Modeling Drilling & Fluidization Processes with DEM -...
Transcript of Modeling Drilling & Fluidization Processes with DEM -...
DEM for modeling rock drilling
– Breaking rock challenges
– Relevant capabilities in STAR-CCM+®
– Example without coupling to fluid flow
– Using overset mesh to model drill-bit motion
DEM for modeling flow of solids in fluidized beds
– Coarse-grain model in STAR-CCM+
– Industrial scale fluidized bed example
• Simulation results for large particle size distribution
Summary
Outline
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Rock Cutting Complexity
Rock cutting:
– Complex non-equilibrium and non-
steady-state processes
– Wide range of length-scales
• From grain scale
• To bore-hole / reservoir dimensions
– Wide range of time-scales
• From sound waves period in solids
• To hours of advancing drill-bit
through inhomogeneous rock
Can numerical modeling help?
– In improving drill-bit design
– In optimizing operation parameters
(rpm, ROP, WOB)
– Reduce bit balling
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Modeling Rock using DEM
DEM models individuals grains in
rock
– Accurate grain scale physics
• Resolution of grains-cutter contacts
• Can reproduce removing cuttings
– Limited to smaller length scales
and timescales
Model inputs
– Bit Design
• Nozzle selection
• Teeth configuration, etc
– Operation parameters
• Weight on Bit (or ROP), RPM…
– Rock properties
Observables
– Rate of penetration (or WOB)
– Torque
– Cuttings attached to drill bit
– Stand pipe pressure
Model challenges
– Simulation time
– Far Boundaries
– Calibrating model of rock
– Simulating flow of drilling fluid in borehole
– Reproducing bit balling
– Reproducing realistic cutting flows
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10.02 – Maximum Packing option in Random Injector
Small “seeds” injected grow automatically rearrange themselves until
max packing reached
Mimics rock-genesis process
Material Genesis Procedure
The Parallel Bonds model introduces attractive inter-particle forces to the particle system
Model uses the concept of a massless bar connecting a pair of bonded particles
The bar(bond) can transmit force and torque between particles and it is also subject to breaking under load
– The stress limit values are calculated based on beam theory
Reference: Potyondy, D.O, and Cundall, P.A. 2004. “A bonded-particle model for rock”, Int. J. Rock Mechanics & Mining Sciences 41 pp. 1329–1364.
DEM Parallel Bonds Model in STAR-CCM+
~75000 particles with
Gaussian size distribution
which
Particles settled and bonded
with about 180000 bonds
Bond strength distributed
according to Gaussian
distribution (with mean value
of bond strength = 1% of
Young’s modulus).
Monitoring amount of broken bonds
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Modelling drilling fluid
Possible in latest version 9.06
because of compatibility of DEM
with Overset Mesh
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Results with overset mesh
Rock is permeable with void
fraction =0.4
Solution for drilling fluid flow was
obtained using 2-way coupling
model
Jet flow form nozzles results in
large drag forces on bonded
grains
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Industrial Scale Fluidized Bed Study
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3 m
d=0.6 m
0.4 m
d=0.1 m
0.4
6 m
outlet
air inlet
dis
trib
uto
r
Mesh size
20 mm
Amount and size distribution of particles
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Fines:
Mass:~ 108 kg
Diameter: ~500 microns
Count: ~716,000,000
Coarse particles:
Mass:~ 108 kg
Diameter: ~1mm
Count: ~80,000,000
DEM parcel represents some number of identical unresolved particles
dparcel
l3 -number of particles in parcel
Fluid-particle interaction (drag, lift etc.) are calculated for a representative
particle and applied to the entire parcel
– while the contact dynamics are calculated on the parcel scale
Coarse Grain Particle
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particlesparcel
Faster DEM computing time
Example for Gidaspow drag force calculation
𝑪𝒅 =
𝟒
𝟑
𝟏𝟓𝟎 𝟏 − 𝜶𝒑
𝜶𝒑𝑹𝒆𝒑+ 𝟏. 𝟕𝟓 ; if 𝜶𝒑 < 𝜶𝒎𝒊𝒏; 𝐄𝐫𝐠𝐮𝐧 𝐞𝐪𝐮𝐚𝐭𝐢𝐨𝐧 𝐛𝐚𝐬𝐞𝐝
𝟐𝟒 + 𝟑. 𝟔𝑹𝒆𝒑𝟎.𝟔𝟖𝟕
𝑹𝒆𝒑𝜶𝒑
−𝟑.𝟔𝟓; if 𝜶𝒑 ≥ 𝜶𝒎𝒊𝒏; 𝐖𝐞𝐧 𝐘𝐮 𝐦𝐨𝐝𝐞𝐥
– Here 𝛼𝑝 is solid void fraction, 𝛼𝑚𝑖𝑛 is the cutoff void fraction (=0.8), 𝑅𝑒𝑝 is the
particle Reynolds number, 𝑑 is particle diameter
𝐹𝑑𝑟𝑎𝑔 𝑝𝑎𝑟𝑐𝑒𝑙 = 𝑙3𝟏
𝟐𝝆𝒇𝒗
𝟐𝑪𝒅𝑨𝒅 - this drag force is applied to parcel containing 𝑙3
particles, as a result:
Acceleration, velocity and displacement of parcels due to scaled drag is similar to
acceleration, velocity and displacement and of fine particles due to original
unscaled drag force
Coarse Grain Details
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Parcel Size distribution
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Fine:
9 mm; 109,000
Coarse:
18 mm; 14,000
Fine:
12 mm; 46,000
Coarse:
12 mm; 46,000
We define the mean size of particles 𝑑
– Equivalent mono-disperse system provides the same total surface area
𝑑 =
𝑖=1
𝑁𝑝𝑎𝑟𝑐𝑒𝑙𝑠 𝑙𝑖3𝑑𝑖
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𝑖=1
𝑁𝑝𝑎𝑟𝑐𝑒𝑙𝑠 𝑙𝑖3𝑑𝑖
2
The frictional pressure drop 𝛻𝑃 for bed with size distribution
−𝛻𝑃
𝐿= 150
1 − 𝛼𝑝2
𝛼𝑝3
𝜇𝑓𝑢
𝑑2+ 1.75
1 − 𝛼𝑝
𝛼𝑝3
𝜌𝑓𝑢2
𝑑
Size Distribution Correction to Pressure Drop
(Theory)
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The fluidization velocity estimate for mixed particles sizes
For our test case (used obtained from analysis of the simulation results)
Fluidization velocity (theory)
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Inlet velocity (m/s) 5 7 8 9 10 11
Superficial (m/s) 0.139 0.194 0.222 0.250 0.278 0.306
Inlet velocity (m/s) 12 13 15 20 30 50
Superficial (m/s) 0.333 0.361 0.417 0.556 0.833 1.39
Simulation details
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L(t)
Cells for averaging void
fraction to get
Height of bed 𝐿 𝑡 = 2 𝑦 + 𝑑is double of center of mass
height
Pressure Drop is calculated as surface average of
pressure on the inlet boundary
Results for Pressure Drop
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