Boiler Tube Calculations - ASME Section I - PDF

^ Chapter 2 • Code Calculations - ASME Section I OBJECTIVE 1 Given the tube material specification numbers and other necessary parameters, use the formulas inASME BPVC Section 1, PG-27.2.1 to calculate either the minimum required wall thickness or the maximum allowable working pressure for a boile...

^ Chapter 2 • Code Calculations - ASME Section I OBJECTIVE 1 Given the tube material specification numbers and other necessary parameters, use the formulas inASME BPVC Section 1, PG-27.2.1 to calculate either the minimum required wall thickness or the maximum allowable working pressure for a boiler tube. MATERIAL SPECIFICATIONS Each section of the ASME Boiler and Pressure Vessel Code lists the materials approved for constructing boilers or pressure vessels according to that section. A specification is a technical description of a group of materials that have similar properties and are selected for certain applications. The material specification document states specific requirements, such as manufacturing and heat treatments, and chemical composition. Section I specifications are listed in paragraphs PG-6 to PG-9. Each steel specification listed in Section I has several types or grades. These are listed in Section II, Part D, Table 1A. Engineering design of boilers and pressure vessels draws upon principles of stress analysis, metallurgy, welding, and corrosion. One of the primary mechanisms in boiler design is the reduction of metal strength at elevated temperatures. The maximum allowable stress for a given metal drops off as the operating temperature rises. For this reason, tables in Section II of the ASJVIE Boiler and Pressure Vessel Code are used to determine the maximum allowable stress at the design temperature. Metal selection for boiler design must also account for various failure mechanisms that occur in high-pressure boilers, such as creep and fatigue. The design formulas in this chapter contain factors and coefficients to account for pipe threading, tube expansion, high-temperature effects, and efficiency reduction. Efficiency is the percentage of a materials strength that remains after some fabrication activity. One example is ligament efficiency, which is related to the amount of material left in the ligaments between drilled holes. Another example is efficiency of longitudinal welded joints. For seamless cylinders, the efficiency is 100% or 1. But for longitudinal seam welds in vessels operating at high temperatures, a strength reduction factor must be considered PanGlobal 2018 Academic Extract Boiler and Pressure Vessel Code Volume 1 and 2 The 2018 PanGlobal ASME Academic Extract, Volumes 1 and 2 will be the reference documents for this chapter. You will need a copy of each volume to complete the work in this chapter. 66 3rd Class Edition 3 • Part A2 Code Calculations - AS ME Section I ' Chapter 2 7® READING ASTM/ASME MATERIAL SPECIFICATION AND GRADE NUMBERS As shown in Figure 1, materials approved for boiler and pressure vessel construction have an ASTM/ASME specification number and a material type or grade designator. Figure 1 -ASTM/ASME Material Specifications SA-213-T22 S-ASME A - ferrous spec number grade/type Specification Number The specification number refers to a particular ASTM/ASME standard. The specification covers a group of metals that have a common material grouping (carbon steel, alloy steel, stainless steel) and product category (e.g., plate, pipe, tubing, forgings). Within a given specification, there will be several type/grade numbers. Table 1 shows some examples of specification numbers from PG-9. Table 1 - Examples of Specification Numbers (PG-9) Spec Number Category of Material Type of Product SA-182 Alloy steel Rolled or forged pipe flanges Note: The spec for SA-182 includes ferritic low alloy and austenitic and duplex stainless, but PG-9.1 says "ferritic only," meaning that only the low alloy ferritic grades (1, 2, 11, 12, 22) are permitted for boiler parts. Stainless steel grades of SA-182 are allowed for superheater parts as per PG-9.2. SA-335 SA-731 Ferritic alloy steel Pipe for high-temperature Ferritic and martensitic stainless steel 3rd Class Edition 3 • Part A2 service Seamless, welded pipe 67 ?& Chapter 2 • Code Calculations - AS ME Section I Type/Grade Designation There are different type/grade numbers within each specification, and the steel type or grade numbers are somewhat complicated. Here are some type/grade symbols used in Section I. 1. Carbon steel: The letters A, B, C, and D are used with carbon steel to indicate increasing tensile or yield strength, or an increase in carbon content. Increasing strength may also be indicated with numerical grade numbers such as 55, 60, 65, and 70. 2. Pipe: The letters F, E, and S are used with pipe to indicate the method of manufacture: F - furnace butt welded pipe E - electric resistance welded pipe S - seamless pipe 3. ASTM grade designators for pipe, tube, and forging products use a letter followed by a number. The letter indicates the type of product: P - pipe T - tube TP - tube or pipe WP - welded pipe F - forging The numbers may designate alloy or stainless steel. For example, TH means tube plus Grade 11 steel, as shown in points 4 and 5 below. 4. Alloy steels: High-temperature alloy steels are used extensively for boiler tubing and piping. These are low and medium alloys with chromium content up to 12%. There are two main categories of these steels, and these grade numbers are found in Section II, Part D, Table 1A. Low alloy (ferritic) steels generally have 3%-4% by weight of alloying elements such as chromium, nickel, molybdenum (moly), and vanadium. Some examples include the following: T2/P2 l/2Cr - l/2Mo T11/P11 1 l/4Cr - l/2Mo - Si T12/P12 12Cr - l/2Mo Note: The alloy content is expressed in percent by weight. When the chemical composition has no percent value, it means that there is only a small fraction of one percent. Medium alloy (martensitic) steels that have 9% to 12% chromium were developed as creep-resistant steels. They have greater high-temperature strength than the low alloy types. Some examples include the following: T91/P91 9Cr-lMo-V-Nb T92/P92 9Cr-1.8W- 0.5Mo-V-Nb T122/P12 UCr-2W-0.5Mo-Cu-V-Nb 5. Stainless steel: Type numbers may be based on the Society of Automotive Engineers (SAE) designation system for stainless steels. Stainless steel has a chromium content above roughly 12%. (The exact percentage may vary according to the reference.) Several grades of stainless steel are used in boiler construction such as the following: Ferritic stainless steel 400 series (405,409,429,430,439, 444,446) Martensitic stainless steel 400 series (410, 416, 420, 420C, 431, 440C) Austenitic stainless steel 200 and 300 series (201,202, 304, 309,316,321,347,348) Duplex stainless steel Grade F51 with 22Cr-5Ni-3Mo 68 <— 3rd Class Edition 3 ' Part A2 Code Calculations-ASME Section I • Chapter 2 T® There can be many different grades of a particular material, such as SA-182-F1 (a low alloy steel), SA-182-F304 (an austenitic stainless steel), or SA-182-F51 (a duplex stainless steel). Each grade has different characteristics, properties, and applications. When doing calculations, you will be given a material specification number. These numbers are ASME specs with a prefbc SA for ferrous materials and SB for non-ferrous. When doing a calculation, look up the spec number in Section I, PG-6 or PG-9 and write out the title or description listed. PG-6 deals with steel plate. PG-9.1 deals with boiler pipes, tubes, and pressure containing parts. PG-9.2 deals with all superheater parts. The specification titles in PG-6 and PG-9 contain important data such as material type (carbon or alloy; ferritic or austenitic) and type of product (seamless or welded; pipe, tube, or plate). This information may not be explicitly stated in the question you are trying to solve. So the information listed in PG-6 and PG-9 may help you determine the coefficients (C, E, e, y, and w) that are used in the formulas. This information will also help indicate the correct part of Section II, Part D, Table 1A to use, with information such as whether the metal is carbon steel or a low alloy steel. The table is arranged in order according to the category of steel. Self-Test 1 PG-9 Pipes, tubes, and pressure containing parts Check the following material specification numbers in Section 1, PG-9 and state the type of steel (carbon or alloy, ferritic or austenitic) and type of product (seamless or welded; tube or pipe). Spec number E.g. SA-192 1 SA-335 2 SA-209 3 SA-210 4 SA-250 5 SB-515 Type of steel Type of product Carbon steel ; Seamless boiler tubes 3rd Class Edition 3 • Part A2 69 Chapter 2 ' Code Calculations - ASME Section I BASIC CALCULATIONS FOR CYLINDRICAL VESSELS Figure 2 - Stress in a Cylindrical Vessel Under Internal Pressure In a cylindrical vessel under internal pressure, the principles of stress analysis show us that the wall stress acts in two principal directions: circumferential and longitudinal, as illustrated in Figure 2. It can be shown mathematically that the circumferential stress is double the longitudinal stress. Therefore, the basis for designing a cylindrical shape is the larger of the two, that is, the circumferential stress. The basic formulas for determining how thick a cylinder needs to be to contain a specific internal pressure or for determining the maximum allowable working pressure (MAWP) permitted for a cylinder of a given thickness, are as follows: Thickness t = MWAPP - 2a 2ta D where t = thickness of wall P = internal pressure a = circumferential stress However, as used in calculations related to boiler tubes, pipes, and headers, other factors also need to be considered. Calculations must take into account factors such as how the component is constructed (welded, seamless), the temperature it will be subject to, and allowances for threading. This leads to the more complete formulas used in PG-27, such as the following: t = -^PD— + 0.005D + e 2Sw+P ' "" and P = Sw 2t-0.01D-2e [D- (t- 0.005 D - e) In these formulas, the symbol for circumferential stress is substituted with S for the allowable stress of the material. 70 3rd Class Edition 3 • Part A2 Cocte Calculations - ASME Section I • Chapter 2 SYMBOLS USED IN THE FORMULAS OF PG-27 The following section describes the factors and coefficients used in boiler design calculations. Always include a code reference in your calculations that states the ASME code section, paragraph, and year of publication. The calculations included in this chapter are all based on ASME BPVC Sections I and 11-2015 as found in the 2018 PanGlobal ASME Academic Extract Volumes 1 and 2. PG-27 of ASME Boiler and Pressure Vessel Code, Section 1-2015 is titled "Cylindrical Components Under Internal Pressure." Its intent is best described in PG-27.1 General, which states, in part: The equations under this paragraph shall be used to determine the minimum required thickness or the maximum allowable working pressure of piping, tubes, drums, shells, and headers in accordance with the appropriate dimensional categories as given in PG-27.2.1, PG-27.2.2, and PG-27.2.3 for temperatures not exceeding those given for the various materials listed in Tables 1A and 1B of Section II, Part D. Note: Tables 1A and 1B of Section II, Part D (found in Vol. 2 of the PanGlobal ASME Academic Extract) span four pages each. Reference the line number on the first page to follow along each page until you find the correct temperature value required. 3rd Class Edition 3 • Part A2 71 r®- Chapter 2 • Code Calculations - ASME Section I The symbols in the formulas to be used in this chapter are found inASME BPVC, Section I, PG-27.3 and are defined in Table 2, Symbols from ASME Section I, PG-27.3. Table 2 - Symbols from ASME Section 1, PG-27.3 Unit Symbol Definition Minimum required thickness mm Maximum allowable working MPa (gauge pressure (MAWP) Details See PG-27.4.7 pressure) Outside diameter of cylinder mm Inside radius of cylinder mm Efficiency* of longitudinal welded Find values allowed for E in PG-27.4.1. The value joints or of ligaments between openings, whichever is lower. *Percentage of allowable stress No units for this factor remaining after drilling holes or of E for seamless cylinders is 1 .00. To determine the value for E, also check the ASME specification in PG-9 as several of these specs list the materials as seamless or welded. welding a material Maximum allowable stress value at the operating temperature of MPa See PG-27.4.2 and Section II, Part D, Table 1A the metal Minimum allowance for threading See PG-27.4.3 and structural stability Thickness factor for expanded See PG-27.4.4 tube ends The values allowed for y are between 0.4 and 0.7 and are listed in PG-27.4.6 (e.g., forferritic steel at 550°C, the value of y is 0.7). To determine this coefficient, you need to know if the steel is austenitic or ferritic. General guidelines: Austenitic - Stainless steels in the 200 and 300 series (e.g., A temperature coefficient No units for this factor TP304, 18Cr-8Ni; TP347, 18Cr-10Ni-Cb; TP316, 16Cr-10Ni-2Mo) - Duplex stainless steels (e.g., F51) Ferritic - Carbon steel - Low alloy ferritic (Grades 5, 11, 12, and 22) - Medium alloy martensitic (Grades 91 and 92) - Ferritic and martensitic stainless steel in the 400 series (e.g., TP410, 13Cr) Refer to PG-26 and Table PG-26. Note that w equals 1 .0 for the following: Weld joint strength reduction factor for components operating w in the creep range. This factor applies to longitudinal seam welds. No units for th is factor - Carbon steel at all temperatures (see Table PG26, Note 3). - Cr-Mo alloy steels up to 427°C* -Austenitic stainless steels up to 510°C* *For higher temperatures, refer to Table PG-26. 72 3rd Class Edition 3 • Part A2 Code Calculations - ASME Section I ' Chapter 2 BOILER TUBE CALCULATIONS It is extremely important that the correct units be applied when performing code calculations. In the following calculations, pressure (P) will be in megapascals, and the thickness {t), outside diameter (OD) (D), and inside radius (r) will be in millimetres. To calculate the required minimum wall thickness or the MAWP of ferrous boiler tubing, up to and including 125 mm OD, the following formulas, as given in PG-27.2.1, are used: PD Minimum thickness: t = _/'""_ + 0.005D + e 2Sw+P MAWP: P = Sw 2t-O.OW-2e \D-{t-0.005D-e) Example 1: Calculate minimum tube wall thickness Calculate the minimum required wall thickness of a superheater tube. The tube is 76.2 mm OD and is connected to a header by strength welding. The MAWP is 4150 kPa gauge and the average tube temperature is 400°C. The tube material is alloy (Cr-Mo) steel with the specification number SA-213-T11. Solution 1 PG-9.2 (superheater parts) says that the specification number SA-213 is "seamless austenitic and ferritic alloy steel tubes" and is allowed for use in superheaters. The question states that the steel is alloy (Cr-Mo); that is, it is a chrome-moly steel. This information will be needed to determine w below. From PG-27.2.1, the formula used to calculate minimum wall thickness is as follows: t = -^PD— + 0.005D + e 2Sw+P Given: P = 4150 kPa= 4.15 MPa D = 76.2mm First, use ASME BPVC, PG-27.4 to look up the required factors for the formula: e = 0 (as per PG-27.4.4, the tubes are to be the strength welded to the header) w = 1.0 (as per PG-27.4.1 and Table PG-26; SA-213-T11 is a Cr-Mo steel and its weld strength reduction factor at a temperature of400°C is 1.0) s = 102 MPa (as per Table 1A for SA-213-T11 at 400°C)* ^Note: This 102 MPa value for 5 is found in Section II, Part D, Table 1A. First locate the specification number, SA-213-T11, in the column under the headings "Spec. No." and Type/Grade. Then scan across the table pages to the 400°C" column under Maximum Allowable Stress, MPa, for Metal Temperatures, °C, Not Exceeding. The corresponding value is 102 MPa. 3rd Class Edition 3 • Part A2 73 ^ Chapter 2 • Code Calculations - AS ME Section I Convert the pressure units 4150 kPa = 4.15 MPa Now, complete the calculation by substituting all factors into the formula: t = ^PD ^+O.OQ5D+e 2Sw+P 4.15MPax 76.2mm t = ————"——^ ^ _^ 0.005 x 76.2 mm + 0 mm (2 x 102 MPa x 1) + 4.15 MPa 316.23 =^Tt+o'381mm = 1.90 mm (Ans.) Example 2: Calculate maximum allowable working pressure Calculate the MAWP, in kilopascals, for a watertube boiler tube that has a 76.2 mm OD and a wall thickness of 3.76 mm. The tube is expanded into the drum and located in the furnace area of the boiler. The thickness of the tube after expanding over the length of the seat plus 25 mm is 2.96 mm. The tube material is SA-213-T22, with a mean wall temperature of482°C. Solution 2 From PG-9, you see that SA-213 is seamless austenitic and ferritic alloy steel tubes. The specification is permitted in Section I, but marked "ferritic only." From Section II, Part D, Table 1A, we see that Grade T22 is 2 14Cr - IMo. This is a Cr-Mo or chrome-moly steel. We will need this information to find the weld joint strength reduction factor w. From PG-27.2.1, the formula used to find the MAWP is as follows: 2t-0.01D-2e P = Sw\ \D-(t-0.005D-e)\ Given: t = 3.76 mm, and t along the seat (after expanding) is 2.96 mm D = 76.2mm SA-213-T22at482°C Use the given information to look up the required factors for the formula: e = 1.0 mm (PG-27.4.4 states that e = 1.0 mm for tubes expanded into tube seats except if it meets certain conditions, which are listed. For a 76.2 mm tube, e may equal zero (0) if the thickness of the tube, after expanding, is 3.43 mm or greater. Since the tube end is 2.96 mm it does not meet the condition set in (c), therefore e = 1.) w = 0.91 (Using Table PG-26, go to the row marked Cr-Mo" and follow it across to the temperature column 482°C.) S = 80.9 MPa (the stress value for SA-213-T22 at 500°C) ^ ^Note: This 80.9 MPa value for S is found in Section II, Part D, Table 1A. Find SA-213-T22 in row 4 of the table and scan across to find the temperature. You will notice that there is no column for 482°C, so take the next higher temperature, which is 500°C. Use the value of 80.9 MPa from this column. 74 3rd Class Edition 3 • Part A2 Coote Calculations -ASME Section I • Chapter 2 In general, when a temperature given in a problem does not appear in Section II, Part D, Table 1A, select the next highest temperature from the table. Though interpolation is acceptable, this practice is not used at the Third Class level. Therefore, do not interpolate. Now, substitute the values of all factors into the formula: p = Su,[_2f,-aolD-Je [D-(t-0.005D-e)\ ~(2 x 3.76 mm) - (0.01 x 76.2 mm) - (2 x 1.0 mm) P = 80.9MPax0.91x |r/^"v/"/^/ v"'^/ll^"7 v""-^ 176.2 m - (3.76 mm - 0.005 x 76.2 mm - 1.0 mm) = 73.62 MPax = 73.62 MPax \(7.52 mm - 0.762 mm - 2.0 mm) | 76.2 mm - (2.379 mm) 4.758 mm 1 L73.821 mmj = 73.62MPax0.0644 = 4.75 MPa (Ans.) 3rd Class Edition 3 • Part A2 T© ?& Chapter 2 • Code Calculations - AS ME Section I 3rd Class Edition 3 • Part A2