Science and Engineering Article

Conductance

The word “reciprocal” is sometimes used to mean “the opposite of.” The opposite, or reciprocal, of resistance is called conductance. As described above, resistance is the opposition to current flow. Since resistance and conductance are opposites, conductance can be defined as the ability to conduct current. For example, if a wire has a high conductance, it will have low resistance, and vice-versa. Conductance is found by taking the reciprocal of the resistance. The unit used to specify conductance is called “mho,” which is ohm spelled backwards. The symbol for “mho” is the Greek letter omega inverted ( ). The symbol for conductance when used in a formula is G. Equation (1-5) is the mathematical representation of conductance obtained by relating the
definition of conductance (1/R) to Ohm’s Law, Equation (1-4).

Example: If a resistor (R) has five ohms, what will its conductance (G) be in mhos?

Solution:

Ohm’s Law

In 1827, George Simon Ohm discovered that there was a definite relationship between voltage, current, and resistance in an electrical circuit. Ohm’s Law defines this relationship and can be stated in three ways.

1. Applied voltage equals circuit current times the circuit resistance. Equation (1-2) is a mathematical respresentation of this concept.

2. Current is equal to the applied voltage divided by the circuit resistance. Equation (1-3) is a mathematical representation of this concept.

3. Resistance of a circuit is equal to the applied voltage divided by the circuit current. Equation (1-4) is a mathematical representation of this concept.

where
I = current (A)
E = voltage (V)
R = resistance (Ω)

If any two of the component values are known, the third can be calculated.

Example 1: Given that I = 2 A, E = 12 V, find the circuit resistance.

Solution:
Since applied voltage and circuit current are known, use Ohm’s Law to solve for resistance.

Example 2: Given E = 260 V and R = 240 Ω , what current will flow through a circuit?
Solution:

Since applied voltage and resistance are known, use Ohm’s Law to solve for current.

Example 3: Find the applied voltage, when given circuit resistance of 100 Ω and circuit current of 0.5 amps.

Solution:
Since circuit resistance and circuit current are known, use Ohm’s Law to solve for applied voltage.

Example 3: Find the applied voltage, when given circuit resistance of 100 Ω and circuit current of 0.5 amps.
Solution:
Since circuit resistance and circuit current are known, use Ohm’s Law to solve for applied voltage.

System Internationale (SI) Metric System

Electrical units of measurement are based on the International (metric) System, also known as the SI System. Units of electrical measurement include the following:

• Ampere
• Volt
• Ohm
• Siemens
• Watt
• Henry
• Farad

Appendix A provides more information concerning the metric system, metric prefixes, and powers of 10 that are used in electrical measuring units.

Voltage

Voltage, electromotive force (emf), or potential difference, is described as the pressure or force that causes electrons to move in a conductor. In electrical formulas and equations, you will see voltage symbolized with a capital E, while on laboratory equipment or schematic diagrams, the voltage is often represented with a capital V.

Current

Electron current, or amperage, is described as the movement of free electrons through a conductor. In electrical formulas, current is symbolized with a capital I, while in the laboratory or on schematic diagrams, it is common to use a capital A to indicate amps or amperage (amps).

Resistance

Now that we have discussed the concepts of voltage and current, we are ready to discuss a third key concept called resistance. Resistance is defined as the opposition to current flow. The amount of opposition to current flow produced by a material depends upon the amount of available free electrons it contains and the types of obstacles the electrons encounter as they attempt to move through the material. Resistance is measured in ohms and is represented by the symbol (R) in equations. One ohm is defined as that amount of resistance that will limit the current in a conductor to one ampere when the potential difference (voltage) applied to the conductor is one volt. The shorthand notation for ohm is the Greek letter capital omega (W). If a voltage is applied to a conductor, current flows. The amount of current flow depends upon the resistance of the conductor. The lower the resistance, the higher the current flow for a given amount of voltage. The higher the resistance, the lower the current flow.

Conductors

Conductors are materials with electrons that are loosely bound to their atoms, or materials that permit free motion of a large number of electrons. Atoms with only one valence electron, such as copper, silver, and gold, are examples of good conductors. Most metals are good conductors.

Insulators

Insulators, or nonconductors, are materials with electrons that are tightly bound to their atoms and require large amounts of energy to free them from the influence of the nucleus. The atoms of good insulators have their valence shells filled with eight electrons, which means they are more than half filled. Any energy applied to such an atom will be distributed among a relatively large number of electrons. Examples of insulators are rubber, plastics, glass, and dry wood.

Resistors

Resistors are made of materials that conduct electricity, but offer opposition to current flow. These types of materials are also called semiconductors because they are neither good conductors nor good insulators. Semiconductors have more than one or two electrons in their valence shells, but less than seven or eight. Examples of semiconductors are carbon, silicon, germanium, tin, and lead. Each has four valence electrons.

Voltage

The basic unit of measure for potential difference is the volt (symbol V), and, because the volt unit is used, potential difference is called voltage. An object’s electrical charge is determined by the number of electrons that the object has gained or lost. Because such a large number of electrons move, a unit called the “coulomb” is used to indicate the charge. One coulomb is equal to 6.28 x 1018 (billion, billion) electrons. For example, if an object gains one coulomb of negative charge, it has gained 6,280,000,000,000,000,000 extra electrons. A volt is defined as a difference of potential causing one coulomb of current to do one joule of work. A volt is also defined as that amount of force required to force one ampere of current through one ohm of resistance. The latter is the definition with which we will be most concerned in this module.

Current

The density of the atoms in copper wire is such that the valence orbits of the individual atoms overlap, causing the electrons to move easily from one atom to the next. Free electrons can drift from one orbit to another in a random direction. When a potential difference is applied, the direction of their movement is controlled. The strength of the potential difference applied at each end of the wire determines how many electrons change from a random motion to a more directional path through the wire. The movement or flow of these electrons is called electron current flow or just current.

To produce current, the electrons must be moved by a potential difference. The symbol for current is (I). The basic measurement for current is the ampere (A). One ampere of current is defined as the movement of one coulomb of charge past any given point of a conductor during one second of time.

If a copper wire is placed between two charged objects that have a potential difference, all of the negatively-charged free electrons will feel a force pushing them from the negative charge to the positive charge. This force opposite to the conventional direction of the electrostatic lines of force is shown in Figure 9.

The direction of electron flow, shown in Figure 10, is from the negative (-) side of the battery, through the wire, and back to the positive (+) side of the battery. The direction of electron flow is from a point of negative potential to a point of positive potential. The solid arrow shown in Figure 10 indicates the direction of electron flow. As electrons vacate their atoms during electron current flow, positively charged atoms (holes) result. The flow of electrons in one direction causes a flow of positive charges. The direction of the positive charges is in the opposite direction of the electron flow. This flow of positive charges is known as conventional current and is shown in Figure 10 as a dashed arrow. All of the electrical effects of electron flow from negative to positive, or from a higher potential to a lower potential, are the same as those that
would be created by a flow of positive charges in the opposite direction. Therefore, it is important to realize that both conventions are in use and that they are essentially equivalent; that is, all effects predicted are the same. In this text, we will be using electron flow in our discussions.

Generally, electric current flow can be classified as one of two general types: Direct Current (DC) or Alternating Current (AC). A direct current flows continuously in the same direction. An alternating current periodically reverses direction. We will be studying DC and AC current in more detail later in this text. An example of DC current is that current obtained from a battery. An example of AC current is common household current.

Real and Ideal Sources

An ideal source is a theoretical concept of an electric current or voltage supply (such as a battery) that has no losses and is a perfect voltage or current supply. Ideal sources are used for analytical purposes only since they cannot occur in nature. A real source is a real life current or voltage supply that has some losses associated with it.

Free Electrons

Electrons are in rapid motion around the nucleus. While the electrostatic force is trying to pull the nucleus and the electron together, the electron is in motion and trying to pull away. These two effects balance, keeping the electron in orbit. The electrons in an atom exist in different energy levels. The energy level of an electron is proportional to its distance from the nucleus. Higher energy level electrons exist in orbits, or shells, that are farther away from the nucleus. These shells nest inside one another and surround the nucleus. The nucleus is the center of all the shells. The shells are lettered beginning with the shell nearest the nucleus: K, L, M, N, O, P, and Q. Each shell has a maximum number of electrons it can hold. For example, the K shell will hold a maximum of two electrons and the L shell will hold a maximum of eight electrons. As shown in Figure 8, each shell has a specific number of electrons that it will hold for a particular atom.

There are two simple rules concerning electron shells that make it possible to predict the electron distribution of any element:
1. The maximum number of electrons that can fit in the outermost shell of any atom is eight.
2. The maximum number of electrons that can fit in the next-to-outermost shell of any atom is 18.

An important point to remember is that when the outer shell of an atom contains eight electrons, the atom becomes very stable, or very resistant to changes in its structure. This also means that atoms with one or two electrons in their outer shell can lose electrons much more easily than atoms with full outer shells. The electrons in the outermost shell are called valence electrons. When external energy, such as heat, light, or electrical energy, is applied to certain materials, the electrons gain energy, become excited, and may move to a higher energy level. If enough energy is applied to the atom, some of the valence electrons will leave the atom. These electrons are called free electrons. It is the movement of free electrons that provides electric current in a metal conductor. An atom that has lost or gained one or more electrons is said to be ionized or to have an ion change. If the atom loses one or more electrons, it becomes positively charged and is referred to as a positive ion. If an atom gains one or more electrons, it becomes negatively charged and is referred to as a negative ion.

Potential Difference

Potential difference is the term used to describe how large the electrostatic force is between two charged objects. If a charged body is placed between two objects with a potential difference, the charged body will try to move in one direction, depending upon the polarity of the object. If an electron is placed between a negatively-charged body and a positively-charged body, the action due to the potential difference is to push the electron toward the positively-charged object. The electron, being negatively charged, will be repelled from the negatively-charged object and attracted by the positively-charged object, as shown in Figure 7.

Due to the force of its electrostatic field, these electrical charges have the ability to do work by moving another charged particle by attraction and/or repulsion. This ability to do work is called “potential”; therefore, if one charge is different from another, there is a potential difference between them. The sum of the potential differences of all charged particles in the electrostatic field is referred to as electromotive force (EMF).

The basic unit of measure of potential difference is the “volt.” The symbol for potential difference is “V,” indicating the ability to do the work of forcing electrons to move. Because the volt unit is used, potential difference is also called “voltage.” The unit volt will be covered in greater detail in the next chapter.

Electrostatic Field

A special force is acting between the charged objects discussed above. Forces of this type are the result of an electrostatic field that exists around each charged particle or object. This electrostatic field, and the force it creates, can be illustrated with lines called “lines of force” as shown in Figure 4.

Charged objects repel or attract each other because of the way these fields act together. This force is present with every charged object. When two objects of opposite charge are brought near one another, the electrostatic field is concentrated in the area between them, as shown in Figure 5. The direction of the small arrows shows the direction of the force as it would act upon an electron if it were released into the electric field.

When two objects of like charge are brought near one another, the lines of force repel each other, as shown in Figure 6.

The strength of the attraction or of the repulsion force depends upon two factors: (1) the amount of charge on each object, and (2) the distance between the objects. The greater the charge on the objects, the greater the electrostatic field. The greater the distance between the objects, the weaker the electrostatic field between them, and vice versa. This leads us to the law of electrostatic attraction, commonly referred to as Coulomb’s Law of electrostatic charges, which states that the force of electrostatic attraction, or repulsion, is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them as shown in Equation 1-1.

If q1 and q2 are both either Figure 7 Potential Difference Between Two Charged Objects positively or negatively
charged, the force is repulsive. If q1 and q2 are opposite polarity or charge, the force is attractive.

Electrostatic Forces 

One of the mysteries of the atom is that the electron and the nucleus attract each other. This attraction is called electrostatic force, the force that holds the electron in orbit. This force may be illustrated with lines as shown in Figure 3.

Without this electrostatic force, the electron, which is traveling at high speed, could not stay in its orbit. Bodies that attract each other in this way are called charged bodies. As mentioned previously, the electron has a negative charge, and the nucleus (due to the proton) has a positive charge.

The First Law of Electrostatics

The negative charge of the electron is equal, but opposite to, the positive charge of the proton. These charges are referred to as electrostatic charges. In nature, unlike charges (like electrons and protons) attract each other, and like charges repel each other. These facts are known as the First Law of Electrostatics and are sometimes referred to as the law of electrical charges. This law should be remembered because it is one of the vital concepts in electricity. Some atoms can lose electrons and others can gain electrons; thus, it is possible to transfer electrons from one object to another. When this occurs, the equal distribution of negative and positive charges no longer exists. One object will contain an excess of electrons and become negatively charged, and the other will become deficient in electrons and become positively charged. These objects, which can contain billions of atoms, will then follow the same law of electrostatics as the electron and proton example shown above. The electrons that can move around within an object are said to be free electrons and will be discussed in more detail in a later section. The greater the number of these free electrons an object contains, the greater its negative electric charge. Thus, the electric charge can be used as a measure of electrons.

The Atom

Elements are the basic building blocks of all matter. The atom is the smallest particle to which an element can be reduced while still keeping the properties of that element. An atom consists of a positively charged nucleus surrounded by negatively charged electrons, so that the atom as a whole is electrically neutral. The nucleus is composed of two kinds of subatomic particles, protons and neutrons, as shown in Figure 1.

The proton carries a single unit positive charge equal in magnitude to the electron charge. The neutron is slighty heavier than the proton and is electrically neutral, as the name implies. These two particles exist in various combinations, depending upon the element involved. The electron is the fundamental negative charge (-) of electricity and revolves around the nucleus, or center, of the atom in concentric orbits, or shells.

The proton is the fundamental positive charge (+) of electricity and is located in the nucleus. The number of protons in the nucleus of any atom specifies the atomic number of that atom or of that element. For example, the carbon atom contains six protons in its nucleus; therefore, the atomic number for carbon is six, as shown in Figure 2.

In its natural state, an atom of any element contains an equal number of electrons and protons. The negative charge (-) of each electron is equal in magnitude to the positive charge (+) of each proton; therefore, the two opposite charges cancel, and the atom is said to be electrically neutral, or in balance.

Introduction

There are two types of pressurizer : static and dynamic. A static pressurizer is a partially filled tank with a required amount of gas pressure trapped in the void area. A dynamic pressurizer is a tank in which its saturated environment is controlled through use of heaters (to control temperature) and sprays (to control pressure).

This chapter focuses on the dynamic pressurizer. A dynamic pressurizer utilizes a controlled pressure containment to keep high temperature fluids from boiling, even when the system undergoes abnormal fluctuations.

Before discussing the purpose, construction, and operation of a pressurizer, some preliminary information about fluids will prove helpful. The evaporation process is one in which a liquid is converted into a vapor at temperatures below the boiling point. All the molecules in the liquid are continuously in motion. The molecules that move most quickly possess the greatest amount of energy. This energy occasionally escapes from the surface of the liquid and moves into the atmosphere. When molecules move into the atmosphere, the molecules are in the gaseous, or vapor, state.

Liquids at a high temperature have more molecules escaping to the vapor state, because the molecules can escape only at higher speeds. If the liquid is in a closed container, the space above the liquid becomes saturated with vapor molecules, although some of the molecules return to the liquid state as they slow down. The return of a vapor to a liquid state is called condensation. When the amount of molecules that condense is equal to the amount of molecules that evaporate, there is a dynamic equilibrium between the liquid and the vapor.

Pressure exerted on the surface of a liquid by a vapor is called vapor pressure. Vapor pressure increases with the temperature of the liquid until it reaches saturation pressure, at which time the liquid boils. When a liquid evaporates, it loses its most energetic molecules, and the average energy per molecule in the system is lowered. This causes a reduction in the temperature of the liquid.

Boiling is the activity observed in a liquid when it changes from the liquid phase to the vapor phase through the addition of heat. The term saturated liquid is used for a liquid that exists at its boiling point. Water at 212oF and standard atmospheric pressure is an example of a saturated liquid. Saturated steam is steam at the same temperature and pressure as the water from which it was formed. It is water, in the form of a saturated liquid, to which the latent heat of vaporization has been added. When heat is added to a saturated steam that is not in contact with liquid, its temperature is increased and the steam is superheated. The temperature of superheated steam, expressed as degrees above saturation, is called degrees of superheat.

General Description

The pressurizer provides a point in the reactor system where liquid and vapor can be maintained in equilibrium under saturated conditions, for control purposes. Although designs differ from facility to facility, a typical pressurizer is designed for a maximum of about 2500 psi and 680°F.

Dynamic Pressurizers

A dynamic pressurizer serves to:

• maintain a system’s pressure above its saturation point,
• provide a means of controlling system fluid expansion and contraction,
• provide a means of controlling a system’s pressure, and
• provide a means of removing dissolved gasses from the system by venting the vapor space of the pressurizer.

Construction

A dynamic pressurizer is constructed from a tank equipped with a heat source such as electric heaters at its base, a source of cool water, and a spray nozzle. A spray nozzle is a device located in the top of the pressurizer that is used to atomize the incoming water.

A dynamic pressurizer must be connected in the system to allow a differential pressure to exist across it. The bottom connection, also called the surge line, is the lower of the two pressure lines. The top connection, referred to as the spray line, is the higher pressure line. Differential pressure is obtained by connecting the pressurizer to the suction and discharge sides of the pump servicing the particular system. Specifically, the surge (bottom connection) is connected to the pump’s suction side; the spray line (top connection) is connected to the pump’s discharge side. A basic pressurizer is illustrated in Figure 15.

The hemispherical top and bottom heads are usually constructed of carbon steel, with austenitic stainless
steel cladding on all surfaces exposed to the reactor system water. The pressurizer can be activated in two ways. Partially filling the pressurizer with system water is the first. After the water reaches a predetermined level, the heaters are engaged to increase water temperature. When the water reaches saturation temperature, it begins to boil. Boiling water fills the void above the water level, creating a saturated environment of water and steam. The other method involves filling the pressurizer completely, heating the water to the desired temperature, then partially draining the water and steam mixture to create a steam void at the top of the vessel.

Water temperature determines the amount of pressure developed in the steam space, and the greater the amount of time the heaters are engaged, the hotter the environment becomes. The hotter the environment, the greater the amount of pressure.

Installing a control valve in the spray line makes it possible to admit cooler water from the top of the pressurizer through the spray nozzle. Adding cooler water condenses the steam bubble, lowers the existing water temperature, and reduces the amount of system pressure.

Operation

The level of water within a pressurizer is directly dependant upon the temperature, and thus the density, of the water in the system to which the pressurizer is connected. An increase in system temperature causes the density of the water to decrease. This decreased density causes the water to expand, causing the level of water to increase in the vessel. The increased level of water in a pressurizer is referred to as an insurge. An insurge compresses the vapor space, which in turn causes the system pressure to rise. This results in slightly superheated steam in contact with the subcooled pressurizer liquid. The superheated steam transfers heat to the liquid and to the pressurizer walls. This re-establishes and maintains the saturated condition.

A decrease in system temperature causes the density to increase which causes the system water volume to contract. The contraction (drop) in pressurizer water level and increase in vapor space is referred to as an outsurge. The increase in vapor space causes the pressure to drop, flashing the heated water volume and creating more steam. The increased amount of steam re-establishes the saturated state. Flashing continues until the decrease in water level ceases and saturated conditions are restored at a somewhat lower pressure.

In each case, the final conditions place the pressurizer level at a new value. The system pressure remains at approximately its previous value, with relatively small pressure variations during the level change, provided that the level changes are not too extreme.

In actual application, relying on saturation to handle all variations in pressure is not practical. In conditions where the system water is surging into the pressurizer faster than the pressurizer can accommodate for example, additional control is obtained by activating the spray. This spray causes the steam to condense more rapidly, thereby controlling the magnitude of the pressure rise.

When a large outsurge occurs, the level can drop rapidly and the water cannot flash to steam fast enough. This results in a pressure drop. The installed heaters add energy to the water and cause it to flash to steam faster, thereby reducing the pressure drop. The heaters can also be left on to re-establish the original saturation temperature and pressure. In certain designs, pressurizer heaters are energized continuously to make up for heat losses to the environment.

The pressurizer’s heater and spray capabilities are designed to compensate for the expected surge volume. The surge volume is the volume that accommodates the expansion and contraction of the system, and is designed to be typical of normal pressurizer performance. Plant transients may result in larger than normal insurges and outsurges. When the surge volume is exceeded, the pressurizer may fail to maintain pressure within normal operating pressures.

Pressurizer operation, including spray and heater operation, is usually automatically controlled. Monitoring is required in the event the control features fail, because the effect on the system could be disastrous without operator action.

<< Mixed-Bed Demineralizer