ENVIRONMENTAL PROTECTION AGENCY. APTI 413: Control of Particulate Matter Emissions. Student Manual: Chapter 1

Transcription

1 ENVIRONMENTAL PROTECTION AGENCY APTI 41: Control of Particulate Matter Emissions Student Manual: Chater 1

2 A P T I : 4 1 C O N T R O L O F P A R T I C U L A T E M A T T E R E M I S S I O N S, 5 T H E D I T I O N Student Manual C 2 Technoloies, Inc Fountain Way Suite 200 Newort News, VA 2606 Phone Fax The rearation of this manual was overseen by the oranizations of the Environmental Protection Aency (EPA) and the National Association of Clean Air Aencies (NACAA*), and the revision of materials was coordinated and manaed by the Tidewater Oerations Center of C 2 Technoloies, Inc., Newort News, Virinia. Valuable research and feedback was rovided by an advisory rou of subject matter exerts comosed of Dr. Jerry W. Crowder, TX; Dr. Tim Keener, OH; Dr. Doulas P. Harrison, LA., and Mr. Tim Smith, Senior Air Quality Secialist, EPA, Office of Air Quality Plannin and Standards. Acknowledements and thanks are also extended to Ruters University, esecially Francesco Maimone, Co-Director of the Ruters Air Pollution Trainin Proram, which hosted the ilot of the revised materials, and the additional reference sources that can be found throuhout the manuals. *The National Association of Clean Air Aencies (NACAA) reresents air ollution control aencies in 5 states and territories and over 165 major metroolitan areas across the United States. State and local air ollution control officials formed NACAA (formerly STAPPA/ALAPCO) over 0 years ao to imrove their effectiveness as manaers of air quality rorams. The associations serve to encourae the exchane of information amon air ollution control officials, to enhance communication and cooeration amon federal, state, and local reulatory aencies, and to romote ood manaement of our air resources.

3 Table of Contents Basic Concets Gas Temerature... 1 Absolute Temerature... 2 Standard Temerature Gas Pressure... Barometric Pressure... Gaue Pressure... Absolute Pressure Molecular Weiht and the Mole Equation of State... 5 Volume Correction... 6 Molar Volume... 7 Gas Density Viscosity... 8 Liquid Viscosity... 9 Gas Viscosity... 9 Kinematic Viscosity Reynolds Number Calculation of Dew Point Review Questions Review Question Answers Review Problems Review Problem Solutions References... 19

4 Chater 1 This chater will take aroximately 2.5 hours to comlete. O B J E C T I V E S Terminal Learnin Objective At the end of this overview chater, the student will be able to understand basic science concets necessary for the control of articulate matter emissions. Enablin Learnin Objectives 1.1 Distinuish between two tyes of as temerature. 1.2 Distinuish between three tyes of as ressures. 1. Calculate the molecular weiht of as mixtures. 1.4 Identify the five arameters in the Ideal Gas Law. 1.5 Distinuish between the two tyes of viscosity. 1.6 Define two tyes of Reynolds Number. 1.7 Calculate Dew Point Basic Concets This chater distinuishes the basic concet used to reulate articulate matter emissions by examinin various control concets and methods. 1.1 Gas Temerature There are several scales available for measurin temerature. The Fahrenheit scale and the Celsius or Centirade scale, both of which are based on the roerties of water, are the two most commonly used scales for measurin temeratures. As shown below in Fiure 1-1, the Fahrenheit scale searates the freezin and boilin oints into 180-deree units. The Fahrenheit scale sets the freezin temerature of water at 2 F, and the normal boilin temerature of water at 212 F. The Celsius scale searates the freezin and boilin oints into 100-deree units. The Celsius scale sets the freezin temerature of water at 0 C and the normal boilin temerature at 100 C. The followin relationshis convert one scale to another: (1-1) (1-2) F 1.8 C + 2 F 2 C 1.8 Checks on Learnin End of Chater Review Fiure 1.1 In this course, the USEPA standard temerature of 68 F will be used 1

5 Absolute Temerature Fahrenheit and Celsius scales can be used in daily ractices, but both create difficulties when formin temerature ratios or when takin roots and owers of neative temeratures. The best resolve to these situations is an absolute temerature scale, which is a scale with zero set as its lowest value. Exeriments with ideal ases have shown that, under constant ressure, for each chane in Fahrenheit deree below 2 F the volume of as chanes 1/ Similarly, for each Celsius deree below 0 C the volume chanes 1/ Therefore, if this chane in volume er temerature deree is constant, then theoretically the volume of as would become zero at Fahrenheit derees below 2 F, or at F. On the Celsius scale, this condition occurs at Celsius derees below 0 C or at a temerature of C. Absolute temeratures determined by usin Fahrenheit units are exressed as derees Rankine ( R). Absolute temeratures determined by usin Celsius units are exressed as Kelvin (K). As shown below in Fiure 2-2 the followin aroximate relationshis convert one scale to the other: (1- & 1-4) R F K C + 27 Standard Temerature There is not a common temerature that is reconized by all rous. One articular temerature of interest is standard temerature. USEPA has two standard temeratures, one for air monitorin, and one for all other alications. The standard temeratures used by various rous are listed in Table 1-1. Table 1-1 Standard Temeratures Grou Tstd USEPA (General) 68 F (20 C) USEPA (Air monitorin) 77 F (25 C) Industrial hyiene 70 F (21.1 C) Combustion 60 F (15.6 C) Science 2 F (0 C) Examle 1-1 The as temerature in the stack of a wet scrubber system is 10 F. What is the absolute temerature in Rankine and Kelvin? 2

6 Solution Absolute Tem. R 460 R + 10 F 590 R 590 R Absolute Tem. K K 1.2 Gas Pressure A body may be subjected to three kinds of stress: shear, comression, and tension. Fluids are unable to withstand tension stress; therefore, they are subject only to shear and comression stress. Unit comressive stress in a fluid is termed ressure and is exressed as force er unit area (e.., lb f /in 2 and Newtons/m 2 ). Pressure is equal in all directions at a oint within a volume for fluid and acts erendicular to a surface. Barometric Pressure Barometric ressure and atmosheric ressure are synonymous. These ressures are measured with a barometer and are usually exressed as inches or millimeters of mercury (H). Standard barometric ressure is internationally reconized and is the averae atmosheric ressure at sea level, 45 N latitude and at 5 F. Standard barometric ressure is equivalent to a ressure of ounds force er square inch exerted at the base of a column of mercury inches hih. Other equivalents to standard ressure are listed in Table 1-2. Weather and altitude are resonsible for barometric ressure variations. Table 1-2. Standard Pressure Units Value Atmoshere (atm) 1 Pounds force er square inch (si) Inches of mercury (in H) Millimeters of mercury (mm H) 760 Feet of water column (ft WC).92 Inches of water column (in WC) 407 Kiloascals (kpa) 101. Millibars (mb) 101 Gaue Pressure The ressure inside an air ollution control system is termed the aue or static ressure and is measured relative to the revailin atmosheric ressure, as shown in Fiure 1-2. If the system ressure is reater than the atmosheric ressure, then the aue ressure is exressed as a ositive value. If the system ressure is smaller, then the aue ressure is exressed as a neative value. The term vacuum desinates a neative aue ressure. Gaue or static ressures in air ollution systems are usually exressed in inches of water column (in WC).

7 Fiure 1-2. Definition of ositive and neative aue ressures. Absolute ressure the alebraic sum of the atmosheric ressure and the aue ressure. Absolute Pressure The aue ressures commonly used in reference to air ollution control systems share an attribute that causes difficulties in the use of normal temerature scales they can have neative values. As a result, calculations involvin ressure ratios and roots and owers of ressure must use absolute ressure. Absolute ressure is the alebraic sum of the atmosheric ressure and the aue ressure: (1-5) P P b + P Where P absolute ressure P b barometric or atmosheric ressure P aue ressure An air ollution control device has an inlet static ressure of -25 in Examle 1-2 WC. What is the absolute static ressure at the inlet of the air ollution control device if the barometric ressure at the time is in H? Solution Convert the barometric ressure units to in WC : 407 in WC Pb in H 406 in WC in H Add the barometric and aue (static) ressures : P 406 in WC + (-25 in WC) 81in WC 1. Molecular Weiht and the Mole The molecular weiht of a comound is the sum of the atomic weihts of all the atoms in the molecule. The atomic weiht of an atom is based on an arbitrary scale of the relative masses of the elements, usually based on a carbon value of 12. The chemical identity of an atom is determined by the number of rotons in its nucleus and is called the atomic number. Values of atomic number and atomic weiht can be found in a Periodic Table of Elements. 4

8 Mixtures of molecules do not have a true molecular weiht; however, they do have an aarent molecular weiht that can be calculated from the comosition of the mixture: Periodic Table htt://education.jlab.or /beamsactivity/6thra de/tableofelements/stu 01.l.html Moles can be exressed in terms of any mass unit: ram-moles, kiloram-moles, ouncemoles, ound-moles and ton-moles (1-6) MW mixture n i 1 χ i MW where χ i is the mole fraction of comonent i and MW i is its molecular weiht. Proerties of a contaminated as can be aroximated by the roerties of air, which is itself a mixture of molecules. The aarent molecular weiht of air is 28.95, or aroximately 29. A mole is a mass of material that contains a certain number of molecules. Moles can be exressed in terms of any mass unit; thus, e.., there are ram-moles, kiloram-moles, ounce-moles, ound-moles and ton-moles. The relationshi between the different tyes of moles is the same as the relationshi between the corresondin mass units. Thus, there are 1,000 ram-moles in a kiloram-mole, 45.6-ram-moles in a oundmole, 16 ounce-moles in a ound-mole and 2,000 ound-moles in a ton-mole. The ram-mole is the mass of material that contains Avoadro's number of molecules, aroximately 6.02 x The mass of a mole is numerically equal to the molecular weiht. For oxyen, which has a molecular weiht of 2, there are 2 rams er rammole, 2 kilorams er kiloram-mole, and 2 ounds er-ound mole. However, only the ram-mole contains Avoadro's number of molecules. The kiloram-mole contains 1,000 times Avoadro's number of molecules; the ound-mole contains 45.6 times. i 1.4 Equation of State Equations of state relate the ressure, volume, and temerature roerties of a ure substance or mixture by semi-theoretical or emirical relationshis. Over the rane of temerature and ressure usually encountered in air ollution control systems, these values may be related by the ideal or erfect as law: (1-7) Where P absolute ressure V as volume n number of moles R as constant T absolute temerature PV nrt Here, R is referred to as the universal as constant, and its value deends on the units 5

9 of the other terms in the equation. Values of R include: 10.7sia ft /lb mole R 0.7atm ft /lb mole R atm cm / mole K 8.1x 10 kpa m /k mole K Volume Correction A useful relationshi can be develoed from the ideal as law by notin that PV/T nr, and that, for a iven number of moles of a as, nr is a constant. Thus, at two different conditions for the same as, we may write equation 1-8. Equation 1-9 allows volumes (or volumetric rates) to be corrected from one set of temerature and ressure conditions to another. One common calculation (1-10) is to convert volumetric flow rate from actual conditions to standard conditions, or vice versa (1-11). SCFM standard cubic feet er minute ACFM actual cubic feet er minute (1-8) (1-9) (1-10) (1-11) 1 P1 V1 T 1 V V 2 P2V T P SCFM ACFM P P ACFM SCFM P 2 2 P 2 T1 P1 T2 actual std std actual T T std actual T T actual std Examle 1- A articulate control system consists of a hood, ductwork, fabric filter, fan, and stack. The total as flow enterin the fabric filter is 8,640 scfm. The as temerature in the inlet duct is 20 F and the static ressure is -10 in WC. The barometric ressure is 28.0 in H. If the inlet duct has inside dimensions of feet by 4 feet, what is the velocity into the fabric filter? 6

10 Solution Convert the static ressure to absolute ressure : 407 in WC P 28.0in H ( 10 in WC) 75 in in H + WC Convert the as temerature to T actual 20 F R absolute temerature : Convert the inlet flow rate to actual conditions : Q actual 780 R 407in WC 8,640scfm 1,85acfm 528 R 75in WC Calculate the velocity: 1,85 ft V min 1,154 ft ft 4ft min Molar Volume The ideal as law can also be rearraned to calculate the volume occuied by a mole of as, called the molar volume: (1-12) Examle 1-4 V RT n P What is the molar volume of an ideal as at 68 F and 1 atm? At 200 F and 1 atm? Solution At68 Fand1atm : V n RT P atm ft 0.7 lb mole R 1atm ( 528 R) 85.4 ft lb mole At 200 F and 1 atm : V n or RT P atm ft 0.7 lb mole R 1atm ( 660 R) ft lb mole Gas Density V 660 R ft n 528 R lb mole 7

11 D E S I G N C U S T O M I Z A T I O N Finally, we can use the ideal as law to estimate as density. Density is the ratio of the mass of a material to the volume that material occuies. For accurate values, as densities should be determined from reference texts. However, an estimate of the as density can be determined from the ideal as law. Reconizin that the number of moles is iven by mass (m) divided by molecular weiht (MW), the ideal as law may be written: Gas Viscosity increases with an increase in temerature. (1-1) PV m MW The as density (ρ) can then be estimated from: RT (1-14) ρ m v P MW RT (1-15) Density can also be estimated from the molecular weiht and molar volume: MW 85.4 ρ Where Ρ absolute ressure (in H) Τ absolute temerature ( R) 1.5 Viscosity 528 T P Viscosity is the roerty associated with a fluid resistance to flow. Viscosity is the result of two henomena: (1) intermolecular cohesive forces and (2) momentum transfer between flowin strata caused by molecular aitation erendicular to the direction of motion. Between adjacent strata of a movin Newtonian fluid, a shearin stress, σ, occurs that is directly roortional to the velocity radient or shear rate, Γ (see Fiure 1-). This is exressed in the equation: (1-16) σ Γ dv dy Where σ shear stress roortionality constant Γ shear rate or velocity radient (dv/dy)

12 The roortionality constant,, is called the coefficient of viscosity, the absolute viscosity or merely viscosity. It should be noted that the ressure does not aear in Equation 1-16, indicatin that the shear stress and viscosity are indeendent of ressure. Actually, viscosity increases very slihtly with ressure, but this variation is neliible in most enineerin calculations. Fiure 1-. Shearin stress in a movin fluid Liquid Viscosity decreases with an increase in temerature. Liquid Viscosity In a liquid, transfer of momentum between strata flowin at slihtly different velocities is small comared to the cohesive forces between molecules. Hence, viscosity in liquids is redominantly the result of intermolecular cohesion. Because forces of cohesion decrease raidly with an increase in temerature, liquid viscosity decreases with an increase in temerature. Gas Viscosity In a as, the molecules are too far aart for intermolecular cohesion to be effective. Thus, the viscosity in ases is redominantly the result of an exchane of momentum between flowin strata caused by molecular transfer. Since molecular motion increases as temerature increases, as viscosity increases with an increase in temerature. The viscosity of air at any temerature may be estimated from: (1-17) Where absolute viscosity T ref T ref ref absolute viscosity at reference temerature Τ absolute temerature reference absolute temerature Τ ref 9

13 The viscosity of air containin other ases imortant in air ollution control alications can also be estimated from: (1-18) Τ +.24 x 10-5 Τ x y Where absolute viscosity (microoise) Τ absolute temerature x water vaor content (fraction) y oxyen content (fraction) The viscosity of air at 68 F is 1.21 x 10-5 lb m /ft. sec or 1.8 x 10-4 /cm sec Kinematic Viscosity The ratio of the absolute viscosity to the density of a fluid, known as kinematic viscosity, often aears in dimensionless numbers, such as the Reynolds Number. Kinematic viscosity is defined accordin to the followin relationshi and is used to simlify calculations: Dimensionless numbers htt:// extract8.htmltemerature. htt://en.wikiedia.or/wiki/ Dimensionless_numbers (1-19) Where υ kinematic viscosity absolute viscosity ρ density viscosity v ρ Reynolds Number Is the ratio of inertial forces to viscous forces in a flowin fluid. Reynolds Number Reynolds Number is the ratio of inertial forces to viscous forces in a flowin fluid. A tyical inertial force er unit volume of fluid is ρν 2 /L. A tyical viscous force er unit volume of fluid is ν/l 2. The first exression divided by the second rovides the dimensionless ratio known as the Reynolds Number: (1-20) Re Lvρ Where Re Reynolds Number L characteristics system dimension ν fluid velocity ρ fluid density fluid viscosity 10

14 The linear dimension, L, is a lenth characteristic of the flow system. It is equal to four times the mean hydraulic radius, which is the cross-sectional area divided by the wetted erimeter. Thus, for a circular ie, L is the ie diameter, D, and the Reynolds Number (sometimes termed the Flow Reynolds Number) takes the form: (1-21) Re Dvρ Particle Motion Most article motion in air ollution control devices occurs in the Stokes and Transitional Reions. Reynolds Number in this form is used to distinuish between laminar and turbulent flow. In laminar flow, the fluid is constrained to motion in layers, or laminae, by the action of viscosity. These layers of fluid move in arallel aths that remain distinct from one another. Laminar flow occurs when the Reynolds Number is less than about 2,000. In turbulent flow, the fluid is not restricted to arallel aths but moves forward in a random, chaotic manner. Fully turbulent flow occurs when the Reynolds Number is reater than about,000. Between Reynolds Numbers of 2,000 and,000, the flow may be laminar or turbulent, deendin on the flow system conditions. Pie or duct vibration, for examle, can cause turbulent conditions to exist at Reynolds Numbers sinificantly below,000. It is worth notin that, rimarily because of the size, flow in air ollution control equiment is always turbulent. Laminar conditions are resent only in the very thin boundary layers that form near surfaces. A form of Reynolds Number that is of reater interest in this course is the Particle Reynolds Number. Here, the characteristic system dimension is the article diameter, d, and the velocity, v, is the article velocity relative to the as stream: (1-22) Re Particle Reynolds Number is used to characterize flow conditions when articles move throuh or with a flowin fluid. Particle Reynolds Numbers less than about one indicate laminar conditions and define what is commonly termed the Stokes Reion. Values over about 1,000 indicate turbulent conditions and define what is commonly termed the Newton Reion. Particle Reynolds Numbers between 1 and 1,000 indicate transitional conditions. Most article motion in air ollution control devices occurs in the Stokes and Transitional Reions. Examle 1-5 Calculate the Particle Reynolds Number for a 2m diameter article movin throuh 10 C still air at a velocity of 6 m/sec. Solution From Aendix B, the density of air at 20 C is 1.20 x 10 - /cm and the viscosity is 1.80 x 10-4 /cm(sec) D v ρ 11

15 Estimate the as density at10 C. 29K ρ 1.20x x10 28K Estimate the as vicosity at10 C. 4 29K 1.80x x10 28K CalculateParticle Reynolds Number : Re d v ρ (2x cm) 2 ( 6x10 cm ) 1.75x10 cm 4 4 cm sec 1.24x10 sec cm sec cm Examle 1-6 Calculate the Particle Reynolds Number for a as stream movin throuh a 200 cm diameter duct at a velocity of 1,500 cm/sec. Assume that the articles are movin at the same velocity as the as stream and are not settlin due to ravity. Assume a as temerature of 20 C and standard ressure. Solution Since there is no difference in velocity between the as stream and the article, the Particle Reynolds Number is zero. The Flow Reynolds Number is: 1.20x10 sec Dvρ cm Re 2.00x x10 cm sec ( 200cm)( 1,500 cm ) 6 Why is Dew Point imortant? This condensate can form aste on fabric filters makin them unusable 1.7 Calculation of Dew Point Many as streams that must be treated for articulate emissions may also contain sinificant amounts of water vaor or another condensable comonent. In most cases, for examle, if articulate control is to be accomlished usin fabric filters, it is necessary that the as stream be maintained at a temerature sufficient to revent the water or other comonent from condensin as condensation will cause the articulate matter to collect on the filters as a aste that cannot be easily cleaned. The temerature at which condensation occurs is also known as the dew oint temerature. At the dew oint temerature the artial ressure of the condensable comonent is equal to its vaor ressure 12

16 Where Ρ i P * yρ P i artial ressure of the condensable comonent P* vaor ressure of the condensable comonent y i mole fraction of the condensable comonent in the as P total ressure Vaor ressure as a function of temerature can be obtained from the Antoine equation. Where B lo 10 P* A T + C P* vaor ressure, m H T Temerature, C A, B, and C are unique constants for each comonent Tables of Antoine constants may be found in numerous standard references and is offered in Aendix C. i For water, values of the vaor ressure as a function of temerature may be obtained directly from Vaor Pressure Tables (available widely on the internet. Examle 1-7 The mol fraction of water in the stack as from a combustion rocess contains 14 mol% water vaor. What is the dew oint temerature if the total ressure is 1 atm? The Antoine constants for water are: Where to see Steam Tables htt://ye.dyndns.or/fre esteam/ Solution A B C At the dew oint temerature: P* P i y i P 0.14 (1) 0.14 atm or mmh From the Antoine equation: lo 10 P* T Solve for T to obtain: T 5 C 1

17 Review Questions 1. How does the article Reynolds number chane when the as temerature is increased? a. Increases b. Decreases c. Remains unchaned 2. How does the as viscosity chane as the temerature is increased? a. Increases b. Decreases c. Remains unchaned. Flow in air ollution control equiment is always turbulent, and Laminar conditions are only resent in the very thin boundary layers that form near surfaces. a. True b. False 4. When Particle Reynolds Numbers indicate laminar conditions that exist within the a. Flow Reynolds Reion b. Newton Reion c. Stokes Reion d. Viscous Reion 14

18 Review Question Answers 1. How does the article Reynolds number chane when the as temerature is increased? (see ae 10) b. Decreases 2. How does the as viscosity chane as the temerature is increased? (see ae 9) a. Increases. Flow in air ollution control equiment is always turbulent, and Laminar conditions are only resent in the very thin boundary layers that form near surfaces. (ae 10) a. True 4. When Particle Reynolds Numbers indicate laminar conditions that exist within the c. Stokes Reion 15

19 Review Problems 1. The flows from Ducts A and B are combined into a sinle Duct C. The flow rate in Duct A is 5,000 scfm, the as stream temerature is 50 F and the static ressure is -2 in WC. The flow rate in Duct B is 4,000 acfm, the as stream temerature is 400 F and the static ressure is -5 in WC. What is the flow rate in Duct C? Assume a barometric ressure of in H. (see ae 6) 2. Calculate the Particle Reynolds Numbers for the followin articles. Assume a as temerature of 20 C and a ressure of 1 atm. (see ae 10) a. 10 m article movin at 1 ft/sec relative to the as stream b. 10 m article movin at 10 ft/sec relative to the as stream c. 100 m article movin at 1 ft/sec relative to the as stream d. 100 m article movin at 10 ft/sec relative to the as stream 16

20 Review Problem Solutions 1. The flows from Ducts A and B are combined into a sinle Duct C. The flow rate in Duct A is 5,000 scfm, the as stream temerature is 50 F and the static ressure is -2 in WC. The flow rate in Duct B is 4,000 acfm, the as stream temerature is 400 F and the static ressure is -5 in WC. What is the flow rate in Duct C? Assume a barometric ressure of in H. (see ae 6) Solution Calculate the absolute ressure in Duct B : 407 in WC Ρ 29.15in H + ( 5in WC) 61.5in WC 29.92in H Convert the flow in Duct B to standard conditions : 528 R 61.5in WC QB 4,000acfm 2,181scfm 860 R 407 in WC Combine flows : Q c 5,000 scfm + 2,181scfm 7,181scfm 2. Calculate the Particle Reynolds Numbers for the followin articles. Assume a as temerature of 20 C and a ressure of 1 atm. (see ae 10) a. 10 m article movin at 1 ft/sec relative to the as stream b. 10 m article movin at 10 ft/sec relative to the as stream Solution a & b Re d vρ 4 ( 10x10 cm)( [ 1.0 ft )( 0.48 cm )] sec 1.80x x10 ft cm sec cm 0.20 Re d v ρ 4 ( 10x10 cm)( [ 10.0 ft )( 0.48 cm )] sec 1.80x10 4 cm sec 1.20x10 ft cm 2.02 c. 100 m article movin at 1 ft/sec relative to the as stream d. 100 m article movin at 10 ft/sec relative to the as stream 17

21 Solution c & d Re d v ρ 4 ( 100x10 cm)( [ 1.0 ft )( 0.48 cm )] sec 1.80x10 4 cm sec 1.20x10 ft cm 2.0 Re d v ρ 4 ( 100x10 cm)( [ 10.0 ft )( 0.48 cm )] sec 1.80x10 4 cm sec 1.20x10 ft cm

22 References Cenel, Y.A., and M.A. Boles, Thermodynamics: An Enineerin Aroach, McGraw- Hill, New York, Himmelblau, D.M., Basic Princiles and Calculations in Chemical Enineerin, Prentice-Hall, Enlewood Cliffs,