METHODS AND TREATMENTS FOR INTERNAL FLOOD PROBABILISTIC RISK ASSESSMENTS

ANS PSA 2013 International Topical Meeting on Probabilistic Safety Assessment and Analysis Columbia, SC, September 22-26, 2013, on CD-ROM, American Nuclear Society, LaGrange Park, IL (2013)

METHODS AND TREATMENTS FOR INTERNAL FLOOD PROBABILISTIC RISK ASSESSMENTS

Robert J. Wolfgang, P.E.

ERIN Engineering and Research, Inc. 158 West Gay Street, Suite 400

West Chester, PA 19380 [email protected]

ABSTRACT

It is desired that a consistent and reasonable set of assumptions and methods be established in order to adequately evaluate various internal flood hazards without imposing excessive conservative treatments. Using a few basic kinematic principles and fluid flow analysis, the basis behind the distance from a pipe break to a particular target for a spray hazard scenario can be evaluated given the water pressure and size of break. The evaluation of the resistance afforded insulated pipe enclosed by aluminum sheet metal lagging can be analyzed in order to determine whether a pipe break resulting in a flow rate on the order of 100 gpm poses a spray hazard for nearby components. Given a typical piping arrangement for fire protection piping, the forces resulting from a full diameter pipe rupture can be analyzed to determine whether existing pipe restraints are sufficient to prevent the pipe from exceeding its tensile strength due to imposed bending stresses, which could then cause damage to other nearby equipment and structures due to “pipe whip” effects. For typical hollow metal doors found throughout a nuclear facility, the use of a simplistic finite element model can be employed to estimate the height of water required for door failure due to hydrostatic pressure.

Key Words: Internal Flood PRA, Door Failure, Spray, Pipe Whip

1 INTRODUCTION

The following sections provide several methods and treatments that can be utilized to address various internal flood risk hazards, such as the distance of impact from spray hazards, failure of doors allowing propagation to other areas, and whether “pipe whip” effects is a credible hazard from moderate energy systems. Several water sources within a nuclear plant contain insulation wrapped with aluminum lagging, and a simple analysis to determine whether the lagging thickness is sufficient to prevent a spray hazard from affecting components at a distance can be determined. The use of a set of methods and treatments that have a quantifiable basis will help provide the analyst with a reasonable and consistent set of assumptions when creating a probabilistic risk assessment (PRA) internal flood model.

2 DISCUSSION OF METHODS AND TREATMENTS

2.1 Estimation of Impact Distance Due to Spray Hazard

The following simplified analysis for pipes experiencing a small rupture (≤100 gpm) shows the estimated horizontal distance of water travel from the break to the floor. The purpose of this analysis is to estimate a sufficient “radius of influence” when determining those water sources that could inflict spray damage upon nearby equipment. The EPRI guidance document quotes an


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estimate of 10 horizontal feet for liquid flood sources and 20 horizontal feet for high-energy flood sources [1]. Using conservative assumptions regarding the piping configuration and spray pattern geometry, the below analysis predicts a distance of about 16 feet for a pipe rupture with a 100 gpm flow rate and internal pressure of 100 psig. Figure 1 shows a simplified sketch of the postulated piping configuration and emergent spray pattern using a spreading angle of only 0.5°, which tends to maximize the spray distance. Table I provides a listing of the variables and their values used in this analysis.

Table I. Inputs and Parameters for Spray Analysis Variable Value and Units Description

62.4 lbf/ft3 Weight density of water [2] g 32.2 ft/s2 Gravitational accelerationqr 0.223 ft3/s 100 gpm spray flow in ft3/s P 1.44E+04 lbf/ft2 Water pressure of 100 psig in lbf/ft3 θ 8.727E-03 Spreading angle of 0.5 degrees in radiansC 0.61 Flow coefficient for sharp-edged hole [3]

Figure 1. Simplified Sketch of Pipe Configuration and Spray Pattern

Internal Flood PRA Methods and Treatments

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Table I. Inputs and Parameters for Spray Analysis Variable Value and Units Description

h 17 ft Height of unobstructed pipe above floor

From Ref. [2], Eq. 1 given below was used to determine the equivalent diameter in feet of the pipe rupture based on the above parameters given in Table I.

(1)

From Eq. 1, the break diameter was calculated as 0.062 ft (0.747 in). The use of Eq. 2 was used to determine that the initial velocity of the spray flow exiting the pipe break was 73.1 ft/s.

(2)

The following differential equation (Eq. 3) was used to describe the velocity (dx/dt) as a function of distance from the pipe break and spreading angle. This equation can then be solved to determine the distance traveled from the pipe break by a given quantity of water as a function of time. Figure 2 depicts the graphical solution of Eq. 3.

(3)

vr

qr

dr

2

4

2

2tan

2

x

d

q

dx

dy

r

r

Figure 2. Distance Traveled by Water from Pipe Break as a Function of Time

Pg

C

qd r

r

2

4


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To determine the time it takes for the same quantity of water emanating from the pipe break to reach the floor, the kinematic equation given below (Eq. 4) can be used to relate the vertical height as a function of time. The time it takes for a given quantity of water to reach the floor was determined to be 1.03 seconds.

(4)

Based on the solution to Eq. 3, the water exiting the pipe break will have traveled a distance of 15.7 feet in 1.03 seconds. Therefore, for a given spray hazard, it appears reasonable that the EPRI guidance of 10 feet given in Ref. [1] can be used, with a range of 16 feet used as a bounding distance to account for any uncertainties associated with the radius of influence.

2.2 Estimate of Whether Pipe Whip is Credible Due to Ruptured Pipe

The following simplified analysis for a typical fire protection pipe of 4 inches in diameter experiencing a large pipe break with a postulated flow rate of 3,000 gpm was used to determine the dynamic loading and associated bending stresses to determine if “pipe whip” is a concern for such flood events. Figure 3 shows a sketch defining the control volume and variables at two different locations. The parameters at point 1 represent the condition just upstream the pipe rupture, while point 2 represents the condition at the pipe exit. Table II provides a listing of the variables and their values used in this analysis.

2

2

1)( tghty c

Figure 3. Control Volume of Fire Protection Pipe Rupture


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Table II. Inputs and Parameters for Pipe Whip Analysis Variable Value and Units Descriptiondi, dd 4.026 in Inside diameter of pipe (Schedule 40 pipe)

do 4.5 in Outside diameter of pipeAA 0.088 ft2 Inside area of pipe

P1 38.5 psig Pressure upstream pipe rupture (Eq. 5) P2 0 psig Atmospheric pressure at pipe exit 1.938 slug/ft3 Mass density of water [2] 62.4 lbf/ft3 Weight density of water [2]ce 2.25 in Distance from centroid to outer pipe radiusI 7.233 in4 Moment of inertia for pipe (Eq. 12) Q 3000 gpm Postulated flow rateKe 1 Pipe exit resistance coefficient [2]

v1, v2 75.6 ft/s Flow velocity based on flow rate w1, w2 13.0 slug/s Mass flow rate

Equation 5 from Ref. [2] computed the pressure drop from point 1 to point 2 to be 38.5 psig based on the postulated flow rate for a full diameter pipe break. Equations 6 and 7 from Ref. [4] show the control volume force balances that were used to calculate the reaction forces in the x and y directions, respectively. The x-momentum flux (w2v2) was taken as positive in the outward direction, and the y-momentum flux (w1v1) was defined as positive in the inward direction. The reaction force in the x-direction (Rx) was calculated to be 979.5 lbf, and the reaction force in the y-direction (Ry) was calculated to be 1469 lbf.

(5)

(6)

(7)

Equations 8 and 9 calculate the bending moments along the length of the pipe in the extended x- and y-directions, and equations 10 and 11 calculate the stress due to these bending moments, respectively. The moment of inertia for cylindrical pipe is calculated using Eq. 12 [4]. The independent variable “u” represents the length of the moment arm in either the x- or y-direction in inches.

(8)

(9)

41

2

1

00001799.0

d

QKP e

uRuM xy )(

uRuM xy )(

2222 vwAPRx

1111 vwAPRy


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(10)

(11)

(12)

Figures 4 and 5 depict the bending stress along the length of pipe in the x- and y-directions, respectively. Assuming that piping for such moderate energy systems is constructed of ordinary structural steel, the tensile strength is in the range of 50 to 65 ksi, based on Table 5.1.1 of Ref. [4]. The above analysis shows that the bending stress is largest in the x-direction and approaches the tensile strength in the range of 9 to 12 feet from the location of a postulated break. The photograph in Figure 6 shows a typical run of fire protection piping with piping supports estimated to be spaced within this distance. Also, given that most pipe ruptures are generally not expected to yield a full flow break, the probability of exceeding the pipe bending stress is considered unlikely. Given this analysis and these considerations for moderate energy water systems, it is not unreasonable to conclude that pipe whip is not a significant damage mechanism for plant components.

I

cuM exx

)(

I

cuM eyy

)(

44

64 io ddI

Figure 4. Plot of Bending Stress as a Function of Distance in the x-direction

Figure 5. Plot of Bending Stress as a Function of Distance in the y-direction


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2.3 Insulated Pipes with Aluminum Lagging

Insulated and lagged pipes are not considered to be significant spray sources. Instead, the lagging is expected to contain the leaks, with only dripping at the seams being of concern. The following analysis shows that a direct impingement of flow from a typical one inch diameter pipe with insulated lagging reveals that the dynamic pressure will not exceed the tensile strength for the aluminum lagging. The water pressure inside the particular pipe analyzed was estimated to be about 70 psig. Figure 7 represents a sketch of the insulated potable water line encapsulated by aluminum sheet metal, of which a thickness of 0.03” was assumed based on direct measurement. Figure 7 also depicts that the assumed spray flow pattern was a uniform one inch diameter stream of water, imposing a resultant force on the metal lagging due to jet impingement and stagnation of flow. Also, there was no credit given to the insulation surrounding the pipe acting as a buffer or flow resistance, which tends to maximize the pressure imposed on the metal lagging. Table III provides a listing of the variables and their values used in this analysis.

Figure 6. Typical Run of Fire Protection Piping Showing Pipe Restraints


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Table III. Inputs and Parameters for Pipe with Lagging Variable Value and Units Description

d 1 in Diameter of pipe breakA 5.45E-03 ft2 Area of pipe breakC 0.61 Flow coefficient for sharp-edged hole [3]p 70 psig Water pressure inside pipegc 32.2 (lbm·ft/s2)/lbf Gravitational acceleration constant 62.4 lbm/ft3 Mass density of water [2] 62.4 lbf/ft3 Weight density of water [2]

The first step in this analysis was to determine the expected flow rate from a one inch break using Eq. 13 from Ref. [2]. This yielded an estimated flow rate of 152 gpm, which is just beyond the maximum spray flow limit of 100 gpm quoted in Ref. [1]. From the flow rate, the velocity of the water stream exiting the break can be determined using Eq. 14. The calculated velocity was found to be 62.3 ft/sec, which was then used to determine the stagnation pressure

Figure 7. Piping Configuration for Insulated Pipe with Lagging


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using Eq. 15 [2]. The stagnation pressure imposed on the inner surface of the aluminum lagging was calculated to be 26.1 psi.

(13)

(14)

(15)

Using the stagnation pressure of 26.1 psi, a finite element model depicting a cylindrical tube of aluminum sheet metal with this imposed pressure loading was constructed to determine if any of the resulting stresses exceeded the tensile strength for aluminum. For pure rolled aluminum, the minimum tensile strength was found to be 13,000 psi, with a Young’s modulus of 10E+06 psi and Poisson’s ratio of 0.33 [4]. The commercially available finite element program used was LISA, version 7.6.0 [5].

Figure 8 shows the finite element model structure, which consisted of 4-node quadrilateral shell elements equal to the thickness of the aluminum sheet metal (0.03 inch) radially arranged to approximate a hollow cylinder 4 inches in diameter. The total number of nodes and elements was 1088 and 1056, respectively. The applied constraints were modeled to simulate the metal bands that were spaced at approximately 10 inch intervals that keep the aluminum lagging in place. This basic configuration was confirmed from multiple walkdowns at various nuclear facilities. The applied constraints restricted movement in the upper half of the modeled cylinder in both the opposite and normal directions to the applied pressure loading. Movement in the lengthwise direction was constrained at only one end so as not to overly constrain the model, which can tend to yield exaggerated stress levels. The stagnation pressure of 26.1 psi was applied over an area equal to the jet impingement area of 0.79 in2. To maximize the calculated stress for this given situation, the pressure loading was applied to an area midway between the modeled constraints simulating the metal bands.

p

dCQ 2236

cs g

vp

1442

1 2

2

1246048.7

d

Qv


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The resulting maximum stresses are shown below in Figure 9, which shows a maximum value of 5,006 psi in the area of the applied pressure loading, and is much less than the minimum tensile strength of 13,000 psi [4]. Figure 10 shows an exaggerated view of the nodal displacements and their range of values, of which the maximum value is only 0.0065 inches.

Figure 8. Finite Element Model of Aluminum Lagging

Figure 9. Maximum Stresses (psi) from Finite Element Model


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2.4 Estimate of Door Failure Due to Hydrodynamic Loads

Hollow metal doors are used for many purposes, such as fire barriers and as a means to control access to several rooms throughout a nuclear facility. These types of doors are also designed to many different specifications that make it difficult to determine just how each one would individually fail due to excessive water pressure. In an attempt to provide a better sense of engineering judgment, the typical design for a hollow metal door used throughout many U.S. nuclear facilities was adopted as the basis for a finite element structural analysis. The finite element model of this typical door was subjected to various hydrostatic loads to determine a representative height of water at which the minimum tensile strength for structural steel would be achieved for configurations against the door jamb and against the latch. The same finite element software program (LISA [5]) that was used for the aluminum lagging analysis was also used for this door analysis.

Figure 11 shows an isometric hand sketch of the proposed typical hollow metal door with vertical stiffeners spaced at 6 inch intervals. The outside dimensions for the door were 3 feet wide by 7 feet thick. The spacing between the front and back faces of the door was modeled as being 1.75 inches. The sheet metal used for the door was 0.048” thick (18 gauge) sheet metal.

Figure 10. Nodal Displacements (inches) from Finite Element Model


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The average pressure was applied uniformly to each face element according to the hydrostatic pressure of water between the top and bottom of each of the elements. Figure 12 shows an example of the applied pressure loading for a water height of 5 feet. Pictures of the finite element mesh, pressure loading, and boundary conditions to show pressure against the latch or jamb are shown in Figure 13. The finite elements used for the door faces were 6 inch quadrilateral plate elements with each element having 8 nodes to estimate stress distribution and displacements. Each node has one translational and two rotary degrees of freedom. Smaller elements were used for the stiffeners and edges around the door.

For the case with pressure loading against the latch mechanism, a water height of 5 feet was found to produce a maximum nodal stress just below that of the tensile strength for structural steel. Against the door jamb, a water height of 11 feet exhibited a maximum stress that was near the tensile strength. A tensile strength of 45 ksi (Table 6.2.11a of Ref. [4]) was used as the representative failure stress based on the minimum tensile strength for low and intermediate strength carbon steel plates. The stress distribution and exaggerated view of nodal displacements are shown in Figure 14 for the two loading configurations.

In an effort to benchmark these door failure results, an actual occurrence of door failure due to excessive hydrostatic loads was experienced at the French nuclear plant Blayais and is referenced here. On December 27, 1999, a combination of the incoming tide and exceptionally high winds produced by Storm Martin caused a sudden rise of water in the estuary, flooding parts of the plant [6]. Although details of dimensions and material construction were not identified for this particular door suffering hydrostatic failure, it can be seen in Figure 15 that the plastic deformation at time of failure is strikingly similar to the shape depicted in Figure 14 for loading

Figure 11. Isometric Sketch of Hollow Metal Door with Vertical Stiffeners


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against the door latch. Although somewhat limited, this does provide some physical evidence that the numerical results estimated above for door failure are reasonable.

Figure 13. Finite Element Model of Hollow Metal Door with Pressure against the Latch (Left) and against the Door Jamb (Right)

Figure 12. Hydrostatic Pressure Loading for Water Height of 5 Feet


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Figure 14. Finite Element Model of Hollow Metal Door Showing Stress Distribution and Exaggerated View of Nodal Displacements at or near Tensile Stress against the Latch (Left) and against the Door Jamb (Right)


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3 CONCLUSIONS

The above methods discussed above were meant to provide a reasonable set of analyses to help the internal flood analyst provide a more realistic estimate of internal flood hazards by validating the assumptions and methods used.

Based on a set of conservative assumptions, the impact distance due to a spray hazard from a pipe rupture of 100 gpm was found to be approximately 16 feet, which can be used in lieu of the 10 foot rule found in Ref. [1] for a more bounding analysis when considering the scope of water sources that could impact susceptible equipment.

The pipe whip effect was investigated using a typical fire protection pipe with a moderately large flow rate (3,000 gpm) to show that this damage mechanism is not particularly pertinent for

Figure 15. Cable Gallery Access Door Failure Due to Excessive Hydrostatic Loading at French Nuclear Plant


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moderate energy systems that are classified as being below 200°F with pressures less than 275 psig. Most water sources of concern are typically no higher than 140°F and typically less than 140 psig. However, for high energy line break scenarios, pipe whip effects may still need to be considered if susceptible equipment is located nearby.

For pipes that are insulated and wrapped with a layer of aluminum sheet metal, the flow rates associated with spray scenarios (~100 gpm) were shown to not challenge the structural integrity of the aluminum metal, such that lagged piping would not pose a spray hazard to equipment located within the “sphere of influence.” However, since the lagging is obviously not meant to be watertight, a large pipe rupture can still result in a significant release of water, which may then lead to submergence of equipment within the area if adequate drainage is unavailable.

Finally, the hydrostatic loading due to a height of water against a hollow metal door was examined using a simplistic finite element model. Although a myriad of different door designs, dimensions, materials, and configurations are used throughout a nuclear facility, a “typical” set of dimensions and materials were used to obtain a rough estimate for door failure, whether against the latch or door jamb. In general, the proposed failure height for such a door against the latch was found to be about 5 feet, and against the door jamb a failure height of 11 feet was estimated.

4 ACKNOWLEDGMENT

The author would like to acknowledge the expert knowledge of Karl Fleming for his comprehensive and detailed methodology found in the EPRI guidance document for the development of internal flood PRAs [1].

5 REFERENCES

1. Guidelines for Performance of Internal Flooding Probabilistic Risk Assessment. EPRI, Palo Alto, CA: 2009. 1019194.

2. Flow of Fluids through Valves, Fittings, and Pipe, Technical Paper No. 410, Crane Company, New York, USA (1986).

3. G. Shaw and A. Loomis, Cameron Hydraulic Data, Fourteenth Edition, Fifth Printing, Ingersoll-Rand Company, Woodcliff Lake, USA (1970).

4. E. Avallone and T. Baumeister, Marks’ Standard Handbook for Mechanical Engineers, Ninth Edition, McGraw-Hill Book Company, New York, USA (1986).

5. “LISA-Finite Element Technologies (Sonnenhof Holdings),” Version 7.6.0, http://www.lisa-fet.com (2011).

6. J. M. Mattéi, E. Vial, V. Rebour, H. Liemersdorf, M. Türschmann, “Generic Results and Conclusions of Re-evaluating the Flooding Protection in French and German Nuclear Power Plants,” Eurosafe Forum 2001, Paris, France, November 6, 2001.

METHODS AND TREATMENTS FOR INTERNAL FLOOD PROBABILISTIC RISK ASSESSMENTS

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