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Fluid Flow Transition in Ductile Rocks: Instabilities & Blob Dynamics

Explore the transition from pervasive to segregated fluid flow in ductile rocks, with a focus on porosity waves, disaggregation conditions, and geologically relevant scenarios. The study covers 1D and 2D flow instabilities, analysis of solitary vs. periodic solutions, and differential compaction models. Detailed insights into dike-like waves and the comparison between blob and dike models are also presented. The study delves into the growth and behavior of porosity waves, offering a comprehensive look at fluid dynamics in geological formations.

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Fluid Flow Transition in Ductile Rocks: Instabilities & Blob Dynamics

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  1. Transition from Pervasive to Segregated Fluid Flow in Ductile RocksJames 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

  2. lithosphere

  3. 1D Flow Instability, Small f (<<1-f) Formulation, Initial Conditions t = 0 8 f f = , disaggregation condition 6 d f 4 2 -250 -200 -150 -100 -50 0 z 1 0.5 p 0 -0.5 -1 -250 -200 -150 -100 -50 0 z 1 0.5 p 0 -0.5 -1 1 1.5 2 2.5 3 3.5 4 4.5 5 f 1D Movie? (b1d)

  4. 1D Final t = 70 5 4 3 f 2 1 -350 -300 -250 -200 -150 -100 -50 0 z 1 0.5 p 0 -0.5 -1 -350 -300 -250 -200 -150 -100 -50 0 z 1 0.5 p 0 -0.5 -1 1 1.5 2 2.5 3 3.5 4 4.5 5 f • Solitary vs periodic solutions • Solitary wave amplitude close to source amplitude • Transient effects lead to mass loss

  5. 2D Instability

  6. Birth of the Blob • Stringent nucleation conditions • Small amplification, low velocities • Dissipative transient effects Bad news for Blob fans:

  7. Is the blob model stupid?A differential compaction model Dike Movie? (z2d)

  8. The details of dike-like waves Comparison movie (y2d2)

  9. Final comparison • Dike-like waves nucleate from essentially nothing • They suck melt out of the matrix • They are bigger and faster • Spacing dc, width dd • But are they solitary waves?

  10. 5.2 5 4.8 4.6 4.4 4.2 4 3.8 3.6 3.4 0 5 10 15 20 25 30 35 Velocity and Amplitude Blob model Dike model 40 amplitude amplitude velocity velocity 35 30 25 20 15 10 5 0 0 0.5 1 1.5 2 2.5 3 3.5 t t time / time /

  11. 1D Quasi-Stationary State Horizontal Section Vertical Section Phase Portrait 35 35 Pressure, Porosity Pressure, Porosity 6 30 30 4 25 25 f1 20 20 2 15 15 p 0 10 10 f1 -2 5 5 0 0 -4 -5 -5 -6 -10 -10 4.5 5 5.5 -60 -40 -20 0 0 10 20 30 40 f x/d y/d • 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

  12. 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-f? Can we predict the conditions (fluxes) for disaggregation? Simple 1D analysis

  13. Mathematical Formulation Incompressible viscous fluid and solid components Darcy’s law with k = f(f), Eirik’s talk Viscous bulk rheology with 1D stationary states traveling with phase velocity w (geological formulations ala McKenzie have )

  14. Balancing ball

  15. H(omega)

  16. Phase diagram

  17. Sensitivity to Constituitive Relationships

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