# Optimized design of large-diameter high-pressure equipment flanges

A bolted flange connection is the most commonly used form of detachable connection structure in the petroleum and chemical industry, which is widely used and is used as a standard part by many countries. Corresponding standards have been developed for designers to choose from. China has also developed corresponding industry standards, such as GB/T 13402-2019 “large diameter steel pipe flange“, HG/T 20592-20635-2009 “steel pipe flanges, gaskets, fasteners“, NB/T 47020-47027- 2012 “Pressure Vessel Flanges, Gaskets, Fasteners” and SH/T 3406-2013 “Petrochemical Steel Pipe Flanges”. The use of standard flanges simplifies calculations, reduces design costs, improves design efficiency, and ensures the reliability and interchangeability of flanges. However, with the large scale and specialization of equipment, some flanges are often encountered beyond the standard use limitations, which need to be in accordance with GB/T 150.1-150.4-2011 “Pressure Vessel” or ASME Sec.Ⅷ Div.1-2021 “Rules for Construction of Pressure Vessel” mandatory. of Pressure Vessel” mandatory appendix 2 method for design or structure optimization.

The bolted flange connection consists of flanges, sealing gaskets and fasteners. The flange sealing surface is compressed by the action of the bolt preload, which presses the sealing gasket clamped between a pair of flanges so that the gasket elastically or plastically deforms under the action of the bolt preload to fill the micro-geometric gaps in the flange sealing surface and achieve the sealing purpose. The main failure mode to be considered in flange design is leakage between flange sealing surfaces, for which it is necessary to ensure that the bolts, gaskets and flanges have sufficient strength. Reasonable flange design is based on the main failure mode selection of the appropriate gasket, configuration of a set of appropriate bolts, and determining the appropriate size of the flange structure to avoid leakage of the flange connection. In the paper, the optimized design of flanges for large-diameter high-pressure equipment is introduced by taking the filter separator in an offshore platform engineering project as an example.

## 1. Project example

An offshore platform project has a filter separator at the entrance of the trim ethylene glycol treatment system. In order to facilitate the installation and maintenance of the upper polymerization filter inside the separator, the upper head needs to be designed as a flange connection. The design parameters of the filter separator are inner diameter Φ1200mm, design pressure 13.2MPa, design temperature 70℃, cylinder material Q345R (normalized), thickness 54mm, corrosion margin 4mm, flange material 16MnⅣ. Flange size, high pressure, the parameters are beyond the existing equipment flange standard range, so reference GB/T 13402-2019, select the size that is closer to the DN1200mm A series Class 900 pipe flange; its structural dimensions are shown in Table 1.

Table.1 Flange structure size before and after optimization

Flange status | Original design | After optimization |

Outer diameter of flange/mm | 1785 | 1760 |

Flange cone neck small end diameter/mm | 1262 | 1316 |

Flange cone neck large end diameter/mm | 1343 | 1412 |

Flange height/mm | 419 | 350 |

Minimum thickness of flange ring/mm | 233.4 | 200 |

Bolt hole center circle diameter/mm | 1587.5 | 1600 |

Bolt specifications | M100 | M80 |

Number of bolts | 24 | 28 |

Flange protrusion diameter/mm | 1 384 | 1 472 |

Raised surface height/mm | 7 | 21 |

However, applying the pipe flange to the filter separator has the following problems:

- (1) Because of the high design pressure of the equipment, in order to enhance the sealing effect between the flanges, it is necessary to change the original flange protruding surface sealing to annular connecting surface sealing, and the gasket is changed to the metal annular gasket.
- (2) The flange diameter is larger, so the selected bolt specification is larger, which affects the thickness of the flange neck and makes the flange axial stress larger.
- (3) The flange stress calculation needs to be qualified, need to optimize the flange structure size.

## 2. Equipment flange optimization design

### 2.1 Gasket design

#### 2.1.1 Gasket form determination

Gasket design is the basis of the entire flange connection design; gasket form, material, inner diameter and width selection will have a great impact on the flange connection design results. The design pressure of the filter separator is high; in order to ensure that the gasket is not damaged in the working process and maintains excellent sealing performance, the gasket coefficient m, specific pressure y should be selected higher metal gasket. Compared with a metal winding gasket, an octagonal metal gasket has a certain radial self-tightening effect, good sealing effect, not easy to leak, long service life, and can be reused. Compared with an elliptical gasket, the octagonal metal gasket is easy to process and manufacture, so an octagonal metal gasket is chosen as the sealing gasket of the flange. Gasket material selection of stainless steel UNS S31603, material hardness is not greater than 150 HBS.

#### 2.1.2 Gasket size determination

Reference GB/T 150.3-2011 “Pressure Vessel Part 3: Design” Appendix C.6 part of the “octagonal metal gasket and elliptic gasket sealing”, select the octagonal metal gasket suitable for Class 900 ring number R105, octagonal metal gasket cross-section dimensions and flange ring connecting surface trapezoidal groove dimensions are shown in Figure 1. The center circle diameter of this type of octagonal metal gasket cannot meet the requirements of the equipment and needs to be re-determined. In the case of a certain diameter of the bolt center circle, with the increase of the gasket center circle diameter, the bolt preload state and the operating state of the design load increases, the internal pressure caused by the total axial force arm decreases, affecting the design of the moment change. Through the calculation of different gasket center circle diameters, the flange calculation moment with the gasket center circle diameter change curve is obtained, see Figure 2.

Figure.1 R105 octagonal metal gasket cross-section dimensions and flange ring connection surface trapezoidal groove size

Figure.2 Gasket center circle diameter on the flange calculation moment curve

From the curve in Figure 2, it can be seen that the gasket center circle diameter is about 1380mm when the flange calculation moment value is the smallest, the gasket center circle diameter is less than 1380mm, the flange calculation moment with the gasket center circle diameter increases gradually decreases. When the gasket center circle diameter is larger than 1380mm, the flange calculation moment increases slowly with the increase of the gasket center circle diameter. To minimize the flange calculation moment, the center circle diameter of the gasket should be selected near 1380mm; in this case, the center circle diameter of the flange gasket is finally taken as 1372mm.

### 2.2 Bolt design

After the gasket material and size are determined, the gasket can be calculated in the pre-tensioning and operating conditions of the required compression load. The bolt provides the compression load, and the minimum bolt area required for preloading and operating conditions can be calculated accordingly:

Formula (1) – Formula (2) in Am1 for the pre-tensioned state of the minimum required bolt area, A_{m2} for the operating state of the minimum required bolt area, S_{a} for the permissible stress of the bolt at room temperature, the permissible stress of the bolt at the design temperature, Wm1 for the pre-tensioned state of the minimum bolt load, W_{m2} for the operating state of the minimum required bolt load. The selection of bolt specifications and the number of actual uses of bolts should make the total cross-sectional area Ab equal to A_{m1} and A_{m2} in the larger value. The bolt material selected is 35CrMoA because the bolt specification exceeds the recommended value in GB/T 150.3-2011 in order to facilitate the design of the bolt configuration, according to TEMA-10th-2019 “Standards of the Tubular Exchanger”. Manufacturers Association”, Part 9, Table D-5M recommended bolt spacing requirements, calculated to meet the bolt configuration requirements of the bolt specifications and number, see Table 2.

Table.2 Bolt specifications and number of bolts to meet the requirements of the bolt configuration

Bolt nominal diameter dB/mm | Number of bolts n | Bolt center circle diameter Db/mm | Total cross-sectional area of required bolts Am/mm2 | Actual total cross-sectional area of bolts Ab/mm2 | Bolt section allowance percentage/% |

100 | 24 | 1 587.5 | 105 757.8 | 176 449.6 | 66.8 |

90 | 28 | 1 645.0 | 105 757.8 | 165 503.2 | 56.5 |

80 | 28 | 1 600.0 | 105 757.8 | 129 546.9 | 22.5 |

76 | 32 | 1 632.0 | 105 757.8 | 133 023.8 | 25.8 |

As can be seen from Table 2, if the nominal diameter of 76mm bolts, in order to meet the total cross-sectional area of the required bolts Am, the number of bolts required is the largest in order to ensure that the operating space of the machine, the number of bolts will inevitably make the bolt’s center circle diameter increases accordingly. Suppose the nominal diameter of 100mm bolts, although to meet the required total cross-sectional area of bolts, the number of bolts required is less. In that case, the bolt center circle diameter is smaller. Still, the corresponding nut size is the largest, so the bolt center to the root of the flange cone neck of the spacing is larger than other sizes of bolts, the impact of the flange cone neck size δ_{1} and the cone neck axial stress σ_{H}. If the nominal diameter of 90mm bolts, in order to ensure that the machine The center circle diameter of the bolt will be maximized if the nominal diameter of 90mm bolts is selected to ensure the operating space of the machine. The selection of nominal diameter 90mm and 100mm bolt cross-section margin is too large, easy to cause material waste. Comprehensive consideration: choosing the nominal diameter of an 80mm bolt is the most appropriate.

### 2.3 Flange structure optimization

#### 2.3.1 The influence of flange structure size on flange stress

The flange load is carried by the flange ring, cone neck and cylinder 3 parts together. The load applied on the flange produces 3 stresses on it, which are the cone neck axial stress σ_{H}, the flange ring radial stress σ_{R} and the flange ring circumferential stress σ_{T}. The Waters method used for flange design is mainly to make the 3 stresses as close as possible to the corresponding permissible stresses, that is:

In the formula: [σ]_{f}^{t} is the permissible stress value of the flange material under the design temperature, unit MPa.

In actual engineering, the flange 3 stresses in the calculation often ignored the container pressure in the cone neck on the axial stress, as well as pressure under the action of the flange 3 parts of the flange due to the deformation of the coordination of the stresses generated by the calculation of the value of the 3 stresses should be less than the specified permissible stresses, respectively, and retain a certain amount of richness. The influence curve of flange ring thickness δ_{f} and cone neck thickness δ_{1} on the 3 stresses of the flange are shown in Fig.3 and Fig.4, respectively.

Figure.3 Relationship curve of flange ring thickness on flange stresses

It can be seen from Fig. 3, with the increase of flange ring thickness, flange ring radial stress σ_{R} greatly decreased, cone neck axial stress σH, although decreased, the downward trend is far less obvious than the flange ring radial stress, the flange ring to the downward trend of the stress σ_{T} has less influence, when the flange ring and the cone neck stiffness is comparable, but also make the ring to the stress σ_{T} appear upward trend. As can be seen from Fig.4, with the increase of the thickness of the large end of the cone neck, the cone neck axial stress σ_{H} decreases greatly. The flange ring annular stress σ_{T} decreases, but the decreasing trend is far less obvious than the cone neck axial stress σ_{H}, while the flange ring radial stress σ_{R} increases gradually.

Fig.4 Relationship curve of the influence of the thickness of the large end of the cone neck on the flange stress

#### 2.3.2 Recommended method of flange size adjustment

The flange size is determined by assuming first and then checking the stress. Usually, after assuming the flange size at one time, the calculated stress cannot be well approximated to its corresponding allowable stress, and the flange size must be adjusted. The influence of flange ring thickness δf and taper neck thickness δ_{1} on the three stresses of the flange are related to each other.

#### 2.3.3 Calculation of flange stress and structure size adjustment

According to the determined gasket form, size, bolt specification and bolt hole center circle diameter, SW6 software is applied to calculate the designed flange stress.

The original design flange cone neck axial stress and flange ring annular stress are too large; the sensitive factor that affects these two stresses is the cone neck big end thickness δ_{1}. After several adjustments, the flange cone neck big end thickness δ_{1} is adjusted to 102mm. At the same time, the thickness of the flange ring δ_{f} is reduced to 200mm (take the permissible stresses of the thickness of the forging material under the material) in order to make the flange each part of the load carrying capacity of each part of the flange is relatively close. The optimized flange structure size is shown in Table 1, which shows that the optimized flange stresses meet the corresponding allowable stress requirements.

Large-diameter flanges often have the problem of insufficient flange rigidity, which will make the compression stress of the gasket drop during operation due to pressure rise, leading to the sealing failure of the flange connection joint. In order to ensure the sealing of flange joints, the 2007 edition of ASME Ⅷ Div.1 mandatory appendix 2 supplemented the flange stiffness index J to control the flange angle of the calibration method, GB/T 150.3-2011 on the overall flange also incorporates the requirements of flange stiffness calibration. Based on the above provisions of the optimized flange stiffness index J = 0.613 < 1, to meet the requirements.

## 3. Conclusion

The gasket is an important element to ensure the sealing of the flange, and the selection of a suitable gasket is the basis of flange design. For equipment flanges with high-pressure levels (not less than Class 900 (PN 150)), it is recommended to prioritize the use of an annular connecting surface. When carrying out the selection and arrangement of bolt specifications, if larger specification bolts are used, it is necessary to consider both the force arm of the flange torque and also the thickness dimension of the large end of the flange cone neck.

By analyzing the influencing factors of flange stress, the original design flange size is adjusted according to the recommended adjustment method of structure size. After increasing the thickness of the flange cone neck’s big end and reducing the thickness of the flange ring, the flange stress calibration is qualified. After the improvement, the outer diameter of the flange is reduced by 25mm, the thickness of the flange disc is reduced by 33.4mm, and the quality of the flange is reduced by 130kg. The optimized flange structure is more reasonable, the sealing performance is reliable, and the purpose of saving materials is achieved at the same time.

Author: Zhao Zhoulin