Sand erosion rate prediction
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:
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:
The values for K, n, and F(a) are derived from sand-blasting tests on small material samples.
Salama and Venkatesh ModelSalama 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
1. This approximation is reasonable for gas flows, but does not account for the particle drag effects in liquid flows.
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 updated the Salama and Venkatesh model for gas/liquid systems and developed a new equation as follows:
Tulsa ECRC ModelA 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:
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.
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