Hot pipelines in permafrost hydraulic: thermal and structural considerations

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Hot pipelines in permafrost hydraulic: thermal and structural

considerations

DIVISION OF BUILDING RESEARCH

HOT PIPELINES IN PERMAFROST

HYDRAULIC, THERMAL AND STRUCTURAL CONSIDERATIONS

by

W. A. Slus archuk

Internal Report No. 394 of the

Division of Building Res earch

Ottawa January 1972

I i,jl

The oil and gas potential of the northern part of Canada has

captured public attention in recent months. Should this potential

become reality, there will be a need to transport oil by pipeline

through permafrost regions. Construction in these areas poses

special problems primarily because of thawing that may be caused

by such activity. The Division of Building Research has developed

for the construction industry a very considerable amount of know-ledge over the past 20 years on building techniques appropriate for

permafrost conditions. Buried hot pipelines, however, raise

ques-tions concerning design and maintenance, under thawing condiques-tions, not unlike those associated with the construction of dykes and

reservoirs in permafrost areas ..

For these, there are not yet satisfactory answers. 'In response

to this need, the Division has undertaken a study of the properties

and behaviour of thawing soil. One of the first steps in the study

was to give consideration to the conditions impos ed on the ground

by a hot pipeline. This report presents the results of the

investiga-tion.

Ottawa

January 1972

N. B. Hutcheon, Director

Page

HYDRAULIC ANALYSIS 2

THERMAL ANALYSIS 3

Steady-State Condition: Buried Pipeline 3

Heat Lost versus Heat Gained in Pipeline 5

Temperature Change along Pipeline 5

Temperature Change after Shutdown 7

Steady-State Condition: Elevated Pipeline 8

Transient Condition: Buried Pipeline 8

STRUCTURAL ANALYSIS 9 Circumferential Stress 9 Flexural Stress 10 Thermal Stress 11 CONCLUSION 11 BIBLIOGRAPHY 12

1 hp

=

550 ft Ib

sec

=

2, 545 Btu/hr

1 barrel

=

42 gallons (U. S. )

₌

5. 63 ft3

1 Btu in. ft2 hr 0 F

=

0.173 hp mile QF 1 Btu

=

sec

1.

41 hp

HYDRAULIC, THERMAL AND STRUCTURAL CONSIDERATIONS by

W. A. Slusarchuk

Significant technical problems are associated with the construc-tion of hot ( ｾ 1500 _{F: oil) large -diameter pipelines in permafrost as}

evidenced by the long, costly delays of the Trans -Alaska Pipeline

project. Similar problems are present for warm ( ＧｾＸＰﾰ F: unrefrigerated natural gas) pipelines and others exist for cool ( "" 250

F: refrigerated natural gas) and cold ＨｾＧ -1700

F: liquid natural gas) pipelines. Some

0:

the most difficult technical problems result from a lack of knowledge of the behaviour of permafrost when it is subjected simultaneously to thermal and structural loads. If the thermal loads are sufficient to melt the permafrost, large settlements may result or thawed soil

round the pipe may become unstable on slopes. Consideration must be given to thes e effects on the structural stability of the pipeline.

A general quantitative analysis was undertaken on the hydraulic, thermal and structural aspects of a hot pipeline in permafrost. The complex nature of the analysis quickly became apparent. Changing conditions along the pipeline (fluid and soil properties; temperature, heat flow, internal pressure, etc.) and transient factors such as ground surface temperature and rate of fluid flow make a reasonably accurate solution very difficult. Possibly the best method of obtaining a solution for any particular pipeline would be to use numerical tech-niques, which would involve large amounts of c ornput e r time. An insight into the interaction between the pipeline and the permafrost, however, can be obtained for general cases by selecting average values to characterize certain variables in the analysis.

Repr es entative situations were chosen for pipelines maintained at above-freezing temperatures, i , e., oil and unrefrigerated natural gas, and do not directly pertain to pipelines maintained at below-freezing temperatures. Special consideration is given to hot, large-diameter oil pipelines similar to that proposed for transporting oil out of the Prudhoe Bay area of Alaska.

HYDRAULIC ANALYSIS

In order to move oil through a pipeline, large amounts of energy

must be put into the system. Pumps provide it by raising the pressure

of the oil and this energy is converted into heat uniformly along the

pipeline by the frictional resistance of the oil to viscous flow. The

heat flows into the permafrost; the amount can be determined by the horsepower requirements for the rates of flow desired, since the

input energy is converted into heat between pumping stations. For rates

of flow of O. 5 and 2. 0 million barrels per day (the minimum and maximum proposed for the pipeline from Prudhoe Bay) the required horsepower may be calculated by the following equations:

0

/::..P HP = 0 550 and liP f LyV G ::: 2gD where (1) (2) HP

0

₀ /::..P f L y V g D = =

=

=

=

=

=

=

=

required horsepower flow of oil, fe / sec

pres sure drop in length of pipe L, lb /ft2

friction factor, dimensionless length of pipe, ft

unit weight of oil, Ib /ft3

average flow velocity, ft/sec

gravitational acceleration, ft/sec2

diameter of pipe, ft

For an average crude oil flowing in a 4-ft diameter pipe at

approximately 1500 _{F the horsepower requirements for the minimum}

and maximum proposed rates of flow for Prudhoe Bay were found to be approximately:

minimum rate of flow (0. 5 million barrels/day) maximum rate of flow (2. 0 million barrels/day) = =

[

[

10.3 hp /mile 26, 200 Btu/hr mile 527 hp /mile 1,340,000 Btu

/h

r mile

The thermal load exerted on permafrost will vary considerably, depending upon the rate of flow.

A better appreciation of the effects of the various factors may be obtained by substituting for Q in equation (l) the expression

o

Q

=

o

( 3)

to give for the energy dissipation (hp /mile)

TT

4400g ( 4)

From equation (4) it is apparent that the horsepower per mile is very sensitive to the rate of flow of the oil as it increases with velocity to the third power. Horsepower per mile also increases directly with y, D and

f.

The unit weight, y, depends on the type of crude oil being pumped and the friction factor, f, depends on the viscosity. This, in turn, is a function of temperature. The

viscosity increases exponentially with decreasing temperature and f increases with increasing viscosity (decreasing temperature). For example, if oil temperature is lowered from 1500

F to 50° F, then f increases to such an extent that 50 per cent more horsepower is required at the maximum rate of flow. For pumping stations located approximately 60 miles apart the maximum pressure in the pipeline will be approximately I, 000 psi with a 35, 000 hp input required at each station for maximum rate of flow.

THERMAL ANALYSIS

Steady-State Condition: Buried Pipeline

The heat flowing from a buried insulated pipe for a steady-state condition may be calculated by the following formula,

Q

=

K (T - T

G) (5)

c t p

where

Q

=

heat flowing out of pipe, hp/rnile

c

K

₌

thermal transfer coefficient, hpj/rn i l e OF t

and

=

=

temperature of the pipe, ° F

mean annual ground temperature, ° F

K

=

O. 346n K s ( 6) t K In

｛ｾ

I s r _j(d)2

₁₁

In ( - )

+

₊

₊

K. r -to r

J

1 1 Insulation Soil effect effect where

K

=

thermal conductivity of soil, Btu in/ft2 hr of s

K.

=

thermal conductivity of insulation, Btu inlfe hr of 1

r

=

radius from centre of pipe to outside of insulation, ft t.

=

thickness of insulation, ft

1

d

=

distanc e from ground surface to centre of pipe (depth of pipe burial), ft.

As may be noted from equation (6), the thermal transfer coefficient is a function of five variables, insulation thickness, pipe diameter,

thermal conductivity of i.n s ul ation, thermal conductivity of soil. and pipe burial depth. Figures 1 to 5 provide an appreciation of the effect of the variables on the therm al transfer coefficient. The heat flow out of the pipe may be obtained by selecting the relevant thermal transfer coefficient from one of the plots inFigures 1 through 5 and using this value in

equation (5).

Figure 1 shows that the therm al transfer coefficient decreas es with increasing thickness of insulation. The plots indicate that

relatively little benefit is derived from insulation of thicknes s gr eater than 3 to 4 in. They also show that insulation has its greatest relative effect in soils that have the highest thermal conductivity values. Figure 2 clearly illustrates how the thermal transfer coefficient increases with increasing pipe diameter; Figures 3 and 4 indicate how the th er m al transfer coefficient is affected by changes in the thermal conductivity

of the soil and insulation. The importance of the thermal conductivity of the soil is shown by the plot in Figure 4; a change in conductivity value from 2. 5 to 5. 0 changes the transfer coefficient from

1.

2 to 2. 4, a 100 per cent increase in heat loss. Figure 5 shows that the therma.l transfer coefficient is not significantly affected by depth of burial if

some insulation is around the pipe. For an urrin s u l at ed pipe, however, the depth of burial is a factor that must be considered.

Heat Lost versus Heat Gained in Pipeline

The steady-state heat loss may be compared with the heat generated in the pipe by viscous flow. For maximum rate of flow the heat generated per mile was calculated at 527 horsepower per mile. The net heat gain or loss per mile is presented in Table I for four cases, assuming that the oil temperature is 1500

F, the average ground temperature 300

F, and that burial depth is 8 ft. For cases (a), (c) and (d) the net heat gain is positive, indicating that the temperature of the oil must increas e until the temperature difference, T - T , is great enough to conduct the excess heat away. If the oil

Ｆｭｰ･ｲｾｵｲ･

rn u st not exceed some upper value, e. g. 180 to 1900

ｆｾ and if raising the oil temperature does not create a sufficiently large temperature difference before the upper limit is reached, then the rate of flow rn u st be reduced to reduce the heat generated by viscous flow. For

case (b), however, there is insufficient heat to maintain the oil temperature at 1500

F and the oil temperature will drop. As it drops viscosity increases and additional horsepower is required to main-tain a constant rate of flow. If sufficient extra horsepower is not available to meet the additional requirements then the rate of flow will be reduced.

Temperature Change Along Pipeline

One needs to be able to estimate temperature change along the length of a pipeline because temperature affects viscosity of oil and hence the horsepower requirement and rate of flow. It is necessary to know, in general terms, whether upper and lower oil temperature

limits may be exceeded. A relation between oil temperature and distance along a pipeline can be developed as follows:

Heat input - Heat output = Heat associated with a change in oil temperature,

or

where

1. 41CQ dT

o (7)

T = temperature of the oil at any point in the pipeline, OF L = distance along pipeline, miles

C = volum etric heat capacity, Btu/ft3 of HP = average heat input per mile. hp /mile

Separating the variables and integrating equation (7) gives an expression for T: T

₌

HP

-

+

T G

+

(T. K t 1 T _ HP) ( G K exp \ t LK t

1.

41CQ o

)

₍₈₎

where T.

=

initial temperature of oil at L

=

0, 0 F.

1

For example. cas es listed in Table II were investigated using equation

(8) and are plotted in Figure 6. It shows that oil temperature may increase or decrease along the pipeline, depending upon the rate of flow and the thermal transfer coefficient which reflects the amount of insulation present and the thermal conductivity of the soil.

Differentiating equation (8) with respect to distance gives the temperature gradient along the pipeline. This can be described by the following equation, dT

ｾｐＩ

K ) exp ( LK (T i - T -

(

t t

)

(9)

-

=

dL G 1. 41CQ 1. 41 CQ t 0 0 where dT

temperature gradient, °F /mile.

-

=

The results of equation (9) are plotted in Figure 7 for cases 1, 2 and 3; the plots indicate that the temperature of the oil will not generally rise or fall more than 10

F in 10 miles, and in most instances that the temperature change in the oil will be much less at the higher rates of flow.

Temperature Change After Shutdown

Information On the rate of change in oil temperature after

shutdown is required to estimate how much time is available for repair Or maintenance operations before the lower oil temperature limit is reached. An equation for temperature change after shutdown can be developed by equating heat loss from the pipe to that associated with change in oil temperature.

Heat flow out of pipe :: Heat from change in temperature of oil, or

where

2545 K

t (T - TG) dt = C V dTa (10)

T :: temperature of oil at any time after shutdown, 0 F t :: time after shutdown, hr

V

=

volume of oil, ft3 / m ile .

a

Separating the variables and integrating gives the following expression:

2545K _, T T G

+

(T. - T )

(

-t , (11 ) :: _{exp t} I 1 G CV ) a where

T. :: _{initial temperature at shutdown ( t} ::

o ),

of.

1

Equation (11) is plotted in Figure 8 for four situations. If a lower temperature limit of 500

F is used, for example, Figure 8 shows that (a) for the uninsulated pipe all repair work would have to be

completed within 5 days to a week, depending upon the initial temperature of the oil, and that (b) for an insulated pipe the time for repair work could be extended to 3 or 4 weeks, or longer in some cases.

Steady-State Condition: Elevated Pipeline

The ice and water content is very high in some permafrost areas and because of stability or settlement considerations a pipeline would probably have to be built above ground. The heat flow out of an elevated pipe is governed by equation (5), with the thermal transfer coefficient defined as

o.

346n

K.

K

₌

1 t

(

r \ In \ r s-t, ) 1 (12)

The results of a parametric study based on equation (12) are presented in Figures 9 through 11. Figure 9 shows that the thermal transfer coefficient decreases with increasing insulation thickness, and Figures 10 and 11 illustrate the coefficient increase with increasing pipe

diameter and thermal conductivity of the insulation. Transient Condition: Buried Pipeline

It is extremely difficult, if not impossible, to obtain a closed form solution for the transient heat flow problem round a buried

pipeline for rn o st natural conditions in permafrost. Consequently numerical methods must be used to estimate the extent of the thaw zone and how

quickly the thaw front is advancing. The amount and rate of thawing round a pipeline and the amount of water liberated significantly influences the settlement, rate of settlement and stability of the melted permafrost and hence the safety of the pipeline. Figures 12 and 13 graphically illustrate how the 320

F isotherm advances round a pipeline and how large thaw depths occur in relatively short times.

As well as the extent of the thaw bulb, Figure 12 shows how quickly equilibrium above the pipe is reached, i , e., within one year. Below the pipe the thaw bulb continues to enlarge for ma.ny years, and only after approximately 15 years does the 320

F isotherm tend to approach equilibrium. Both Figures 12 and 13 show that greater thaw depths o c cu r in the warmer permafrost regions. Figure 13 also indicates the effect of water content on the penetration rate of the 320

Although the frozen water content is a major factor in determining the rate at which the 320

F isotherm advances, the ratio of the thermal conductivity of the unfrozen soil to the frozen soil is a determining factor. The greater the ratio of K unfrozen / K frozen the greater the equilibrium thawing depth will be, because an increase in the

ratio of K unfrozen / K frozen is equivalent to increasing the

pipeline temperature for a hom Jgeneous soil. Figure 14 (Lachenbruch, 1970) shows how the thaw bulb increases in size with increase in

pipeline temperature.

A parametric study should be carried out for the transient condition in order that a better appreciation may be obtained of the time dependence of the amount and rate of thawing round a hot pipeline in permafrost. Such parameters as water content, thermal conductivity of frozen and unfrozen soil, pipe and average ground temperature,

insulation thickness round pipe, geometry as an initial condition

(e. g. berm) or as a time condition (e. g. settlement) could be investigated to advantage. The numerical analysis should be expanded to give heat flux at the ground and pipe boundaries and amount of water liberated upon thawing, as well as the temperature profile.

STRUCTURAL ANALYSIS

An elementary analysis only was undertaken of the structural aspects and consequently the picture of some of the loads and stresses is a general one in this Section. Stresses due to torsion, local

buckling, vibration, earthquakes, crack propagation or plastic strain are considered to be beyond the scope of this report.

Circumferential Stres s

The circumferential stress induced in a pipe by internal pressure may be calculated by the following formula

PD

a

=

c 2t

P

where

a

₌

circumferential stres s , lb/in. a c

P

₌

internal pipe pressure, Ib/in. 2

D

₌

diam eter of pipe, In. t

₌

thickness of pipe, in.

p

For maximum rate of flow the greatest internal pressure was calculated to be approximately 1, 000 psi. For a 48 -In, diameter pipe with 60, 000 psi strength steel the thickness of pipe may be calculated by equation (13) to be O.4 in. With a safety factor of

1. 25 the pipe should be approximately

1

in. thick.

Flexural Stress

The flexural stress of bending is given by

where

= l2Mc

I ( 14)

a

f

=

flexural stres s , Ib/in. 2 M

=

moment at a section, ft-lb

c

=

distance from neutral axis to extreme fibre, in. I

=

moment of inertia of pipe, in. 4

For a 48-In, diameter pipe with a i-in. wall thickness and a yield strength of 60, 000 psi the ma.ximum moment ma.y be calculated by equation (14)to be 4.37 x 106 ft-lb. Using this value for the maximum moment, values may be obtained for the maximum length and deflection of a pipe for various support conditions, assuming that the steel is not strained beyond the elastic limit. The equations for rna xim urn span length and for rn a xirnurn deflection at rnaxirnum span length are listed in Table III; the pipeline loadings are listed in Table IV.

It may be noted (Table IV) that the greatest downward loads on the pipeline are present when the water table is below the pipe. If the water table is above the bottom of the pipe, then les s downward load per linear foot is exerted on the pipe, with the least downward load being present when the water table is at the ground surface. When the soil is a slurry, the res ultant forces act vertically upward.

In Figure 15 the rnaximurn span length and deflection for the simple support case are plotted as a function of pipeline loading based upon the equations and values in Tables III and IV. The plots indicate how the rn aximurn allowable span length and rn aximurn deflection decrease with increasing pipeline load.

Thermal Stress

The stresses resulting from thermal expansion or contraction may be calculated by the following equation,

where

= En6T ( 15)

°th

=

thermal stres s, Ib/in. 2

n

=

thermal coefficient of expansion, l/oF 6T

=

temperature change, ° F.

For 6 T

=

100°F and n

=

6. 5 x 10-ｾ the axial thermal stress is

191 500 psi. Such a thermal stress would produce an axial thrust in

the pipeline of approximately

1.

5 million pounds if restrained or an expansion of 3. 4 ft per mile if unrestrained.

CONCLUSION

A preliminary investigation of the hydraulic, therm al and structural aspects of hot pipelines in permafrost has been undertaken to provide general background information for future geotechnical

analysis. In this context, it is concluded that additional information on the factors affecting the transient heat flow problem round a pipeline in permafrost is required.

BIBLIOGRAPHY

1.

Ca r s Iaw , H. S. and J. C. Jaeger. Conduction of Heat in Solids,

Oxford Press, 1959.

2. Eckert, E. R. G. Heat and Mass Transfer, McGraw-Hill, 1963.

3. Lachenbruch, A. H. Some Estimates of the Thermal Effects of

a Heated Pipeline in Perm afr o st , USGS Circular 632, 1970.

4. McAdams, W. H. Heat Transmission, McGraw-Hill, 1954.

5. Seely, F. B. and J. O. Smith. Resistance of Materials, John

Wiley and Sons, 1959.

6. Streeter, V. L. Fluid Mechanics, McGraw-Hill, 1958.

7. Handbook of Steel Construction, Canadian Institute of Steel

NET HEAT GAINED OR LOST

K K.

Insulation Heat

in-s 1

K Q

(Btu in. / (Btu in. / Thickness t c Heat out

Case ft2 hr of) ft2 hr OF) (in. ) (hp/mile OF) (hp/mile) (hp/mile)

a

5. 0

-

-

2.3

276

+251

b

15. 0

_-

-

7.2

864

-337

c

5.0

0.15

2

1,0

120

+407

TRANSFER COEFFICIENTS FOR VARIOUS RATES OF FLOW AND INSU LA TION THIC KNESS

Rate of Flow Case (barrels/day) 1 2,000,000 2 2,000,000 3 500,000 4 500,000 Insulation Thickness (in. ) 2 2 Transfer Coefficient Temperature K T i TG t (hp/mile ° F) (0 F) (0 F) 1.2 150 30 7.2 150 30 1.2 150 30 7.2 150 30

EQUATIONS FOR MAXIMUM SPAN LENGTH AND DEFLECTION OF PIPELINE

(2

{2

1/2

)

Support Type Simple Cantilever

Cantilever (free but guided at free end)

Equation for 1 J._M

v

8 ( max

C>M

,j2 \ max

J3(

Mm a x

max Equation for I::. max

M

2 1440 ( max \ \ WEI )

M

2 864( m:lX \ WEI )

M

2 648 ( max \ WEI )

M

2 598 ( m:lX WEI ) Cantilever (simple support under free end) Fixed at both end s

"ra-(

M m a x ,1/2

W

)

jU(

M m a x \

1/2

\ W ) 648

M

2 max WE-I-)

W

=

load per linear foot, lb/ft

E

=

Young's modulus, ｬ｢Ｏｩｮｾ

1

=

span length, ft

DESCRIPTION AND VALUES OF LOADING

Load with Load with Load with

Water Table Water Table

Water Table at Ground at Ground

Load Surface, but Surface and

below Pipe Soil not a Soil is a

Slurry Slurry

(lb/En ft) (lb/lin ft) (lb/lin ft)

Pipe only 2501 -530T .. 12501 Pipe + oil _{930 1 +1501 -570 1} Pipe + oil + 1 ft over-burden 1330 1 _{310 1 -570 T} Pipe

+

oil + 4 ft over-burden 25301 _{7901 -570}T Pipe + oil + 8 it over-burden 4130 1 _{1430 1 -570 1}

For these calculations the following values were assumed.

5 soil = 100 Ib /ft3

6 = 62. 4 Ib/ft3 _and

water

l.LJ ...J ｾＸｲＭＭＭＭＭＭＭＬＮＭＭＭＮＮＮＮＮＬＮＮＮＭＭＭＮＮＮＮＮＮＭＭＭＭＮＭＭＭＭＭＭＭＭｲＢＭＭＭＢＢＢＢＧＭＭＭＭＭＧ

7

6

- K j = 1.00

5

[Ks & KiJ

=1

BTU IN.

J

LF

T2 H R 0

F

4

3

2

INSULATION THICKNESS, INCHES

K_s = 15.0

- - - - _{K s} = 5.0

PIPE DIAMETER = 42 INCHES

DEPTH = 8 FEET

1

ｾＭ

_...

--...

_ｾｾ

---K.

=

1

00 I .

--

--

---

...

-

- - - _ _ _ _ Ki = 0.15 - - - K_j = 0.15

I-ｾ

6

u n,

:::c

u, u.. w

o

4

u ｾ w u.. Vl

z

2

«

ｾ I-...J

«

ｾｏｬＭ

_ _

---I.._-_....l..-_----''----'''''''''--_..l...-_ _

- - - L _ - _ - - I

ｾ

a

:::c

I

-FIGURE 1

THERMAL TRANSFER COEFFICIENT AS A FUNCTION OF INSULATION

THICKNESS (BURIED PIPE)

13"+7S8-1

tj

=

3. A" ..- » > "tj = 1 . A"

..-"-...

..-

...

..-"-...

-

--

,,-...,.,,""'"

...,.,,/

. /

_---1;=3 0"

---

.

---

--Kj = 1 .

a

BTU I N/ FT 2 H R 0 F - - - Kj = O. 1 5 BTU I N./ FT2 H R 0 F K_s

=

7 . 5 BTU I N/ FT 2 H R 0F

BURIAL DEPTH

=

8FEET

<..>

.

I -Z

2. 0

u.J u.. u.. ｾ

1. 5

<..> c::: u.J u; V)

z

1.

0

«

c::: I -...J <t: ｾ

0.5

c::: u.J ::I: I -u.. o u.J ...J ｾ

2.5

-

a.. ::I:

45

40

35

30

25

20

15

10

5

0'

I I I I I I I I I

o

PIPE DIAMETER,

INCHES

FIGURE

2

THERMAL TRANSFER COEFFICIENT AS A FUNCTION OF PIPE DIAMETER (BURIED

u.. I Ii = 1.0" 0 _3.0 l..L.J --l

-:E

--

a. :::I: 2.5 1--z: l..L.J

-:: 2.0

I

/

ｾｬｩ］ＶＮＰＢ u.. u.. l..L.J 0 U e:::

1.

5 l..L.J u.. VI

ｾ

z: K_s = 7.5 BT U I N./FT2 H R of

«

e::: PIPE DIAMETER = 42 INCHES

I -

1.

0

BURIAL DEPTH = 8 FEET

--l

«

:E e::: ｾ 0.5 I

-o

O. 1

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

THERMAL CONDUCTIVITY OF INSULATION, BTU IN./FT2 HR

of

loG

FIGURE 3

THERMAL TRANSFER COEFFICIENT AS A FUNCTION OF INSULATION CONDUCTIVITY

ｾＸ

__

ＭＭＭＭＭＭｾＭＭＭＭＭＭＭｲＭＭＭＭＭＭＭＭＭＭＮ

NO INSULATION PRESENT

PIPE DIAMETER = 42 INCHES

BURIAL DEPTH

=

8 FEET

u

ｾＴ

UJ

o

u

e::::

UJ u..

2

(/)

z

c::(

e::::

I-...JO

c::( ..1....- ....1....- _ _ _

:2:

0

5

10

15

e::::

ｾｔｈｅｒｍａｌ

CONDUCTIVITY OF SOIL, BTU IN.lFT2 HR

of

I-:2:

-

0.. :J:

1-"'6

z

UJ

FIGURE

4

THERMAL TRANSFER COEFFICIENT AS A FUNCTION OF

SOl L CON DUCT I V I TY (B URI ED PIP E)

13RｾＷ s:'i>-"+

u.. 0

I

Kj

=

0.30 BTU I N./ FT 2 H R 0 F UJ

:: 5

r<s

=

7.5 BT U I N./FT 2 H R of ｾ

-a.. I PIPE

::I: DIAMETER

=

42 INCHES

-I -

4

:z UJ tj

=

0.0" u

-u.. u.. UJ

3

0 u ｾ

_I

_{t j =1 .0"} UJ u.. V1

₂

z

«

ｾ l -

I

t j= 3.0" ....J

«

₁

ｾ

_I

tj = 6 .A" ｾ UJ ::I: I

-o

o

1

2

3

4

5

6

DEPTH OF BURIAL OF PIPE, FT

7

8

9

FIGURE

5

THERMAL TRANSFER COEFFICIENT AS A FUNCTION OF PIPE BURIAL DEPTH

- - - PIPELINE INSULATED; K_t= 1.2 HP/MILE of - - - _{PIPELINE UNINSULATED; Kt}=7.2 HP/MILE of

190

r-AVERAGE GROUND TEMPERATURE = 30°F BURIAL DEPTH = 8 FEET

o

90

2 MILLION BARRELS/DAY 0.5 MILLION BARRELS/DAY

--

- - _ /""'0 = 2 MILLION BARRELS/DAY --- -- --L. _ 0

--

_--

_--

----

---0.5 MILLION BARRELS/DAY

110

170

- J

ｾ

130

=>

..,...

<: c:::: l.J.J 0-:E l.J.J I -LJ..

o

LJ.. o

900

800

200

300

400

500

600

700

DISTANCE FROM START OF PIPELINE, MILES

100

70 '

I " " I I I I I I I

a

00 = 2 MIL L ION BAR RE L S/ DAY

0.050

900

800

700

600

500

00

=

O.5 MIL L ION BAR RE L S/ DAY

400

300

200

100

PIP ELI N E INS U LA TE D

- - - - PIPELINE UNINSULATED [ 0 0 = 2 MILLION BARRELS/DAY _

-

-

-

---.,...,

,

...

- O.

100...

I I I I I I I I I

o

l__

+-__

+-__

+-_--I__

I

--+__

I

-+__-+__

_I

₁

ＭＭ｜ｉ｟ｾｾｉ

ｾ

I

I

I

ｾ

01

l.I..J ...J

-0.075

Cl e:( e:::: <..:> ｾ

-0.025

ｾ l -e:( e:::: l.I..J a..

-0.050

:E l.I..J I -:E

0.025

-

L.L. o

DISTANCE ALONG PIPELINE, MILES

- - - PIP E LI N E INS U LA TEDi Kt

=

1 . 2 H P/ MIL E 0 F

----PiPELINE UNINSULATEDi Kt=7.2 HP/MILEoF AVERAGE GROUND TEMPERATURE = 30°F

BURIAL DEPTH

=

8 FEET

\

\

\

\

\

\

\

\

\

\

\

\

\

\_\

70

t- \

\

\

\

\

\

\ \

"

,

SOt-

,

<,

-,

'"

'"

_<,

"'

...

_...

<,

"

... ...

...

""'"

"""-

...

--:J

-30'

,

, - - ＭＭＧＭＭｾ｟ｉ

---.---0

4

8

12

16

20

24

28

32

36

TIME AFTER SHUT-DOWN, DAYS

o

....J.

110

130

L.L.

o

ｾ

90

:::::> l -e:( c::: l.LJ 0-ｾ l.LJ I -L.L. o

K_j = 0.3 Kj = 0.5

PIPE DIAMETER = 48 INCHES [KJ =

[B

T U I N./ FT 2 H R 0

FJ

LLJ ---J

I

-ｾＴ

u w... w... LLJ

°3

_u

0::: LLJ w... Vl

22

ｾ 0::: I ----J ｾ

:E 1

0::: LLJ

:::c

I -o

:E5

-

0..

:::c

K_j = 0.1

10

9

8

4 5 6

7

INSULATION THICKNESS, INCHES

3

2

o '

I I I I I I I I I

1

FIGURE

9

THERMAL TRANSFER COEFFICIENT AS A FUNCTION OF INSULATION THICKNESS

ｾ］ＭＭＭＭＭＭ］

-ｾ t j = 6 " o LL.I ...J ｾ

5

-

0-:c ｾ I -Z

4

LL.I

u

u; u.. LL.I

a

3

u ｾ LL.I u, V'l

z

2

«

ｾ I -...J

«

ｾ

1

ｾ LL.I :c I -Kj =

o.

2 BTU I N./ FT 2 H R 0 F tj = 1" tj = 2"

54

48

42

36

30

24

18

12

6

o '

! I ! I I I I I I

o

PIPE DI AMETER, INCHES

FIGURE

10

THERMAL TRANSFER COEFFICIENT AS A FUNCTION OF PIPE DIAMETER (ELEVATED

1.0

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

THE RMAL CON DUCT I V I TY 0 FIN SULATION , BTU I N./F T2 HR

0

F

o '

! ! I I !

O. 1

! ! ! J

u..

I

PIPE DIAMETER = 48 INCHES

0 I..LJ

/

/ t j = 2" - J

10

-:2:

-

o, :::I:

.

I -

₈

z

I..LJ

-U

-

_u..

6 I

/

/ '

u.. ｾｴｩ］ 4" I..LJ 0 U a:::: I..LJ u.. (/)

4

z

«

a:::: l

-V

/ '

ｾ - tj = 10" - J

«

₂

:2: a:::: I..LJ :::I: I

-FIGURE

11

THERMAL TRANSFER COEFFICIENT AS A FUNCTION OF INSULATION CONDUCTIVITY

10 ..--t ｾ ""-(A,oril)

-ＭＭＭＭＭｾＭＭＭＭＭＭＭＭＭ ( (September)

,

_,

\ \

x

ｾ ｾ

ｔｾａｉｗｅｄ

--c:::::----...

ｾＯ

(Sep,-;;:;;;';rj---

/?Ai

t

ＮＬＬｾｾ

ｾｾｏ

ｾｏｒｉｚｏｎｔａｌ DISTANCE FROM CENTERLINE(FEET)

.co

-30 -20 -10 0 fO 20 JO 40

I , , ,

, t '

I I

- - - ; : - : - - ｾ

DEPTH(FEET)

FI GURE

12

ADVANCING THAW ZONE AROUND A HOT PIPELINE

(After A.H. Lachenbruch, 1970)

70

60

ｾ

40/'1'"

:=.

F::::q

0:

ｾｉｽ

ｾｏ

::::}

,

ｾＡｉＡＧＬｾｴ

ｾｾｊＺｾ

::; .:.

if

20 :

J

.j ./::'

.-:::::{?::::"

...

::/)::

.. BR It7S7-2.

o

II---L._----L..-_..L...---I-_----'--_..L...---'-_---'--_""'---'-_ _

o

2 4 6 8 10 12 14 16 18 20

TIM E

(years)

FIGURE 13

DEPTH OF THAW ZONE UNDER A HOT PI PEllNE

5°r-

u

°

rol- l()Dr 0cx). II {:

2°1-

20°t-

,21

0.3

ｾｲ

I ｾ 4 5'

I

80°1

I

0.1

I I()D u

-t

ｾｉｾ

t

Ｂｾ

°

"s-

6' CX) u ｾ ｾ

o

_,

_°

c'oc,o/ ｾＯ

200

ｾ

_-3°

II CX) ｾ III

I

0.03

...

_ｾ

-2°

J2

0.400

...

0

....

-{:

I

_1°

•

41)

800

I

0.01

en =41) 0 u

_:g

₁

-0.5°

...

u 0 ₀ -.:::: ;: 41) ₀

-

c:

］ｾ

I

-0.3°

e: I

.003

I I I

2

5

10

20

50

100

200

500

1000

rand d

I

feet

A.H. Lachenbruch, 1970 )

FIGURE

14

EQUILIBRIUM POSITION OF 32°F ISOTHERM AROUND A HOT PIPELINE(After

Vl -1150 l.LJ 350

I-

\

:::I: e..> z.

-ｾ

300

ｾ

ｾ｜

-z. 125 0

-\

PIPE PIPE, OIL PIPE, OIL PIPE, OIL l

-e..>

\

PLUS PLUS PLUS PLUS l.LJ

:::I: _ONLY

\

OIL I ' OVERBURDEN 4'OVERBURDEN 8'OVERBURDEN --l

l - _LL.

ｾ

250

j

\\1 1

₁

₁

100 l.LJ C l.LJ --l l.LJ e:::: z. l -e:( _Z. c.. l.LJ Vl 200

\

75 e..> ｾ

,

e..>

-=:> <, _I -ｾ

"

Vl

-

_"

e:(

"

x

150

...

₅₀ --l e:( l.LJ ｾ < , _ SPAN LENGTH ｾ

-

...

-

--

--

ｾ=:>

-

--100 t.,

---

--

---

₂₅

x

DEFLECTION - - - e:( ｾ 50 ₀ 0 1000 2000 3000 4000 5000

LOAD PER LINEAR FOOT OF PI PE, POUNDS/FOOT