David Leleu, Andreas Pfennig dleleu@uliege.be
Products, Environment, and Processes (PEPs)
Coalescence Modelling for
Settler Design
agenda
introduction
coalescence probability
contact time
coalescence time
summary
settling simulation
coalescence probability: fundamental
investigation
pnon−coal,Δt = exp −
tcoal
Δt
pcoal = 1− exp −
tcontact
tcoal
pnon−coal = exp −
tcontact
tcoal
∆t
n=tcontact
Δt
tcontact
pnon−coal,nΔt = pnon−coal,Δtn
pnon−coal,nΔt = exp −
tcoal
nΔt
p
𝑐𝑜𝑎𝑙,𝐶&𝑇= exp −
tcoal
contact time: motion simulation
assumptions:
drops follow
contour during the
sedimentation
detachment angle =
random between π/2
and π
α
collisionα
detachmenttcontact ≈ 2
d1+d2
vrelative
contact time: simulations vs model
0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8big drop diameter in mm
s m a ll d ro p d ia m e te r i n m m 0.840 0.924 1.01 1.09 1.17 1.26
tcontact = 𝛽 2
d1+d2
vrelative
coalescence time: film drainage process
tcoalescence=
3π1.5μ
R
f
R
a
1.5
4rs∗Fdriving hmin
close-packed zone
drops deformation
film drainage
Fdriving ∝ ΔPhydro − ΔPflow
polydispersed packing
μ ∈ 0;1mm and σ ∈ 0; 50%
ε ∈ [70%; 80%]
summary
pcoal = 1− exp −
tcontact
tcoal
tcontact ∝
vrelative
d1+d2
Fdriving=
Fbuoyancy
Fturbulences
Fhydrostatic_pressure
dimple ∝ ቊ
drops diameter
settling simulation
20 40 60 80 100 120 140 160 180 ce ll h e ig th in m m 0.2 0.4 0.6 0.8 1 local holdupDavid Leleu, Andreas Pfennig dleleu@uliege.be
Products, Environment, and Processes (PEPs) Department of Chemical Engineering
Université de Liège
www.chemeng.uliege.be/Pfennig
