Separator Jetting – Movement of Solids in Separators (B-FSM-114)
How then do we calculate the amount and size of solids that settle in the production separator?
As a first-order basis I use a mechanistic approximation detailed as follows.
- Calculate residence time of liquid (water) in vessel (weir height and inlet to weir distance)
- Calculate fall (capture) velocity as vertical distance divided by residence time
- Use Stokes Law to calculate size of particle matching capture velocity
- Particles with diameter greater than capture size are collected within the separator – smaller particles pass through with produced water
- Sum the total of all particles greater than cut off size gives total amount of solids settled in separator
An example is provided as detailed below.
First calculate the cut-off size of solids that is captured in the vessel:
- Water volume in vessel = ½(π/4)d²L = 0.393(2.5)²(8)=19.63m³
- Water flow rate = 0.0828 m³/s, ∴ RT=V/Q=19.63/0.0828=237 sec=3.95 min
- Horizontal velocity = Q/A = 0.0828m³/2.45m² = 0.0336 m/s
- What size particle falls in 1.25m/237s = 0.00527 m/s?
- Stokes law: 𝒗_𝑽=(𝒈𝒅^𝟐 (𝝆_𝒔−𝝆_𝒍 ))/𝟏𝟖𝝁→𝐝=√(𝟏𝟖𝝁𝒗/𝒈(𝝆_𝒔−𝝆_𝒍 ) ) = 71 micron
- Particles greater than ~70 microns captured in separator, with the rest passing into the produced water treatment system
The second step is to calculate the amount of captured solids in the vessel.
- Assume all solids are in the water phase at 100 ppmv
- Qw=45,000 BPD, ∴ Qs=4.5 BPD=0.715 m³/d=1896 kg/d
- Calculate total weight of particles greater than capture size (use a spreadsheet)
- Effective volume of solids is 1372kg/2650 kg/m³/0.62=0.835m³/d
- Time to fill water section = 19.63m³/0.835m³/d=23.5 days
- Solids should be removed at 10% = ~2.5 days
- Rawlins, C.H., “Design of a Cyclonic Solids Jetting Device and Slurry Transport System for Production Systems”, paper 166118, presented at the SPE Annual Technical Conference and Exhibition, New Orleans, LA, 30 September – 2 October, 2013. https://doi.org/10.2118/166118-MS
Next week I will cover the behavior of settled solids.