This engineering article describes the behavior of perlite when used to insulate cryogenic systems. These requirements are given primarily to maintain the integrity of the cold box piping, equipment, and structure.
Perlite Loading Procedure
This standard applies to all perlite insulated cold boxes, cold cans, and crossover ducts.
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4. DEFINITIONS AND ABBREVIATIONS
4.1 Mechanical joint is a joint in a piping system in which the pressure seal is affected by close-fitting mating surfaces held in compression by mechanical means. This includes flanged joints, screwed joints, and compression type joints. Bimetallic transition joints or welded joints are not included.
4.2 Ratcheting failure is a mode of failure that occurs in cyclic service in which a component yields during part of the cycle, but is not “yielded back” in the balance of the cycle. The component yields further on successive cycles until stresses are relieved, or until the component breaks.
4.3 DN: Nominal diameter; used as a prefix with nominal pipe sizes expressed in millimeters.
4.4 NPS: Nominal pipe size; used as a suffix with nominal pipe sizes expressed in inches.
5. PERLITE LOADING ON COLD BOX PIPING AND STRUCTURES
5.1 General
5.1.1 Perlite insulation inside a cold box will exert static pressure forces on the piping, equipment, and the walls of the cold box. These static forces are due entirely to the weight of the perlite. As long as a surface on which static perlite forces are acting remains stationary (i.e., does not try to move through the perlite), static forces are the only perlite forces which will act on that surface. However, when a piece of equipment moves through the perlite as a result of thermal expansion and contraction, it will disturb the static condition of the perlite and experience perlite drag forces which resist its movement. In the static condition, perlite will exert vertical pressure forces on horizontal surfaces along with lateral pressure forces and frictional shear forces on vertical surfaces. Jannsen’s method (traditionally used for silo design) provides a useful approach for calculating these forces.
5.1.2 When piping and other equipment inside a cold box moves in response to thermal expansion and contraction, perlite insulation will exert drag forces which resist the movement. These forces are due to the shearing rupture of perlite particles in a localized zone around the moving pipe or piece of equipment. The magnitude of these forces depends on the size of this localized zone, the direction of motion (that is, up, down, or sideways), the orientation of the moving piece of equipment, and on the shear strength of the perlite, which itself is a function of the static lateral pressure. (The static lateral pressure acts as a confining pressure so that the shear rupture strength increases as the confining pressure increases.)
5.1.3 Air Products’ proprietary experimental studies have been used along with published data on the shear rupture strength of perlite to develop a correlation for perlite drag forces which resist the vertical movement of horizontal pipes and horizontal equipment surfaces. The studies showed that perlite drag forces are larger when equipment is moving upward during warm-up, and smaller when equipment is moving downward during cool-down. One reason for this is the relatively small pressure acting on the bottom half of an object that is moving upward through perlite, whereas, an object which is moving downward will have pressure acting on both the top and bottom surfaces and these will tend to cancel one another. Also, during cool-down the equipment inside a cold box shrinks in volume and opens up voids into which the perlite can flow. When this happens, the lateral confining pressure on the perlite is partially released and allows the perlite to become loose or fluffy and much less restrictive to the thermal movement of piping and other equipment. It is important to recognize that this type of loading might lead to a ratcheting mode of failure if the stress level exceeds the yield strength of the material. Ratcheting failure has been observed in the Plaquemine and CEP cold boxes, in which lines connected to the top of the column (where thermal movements are high) were bent downward a distance that was many times greater than the thermal movement experienced during one thermal cycle.
5.1.4 Drag forces which resist the vertical movement of vertical pipes and vertical equipment surfaces were shown experimentally to be similar in magnitude to the static frictional shear forces which act on vertical surfaces. Vertical drag forces on all vertical surfaces, therefore, shall be estimated using Jannsen’s method.
5.2 Perlite Static Pressures
5.2.1 For perlite with bulk density in the range of 32 to 80 kg/m3 (2 to 5 lbf/ft3), the average static vertical pressure, q, can be calculated by dividing the height of the box into zones of equal hydraulic radius. A new zone shall be designated for each change in hydraulic radius. For each zone then, working down from the top of the box:
where: k = (1- sin φ) / (1+ sin φ) = 0.289 for = 33.5. µ= coefficient of friction between perlite and cold box wall and vessels, estimated to be 0.33. = bulk density of perlite, for design use 55 kg/m3 (3.5 lbf/ft3), includes 15% compaction. γ = angle of internal friction (angle of repose) of the perlite, 33.5. R = hydraulic radius, the ratio of the perlite cross-sectional area to the wetted perimeter h = height from top of zone. q‘ = pressure at top of zone (from previous calculation).
5.2.2 The static lateral pressure, p, is assumed to be proportional to the static vertical pressure and is given by p = kq
5.2.3 The frictional shear stress, V, is related to static lateral pressure by V = p
5.3 Estimated Vertical Perlite Loads
5.3.1 Static Forces on Horizontal Surfaces
5.3.1.1 Vertical loading on horizontal pipes which do not experience vertical movement greater than 6 mm (0.25 in) during the life of the plant shall be estimated using the static vertical pressure, q, at that elevation times the pipe diameter. Static vertical loading on the horizontal surfaces of other equipment shall be estimated as the static pressure, q, at that elevation times the horizontal surface area.
5.3.2 Drag Forces on Horizontal Surfaces
5.3.2.1 Vertical loading on horizontal runs of piping which experience vertical movement greater than 6 mm (0.25 in), due to the thermal expansion and contraction of the equipment to which they are attached, shall be estimated using the drag pressure, W, at that elevation times the pipe diameter. W is given by the correlation: W = q + [ (0.58q + 1.08 ) [ [ -62 / (D + 10 )2 ] + (1.38 / D) + 0.29 ] ] where W = drag pressure, psi. q = average static vertical pressure, psi. D = outside diameter of the pipe, in. In SI units, W = q + [ (0.58q + 7448 ) [ [ -0.04 / (D + 0.254 )2 ] + (0.035 / D) + 0.29 ] ] where W = drag pressure, N/m2. q = average static vertical pressure, N/m2. D = outside diameter of the pipe, m.
5.3.2.2 The vertical drag pressures on horizontal surfaces of equipment other than piping may be estimated by choosing a characteristic dimension to use as D in the equation for the drag pressure, W.
5.3.3 Static and Drag Forces on Vertical Surfaces
5.3.3.1 The estimated average vertical load on vertical piping and all other vertical surfaces which contact the perlite shall be estimated as the frictional shear stress, V, times the vertical surface area in contact with the perlite. This load shall be the same whether the vertical surface remains stationary or experiences vertical movement. In situations where the frictional shear stress acting on a particular vertical surface varies from one elevation to another, an appropriate average value should be used.
5.4 Estimated Lateral Perlite Loads
5.4.1 Static Forces on Vertical Surfaces
5.4.1.1 The lateral perlite load on stationary vertical surfaces shall be estimated as the lateral perlite pressure, p, times the vertical surface area.
5.4.2 Drag Forces on Vertical and Horizontal Surfaces
5.4.2.1 When lateral thermal movement of piping and other equipment is large enough to warrant concern [greater than 13 mm (0.5 in)], the lateral perlite forces which resist this movement can be estimated by assuming that the drag pressure, W, resists lateral movement which is perpendicular to the surface, and the shear stress, V, resists lateral movement which is parallel to the surface.
5.5 Limitations of Jannsen’s Method
5.5.1 Jannsen’s method assumes that the vertical static pressure at a given elevation is uniform across the section. In reality, there will be some variation in the vertical static pressure over the cross-section. In general, vertical pressure is lower near vertical surfaces where frictional shear stresses act, and higher in areas away from vertical surfaces.
5.5.2 Jannsen’s method assumes that the specific weight is constant, and that the Jannsen ratio k is constant.
5.5.3 Stationary lines might still be subjected to loading from perlite if they are located near moving equipment.
6. EXAMPLE CALCULATION
6.1 The following is an example using the methods described to calculate the static pressure, q. Figure 6.1 shows an elevation drawing of a cold box containing three pieces of equipment which cause changes in hydraulic radius. To the left of the drawing is a graph representing the vertical static pressure, q, corresponding to each elevation.
6.1.1 The following data was used for this example: γ = 55 kg/m3 box dimensions: 3.95 m x 3.65 m x 20.90 m perlite depth: 20.60 m
6.1.2 The drawing is first divided into zones of equal hydraulic radius as shown. The perlite cross sectional area and wetted perimeter are then calculated to determine the hydraulic radius for each zone.
| Zone | Cross sectional area (mm2) | Wetted Perimeter (mm) | Hydraulic Radius (mm) |
| 1 | 14,417,500 | 15,200 | 949 |
| 2 | 11,507,109 | 21,247 | 542 |
| 3 | 11,943,005 | 20,776 | 575 |
| 4 | 11,063,737 | 24,528 | 451 |
| 5 | 11,943,005 | 20,776 | 575 |
| 6 | 14,417,500 | 15,200 | 949 |
6.1.3 Static Pressure for Each Zone
6.1.3.1 For zone 1, the static pressure is:
6.1.3.2 For zone 2, the static pressure is:
6.1.3.3 For zone 3, the static pressure is:
6.1.3.4 For zone 4, the static pressure is:
6.1.3.5 For zone 5, the static pressure is:
where is q4 at the very bottom of zone 4 (h4=4.924 m) times the ratio of A4 to A5. This is because the hydraulic radius of zone 5 is greater than that of zone 4. However, throughout all of zone 5, q5 is less than (q4 at the very bottom of zone 4) so q5 then becomes: q5 = q4 = 2730 N/m2 for all h5
6.1.3.6 For zone 6, the same is true as in zone 5, and therefore the static pressure throughout zone 6 remains constant and equal to that calculated in zone 5. q6=q5 = 2730 N/m2 for all h6
6.1.4. The values of the shear stress, V, and the drag pressure, W, are then determined from their correlations to the static pressure, q, given in paragraphs 5.2 and 5.3 respectively.