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**INTRODUCTION:**

This web page addresses issues related to the operating pressure, test pressure, diameter, wall thickness and specified minimum yield stress (SMYS) of steel pipelines.

**DEFINITIONS:**

**Force** = a push or a pull in a particular direction

**Stress = Force / (perpendicular area)**

**Compressive Stress** = a stress that tends to push together molecules within the stressed material

**Tensile Stress** = a stress that tends to pull apart molecules within the stressed material.

**Hoop Stress = Sh** = the pipe material stress tangential to the pipe.

In a properly supported pipe containing a fluid under pressure the largest tensile stress is the hoop stress.

**Yield Stress = Sy** = stress at which permanent deformation of the stressed material commences. This stress is also known as the "elastic limit". The yield stress is a function of the intercrystaline binding energy of the material. At the yield stress point the material has reached the maximum elastic energy that it can store without causing a change in molecular arrangement.

In most materials the tensile yield stress is less than the compressive yield stress, so generally the term Yield Stress refers to tensile yield stress.

The tensile yield stress is a material property which for a material such as steel , which is composed of a large number of small randomly oriented crystals, is independent of direction and geometry.

For a typical batch of high strength pipe steel the average value of **Sy** is:

**Sy = 57,000 psi**

However, due to uncontrolled variations in trace element concentration, crystal size (forging), etc. the **Sy** value for any individual pipe length could be in the range:

**52,000 psi < Sy < 62,000 psi**.

A pipeline under pressure is only as strong as its weakest individual pipe length. Hence in terms of yield stress the primary concern is the pipe length with the smallest **Sy** value. That smallest **Sy** value is called the **Specified Minimum Yield Stress (SMYS)** and is typically **52,000 psi**.

There is a further concern. The wall thicknesses of individual pipe lengths are also subject to random variation. For example, the pipe wall thickness might be specified as **0.281 inches +/- 10%** in which case the actual pipe wall thickness **T** lies in the range:

**(0.281 - .0281) inches < T < (0.281 + .0281) inches**

or

**0.2529 inches < T < .3091 inches**

In this case the primary concern is the pipe length with the smallest **T** value.

The pipeline needs to be designed such that if the pipe length with the smallest **Sy** value is also the pipe length with the smallest **T** value, the inequality:

**Sh < Sy**

must still be met under the extreme conditions of a hydraulic pressure test.

**BARLOWS FORMULA:**

Consider a pipe containing a fluid under compression. The pipe wall is stationary so the net force on the pipe is zero. The radial force on the pipe by the fluid is balanced by the compression force due to the external atmosphere and by the tensile force exerted by the pipe wall.

Let **D** = inside diameter of pipe

Let **T** = pipe wall thickness

Let **Pa** = absolute atmospheric pressure (with respect to a vacuum)

Let **Pf** = absolute contained fluid pressure (with respect to a vacuum)

Let **Pg = (Pf – Pa)** = Gauge Pressure

Most pressure gauges actually measure **Pg** which is the difference between the unknown fluid pressure and atmospheric pressure

Let **Sh** be the hoop stress.

**Assume that the hoop stress Sh is evenly distributed throughout the pipe material.** This is a crucial assumption which is not always valid. However, this assumption is generally used in the design of new steel pipelines.

Let **L** = length of a short pipe section.

The positive radial force **Ff** exerted by the contained fluid on the pipe length **L** is:

**Ff = Pf D L**

The negative radial force **Fa** exerted by the atmosphere on the pipe length **L** is:

**Fa = - Pa (D + 2 T) L**

The negative radial force **Fw** exerted by the pipe wall over pipe length **L** is:

**Fw = - Sh 2 T L**

Since the net force on the pipe is zero:

**Ff + Fa + Fw = 0**

or

**Ff = - Fa - Fw**

or

**Pf D L = Pa (D + 2 T) L + Sh 2 T L**

or

**(Pf – Pa) D = Pa 2 T + Sh 2 T**

or

**(Sh + Pa) = [(Pf – Pa) D / (2 T)]
= [(Pg D) / (2 T)]**

Rearranging this formula gives:

**Pg = (Sh + Pa) (2 T) / D**

In practical pipelines:

**Sh >> Pa**

so this formula simplifies to:

**Pg = (2 Sh T) / D**

This is Barlows Formula which relates the average hoop stress **Sh** to the gauge pressure **Pg**, pipe diameter **D** and pipe wall thickness **T**.

**MAXIMUM ALLOWABLE PRESSURE (MAP):**

In order to prevent damage to the pipe due to the pipe material going beyond its elastic limit the inequality:

**Sh < Sy**

must always be satisfied, even during the most extreme pressure tests.

**ENBRIDGE LINE 9:**

If there is 100% certainty that everywhere on the pipeline:

**Sy > 52,000 psi**

and that:

**T > 0.25 inches**

and that:

**D = 30 inches**

then the Maximum Allowable Pressure **(MAP)** in the pipe is:

**(MAP) = ( 2 X 52,000 psi X 0.25 inch) / 30 inch
= 866.67 psi**

This is the pressure at which a hydraulic pressure test should be conducted.

**PRESSURE TESTING:**

In the above calculations there is no allowance for corrosion, cracking, erosion or other pipe aging mechanisms. In my view with a 40 year old pipeline the only certain way to detect a localized pipe aging problem is via a hydraulic pressure test.

In the case of Enbridge Line 9 the last hydraulic pressure test was done about 20 years ago. It is possible that undetected corrosion or other aging processes that effectively reduce pipe strength have occurred since the last hydraulic pressure test.

Hence the pipe should be subject to another hydraulic pressure test. If that test pressure is less than 866.67 psi then the new test pressure becomes the new **(MAP)** value for calculation of Maximum Allowable Operating Pressure **(MAOP)**.

**NON-CRITICAL LOCATIONS:**

In non-critical locations where life safety or major property damage is not an issue then:

**Sh < (2 / 3) Sy**

and the maximum allowable operating pressure (MAOP) is given by:

**(MAOP) = Sh (2 T) / D
< (2 /3) Sy (2 T) / D
= (2 / 3) (MAP)
= 0.666 X 866.67 psi
= 577.7 psi**

However, there is a problem with an MAOP that results in:

**Sh = (2 / 3) Sy**

It makes pipeline maintenance in subsequent years much more expensive. There is zero alowance for cracks that initiate at dielectric coating defects. Inline inspection tools (pigs) cannot find tiny cracks, especially adjacent to welds. For economical long term pipeline maintenance it is better to set the MAOP such that:

**Sh = (1 / 2) Sy**

Then during a subsequent pressure test at 150% of MAOP:

**Sh = (3 / 4) Sy**

This choice allows a crack to penetrate up to (1 / 4) of the pipe wall thickness, and hence be of detectable size, before the pipe fails under a pressure test. If a crack has penetrated (1 / 4) of the pipe wall thickness that crack is usually detectable with an inline inspection tool (pig) before the pressure test is conducted. Then the defective section of pipe can be replaced prior to the pressure test.

**LIFE SAFETY LOCATIONS:**

At locations where a pipe rupture will likely lead to loss of life, then the guide is that:

**Sh < (1 / 3) Sy**

In order to meet this requirement while maintaining the same (MAOP) value it is necessary to increase the pipe wall thickness.

Let **Tl** = pipe wall thickness **T** at life safety locations.

**577.7 psi = (MAOP)
= Sh (2 T) / D
< (1 / 3) Sy (2 Tl) / D**

Solving for **Tl** gives:

**Tl > 3 D (MAOP) / (2 Sy)
= (3 X 30 inches X 577.7 psi) / (2 X 52,000 psi)
= .500 inches**

If there is a random **+/- 10% variation** in pipe wall thickness the nominal pipe wall thickness should be **0.550 inches** to ensure an actual minimum pipe wall thickness of **0.500 inches**.

If the nominal pipe wall thickness at life safety locations is **Tl = 0.281 inches** with an actual minimum wall thickness of **0.250 inches** then:

**(MAOP) = Sh (2 T) / D
< (1 / 3) Sy (2 Tl) / D
= (1 / 3) X 52,000 psi X (2 X 0.250 inches) / (30 inches)
= 288.89 psi**

**STORM SEWERS:**

An issue that is of concern in Toronto is that in the event of a rupture failure of Enbridge Line 9 a large quantity of oil would likely flow into the Toronto storm sewer system. That oil would then flow into Lake Ontario and might then flow into the City of Toronto potable water intakes. The potential scope of the possible environmental and property damage is so large that in the view of this author the maximum allowable material operating stress on Enbridge Line 9 pipe anywhere near a storm sewer grate should be restricted to:

**Sh < (Sy / 2)**.

In order to meet this requirement while maintaining the same (MAOP) value it is necessary to increase the pipe wall thickness.

Let **Ts** = pipe wall thickness **T** at storm sewer threatened locations

**577.7 psi = (MAOP)
= Sh (2 T) / D
< (1 / 2) Sy (2 Ts) / D**

Solving for **Ts** gives:

**Ts > D (MAOP) / ( Sy)
= (30 inches X 577.7 psi) / (52,000 psi)
= .333 inches**

If there is a random **+/- 10% variation** in pipe wall thickness the nominal pipe wall thickness should be **0.375 inches** to ensure a minimum actual pipe wall thickness of **0.333 inches**.

The above calculations represent my professional opinion based on a deep understanding of the underlying science and the potential risks to the public rather than on any particular regulation.

**SUMMARY:**

If Enbridge is convinced that there has been no deterioration in Enbridge Line 9, the pipe should be hydraulically pressure retested at its Maximum Allowable Pressure (MAP) of:

**(MAP) = 866.67 psi**.

If the hydraulic pressure retest at 866.67 psi is successful the Maximum Allowable Operating Pressure (MAOP) for Enbridge Line 9 should be:

**(MAOP) = 577.77 psi**

In the event that the hydraulic pressure retest is done at a Test Pressure less than 866.67 psi then the Maximum Allowable Operating Pressure (MAOP) for Enbridge Line 9 should be:

**(MAOP) = (2 / 3) (Test Pressure)**.

At locations where human life is at risk the Enbridge Line 9 pipe actual wall thickness should be everywhere greater than **0.500 inches**, indicating that for pipe with a +/- 10% variation in wall thickness the nominal wall thickness should be **0.550 inches**.

At locations where a pipe rupture could lead to oil flow into the Toronto storm sewer system the pipe actual wall thickness should be everywhere greater than **0.333 inches**, indicating that for pipe with a +/- 10% variation in wall thickness the nominal wall thickness should be **0.375 inches**.

At locations where a pipe rupture would have little environmental consequence the Enbridge Line 9 actual pipe wall thickness should be everywhere greater than **0.250 inches**, indicating that for pipe with a +/- 10% variation in wall thickness the minimum nominal wall thickness should be **0.281 inches**. However, in order to reduce the cost of future pipeline maintenance this author recommends use of pipe with a nominal wall thickness of **0.375 inches** whenever a pipe length with a smaller wall thickness is replaced. In view of the potential cost consequences of a pipeline rupture in the Greater Totonto Area it would probably make economic sense for Enbridge to upgrade every Line 9 pipe length in the GTA to a minimum nominal wall thickness of **0.375 inches**.

The Maximum Allowed Operating Pressure (MAOP) at locations where human life is at risk and the pipe wall thickness is nominally 0.281" should be reduced to **288.89 psi**.

**SUMMARY EMAIL:**

The following email related to Enbridge Line 9 was circulated on March 8, 2014.

Hello All:

The simple truth is that the pipeline is an accident waiting to happen unless there is a hydro static test to 150% of maximum approved operating pressure (MAOP). If a pipe section is so cracked that it cannot withstand this test that section of pipe needs to be replaced now. Enbridge can use pigs to identify and replace most cracked sections before a hydro static test. However, pigs are not 100% reliable, especially with respect to external cracks that are adjacent to welds. Hence there is no substitute for a full scale hydro static test to 150% of MAOP. Testing to 125% of MAOP, as contemplated in CSA Z662-11, is not good enough because it does not give an adequate working life to the pipe after the test. A test to 125% of MAOP on a 0.25 inch wall pipe merely shows that there are 0..05 inches (1.27 mm) of safety margin. Cracks are known to penetrate such pipe wall at rates in the range .15 mm / year to .40 mm/ year.

Hence under CSA Z662-11 the working life of the pipe after pressure testing until the next pressure test is in the range:

(1.27 mm / .40 mm) = 3.2 years to (1,27 mm / ,15 mm) = 8.5 years.

I highly doubt that we want to revisit this matter only three years hence. Thus it is essential that everyone insist on a hydro static pressure test to 150% of MAOP. TELL YOUR FEDERAL MPs AND PROVINCIAL MPPs THAT NOTHING LESS THAN A HYDRO STATIC PRESSURE TEST TO 150% OF MAOP is satisfactory. CSA Z662-11 is intended for new pipelines in rural areas, not for old pipelines in the middle of Toronto. The NEB process and CSA Z662-11 are both designed to maximize pipeline company profits, not address public safety. THIS PIPELINE DOES NOT MEET PROVINCIAL SAFETY STANDARDS!

Absent a pressure test to 150% of MAOP everyone should assume that eventually there will be a rupture failure, and if that failure occurs in the GTA the cost will be many billions of dollars. Enbridge is a large company but I doubt its capacity to fund a $10 billion to $20 billion spill clean up. Hence Enbridge should carry third party insurance of $10 billion to $20 billion per incident. If Enbridge has to choose between properly fixing the pipe and paying the insurance premium on a $20 billion policy it will probably choose to fix the pipe, which is what it should have done in the first place.

Best Regards,Charles Rhodes, P. Eng., Ph.D.

Xylene Power Ltd.

This web page last updated March 14, 2014.

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