## Erosion and Sand Management

Yong Bai, Qiang Bai, in Subsea Engineering Handbook (Second Edition), 2019

### 18.4.5 Erosion in Long Radius Elbows

In this model, the erosion condition in a long radius elbow has been studied on the basis of a standard elbow mechanistic model. To extend the mechanistic model to be able to predict the penetration rate in long radius elbows, a new term called the *elbow radius factor* is introduced [13]. The elbow radius factor (ERF_{r/d}) is defined as follows:

where *Pn*_{L} is the maximum penetration rate in the long radius elbow, and *Pn*_{std} is the maximum penetration rate in a standard elbow. The introduction of elbow radius factor preserves the accuracy of the mechanistic model for standard elbows and extends it to predict penetration rates in long radius elbows.

where,

ERF

_{r/d}: elbow radius factors for long radius elbows;*C*_{std}:*r/d*of a standard elbow;*C*_{std}is set equal to 1.5;*ρ*_{f}: fluid density;*μ*_{f}: fluid viscosity;*d*_{p}: particle diameter;*r*: radius of curvature of the elbow.

This equation accounts for the elbow radius curvature effect in different carrier fluids and sand particle size. Note that this equation is based on a sand particle density of 165.41b/ft^{3}.

The model did not investigate the effects of turbulent fluctuation on the erosion predictions because direct impingement is the dominant erosion mechanism for elbows. However, as the radius of curvature increases significantly, the long radius elbow becomes closer to a straight section of pipe and the random impingement mechanism can become important.