The commonly used practice for controlling sand erosion in gas and oil producing wells is to limit production velocity; the critical velocity is called fluid threshold velocity, below which an allowable amount of erosion occurs.

The API RP14E guideline limits the production rates for avoiding erosional damage and the recommended velocity limitation described by the Equation (18-8). The recommended value for the constant C is 100 for continuous service and 125 for intermittent service. When sand is present, API RP 14E suggests that the value of C should be smaller than 100 but does not indicate what the value should be.The recently developed methods for predicting threshold velocities are based on the penetration rates in elbow geometry because the sections with this geometry are more susceptible to erosion damage than a straight pipe section.

Salama and Venkatesh Model

Salama and Venkatesh developed a model for predicting the penetration rate for an elbow. Their suggested equation is:

File:Salma and venkatesh model formula 1.png
Salma and venkatesh model formula 1
File:Salma and venkatesh model formula 2.png
Salma and venkatesh model formula 2

By assuming the hardness of T is equal to 1.55105 psi and allowing the penetration rate of h to equal mil/yr, Salama and Venkatesh obtained an expression for the erosion velocity of threshold velocity for sand erosion.

The authors also suggested that this equation be used for gas flows only and indicated that particle-impact velocity in gas flows with low density and viscosity nearly equals the flow stream velocity. They noted that this equation is not valid for liquid flows because the threshold velocity given by this equation actually represents the particle-impact velocity, which is generally lower than the flow stream velocity.

Svedeman and Arnold Model

On the basis of Salama and Venkatesh’s work, Svedeman and Arnold suggested the following formula for predicting a threshold velocity based on the penetration rate of 5 mil/yr.

Shirazi et al. Model

Shirazi et al.proposed a method for calculating the penetration rates for various pipe geometries, in which the following expression is used for calculating the maximumpenetration rate in elbows for carbon steel material.

This method accounts for many of the physical variables in the flow and erosion processes and includes a way to predict the maximum penetration rate for sand erosion. The capabilities of the method are evaluated by comparing predicted penetration rates with experimental data found in the literature.

A major difference between this method and the earlier work lies in that this method is developed to finding the “characteristic impact velocity of the particles” on the pipe wall, vp. This characteristic impact velocity of the particles depends on many factors, including pipe geometry and size, sand size and density, flow regime and velocity, and fluid properties. Given an allowable penetration rate (of 5 or 10 mil/yr), a threshold flow stream velocity can be readily calculated and combined with the procedure of impact velocity particles using the iterative solution procedure as shown in the following section.

Particle Impact Velocity

Generally, the erosion rate is proportional to the particle impact velocity, so there is a necessity to analyze the characteristic impact velocity in detail. A simple model is used to describe the characteristic of impact velocity of particles.

The behavior of the particles in the stagnation region mainly depends on:

  • Pipe-fitting geometry;
  • Fluid properties;
  • Sand properties.

A simplified particle-tracking model is used to compute the characteristic impact velocity of the particles. This model assumes that the article is traveling through an inside diameter flow field that is assumed to have a linear velocity in the direction of the particlemotion and uses a simplified drag-coefficientmodel. The impact velocity depends on:

  • Flow stream velocity;
  • Characteristic length scale;
  • Fluid density and viscosity;
  • Particle density and diameter.

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.

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 increase significantly, the long radius elbow becomes closer to a straight section of pipe and the random impingement mechanism can become important.


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