Measurement and Control Basics 3rd Edition (complete book)

Chapter 8 – Analytical Measurement and Control

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infinity, hence, they are called “strong” acids. On the other hand, an acid such as acetic (HC2H3O2 or C H3COOH) breaks up as follows: (CH3COOH ↔ H+ + CCH3COO–). For this acid, very few hydrogen ions show up in the solution--less than one in every one hundred undissociated molecules. It therefore has a low dissociation constant and is called a “weak” acid. Thus, the strength of an acid solution depends on the number of hydrogen ions available. That number depends, in turn, on the weight of the compound and, in water, the dissociation constant of the particular compound.

When the free hydroxyl ions (OH–) predominate, the solution is alkaline or basic. For example, sodium hydroxide (NaOH) in water completely dissociates as follows: (NaOH → Na+ + OH–). It is therefore a strong base. On the other hand, ammonium hydroxide (NH4OH) weakly dissociates into NH+4 ions and OH- ions and thus is a weak base.

Pure water dissociates into H+ and OH– ions, as follows:

(HOH → H+ + OH–). However, it is considered extremely “weak” because very little of the HOH breaks up into H+ and OH– ions. So few water molecules dissociate vis-à-vis those that are undissociated that the value of (HOH) can be considered equal to one or 100 percent. The ionization constant of water has been determined to have a value of 10-14 at 25°C. The product of the activities (H+)(OH–) is then 10-14.

If the concentrations of hydrogen ions and hydroxyl ions are the same, they must be 10+7 and 10-7, respectively. Regardless of what other compounds are dissolved in the water, the product of the concentrations of H+ ions and OH– ions is always 10-14. Therefore, if you add a strong acid to water, many hydrogen ions are added and will reduce the hydroxyl ions accordingly. For example, if you add HCl at 25°C until the H+ concentration becomes 10-2, the OH– concentration must become 10-12.

It is awkward to work in terms of small fractional concentrations such as 1/107, 1/1012, 1/102. For that reason, in 1909 Sorenson proposed that for convenience the expression “pH” be adopted for hydrogen-ion concentration to represent degree of acidity or activity of hydrogen ions. This term was derived from the phrase the power of hydrogen. Sorenson defined the pH of a solution as the negative of the logarithm of the hydrogen-ion concentration, or

pH = –log10 [H+]

(8-4)

He also defined it as the base 10 log of the reciprocal of the hydrogen-ion concentration:

pH = log 1/[H+]

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This means that if the hydrogen-ion concentration is 1/10x, the pH is said to be x. In pure water, where the concentration of the hydrogen ion is 1/107, the pH is therefore 7.

If we know the OH ion concentration but not the H+ ion concentration of an aqueous solution, we can still calculate the pH by using the following relationship:

[OH– ][H+] = 10-14

(8-5)

For example, if [OH– ] = 10-2, then [H+] = 10-14 /10-2 = 10-12, and the

pH = –(–12) = 12. The acidity or basicity of a solution can be expressed either in terms of its H+ ion concentration, its OH– ion concentration, or its pH, as shown in Table 8-1.

Table 8-1. Acidity or Basicity of Aqueous Solutions

Solution	[H+]	[OH– ]	pH	Nature of Solution
0.01 M HCl	10–2	10–12	2	Acidic
10–5 M HCl	10–5	10–9	5	Acidic
H O (pure water)	10–7	10–7	7	Neutral
2
10–5 M NaOH	10–9	10–5	9	Basic
0.01 M NaOH	10–12	10–2	12	Basic

Example 8-2 shows a typical calculation to obtain hydrogen ion concentration and pH values based on a given OH ion concentration.

EXAMPLE 8-2

Problem: The [OH– ] ion concentration of an aqueous solution is 10–8. What are the values of the H+ ion concentration and pH?

Solution: First, use Equation 8-5 — [OH – ][H+] = 10–14 — to determine [H+]. Since [OH– ] = 10–8, we obtain [H+] = 10–14/10–8 = 10–6. Then, we determine the pH value using Equation 8-4:

pH = –log10 10–6 = –(–6) = 6

pH Electrode Systems

Industrial electrode systems for pH determinations consist of two separate electrodes. The first is the active or measuring electrode, which produces a voltage that is proportional to the hydrogen-ion concentration. The second

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is a reference electrode, which serves as a source of constant voltage against which the output of the measuring electrode is compared.

A number of measuring electrodes have been developed for pH applications, but the glass electrode has evolved as the universal standard for industrial process purposes. Typically, it consists of an envelope of special glass that is designed to be sensitive only to hydrogen ions. It contains a neutral solution of constant pH (called buffer solution) and a conductor, immersed in the internal solution, which makes contact with the electrode lead.

The electrode operates on the principle that a potential is observed between two solutions of different hydrogen-ion concentration when a thin glass wall separates them. The solution within the electrode has a constant concentration of hydrogen ions. Whenever the hydrogen-ion concentration of the solution being measured differs from that of the neutral solution within the electrode, a potential difference (or voltage) is developed across the electrode. If the solution being measured has a pH of 7.0, the potential difference is 0. When the pH of the measured solution is greater than 7.0, a positive potential exists across the glass tip. When the pH is less than 7.0, a negative potential exists.

The glass electrode responds predictably within the 0 to 14-pH range. It develops 59.2 mv per pH unit at 25°C, which is consistent with the Nernst equation:

		E =	RT	ln	[H + ]outside		(8-6)
					[H + ]inside
			F
where
E	=	potential (v)
R	= the gas law constant
F	= Faraday's number, a constant
T	=	temperature (K)
[H+]	=	the hydrogen-ion concentration

Many types of glass electrodes are available, and which one you choose to use will usually depend on the temperature range and physical characteristics of your process. The reference electrode is used to complete the circuit so the potential across the glass electrode can be measured.

Because of the temperature coefficient of the glass electrode, you must compensate the system for temperature if it is to continue to read pH correctly. This is done manually at a point where the temperatures do not vary widely. Otherwise, it is done automatically by means of a tempera-

208 Measurement and Control Basics

ture element, which is located in the vicinity of the electrodes and connected into the circuit. Therefore, the industrial pH assembly can consist of as many as three units: the glass measurement electrode, the reference electrode, and a temperature element mounted in holders of differing designs.

pH Measurement Applications

Applications for pH measurement and control can be found in wastetreatment facilities, pulp and paper plants, petroleum refineries, power generation plants, and across the chemical industry. In other words, continuous pH analyzers can be found in almost every industry that uses water in its processes.

Figure 8-2 shows an example of pH control—a P&ID of the manufacturing of disodium phosphate using flow and pH control. The automatic control system shown in the figure produces a high-purity salt and prevents unnecessary waste of both reagents (i.e., soda ash and phosphoric acid).

FT	FIC		AIC
100	100		101
FE		FV	AV
100			101
		100
Soda			Phosphoric
Ash		M	Acid
			AE
			101
			pH
			Salt
			Product

Figure 8-2. P&ID for production of disodium phosphate

Density and Specific Gravity Measurement

Control of the more common variables, such as flow, temperature, and pressure, is the basic criterion for process control. However, there are cases where measuring density or specific gravity (SG) is the best way to determine and control the concentration of a process solution. For a fluid, density is defined as the mass per unit volume and is usually expressed in

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units of grams per cubic centimeter (g/cm3) or pounds per cubic foot (lb/ft3). The specific gravity of a fluid is the ratio of the density of the fluid to the density of water at 60°F (15.5°C).

Hydrometer

The simple hand hydrometer consists of a weighted float that has a smalldiameter stem proportioned such that more or less of the scale is submerged according to the specific gravity. These hydrometers are widely used for “spot” or off-line intermittent specific gravity measurements of process liquids. A typical use for a hydrometer is checking the state of discharge for a lead-acid cell by measuring the specific gravity of the electrolyte. Concentrated sulfuric acid is 1.835 times as heavy as water (the reference with a specific gravity of 1) for the same volume. Therefore, the specific gravity of the acid equals 1.835.

In a fully charged automotive cell, the mixture of sulfuric acid and water results in a specific gravity of 1.280 at a room temperature of 70°F. As the cell discharges, more water is formed, lowering the specific gravity. When the gravity falls to about 1.150, the cell is completely discharged. Specific gravity readings are taken with a battery hydrometer, as shown in Figure 8-3. Note that the calibrated float that has the SG marks will rest higher in an electrolyte of higher specific gravity.

1.150	1.280

Figure 8-3. Hydrometer to test specific gravity of battery fluid

The importance of specific gravity is evidenced by the fact that the opencircuit voltage of the lead-acid cell is given approximately by the following equation:

V = (SG + 0.84) volts

(8-7)

For SG = 1.280, the voltage is 1.280 + 0.84 = 2.12 v. This value is for a fully charged single-cell battery.

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Example 8-3 shows how to calculate the no-load voltage of a battery.

EXAMPLE 8-3

Problem: The specific gravity of a six-cell lead-acid battery is measured as 1.22. Calculate the no-load voltage of the battery.

Solution: Use Equation 8-7 to calculate the voltage of a single cell:

V = SG + 0.84 (volts)

V = 1.22 + 0.84v

V = 2.06v

Since the battery has six cells, the no-load voltage of the battery is as follows:

V = 6 x (2.06)v

V = 12.36v

The problem with the simple hydrometer is that it cannot perform the continuous measurement that process control requires. However, you can use the photoelectric hydrometer shown in Figure 8-4 to obtain a continuous specific gravity value. In this instrument, a hydrometer is placed in a con- tinuous-flow vessel. Since the instrument stem is not opaque, it affects the amount of light passing through a slit to the photocell as the stem rises and falls. You can use this instrument in any specific gravity application that is not harmful to the instrument and that is normally accurate to two or three decimal places.

Fixed-Volume Method

A common continuous density-measuring device that utilizes the fixedvolume density principle is the so-called displacement meter, which is schematically illustrated in Figure 8-5. In this device, liquid flows continuously through the displacer chamber, with the buoyant body, or displacer, completely immersed. The buoyant force is exerted on the displacer. It is dependent on the weight of the displaced liquid and, in turn, is a function of the volume and specific gravity.

If the volume is constant, the force will vary directly with the specific gravity. An increase in specific gravity will produce a greater upward force on the displacer and on the left end of the rigid beam. Since the beam moves about a fulcrum located between the displacer and the balancing

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Light Source

Photoelectric

Cells

Liquid Out

Liquid In

Figure 8-4. Photoelectric hydrometer

Fluid In
	Displacer
	Fulcrum	Nozzle Tip
		Air Supply
Fluid Out	Balancing Bellows	Density
		Signal

Figure 8-5. Buoyancy-type density measurement

212 Measurement and Control Basics

bellows, this upward force causes the right-hand end of the beam to move closer to the nozzle. This, in turn, created an increase in the pressure at the nozzle that is sensed by the balancing bellows, which will expand. As the bellows expand, the right-hand end of the beam moves away from the nozzle, moving the baffle away from the nozzle tip and causing a reduction in pressure in the pneumatic system. The bellows will move just enough to reestablish a new position or torque balance with somewhat different pressure. This is read on a pressure instrument that is calibrated in density or specific gravity units.

Differential-Pressure Method

One of the simplest and most widely used methods of continuous density measurement uses the pressure variation produced by a fixed height of liquid. As Figure 8-6 shows, the difference in pressure between any two elevations below the surface is equal to the difference in liquid pressure (head) between these elevations, regardless of the variation in level above the higher elevation.

Liquid Level

h1

Elevation 2

h2

h

Elevation 1

Figure 8-6. Differential pressure density measurement method

This difference in elevations is represented by dimension h. This dimension must be multiplied by the specific gravity of the liquid to obtain the difference in head in inches of water, which is the standard unit for measurement calibration. To measure the change in head that results from a change in specific gravity from minimum (SGmin) to maximum (SGmax), you must calculate the difference between hSGmin and hSGmax:

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		dP = h (SGmax – SGmin)	(8-8)
where
dP	=	differential pressure (inches of water)
h	=	the difference in elevations (inches)
SGmin	=	minimum specific gravity
SGmax	=	maximum specific gravity

It is common practice to measure only the span of actual density changes. This is done by elevating the instrument “zero” to the minimum pressure head to be encountered, allowing the entire instrument working range to be devoted to the differential caused by density changes. For example, if SG = 1.0 and h = 100 in., the range of the measuring instrument must be elevated h x SG, or 100 in. of water. For SG = 0.9 and h = 100 in., the elevation would be 90 in. of water. Thus, the two principal relationships to be considered in this type of measuring device are as follows:

Span = h (SGmax – SGmin)	(8-9)
Elevation = h X SGmin	(8-10)

The calculation of the span for a typical differential-pressure type density instrument is illustrated in Example 8-4.

EXAMPLE 8-4

Problem: Calculate the span in inches of a differential-pressure type density instrument if the minimum specific gravity is 0.90, the maximum specific gravity is 1.10, and the difference in liquid elevation is 20 inches.

Solution: Using Equation 8-9, we obtain the following:

Span = h (SGmax – SGmin)

Span = 20 inches(1.10 – 0.90)

Span = 4 inches

Figure 8-7 shows an instrument that uses a differential-pressure method to determine density. This application consists of a process tank and two bubbler tubes that are installed in the fluid of the tank, so that the end of one tube is lower than the end of the other. The pressure required to bubble air into the fluid is equal to the pressure of the fluid at the ends of the bubble tubes.

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	High	AIT	Signal Proportional
			to Fluid Density
		Low
	Air		dP Cell
	Purge

Figure 8-7. Air purge dP density measurement method

Since the outlet of one tube is lower than that of the other, the difference in pressure will be the same as the weight of a constant-height column of liquid. Therefore, the differential-pressure measurement is equivalent to the weight of a constant volume of the liquid and can be represented directly as density.

Nuclear Method

You can also use nuclear devices to measure density. They operate on the principle that the absorption of gamma radiation increases with the density of the material being measured. A representative radiation-type den- sity-measuring element is depicted in Figure 8-8. It consists of a constant gamma-ray radiation source (which can be radium, cesium, or cobalt), which is mounted on a wall of the pipe, and a radiation detector, which is mounted on the opposite side. Gamma rays are emitted from the source, through the pipe, and into the detector. Materials flowing through the pipeline and between the source and detector absorb radioactive energy in proportion to their densities. The radiation detector measures the radioactive energy that is not absorbed by the process material. The amount that is measured varies inversely with the density of the process stream. The radiation detector unit converts this energy into an electrical signal, which is transmitted to an electronics module.