1
Tempelet
(Svalbard)
Loggelinje
Silicified Carbonates
Carbonates
Midterhuken
(Svalbard)
Loggelinje
chalk
2
1) Porosity
Ideal
Porosity:
Cubic
packing

 = 47.6 %
Vp
Vtot
100 % 
Vtot  Vmatrix
100 %
Vtot
Vp = pore volume
Vmatrix = grain volume
Vtot = bulk volume
Rombic
packing
 = 26 %
Porous sandstone
Cubic packing,
different grain size
 = 12.5 %
water
Pore size:
10 - 50 m
oie
Sand
grain
3
3
Effective porosity eff is the porosity of interconneceted pores
Residual porosity res is the porosity of the remaining pores
Total porosity:
tot = eff + res
Typical effective Sandstone:  = 10 - 40 % depending on grain shape
Limestone and dolomite:  = 5 - 25 % depending on fractures
porosity:
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
4
4
2) Saturation
A porous medium (reservoir or core plug) usually contains several
fluids: water, oil, gas
Saturation = the fraction of the total pore volume Vp which contains the actual fluid
Water saturation:S w 
Vw
Vp
Oil saturation: S o 
Vo
Vp
Gas saturation: S g 
Vg
Vp
Normally, the entire pore volum will be filled be fluids, hence:
S w  So  S g  1
The porosity determines the amount of oil in the reservoir
unit Rm3
OIP = V So = V (1 - Swc)
Oil In Place (OIP):
V = the totale pore volume (PV)
So = the oil saturation
Swc = “connate water” – the original water saturation
Stock Tank Oil Originally In Place (STOOIP):
STOOIP = OIP /Bo=V (1 - Swc)/Bo
unit Sm3
Bo = “oil formation volum factor” = the ratio between the oil volume in the reservoir
and 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.
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5
3) Miscible and immiscible fluids
The molecules in a liquid is held together by electrostatical forces
(van der Waals forces) acting between the molecules
a) water and oil are immiscible
The van der Waals force is larger
between like molecules.
b) water and alcohol (ethanol) are miscible
The van der Waals force is larger
between unlike molecules.
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6
4) Wettability
Pipette
with water
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 
Oil
Water
drop

Water wet
oil wet
Neutrally wet
oil
water
water oil
  180o
oil
solid
water
Vann
solid
=0
 = 90o
= 0 - 30o strongly water-wet
 = 30o - 90o preferably water-wet
 = 90o – neutrally wet
 = 90o - 150o preferably oil-wet
 = 150o - 180o strongly oil-wet
Wettability may also be quantified by capillary
pressure properties. We will return to this later.
solid
  180o
Most oil reservoirs are water wet:
water
oil
Sand
grain
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7
5) Viscosity
Viscosity is internal fluid friction
Shear forces act between different fluid layers and between the fluid and container walls
v
F
y
dv v
F

The
velocity
gradient
in
the
y-direction:
Shear tension:  
dy y
A
Empirical studies
dv
 = the viscosity coefficient or

shows that for
simply the viscosity
dy
most fluids:
This is a Newtonian fluid
Unit: 1 Pas = 1 Ns/m2 = 10 P (poise)
8
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:
Q  a  A  p
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
Q
KA pB  p A
Q

L
core
plug
A
pB
pA
Q = volume per unit time (volume flow rate)
K = the absolute permeability of the medium
 = the fluid viscosity

Q
L
m3 m 
Permeability
2
K 
 Pa  s

m

unit
A pB  p A
s  m 2 Pa 

This is a rather large unit. Therefore we define a new unit der:1 darcy (D)


1cm3 /s 1cm   3
1 cm 2 / s
12
2
1 darcy  1cP 


10
Pa

s

 
  0.98692 10 m
2
5
cm
1atm  
1.01325 10 Pa 

1 millidarcy (mD) = 10-3 D = 0.98692·10-15 m2
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9
7) Relative permeability
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
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?
The flow possibility for one fluid may then depend on the saturation of the fluids present
Oil may flow
more easily
in this case:
water along the
Sand grain pore walls
(water wet)
than here:
oil
olje
Sand grain
Sand grain
Sand grain
oil
Water will
flow more
easily than
the oil
We see that the oil will flow more easily when more oil is present (large So)
10
Capillary pressure curves in capillary tubes
One simple
capillary tube
oil
h
water
pc
 g

2 ow cos  1
 g R
oil
Height;
Cap. press
A battery of tubes with varying radius and therefore varying capillary pressure:
oil
Water/oil
contact
(OWC)
water
0
Fre water level Siw
Water sat. (Sw)
(FWL)
1.0
water
small
Tube radius (R )
large
• There is a linear relation between capillary pressure pc and height h.
11
• The total water saturation Sw below h in all tubes decrease when the tubes get thinner
Darcy’s equations
u1  
K1
p1  1 g 
u2  
K2
p2   2 g 
3 equations

1  1 ( p1 ) og 2  2 ( p2 )
Equations of state
Viscosity

3 equations
1  1 ( p1 ) og 2  2 ( p2 )
Continuity of equation
Saturation
The capillary pressure
( 1S1 )
0
t
(  2 S2 )
  (  2u 2 )  
0
t
  ( 1u1 )  
S1  S2  1
p2  p1  pc (S1 )
Total 14 equations
2 equations
2 equations
1 equation
1 equation
1 equation
1 equation
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From the continuity equations we have:
uw
S w ( f wu )
S w
f w
S w



u

0
x
t
x
t
x
t
Hence
Introduce
Finally we get:
u f w S w

0
 x
t
S w
f w   w  w
x
u  d w S w   S w  S w
  w
0
 

  dS w x x 
x  t
This is called the
saturation 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.
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1414
Well logging
Goal: Petrophysics as function of depth in reservoir
•lithological (rock type)
•porosity
•saturation
tool
A tool with instruments
lowered into the borehole.
The instruments in the probe measures the properties
of formation and transmits data via mud to the surface
Reservoir
15
Tempelet
(Svalbard)
Loggelinje
Silicified Carbonates
Carbonates
Midterhuken
(Svalbard)
Loggelinje
chalk
16
Two methods
a) Measurement While Drilling (MWD)
Logging While Drilling (LWD)
Tool at the bottom of the drill string. Signals transmitted as pressure waves
through mud.
Loggesonde
Kraftkilde
Øvre
transmitter
Slammotor
Øvre
transmitter
Mottaker
antenne
Resisitivitetssensor
Borekrone
Gammasensor
b) Wireline Logging
Drill string is pulled up and the probe is sent down with a wire
that transfer data to / from the logging instruments.
Expensive, less common
17
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 formation
outside invasion zone for drilling fluids
Drilling Fluids (mudfiltratet) penetrates
the formation (invasion). This may give false results.
18
1. Neutron-log
Atom nuclei consist of positively charged protons and neutrons without charge
Protons and neutrons have roughly the same mass.
Sonde
Clamp
from a source in the tool (1 MeV = 1.6 ° 10-13 Joules)
• Neutrons lose energy when colliding with atomic
n
Neutron
source
Gammadetector
• Neutrons with energy 3-4 MeV sent into the formation
Formation
n
n
n
n

Si
kjerne
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
19
Most effective if the neutrons collide with protons (p),
ie hydrogen nuclei
Much hydrogen ….. Increased gamma radiation.
Sonde
Clamp
Formation
p
p
n
n
Neutronsource
Gammadetector
n
n
p
p
n

Si
kjerne
If the detector detects gamma radiation
we have a neutron-gamma log
Most probes simultaneously measure the epithermal
neutrons (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 formation
ie, 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.
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2. Gamma-log
It measures naturally occurring radioactivity in the formation.
Only gamma-rays have sufficient penetration ability in the formation of
reaching the detector in the logging tool
Sonde
Formatjon
Radioactive isotopes:

Gammadetector
40K
nuclei

238U
nuclei
• Occur in the earth (crust)
• Type and rate of radioactivity depends on the mineral typ
• 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
21
Important isotopes
1)
40K
; T1/2 = 1.3·1010 year
40K
+
E=1.46 MeV
40Ca
40Ar
2) 232Th ; T1/2 = 1.4·1010 year
Thorium-series:
232Th
  + 228Ra      208Pb
3) 238U ; T1/2 = 4.5·109 year
Uranium-series:
238U
  + 234Th  8 6   206Pb
22
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
23
Petrophysics from gamma-log:
1) Lithology (rock type) – Identify shale and clean sand
(in addition to mud log)
2) Clay content. Gamma-index:
GRlog  GRmin
I GR 
GRmax  GRmin
0 < IGR < 1
GRmin = intensity of the clean zone (without clay / shale)
GRmax = intensity of the assumed pure clay zone
GRlog = 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.
24
3. Density log (gamma-gamma log)
mud
Formation
Principal:
A radioactive source (60Co, 137Cs)
- gamma radiation.
tool
clamp
Gammadetectors
Radioactiv
source
Gamma radiation (photons) scattered from electrons
of atoms in the formation. Photons lose energy.
Those who lose the most energy are those scattered back
the probe.
This decreases the number of electrons with the original
energy recorded in the detectors.
led
Borehole
Absoprbsjonskoeffisienten is proportional to the number
electrons in the Z atom (molecule) which in turn depends
mass density b .
Gamma-gamma log measures density in formation
25
Bulk Mass of formation is the sum mass of pore volume (liquid)
and matrix (rock) :
b   f  (1   )  m
Porosity:
 m  b

m   f
The matrix density m and the fluid density f til reservoir fluids is known, porosity
may 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
26
Gamma-log Neutron-log Density-log
Sandstone
Gas
Sandstone
Semented
gamma-log:
Sandstone: low natural gamma
• high for shale
Low neutron pga gas (low HI)
• fingerprint for minerals
Cemented sandstone: high density
• identify layers
Oil
Shale
Takbergart
Oil
Semented
Shale
High 
Shale:for
highoil/water
gamma, much water
• high
• low
for gas
Sandstone
with oil: density log
and for
neutron
log depends
• high
shale
Increasing effect on the density log
the transition to the water zone
Low 
Sandstone
Sandstone with oil: HI high,
high neutron-log,
high density
Cemented sandstone: high density
Neutronlog:
on porosity
Sandstone
Density-log (gamma-gamma log):
• high in shale
and cemented layers
• higher in oil/water compared
to gas
Vann
Semented
Coal
Shale: high radio activity,
A lot of water (bound in clay),
high density
Cementert sandstone: high density
Coal: high water content, inc. neutron
Sandstones with low porosity,
Increased density, less water
27
Phase Coherency
28
CPMG Sequence
29
Slow Relaxation
Fast Relaxation
T2 is a measure of Poresize
30
Poresize Distribution -NMR
31
NMR
1   S  1  S 1
 1 
 
Ti 
V  Tib
V Tis
i = 1,2
1H
1H
32
MWD forts …
PTEK100 H2011 - Boreteknologi
Azimuthal Deep Resistivity (ADR) tool
3333
BAT Sonic tool
3434