multiphase flow in porous media · 1.) „flow in porous media implies inlet and outlet of...

01.07.2014 Manuel Hirschler

Multiphase Flow in Porous Media

M. Hirschler*, P. Kunz, M. Huber, W. Säckel, U. Nieken


• Applications at the Institute of Chemical Process Engineering

• SiPEr – „SPH in Process Engineering“

• Recent developments

• Open boundary conditions for ISPH

• Interface dynamics

• Conclusions

Outline


Porous materials are widely used in chemical engineering

• Heterogeneous Catalysis and Adsorption

• Open-porous membranes (precipitation membrane)

• Emerging particle morphologies by spray processes

• Gas Diffusion Layer in PEM fuel cells

Applications in Chemical Process Engineering

S. Biedasek, PhD-thesis, University Hamburg 2009

System:

Polysulfon / NMP /

Wasser (/PVP)M. Hirschler ICVT, 2014 Strathmann, 1977

M. Huber ICVT, 2011


• common ground

dynamic structure evolution on mesoscopic scale

E.g. precipitation of phase inversion membranes:

Applications in Chemical Process Engineering

Coagulation

bath

Polymer

solution

Polymer

SolventNon-

Solvent

CP

Vitrification point

system:

Cellulose acetat (polymer) /

acetone (solvent) /

water (nonsolvent)

polymer solvent


SPH code for massively parallelized architectures

• hybrid MPI/OpenMP

• Incompressible SPH (ISPH)

• Compressible SPH

• Dimensionless variables

Predictor-corrector scheme

• Solving of global linear equation system

Additional libraries:

• PETSC (linear solvers)

• HYPRE (preconditioning)

SiPEr – „SPH in Process Engineering“

Reference: single core!


Basic SPH formulation:

• Singlephase flow (Shao & Lo, 2003)

• Multiphase flow (Szewc et al., 2012 / Hu & Adams, 2006)

Additional Physics:

• Surface tension (CSF) (Morris, 2000)

• Contact line dynamics (CLF) (Huber et al., 2013)

• Heat & Mass transfer (Brookshaw, 1985 / Hirschler et al., 2014)

• Non-Newtonian rheology (e.g. Keller & Nieken, 2010)

Boundary conditions:

• (Free surfaces) (Bonet & Lok, 1999)

• Solid walls (Morris et al., 1997 / Colagrossi et al., 2003)

• Open boundary conditions (later on…)



Implementation details of boundary conditions:

• Periodic boundary conditions

• Free-slip boundary conditions

• No-slip boundary conditions

• (Open boundary conditions)



Goal:

„Application of SPH to Process Engineering Problems“

But:

„New physics sometimes asks for novel approaches“

2 recent developments:

• Methodical: Open boundary conditions for ISPH

• Application: Interface dynamics (e.g. capillary rise)

Recent developments


Motivation:

1.) „Flow in porous media implies inlet and outlet of fluids“

In many cases, modified periodic boundary conditions can be applied

(e.g. flow in a channel with equal in- and outlet size)

2.) „Shrinkage without free surfaces in the framework of mirror BCs.“

Goal: Open-pressure boundary conditions!

Open boundary conditions for ISPH


• Mirror particles for „inlet/outlet particles“

What happens in a predictor-corrector integration step?

Example: static water column

1.) Acceleration of fluid

due to gravity.

2.) Acceleration of fluid due to

resulting pressure field.


Solid wall

Mirror particles

Fluid domain

Free surface

Mirror particles

g

p


• Mirror particles for „inlet/outlet particles“

Now, consider another way!

1.) Acceleration of solid wall

due to gravity.

2.) Acceleration of fluid due to

resulting pressure field.


Solid wall

Mirror particles

Fluid domain

Free surface

Mirror particles

g

p



…

Inflow

Fluid domainMirror particles Mirror particles

Fluid domain

Solid wall

Mirror particles

Free surface

Mirror particles

g

p

v ≠ f(fluid)

v = const.

v = f(fluid)

v ≠ const.


Implementation details:

• Open boundary divided in segments

• Each segment has its own, time depending mirror axis


Open-velocity boundary Open-pressure boundary


Example: channel flow (2D)

• Open-pressure boundary (Δp = 30 Pa)

• ReD = 1

• η = 0.01 Pas

• ρ = 1000 kg/m³

• Mean time for 1 particle to move through the channel: t* = 1.5

Open boundary conditions for ISPH (validation)

3

1


• Flow around a cylinder (Re = 0.0141, h/L0 = 1.55)

Open boundary conditions for ISPH (applications)

ISPH OpenFOAM18D

6D D


• Flow around a cylinder (Re = 0.0141, h/L0 = 1.55)

• Cone flow (Re = 0.0025, h/L0 = 1.55, din/dout = 2)

Open boundary conditions for ISPH (applications)


Advantages

• Easy to implement into existing algorithm

• Applicable to 3D

• Applicable to multi-directional inflow/outflow conditions

• Stable algorithm even for uncompensated kernel support in ISPH

Disadvantages

• Lack of uncompensated kernel support at curved interfaces

-> Solution: Corrected SPH (Bonet & Lok, 1999)

• Large „steps“ at boundary can cause instabilities at low smoothing lengths

due to errors in pressure estimation

Open boundary conditions for ISPH (discussion)


Interface dynamics

[1] Brackbill et. al: A continuum method for modelling surface tension, Journal of computational Physics, 100 (1992)[2] Hassanizadeh, Gray: Thermodynamic basis of capillary pressure in porous media, Water Resources Research 29 (10) (1993)[3] Brochardwyart, de Gennes: Dynamics of partial wetting, Advances In Colloid and Interface Science 39 (1992) 1–11

• Momentum balance for a contact line

tangential to the wall [2] CLF [3]:

• Momentum balance for an interface:

(𝑝𝑤−𝑝𝑛) 𝑛 = 𝜏𝑤 − 𝜏𝑛 𝑛 − 𝜎𝑤𝑛𝜅𝑤𝑛

𝑛 + 𝛻𝜎𝑤𝑛

• Remaining term CSF [1]:

𝑓𝑤𝑛 = 𝜎𝑤𝑛𝜅𝑤𝑛 𝑛𝑤𝑛

𝑓𝑤𝑛𝑠 = 𝜎𝑛𝑠 − 𝜎𝑤𝑠 + 𝜎𝑤𝑛 𝜈𝑛𝑠 ⋅ 𝜈𝑤𝑛

𝜈𝑛𝑠

𝑓𝑤𝑛𝑠 = 𝜎𝑛𝑠 − 𝜎𝑤𝑠 − 𝜎𝑤𝑛 cos 𝜃0 = 0

• At equilibrium:


Interface dynamics (capillary rise)

Phases Velocity

𝜌2

𝜌1 𝑔𝑧 = 9.81𝑚

𝑠

[mm]𝑧 = 𝐻

𝑧𝑒𝑞

z= 0


Interface dynamics (capillary rise)

Observations:

• Theoretic imbibition velocity

close to the simulation

• Significant influence of

Dynamic contact angle on the

dynamics of capillary rise

• Deviations due to:

• Poiseuille-flow assumption

• No curved interface at start of

simulation

• Comparison with theoretical model for time dependent height.

• Influence of dynamics contact angle cannot be neglected.


Interface dynamics (drainage)

p = 1200 Pa

p = 1500 Pa

Experiment by N. Karadimitriou, Utrecht University

Theoretic entry pressure:

pe ≈ 1200 𝑃𝑎

Observations:

• Similar intrusions

in simulation and

experiment

• Only partial

drainage for

p = 𝑝𝑒


• Application of SPH to problems in Chemical Process Engineering

• SiPEr

• ISPH algorithm for multiphase flow in porous media

• Introduction of open boundary conditions for ISPH

• Open-pressure boundary conditions

• Applications (e.g. cone flow)

• Application to wetting phenomena in porous media

• Capillary rise

• Drainage of porous network

Conclusions


PostDoc and Ph.D. position in Innsbruck, Austria

multiphase flow in porous media · 1.) „flow in porous media implies inlet and outlet of...

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