## Prediction of Sand Erosion Rate

Knowing a facility’s erosion risk is of the utmost importance for well management optimization against sand production. Normally, the sand erosion models consider the erosion process into three stages. First, the fluid flow in the facilities is modeled or in some way approximated. This flow prediction is then used to derive the drag forces imparted by the fluid on the particles (sands); hence, the trajectories of a large number of particles are predicted.

Computational fluid dynamics (CFD) software has been used to model the fluid flow and particle trajectories. It has been shown to be good at predicting erosion locations and erosion scar shapes. Second, the damage due to the individual particles’ impact on a wall is calculated using a material-specific empirical or a theoretically derived impact damage model. Last, the average impact damage of a large number of particles can then be used to predict the distribution and depth of erosion damage on a surface. However, the physical process is only partially understood and the prediction of the critical conditions has to rely on empirical or semiempirical models.

On the basis of experimental results, the sand erosion rate can be summarized in relation to the kinetic energy of sand fragments through the following parameters:

• Fluid velocity;
• Fluid density;
• Size of the sand fragments;
• Sand production rate;
• Pipe or conveyance diameter;
• System geometry;
• Metal hardness (resistance to erosion).

The sand erosion rate is expressed in the following form based on the impact damage model:

File:Sand erosion rate.png
Sand erosion rate

where,

E: sand erosion rate, kg of material removed/kg of erodant;

Vp: particle impact velocity;

A: a constant depending on the material being eroded and other factors;

a: particle impact angle;

F(a): material dependent function of the impact angle, which is between 0 and 1.0;

n: material dependent index.

## Huser and Kvernvold Model

Huser and Kvernvold developed the following impact damage equation:

File:Huser and Kvernvold impact damage equation.png
Huser and Kvernvold impact damage equation

The values for K, n, and F(a) are derived from sand-blasting tests on small material samples.

## Salama and Venkatesh Model

Salama and Venkatesh developed a method similar to that of Huser and Kvernvold, although they simplified their model by making a conservative assumption that all sand impacts occur at about 30 , therefore, F(a) is set to
File:Relationship for Ductile and Brittle Materials.png
Relationship for Ductile and Brittle Materials

1. This approximation is reasonable for gas flows, but does not account for the particle drag effects in liquid flows.

File:Salma and venkatesh model.png
Salma and venkatesh model

The predicted erosion rate based on the above equation is an average of 44% greater than the measured value in comparison with experimental air/sand tests of elbows. This method is consistently conservative. Svedemanand Arnold also suggested using this equation, but they gave values of Sk for gas systems, with an Sk of 0. 017 for long radius elbows and an Sk of ¼0.0006 for plugged tees.

## Salama Model

Salama updated the Salama and Venkatesh model for gas/liquid systems and developed a new equation as follows:

## Tulsa ECRC Model

A range of particle models have been developed by the University of Tulsa Erosion Corrosion Research Center (ECRC) based on a significant amount of research work on pipe component erosion. Those models are utilized with an impact damage model of the form:
File:Tulsa ECRC Model.png
Tulsa ECRC Model
File:Tulsa ECRC, Model.png
Tulsa ECRC, Model

In the above equation the coefficient of FM accounts for the variation in material hardness. McLaury and Shirazi give typical values of FM for a number of different steels ranging from 0.833 to 1.267, suggesting a 25% in erosion resistance between different steels. These values have been derived from impingement tests.

## 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.