Mixing and reactions in multiphase systems: insights from

Mixing and reactions in multiphase systems: insights from microfluidics

joaquin.jimenez@eawag.ch / jjimenez@ethz.ch

Joaquin (Quino) Jimenez-Martinez

Department of Water Resources and Drinking Water, EAWAGDepartment of Civil, Environmental and Geomatic Engineering, ETH Zurich

www.sepgroup.ethz.ch

Summer School - Cargese 2018 | 29.06.2018 | 1

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Multiphase systems: applications

Middleton et al. AE (2015)

Storage (CO2, H2, nuclear waste)

Hydraulic fracturing

EOR

Rejniak et al. FiO (2013)

MedicineChemical engineering

Britton et al. JPCA (2005)

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Unsaturated zone

modified from Chorover et al. ELEM. (2007)

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Pore-scale experiments

millifluidics (Univ. Rennes, FR) microfluidics (LANL, US)

homogeneous phases distribution (in statistical sense)

sharp injections (continuous and pulse)

to study systematically the impact of phases saturation on mixing and reactions:

Jimenez-Martinez et al. WRR (2017)

P: 0-10 MPa T: 0-80 CPorter et al. Lab Chip (2015)

photo-bleaching

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Pore-scale experiments

millifluidics – soft lithography

de Anna et al. ES&T (2014)

microfluidics – standard photolithography and ICP DRIE (thin oxide layer)(inductively coupled plasma-deep reactive ion etching)

e.g., Chomsurin and Werth WRR (2003)

others: geo-material micromodels (laser etching)

Utica shale

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fluid-fluid mixing and reaction

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single phase Sw = 1 Pe = 54

multi phase Sw = 0.7 Pe = 78

Jimenez-Martinez et al. GRL (2015)

Continuous injection

Water+

Air (immobile)

1

0

c

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Mixing volume and interface lengthMixing volume 0 < c < 1

Interface length c = 1/2

Sw = 1 Pe = 54

Sw = 0.7 Pe = 78

Jimenez-Martinez et al. GRL (2015)Summer School - Cargese 2018 | 29.06.2018 | 8

2

spec 2 2 3/2

2

( 4 )

id c Kr

dc c K

2

mix ( )r D c

22

2( )id c

r D cdc

spec mixr r r

de Simoni et al. WRR (2005, 2007)

Willmann et al. WRR (2010)

Global reaction rate

Total mass of reaction product P

A Bc c K A Bc c c

Jimenez-Martinez et al. GRL (2015)

Mixing-induced reactivity

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Jimenez-Martinez et al. GRL (2015)

Temporal dynamics of concentration gradients

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Heterogeneous flow

Velasquez-Parra et al. (in prep.)

particle trackingfully saturated Sw = 1

partially saturated Sw = 0.7

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velocity field velocity pdfs

Velasquez-Parra et al. (in prep.)

Impact of phases saturation on velocities

high velocities

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Sw = 1

Sw = 0.7

velocity field

Velasquez-Parra et al. (in prep.)

velocity pdfs

high velocities

Impact of phases saturation on velocities

de GennesJFM (1983)

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Sw = 1

Sw = 0.7

Impact of phases saturation on velocities: correlation

Velasquez-Parra et al. (in prep.)

time discretization: power lawspace discretization: exponential

e.g., de Anna et al. PRL (2013); Datta et al. PRL (2013)Summer School - Cargese 2018 | 29.06.2018 | 14

𝜏𝑐 = 𝜆/𝑢𝑚𝑖𝑛 : correlation length𝜆

Sw = 1.00 Sw = 0.7

intermittency

Impact of phases saturation on accelerations

Velasquez-Parra et al. (in prep.)

e.g., de Anna et al. PRL (2013); Kang et al. GRL (2014)Summer School - Cargese 2018 | 29.06.2018 | 15

resultant accelerations (x,y)

longitudinal accelerations (x) transverse accelerations (y)

Impact of phases saturation on accelerations

Velasquez-Parra et al. (in prep.) Summer School - Cargese 2018 | 29.06.2018 | 16

Impact of phases saturation on accelerations: correlation

Velasquez-Parra et al. (in prep.)

time discretization

longitudinal (x) transversal (y)

resultant

absolute

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Fully saturated Sw = 1 Pe = 137

Partially saturated Sw = 0.83 Pe = 34

Jimenez-Martinez et al. WRR (2017)

Pulse-line injectionphoto-bleaching

Water+

Air (immobile)

1

0

c

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Mixing dynamics

Scalar dissipation rate

e.g., Ottino (1989); Le Borgne et al. AWR (2010)

For a Dirac delta injection

e.g., Pope (2000); Le Borgne et al. AWR (2010)

Jimenez-Martinez et al. WRR (2017)

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Shear-enhanced mixing model

e.g., Meunier and Villermaux JFM (2010)

shear deformation of a volume of fluid

𝐿0 𝐿

Elongation

Jimenez-Martinez et al. WRR (2017)

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Shear-enhanced mixing model𝑐(𝑡)

Average concentration Warped (deforming) time

Average mixing scale

e.g., Ranz AIChE (1979); Meunier and Villermaux JFM (2010); Le Borgne et al. JFM (2015)

Mixing time

Villermaux CRM (2012); Le Borgne et al. JFM (2015)

Jimenez-Martinez et al. WRR (2017)

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Shear-enhanced mixing model

Average scalar dissipation rate

e.g., Jimenez-Martinez et al. GRL (2015)

Scalar dissipation rate

Jimenez-Martinez et al. WRR (2017)

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Model vs. data

Jimenez-Martinez et al. WRR (2017)

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Soil = 0.46 Sw = 0.54

Jimenez-Martinez et al. GRL (2016)

Three phase - continuous injection

Oil + Water (mobile/immiscible) + scCO2

analogous: biosolvent displacing wetting-NAPL and water Summer School - Cargese 2018 | 29.06.2018 | 24

Mixing degree

Jimenez-Martinez et al. GRL (2016)

Mixing in dynamic systems

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Spatial statistics-Correlation length Sw field

Jimenez-Martinez et al. GRL (2016)

The role of a mobile/immiscible phase

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Mobility of the immiscible phase…

limits flow in some areas and redirects flow to unswept areas.

induces capillary cross-flow at the edge of the fingers.

Mixing and reaction rates are enhanced…

limited finger coalescence by the presence of immiscible phase clusters.

the ramified finger structure, large concentration gradients (normal to the average flow).

preferential flow-paths and bottlenecks, persistent slow increase of finger concentrations.

Phases saturation impact on mixing and reaction

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Porter, M.L. (now at Bureau of Reclamation)

Hyman, J.D.

Carey, J.W.

Viswanthan, H.S.

Méheust, Y.

Le Borgne, T.

de Anna, P. (now at UNIL)

Tabuteau, H.

Turuban, R.

collaborators: N. Linde (UNIL); D. Jougnot (CNRS); I. Lunati (UNIL); A. Ferrari (EMPA)

M. Dentz (CSIC); J. Hidalgo (CSIC); L. Perez (CSIC)

Velasquez-Parra, A.

Willmann, M.

Hamada, M. (now at UNIL)