Operator Generic Fundamentals Thermodynamic Properties of Steam

Operator Generic Fundamentals Thermodynamic Properties of Steam
K1.01 Define energy and work. K1.02 Describe effects of pressure and temperature on density or specific volume of a liquid. K1.03 Describe the effects of pressure and temperature on density or specific volume of a gas. K1.04 Define the following terms: Latent heat of vaporization K1.05 Define the following terms: Vaporization line K1.06 Define the following terms: Critical point K1.07 Define the following terms: Vapor dome K1.08 Define the following terms: Saturated liquid K1.09 Define the following terms: Wet vapor K1.10 Define the following terms: Saturated vapor K1.11 Define the following terms: Vapor pressure K1.12 Define the following terms: Moisture content K1.13 Define the following terms: Quality K1.14 Define the following terms: Superheated vapor K1.15 Define the following terms: Supersaturated vapor K1.16 Define the following terms: Subcooled and compressed liquids K1.17 Define the following terms: Subcooling K1.18 Define the following terms: Specific heat K1.19 Define the following terms: Enthalpy K1.20 Identify the following terms on a T-s diagram: Critical point K1.21 Identify the following terms on a T-s diagram: Saturated liquid line K1.22 Identify the following terms on a T-s diagram: Saturated vapor line K1.23 Identify the following terms on a T-s diagram: Solid, liquid, gas, vapor, and fluid regions K1.24 Explain the usefulness of steam tables to the Control Room operator. K1.25 Explain and use saturated and superheated steam tables. K1.26 Apply specific heat in solving heat transfer problems. Operator Generic Fundamentals Thermodynamic Properties of Steam

Terminal Learning 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 on the following TLOs: Explain compression processes and the laws associated with them. Use Mollier diagram and steam tables to determine properties of a fluid. TLO 1 is not tested by the NRC, but the concepts help better under stand pressurizer concepts as well as cycle efficiency. TLOs

Compression Processes
TLO 1 – Explain compression processes and the laws associated with them. 1.1 Describe the ideal gas laws and how to solve for an unknown pressure, temperature, or volume. 1.2 Describe the effects of pressure and temperature changes on confined fluids. TLO s

Gas Laws ELO 1.1 – Describe the ideal gas laws and to solve for unknown variables. Because of their interrelated effect, temperature, pressure, and volume must always be specified when gases are discussed Their quantitative relationships expressed in gas laws Gas laws useful because at low pressures, all real gases behave like a perfect gas Monatomic gas behavior similar to perfect gas behavior; ideal gas law therefore accurate for predicting gas behavior Accuracy decreases with diatomic and polyatomic gases ELO 1.1

Boyle’s and Charles’s Laws
At low pressures, volume of a gas at constant pressure directly proportional to temperature of gas Boyle’s Law At low pressures, volume of a gas at constant temperature is inversely proportional to absolute pressure of gas Figure: Charles’s Law for Constant Pressure Boyle's Law: V and P Related KAs - Figure: Boyle's Law ELO 1.1

Boyle - pressure of gas expanding at constant temperature varies inversely to volume (𝑃1)(𝑉1)=(𝑃2)(𝑉2)=(𝑃3)(𝑉3)= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 Charles - pressure of gas varies directly with temperature when volume is held constant, and volume varies directly with temperature when pressure held constant 𝑉 1 𝑉 2 = 𝑇 1 𝑇 2 𝑜𝑟 𝑃 1 𝑃 2 = 𝑇 1 𝑇 2 Figure: Combined Gas Law ELO 1.1

Combined gas law: 𝑃 1 𝑉 1 𝑇 1 = 𝑃 2 𝑉 2 𝑇 2 = 𝑃𝑉 𝑇 Temperature and Pressure MUST BE IN ABSOLUTE Stress Absolute scales for T & P Figure: PTV Diagram for Combined Gas Law ELO 1.1

Example Problem A compressor discharges into an air receiver and cycles off when the pressure in the receiver reaches 160 psia. During the compression, heat was added to the air and its temperature in the receiver is 140°F. Assuming no air loads are in service, at what temperature (°F) should the compressor restart to maintain the receiver above 150 psia? Show that this is a constant volume problem. Figure: PTV Diagram for Combined Gas Law ELO 1.1

Example Problem Solution
A compressor discharges into an air receiver and cycles off when the pressure in the receiver reaches 160 psia. During the compression, heat was added to the air and its temperature in the receiver is 140°F. Assuming no air loads are in service, at what temperature (°F) should the compressor restart to maintain the receiver above 150 psia? 𝑃 1 𝑉 1 𝑇 1 = 𝑃 2 𝑉 2 𝑇 2 The receiver volume is constant, therefore: 𝑃 1 𝑇 1 = 𝑃 2 𝑇 2 𝑇 1 °𝑅 =460°+140℉=600°𝑅 𝑃 1 =160 𝑝𝑠𝑖 𝑃 2 =150 𝑝𝑠𝑖 160 𝑝𝑠𝑖 600°𝑅 = 150 𝑝𝑠𝑖 𝑇 2 𝑇 2 = 600× 𝑇 2 °𝑅 =562.5°𝑅 𝑇 2 °𝐹 =562.5°𝑅−460°=102.5℉ Keep in mind that as an operator, we want to make sure the compressor “kicks on” at the proper pressure, but temperature. ELO 1.1

Ideal Gas Law Combining results of Charles' and Boyle's experiments, the following is obtained using the specific volume 𝑣 = V/M : 𝑃𝑣 𝑇 =𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 This constant called universal gas constant and is designated by R0, thus ideal gas equation becomes: 𝑃𝑣 = 𝑅0𝑇 Pressure and temperature are absolute values ELO 1.1

Ideal Gas Law One mole of any substance is that amount having Avogadro’s Number of x 1023 atoms: 𝑁𝑢𝑚𝑏𝑒𝑟 𝑚𝑜𝑙𝑒𝑠= 𝑀𝑎𝑠𝑠 𝑔𝑟𝑎𝑚𝑠 𝐴𝑡𝑜𝑚𝑖𝑐 𝑀𝑎𝑠𝑠 𝑔𝑟𝑎𝑚𝑠 𝑚𝑜𝑙𝑒 , or mass = (# moles)(GMW) At STP: 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑇 = 0°𝐶=460°𝑅 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑃 =1 𝑎𝑡𝑚 𝑉𝑜𝑙𝑢𝑚𝑒 𝑉 = 𝑛 𝑙𝑖𝑡𝑒𝑟𝑠 𝑚𝑜𝑙𝑒 ELO 1.1

Ideal Gas Law Individual gas constant (R) obtained by dividing universal gas constant (Ro) by molecular weight (MW) of gas Units of R must always be consistent with units of pressure, temperature, and volume used in gas equation No real gases follow ideal gas law or equation completely Also keep in mind that the Ideal Gas law doesn’t really apply to our steam systems either because we operate at higher pressures than where this applies. Plus we use steam. This concept, however, can apply to things like our Hydrogen and/or Nitrogen pressure systems. ELO 1.1

Ideal Gas Law – Compression Process
ELO 1.2 – Describe the effects of pressure and temperature changes on confined fluids. Most common use of gas behavior is compression process using ideal gas approximations Process may occur at constant temperature (PV = constant), constant volume, or adiabatic (no heat transfer) Results in work performed on system and is essentially area under a P-V curve Figure: Pressure-Volume Diagram ELO 1.2

Compressibility of Fluids
Fluid is any substance that conforms to shape of its container May be either a liquid or a gas A fluid may be considered incompressible when velocity of fluid is greater than one-third speed of sound for fluid, or if liquid Treatment of a fluid considered incompressible is easy because density assumed to be constant, giving a simple relationship for state of the substance Variation of fluid density with changes in pressure a primary factor considered in deciding whether a fluid is incompressible Once substance becomes a gas, process becomes more difficult ELO 1.2

Constant Pressure Process
To determine work done in a constant pressure process, following equation used: W1-2a = P(ΔV) To determine work done in a constant temperature process, following equation used: W1-2b = T(ΔV) Figure: P-V Diagram for Gas ELO 1.2

Constant Volume Process
Work done is product of volume and change in pressure: 𝑊1−2𝑐=𝑉(Δ𝑃) Power requirement for pumps that move incompressible liquids (such as water) determined from replacing volume (V) with product of specific volume and mass: 𝑊1−2𝑐=𝑚𝑣(Δ𝑃) Taking time rate of change of both sides determines power requirements of pump Figure: P-V Diagram for Gas 𝑊 1− 2 𝑐 = 𝑚 𝑣(∆𝑃) ELO 1.2

Effects of Pressure Changes on Fluid Properties
Predominant effect of an increase in pressure in a compressible fluid such as a gas is increase in density of fluid Increase in pressure of incompressible fluid will not have a significant effect on density Increasing pressure of 100°F water from 15 psia to 15,000 psia will only increase density by approximately 6% ELO 1.2

Effects of Pressure Changes on Fluid Properties
Increase in temperature will tend to decrease density of any fluid Effect of a temperature change will depend on whether fluid is compressible If fluid is gas, it will respond as predicted by ideal gas laws A 5% increase in absolute temperature will result in a 5% increase in absolute pressure If fluid is incompressible liquid in closed container, increase in temperature could be catastrophic Rule of thumb for water in a water-solid system 100 psi increase for every 1°F increase in temperature If fluid is incompressible liquid in closed container, increase in temperature will have a tremendously greater and potentially catastrophic effect As fluid temperature increases, it tries to expand, but expansion prevented by walls of container Because fluid incompressible, results in tremendous increase in pressure for relatively minor temperature change Change in specific volume for a given change in temperature is not the same at various beginning temperatures, resultant pressure changes will vary ELO 1.2

Thermodynamic Properties of Steam
TLO 2 – Use Mollier diagram and steam tables to determine properties of a fluid. 2.1 Define the following terms: Critical point Saturation Triple point Subcooled liquid Sublimation Saturated liquid Fusion Wet vapor Supersaturated vapor Saturated vapor Superheated vapor Quality Moisture content Vapor pressure curve Vaporization dome Vaporization Condensation ELOs

Enabling Learning Objectives for TLO 1
2.2 Predict the effect change of phase will have on plant response. 2.3 Describe the following types of property diagrams: Pressure-temperature diagram Pressure-specific volume diagram Pressure-specific enthalpy diagram Specific enthalpy-temperature diagram Temperature-specific entropy diagram Mollier diagram 2.4 Describe the use of steam tables and Mollier diagram, and when given sufficient information to indicate the state of the fluid, determine any unknown properties for the fluid. ELOs

Steam Terms ELO 2.1 – Define the following terms: saturation, subcooled liquid, saturated liquid, wet vapor, saturated vapor, superheated vapor, quality, moisture content, vapor pressure curve, vaporization dome, vaporization, condensation, critical point, triple point, sublimation, fusion, and supersaturated vapor. Must understand relationship between Phase change State change Many of above terms used in T-s and Mollier diagrams Some of these terms are minor in nature and rarely used, while others are important to understanding the various states/phases of properties used in our thermodynamic cycle. The minor ones are presented first. More information about these “minor terms” is available in the Student Guide. ELO 2.1

Saturation Saturation - condition in which a mixture of vapor and liquid can exist together at a given temperature and pressure Saturated liquid to saturated steam Saturation temperature Temperature at which vaporization (boiling) starts to occur for a given pressure Saturation pressure Pressure at which vaporization (boiling) starts to occur for a given temperature Saturation temperature/pressure for water 14.7 psia and 212°F ELO 2.1

Subcooled Liquid Subcooled liquid - temperature lower than saturation temperature for given pressure In secondary cycle – condensate and feedwater Heat added to subcooled liquid raises temperature until saturated Called Sensible Heat ELO 2.1

Saturated Liquid Saturated liquid - temperature equal to saturation temperature for given pressure No vapor content Addition of heat causes liquid to vaporize until saturated vapor No change in temperature ELO 2.1

Wet Vapor Wet vapor- Substance whose temperature is equal to the saturation temperature for a given pressure Some combination of liquid/vapor content Between a saturated liquid and a saturated vapor Addition/removal of heat causes liquid/vapor content to change Example: Turbine exhaust in condenser ELO 2.1

Saturated Vapor Saturated vapor - substance that exists entirely as a vapor at saturation temperature for a given pressure Sometimes referred to as: dry steam or saturated steam Moisture content equal to zero Example: Steam exiting steam generator is “almost” 100% quality Addition of heat to a saturated vapor results in an increase in temperature ELO 2.1

Superheated Vapor Superheated vapor - vapor at temperature greater than saturation temperature Sometimes called superheated steam Example(s): Reheated steam entering low pressure turbine Steam leaving B&W once-through steam generator ELO 2.1

Quality Quality (x) – ratio of mass of vapor to total mass of both vapor and liquid Applies to a wet vapor As heat added to wet vapor Quality increases If mass of vapor is 0.2 lbm and mass of liquid is 0.8 lbm, quality is 0.2 or 20 percent 𝑥= 𝑚 𝑣𝑎𝑝𝑜𝑟 𝑚 𝑙𝑖𝑞𝑢𝑖𝑑 + 𝑚 𝑣𝑎𝑝𝑜𝑟 B A Figure: T-s Diagram for Water ELO 2.1

Moisture Content Moisture (M) is ratio of mass of liquid to total mass of liquid and vapor Opposite of quality Moisture of mixture in previous example would be 0.8 or 80 percent M = 𝑚 𝑙𝑖𝑞𝑢𝑖𝑑 𝑚 𝑙𝑖𝑞𝑢𝑖𝑑 + 𝑚 𝑣𝑎𝑝𝑜𝑟 Relationship of moisture content to quality 𝑀=1−𝑥 𝑥=1−𝑀 ELO 2.1

Vapor Pressure Curve Relationship between saturation pressure and saturation temperature Higher pressure, higher saturation temperature Vapor/liquid mixture at saturation when conditions of pressure and temperature fall on curve Figure: Vapor-Pressure Curve ELO 2.1

Vaporization & Vaporization Dome
Vaporization - process of changing a substance from a saturated liquid to a saturated vapor Heat added called “latent heat of vaporization” Value dependent on pressure Vaporization Dome - the region bounded by the saturated-liquid line and saturated-vapor line Everything “under the dome” considered a wet vapor ELO 2.1

Condensation Condensation – process of removing latent heat from a saturated vapor to a saturated liquid Condensing process actually starts with a wet vapor Process also called “removal of latent heat of vaporization” Processes of vaporization and condensation exact opposite of each other ELO 2.1

Minor Steam Terms Critical point - temperature and pressure at which a gas and liquid cannot exist in equilibrium as distinguishable phases psia, 705.1oF No latent heat of vaporization Triple point - point at which all three phases can exist together psia, 32.02oF Sublimation - values of pressure and temperature at which a substance can exist as both a solid and gas in equilibrium Fusion - change of phase from solid to liquid For example, addition of heat causes ice to melt to water Supersaturated vapor - moisture-free gas that results from rapid pressure decrease and expansion where temperature drops below Tsat for existing pressure ELO 2.1

Knowledge Check Any vapor having a temperature above saturation temperature is a... saturated vapor. superheated vapor. dry saturated vapor. wet saturated vapor. Correct answer is B. Correct Answer is B. NRC Bank Question – P574 ELO 2.1

State and Phase Changes
ELO 2.2 – Predict the effect a change of phase will have on plant response. Properties of a substance include: pressure, temperature, specific volume, and internal energy When two or more properties of a substance fixed, state established Except between a saturated liquid and a saturated vapor Need third property, such as specific volume, to define state When a property changes, a "change of state" has occurred Every state unique, every property has only one value at that state Phase change Saturated liquid to saturated vapor Subcooled liquid to a solid Related KAs K1.02 Describe effects of pressure and temperature on density or specific volume of a liquid Define the following terms: K1.08 Saturated liquid ; K Wet vapor 2.1* 2.1; K Saturated vapor A phase change is a state change, but a state change is not always a phase change ELO 2.2

State vs Phase Change State A - initial state
State B - saturated liquid line (212°F) Line AB - liquid heated from subcooled to saturation temperature Figure: T-v Diagram ELO 2.2

State vs Phase Change Point C - saturated vapor state
Line BC - constant temperature phase change liquid to vapor Line CD - steam is superheated at constant pressure Temperature and volume both increase during the process Figure: T-v Diagram ELO 2.2

State vs Phase Change Raise process pressure to 100 psia
Point E - initial state Specific volume being slightly less than psia and 60°F Point F - new vaporization temperature 327.8°F Figure: T-v Diagram ELO 2.2

State vs Phase Change Point G - saturated-vapor state
Line GH - constant-pressure process in which steam is superheated In a similar manner, a constant pressure of 1,000 psia is represented by line IJKL, with the saturation temperature being 544.6°F Figure: T-v Diagram ELO 2.2

Five States of Water State Definition Characteristics Subcooled Liquid
(Compressed Liquid) Liquid below its boiling temperature Heat addition is sensible (fluid is 100% liquid phase) Saturated Liquid Liquid at its boiling temperature Heat addition will cause boiling Wet Vapor Liquid and vapor mixture at its boiling temperature Two phases (liquid and vapor) co-exist simultaneously within the fluid Saturated Vapor Vapor (steam) at its boiling temperature Fluid is 100% vapor (no liquid remains) Superheated Vapor Vapor (steam) above its boiling temperature Heat addition is sensible ELO 2.2

Knowledge Check A liquid is saturated with 0 percent quality. Assuming pressure remains constant, the addition of a small amount of heat will... raise the steady-state liquid temperature above the boiling point. result in a subcooled liquid. result in some of the liquid vaporizing. result in a superheated liquid. Correct answer is C. Correct answer is C. NRC Bank Question – P674 Analysis: Since the liquid was saturated with 0 percent quality, heat addition at a constant pressure will result in the liquid changing phase to a wet vapor with some amount of quality and moisture content. If enough heat is added it will become a saturated vapor. Since the STEM of the question stated that a “small amount of heat is added”, some of the liquid will vaporize. ELO 2.2

Pressurizer Principle of Operation
RCS fluid is relatively incompressible Pressures applied equally throughout system Pressure controlled by varying vapor pressure in pressurizer Connected remotely from RCS piping Pressurizer temperature will not affect the RCS Hot leg temperature is subcooled ELO 2.2

Pressurizer System General
This section briefly discusses pressurizer operation with regards to saturated/superheated conditions and how changes in level affects steam volume size and therefore, pressure. Figure: Typical Westinghouse Pressurizer System ELO 2.2

Pressurizer Operation
Establishes normal operating pressure during startup Maintaining coolant pressure for a given temperature maintains subcooled liquid in RCS Subcooling margin Limits pressure changes caused by thermal expansion Prevents RCS pressure from exceeding safety limit value Figure: Typical Westinghouse Pressurizer ELO 2.2

Pressurizer Principle of Operation
Once normal operating temperature reached, RCS operated essentially as a constant mass system TAvg increases from no load to full load, so pressurizer level will also increase to maintain constant mass Level control system adjusts pressurizer level ELO 2.2

Pressure Control Pressurizer provides inherent pressure-control characteristics of a saturated system with liquid-vapor interface Design pressure control features consisting of immersion heaters and cooling sprays require a control system Heaters and spray needed for larger volume changes and to establish initial saturated conditions in the pressurizer ELO 2.2

Inherent Pressure Control - Insurge
Coolant expansion caused by an increase in TAvg Steam bubble compressed Pressure and temperature rise Some steam condenses to water (due to PZR Spray) Steam bubble mass decreases Minimizes pressure rise As vapor condenses (latent heat of condensation), it transfers heat to liquid, slightly raising its temperature at the surface ELO 2.2

Inherent Pressure Control – Slow Outsurge
Decrease in Tavg, due to coolant contraction causes outsurge Level lowers and pressure tries to drop As pressure tries to drop saturated liquid flashes to steam and mitigates the pressure drop Steam bubble expands Pressure and temperature stay at saturation conditions NOTE: In the NRC bank a few questions state that a “10% outsurge occurs. Level changes by that much WILL impact system pressure. The system is designed to minimize pressure changes on “small level changes only”. ELO 2.2

Inherent Pressure Control – Rapid Outsurge
Decrease in Tavg, due to coolant contraction causes outsurge Pressure falls below saturation pressure Some water flashes to steam Steam bubble mass increases Minimizes drop in pressure Water flashing to steam (removing latent heat of vaporization) has a cooling effect on water volume Net result: temperature and pressure stabilize at new lower values until heaters can raise pressure back up NOTE: In the NRC bank a few questions state that a “10% outsurge occurs. Level changes by that much WILL impact system pressure. The system is designed to minimize pressure changes on “small level changes only”. ELO 2.2

Pressurizer Heaters and Sprays
Pressure-control system with heaters and spray is operational requirement Heaters necessary for raising pressurizer liquid to saturation temperature for desired system pressure Spray cools the steam bubble and causes it to condense. The cooler water and lowering pressure result in a lower saturation temperature and pressure Figure: Typical Westinghouse Pressurizer ELO 2.2

Pressurizer Heaters and Sprays
Heaters raise pressurizer liquid to saturation temperature Large insurge Cooling sprays lower temperature Corresponding to desired pressure Process Cooling sprays lower pressure by condensing steam Heaters push inherent control process to higher equilibrium pressures Compensates for errors between actual and desired pressure ELO 2.2

Phase Changes & Pressurizer Operation
Knowledge Check – NRC Question A pressurizer is operating in a saturated condition at 636°F. If a sudden 10 percent liquid outsurge occurs, pressurizer pressure will __________; and pressurizer temperature will __________. remain the same; decrease remain the same; remain the same decrease; decrease decrease; remain the same Correct answer is C. Correct answer is C. NRC Question P774 Analysis: When the outsurge occurs, the vapor bubble (saturated steam region) within the pressurizer expands, causing pressure to drop. Because the system is saturated, any reduction in pressure will cause some of the saturated water to flash to steam. This flashing of water to steam helps mitigate the pressure drop as thermodynamic equilibrium is attained at a new lower pressure. The temperature is also lower due to the new lower pressure (saturated system). ELO 2.2

Property Diagrams ELO 2.3 – Describe the types of property diagrams: pressure- temperature diagram, pressure-specific volume diagram, pressure- specific enthalpy diagram, specific enthalpy-temperature diagram, temperature-specific entropy diagram, and Mollier diagram. Related KAs Identify the following terms on a T-s diagram: K Critical point 1.9* 2.0* K Saturated liquid line 2.1* 2.1 K Saturated vapor line K Solid, liquid, gas, vapor, and fluid regions 1.9* 1.9* There are several way to visualize state and phase changes in thermodynamic processes. Our processes mostly use the Temperature-Specific Entropy (T-s) Diagram and the Specific Enthalpy-Specific Entropy (Mollier) Diagrams. There are not any bank questions that require you to draw or label various diagrams, but understanding the T-s and Mollier diagrams will assist in answering many bank questions. Figure: T-s Diagram for Water ELO 2.3

Property Diagrams Property diagrams normally depict 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 Common property diagrams Pressure-temperature (P-T) diagrams Pressure-specific volume (P-ν) diagrams Pressure-specific enthalpy (P-h) diagrams Specific enthalpy-temperature (h-T) diagrams Temperature-specific entropy (T-s) diagrams Specific enthalpy-specific entropy (h-s) or Mollier diagrams ELO 2.3

Pressure-Temperature Diagram
Sublimation curve separates solid and vapor phases Fusion curve separates solid and liquid phases Vaporization line separates liquid and vapor phases Triple point where three lines meet Only point where all three phases exist in equilibrium Critical point where vaporization line ends: Figure: P-T Diagram for Water ELO 2.3

Pressure-Specific Volume Diagrams
P-ν diagram can be constructed for any pure substance Different from P-T diagram, there are regions on a P-ν diagram in which two phases exist together Liquid-vapor region water and steam exist together Point A water with a specific volume (νf) given by point B exists together with steam with a specific volume (νg), given by point C Dotted lines are lines of constant temperature Vapor dome is region bounded by saturated liquid line and saturated vapor line Figure: P-v Diagram for Water ELO 2.3

Quality of mixture at any point in liquid-vapor region can be found because specific volumes of water, steam, and mixture all known Quality found using: 𝑣=𝑥 𝑣 𝑔 + 1−𝑥 𝑣 𝑓 𝑥= 𝑣− 𝑣 𝑓 𝑣 𝑔 − 𝑣 𝑓 = 𝑣− 𝑣 𝑓 𝑣 𝑓𝑔 Where: v = specific volume of the mixture (ft3/lbm) x = quality of the mixture (no units) vg = specific volume of the vapor (ft3/lbm) vf = specific volume of the liquid (ft3/lbm) vfg = specific volume change of vaporization (ft3/lbm) or 𝑣𝑓𝑔=𝑣𝑔−𝑣f ELO 2.3

On P-v diagram, triple point becomes a line, which separates solid- liquid, solid-vapor, and liquid-vapor regions, shown in figure: Triple Point Line Figure: P-v Diagram for Water ELO 2.3

P-V-T Property Diagram
Relationship of properties when saturated must be looked at using three properties Diagram shows how specific volume changes while temperature and pressure remain constant Addition on heat drives mixture to right across liquid and vapor dome at constant temperature and pressure All three properties required to know where mixture located on saturation line Figure: Pressure-Temperature-Specific Volume Diagram ELO 2.3

P-V-T Property Diagram
Figure shows a similar three-dimensional representation of a P-V-T diagram, along with associated two-dimensional P-T and P-v property diagram projections, for clarity P-T Figure: Pressure–Temperature–Specific Volume Diagram Projections ELO 2.3

Pressure-Specific Enthalpy
A P-h diagram can be constructed for any pure substance and exhibits the same features as a P-ν diagram Two phases may exist together Liquid-vapor region water and steam exist together At point A, water with an enthalpy (hf) given by point B, exists together with steam with an enthalpy (hg) given by point C Figure: P-h Diagram for Water ELO 2.3

Pressure-Enthalpy Diagrams
Quality of mixture at any point in liquid-vapor region can be found using: ℎ=𝑥 ℎ 𝑔 + 1−𝑥 ℎ 𝑓 𝑥= ℎ− ℎ 𝑓 ℎ 𝑓𝑔 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 = specific enthalpy change of vaporization (BTU/lbm) or 𝐵𝑇𝑈 𝑙𝑏𝑚 ℎ𝑓𝑔 =ℎ𝑔−ℎ𝑓 ELO 2.3

Specific Enthalpy-Temperature
An h-T diagram can be constructed for any pure substance Two phases may exist together Region between saturated liquid line and saturated vapor line represents area of two phases existing at same time Vertical distance between the two saturation lines represents latent heat of vaporization Figure: h-T Diagram for Water ELO 2.3

Temperature-Specific Enthalpy
Relationship between temperature and specific enthalpy can also be shown with axis rotated on T-h Diagram 32oF 705oF This graph, even though seldomly used, is a good representation of the specific enthalpy (sensible heat) added to a subcooled liquid to raise the temperature to saturation, then the specific enthalpy (latent heat of vaporization) needed to raise a saturated liquid to a saturated vapor, then the specific enthalpy to raise a saturated vapor to a superheated vapor. Keep in mind that because this is looking at the “intensive” property of specific enthalpy, it is the heat added “per lbm” (BTU/lbm). Figure: T-h Diagram ELO 2.3

Temperature-Specific Entropy Diagram
T-s - used to analyze energy transfer system cycles Work done by or on system heat added to or removed from system Point B (sf) – specific entropy of saturated liquid (fluid) Point C (sg) – specific entropy of saturated vapor (gas) Point A – specific entropy of a wet vapor Even though it is early in the CYCLE discussion, it might be helpful to draw the T-s diagram on the board and show the four processes in an IDEAL secondary steam system. Noting that the area under the curve for a given process is the change in specific enthalpy (BTU/lbm). Subcooled FW to 100% saturated steam (SG process) 100% saturated steam to wet vapor (Isentropic single turbine process) Wet vapor to subcooled condensate (Condensing process) Subcooled condensate to subcooled feedwater (Pump process) Figure: T-s Diagram for Water ELO 2.3

Temperature-Entropy Diagram
Quality of the mixture at any point in the liquid-vapor region can be found using: 𝑠=𝑥 𝑠 𝑔 + 1−𝑥 𝑠 𝑓 𝑥= 𝑠− 𝑠 𝑓 𝑠 𝑓𝑔 Where: s = specific entropy of the mixture (BTU/lbm-°R) x = quality of the mixture (no units) sg = specific entropy of the saturated vapor (BTU/lbm-°R) sf = specific entropy of the saturated liquid (BTU/lbm-°R) sfg = specific entropy change of vaporization (BTU/lbm-°R) or 𝑠𝑓𝑔 =𝑠𝑔−𝑠𝑓 NOTE: Once QUALITY (X) is found, the quality can be used to find the specific enthalpy of the wet vapor. h = hf + X(hfg). This process will be used several times to find the exhaust specific enthalpy from the turbine (hexh). ELO 2.3

Specific Enthalpy-Specific Entropy
Chart on which enthalpy (h) versus entropy (s) is plotted Frequently called the Mollier diagram Contains constant temperature lines constant pressure lines constant moisture constant superheat lines Used when quality is > 50 percent and for superheated steam Main process of our thermodynamic cycle used by Mollier Diagram is the – Specific Work/Work of the turbine (hstm – hexh); or (m-dot)x(hstm – hexh). The various lines of the Mollier diagram is explained in greater detail in the next ELO. Figure: Mollier Diagram ELO 2.3

Steam Tables and Mollier Diagram
ELO 2.4 – Describe the use of steam tables and Mollier diagram, and given sufficient information to indicate the state of the fluid, determine any unknown properties for the fluid. Related KAs – K1.24 Explain the usefulness of steam tables to the Control Room operator K1.25 Explain and use saturated and superheated steam tables Figure: Mollier Diagram ELO 2.4

Steam Tables Steam tables consist of two sets of tables of energy transfer properties of water and steam: Saturated steam tables Table 1 – Temperature Table Table 2 – Pressure Table Superheated steam tables (Table 3) Tables are tabulations of pressure (P), temperature (T), specific volume (ν), specific enthalpy (h), and specific entropy (s) Appendix E: Engineering Conversion Factors Rarely used Conversions provided on NRC Equation Sheet Notation used in steam tables Some tables use v for specific volume because there is little possibility of confusing it with velocity ELO 2.4

Steam Tables – Table 1 In order to solve problems in Thermodynamics, information concerning "state" of substance studied must be obtained Usually, two properties (ν, p, T, h, s) of substance must be known in order to determine other needed properties (Note: temperature and pressure not independent properties in a saturated system; if one is used, another property must be known to solve problem) These other properties usually obtained utilizing either Mollier diagram if substance is steam Saturated and superheated steam tables Figure: Portion of a Typical Saturated Steam Temperature Table ELO 2.4

Steam Tables – Table 2 Sat. NOTE: MUST convert from PSIG to PSIA when using this table. ALL values provided in Steam Tables (Table 1 , 2, or 3) are in PSIA! Figure: Portion of a Typical Saturated Steam Pressure Table ELO 2.4

Steam Tables Definitions
T = temperature (゜F) P = pressure (psi) 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) 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) Sh, number of degrees of superheat, not provided in all versions of the Steam Table. All you have to do is take Tact – Tsat to get Sh ELO 2.4

Steam Tables Practice What is saturation temperature for 225 psig?
What is the specific enthalpy of saturated vapor at 1,420 psia? What saturation pressure has the highest enthalpy per lbm? What is the enthalpy of saturated vapor at atmospheric pressure? How much energy must be added to 2 lbm of saturated water at 552oF to convert it to dry saturated steam at the same temperature? Answers (may vary slightly based on version of Steam Tables used): 1.) 397oF 2.) BTUs/lbm 3.) 460 psia 4.) BTUs/lbm 5.) hfg= BTUs/lbm but there are 2 lbm so BTUs ELO 2.4

Steam Tables 𝑥= 𝑣− 𝑣 𝑓 𝑣 𝑓𝑔 Key properties of steam-water mixtures:
𝑥= 𝑣− 𝑣 𝑓 𝑣 𝑓𝑔 Key properties of steam-water mixtures: Steam quality (x) mass of steam present per unit mass of steam-water mixture Steam moisture content (M) mass of water present per unit mass of steam-water mixture Relationships are used with saturated steam tables 𝑣= 𝑥 𝑣 𝑔 +𝑀 𝑣 𝑓 𝑥= ℎ− ℎ 𝑓 ℎ 𝑓𝑔 ℎ=𝑥 ℎ 𝑔 +𝑀 ℎ 𝑓 𝑥= 𝑠− 𝑠 𝑓 𝑠 𝑓𝑔 𝑠=𝑥 𝑠 𝑔 + 𝑀𝑠 𝑓 ELO 2.4

Steam Tables Same approach can be used to solve for specific enthalpy or entropy of a mixture In place of f, g, and f g, just use hf, hg, hfg or sf, sg, sfg 𝑣=𝑥 𝑣 𝑔 + 1−𝑥 𝑣 𝑓 Same as 𝑣= 𝑀𝑣 𝑓 + 𝑋𝑣 𝑔 Same as 𝑣= 𝑣 𝑓 + 𝑥 𝑣 𝑔 − 𝑣 𝑓 Same as 𝑣= 𝑣 𝑓 + 𝑋𝑣 𝐹𝐺 Same as 𝑣= 𝑣 𝑔 − 𝑀𝑣 𝑓𝑔 𝑥= 𝑣− 𝑣 𝑓 𝑣 𝑓𝑔 ELO 2.4

Steam Tables Practice Problems
What is hfg for saturated water at 542°F? Answer: 654.4 BTUs must interpolate between given values What is hfg for saturated water at 950 psig? Answer: ~655 BTUs, if you got 650 it is because you read the psia line Answer: 1.) BTUs Must interpolate between given values. Answer: 2.) ~655 BTUs, if you got 650 it is because you read the 950 psia line. ELO 2.4

Steam Tables Use – Example 1
What are the specific volume, enthalpy, and entropy of steam having a quality of 90 percent at psig? From the steam tables at psia 𝑣 𝑓 = 𝑓 𝑡 3 𝑙𝑏𝑚 ℎ 𝑓 = 𝐵𝑇𝑈 𝑙𝑏𝑚 𝑠 𝑓 = 𝐵𝑇𝑈 𝑙𝑏 𝑚 _ °𝑅 𝑣 𝑓𝑔 = 𝑓 𝑡 3 𝑙𝑏𝑚 ℎ 𝑓𝑔 = 𝐵𝑇𝑈 𝑙𝑏𝑚 𝑠 𝑓𝑔 = 𝐵𝑇𝑈 𝑙𝑏 𝑚 _ °𝑅 𝑣= 𝑣 𝑓 +𝑥 𝑣 𝑓𝑔 𝑣= 𝑓 𝑡 3 𝑙𝑏𝑚 𝑓 𝑡 3 𝑙𝑏𝑚 = 𝑓 𝑡 3 𝑙𝑏𝑚 ℎ= ℎ 𝑓 +𝑥 ℎ 𝑓𝑔 ℎ= 𝐵𝑇𝑈 𝑙𝑏𝑚 𝐵𝑇𝑈 𝑙𝑏𝑚 =1, 𝐵𝑇𝑈 𝑙𝑏𝑚 𝑠= 𝑠 𝑓 +𝑥 𝑠 𝑓𝑔 𝑠= 𝐵𝑇𝑈 𝑙𝑏 𝑚 _ °𝑅 𝐵𝑇𝑈 𝑙𝑏 𝑚 _ °𝑅 = 𝐵𝑇𝑈 𝑙𝑏 𝑚 _ °𝑅 ELO 2.4

Saturated water at 1,100 psia is heated in a steam generator. What is the temperature, pressure and steam quality of the output if BTU/lbm of heat is added? From steam tables at 1,100 psia 𝑇𝑠𝑎𝑡 = °𝐹 ℎ𝑓 = BTU/lbm ℎ𝑓𝑔 = BTU/lbm ℎ𝑔 = 1,188.6 BTU/lbm ELO 2.4

Steam Tables Use – Example 2 Continued
Since 600 BTU/lbm of heat is added, the enthalpy of output is 1, BTU/lbm This is less than enthalpy of saturated steam at 1,100 psia Output is a steam-water mixture at 1,100 psia and °F 𝑥 = ℎ− ℎ 𝑓 ℎ 𝑓𝑔 𝑥= 1,157.55𝐵𝑇𝑈 𝑙𝑏𝑚 − 𝐵𝑇𝑈 𝑙𝑏𝑚 𝐵𝑇𝑈 𝑙𝑏𝑚 𝑥= 600 𝐵𝑇𝑈 𝑙𝑏𝑚 𝐵𝑇𝑈 𝑙𝑏𝑚 𝑥=0.95 Therefore, x = 0.95, T = oF, and P = 1,100 psia ELO 2.4

Find the specific entropy of 97 percent quality steam at 556°F. 𝑃𝑠𝑎𝑡=1,096.9 𝑝𝑠𝑖𝑎 𝑠𝑓= 𝐵𝑇𝑈 𝑙𝑏𝑚°𝑅 𝑠𝑓𝑔= 𝐵𝑇𝑈 𝑙𝑏𝑚°𝑅 𝑠𝑔= 𝐵𝑇𝑈 𝑙𝑏𝑚°𝑅 These values are from the 2000 ASME Steam Tables and might vary slightly depending on which Steam Tables you use. ELO 2.4

Steam Tables Use – Example 3 Continued
𝑥= 𝑠− 𝑠 𝑓 𝑠 𝑓𝑔 𝑠=𝑋 𝑠 𝑓𝑔 + 𝑠 𝑓 𝑠= 𝐵𝑇𝑈 𝑙𝑏𝑚–°𝑅 𝐵𝑇𝑈 𝑙𝑏𝑚–°𝑅 𝑠=0.603 𝐵𝑇𝑈 𝑙𝑏𝑚–°𝑅 𝐵𝑇𝑈 𝑙𝑏𝑚–°𝑅 𝑠=1.36 𝐵𝑇𝑈 𝑙𝑏𝑚–°𝑅 ELO 2.4

Steam Tables - Superheat
Superheat is degrees of temperature above Tsat for a vapor 𝑆ℎ =𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 – 𝑇𝑠𝑎𝑡 Sh = superheat Temperature = measured temperature of steam Tsat = temperature of saturated steam at that pressure Newer version of Steam Tables do not list degrees of superheat. Figure: Superheat Steam Temperature Table ELO 2.4

Superheated Steam Table Use
Determine the degrees of superheat for steam at 1,200 psia and 1,000°F. Determine the specific enthalpy of steam at 1,085 psig and 244°F superheat. Find the specific volume, enthalpy and entropy of superheated steam at 1,000 psia and 660°F. How many degrees of superheat does it have? 433oF superheat 1384 BTUs/lbm  = ft3/lbm h = BTU/lbm s = BTU/oR lbm Sh = oF These values are from the 2000 ASME Steam Tables and might vary slightly depending on which Steam Tables you use. 1.) 433oF superheat 2.) BTUs/lbm 3.) Sh = °F  = h = s = ELO 2.4

Steam Tables - Subcooled
Subcooling is amount of degrees F a liquid is below saturation temperature for given pressure Subcooled liquid tables not provided Use “Saturation Fluid” value of Temperature Table Since liquid essentially incompressible, energy provided to fluid is mostly due to its temperature, not pressure A simple rule of use for determining a value (like specific enthalpy) for a substance: Go to Table 2 for the pressure and temperature provided to determine if subcooled, saturated, or superheated. If subcooled, use hf for the temperature provided If superheated, use Table 3 for the pressure provided If saturated, Table 1 OR 2 can be used ELO 2.4

Steam Tables - Practice
What is the specific enthalpy of a lbm of subcooled water at 1,005 psig and 524°F? How many degrees of subcooling does the fluid possess? Answers: BTUs/lbm 23 degrees of subcooling BTUs/lbm 23 degrees of subcooling ELO 2.4

Mollier Diagram Specific Entropy vs Specific Enthalpy
Constant enthalpy (blue line) Used in throttling processes Constant entropy (red line) Constant Pressure Line (green line) Figure: Mollier Diagram ELO 2.4

Mollier Diagram Constant % Moisture line
“Third” property sometimes used to determine state of wet vapor Recall Quality/Moisture Content relationship M = 1 – X X = 1 - M Figure: Mollier Diagram – Constant Percent Moisture Lines ELO 2.4

Mollier Diagram Superheat Lines Low Pressure Turbine inlet
Heat added at constant pressure to HP exhaust MSR Figure: Mollier Diagram - Constant-Superheat Lines ELO 2.4

Mollier Diagram Constant temperature lines called isotherms
At Saturation Line, curve follows pressure line Wet vapor temperature at Tsat for pressure Figure: Mollier Diagram - Constant-Temperature Lines ELO 2.4

Mollier Diagram Mollier diagram with: constant temperature
constant superheat constant percent moisture constant pressure lines Figure: Mollier Diagram - Labeled ELO 2.4

Mollier Diagram - Example 1
Using the Mollier diagram, determine the specific enthalpy, specific entropy, and temperature of steam if its quality is 90 percent and its pressure is 1,000 psia. ELO 2.4

Mollier Diagram - Example 1 Solution
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 𝑀=0.10 (𝑜𝑟 10%) Identify the appropriate moisture-content line (i.e., 10 percent) that corresponds to a quality of 90 percent. The intersection of the isobar and moisture content line represents the precise state of the saturated mixture. 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. ℎ=1,125 𝐵𝑇𝑈 𝑙𝑏𝑚 , 𝑠=1.324 𝐵𝑇𝑈 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. ELO 2.4

Mollier Diagram - 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? ELO 2.4

Mollier Diagram - Example 2 Solution
Using diagram, locate intersection of the 700 psia and the 680°F lines in the superheat region h ≈ 1,333 BTU/lbm Follow a constant-entropy line downward to 140-psia line h ≈ 1,175 BTU/lbm Δh = 1,178 -1,333 = -155 BTU/lbm ELO 2.4

NRC Mollier Practice Knowledge Check
A nuclear power plant is maintained at 2,000 psia with a pressurizer temperature of 636oF. A pressurizer relief safety valve is leaking to a collection tank that is being held at 10 psig. With 100 percent quality saturated steam in the pressurizer vapor space, which one of the following is the approximate temperature of the fluid just downstream of the relief valve? 280oF 240oF 190oF 170oF Correct answer is B. TOPIC: KNOWLEDGE: K1.15 [2.8/2.8] QID: P76 See next slide - ANSWER: B NOTE: This is what is called a “constant enthalpy” (isenthalpic) process. This is also related to the problem associated with TMI that initiated GFE training. ELO 2.4

NRC Mollier Solution Since the PRT (Quench Tank) contains a wet vapor, you can also determine the temperature by looking it up in the Steam Table. It will be the Tsat for the ABSOLUTE pressure provided. The correct answer: B. 240oF ELO 2.4

Steam Tables and Mollier Diagram
Knowledge Check – NRC Question 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? 1,193 Btu/lbm 805 Btu/lbm 418 Btu/lbm 388 Btu/lbm Correct answer is C. Correct answer is C. NRC Question P1875 One VERY important concept to understand in the turbine process is that the secondary system is approximately 33% efficient. Which means if your plant generates 3600 Mwth then it generates approximately 1200 Mwe. Also since the steam entering the turbine is around 1000 psia and its hstm is around 1200 BTU/lbm, it stands to reason that we are only getting about 1/3 of the energy out of that steam. That means the turbine exhaust is around 800 BTU/lbm. That means the “specific work” done by the turbine is about 400 BTU/lbm. That means the answer MUST be “C” or “D”! (1/3 = 400/1200). Also the better the vacuum, the more work out of the turbine. 28 inHg vacuum equates to about 1 psia on the Mollier Diagram. Draw the Mollier Diagram on the board showing the data points. Note that since the process is “ideal” the specific entropy at the turbine inlet is the same as the turbine exhaust. That can be used to determine the quality and then the specific enthalpy of the turbine exhaust. It is always a good idea to back up your MOLLIER work with STEAM TABLE work if possible! ELO 2.4

Module Summary Review Activity
Complete the following table: Temp (oF) Pressure (psia) Moisture Content Quality Specific Volume – v (ft3/lbm) Specific Enthalpy – h (BTU/lbm) Specific Entropy – s (BTU/lbmoR) 228oF 20.031 4% 96% 19.261 1,117.8 656oF 2300.9 1% 99% 1,107.3 548oF 1027.9 0.5% 99.5% 1,188.3 102oF 1.0092 14% 86% 960.6 364oF 160.89 12% 88% 1092.5 Temp (oF) Pressure (psia) Moisture Content Quality Specific Volume – v (ft3/lbm) Specific Enthalpy – h (BTU/lbm) Specific Entropy – s (BTU/lbmoR) 228oF 96% 656oF 1% 548oF 99.5% 102oF 14% 364oF 88% The unfilled table is directly behind the filled table and will show in Slide Show mode. Click to see the filled table. Optional Activity – Have students use steam tables to fill in values for table above, then review results with class, or call on selected students to find a specific table cell answers during module review. NOTE: These values were calculated from the 2000 steam tables (newer version). Depending on the version of Steam Tables used, these values might vary slightly. Summary

NRC KA to ELO Tie KA # KA Statement RO SRO ELO K1.01 Define energy and work. 1.9 2.0 K1.02 Describe effects of pressure and temperature on density or specific volume of a liquid. 2.4 2.5 1.2 K1.03 Describe the effects of pressure and temperature on density or specific volume of a gas. 2.3 K1.04 Define the following terms: Latent heat of vaporization 2.1 K1.05 Define the following terms: Vaporization line K1.06 Define the following terms: Critical point K1.07 Define the following terms: Vapor dome 1.8 K1.08 Define the following terms: Saturated liquid 2.8 K1.09 Define the following terms: Wet vapor K1.10 Define the following terms: Saturated vapor K1.11 Define the following terms: Vapor pressure 1.7 K1.12 Define the following terms: Moisture content K1.13 Define the following terms: Quality K1.14 Define the following terms: Superheated vapor K1.15 Define the following terms: Supersaturated vapor K1.16 Define the following terms: Subcooled and compressed liquids 2.6 2.7 K1.17 Define the following terms: Subcooling 3.0 3.2 K1.18 Define the following terms: Specific heat K1.19 Define the following terms: Enthalpy K1.20 Identify the following terms on a T-s diagram: Critical point K1.21 Identify the following terms on a T-s diagram: Saturated liquid line K1.22 Identify the following terms on a T-s diagram: Saturated vapor line K1.23 Identify the following terms on a T-s diagram: Solid, liquid, gas, vapor, and fluid regions K1.24 Explain the usefulness of steam tables to the Control Room operator. 3.1 K1.25 Explain and use saturated and superheated steam tables. 3.3 3.4 K1.26 Apply specific heat in solving heat transfer problems. K1.01 was covered in ELO 2.3 of the previous topic ( – Units and Properties).

Operator Generic Fundamentals Thermodynamic Properties of Steam

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