## Liquid Desander – Apex Solids Threshold (B-FSM068)

The maximum concentration of solids in the inlet flow stream that a desander can treat is a function of desander, fluid, and particle properties. The full calculation routine is provided in the reference paper – see equations 2-5. A summary is as follows;

• The settling of solids from the cyclone, through the apex, and into the accumulator does not follow a simple Stokes settling calculation (i.e. particle settling in a laminar flow regime)
• The calculation routine starts with settling based on the Newton’s law region of turbulent flow settling – which is a function of particle diameter, solid-fluid density differential, and particle sphericity
• The Reynolds number for the settling particle – using liquid density, particle diameter, turbulent flow settling velocity, and fluid viscosity – is then determined
• A hindered settling velocity, based on work from Richardson and Zaki, is calculated using the Reynolds number, volumetric concentration of solids, and turbulent settling velocity
• This final hindered settling rate determines the number of particles passing through the apex – which is converted to a mass rate. The inlet concentration is calculated based on the mass rate through the apex combined with the recovery efficiency of the cyclone

The results of this calculation routine for several size (diameter) desanders are shown on the following figure. The graph shown plots the inlet particle mean size (x-axis) versus the inlet threshold concentration on the y-axis (g/L or ppmw). The data shown is valid for sand in water only with the parameters stated.

To use the graph first determine the average or mean particle size of the sand in the inlet stream. Then travel vertically from that value until intersecting the corresponding line for the diameter of your desander. Travel horizontally from that point to get the inlet threshold concentration.

Example: A vessel filled with 2” (50 mm) desander liners treating produced water containing sand at 150 micron diameter. The operating line for this size desander is the solid red line. Traveling upward from 150 microns will intersect this line at ~2100 ppmw solids (right side axis). Operating below this point, i.e. 500 ppmw solids, then the desander will operate effectively. If the solids concentration is higher – i.e. at 20 wt.% solids (200,000 ppmw) from jetting slurry – then the liner will choke and plug.

The next article will discuss Apex Flux Balancing – a process design added to overcome the concentration limitations.

References:

1. Rawlins, C.H., “Particle Transfer Between the Cyclone and Accumulator Sections of a Desander”, SPE Production & Operations, paper SPE-191147-PA, 2018. https://doi.org/10.2118/191147-PA