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.

## Contents

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

## References

[1] E.S. Venkatesh, Erosion Damage in Oil and Gas Wells, Proc. Rocky Mountain Meeting of SPE, Billings, MT (1986) 489–497. May 19-21.

[2] N.A. Barton, Erosion in Elbows in Hydrocarbon Production System: Review Document, Research Report 115, HSE, ISBN 0 7176 2743 8, 2003.

[3] American Petroleum Institute, Recommended Practice for Design and Installation of Offshore Production Platform Piping Systems, fifth ed., API- RP-14E, 1991.

[4] Det Norsk Veritas, Erosive Wear in Piping Systems, DNV- RP- O501 (1996).

[5] A. Huser, O. Kvernvold, Prediction of Sand Erosion in Process and Pipe Components, Proc. 1st North American Conference on Multiphase Technology, Banff, Canada, pp. 217–227 (1998).

[6] M.M. Salama, E.S. Venkatesh, Evaluation of API RP 14E Erosional Velocity Limitation for Offshore Gas Wells, OTC 4485, Offshore Technology Conference, Houston, Texas, 1983.

[7] S.J. Svedeman, K.E. Arnold, Criteria for Sizing Multiphase Flow Lines for Erosive/ Corrosive Service, SPE 26569, 68th Annual Technical Conference of the Society of Petroleum Engineers, Houston, Texas, 1993.

[8] M.M. Salama, An Alternative to API 14E Erosional Velocity Limits for Sand Laden Fluids, OTC 8898, pp. 721 –733, Offshore Technology Conference, Houston, Texas (1998).

[9] P.D. Weiner, G.C. Tolle, Detection and Prevention of Sand Erosion of Production Equipment. API OSAPR Project No 2, Research Report, Texas A&M University, College Station, Texas, 1976.

[10] T. Bourgoyne, Experimental Study of Erosion in Diverter Systems. SPE/IADC 18716, Proc SPE/IADC Drilling Conference, New Orleans, 28 February - 3 March, pp. 807–816, 1989.

[11] B.S. McLaury, S.A. Shirazi, Generalization of API RP 14E for Erosive Service in Multiphase Production, SPE 56812, SPE Annual Technical Conference and Exhibition, Houston, Texas, 1999.

[12] S.A. Shirazi, B.S. McLaury, J.R. Shadley, E.F. Rybicki, Generalization of the API RP 14E Guideline for Erosive Services, SPE28518, Journal of Petroleum Technology, August 1995 (1995) 693–698.

[13] B.S. McLaury, J. Wang, S.A. Shirazi, J.R. Shadley, E.F. Rybicki, Solid Particle Erosion in Long Radius Elbows and Straight Pipes, SPE 38842, SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 1997.

[14] J. Tronvoll, M.B. Dusseault, F. Sanfilippo, F.J. Santarelli, The Tools of Sand Management, SPE 71673, 2001, SPE Annual Technical Conference and Exhibition held in New Orleans, Louisiana, 2001.