1 2 Tempelet (Svalbard) chalk Carbonates Silicified Carbonates Loggelinje Midterhuken (Svalbard) Loggelinje.

1

2

Tempelet (Svalbard)

chalk

Carbonates

Silicified Carbonates

Log

geli

nje

Midterhuken (Svalbard)

Log

geli

nje

33

Cubic packing

= 47.6 %

Rombicpacking

= 26 %

Cubic packing,different grain size

= 12.5 %

1) PorosityPorosity:

%100%100

tot

matrixtot

tot

p

V

VV

V

V

Vp = pore volumeVmatrix = grain volumeVtot = bulk volume

Ideal

Porous sandstone

Sand grain

water

oiePore size:10 - 50 m

44

Effective porosity eff is the porosity of interconneceted poresResidual porosity res is the porosity of the remaining pores

Typical effective porosity:

Sandstone: = 10 - 40 % depending on grain shapeLimestone and dolomite: = 5 - 25 % depending on fractures

Total porosity: tot = eff + res

How do we measure the porosity eff ?

1. In situ measurements in the reservoir (well logging) 2. Core analysis: drilling cores from the reservoir followed by laboratory analysis

• Drilled cores (d = 2,5 - 5´´)• Drilling sylindrical core plugs (d = 1,5´´, h = 3 ´´)• Clean and dry plugs

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2) SaturationA porous medium (reservoir or core plug) usually contains severalfluids: water, oil, gas

Saturation = the fraction of the total pore volume Vp which contains the actual fluid

Water saturation:p

ww V

VS Oil saturation:

p

oo V

VS Gas saturation:

p

gg V

VS

Normally, the entire pore volum will be filled be fluids, hence:

1 gow SSS

The porosity determines the amount of oil in the reservoir

V = the totale pore volume (PV)So = the oil saturationSwc = “connate water” – the original water saturation

Stock Tank Oil Originally In Place (STOOIP):

Bo = “oil formation volum factor” = the ratio between the oil volume in the reservoirand the oil volume in the stock tank at the surface (Rm3/Sm3). Often Bo > 1 because gas is released from the oil when brought to the surface.

Oil In Place (OIP): OIP = V So = V (1 - Swc) unit Rm3

STOOIP = OIP /Bo=V (1 - Swc)/Bo unit Sm3

66

3) Miscible and immiscible fluids

a) water and oil are immiscible

The van der Waals force is largerbetween like molecules.

The molecules in a liquid is held together by electrostatical forces (van der Waals forces) acting between the molecules

b) water and alcohol (ethanol) are miscible

The van der Waals force is largerbetween unlike molecules.

77

4) Wettability

= 0 - 30o strongly water-wet = 30o - 90o preferably water-wet = 90o – neutrally wet = 90o - 150o preferably oil-wet = 150o - 180o strongly oil-wet

Most oil reservoirs are water wet:

Wettability is the ability of one fluid to spread on a solid surface in the presence of other fluids

The wettability is defined by the wetting angle

Sandgrain

water

oilWettability may also be quantified by capillary pressure properties. We will return to this later.

solidwater

oil

= 0

Water wet

Vannoil

solid

water

= 90o

Neutrally wet

solid

water oil

180o

180o

oil wet

Pipette with water

Oil

Waterdrop

88

5) ViscosityViscosity is internal fluid friction

Shear forces act between different fluid layers and between the fluid and container walls

y

Fv

Shear tension:A

F The velocity gradient in the y-direction:

y

v

dy

dv

Empirical studiesshows that formost fluids: dy

dv = the viscosity coefficient or simply the viscosity

Unit: 1 Pas = 1 Ns/m2 = 10 P (poise)This is a Newtonian fluid

99

6) Darcy’s law og permeability

A pressure difference p is needed for a fluid to flow through a porous medium.

Henri Darcy (1856) discovered that the volume flow rate Q through a filter of cross section A:

pAaQ where the proportional constant a depends on both the fluid and the filter

The modern version av Darcy’s law for fluid flow in a porous medium (e.g a core plug):

L

ppKAQ AB

L

pBpA

Q A coreplug

Q = volume per unit time (volume flow rate)K = the absolute permeability of the medium = the fluid viscosity

Permeabilityunit

22

3

mPa

m

ms

msPa

AB pp

L

A

QK

This is a rather large unit. Therefore we define a new unit der:1 darcy (D)

2125

23

2

3

m 1098692.0Pa101.01325

s/cm 1sPa10

1atm

1cm

cm

/s1cm1cPdarcy 1

1 millidarcy (mD) = 10-3 D = 0.98692·10-15 m2

1010

7) Relative permeability

The flow possibility for one fluid may then depend on the saturation of the fluids present

Oil may flow more easily in this case: than here:

Sand grain

Sand grain

olje

water along thepore walls(water wet)

Sand grain

Sand grain

oil

Water willflow moreeasily thanthe oil

A sentral question arises: Does Darcy’s law and the permeability concept also apply when there are more than one fluid flowing in the porous medium?

Single phase flow: The absolute pemeabilitty K i Darcy’s equation is independent of the fluid, and depends only on the properties of the porous medium.

Multiphase flow: Several immiscible fluid phases (water, oil, gas) flow simultaneously through the porous medium

We see that the oil will flow more easily when more oil is present (large So)

oil

1111

Capillary pressure curves in capillary tubes

oil

water Rgg

ph owc 1cos2

One simplecapillary tube

oil

water

1.0Siw

water

oil

Fre water level(FWL)

Water/oilcontact (OWC)

Hei

ght;

C

ap.

pre

ssWater sat. (Sw)

0

Tube radius (R )small large

A battery of tubes with varying radius and therefore varying capillary pressure:

• There is a linear relation between capillary pressure pc and height h.• The total water saturation Sw below h in all tubes decrease when the tubes get thinner

12

Darcy’s equations equations3 11

11 p

Kgu

equations 3 222

2 gu

pK

Equations of state equations 2 )( og )( 222111 pp

equations 2 )( og )( 222111 pp Viscosity

Continuity of equation equation 1 0)(

)( 1111

t

S

u

equation 1 0)(

)( 2222

t

S u

Saturation equation 1 121 SS

The capillary pressure equation 1 )( 112 Sppp c

Total 14 equations

13

x

Sf w

www

From the continuity equations we have:

0)(

t

S

x

fu

t

S

x

uf

t

S

x

u wwwwww

Hence 0

t

S

x

fu ww

Introduce

Finally we get: 0

t

S

x

S

xx

S

dS

du www

w

w

w

This is called thesaturation equation

2. order partiell differential equation for Sw(x,t); non-linear with coeffisients which are functions of the independent variable Sw . The equation must be solved numerically.

When Sw has been found, we may calculate fw and uw og uo, and finally pw the po,all as functions og x and t.

1414

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Well logging

Goal: Petrophysics as function of depth in reservoir

A tool with instrumentslowered into the borehole.

The instruments in the probe measures the propertiesof formation and transmits data via mud to the surface

•lithological (rock type)•porosity •saturation

Reservoir

tool

16

Tempelet (Svalbard)

chalk

Carbonates

Silicified Carbonates

Log

geli

nje

Midterhuken (Svalbard)

Log

geli

nje

17

Øvretransmitter

Mottakerantenne

Øvretransmitter

Gamma-sensor

Logge-sonde

Kraft-kilde

Bore-krone

Slam-motor

Resisitivitets-sensor

a) Measurement While Drilling (MWD) Logging While Drilling (LWD)Tool at the bottom of the drill string. Signals transmitted as pressure waves through mud.

b) Wireline Logging

Drill string is pulled up and the probe is sent down with a wirethat transfer data to / from the logging instruments.Expensive, less common

Two methods

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Log tools must withstand:

  high reservoir pressure, 1000 atm  high reservoir temperatures, 120 ° C  large mechanical stresses  For time-efficient electronics

The tools measure into the formationoutside invasion zone for drilling fluids

Drilling Fluids (mudfiltratet) penetratesthe formation (invasion). This may give false results.

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1. Neutron-log Atom nuclei consist of positively charged protons and neutrons without chargeProtons and neutrons have roughly the same mass.

• Neutrons with energy 3-4 MeV sent into the formation from a source in the tool (1 MeV = 1.6 ° 10-13 Joules)

• Neutrons lose energy when colliding with atomic    nuclei, hydrogen, in the formation•When the energy is reduced to a they may be “captured” by nuclei

• This excited nuclei emit gamma rays

• This radiation can be detected in a gamma-   detector in the tool

nNeutronsource

Gamma-detector

Sond

e Formation

Clamp

Sikjerne

n n n

n

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Much hydrogen ….. Increased gamma radiation.

Most effective if the neutrons collide with protons (p),ie hydrogen nuclei

If the detector detects gamma radiationwe have a neutron-gamma log

Most probes simultaneously measure the epithermalneutrons (En> 1 eV). It is called the neutron-neutron log

The response from nøytronloggen is a measure of hydrogen-containing fluid (oil, water, gas) in the formationie, hydrogen index (HI)

Since these fluids are located in the pores, it is a measure of porosity.

Problem 1: Response from all hydrogen. Also from water bound to clay..

Problem 2: The gas has a low HI, - underestimation of porosity. - Detect gas layer.

nNeutron-source

Gamma-detector

Sond

e Formation

Clamp

Sikjerne

n n

p

n

n

p

p p

21

Radioactive isotopes:

• Occur in the earth (crust)• Type and rate of radioactivity depends on the mineral type• Depends on rock type, occurs particularly in shale• Radioactivity is a "finger print" of great interest to the   lithologic and stratigraphic description of the reservoir

2. Gamma-log

It measures naturally occurring radioactivity in the formation.Only gamma-rays have sufficient penetration ability in the formation ofreaching the detector in the logging tool

Gamma-detector

Sond

e

Formatjon

40Knuclei

238Unuclei

22

Important isotopes

1) 40K ; T1/2 = 1.3·1010 year

40K

40Ar

40CaE=1.46 MeV

+ -

2) 232Th ; T1/2 = 1.4·1010 year

232Th + 228Ra 208PbThorium-series:

3) 238U ; T1/2 = 4.5·109 year

Uranium-series: 238U + 234Th 8 6 206Pb

23

The most important minerals that may contain radioactivity are:

1) Quartz [SiO2] (sandstone) – Clean regular lattice – little room to accommodate radioactive isotopes

2) Carbonates (chalk) [ CaCO3 ] – Deposits of living organisms - clean

3) Dolomitt [ CaMg(CO3)2 ] – Traces of Uranium

4) Feltspat [KAlSi3O8] and mica clay and shale - Crystalline, containingAl, K, Na, Ca, Ba – silicates poor crystal structure, ie foreign atoms (eg. radioactive)          can take place: thus much radioactivity

24

Petrophysics from gamma-log:

1) Lithology (rock type) – Identify shale and clean sand (in addition to mud log)

2) Clay content. Gamma-index:

min

minlog

GRGR

GRGRI

maxGR

GRmin = intensity of the clean zone (without clay / shale)GRmax = intensity of the assumed pure clay zoneGRlog = intensity of the current zone

3) The turning points in the IGR-curve defines the transition     between the layers.

4) Depth Reference. Can be used to determine casing need.

0 < IGR < 1

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3. Density log (gamma-gamma log)

A radioactive source (60Co, 137Cs) - gamma radiation.

Principal:

mud

clamp

Radioactivsource

Gamma-detectors

Bore-hole

Formationto

ol

led

Gamma radiation (photons) scattered from electronsof atoms in the formation. Photons lose energy.Those who lose the most energy are those scattered backthe probe.

This decreases the number of electrons with the originalenergy recorded in the detectors.

Absoprbsjonskoeffisienten is proportional to the numberelectrons in the Z atom (molecule) which in turn dependsmass density b .

Gamma-gamma log measures density in formation

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mfb )1(

Bulk Mass of formation is the sum mass of pore volume (liquid)and matrix (rock) :

Porosity:

fm

bm

The matrix density m and the fluid density f til reservoir fluids is known, porositymay be found vi by measuring b with the density log.

We must expect that the density-log records:

•High density of shale and cemented layers•Greater density in the oil-bearing sandstone layers than the layer of gas•Greater density in lower porosity layers•Slightly greater density in the water zones than in the oil zones

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Gas

Oil

Oil

Van

n

Neutron-log

Shale

Sand-stone

Semented

Semented

Semented

Sand-stone

Sand-stone

Sand-stone

Coal

Shale

Tak-berg- art

High

Low

Gamma-log Density-log Shale: high radio activity,A lot of water (bound in clay), high density

Sandstone: low natural gammaLow neutron pga gas (low HI)

Cemented sandstone: high density

Sandstone with oil: HI high,high neutron-log,high densityCemented sandstone: high density

Shale: high gamma, much water

Sandstone with oil: density log and neutron log depends on porosity

Increasing effect on the density log the transition to the water zone

Cementert sandstone: high density

Coal: high water content, inc. neutron

Sandstones with low porosity, Increased density, less water

gamma-log:• high for shale• fingerprint for minerals• identify layers

Neutronlog: • high for oil/water• low for gas• high for shale

Density-log (gamma-gamma log):• high in shale and cemented layers• higher in oil/water compared to gas

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Phase Coherency

29

CPMG Sequence

30

Fast Relaxation

Slow Relaxation

T2 is a measure of Poresize

31

Poresize Distribution -NMR

32

NMR

1H

1H

isibi TV

S

TV

S

T

111

1

i = 1,2

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PTEK100 H2011 - Boreteknologi

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Azimuthal Deep Resistivity (ADR) tool

MWD forts …

3434

BAT Sonic tool