This example illustrates the calculation process for determining the maximum penetration rate for a long radius elbow. The calculation includes the following steps:

  • Determine the elbow radius factor (ERFr/d).
  • Calculate the particle impact velocity;
  • Equivalent stagnation length L
  • Dimensionless parameters, NRe and F;
  • vp/v.
  • Compute the penetration rate in a standard elbow.
  • Determine the penetration rate in long radius elbow.

In this example, a 2-in. pipe with a Schedule 40, ASTM 234 Grade WPB seamless elbow with an ID of 2.067 in. was used. The r/d ratio of the elbow was 3.0, and the liquid used was clay/mud at a velocity of 25 ft/s; the sand rate is 1800 ft3/D.

Elbow Radius Factor

In this calculation, the unit of density is lb/ft3 and the viscosity of mf is cp. The calculated ERFr/d is 0.304.

Input Data for Calculating Penetration Rate

Particle Impact Velocity

The particle impact velocity is calculated based on the methods illustrated.

1: Equivalent Stagnation Length L.

Calculation of the equivalent stagnation length L
File:Equivalent Stagnation Length Calculated.png
Equivalent Stagnation Length Calculated

2: Compute NRe and F:
Compute Nre Calculating

The dimensionless numbers NRe and F are calculated using parameters with consistent units. These parameters are used for:

3: Determine the vp/v of a Valve.

Penetration Rate in Standard Elbow

In this example, semirounded corner sand is assumed.
File:Penetration Rate example.png
Penetration Rate example


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