Leakage of Oil Following Rupture of Pipeline P/15-4 to Hook of Holland

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LEAKAGE OF OIL FOLLOWING RUPTURE OF PIPELINE P/15-4 TO HOOK OF HOLLAND

C. Kranenburg

Report No. 11-83

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Laboratory of Fluid Mechanics

Department of Civil Engineering

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Delft University of Technology

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LEAKAGE OF OIL FOLLOWING RUPTURE OF PIPELINE PjIS-4 TO HOOK OF HOLLAND

C. Kranenburg

Report No. II - 83

Laboratory of Fluid Mechanics Department of Civil Engineering Delft University of Technology Delft, The Netherlands

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CONTENTS 1. Scope of work 2. Computer model

3. Presentation of results

References

Tables Figures

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1• Scope of work

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This report presents computational results concerning the

buoyancy-driven leakage of oil resulting from a possible rupture of

the planned pipeline P/lS-4 to Hook of Holland. The computations

were commissioned by R.J. Brown and Associates (Netherlands) b.v. (RJBA Job No. 7004.02). The specifications of the pipeline and oil as made available by RJBA are listed in Table J. Assumed proper ties

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of seawater are also l~sted. Leak volumes up to 400 m were calculated as functions of time af ter rupture for two oil temperatures (50 C and

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IS C) and four p~pe inclinations, namely 0 (horizontal pipe), 0.001,

0.002 and 0.01.

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2. Computer model

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The applied computer model, which was developed earlier by the Laboratory of Fluid Mechanics, is described in Ref. land, slightly modified, in Ref. 2. The more important as sureptions on which the model

is based, are:

before rupture the pipeline ~s completely filled with oil, that is, free gas is absent;

the oil is a newtonian fluid with constant properties;

the pipeline is infinitely long and has a constant (small) inclination,

or is horizontal;

the ruptured pipe 1.S cleanly cut through, and the flows at both si.des of the rupture are not influenced byeach other or by the sea bed.

The model calculates the buoyancy-driven two-layer flow of oil and seawater in the pipe, taking into account (laminar or bwTbulent) friction and

internally critical flow at the rupture. Besidies the volume of leaked

oil, the lengths of the two intruding water layers are calculated as functions of time after rupture. The computer model has been verified with experiments

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in a laboratory model pipelime•

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3. Presentation of results

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Figs. 1 Calculatthrough 3.ed leThe followingak volumes versussymbols are wtime aftteedr rupture are shown inin these figures:

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V total leak volume (in m3), that is, the volume of oil leaked from

both parts of the ruptured pipe; I inclination of pipeline;

t time af ter rupture (in hours).

Figs land 2 show results for the first three days af ter rupture.

Since the viscosities decrease as the temperature increases, the leak rates increase w ith temperature. At relatively steep inclinations

(here larger than 0.01) the influence of the viscosities vanishes, however, since the condition of internally critical flow then controls

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the flow. Figs. and 2 show that after a certain initial period the

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relation between leak volume and time becomes linear in the case of the inclined pipelines. The excess weight of the water layer (in fact the

component along the pipe axis) is then balanced by friction at pipe wall

and interface between oil and water.

Fig. 3 shows the total leak volumes for the horizontal pipeline. Since the axial component of the excess weight of the water layer now vanishes, considerably lower flow rates result. For large times the

leak volume increases as the square root of time.

Table 2 gives a summary of times af ter rupture for var~ous total leak volumes.

The results indicate laminar flow of the oil layer in all cases. In the case of the horizontal pipeline the flow in the water layer changes from turbulent to laminar af ter about 16 h (at ISo C), or af ter about

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3 h (at SC). The water layer is always turbulent in the case of the inclined pipelines.

The lengths (in m) of the intruding water layers can be estimated from Figs. 1 through 3 in the following way:

horizontal pipeline (water layers of equal lengths ~n böth parts of the ruptured pipeline): multiply V bij 18 m-2;

inclined pipelines (water layer in part sloping downward from rupture, negligible volume of water in part sloping upward from rupture at

inclinations selected): multiply V bij 36 m-2 •

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A low point in an inclined pipeline wil1 stop furthei intrusion of the water layer. Laboratory experiments indicate, however, that this does not noticeably reduce the leak rate until nearly all oil has been discharged from the pipe section conce~ned.

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-3-References

1. C. Kranenburg, Exchange flow of oil and sea-water in a ruptured

submarine pipeline, Report No. 1-83, Laboratory of Fluid Mechanics,

Department of Civil Engineering, Delft University of Technology, 1983. 2. C. Kranenburg, Buoyancy--driven leakage from a ruptured submarine

pipeline, COITD11unicationson Hydraulics, Report; No. 83-5, Department of Civil Engineering, Delft University of Technology, 1983.

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inner diameter inclinations density of oil

dynamic viscosity of oil at r:O C

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(kinematic viscosity of oil at 5° C)

dynamic viscosity of oil at 15° C (kinematic viscosity of oil at 15° C)

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density of seawater

kinematic viscosity of seawater at 5° C

kinema tic viscosity of seawater at 15° C

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0.3032 m 0,0.001,0.002,0.01 847,7 kg/m3 62.5 cP (74 x 10-6 m2/s) 22.5 cP (27 x 10-6 m2/s) 1025 kg/m3 1.6 x 10-6 m2/ s 1• 1 x 10-6 m2/s

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Table 1. Properties

of

pipe, oil and seawater.

Total leak I = 0 I = 0.001 I = 0.002 I = 0.01 volume ₁_5°_C _S_O_C ₁_5°_C (m3) SOC 15°C SoC 15°C SoC 100 20 14 13 9 9 6 3 3 200 75 40 29 20 19 14 7 6 300 160 80 45 32 29 21 10 9 400 290 130 61 43 39 28 14 12

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Table 2. Times af ter rupture (in hours) for var~ous total leak volumes.

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