Hot Tap Sizing

Introduction

When a compressible fluid, such as natural gas or air, is passed through an orifice, the rate of flow is determined by the area of the orifice opening; the absolute upstream pressure is 𝑃₁; and the absolute downstream pressure is 𝑃₂: unless the ratio 𝑃₂/𝑃₁. equals or is less than the critical ratio. When 𝑃₂/𝑃₁ equals or is less than the critical ratio downstream pressure no longer effects rate of flow through the orifice, and flow velocity at the vene contracta is equal to the speed of sound in that fluid under that set of condition. This is commonly referred to as critical or sonic flow. Orifice equations are therefore classified as “sonic” or “subsonic” equations.

1. Critical Flow Ratio – The equations for the critical flow of a compressible gas based on 𝑃1 and the ratio, k of the specific heats of the gas for constant pressure, 𝐶_𝑝, and constant volume 𝐶_𝑣.

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

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

For natural gas this ratio is 0.55

2. Subsonic Orifice Flow Equation – Subsonic Flow conditions exist where 𝑃₂≥𝑃₁𝑅_𝐶

A=\frac{Q}{4645kF}\sqrt{\left(\frac{MTZ}{P_1(P_1-P_2} \right)} \~\
F=\sqrt{\left( \frac{ \frac{P_1}{P_2}^{\frac{k-1}{k}}\left( \left( \frac{P_1}{P_2}\right)^{\frac{k-1}{k}} -1\right) }{\frac{k-1}{k} \left(\frac{P_1}{P_2}-1 \right)} \right)}

A=\frac{Q}{4645kF}\sqrt{\left(\frac{MTZ}{P_1(P_1-P_2} \right)} \\~\\ 
F=\sqrt{\left( \frac{ \frac{P_1}{P_2}^{\frac{k-1}{k}}\left( \left( \frac{P_1}{P_2}\right)^{\frac{k-1}{k}} -1\right)     }{\frac{k-1}{k} \left(\frac{P_1}{P_2}-1 \right)}   \right)}

M=28.964G

Where:
𝐴−Calculated orfice area (in2)
𝑄−Flow Rate (ft3/min)
𝑀−Molecular Weight of Gas
𝐺−Gas Specific Gravity
𝑇−Flowing Temperature (°R)
𝑍−Gas Compressibility Factor
𝑃₁−Pressure (psig)
𝑃₂−Pressure loss through orifice (psi)

3. Sonic Orifice Flow Equation – Sonic Flow conditions exist where 𝑃₂<𝑃₁𝑅_𝑐

A=\frac{Q(MTZ)^{1/2}}{6.32R_ckP_1}

A=\frac{Q(MTZ)^{1/2}}{6.32R_ckP_1}

Where:
𝐴−Calculated orifice area (in2)
𝑄−Flow Rate (ft3/min)
𝑀−Molecular Weight of Flowing Gas
𝑅_𝑐=Critical Flow Ratio
𝑇−Flowing Temperature (°R)
𝑘−Orifice coefficient, use (1/𝐹𝜌𝑣²)
𝑍−Gas Compressibility Factor for inlet conditions
𝑃₁−Pressure(psig)

Case Guide

Part 1: Create Case

Input Parameters

• Operating Temperature (°F)
• Operating Pressure (psig)
• Flow Rate(MCFH)
• Pressure Loss Through Orifice (psi)
• Orifice Coefficient
• Gas Specific Gravity
• Gas Compressibility Factor
• Molecular Weight
• Specific Heat Ratio
• Critical Flow Ratio
• Nominal Branch Size
• C – Factor
• Hole Cutter Diameter (in)

Part 2: Outputs/Reports

Results

• Branch Gas Velocity (ft/sec)
• Flowing Conditions
• Calculated Orifice Area (in2)
• Calculated Tap Diameter( in)
• Erosional Velocity (ft/sec)
• Sonic Velocity (ft/sec)

References

• ASME – Boiler and Pressure Vessel Code, Section VIII
• API – RP 520 Part 2
• ASME B31.8 Gas Transmission and Distribution Piping Systems
• ASME B31.3, B31.4 and B31.8 – Full Encirclement Sleeves (See Appendices)

Appendix

Even though Technical Toolboxes does not provide software for a full-encirclement reinforcing saddles, many operators use them to provide reinforcement for branch outlets in accordance with ASME B31.3, B31.4, B31.8 and other applicable design codes. Full-encirclement reinforcing saddles are designed to fully encircle the run pipe however; they are not designed to be pressure retaining devices. To avoid gas entrapment during welding and to prevent pressure containment, should a leak develop underneath the saddles; these saddles should be provided with a vent to allow escaping product.

A typical field applied Full Encirclement Reinforcement Weldment Saddle is shown below:

FAQ