Gas Loss from Damage

Introduction

This calculator estimates the amount of gas lost when a pipe segment is damaged. It handles two types of damage — a puncture (a hole in the side wall of the pipe) and a complete severance (the pipe cut in two) — and reports the equivalent puncture diameter, the pressure at the break, the volume of gas lost over a specified duration, and the monetary value of that lost gas.

The values calculated by this method are a rough estimate of the maximum gas lost through a punctured or severed line. Many real-world factors are not accounted for — such as resistance at the break from soil or blockages, an irregular shape and/or rough edges of the opening, and pressure loss from normal system flow — so the method tends to overestimate lost gas volume. Always verify the calculated volume against recorded meter readings where practical.

Background

When a pipe line is punctured or severed, the gas will generally vent into the atmosphere, the rate depending on the line pressure. In the unusual case where the line pressure is less than the surrounding pressure — for example, a low-pressure line submerged in water with a static head greater than the line pressure — the gas will not escape and water will instead enter the line. In nearly all other cases, however, once the object causing the damage has been removed, the gas vents to the atmosphere freely. The only exact way to determine the amount lost is through direct measurement, which is usually only possible when the flow is large enough to register as an anomaly on an upstream meter or gate station. This calculator provides alternative methods for estimating gas lost due to a puncture and due to a complete severance.

Puncture

For a puncture, the flow through the damage is assumed to behave similarly to flow through an orifice meter. A puncture in the side wall of a pipe is obviously not identical to a finely machined, sharp-edged orifice, but the similarities are close enough that a suitable estimating formula can be derived from a general orifice meter equation — in this case, the AGA Report No. 3 orifice equations. As implemented, a “puncture” may be a circular hole, a rip or tear, or an irregularly shaped opening.

Because a real puncture is not exactly circular, not sharp-edged, and may have pieces of pipe material protruding into the flow path, a shape factor parameter is included to decrease the computed flow and account for these deviations from ideal orifice behavior. The user is responsible for selecting an appropriate shape factor value. When solving a puncture, the pressure immediately upstream of the puncture is taken to equal the downstream pressure of the supply piping, and the pressure immediately downstream of the puncture is taken to be atmospheric. The downstream supply-piping pressure is found iteratively: the pressure drop across the supply piping is computed for a trial flow rate, and the process repeats until the flow through the orifice and the flow through the supply piping are equal.

As a rule of thumb, if the area of the damage exceeds about 75% of the pipe’s flow area (puncture size greater than about 75% of the pipe diameter), the puncture assumption is no longer valid and the damage should be treated as completely severed.

Severed Line

For a severed line, the line is assumed to be completely cut and the flow unrestricted, with the severed end open to the atmosphere. The flow along the supply route is treated like normal pipe flow: the pipe components are combined, using their equivalent lengths and diameters, into a single equivalent segment. Flow through that equivalent segment is computed using an upstream (inlet) pressure equal to the specified supply pressure and a downstream (outlet) pressure equal to atmospheric pressure for normal flow, or some higher value in the case of choked (sonic) flow.

Equations

GASCalc computes the gas flow rate through a puncture by combining the puncture flow equation below with a selected pipe flow equation, balancing the two with a trial-and-error process. The pipe pressure drop is calculated using the selected pipe flow equation (see the Pipe Flow calculation reference); the puncture flow is treated as flow through a generic circular orifice, derived from the AGA Report No. 3 orifice meter equations. The applicable form depends on whether flow through the puncture is subsonic or sonic (choked).

Subsonic Flow

The subsonic equations apply when the ratio between downstream/upstream pressure is as follows:

\frac{P_2}{P_1} > \left(\frac{2}{k+1}\right)^{\frac{k}{k-1}}

\frac{P_2}{P_1} > \left(\frac{2}{k+1}\right)^{\frac{k}{k-1}}

Where:
P₁ − Pipe Inlet (Upstream) Pressure, psia
P₂ − Pipe Outlet (Downstream) Pressure, psia
k − Specific Heat Ratio, dimensionless

Then:

Q = 685.68 \times D^2 \times \frac{T_B}{P_B} \times \left(\frac{P_1^2 - P_1 P_2}{SG \times T_F}\right)^{0.5} \times Y_1 \times E

Q = 685.68 \times D^2 \times \frac{T_B}{P_B} \times \left(\frac{P_1^2 – P_1 P_2}{SG \times T_F}\right)^{0.5} \times Y_1 \times E

Where:
Q − Volumetric Flow Rate at the Specified Base Pressure and Temperature, cfh
D − Inside Diameter Equivalent of the Puncture, inches
T_B − Base Temperature, °R
P_B − Base Pressure, psia
P₁ − Pipe Inlet (Upstream) Pressure, psia
P₂ − Pipe Outlet (Downstream) Pressure, psia
SG − Specific Gravity, dimensionless
T_F − Average Gas Flowing Temperature, °R
Y₁ − Expansion Factor, dimensionless
E − Shape Factor, dimensionless

Y_1 = 1 - \frac{0.41}{k} \left(\frac{P_1 - P_2}{P_1}\right)

Y_1 = 1 – \frac{0.41}{k} \left(\frac{P_1 – P_2}{P_1}\right)

Where:
Y₁ − Expansion Factor, dimensionless
k − Specific Heat Ratio, dimensionless
P₁ − Pipe Inlet (Upstream) Pressure, psia
P₂ − Pipe Outlet (Downstream) Pressure, psia

Sonic (Choked) Flow

The choked equations apply when the ratio between downstream/upstream pressure is as follows:

\frac{P_2}{P_1} \leq \left(\frac{2}{k+1}\right)^{\frac{k}{k-1}}

\frac{P_2}{P_1} \leq \left(\frac{2}{k+1}\right)^{\frac{k}{k-1}}

Where:
P₁ − Pipe Inlet (Upstream) Pressure, psia
P₂ − Pipe Outlet (Downstream) Pressure, psia
k − Specific Heat Ratio, dimensionless

Q = 685.68 \times D^2 \times \frac{T_B}{P_B} \times P_1 \times \left(\frac{1 - \left(\frac{2}{k+1}\right)^{\frac{k}{k-1}}}{SG \times T_F}\right)^{0.5} \times Y_1 \times E

Q = 685.68 \times D^2 \times \frac{T_B}{P_B} \times P_1 \times \left(\frac{1 – \left(\frac{2}{k+1}\right)^{\frac{k}{k-1}}}{SG \times T_F}\right)^{0.5} \times Y_1 \times E

Where:
Q − Volumetric Flow Rate at the Specified Base Pressure and Temperature, cfh
D − Inside Diameter Equivalent of the Puncture, inches
T_B − Base Temperature, °R
P_B − Base Pressure, psia
P₁ − Pipe Inlet (Upstream) Pressure, psia
k − Specific Heat Ratio, dimensionless
SG − Specific Gravity, dimensionless
T_F − Average Gas Flowing Temperature, °R
Y₁ − Expansion Factor, dimensionless
E − Shape Factor, dimensionless

Y_1 = 1 - \frac{0.41}{k} \left(1 - \left(\frac{2}{k+1}\right)^{\frac{k}{k-1}}\right)

Y_1 = 1 – \frac{0.41}{k} \left(1 – \left(\frac{2}{k+1}\right)^{\frac{k}{k-1}}\right)

Where:
Y₁ − Expansion Factor, dimensionless
k − Specific Heat Ratio, dimensionless

The absolute pressures are related to the gauge values by P₁ = P_1,gauge + P_atm and P₂ = P_2,gauge + P_atm, where P_1,gauge and P_2,gauge are the gauge pressures immediately upstream and downstream of the puncture (psig) and P_atm is the atmospheric pressure at the puncture (psia).

Case Guide

Part 1: Create Case

Input Parameters

Part 2: Outputs/Reports

Results

Note: Pressure values are entered and displayed in gauge units, while flow rate and volume values represent standard volumes adjusted to the base pressure and temperature. Flow along a supply route cannot exceed the rate that would produce sonic velocity; in severe-damage cases the flow may be limited to sonic speeds, and the downstream pressure may then exceed atmospheric. The number of decimal places shown for any calculated item can be set under File > Preferences > Decimals.

References

• American Gas Association, Report No. 3, Orifice Metering Of Natural Gas, Third Edition, 1992.

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