Course + Lectures notesporousmedia.nl › nfcmr › college › college-week1-2016.pdf · Transport in porous media 3MT130 Leo Pel, Henk Huinink, David Smeulders, Bart Erich, Hans

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L P l H k H i i k D id S ld

Transport in porous media3MT130

Leo Pel, Henk Huinink, David Smeulders, Bart Erich, Hans van Duijn

Faculty of Applied Physics Mechanical Engineering

Eindhoven University of TechnologyThe Netherlands

[email protected]

Transport in Permeable Media

p

5 ECTS 2016

Examination : Oral

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Course + Lectures notes+ additional info

www.phys.tue.nl/nfcmr/college/college.html

Examination : oral

2 days (to be determined)


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Week 1mo 19-4-2016 13:45 15:30 dr.ir. L. Pel Multi media 1 th 21-4-2016 08:45 10:30 dr.ir. L. Pel 1.91 conferenceWeek 2 mo 27-4-2015 Public holidayth 30-4-2015 08:45 10:30 dr.ir. L. Pel HELIX WEST 1.91 Week 3 mo 5-5-2015 Public holidayth 7-5-2015 08:45 10:30 dr.ir. L. Pel HELIX WEST 1.91 Week 4mo 11-5-2015 13:45 15:30 dr.ir. L. Pel HELIX OOST 4.91th 14-5-2015 Public holidayWeek 5 mo 18-5-2015 13:45 15:30 dr.ir. L. Pel HELIX OOST 4.91 Prof. Smeuldersth 21-5-2015 08:45 10:30 dr.ir. L. Pel HELIX WEST 1.91 Smeulders?Week 6


Week 6 th 28-5-2015 08:45 10:30 dr.ir. L. Pel HELIX WEST 1.91 conferenceWeek 7 mo 1-6-2015 13:45 15:30 dr.ir. L. Pel HELIX OOST 4.91 conferenceth 4-6-2015 08:45 10:30 dr.ir. L. Pel HELIX WEST 1.91 Week 8mo 8-6-2015 13:45 15:30 dr.ir. L. Pel HELIX OOST 4.91 th 11-6-2015 08:45 10:30 dr.ir. L. Pel HELIX WEST 1.91

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Experiment: absorption of water in porous media

QuestionsQuestionsWhich is fastest?Which get highest

and of course: WHY


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• 3000 BC – Ecclesiastes 1:7 (Solomon)“All the rivers run into the sea; yet the sea is not full; unto the


; y ;place from whence the rivers come, thither they return again.” • Greek Philosophers (Plato, Aristotle) embraced the concept, but mechanisms were not understood. •17th Century – Pierre Perrault showed that rainfall was sufficient to explain flow of the Seine

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• Drinking Water• Drinking Water• Irrigation and Flood-Control Projects• Hydropower Development


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Drinking water


Aqueduct in Segovia, Spain

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Global Water Volumes & Fluxes (km3)


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Where’s the Water?


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• Water on Earth– 70 % of surface area– 97 % salt-water by volume

• Fresh water– 77 % glaciers– 22 % ground water– <1 % surface water

• Surface water– 50 % freshwater lakes


– 44 % saltwater lakes– 5 % atmosphere– <1 % rivers and streams

http://www.fourmilab.ch/earthview/vplanet.html

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Qanats Iran (>2000 old)


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Hydrology (saturated part)

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Water level / source


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k


q k

p

x(France, 1803-1858)

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Darcy’s Legacy


Place Darcy, Dijon, France.

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Darcy labGemini


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Contaminants traveling at same velocity as the groundwaterDissolved in the ground water

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Ground water contamination (NAPL)


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Polders


Flow through dike

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Flow under dam

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How much to pump in order to keep dry?

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Oil winning- only oil

-no water


How much can we get out?

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Transport in Permeable Media movie

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Civil engineering

Confederation bridge (Canada)

- chloride transport

- ASR

- leaching


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Fire, moisture and porous materials

Transport in Permeable MediaDelft University, Department of Architecture june 2008

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Concrete spalling : boiling water


Channel tunnel (5 cm)

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Fire, moisture and porous materials


HEAT

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Efflorescence on masonry (The Netherlands)


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frost damaged mortar

frost damaged brickfrost damaged brick


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Cultural heritage

salt erosion France

salt damage fresco Denmark


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Moisture/ion transport + crystallization

limestone

Component transport

airflow


Movie of Eric Doehne

Getty Foundation

Na2SO4 solution

1 month in 52 secs

www.getty.edu/conservation/science movie

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Water in coated wood


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Green inksSolvent

(H2O)Co solvent

INK

Co-solventPigment

Humectant Surfactant

Buffer

…..


How are water/co-solvent mixtures absorbed by cellulose (paper) fibers?

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Fungi, porous materials and water


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Drying of food


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Chemistry

- porous catalyst

- drying


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Biological material


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Heat storage by crystals


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Capillary effects

Lotus effect


Water slider

propel their spores into the air

movie

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Scale length time

G dGround

water kilometres years

Building

Material cm hours weeks


Material cm hours-weeks

Measurement / Errors

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Various disciplines:• soil science• civil engineering• building physics• chemical engineering• reservoir engineering

‘SPRAAK VERWARRING’

Darcy’s lawl i


- volume averaging- homogenization- gas lattice model- percolation

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TU-Eindhoven

- Applied Physics (TPM, WDY, MTP)

- Chemistry (Process engineering, Prof Kuipers)

- Mathematics (Prof van Duyn, Prof Pop)

- Architecture (building physics, construction)

- Mechanical engineering (Prof Smeulders)


- BMT

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Problem: moisture transport

Model moisture

Conceptual modelBasic understanding of the system

Mathematical model Simplified model l


Mathematical model prepresenting the reality

Management decisionsExperiment

loop

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Goal coarse:

Introduction in transport in porous media

• basics equations

• ‘simple’ calculations (absorption etc)

• problems (Dupuit)


• simulations: matlab problems

• Examination (oral + article)

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SO WHAT IS YOUR UNDERSTANDING????


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Course (6/7 weeks)

1 Introduction / Porosity/REV2 Surface Tension

porous materials /relative humidityporous materials /relative humidity3 Saturated transport

Darcy’s law: Hydrology, Dupuit4 Unsaturated flow

Darcy’s law Absorption (liquid) / drying (liquid + vapour)

5 Component transport (liquid + component)6 Two phase flow (oil recovery)


p ( y)7 How to measure in porous media

+ articles (website)

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PorosityPorosity

(V(V / V)/ V)


n = (Vn = (Vvv / V)/ V)n = porosity (also expressed as a percentage)n = porosity (also expressed as a percentage)VVvv = volume of the void space= volume of the void spaceV = total volume of the material (void + rock)V = total volume of the material (void + rock)

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Soil: Cubic packing of spheres


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• Bulk volume = (2r)3 = 8r3

Matrix volume r4 3


• Matrix volume =

• Pore volume = bulk volume - matrix volume3

r4

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VolumeBulkVolumePore

Porosity

r3/4r8

VolumeBulkVolumeMatrixVolumeBulk

33


%6.4732

1r8

r3/4r83

=

Porosity is not function pore size

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Cylindrical pore model

• Estimation of porosity accounting to this model:2 lrV

(anisotroop)


78,5%or 785,0422

lrr

lr

V

V

b

p

ebulk volum -V

volumepore -V

radius pipe -r

b

p

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Rhomic packing of spheres


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39,5%or 395,0312

411

3

3

r

r

V

V

V

VV

V

V

b

m

b

mb

b

p

• Estimation of porosity accounting to this model:


312 rVVV bbb

spheres packed-icorthorhomb theofheight -h3

4 umematrix vol-V

3460sin422ebulk volum -V

3m

33 b

r

rrhrr

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Regular Rhombohedral-Packed Spheres

26,0%or 26,0212

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3

3

r

r

V

V

V

VV

V

V

b

m

b

mb

b

p


212 rVVV bbb

rrr

r

rhrr

224on tetrahedrin theheight -h

3

4 umematrix vol-V

2422ebulk volum -V

22

3m

3b

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Packing of Two Sizes of Spheres


Porosity = 14%

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Irregular-Packed Spheres with Different Radii

• The figure shows an example of an idealised porous medium represented by four populations of spheres

(sorted by radii)


(sorted by radii)• The histogram shows the hypothetical grain-size

distribution.

0 < nSAND< 50 %

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MORE POROUS LESS POROUS

Porosity Porosity Varies withVaries with SortingSorting

Well SortedWell SortedSandSand

Poorly SortedPoorly SortedSandSand


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Grain-Size Sorting in Sandstone

Very WellSorted

WellSorted

ModeratelySorted

PoorlySorted

Very PoorlySorted


SORTING

• concrete (high strength) (HPC)

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Grain geometry also effects packing, hence porosity


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MORE POROUSMORE POROUS LESS POROUSLESS POROUS

Porosity Porosity Varies with %Varies with % CementCement

MORE POROUSMORE POROUS LESS POROUSLESS POROUS

NoncementedNoncementedSandSand

CementedCementedSandstoneSandstone


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MORE POROUS LESS POROUS

Fractured ShaleFractured Shale Unfractured ShaleUnfractured Shale

Porosity Porosity Varies withVaries with FracturingFracturing

Fractured ShaleFractured Shale Unfractured ShaleUnfractured Shale


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PorosityPorosityvaries withvaries with

% Cement% Cement

SortingSorting


FracturingFracturing

TPMMechanical compression


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POROSITY IN SANDSTONE

Porosity in Sandstone

QuartzGrain

PorePorosity in SandstoneTypically is Lower ThanThat of Idealized PackedSpheres Owing to:

Variation in Grain Size

Variation in Grain Shape

Cementation

M h i l d Ch i l


Scanning Electron MicrographNorphlet Sandstone

Mechanical and ChemicalCompaction

Photomicrograph by R.L. Kugler

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Pore Throats inSandstone Maybe Lined Witha variety ofcement MineralsinfluencePetrophysical


Scanning Electron MicrographTordillo Sandstone

yProperties

Photomicrograph by R.L. Kugler

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PCubic crystals

PoreThroat


Scanning Electron MicrographNorphlet Formation

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Secondary Electron Micrograph

Clay minerals in Sandstone Reservoirs,

Smalle plates


Jurassic Norphlet Sandstone(Photograph by R.L. Kugler)

~ 10 m

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Authigenic KaoliniteSecondary Electron Micrograph


Carter Sandstone

(Photograph by R.L. Kugler)

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Electron Photomicrograph

Sandstone:Fibrous Authigenic Illite

Illite


Jurassic Norphlet Sandstone

(Photograph by R.L. Kugler)

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Be aware 2D information

3D3D


2D

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Computed micro-tomography (CMT) using a CT scanner or synchrotron.


3D reconstruction: highlighting porosity (gold) The sample shows heterogeneously distributed, larger pores that are connected.

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Brief history of the X-ray:• Discovered by accident in

1895 by Wilhelm Conrad 1895 by Wilhelm Conrad Roentgen. Through his discovery he was awarded the very first nobel prize laureate in Physics (1901).

• The radiation was dubbed “X-ray” radiation as the


X-ray radiation as the nature of it was at the time a mystery to scientists.

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)( ddII

Problem:

)exp(0 wwoowet ddII

wo

“Not very sensitive for water”


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Siretom CT scanner circa 1975:

coarse 128 x 128 matrix

state-of-the-art CT system:

512 x 512 matrix image

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Range of values of porosityMedium Porosity (%)

gravel 25-40g

sand 25-50

silt 35-50

clay 40-70

sandstone 5-30

limestone 0-20

h l 0 10


shale 0-10

fractured basalt 5-50

fractured crystalline rock 0-10

dense crystalline rock 0-5

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Macroscopic coefficient:= porosity

lithithiidfl

Better definition: all materials

averagingofvolume

volumeaveragingthewithinvoidsofvolumen

avgV

dvV

n1

calculation


avgV 0

solidfor0

airfor1

Vavg ????

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Consider a porous material (2D)Open space – pore

Solid space – matrix

For 1 block

n = 1/1 = 100%n = 1/1 = 100%

For 2 blocks

n = 2.75/4 = 69%

For 3 blocks

n = 6/9 = 67%


For 4 blocks

n = 8/16 = 50%

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100

Representative Elementary Volume (area) REV

20

30

40

50

60

70

80

90

n (

%)


0

10

0 5 10 15 20 25 30

Sqrt Area Choice error

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Macroscopic coefficient:= porosity

averagingofvolume

volumeaveragingthewithinvoidsofvolumen

averagingofvolume

avgV

avg

dvV

n0

1

calculation

IF Vavg = REV


solidfor0

airfor1

Single valued

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Macro values by taking average


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Advantage

• geometry can stay unknown

• macroscopic measurable

• processes differential functions

Disadvantage


• geometry etc unknown =>

information lost

measure coefficients

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Porosity is macro information

-Lost information pore size

- connectivity

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Molecular scalenot appropriate for modeling

Pore scalevelocity variationsnot appropriate to modelgeometry not observable /too complex to describe- not observable in pores


o obse ab e po es

Continuum scale (REV)Representative elementary volume

equivalent porous medium

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Continuum approach

Rule of thumb

rREV = 40 l pore, grain


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concreteExamples

aggregate grain

cement


Depending on model: large/ small REV

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Example of Dual Porosity Rock: Vuggy Limestone


Core slab with secondary vugs (arrows) resulting from the partial dissolution of earlier dolomite cement (white).

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Example: boundary

Continuum


poro

sity approach

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Macro scale


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Porosity measurement: simple• Measure volume sample

S t t l ith t• Saturate sample with water• Vpores=Vwater

• Problem: water can’t reach small pores


pores(connected pores)

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Skeletal volume & Density by Gas pycnometer

The gas pycnometer provides high-speed, high-precision volume and density measurements for a wide variety of materials including powders,

bj d l i


objects, and slurries.

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Measurement with He : Pycnometer


Vs Vref

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• Helium gas is often used due to its following properties:g p p– The small size of helium molecules makes

the gas rapidly penetrate small pores– Helium is an inert gas that will not be

absorbed on the rock surface and thus yield erroneous results

Alt ti N d CO


• Alternatives: N2 and CO2

• Start with ‘dry’ sample

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• Calculation of the pore volume• Ideal gas law:

• In case of vacuum inside the sample chamber:

nRTpV VpVp 211 • In case of vacuum inside the sample chamber:

• Assuming adiabatic conditions, we obtain:

)(21 solidsrefref VVVpVp

122 VpVpVpV refsref

l d


• Porosity

2pVsolid

mat

solidmatporous V

VVn

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Density = Dry mass per unit volume

Vin volumemass

V= the particular volume used

V volume


S= solid phase, without fluid

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Solid phase density

Under limit is the density of the pure mineral

Vi lf

V= the particular volume used

V volume

Vmineralpureofmass


S= solid phase, without fluid

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Take simple approach

poresVn

totalVn

total

material

total

materialtotal

VV

VVVn 1

m t i l


material

sample

V

m

V

m

VV

material

material

total

material

total

materialn

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Typical materials quatz: 2650 kg/m3

310378.01 n


Building materials

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Coring bit

Samples


Samples

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Volumetric content

component (moisture, oil etc)

n

V

V


(REV measurement, e.g., moisture)

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PORE-SPACE CLASSIFICATION

Total porosity

ntotal =

Effective porosity

n =

VolumeBulk

Pore VolumeTotal

Pore SpacectedInterconne


neff =VolumeBulk

p

• Effective porosity – of great importance;

contains the mobile fluid

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Moisture content

capillary content capillary content

(just let it absorp)

Vacuum content

effcap n

totalvac n


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Moisture content

• m3/m3 (-)( )

• kg/kg (-)(shrinkage)

• kg/m3 (only building physics)

• saturation S=/n (0-1) (>1?)

percentage (but volume or mass)


• percentage (but volume or mass)

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Phase Content

Volume, v

Water MatrixAir

,

Mass, m

a w

a

mw

m

s

s

m

0 1


Volumetric content

Mass content

confusing

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PorosityPorosity TransportTransportPermeabilityPermeability

BE AWARE


Ability to hold water Ability to transmit water

Size, Shape, Interconnectedness

PorosityPorosity PermeabilityPermeability

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Course + Lectures notesporousmedia.nl › nfcmr › college › college-week1-2016.pdf · Transport in porous media 3MT130 Leo Pel, Henk Huinink, David Smeulders, Bart Erich, Hans