 1 Thermodynamic Properties of Steam
Overview
Thermodynamic Properties of Steam
This chapter will introduce the terms associated with liquids and vapors and
demonstrate the use of the steam tables and Mollier diagram to determine
fluid properties.
Operators routinely use steam tables and must be able to quickly and
efficiently determine required properties, such as degrees of subcooling or
superheat. This chapter will prepare the operator to perform these tasks.
Objectives
Upon completion of this lesson, you will be able to do the following:
1. Define the following terms:
a. Saturation
b. Subcooled liquid
c. Superheated vapor
d. Critical point
e. Triple point
f. Vapor pressure curve
g. Quality
h. Moisture content
i. Vaporization line
j. Saturated liquid
k. Wet vapor
Rev 1
3
l. Saturated vapor
m. Supersaturated vapor
n. Sublimation
o. Vaporization
p. Condensation
q. Fusion
2. Predict the effect phase changes will have on plant response.
3. Describe the following types of property diagrams:
a. Pressure-temperature diagram
b. Pressure-specific volume diagram
c. Pressure-enthalpy diagram
d. Enthalpy-temperature diagram
e. Temperature-entropy diagram
f. Mollier diagram
4. Describe the use of steam tables and Mollier diagrams, and when
given sufficient information to indicate the state of the fluid,
determine any unknown properties for the fluid.
ELO 1.1 Steam Terms
Introduction
Most power plants use water as the working fluid to take advantage of the
large amounts of energy transferred during a phase change from liquid to
vapor or from vapor to liquid. This section will introduce thermodynamic
terms that will be used to describe the various states and processes that
water goes through when making a phase change.
Classification of Properties
Properties are classified as either intensive or extensive. Intensive
properties are independent of the amount of mass present and extensive
properties are a function of the amount of mass present. Properties such as
pressure, temperature, and density are intensive, whereas volume and mass
are extensive. If we analyzed half of the RCS, it would have the same
temperature, pressure, and density as the entire RCS, but only one-half the
volume and mass.
Thermodynamic calculations are typically performed on a per-unit-mass
level. We accomplish this by using intensive properties and/or dividing
external properties by the total mass (to obtain new intensive properties).
For example, the volume per unit mass is called the specific volume:
𝑣≡
𝑉
𝑀
The internal energy per unit mass is called the specific internal energy:
𝑢≡
4
𝑈
𝑀
Rev 1
Intensive properties are useful because they are independent of material
amounts and, therefore, can be tabulated or graphed without reference to the
amount of material under study.
The figure below shows a cylinder partially full of water with the water
supporting a piston. The specifics discussed below will illustrate intensive
properties.
Figure: Piston-Cylinder Arrangement
The above piston-cylinder system contains 1 lbm of water at 60°F. The
piston maintains a constant pressure of 14.7 psia in the cylinder. As we
transfer heat to the water, its temperature will increase. This will increase
the water’s specific volume slightly, while the pressure remains constant
(since the piston is free to move). When the temperature reaches 212°F,
additional heat transfer results in a phase change (i.e. boiling), as indicated
in the second frame above.
Boiling steadily converts the liquid into vapor (as long as heat addition
continues), and temperature and pressure will remain constant while the
specific volume increases. Upon conversion of all the liquid to vapor,
further addition of heat results in an increase in both temperature (i.e.
superheating) and specific volume of the vapor.
In this example, the temperature, pressure, and specific volume are
intensive properties, which are independent of the total mass of the system,
but provide useful information about the state of the water and its individual
phases.
State
The properties of a substance include pressure, temperature, specific
volume, and internal energy. When two or more properties of a substance
are fixed, the state of the substance is established. When a property
changes, a "change of state" has occurred. Every state is unique in that
every property has one and only one value at that state.
Rev 1
5
Pressure and temperature are common properties used to define a state
because they are easy to measure with commonplace instruments. Some
substances, however, require that a third property be determined, such as
internal energy or specific volume, to find the state.
For instance, 60°F water at atmospheric pressure is enough to define the
state of a subcooled (compressed) liquid. But if the temperature is 212°F at
atmospheric conditions, the fluid could exist anywhere between a saturated
liquid and a saturated vapor. Therefore, we need a third property, such as
specific volume, to define the state.
Phase
We use the molecular structure of a substance to define the phase. Phases
include solids, liquids, vapors, gases, and plasmas. Solid, liquid, and gas
phases are familiar, but the vapor phase may be difficult to distinguish from
the liquid or gas phase depending on its properties. The plasma phase will
not be discussed here since it involves ionized particles whose behavior is
primarily controlled by the electromagnetic forces acting upon them and do
not occur during plant operation.
Changes in Phase and State
A phase change is indicative of a change in molecular or atomic spacing.
Melting occurs when the fluid changes from the solid phase to the liquid
phase. Solidification is the opposite change, as the fluid goes from liquid
phase to solid phase. Vaporization is the change from liquid phase to
gaseous (or vapor) phase while condensation describes the opposite phase
change, from vapor to liquid. Sublimation is a direct change from a solid
phase to a gas phase with no liquid phase present.
We will examine thermodynamic processes in later discussions. For now,
all we need to know is that a thermodynamic process occurs whenever a
working substance changes state. During the change in state, a phase
change may or may not take place. For example, water boiling in an SG
undergoes a change of state and phase. On the other hand, a pump can
increase water pressure, causing the water to undergo a change in state
(pressure, temperature, and density have been changed by the pump) with
no change in phase.
Saturation
Saturation is a condition in which a vapor and liquid exist together in
equilibrium. The temperature at which this occurs for a liquid-vapor
mixture is called the saturation temperature (or boiling point) and the
pressure is referred to as the saturation pressure. For water at 212°F, the
saturation pressure is 14.7 psia; for water at 14.7 psia, the saturation
temperature is 212°F.
For any pure substance, there is a distinct relationship between saturation
pressure and saturation temperature; the higher the pressure, the higher the
6
Rev 1
saturation temperature (and vice versa). A vapor-liquid mixture is at
saturation whenever the conditions of pressure and temperature fall on the
vapor-pressure curve, as shown below.
Figure: Vapor-Pressure Curve
Saturated and Subcooled Liquids
A saturated liquid is one that exists at its saturation temperature and
pressure. It is a substance in which any drop in pressure and/or rise in
temperature will cause it to boil.
A substance that exhibits a temperature that is lower than the saturation
temperature for its existing pressure is called a subcooled liquid (which
implies that the temperature is lower than the saturation temperature for the
given pressure) or a compressed liquid (which implies that the pressure is
greater than the saturation pressure for the given temperature). These terms
are interchangeable.
Vapor pressure is the pressure of a fluid at which the liquid and vapor
phases are in equilibrium for a given temperature.
The degree of subcooling in a liquid is the difference between the actual
temperature of the liquid and its saturation temperature. We calculate
subcooling as follows:
𝑆𝑢𝑏𝑐𝑜𝑜𝑙𝑖𝑛𝑔 = 𝑇𝑠𝑎𝑡 − 𝑇𝑎𝑐𝑡𝑢𝑎𝑙
Quality
A mixture that is part liquid and part vapor (i.e. under saturation conditions)
has a property referred to as quality (x), which is defined as the ratio of the
mass of the vapor to the total mass of both vapor and liquid:
𝑥=
𝑚𝑣𝑎𝑝𝑜𝑟
𝑚𝑙𝑖𝑞𝑢𝑖𝑑 + 𝑚𝑣𝑎𝑝𝑜𝑟
Rev 1
7
If the masses of vapor and liquid in a saturated mixture are 0.2 lbm and 0.8
lbm, respectively, the quality is 0.2 or 20%. Quality is an intensive property
that is only appropriate for saturated mixtures. The area under the bellshaped temperature vs. specific volume (T-v) curve below shows the region
in which quality is defined.
Figure: T-v Diagram Showing the Saturation Region
Moisture Content
The amount of liquid present in a liquid-vapor mixture is the moisture
content of the vapor. Moisture content (M) is defined as the ratio of the
mass of the liquid to the total mass of both liquid and vapor. The moisture
content for the previous example would be 0.8 or 80 percent. The following
equations show how to calculate the moisture content of a mixture and the
relationship between quality and moisture content.
𝑀=
𝑚𝑣𝑎𝑝𝑜𝑟
𝑚𝑙𝑖𝑞𝑢𝑖𝑑 + 𝑚𝑣𝑎𝑝𝑜𝑟
𝑀 = 1−𝑥
Example of the relationship between quality and moisture content of a
saturated fluid:
The moisture content of the liquid-vapor mixture is 86 percent. What is the
steam quality?
𝑥 = 1−𝑀
𝑥 = 1 − 0.86
𝑥 = 0.14 = 14%
8
Rev 1
Saturated, Supersaturated, and Superheated Vapors
A saturated vapor is a substance that exists as a pure vapor at saturation
temperature and pressure. It is a substance in which any drop in
temperature and/or rise in pressure will cause it to condense. The term "dry
saturated vapor" indicates that the quality is 100 percent and the moisture
content is 0 percent.
A vapor that exists at a temperature that is greater than its saturation
temperature is a superheated vapor. In a superheated vapor (like a
subcooled liquid), the pressure and temperature are independent properties
since the temperature may increase while the pressure remains constant (and
vice versa); hence, only these two properties are necessary to identify the
state of the substance.
A supersaturated vapor is a moisture-free gas that results from the rapid
cooling and/or depressurization of a superheated vapor. This is a
metastable state which will exist only briefly and results from the fact that
phase changes do not take place instantaneously.
For example, supersaturation is frequently encountered in steam turbines
where the expansion associated with the pressure drop across a nozzle
occurs in about 0.0002 seconds. When only slightly superheated (or with a
quality of nearly 100 percent), steam enters a nozzle and the pressure drop
causes the steam to reach a saturated condition, water droplets should
appear immediately; however, the expansion takes place so rapidly that
there is a delay before moisture particles begin to form and equilibrium is
reestablished. This phenomenon is real and a matter for consideration in the
design of steam turbines.
Constant Pressure Heat Addition
The temperature-specific volume diagram shown in the following figure is
convenient for depicting the changes in state upon adding heat to water at a
constant pressure.
Rev 1
9
Figure: T-v Diagram
For example, point A represents an initial subcooled liquid at 14.7 psia and
60°F. Point B represents the saturated-liquid condition at 212°F. Line AB,
therefore, represents the thermodynamic process in which we heat a liquid
from an initial temperature to its saturation temperature. The heat added
during process AB results in a temperature increase (i.e. sensible heat).
At point B, the continued addition of heat leads to a phase change and no
longer results in a temperature increase (i.e. it is latent heat). The added
heat vaporizes more and more of the liquid until reaching point C (the
saturated-vapor state). Line BC is the constant-temperature process in
which the change of phase from liquid to vapor occurs. Line CD represents
the constant-pressure process in which steam becomes superheated. During
this process, both temperature and specific volume increase.
Repeating the process at a higher constant pressure of 100 psia results in
line EFGH. Starting point E indicates that the initial specific volume for a
more highly compressed liquid is slightly less than that at 14.7 psia and
60°F. The higher-pressure liquid requires the addition of more sensible
heat, and vaporization begins at point F, where the temperature is 327.8°F.
Point G is the saturated-vapor state, and line GH is the constant-pressure
process in which the steam is superheated.
In a similar manner, heat addition at a constant pressure of 1,000 psia
results in line IJKL, with a saturation temperature of 544.6°F.
Critical Point
The critical point is the highest temperature and pressure at which a gas and
liquid can exist in equilibrium as distinguishable phases. At or above the
critical point, no definable phase change occurs. At temperatures above the
10
Rev 1
critical point (705.47°F), the substance cannot exist as a liquid, no matter
how great a pressure we exert upon it.
When adding heat at a constant pressure of 3,206.2 psia, as represented by
line MNO, there is no constant-temperature vaporization process (as found
at lower pressures). Rather, at point N (the critical point), the saturatedliquid and saturated-vapor states are essentially identical. The critical
temperature and critical pressure are the temperature and pressure,
respectively at the critical point.
Line PQ represents a constant-pressure heat-addition process in which the
pressure is greater than the critical pressure. Above the critical point, there
is no definite change in phase from liquid to vapor and no definite point at
which there is a change from the liquid phase to the vapor phase. At
pressures above the critical pressure and temperature less than the critical
temperature, the substance is a liquid. At pressures above the critical
pressure and temperature greater than the critical temperature, the substance
is a vapor or gas.
The line NJFB represents saturated-liquid and the line NKGC represents
saturated-vapor.
A pressure-temperature (P-T) diagram shows the lines of equilibrium with
respect to pressure and temperature of any pure substance. The lines
separate the phases of the substance. The sublimation line separates the
solid and vapor phases. The fusion line separates the solid and liquid
phases, and the vaporization line separates the liquid and vapor phases.
The P-T diagram shown in the figure below includes these lines, and the
point where they meet, called the triple point. The triple point is the only
point where all three phases can exist at once in equilibrium.
Figure: P-T Diagram
Rev 1
11
Fusion
Consider a solid substance at a low initial temperature and high initial
pressure (such as Point 1, in the above figure). As sensible heat is added at
constant pressure, the line that characterizes the process moves to the right
on the P-T diagram, until the fusion line is reached. At this point, any
further addition of latent heat will not result in a temperature increase;
rather, the energy will be used to melt the solid and turn it into a liquid.
The latent heat of fusion is the amount of heat we must add to melt a solid
(of unit mass) at a constant pressure. This property is equivalent to the
change in the specific enthalpy of a substance as it changes phase from a
solid to a liquid at a given temperature and pressure. The latent heat of
fusion for solid water is 144.5 BTU/lbm at a pressure of one atmosphere
(14.7 psia) and a temperature of 32°F.
The fusion line represents the values of pressure and temperature at which a
substance can exist as both a liquid and solid in equilibrium. For most
substances, the fusion line curves to the right as pressure increases (i.e. it
exhibits a positive slope). A notable exception to this behavior is water; its
fusion line has a negative slope and its melting point decreases with
increasing pressure. In addition, the specific volume of water decreases as
the phase changes from solid to liquid, which is why solid water floats on
the liquid phase.
Sublimation
The sublimation line represents the values of pressure and temperature at
which a substance can exist as both a solid and gas in equilibrium.
Equilibrium means that there is no net change in the quantity of solid or gas,
as long as the initial conditions of pressure and temperature are not changed
and no heat is added or removed.
When we transfer sensible heat to solid water at a low temperature and
pressure (such as Point 2 in the above figure), the temperature of the
substance will increase until reaching the sublimation line. Additional
latent heat will cause the solid phase to convert to the vapor phase. After all
of the solid has been converted to a vapor, further sensible heat addition
will result in a superheating of the vapor.
Triple Point
The triple point of a substance is the point at which the three phase lines
come together. At this point, all three phases (solid, liquid, and gas) can
exist in equilibrium. The triple point of water, for example, exists at a
temperature of 32.02°F and a pressure of 0.08865 psia.
If sensible heat is added to solid water at 0.08865 psia, the temperature will
increase until it reaches 32.02°F and further latent heat addition will result
in some of the solid becoming both liquid and vapor. When all of the solid
12
Rev 1
is melted and all of the liquid is vaporized, any further sensible heat
addition will lead to the formation of a superheated vapor.
The pressure-temperature diagram is useful for demonstrating how the
solid, liquid, and vapor phases can exist in equilibrium. Along the
sublimation line, the solid and vapor phases are in equilibrium. Along the
fusion line, the solid and liquid phases are in equilibrium. Along the
vaporization line, the liquid and vapor phases are in equilibrium. The only
point at which all three phases may exist in equilibrium is the triple point.
The vaporization line ends at the critical point, since there is no distinct
difference between the liquid and vapor phases above this point.
Condensation
Vaporization, sublimation, and fusion occur when we add heat to a
substance. If heat is removed from a substance, the opposite processes will
occur.
The addition of latent heat to a saturated liquid at a constant pressure will
cause the liquid to evaporate (change to the vapor phase). If latent heat is
removed from a saturated vapor at a constant pressure, condensation will
occur and the vapor will change to a liquid. The latent heat of condensation
is the amount of heat that we must remove per unit mass, and it is equal in
magnitude to the latent heat of vaporization.
Similarly, freezing is the opposite process of melting (or fusion).
Sublimation also has an opposite process, in which a gas converts directly
into solid; this is deposition or desublimation. The figure below illustrates
these terms.
Figure: P-T Diagram with Phases Defined
Rev 1
13
Knowledge Check
Consider a block of ice at 0°F and 0.008 psia. If heat is
added to the ice at a constant pressure, the ice will...
A.
immediately begin to undergo a phase change to a liquid.
B.
immediately begin to undergo a phase change to a vapor.
C.
increase in temperature, until it melts.
D.
increase in temperature, until it vaporizes.
ELO 1.2 Phase Changes
Introduction
The RCS is operated as a constant-mass system and, therefore, must
accommodate changes in volume brought about by changes in temperature.
The temperature in the RCS will increase as load or steam flow decreases
and will decrease as steam flow increases.
The pressurizer is a major component of the RCS and provides inherent
pressure control during plant operations. To understand the functions of the
pressurizer, we will look at a basic pressurizer system layout and discuss the
thermodynamic properties maintained within the pressurizer.
The figure below shows the general arrangement of a Westinghouse
pressurizer and relief system. This system consists of a pressurizer of
sufficient volume for the size of the plant (~1,800 ft3), which is maintained
approximately 50 percent full of saturated water and 50 percent saturated
vapor.
It has heater and spray subsystems, along with overpressure protection
provided by power operated relief valves (PORVs) and safety valves, which
discharge to the pressurizer relief tank (for quenching purposes). The
containment structure houses the pressurizer, pressurizer relief tank, and
associated major components.
14
Rev 1
Figure: Typical Westinghouse Pressurizer System
The pressurizer contains replaceable direct-contact immersion heaters at the
bottom and a spray nozzle at the top, supplied by external interconnecting
piping and control valves. A surge line, attached to the bottom of the
pressurizer, connects to a hot leg of the RCS and is large enough to handle
anticipated insurges and outsurges between the pressurizer and the hot leg.
A decrease in plant load will result in an increase in RCS temperature,
which causes an insurge into the pressurizer and a slight rise in pressure as
the vapor bubble is compressed. The spray system, which is supplied from
RCS cold legs, condenses some vapor in the pressurizer to lower and
maintain system pressure. In the event that the spray system fails to limit a
pressure increase, the PORVs and safety valves will actuate to limit the
excursion.
During an outsurge, which may be caused by an increase in plant load,
pressure is kept above a minimum allowable limit by the immersion heaters.
These heaters will automatically energize, to raise pressurizer temperature
(and, consequently, pressure) and maintain a nearly constant RCS pressure.
For smaller insurges and outsurges, the inherent stability of a saturated
system provides enough pressure control to preclude the need for spray or
heaters.
Pressurizer Design
The pressurizer functions to establish saturated conditions in the RCS for
pressure control. The pressurizer maintains RCS pressure during steadystate operation and limits pressure variations caused by load transients on
the plant. The inherently stable saturated condition established in the
pressurizer allows it to accommodate for expansion and contraction of the
RCS that result from temperature changes. The ability to accommodate
Rev 1
15
expansion also provides RCS overpressure protection by limiting the rate of
pressure increase.
Pressurizer Operating Principle
The pressurizer operates on the principle that for all practical purposes,
water is incompressible; hence, pressure will be essentially constant and
equal throughout a closed hydraulic system. It is possible to control the
pressure in such a system by varying the vapor pressure over a relatively
small vapor water interface in the system, which functions as a heatexchange interface between the liquid and vapor.
In a closed piping system, such as the RCS, small changes in water
temperature can produce large pressure transients, unless a means is
provided to compensate for temperature-induced variations in coolant
volume.
One method of managing coolant volume would be to simply add or
remove water. In this case, however, the total mass of the system would
have to be varied. To accomplish this in a commercial plant, the volumecompensation system would have to be capable of handling letdown and
makeup flow rates of up to 20,000 gpm. Designing a reliable system that is
capable of this response would be difficult and expensive.
A better method involves the addition of a saturated vapor bubble that can
expand and contract in response to coolant volume changes. In this case,
the total mass of the system would remain constant, while the fraction of the
total mass that exists as a vapor would vary as a function of pressure. Since
a given amount of mass occupies more volume as a vapor than it would as a
liquid, the transfer of mass between the vapor and liquid states provides an
inherent mechanism for pressure control.
Once the normal operating temperature is established, it is advantageous to
operate the RCS as a constant-mass system for reasons discussed below.
The pressurizer accommodates changes in coolant volume caused by
loading or unloading the plant. Since the average temperature in the RCS
(TAvg) increases as power increases from no-load to full-load conditions, the
pressurizer's water level will also increase to maintain a constant mass in
the system; hence, pressurizer level changes as a function of TAvg. To
accomplish this, a level-control system is required that can adjust
pressurizer level accordingly.
For normal operations, the pressurizer provides the inherent pressurecontrol characteristics of a saturated system with a liquid-vapor interface. A
system of automatic pressure-control features, consisting of immersion
heaters and cooling spray, will accommodate larger volume transients (e.g.
in cases where the inherent pressure control is not adequate).
16
Rev 1
Pressurizer Response to TAvg Changes
Pressure changes do not affect the volume of the RCS, since water is nearly
incompressible, but changes in temperature will affect the RCS. As
temperature (TAvg) increases, the volume occupied by the liquid will
increase and, as TAvg decreases, the volume occupied by liquid will
decrease. These changes in liquid volume result in pressure transients in the
RCS.
Pressurizer Response to Insurges and Outsurges
A pressurizer exhibits the inherent pressure-control characteristics of a
saturated liquid-vapor system. However, these inherent characteristics by
themselves are inadequate for RCS pressure control; hence, an RCS has
pressure-control features consisting of automatic immersion heaters and
cooling spray.
The inherent pressure-control process functions on the fact that for any
given temperature, there is only one corresponding saturation pressure and
for any given pressure, there is only one corresponding saturation
temperature. At 2,235 psig, a typical RCS pressure, the saturation
temperature is 653°F.
An increase in TAvg due to coolant expansion causes an insurge into the
pressurizer, in turn causing the vapor bubble to be compressed, which tends
to raise system pressure. As soon as system pressure starts to rise above the
saturation pressure for the prevailing temperature, however, some of the
vapor is compressed and condenses to water (i.e. the vapor pressure
temporarily exceeds the saturation pressure for the current temperature and
condensation results).
This has the effect of reducing the mass of the vapor bubble (and increasing
the mass of the liquid phase), which tends to limit the pressure increase.
However, this inherent pressure-control process does not eliminate the
pressure rise. As the vapor condenses, it transfers its heat (the latent heat of
condensation) to the liquid and slightly raises its temperature. The
saturation pressure corresponding to this new, higher temperature is
somewhat higher than the original pressure, which is why the inherent
pressure-control feature does not entirely eliminate the pressure increase,
but only reduces its magnitude.
A decrease in TAvg due to coolant contraction causes an outsurge from the
pressurizer, causing the vapor bubble to expand (which tends to lower
system pressure). However, as soon as system pressure begins to fall below
the saturation pressure for the prevailing temperature, some of the liquid
flashes to vapor. This has the effect of increasing the mass of the vapor
bubble, which tends to minimize the drop in pressure.
The inherent pressure-control process does not eliminate the pressure drop;
as the liquid flashes to vapor, the remaining liquid cools somewhat by
removing the latent heat of vaporization. The saturation pressure
Rev 1
17
corresponding to this new cooler temperature is somewhat lower than the
original pressure; hence, the inherent pressure-control feature minimizes,
rather than prevents, the pressure decrease.
The key to these inherent pressure-control processes of condensation and
vaporization is pressurizer liquid temperature. If the saturation temperature
corresponding to the desired system pressure can be maintained, then
whenever actual pressure begins to deviate from saturation conditions, the
inherent pressure-control features will act to minimize the deviation. Thus,
the saturation pressure corresponding to the prevailing pressurizer liquid
temperature is essentially an equilibrium pressure about which the inherent
features tend to maintain actual pressure.
The inherent features cannot hold pressure exactly at setpoint, however, due
to the cooling and heating of the pressurizer liquid that results from
vaporization and condensation, as previously discussed. The fact that
pressurizer temperature is altered somewhat by the inherent features implies
that saturation pressure itself will stray from the setpoint pressure.
The greater the coolant volume surge (in or out), the more condensation or
vaporization occurs and, consequently, the more heating or cooling of the
pressurizer liquid. For larger coolant temperature (TAvg) transients,
therefore, the final saturation (and actual) pressure will be further from
setpoint. Under these conditions, the inherent features alone are insufficient
to control system pressure and they must be supplemented by heaters and
spray.
A pressure-control system that incorporates heaters and spray is an
operational requirement. The heaters, for example, are necessary for raising
the pressurizer liquid to the saturation temperature for the desired system
pressure during system startups. Normal system shutdowns need the
cooling spray to lower pressurizer temperature to that corresponding to the
desired pressure. The figure below shows a typical Westinghouse
pressurizer heater and spray for operation.
18
Rev 1
Figure: Typical Westinghouse Pressurizer
Safety Injection Accumulator Tanks
Safety injection accumulator tanks hold unheated borated water and are
typically pressurized to several hundred psia via a nitrogen charge (i.e. an
inert static bubble), which serves to inject the water into the RCS when a
significant loss of pressure occurs. Pressure responses to insurges and
outsurges in these and other gas-charged tanks are considerably different
than what occurs in a saturated (i.e. dynamic) pressurizer.
Since the safety injection accumulators do not incorporate a saturated twophase system, there is no inherent means of pressure control. Therefore, an
insurge (such as occurs when filling the safety injection accumulator tanks)
would result in a continuously increasing pressure as the gas volume is
compressed. Conversely, an outsurge would lead to a continuously
decreasing pressure as the gas volume expanded.
The pressure-volume behavior of the accumulator tanks is characterized by
the ideal gas law (PV = nRT). As the volume of a gas is reduced by
compression, its pressure will rise. Hence, a partially filled tank that
incorporates an inert gas bubble is susceptible to pressure variations on
insurges/outsurges and has no inherent mechanism for limiting the resulting
pressure transients.
This contrasting behavior between static and dynamic systems is an
important concept. A relevant example question follows:
Two identical pressurizers are connected to the same location on two
identical RCSs that are operating at 1,000 psia. Pressurizer A contains 50
Rev 1
19
percent nitrogen and 50 percent subcooled water at 300°F. Pressurizer B
contains 50 percent saturated liquid and 50 percent saturated vapor. Which
one of the following identifies the pressurizer that will maintain the highest
pressure, following a sudden 10 percent liquid outsurge, and the associated
reason?
A. Pressurizer A, due to the subcooled water resulting in a smaller
amount of energy being lost, during the outsurge.
B. Pressurizer A, due to the expansion characteristics of nitrogen being
better than the expansion characteristics of saturated vapor.
C. Pressurizer B, due to the vaporizing of saturated liquid, as pressure
begins to decrease.
D. Pressurizer B, due to the expansion characteristics of saturated vapor
being better than the expansion characteristics of nitrogen.
Answer: C - Pressurizer B, due to the vaporizing of saturated liquid as
pressure begins to decrease.
Knowledge Check
During normal operations, the pressurizer fluid is
maintained at _______ conditions and the RCS fluid is
maintained at __________?
A.
subcooled; saturated
B.
saturated; subcooled
C.
superheated; saturated
D.
supersaturated; subcooled
Knowledge Check
Why are subcooled conditions maintained in the RCS?
20
A.
To prevent boiling in the core or prevent departure from
nucleate boiling.
B.
To transfer more heat through the SGs
C.
To lower the net positive suction head for the RCPs.
D.
To allow reflux cooling.
Rev 1
Knowledge Check – NRC Bank
A pressurizer is operating in a saturated condition at
636°F. If a sudden pressurizer level decrease of 10
percent occurs, pressurizer pressure will
______________ and pressurizer temperature will
________________.
A.
remain the same; decrease
B.
remain the same; remain the same
C.
decrease; decrease
D.
decrease; remain the same
ELO 1.3 Property Diagrams
Introduction
When studying thermodynamic processes and properties, it is useful to
illustrate the process on a property diagram which relates the properties of
interest. The phases of a substance and the relationships between a
material's properties are most commonly shown on an appropriate property
diagram.
Property Diagrams
There are many interdependencies between the properties of a working fluid
in a steam plant. At standard atmospheric pressure and a temperature above
212°F, water exists as superheated vapor; between 32°F and 212°F, it exists
as a liquid; and below 32°F; it exists as a solid. Water vapor at 212°F and
standard atmospheric pressure is saturated and has a specific volume 26.8
ft3/lbm. At any other temperature or pressure, saturated water vapor would
have a different specific volume. For example, at 545°F and 1,000 psia, it
would have a specific volume of 0.446 ft3/lbm.
Property diagrams normally depict the relationships between two or more of
the following properties of a substance: pressure (P), temperature (T),
specific volume (ν), specific enthalpy (h), and specific entropy (s). In
saturated mixtures, quality (x) may also be used.
The most common property diagrams are: pressure-temperature (P-T),
pressure-specific volume (P-ν), pressure-specific enthalpy (P-h), specific
enthalpy-temperature (h-T), temperature-specific entropy (T-s), and specific
enthalpy-specific entropy (h-s) or Mollier.
Rev 1
21
Pressure-Temperature (P-T) Diagram
One of the most common ways to present the phases of a substance is via a
P-T diagram, as shown below for pure water.
Figure: P-T Diagram for Water
It is possible to construct a P-T diagram for any pure substance. The line
that separates the solid and vapor phases is the sublimation line, the line that
separates the solid and liquid phases is the fusion line, and the line
separating the liquid and vapor phases is the vaporization line. The point
where the three lines meet is the triple point, which is the only point that all
three phases can exist in equilibrium.
The point where the vaporization line ends is the critical point. At
temperatures and pressures above the critical point, a substance cannot exist
as a liquid, no matter how high the pressure.
Pressure-Specific Volume (P-ν) Diagram
The figure below shows a P-ν diagram for pure water. A P-ν diagram is
different from a P-T diagram in that there are regions on a P-ν diagram in
which two phases exist together.
22
Rev 1
Figure: P-v Diagram for Water
In the liquid-vapor region, for example, both saturated liquid and saturated
vapor exist in equilibrium. At point A, saturated liquid water with a
specific volume νf (identified by point B) coexists with saturated water
vapor that has a specific volume of νg (identified by point C).
The vapor dome is the region bounded by the saturated-liquid line (on the
left side of the dome) and saturated-vapor line (on the right side of the
dome). The dotted lines are lines of constant temperature (i.e. isotherms).
The quality of a mixture at any point in the liquid-vapor region can be
determined since the specific volumes of pure liquids and vapors are known
for all saturated conditions. The quality can be found graphically from the
P-v diagram or by using the following relationship:
𝑣 = 𝑥𝑣𝑔 + (1 − 𝑥)𝑣𝑓
𝑥=
𝑣 − 𝑣𝑓
𝑣 − 𝑣𝑓
=
𝑣𝑔 − 𝑣𝑓
𝑣𝑓𝑔
Where:
v = specific volume of the mixture (ft3/lbm)
x = quality of the mixture (no units, but sometimes expressed in %)
vg = specific volume of the vapor (ft3/lbm)
vf = specific volume of the liquid (ft3/lbm)
vfg = change in specific volume, due to the vaporization process
𝑓𝑡 3
(
) = 𝑣𝑔 − 𝑣𝑓
𝑙𝑏𝑚
Rev 1
23
On the P-v diagram, the triple point becomes a line which separates the
solid-liquid, solid-vapor, and liquid-vapor regions, shown in the figure
below.
Figure: P-v Diagram for Water
In the first two property diagrams, we used the temperature and pressure or
pressure and specific volume to identify the state of a substance. To display
the relationship between pressure, temperature, and specific volume
simultaneously would require both property diagrams since each twodimensional diagram can only represent the state of a substance based on a
pair of properties. Another means of simultaneously displaying the
relationships between three properties is a three-dimensional plot, such as
the one below.
Figure: Pressure-Temperature-Specific Volume Diagram
24
Rev 1
The figure below shows a similar three-dimensional representation of a PT-v diagram, along with the associated two-dimensional P-T and P-v
property diagram projections, for clarity.
Figure: Pressure-Temperature-Specific-Volume Diagram Projections
Pressure-Specific Enthalpy (P-h) Diagram
It is possible to construct a P-h diagram for any pure substance, such as the
one shown in the figure below for pure water. As with a P-ν diagram, there
are regions on a P-h diagram where two phases exist together. Similarly,
we can derive the quality of a mixture graphically from the P-h diagram or
from the specific enthalpies of the pure liquid and pure vapor (hf and hg,
respectively).
Figure: P-h Diagram for Water
Rev 1
25
The following equations define these relationships:
ℎ = 𝑥ℎ𝑔 + (1 − 𝑥)ℎ𝑓
ℎ − ℎ𝑓
𝑥=
ℎ𝑓𝑔
Where:
h = specific enthalpy of the mixture (BTU/lbm)
x = quality of the mixture (no units)
hg = specific enthalpy of the saturated vapor (BTU/lbm)
hf = specific enthalpy of the saturated liquid (BTU/lbm)
hfg = change in specific enthalpy, due to the vaporization process
𝐵𝑇𝑈
(
) = ℎ𝑔 − ℎ𝑓
𝑙𝑏𝑚
Note that this is the same mathematical relationship presented in the
previous section, with the substitution of specific enthalpies for specific
volumes.
Specific Enthalpy-Temperature (h-T) Diagram
The h-T diagram shown below is for pure water. It is possible to construct
such diagrams for any pure substance. As in the previous property
diagrams, there are regions on the h-T diagram where two phases exist
together. The vertical distance between the two saturation lines, at any
temperature below the critical point, represents the latent heat of
vaporization at that temperature.
If pure liquid water existed at point A (i.e. on the saturated liquid line) and
an amount of heat equal to the latent heat of vaporization was added, the
liquid would change phase to a pure saturated vapor (point B), while
maintaining a constant temperature and pressure. As shown in the figure
below, operating outside of the saturation lines would result in the
formation of a subcooled liquid or superheated vapor.
26
Rev 1
Figure: h-T Diagram for Water
The quality of a mixture at any point in the h-T liquid-vapor region can be
determined, using the same relationship presented above.
𝑥=
ℎ − ℎ𝑓
ℎ𝑓𝑔
The relationship between temperature and specific enthalpy can also be
shown on a T-h diagram as shown in the figure below.
Figure: T-h Diagram
Rev 1
27
Temperature-Specific Entropy (T-s) Diagram
Personnel often use a T-s diagram to analyze thermodynamic cycles in
energy-transfer systems, since a T-s diagram allows visualization of the heat
added to or removed from a system. From the definition of specific entropy
(i.e. s = q/Tabs), the amount of heat transferred to or from a system (per unit
mass) is equal to the area under the T-s curve that describes the process.
The T-s diagram shown below is for pure water.
Figure: T-s Diagram for Water
As can be seen on the T-s diagram, if the latent heat of vaporization is
transferred to a saturated liquid at higher temperatures, a smaller gain in
specific entropy is realized (compare, for example, the change in specific
entropy at P2 and P3).
In the liquid-vapor region, a pure saturated liquid with specific entropy of sf
(point B) coexists with a pure saturated vapor with specific entropy of sg
(point C). The quality of a mixture at any point in the liquid-vapor region
can be found, using the following relationship:
𝑠 = 𝑥𝑠𝑔 + (1 − 𝑥)𝑠𝑓
𝑥=
𝑠 − 𝑠𝑓
𝑠𝑓𝑔
Where:
s = specific entropy of the mixture (BTU/lbm-°R)
x = quality of the mixture (no units)
28
Rev 1
sg = specific entropy of the saturated vapor (BTU/lbm-°R)
sf = specific entropy of the saturated liquid (BTU/lbm-°R)
sfg = change in specific entropy, due to the vaporization process
𝐵𝑇𝑈
(
) = 𝑠𝑔 𝑠𝑓
𝑙𝑏𝑚_ °𝑅
Specific Enthalpy-Specific Entropy (h-s) or Mollier Diagram
The specific enthalpy-specific entropy (h-s) diagram is also termed a
Mollier diagram and often includes a series of lines for constant
temperature, pressure, moisture content, and superheat. The Mollier
diagram presents properties for superheated vapors or for saturated systems,
when the quality of the working fluid is greater than 50 percent.
Figure: Mollier Diagram
The following section will cover h-s (Mollier) diagrams in detail.
Knowledge Check
What is the pressure and temperature in the middle of the
triple point line on a P-v diagram?
Rev 1
29
A.
0.08859 psia, 32°F
B.
0.08859 psia, 212°F
C.
14.7 psia, 32°F
D.
14.7 psia, 212°F
Knowledge Check
Which property diagram is frequently used to analyze
thermodynamic cycles in energy-transfer systems?
A.
T-P
B.
T-s
C.
P-v
D.
P-h
ELO 1.4 Steam Tables and Mollier Diagrams
Introduction
Water is the working fluid in a variety of applications; therefore, many
organizations have researched and documented the properties of water at
different temperature-pressure conditions. For our work, we will deal
primarily with the properties of water in the vapor form (steam), and
tabulated steam properties referred to as "Steam Tables."
The Mollier diagram displays these properties in a graphic format. The
properties presented are the same in both formats; however, it is sometimes
easier to use one over the other, depending on the context.
Steam Tables
The steam tables contain two sections that list the liquid and vapor
properties of water: the saturated steam tables and the superheated steam
tables.
The saturated steam tables are typically divided into two parts: one that lists
the water properties at specific saturation temperatures (Tsat) and another
that lists the water properties at specific saturation pressures (Psat). Both are
tabulations of pressure (P), temperature (T), specific volume (ν), specific
enthalpy (h), and specific entropy (s) that generally extend form the triple
30
Rev 1
point (~32°F and ~0.089 psia) to the critical point (~705°F and ~3,200
psia).
The following figures present segments of one version of the saturated and
superheated steam tables, although a number of other formats exist.
Figure: Portion of a Typical Saturated Steam Temperature Table
Portion of a Typical Saturated Steam Pressure Table
In the sample tables shown above:
T = temperature (°F)
P = pressure (psia)
ν = specific volume (ft3/lbm)
νf = specific volume of saturated liquid (ft3/lbm)
νg = specific volume of saturated vapor (ft3/lbm)
νfg = specific volume change of vaporization (ft3/lbm)
h = specific enthalpy (BTU/lbm)
hf = specific enthalpy of saturated liquid (BTU/lbm)
Rev 1
31
hg = specific enthalpy of saturated vapor (BTU/lbm)
hfg = specific enthalpy change of vaporization (BTU/lbm)
s = specific entropy (BTU/lbm-°R)
sf = specific entropy of saturated liquid (BTU/lbm-°R)
sg = specific entropy of saturated vapor (BTU/lbm-°R)
sfg = specific entropy change of vaporization (BTU/lbm-°R)
Sh = number of degrees of superheat (°F)
Note
The steam tables used for the Generic Fundamentals
Course include properties of saturated liquids and
saturated/superheated vapors only. They tabulate
properties of saturated mixtures, between the triple point
and critical point; a separate table is used for
superheated vapors.
Specific-enthalpy and specific-entropy values for liquids and vapors are
typically referenced to a saturated liquid at the triple point (i.e.
approximately 32°F and 0.089 psia). By convention, the specific enthalpy
(hf) and specific entropy (sf) of water at the triple point are considered to be
zero, as identified in the table below.
Figure: Enthalpy and Entropy of Water at Triple Point
Liquid-vapor mixtures exist in many practical nuclear-plant applications
(U-tube SGs, turbines, condensers, etc.) for which the saturated steam tables
are applicable. When dealing with saturated mixtures, it is often necessary
to determine the exact amount of vapor and liquid in the mixture.
Quality (x) is a key property of a saturated mixture, defined as the mass of
vapor present per total mass of the liquid-vapor mixture. Moisture content
32
Rev 1
(M) is the mass of liquid present per total mass of liquid and vapor.
Therefore, x and M are mathematically related by the expression M + x = 1
(or 100 percent).
The following relationships exist between the quality of a liquid-vapor
mixture and the specific volumes, specific enthalpies, or specific entropies
of the individual phases and the mixture itself.
𝑣 = 𝑥𝑣𝑔 + 𝑀𝑣𝑓
𝑣 = 𝑥𝑣𝑔 + (1 − 𝑥)𝑣𝑓
𝑣 = 𝑣𝑓 + (𝑥)(𝑣𝑔 − 𝑣𝑓 )
𝑣 = 𝑣𝑓 + (𝑥)(𝑣𝑓𝑔 )
𝑣 − 𝑣𝑓
𝑥=(
)
𝑣𝑓𝑔
We can use the same approach to solve for the specific enthalpy or specific
entropy of a mixture, as follows:
ℎ = 𝑥ℎ𝑔 + 𝑀ℎ𝑓
ℎ = 𝑥ℎ𝑔 + (1 − 𝑥)ℎ𝑓
ℎ = ℎ𝑓 + (𝑥)(ℎ𝑔 − ℎ𝑓 )
ℎ = ℎ𝑓 + (𝑥)(ℎ𝑓𝑔 )
𝑥=
ℎ − ℎ𝑓
ℎ𝑓𝑔
And,
𝑠 = 𝑥𝑠𝑔 + 𝑀𝑠𝑓
𝑠 = 𝑥𝑠𝑔 + (1 − 𝑥)𝑠𝑓
𝑠 = 𝑠𝑓 + (𝑥)(𝑠𝑔 − 𝑠𝑓 )
𝑠 = 𝑠𝑓 + (𝑥)(𝑠𝑓𝑔 )
𝑥=
𝑠 − 𝑠𝑓
𝑠𝑓𝑔
The exact state of a substance being studied must be obtained to solve
thermodynamic problems. Two independent properties of the substance
(such as v, P, T, h, s, and x) must be known to determine the other
Rev 1
33
properties. These can be obtained from either the Mollier diagram or the
saturated/superheated steam tables, dependent on the state of the substance.
(Note: temperature and pressure are not independent properties in a
saturated system, so if one of these is used, another property must be known
to solve the problem)
We can use the above relationships to determine various properties of a
liquid-vapor mixture. On the following diagram, if point A is 50 percent of
the way between the saturated liquid (point B) and saturated vapor (point
C), the quality (and moisture content) would be 50 percent and, therefore,
can be used to determine the specific entropy of the mixture (using the
relevant expression from above).
Figure: Specific Entropy
We can use the same means to determine the specific volume and specific
enthalpy the mixture, after identifying the relevant values for the saturated
liquid and vapor.
Use of Steam Tables
Multiple examples of the use of steam tables follow.
Example 1
What are the specific volume, specific enthalpy, and specific entropy values
of steam that has a quality of 90 percent at 385 psig?
Solution:
From the steam tables, at 400 psia:
𝑓𝑡 3
𝑣𝑓 = 0.01934 𝑙𝑏𝑚
34
𝑓𝑡 3
𝑣𝑓𝑔 = 1.14162 𝑙𝑏𝑚
Rev 1
𝐵𝑇𝑈
ℎ𝑓 = 424.2 𝑙𝑏𝑚
𝐵𝑇𝑈
𝑠𝑓 = 0.6217 𝑙𝑏𝑚_ °𝑅
𝐵𝑇𝑈
ℎ𝑓𝑔 = 780.4 𝑙𝑏𝑚
𝑠𝑓𝑔 = 0.8630
𝐵𝑇𝑈
𝑙𝑏𝑚_ °𝑅
𝑣 = 𝑣𝑓 + 𝑥(𝑣𝑓𝑔 )
𝑣 = (0.01934
𝑓𝑡 3
𝑓𝑡 3
𝑓𝑡 3
) + (0.9) (1.14162
) = 1.04680
𝑙𝑏𝑚
𝑙𝑏𝑚
𝑙𝑏𝑚
ℎ = ℎ𝑓 + 𝑥(ℎ𝑓𝑔 )
ℎ = (424.2
𝐵𝑇𝑈
𝐵𝑇𝑈
𝐵𝑇𝑈
) + (0.9) (780.4
) = 1,126.6
𝑙𝑏𝑚
𝑙𝑏𝑚
𝑙𝑏𝑚
𝑠 = 𝑠𝑓 + 𝑥(𝑠𝑓𝑔 )
𝑠 = (0.6217
𝐵𝑇𝑈
𝐵𝑇𝑈
𝐵𝑇𝑈
) + (0.9) (0.8630
) = 1.3984
_
_
𝑙𝑏𝑚 °𝑅
𝑙𝑏𝑚 °𝑅
𝑙𝑏𝑚_ °𝑅
Student Tip for Steam Tables
Note
PSIA, PSIA, PSIA! Read the question. For questions
that contain gauge pressure (psig), convert to psia before
you answer the question. You may see it in the stem, the
answer, or both. Look at the numbers first, before you
do the problem. Once you start working the problem, it
is easy to forget that conversion. You will usually see
the pressures ending in a 5, on these types of problems.
When you add 15 psi to your number, you usually have
a number ending in 0, which often corresponds to the
pressure contained in the steam tables.
As an error-prevention tool, use a ruler or a 3x5 card
when using the steam tables. They extend across the
tables and help prevent misalignment errors.
Example 2
An SG heats saturated liquid at 1,100 psia. What is the temperature,
pressure, and steam quality of the final substance, if the SG adds 600
BTU/lbm of heat?
Using the steam tables, find the following properties of saturated steam at
1,100 psi:
𝑇𝑠𝑎𝑡 = 556.28°𝐹; ℎ𝑓 = 557.5
Rev 1
𝐵𝑇𝑈
𝐵𝑇𝑈
𝐵𝑇𝑈
; ℎ𝑓𝑔 = 631.5
; ℎ𝑔 = 1,189.1
𝑙𝑏𝑚
𝑙𝑏𝑚
𝑙𝑏𝑚
35
Thus, the temperature of saturated liquid at 1,100 psia is 556.28°F and its
specific enthalpy is 557.5 BTU/lbm. Since the SG added 600 BTU/lbm of
heat, the final specific enthalpy of the substance is 1,157.5 BTU/lbm. This
is less than the enthalpy of a saturated vapor at 1,100 psia; hence, the final
substance is a liquid-vapor mixture at 1,100 psia and 556.28°F. Using the
previous equation:
𝑥=
ℎ − ℎ𝑓
ℎ𝑓𝑔
1,157.5𝐵𝑇𝑈
𝐵𝑇𝑈
) − (557.5
)
𝑙𝑏𝑚
𝑙𝑏𝑚
𝑥=
𝐵𝑇𝑈
631.5
𝑙𝑏𝑚
(
𝐵𝑇𝑈
𝑙𝑏𝑚
𝑥=
𝐵𝑇𝑈
631.5
𝑙𝑏𝑚
600
𝑥 = 0.95
Therefore, x = 0.95 (or 95%), T = 556.28°F and P = 1,100 psia.
Example 3
Find the specific entropy of 97 percent quality steam at 556°F.
Using the steam tables, find the following properties of saturated steam at
556°F:
𝑃𝑠𝑎𝑡 = 1,097.55 𝑝𝑠𝑖𝑎; 𝑠𝑓 = 0.7575
𝑠𝑔 = 1.3797
𝐵𝑇𝑈
𝐵𝑇𝑈
; 𝑠𝑓𝑔 = 0.6222
;
𝑙𝑏𝑚– °𝑅
𝑙𝑏𝑚– °𝑅
𝐵𝑇𝑈
𝑙𝑏𝑚– °𝑅
Using the equation from above:
𝑥=
𝑠 − 𝑠𝑓
𝑠𝑓𝑔
𝑠 = 𝑋𝑠𝑓𝑔 + 𝑠𝑓
𝑠 = (0.97) (0.6222
𝑠 = 0.604
𝑠 = 1.36
36
𝐵𝑇𝑈
𝐵𝑇𝑈
) + 0.7575
𝑙𝑏𝑚– °𝑅
𝑙𝑏𝑚– °𝑅
𝐵𝑇𝑈
𝐵𝑇𝑈
+ 0.7575
𝑙𝑏𝑚– °𝑅
𝑙𝑏𝑚– °𝑅
𝐵𝑇𝑈
𝑙𝑏𝑚– °𝑅
Rev 1
Thus, the specific entropy of 97 percent quality steam at 556°F is 1.36
BTU/lbm-°R.
Superheated Steam Table
The steam tables also provide data for superheated vapors at various
pressures and temperatures. Most versions present this information in a
form similar to the table below. Generally, an absolute pressure (with its
associated saturation temperature) is listed with a series of temperature
options, below each of which are tabulated the associated specific volume,
specific enthalpy, and specific entropy for that pressure-temperature
combination.
Some versions (such as the table below) also present the associated degrees
of superheat (Sh) and specific-volume, specific-enthalpy, and specificentropy values for the saturated liquid and vapor at that pressure, for
comparison.
Figure: Superheat Steam Temperature Table
Superheated Steam Table Example
Find the specific volume, specific enthalpy, and specific entropy of a
superheated vapor at 1,000 psia and 650°F. How many degrees of
superheat does it have?
Using superheated steam tables, the following properties of superheated
steam at 1,000 psia and 650°F are found:
𝑆ℎ = 105.42°𝐹
𝑣 = 0.5636
𝑓𝑡 3
𝑙𝑏𝑚
ℎ = 1,290.1
𝑠 = 1.4833
Rev 1
𝐵𝑇𝑈
𝑙𝑏𝑚
𝐵𝑇𝑈
𝑙𝑏𝑚– °𝑅
37
Compressed/Subcooled Liquid Tables
We express the amount of subcooling for a subcooled/compressed liquid as
the number of degrees that it exists below its saturation temperature for the
given pressure. Subcooled liquid tables provide specific properties of
subcooled liquids (e.g. v, h, and s), although such tables are not commonly
available.
You may calculate the values of h and s for a subcooled/compressed liquid
using the following formulas and data from the saturated steam tables (note
that the specific volume of a subcooled/compressed liquid will not vary
substantially from that of a saturated liquid at the same pressure, if the
liquid is not highly subcooled):
ℎ = ℎ𝑓 − 𝑐𝑝(𝑇𝑠𝑎𝑡−𝑇)
𝑠 = 𝑠𝑓 − 𝑐𝑝 {ln (𝑇𝑠𝑎𝑡 ,
𝑎𝑏𝑠
)}
𝑇𝑎𝑏𝑠
Subcooling is a concern in many thermodynamic processes. For example, if
the liquid at the intake of a pump is not sufficiently subcooled, the pressure
drop at the pump's suction can cause some of the liquid to flash to a vapor
(i.e. cavitation). This can result in erosion (pitting) of the internal pump
components.
In severe cases, if too much of the liquid is vaporized, the pump may
become "vapor locked." A device that is designed to pump liquid often uses
the pumped liquid to cool its internal components. If the device becomes
vapor locked and there is insufficient cooling, differential expansion of
dissimilar metals in the rotor and casing may lead to pump seizure.
Efficiency
When the various states have been identified for a particular substance that
has undergone a thermodynamic process (for example, a saturated liquid
that is converted to a compressed liquid in a pump), the associated energy
exchanges/conversions may be determined. These energy exchanges and/or
conversions, however, are never 100 percent efficient. The degree of
efficiency is dependent on the thermodynamic process and its inherent loss
mechanisms.
Generally, the efficiency of a component or process depends upon how
much friction exists (in the component and working fluid), heat and
pressure losses in the system, and various other factors. The properties that
affect system efficiency may often be determined through the use of the
tables and figures presented in this section.
In large-scale power-generating processes, operators maximize the
efficiency of each component to provide the highest overall system
efficiency. Each component will affect the system efficiency in a different
manner.
38
Rev 1
Specific Enthalpy-Specific Entropy (h-s) or Mollier Diagram
The state of a substance can be determined (i.e. a point can be defined on a
suitable property diagram), if any two of its independent intensive
properties can be established. A property diagram commonly used in the
evaluation of water systems is the specific enthalpy-specific entropy (h-s)
diagram, also referred to as the Mollier diagram.
On the Mollier diagram shown in the figure below, constant-enthalpy lines
run horizontally and constant-entropy lines run vertically. The diagram
includes a saturated-liquid/vapor line which separates the saturated-mixture
region (below) from the superheated-vapor region (above).
On most versions of the Mollier diagram, the critical point is located on the
saturated-vapor line in the lower-left portion of the diagram. To the right of
the critical point, along the saturation line, the water is a saturated vapor.
To the left, it is a saturated liquid.
Figure: Mollier Diagram
If the pressure of a saturated mixture is held constant and sufficient heat is
added (see figure below), both the specific enthalpy and specific entropy
will increase (h ↑ and s ↑ on the h-s diagram) and the mixture becomes a
pure saturated vapor and, eventually, a superheated vapor.
Rev 1
39
Conversely, if we maintain a constant pressure and remove heat from a
superheated vapor, both the specific enthalpy and specific entropy will
decrease (h ↓ and s ↓ on the h-s diagram), the superheated vapor will
become a saturated vapor and, eventually, a saturated mixture.
Figure: Mollier Diagram – Constant-Pressure Lines
Constant-pressure lines (or isobars) run diagonally, from the lower left to
the upper right, on a Mollier diagram (see the above figure). In the
saturated liquid-vapor region, these isobars also translate into constanttemperature lines (or isotherms), since temperature and pressure are
interdependent in this region (i.e. every saturation pressure has one and only
one associated saturation temperature. Pressure decreases from left to right
across the Mollier diagram. A dashed line labeled "Standard Atmosphere"
generally indicates standard atmospheric pressure (14.696 psia).
The diagrams provide dashed constant-pressure lines showing low pressures
that are typical of steam condensers (i.e. vacuum pressures in units of
inches of mercury (in. Hg). These dual units create a common error trap for
calculations and examinations; always ensure you use the correct pressure
scale.
As the energy content of a saturated vapor or saturated mixture is decreased,
its moisture content increases and its quality decreases. The Mollier
diagram provides lines of constant moisture content (i.e. percent moisture),
40
Rev 1
which lie parallel to and below the saturation line, as shown in the figure
below.
Figure: Mollier Diagram – Constant Percent Moisture Lines
If we add heat to a saturated vapor, it becomes superheated. Lines of
constant superheat on a Mollier diagram connect points that exhibit the
same degree superheat for each pressure. These lines lie above and roughly
parallel the saturation line, as shown in the figure below.
Rev 1
41
Figure: Mollier Diagram - Constant-Superheat Lines
In the saturated liquid-vapor region, as discussed above, the constantpressure lines are essentially constant-temperature lines (due to the
temperature-pressure dependency of saturated mixtures). In the
superheated-vapor region, however, this interdependency is lost.
For example, many pressure values may be associated with a given
temperature in the superheat region; consequently, the Mollier diagram
provides superheat isotherms, which are constant-temperature lines that
begin at the saturation line and move up and to the right, as shown in the
figure below.
As we add heat to a saturated or superheated vapor at a constant pressure,
the temperature and amount of superheat will increase; additionally, the
amount of superheat will increase as steam pressure decreases and
temperature holds constant.
42
Rev 1
Figure: Mollier Diagram - Constant-Temperature Lines
The figure below shows a complete Mollier diagram, with constant
temperature, constant superheat, constant percent moisture, and constant
pressure lines color-coded. Most of the Mollier diagrams that you will use
will not include color-coding for the various lines.
Rev 1
43
Figure: Mollier Diagram - Labeled
Because specific-enthalpy lines are horizontal and specific-entropy lines are
vertical on a Mollier diagram, this chart is useful for analyzing constantenthalpy (e.g. throttling) and constant-entropy (e.g. ideal-turbine) processes.
You can use a Mollier diagram in conjunction with the steam tables
(although they both provide the same thermodynamic information), and
each is better suited to certain types of analyses.
Use of the Mollier Diagram
Example 1
Using the Mollier diagram, determine the specific enthalpy, specific
entropy, and temperature of a saturated mixture, if its quality is 90 percent
and its pressure is 1,000 psia.
1. Determine the correct isobar (constant-pressure line), below the
saturation line.
Quality (x) is provided, although the Mollier diagram provides
moisture content (M); therefore, the following conversion must be
performed:
𝑀 = 1−𝑥
𝑀 = 1 − 0.90
44
Rev 1
𝑀 = 0.10 (𝑜𝑟 10%)
Identify the appropriate moisture-content line (i.e., 10 percent) that
corresponds to a quality of 90 percent.
2. The intersection of the isobar and moisture content line represents the
precise state of the saturated mixture.
3. To determine the specific enthalpy and specific entropy of the
mixture, follow a horizontal and vertical line (respectively) from the
intersection point to the associated axes; a straightedge is useful in
such analyses.
𝐵𝑇𝑈
𝐵𝑇𝑈
ℎ = 1,125
, 𝑠 = 1.324
𝑙𝑏𝑚
𝑙𝑏𝑚– °𝑅
As this is a saturated mixture at 1,000 psia, the saturated temperature
is 545°F.
Note that this problem could also be solved using only the steam
tables.
Example 2
An ideal turbine (i.e., a constant-entropy process) expands superheated
steam at 700 psia and 680°F to 140 psia. What is the change in enthalpy for
this process?
1. Using the Mollier diagram, locate the intersection of the 700 psia and
the 680°F lines in the superheat region. Read h ~ 1,333 BTU/lbm.
2. Follow a constant-entropy line downward to the 140-psia line and
read h ~ 1,175 BTU/lbm.
3.
𝐵𝑇𝑈
𝐵𝑇𝑈
𝐵𝑇𝑈
𝛥ℎ = 1,175
− 1,333
= −155
𝑙𝑏𝑚
𝑙𝑏𝑚
𝑙𝑏𝑚
Knowledge Check
A reactor is shut down with reactor coolant system
pressure at 1,500 psia and core decay heat is being
removed via the steam generators (SGs). What pressure
must be maintained in the SGs to obtain a 110F
subcooling margin in the reactor coolant leaving the
SGs? (Assume the reactor coolant leaves the SGs at the
SG saturation temperature.)
Rev 1
A.
580 psia
B.
600 psia
C.
620 psia
D.
640 psia
45
Knowledge Check
Saturated steam undergoes an ideal expansion process in
an ideal turbine from 1,000 psia to 28 inches Hg vacuum.
Approximately how much specific work is being
performed by the turbine?
A.
1,193 Btu/lbm.
B.
805 Btu/lbm.
C.
418 Btu/lbm..
D.
388 Btu/lbm.
TLO 1 and Module Summary
Properties of Steam Tables and Mollier Diagrams Summary
This module introduced many new thermodynamic terms and properties and
displayed them on various property diagrams. For the remainder of the
thermodynamics course, we will mainly be using the steam tables and
Mollier diagram to analyze cyclic processes. Therefore, it is important that
you have a firm understanding of the thermodynamic definitions, properties,
and relationships before proceeding to future chapters. Ensure that you
have a good understanding of the following:
Class Activity
Break the class into three groups and have them complete the following
table (slide 136).
46
Rev 1
Answers:
ELO1.1 - Define the following terms (some are review from earlier
modules:
















Rev 1
Specific volume (ν) is the total volume (V) of a substance divided
by the total mass (m) of that substance.
Density (ρ) is the total mass (m) of a substance divided by the total
volume (V) occupied by that substance.
Energy is the capacity of a system to perform work or produce heat.
Specific internal energy (u) of a substance is its internal energy per
unit mass. It equals the total internal energy (U) divided by the total
mass (m).
We can describe heat as energy in transit. It occurs on a molecular
level because of temperature differences. The unit of heat is the
British thermal unit (BTU).
Latent heat is the amount of heat added or removed to produce only
a phase change.
Sensible heat is heat added or removed that causes a temperature
change.
Specific enthalpy (h) is defined as ℎ = 𝑢 + 𝑃𝜈, where u is the
specific internal energy (BTU/lbm) of the system being studied, P is
the pressure of the system (lbf/ft2), and ν is the specific volume
(ft3/lbm) of the system.
Entropy is a measure of the inability to do work for a given amount
of heat transferred.
Power is the time rate of doing work. It is equivalent to the rate of
the energy transfer. Power has units of energy per unit time.
Intensive properties are independent of mass (temperature, pressure,
or any specific property).
Extensive properties are a function of the mass of the system (mass,
volume).
Saturation is the combination of temperature and pressure at which a
mixture of vapor and liquid can exist at equilibrium.
Subcooled liquid is a liquid at a temperature below saturation
temperature for its pressure.
Superheated vapor is a vapor at a temperature above saturation
temperature for its pressure.
Critical point is the temperature and pressure above which there is
no distinction between the liquid and vapor phases.
47




Triple point is the temperature and pressure at which all three phases
can exist in equilibrium.
Vapor pressure curve is a graphical representation of the relationship
between temperature and pressure at saturated conditions.
Quality is the fraction of the total mass of a mixture that is in the
vapor phase.
Moisture content is the fraction of the total mass of a mixture that is
in the liquid phase.
The following terms are labels for processes that occur when a substance
changes between the three phases of matter: solid, liquid, and vapor.




Sublimation is the change of phase from solid to vapor.
Vaporization is the change of phase from liquid to vapor.
Condensation is the change of phase from vapor to liquid.
Fusion or melting is the change of phase from solid to liquid.
ELO1.2 - Predict the effect change of phase will have on plant response.
During an outsurge from the pressurizer, the pressure starts to decrease.
This causes some of the liquid in the pressurizer to flash to vapor, creating
additional vapor. This additional vapor within a fixed volume tends to
cause pressure to increase thereby limiting the drop in system pressure.
During an insurge into the pressurizer, the insurge compresses the vapor
bubble, producing an increase in system pressure. As pressure starts to
increase, some of the vapor condenses, as pressure is now slightly above
that of saturation temperature. The system will return to an equilibrium
condition at a slightly higher temperature and pressure than initially.
Temperature and volume changes in a vessel that uses a cover gas can cause
dramatic pressure changes within the vessel, since there is no condensing or
flashing action to minimize the transient pressure response. Thus, an
insurge into a vessel using an ideal gas for pressure control will result in a
higher final pressure than a similar vessel using saturated vapor control.
Conversely, an outsurge would result in a lower final pressure in the vessel
with the cover gas.
ELO1.3 - Describe the following property diagrams:




48
A P-T diagram is a common way to show the phases of a substance.
A P-ν diagram is similar to as a P-T diagram except that there are
regions on a P-ν diagram in which two phases of the material exist
together.
A P-h diagram shows the relationship between pressure and
enthalpy for the given material.
An h-T diagram shows the relationship between enthalpy and
temperature for a pure substance.
Rev 1
Personnel frequently use a T-s diagram to analyze energy transfer
processes. A T-s diagram allows visualization of the heat added to or
removed from a system.
ELO1.4 - Describe the use of steam tables and Mollier diagrams and, when
given sufficient information to indicate the state of the fluid, determine any
unknown properties for a fluid.
The Mollier diagram:





is a chart on which enthalpy (h) versus entropy (s) is plotted.
can be used to determine various properties of a fluid.
is an h versus s plot.
is used only when quality is greater than 50 percent and for
superheated steam.
contains a series of constant temperature, constant pressure, constant
moisture content, and constant superheat lines.
Steam tables can be used to determine various properties of water using the
following equations:
𝑣 = 𝑥𝑣𝑔 + (1 − 𝑥)𝑣𝑓
ℎ = 𝑥ℎ𝑔 + (1 − 𝑥)ℎ𝑓
𝑠 = 𝑥𝑠𝑔 + (1 − 𝑥)𝑠𝑓
𝑥=
𝑣 − 𝑣𝑓
𝑣𝑓𝑔
𝑥=
ℎ − ℎ𝑓
ℎ𝑓𝑔
𝑥=
𝑠 − 𝑠𝑓
𝑠𝑓𝑔
Steam Summary
Now that you have completed this lesson, you should be able to:
1. Define the following terms:
a. Saturation
b. Subcooled liquid
c. Superheated vapor
d. Critical point
e. Triple point
f. Vapor pressure curve
g. Quality
h. Moisture content
i. Vaporization line
j. Saturated liquid
Rev 1
49
k. Wet vapor
l. Saturated vapor
m. Supersaturated vapor
n. Sublimation
o. Vaporization
p. Condensation
q. Fusion
2. Predict the effect phase changes will have on plant response.
3. Describe the following types of property diagrams:
a. Pressure-temperature diagram
b. Pressure-specific volume diagram
c. Pressure-enthalpy diagram
d. Enthalpy-temperature diagram
e. Temperature-entropy diagram
f. Mollier diagram
4. Describe the use of steam tables and Mollier diagrams, and when
given sufficient information to indicate the state of the fluid,
determine any unknown properties for the fluid.
Steam Summary
Now that you have completed this module, you should be able to
demonstrate mastery of this topic by passing a written exam with a grade of
80 percent or higher on the following TLO:
1. Use Mollier diagrams and steam tables to determine properties of a
fluid.
50
Rev 1