1

These powerpoint files were produced for the Earth History class at the Free University Berlin, Department of Geological Sciences

The copyright for texts, graphical elements, and images lies with C. Heubeck, unless otherwise specified.

Download, reproduction and redistribution of theses pages in any form is hereby permitted for private, personal, non-commercial, and class-related purposes use as long as the source is identified.

Despite of my efforts, I cannot guarantee the completeness, correctness and actuality of the material.

Prof. Christoph HeubeckInstitut für Geologische WissenschaftenFreie Universität BerlinMalteserstr. 74-10012249 BerlinGERMANY

ph: ++49-(0)30-83870695 fax: ++49-(0)30-83870734cheubeck@zedat.fu-berlin.de http://userpage.fu-berlin.de/~cheubeck/

Reservoir Petrophysics

Today’s Lecture

Pressure Distribution in a ReservoirBuoyancy / DisplacementOil and water distribution in a reservoirPorosimetryCapillarity

2

Pressure, arbitrary units

Hei

g ht b

elo w

wa t

er s

urfa

c e, f

t

40 50 60 70 80 90

-15

-10

-5

0

5

-20

Wood density = 0.6Water density = 1.00

The longer the wooden beam, the greater the buoyant force at the top of the board

In general:∆p = δh*∆ρ

∆p

Free water surface

Buoyancy

Pressure, arbitrary units

Hei

g ht a

bove

fre e

wat

e r, f

t

40 50 60 70 80 90

0

5

10

15

20

- 5

ρ gas = 0.3

ρ water = 1.00

∆p = 10

ρ light oil = 0.7

ρ heavy oil = 0.9

contact

contact

contact

shale seal

sandstonereservoir

Reservoir Pressure Gradients

Pressure, arbitrary units

Hei

g ht a

bove

fre e

wat

e r, f

t

40 50 60 70 80 90

0

5

10

15

20

- 5

ρga

s =

0.3

ρ water = 1.00

ρlig

ht o

il =

0.7

ρhe

avy

oil =

0.9

shale seal

sandstonereservoir

Reservoir Pressure Gradients Repeat Formation Tester

Pressure, arbitrary unitsde

pth

40 50 60 70 80 90

80

70

60

50

40

90

ρ water = 1.00

sandstonereservoir

shale seal

ρ heavy oil = 0.9

contact

3

The Concept of Displacement Pressure

how to get the oil in the rock !

The Concept of Displacement Pressure

Capillary water

Types of Water in the Reservoir

Structural water (chemically bound)

Hydration water (chemically bound)

Bound water, immobile water, irreducible water

Bound to the grain by capillary force

Capillary water

Water … and what to do about it !

Structural water (chemically bound)

Hydration water (chemically bound)

Bound water, immobile water, irreducible water(“Haftwasser”)

Can’t do much about them !

Displace as much as possible !

4

Capillarity: Definition

Capillarity ...

... is the tendency of wettingliquids to ascend minute openings(< 0.5 mm diameter) through theagency of a molecular surfaceforce, and (possibly) actingagainst the force of gravity.

Observations

• sponge sucking up liquid• sponge on kitchen counter staying wet• water rising through plants

The Concept of Capillary Pressure

Hydrocarbon

The capillary pressure of a rock is a function of 3 variables :

water

rock rock

• hydrocarbon-water interfacial

tension γ, • wettability (expressed as the

contact angle θ), and • radius of of the pore throat r

The Concept of Capillary Pressure

Hydrocarbon

The capillary pressure of a rock is a function of 3 variables :

water

rock rock

r

θ

• hydrocarbon-water interfacial

tension γ, • wettability (expressed as the

contact angle θ), and • radius of of the pore throat r

γ

The Concept of Capillary Pressure

Hydrocarbon

The capillary pressure of a rock is a function of 3 variables :

water

rock rock

r

θ

• hydrocarbon-water interfacial

tension γ, • wettability (expressed as the

contact angle θ), and • radius of of the pore throat

wherePc = displacement pressureγ = oil-water interfacial tension

(„surface tension“)θ = contact angle of wetting fluid

against the solid („wettability“)r = radius of the pore throat

2γ cos θr Pc =

γ

5

Extreme Example of VERY LOW Capillary Pressure

water

rock rock

θ

wherePc = displacement pressureγ = oil-water interfacial tension

(„surface tension“)θ = contact angle of wetting fluid

against the solid („wettability“)r = radius of the pore throat

2γ cos θr Pc =

As γ , Pc

As θ , Pc

As r , Pc

γ

Hydrocarbon

r

Extreme Example of VERY HIGH Capillary Pressure

water

rock rock

θ

wherePc = displacement pressureγ = oil-water interfacial tension

(„surface tension“)θ = contact angle of wetting fluid

against the solid („wettability“)r = radius of the pore throat

2γ cos θr Pc =

As γ , Pc

As θ , Pc

As r , Pc

γ

r

Hydro-carbon

A closer look at these three factors

•Interfacial tension(„surface tension“)

•Wettability

•Radius of the porethroat

1. Interfacial Tension (“Surface Tension”)

The surface tension of a fluid is• a measure of the cohesion of the molecules at a fluid‘s surface• a function of density r and area of cross section

... is an experimentally determined constant:

All values against air; x 10-3 Nm-1

Pure water, 20 deg C 72.25 Brines higherLight crude oils 20-30 Heavy crudes 35 Mercury 500

Surface tension declines with increasing temperature (and shows a complex behavior with pressure)

6

2. Wettability

calcite

oil

quartz

oil

water

water Wetting Liquid

Non-wetting LiquidContact

angle θ

A water-wet system

Water-wet vs. oil-wet

less mobile

mobile

So

100

0

High initial SoRapid declineHigh recovery rate

Time

An oil-wet system

Water-wet vs. oil-wet

Time

So

100

0

Low initial SoLong slow declineLow recovery

less mobile

mobile

Reservoir Wettability

Initially, all reservoirs are thought to be water-wet

Only after migration, reservoirs may change to oil-wet – why ?Complex chemical and physical interactions of HC with mineral surfaces

Rule of thumb:Carbonate reservoirs are generally oil-wet;Siliciclastic reservoirs are generally water-wet

7

Proportions of oil and water in a reservoir

After finding a reservoir, need to estimate the volumeof oil in it

To what degree has oil beencapable of entering thereservoir pore space, displacingthe capillary water ?

Displacement Pressure vs. Buoyancy Pressure

Capillary Pressure and Buoyancy Pressure: Migration

Capillary pressure measures the forcenecessary to displace capillary water from apore space

Buoyancy pressure is the additional force by which water is displaced by lighter oil from a given volume

For a given reservoir and fluid, it is afunction of reservoir height

For a given reservoir and fluid, it is afunction of pore size

Pw

Pnw

Remember ? Pressure Distribution in a Reservoir

4050 4060 4070 4080 4090

Hei

ght a

bove

fre e

wat

e r, f

t

4040

0

50

100

150

200

-50

Oil density = 0.77Water density = 1.00

∆p = 100*(0.433-0.333)=10 psi

∆p = 150*(0.433-0.333)=15 psi

In general:∆p = dh*(ρbrine-ρhc)

Buoyancy pressureOil pressure gradient

slope = 0.333 psi / ftWater pressure gradient

slope = 0.433 psi / ft

Pressure

Pressure Distribution in a Reservoir

4050 4060 4070 4080 4090

Hei

ght a

bove

fre e

wat

e r, f

t

4040

0

50

100

150

200

-50

Pressure

Available buoyancy pressure

Necessary capillary pressure

8

Force Balance in a Reservoir: Saturation Sw, So

Pressure

4050 4060 4070 4080 4090

Heig

ht

ab

ove f

ree w

at e

r , f

t

4040

0

50

100

150

200

-50

Available buoyancy pressure

Necessary capillary pressure

No HC entry into pore space

Beginning HC entry into pore space

Moderate entry into pore space

Strong entry into pore space

SaturationSo <>

Oil saturation(% of pore volume)

100 80 60 40 20 0

10

50

100

200

500

0

20

Oil-water contact

Seal

Sandstone reservoir

Saturation Sw, So as a function of Pressure

Theoretical curve for perfectly sorted pore

space

Seal

Oil-

wat

er c

apill

a ry

P res

sure

(o

il co

lum

n i n

feet

)Oil saturation

(% of pore volume)

Oil-

wat

er c

apill

a ry

P res

sure

(o

il co

lum

n i n

feet

)

100 80 60 40 20 0

10

50

100

200

500

0

20

Oil-water contact

Sandstone reservoir

Saturation Sw, So as a function of Pressure

Actual curve for perfectly sorted pore

space

Seal

Seal

Irreducible Sw

Entry Pressure

Pore space geometry

1 2

3

3 Shuaiba ls; f=11.9%; k=0.163mD Source: Core Lab

2 Sierra Chata ss; f=7.9%; k=0.399 mD Source: Core Lab

1 http://energy.usgs.gov/ factsheets/Petroleum/SEM.html

9

Pore space geometry

1 2

3

Small pores: ~ 100 µ diameter

Large surface area: >>1m2/g

Una pausa ?

To Repeat

The reservoir must be permeable and porous

Oil displaces pore water completely or partially, depending on capillary pressure

Buoyancy helps

Both determine water saturation

Capillary Pressure and Buoyancy Pressure: Migration

Capillary pressure measures the force necessary to displace capillary water from a pore space

Buoyancy pressure is the additional force by which water is displaced by lighter oilfrom a given volume

For a given reservoir and fluid, it is a function of reservoir height

For a given reservoir and fluid, it is a function of pore size

Pw

Pnw

10

How is the largest connected pore throatdiameter estimated ?

Best:•Injection of a known volume of

non-wetting fluid into sample•Measure pressure necessary to

increase saturation•Measure saturation through

resistivity of rock+fluid

Advantages:•Measure capillary properties of pore size

distribution•Quick and easy with Hg

Porosity, permeability, and capillary pressure

Mercury-injection capillary pressure curve

•Place core plugsample in chamber

•Surround withknown volumeof Hg

•Increasepressure in steps, displacewater (or air)

•Measure Hg saturation aftereach pressureincrease

Mercury saturation (% of pore volume)

Mer

c ury

Pr e

ssur

e ( p

s i)

100 80 60 40 20 0

100

500

1000

2000

5000

0

Entrypressure

200

Plateau

Swi

A Test

Mercury saturation (% of pore volume)

Mer

c ury

Pr e

ssur

e ( p

s i)

100 80 60 40 20 0

100

500

1000

2000

5000

0

200

decreasing reservoir quality !

Your Reservoir – how much oil is in it ?

Mercury saturation (% of pore volume)

Mer

c ury

Pr e

ssur

e ( p

s i)

100 80 60 40 20 0

100

500

1000

2000

5000

0

200

Oil saturation (% of pore volume)

Hei

g ht a

bove

OW

C (f

t)

Res

e rvo

ir

OWC

11

Rock Type 1

0

2

4

6

8

10

12

1.82

20

0.71

69

0.28

21

0.11

10

0.04

37

0.01

72

0.00

68

0.00

27

0.00

10

0.00

04

Particle Size, mm

Incr

emen

tal V

olum

e %

0

10

20

30

40

50

60

70

80

90

100

-0.9

-0.5

-0.1

0.35

0.75

1.15

1.56

1.96

2.36

2.77

3.17

3.58

3.98

4.38

4.79

5.19

5.59 6

6.4

6.8

7.21

7.61

8.02

8.42

8.82

9.23

9.63 10

10.4

10.8

11.2

Particle Size, Phi

Cum

ulat

ive

Vol

ume

%

Porosity vs. Permeabiliy, Cap. Pressure Samples

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

0.00 0.05 0.10 0.15 0.20 0.25 0.30porosi ty (v/v)

per

m (m

D)

RT 1 > 3500 k/ phiRT 2 450 - 3500RT 3 150 - 450RT 4 6.32 - 150RT 5 > 6.32

0.1 µ

0.25µ

0.5 µ

5 µ

2 µ

1 µ

2 0 µ

10 µ

3R

XRD Rock Type 1

Quartz75%

llli te/M ica1%

Ferroan Dolomite

4%

Plag Feldspar

4%K-Feldspar

15%

50µ

125µ

1

10

100

1000

10000

100000

0 10 20 30 40 50 60 70 80 90 100

Pseudo-Water Saturation (%)

Hg

Inje

ctio

n Pr

essu

re (p

si)

Hg Capillary Pressure

Particle Size

50µ

Rock Type 2Porosity vs. Permeabiliy, Cap. Pressure Samples

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

0.00 0.05 0.10 0.15 0.20 0.25 0.30porosity (v/v)

perm

(m

D)

RT 1 > 3500 k/ phiRT 2 450 - 3500

RT 3 150 - 450R T 4 6.32 - 150R T 5 > 6.32

0.1 µ

0.25µ

0.5µ

5 µ

2 µ

1 µ

20 µ

1 0 µ

0

2

4

6

8

10

12

1.82

20

0.71

69

0.28

21

0.11

10

0.04

37

0.01

72

0.00

68

0.00

27

0.00

10

0.00

04

Particle Size, mm

Incr

emen

tal V

olum

e %

0

10

20

30

40

50

60

70

80

90

100

-0.87

0.48

1.83

3.17

4.52

5.86

7.21

8.55

9.90

11.25

Laser Particle S ize, Rock Type 2 (phi )

Cum

ulat

ive

Volu

me

%

High-Pressure Hg-Inject ion Capillary Pressure Curves, RT 2

1

10

100

1000

10000

100000

0 10 20 30 40 50 60 70 80 90 100Pseudo-Water Saturation (%)

Hg

Inje

ctio

n P

ress

ure

(psi

)

XRD Rock Type 2

K- Fel dspar14%

P lag Fel dspar

4%

Ferroan Dol omite

5%lll ite/Mica

3% Quartz67%

50µ

125µ

Hg Capillary Pressure

Particle Size

50µ

High-Pressur e Hg-Injecti on Capilla ry Pressure Curves, RT 3

1

10

100

1000

10000

100000

0 10 20 30 40 50 60 70 80 90 100Pse udo-Water Satur ation (%)

Hg

Inje

ctio

n Pre

ssur

e (p

si)

0

2

4

6

8

10

12

1.82

20

0.71

69

0.28

21

0.11

10

0.04

37

0.01

72

0.00

68

0.00

27

0.00

10

0.00

04

Part icle S ize, mm

Incr

emen

tal V

olum

e %

0

10

20

30

40

50

60

70

80

90

100

-0.87

0.48

1.83

3.17

4.52

5.86

7.21

8.55

9.90

11.25

Laser Particle Si ze, Rock Type 3 (phi)

Cum

ulat

ive

Volu

me

%

Rock Type 3Po rosity vs. Permeabiliy, Cap. Pressure Samples

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

0.00 0.05 0.10 0.15 0.20 0.25 0.30porosi ty (v/v)

perm

(mD)

RT 1 > 3500 k/ phiRT 2 450 - 3500RT 3 150 - 450RT 4 6 .32 - 150

RT 5 > 6.32

0.1µ

0.25µ

0.5 µ

5 µ

2 µ

1 µ

20 µ

10 µ

XRD Rock Type 3

Quartz66 %

lllite/Mica4 %

Ferroan Dolomite

7 %

Plag Feldspar

7 %K-Feldspar

11 %

50µ

125µ

Hg Capillary Pressure

Particle Size

50µ

Rock Type 4

0

2

4

6

8

10

12

1.82

20

0.71

69

0.28

21

0.11

10

0.04

37

0.01

72

0.00

68

0.00

27

0.00

10

0.00

04

Particle Siz e, mm

Incr

emen

tal V

olu

me %

0

10

20

30

40

50

60

70

80

90

1 00

-0.87

0.48

1.83

3.17

4.52

5.86

7.21

8.55

9.90

11.25

Laser P article Size, Rock Type 4 (phi)

Cum

ulat

ive

Volu

me %

High-Pressure Hg-Inje ction Capillary Pressure Curves, RT 4

1

10

100

1000

1 0000

10 0000

0 10 20 30 40 50 60 70 80 90 100Pseudo-Water Saturation (%)

Hg

Inje

ctio

n Pr

essu

re (p

si)

Porosity vs. Permeab iliy, Cap . Pressure Samples

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

0.00 0.05 0.10 0.15 0.20 0.25 0.30porosity (v/v)

perm

(mD)

RT 1 > 3500 k/ phiRT 2 450 - 3500RT 3 150 - 450R T 4 6.32 - 150

R T 5 > 6.32

0.1 µ

0.25µ

0.5 µ

5 µ

2 µ

1 µ

20 µ

1 0 µ

XRD Rock Type 4

K-Feldspar6%

Plag Feldspar

8%

Ferroan Dolomite

6%lllite/M ica

7% Quartz65%

50µ

125µ

Hg Capillary Pressure

Particle Size

50µ

12

0

1

2

3

4

5

6

1.82

20

0.71

69

0.28

21

0.11

10

0.04

37

0.01

72

0.00

68

0.00

27

0.00

10

0.00

04

Partic le S ize, mm

Incr

emen

tal V

olum

e %

0

10

20

30

40

50

60

70

80

90

1 00

-0.87

0.48

1.83

3.17

4.52

5.86

7.21

8.55

9.90

11.25

Particle Size, Phi

Cum

ulat

ive V

olum

e %

Porosity vs. Permeabiliy, C ap. Pre ssure Samples

0.01

0.10

1.00

10.00

100.00

1000.00

10000.00

0.00 0.05 0.10 0.15 0.20 0.25 0.30po rosit y (v/v)

per

m (m

D)

RT 1 > 3500 k/phiRT 2 450 - 3500RT 3 150 - 450RT 4 6.32 - 150RT 5 > 6.32

0.1µ

0.25µ

0.5µ

5 µ

2 µ

1 µ

20 µ

10 µ

High-Pres sure Hg -Inject io n C apillary Pre ssure C urves, RT 5

1

10

100

1000

10000

100000

0 10 20 30 40 50 60 70 80 90 100Pseudo-Water Saturation (%)

Inje

ctio

n Pr

essu

re (p

si)

Rock Type 5XRD Rock Type 5

Quart z51 %

ll lite/M ica13 %

Ferroan Dolomite

6 %

Pl ag Fe ldspar

7 %K-Feldspa r

5 %

50µ

125µ

Hg Capillary Pressure

Particle Size

50µ

Petrophysics - Literaure

• Tiab, D., and C. Donaldson, 1996, Petrophysics – Theory and Practice of Measuring Reservoir Rock and Fluid Transport Properties: Gulf Publishing Co., 706 p.

• Various skripts, available as downloadable pdfs from the internet and compiled in the class archive

In what types of large-scale geometric bodies do these conditions exist in the

subsurface ?

Next Lecture

Reservoirs

Petrophysics Links

• http://www.micromeritics.de/ and http://www.micromeritics.com/: Homepages of the leading producer of pore-analytical hardware; gooddownloadable pdf script; link to a visualisation-software company www.pore-cor.com.

• http://www.petrophysics.net/index.htm: “The Petrophysics Portal: The science of measuring rock properties and the realtionship between those. Maintained by Mark Deakin, a consultant. Many links to organizations, companies etc.

• http://www.hendersonpetrophysics.com/ Similar but not as good.

• http://www.mines.edu/~golhoeft/research/petro.html : An article describing the essence of Petrophysics; by Gary R. Olhoeft, Prof. at Colorado School of Mines.

• http://iva.uni-ulm.de/PHYSIK/VORLESUNG/fluidemedien/node46.html