transition from pervasive to segregated fluid flow in ductile rocks james connolly and yuri...
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![Page 1: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/1.jpg)
Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks
James Connolly and Yuri Podladchikov, ETH Zurich
A transition between “Darcy” and Stokes regimes
• Geological scenario• Review of steady flow instabilities => porosity waves
• Analysis of conditions for disaggregation
![Page 2: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/2.jpg)
Lithosphere
Partia lly (3 vol % ) m oltenasthenosphere
Basalt d ikes
Basalt s ills
M assive D unites
R eplacive D unites
R eplacive D unites = reactive transport channeling instability?
Basalt d ikes = se lf propagating cracks?
Basalt s ills = segregation caused by m agica l perm eability barriers?
M assive D unites = rem obilized replacive dunite?
M id-O cean R idge
lithosphere
![Page 3: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/3.jpg)
1D Flow Instability, Small (<<1) Formulation, Initial Conditions
-250 -200 -150 -100 -50 0
2
4
6
8t = 0
z
-250 -200 -150 -100 -50 0-1
-0.5
0
0.5
1
z
p
1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5
1
p =
d, disaggregation condition
1D Movie? (b1d)
![Page 4: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/4.jpg)
1D Final
-350 -300 -250 -200 -150 -100 -50 0
1
2
3
4
5t = 70
z
-350 -300 -250 -200 -150 -100 -50 0-1
-0.5
0
0.5
1
z
p
1 1.5 2 2.5 3 3.5 4 4.5 5-1
-0.5
0
0.5
1
p
• Solitary vs periodic solutions
• Solitary wave amplitude close to source amplitude
• Transient effects lead to mass loss
![Page 5: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/5.jpg)
2D Instability
![Page 6: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/6.jpg)
Birth of the Blob
• Stringent nucleation conditions
• Small amplification, low velocities
• Dissipative transient effects
Bad news for Blob fans:
![Page 7: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/7.jpg)
Is the blob model stupid?
A differential compaction model
Dike Movie? (z2d)
![Page 8: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/8.jpg)
The details of dike-like waves
Comparison movie (y2d2)
![Page 9: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/9.jpg)
Final comparison
• Dike-like waves nucleate from essentially nothing
• They suck melt out of the matrix
• They are bigger and faster
• Spacing c, width d
But are they solitary waves?
![Page 10: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/10.jpg)
Velocity and Amplitude
0 5 10 15 20 25 30 353.4
3.6
3.8
4
4.2
4.4
4.6
4.8
5
5.2
time /
Blob model
amplitudevelocity
0 0.5 1 1.5 2 2.5 3 3.50
5
10
15
20
25
30
35
40
time /
Dike model
amplitudevelocity
![Page 11: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/11.jpg)
1D Quasi-Stationary State
4.5 5 5.5-10
-5
0
5
10
15
20
25
30
35
x/
Horizontal Section
-60 -40 -20 0-10
-5
0
5
10
15
20
25
30
35
y/
Vertical Section
0 10 20 30 40
-6
-4
-2
0
2
4
6
p
Phase Portrait
Pressure,Porosity
Pressure,Porosity
• Essentially 1D lateral pressure profile• Waves grow by sucking melt from the matrix
•The waves establish a new “background”” porosity• Not a true stationary state
1
1
![Page 12: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/12.jpg)
So dike-like waves are the ultimate in porosity-wave fashion:
They nucleate out of essentially nothing They suck melt out of the matrix
They seem to grow inexorably toward disaggregation
But
Do they really grow inexorably, what about 1?
Can we predict the conditions (fluxes) for disaggregation?
Simple 1D analysis
![Page 13: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/13.jpg)
Mathematical Formulation
• Incompressible viscous fluid and solid components
• Darcy’s law with k = f(), Eirik’s talk
• Viscous bulk rheology with
• 1D stationary states traveling with phase velocity
es
s
2 2q
11
d
1
q
mq
pv
f
f
es
s
pv
(geological formulations ala McKenzie have )
![Page 14: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/14.jpg)
Balancing ball
gv h
t x
v p
x
t z
0 ,p
fz
xv
t
1( )s
pf
z
v g h
x v x
sp H
p
0h
vdv g dxx
0 s
Hpdp d
2
2
vE hg
2
2 sp
U H sg
Porosity WaveBalancing Ball
![Page 15: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/15.jpg)
H(omega)
![Page 16: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/16.jpg)
Phase diagram
![Page 17: Transition from Pervasive to Segregated Fluid Flow in Ductile Rocks James Connolly and Yuri Podladchikov, ETH Zurich A transition between “Darcy” and Stokes](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d4b5503460f94a28699/html5/thumbnails/17.jpg)
Sensitivity to Constituitive Relationships