reservoir rock and fluid properties ii
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Measurement of Porosity
The porosity of a reservoir rock may be determined by:
• Core Analysis
• Well Logging Technique
• Well Testing
Reservoir Rock and Fluid Properties, 2008
Core Analysis
1. Calculation from the measurements of the dimensions of a uniformly shaped sample
2. Observation of the volume of fluid displaced by the sample
Volumetrically Gravimetrically
Fluid penetration into the sample should be prevented by coating the sample with paraffin or a similar substance by saturating the core with the fluid into which it is to be
immersed by using mercury
Reservoir Rock and Fluid Properties, 2008
Bulk Volume Measurement
Fluid penetration into the sample should be prevented
by coating the sample with paraffin or a similar substance
by saturating the core with the fluid into which it is to be immersed
by using mercury ( Hazardous – Not being used anymore)
Reservoir Rock and Fluid Properties, 2008
Pore Volume Measurement
Gas Expansion (Helium Porosimeter)
Mercury Injection
Saturation
All these methods yield effective porosity by
• extraction of a fluid from the rock
• introduction of a fluid into the pore spaces of the rock
Reservoir Rock and Fluid Properties, 2008
Porosity Measurement Tools
Helium Porosimeter
Boyle’s law:
Under isothermal conditions;
VPVP 2211
VPVP 22
(1)
(2)
At Time 1 --
At Time 2 --
Reservoir Rock and Fluid Properties, 2008
Helium Porosimeter
In case of a porous plug:
VVVV pb 1
(3)
PPP TT 21 (4)
VPVVVPP pb 22121 (5)
Reservoir Rock and Fluid Properties, 2008
Helium Porosimeter
Then the pore volume;
(6)
PPVP
VVV bp
21
22
1
VPP
VPV
b
21
22
1
1
(7)
Reservoir Rock and Fluid Properties, 2008
1. Weigh dry core sample Wd
2. Measure bulk volume Vb
3. Saturate the sample
4. Weigh saturated core sample Ww
5. Calculate pore volume
6. Calculate porosity ( Assuming density of water = 1)
Saturation (Imbibition)
Water in
Vacuum
water
dw
p
WWV
VWW
b
waterdw
VWWb
dw
Reservoir Rock and Fluid Properties, 2008
3.2 Subsurface Measurement
Surface measurements made on recovered core.
Down hole measurements very sophisticated.
Downhole porosity related to acoustic and radioactive properties of the rock.
Density Log
There exists differences in the density of oil, gas and water. This differences or changes in density vs depth, allows determination of the type of fluids that is/are present in a well.
Needs good description of the mineralogy.
L M F1
L M
F M
L - Quartz = 2.65 g/cm3
M Limestone = 2.71 g/cm3
Sonic Log
Measures response to acoustic energy through sonic transducers
Time of travel related to acoustic properties of the formation.
If mineralogy is not changing then travel time is related to density and hence porosity.
Formation fluids will effect response.
L M FT T 1 T L M
F M
T T
T T
TM - Quartz = 55ms ft-1
TL Limestone = 47 ms ft-1
TF Water =190 ms ft-1
Neutron Log
Another radioactive logging technique
Measures response of the hydrogen atoms in the formation
Neutrons of specific energy fired into formation.
The radiated energy is detected by the tool.
This is related to the hydrogen in the hydrocarbon and water phase.
The porosity determined by calibration
Logging Tools
Density Log
3.3 Average Porosity
Porosity normally distributed
An arithmetic mean can be used for averaging.
a
i
th
is the mean porosity
is the porosity of the
i core measurement
n the number of measurements
n
n
i
i
a
1
Thickness weighted Average Porosity
a
i
th
is the mean porosity
is the porosity of the
i core measurement
n the number of measurements
i
n
i
ii
ah
h1
Areal Weighted Average Porosity
a
i
th
is the mean porosity
is the porosity of the
i core measurement
n the number of measurements
i
n
i
ii
aA
A1
Volumetric Weighted Average Porosity
a
i
th
is the mean porosity
is the porosity of the
i core measurement
n the number of measurements
ii
n
i
iii
aAh
Ah1
Exercise 3
A piece of sandstone with a bulk volume of 1.3 cm3 is contained in a 5 cm3 cell filled with helium at 760 mm Hg. Temperature is maintained constant and the cell is opened to another evacuated cell of the same volume. The final pressure of the two vessels is 334.7 mm Hg. What is the porosity of the sandstone?
Reservoir Rock and Fluid Properties, 2008
Fluid Saturations
Defined as the fraction of pore volume occupied by a given fluid
Sum of the saturations is 100%.
Originally rock is saturated with water before invasion of HC.
A pressure differential is required for the non-wetting phase to displace the wetting phase.
This differential is termed the minimum threshold capillary pressure,
spacepore
gow
gowV
VS
,,
,,
goh
g
o
w
SSS
saturationgasS
saturationoilS
saturationwaterS
ctP
Reservoir Rock and Fluid Properties, 2008
Fluid Saturations
Reservoir Rock and Fluid Properties, 2008
Fluid Saturations
Reservoir Rock and Fluid Properties, 2008
Fluid Saturations
Reservoir Rock and Fluid Properties, 2008
Average Fluid Saturations
Reservoir Rock and Fluid Properties, 2008
Fluid Saturations
Reservoir Rock and Fluid Properties, 2008
Fluid Saturations
Reservoir Rock and Fluid Properties, 2008
Fluid Saturations
Fluid Saturation is the ratio of the volume of a particular fluid occupying some portion of a core sample to the pore volume of that sample
VV
Sp
o
o
VV
Sp
w
w
VV
Sp
g
g
Oil Saturation
Water Saturation
Gas Saturation
Reservoir Rock and Fluid Properties, 2008
Saturations
1. Mass of water collected from the sample is calculated as
2. Mass of oil removed from the core is computed as the mass of liquid less weight of water
3. Oil volume is computed as
4. Oil Saturation can then be determined with the formula
VM www
MMM wLo
ooo MV
1 SSS gwo
VVS poo
Reservoir Rock and Fluid Properties, 2008
Exercise 4
Estimate the fluid saturations in the core plug whose properties are given below:
Diameter of the core plug = 2.54 cm
Length of the core plug = 6 cm
Porosity of the formation = 26 %
Original weight of the core plug before extraction = 20.0 gm
Water volume collected in the graduated tube = 3 cc
Density of water = 1 gm/cc
Dry weight of cleaned and dried core plug = 14.0 gm
Density of oil produced from the same formation = 0.75 gm/cc
Reservoir Rock and Fluid Properties, 2008
Solution 2
1. Weight of water
2. Weight of liquid
3. Weight of oil
4. Volume of oil
Reservoir Rock and Fluid Properties, 2008
gmxVW www0.331
gmWWW dorL0.60.140.20
ccoW oV o 0.475.0
0.3
gmWWW wLo0.30.30.6
Solution 2, continued
5. Bulk volume of the core plug
5. Pore volume of the
core plug
6. Water Saturation
7. Oil Saturation 8. Gas Saturation
Reservoir Rock and Fluid Properties, 2008
322
40.306254.2 cmLπrV b
39.726.040.30 cmVV bp
38.09.7
0.3
VV
Sp
w
w
51.09.7
0.4
VV
Sp
o
o
11.051.038.011 SSS wog
Wettability
Measure of the attraction between rock surface and the fluids in the reservoir
The wetting fluid – the one most attracted to the rock surface
Water Wet (most fields)
Oil Wet (clay&carbonates)
Different types exhibit different production performance
Oil wet systems tend to exhibit early water breakthrough and lower initial water saturation.
Wettability
The definition is based on contact angle of water surrounded by oil
Oil
Water
Water
Water-wet Oil-wet
< 90o = water-wet > 90o = oil-wet 90o = intermediate wettability A variation of up to 20o is usually considered in defining intermediate wettability.
WATER-WET OIL-WET
Ayers, 2001
FREE WATER
GRAIN
SOLID (ROCK)
WATER
OIL
SOLID (ROCK)
WATER
OIL
GRAIN
BOUND WATER
FR
EE
WA
TE
R
OIL
OIL
RIM
< 90 > 90
WATER
Oil
Air
WATER
Effective & Relative Permeability Curves
Effective & Relative Permeability Curves
Rock Compressibility
Reservoir Rock and Fluid Properties, 2008
Rock Compressibility
Reservoir Rock and Fluid Properties, 2008
Rock Compressibility
Reservoir Rock and Fluid Properties, 2008
Rock Compressibility
Reservoir Rock and Fluid Properties, 2008
Rock Compressibility
Reservoir Rock and Fluid Properties, 2008
Rock Compressibility
Reservoir Rock and Fluid Properties, 2008
Rock Compressibility
Reservoir Rock and Fluid Properties, 2008
Rock Compressibility
Reservoir Rock and Fluid Properties, 2008
LESSON OUTCOME
Reservoir Rock and Fluid Properties, 2008
Permeability Concepts
Types of Permeability
Permeability
Is a measure of flow capacity (conductivity)
Depends on continuity of pore space
No unique relationship with porosity
Correlation for similar lithology is possible
Units : Darcy or miliDarcy
Permeability
The permeability of a rock is the description of the ease with which fluid can pass through the pore structure
Can be so low to be considered impermeable.
Such rocks may constitute a cap rock above permeable reservoir.
Also include some clays,shales, chalk, anhydrite and some highly cemented sandstones.
Permeability
Darcy’s Law
The rate of flow of fluid through a given rock varies directly with the pressure applied, the area open to flow and varies inversely with the viscosity of the fluid flowing and the length of the porous rock.
The constant of proportionality is termed Permeability
Mathematical Expression of Permeability
LKAQ
hh 21
Constant of proportionality and for viscous fluids;
m
kK
permeability
viscosity
First introduced by Darcy in 1856 while investigating the flow of water through sand filters for water purification.
Permeability
Darcy’s Law
kA PQ
L
m
3
2
Q flowrate in cm /sec
A cross sectional area of flow in cm
P pressure difference across ther sample, atmos.
viscosity in centipoise
L length of sample in cm.
k permeability in Darcy
m
Permeability
1 Darcy = Permeability which will permit flow of one centipoise fluid to flow at linear velocity of one cm per second under a pressure gradient of one atmosphere per centimetre.
Permeability
1 2A h hQ k
L
m
Taking viscosity as a variable
Poiseuille equation for laminar pipe flow
4r PQ
8 L
mr = radius of pipe of length L
Carmen Kozeny equation
for flow in packed beds
2 3
2'
d 1 dPu
dLk 1
m
k’ = shape factor
d = particle size
There is a very strong relationship between porosity
and permeability
Permeability Comparing equations.
Darcy Q P
kA L
m
Carmen Kozeny
2 3
2'
Q d 1 dPu
A dLk 1
m
It is not surprising therefore that there is a strong
relationship between permeability and porosity
2 3
2'
dk
k 1
Porosity vs Permeability
Porosity is independent
of grain size. Porosity
is generally unaffected
by grain size but
permeability increases
with increasing grain
size.
The better sorted the sand,
the higher are both the
porosity and permeability.
Porosity vs Permeability
Permeability
Practical unit-millidarcy, mD, 10-3 Darcy
Formations vary from a fraction of a millidarcy to more than 10,000 millidarcy.
Clays and shales have permeabilities of 10-2 to 10-
6 mD.
These very low permeabilities make them act as seals between layers.
Factors Affecting Permeability
Permeability is anisotropic
Horizontal permeabilities in a reservoir are generally higher than vertical permeabilities.
Due to reservoir stresses
Particle shape as influenced by depositional process.
Darcy’s Law
For one-dimensional, linear, horizontal flow through a porous medium, Darcy’s Law states that:
dx
dpkAq
m
Flow rate (1 cm3/s)
Cross sectional area (1 cm2)
Viscosity of flowing fluid (1 cp)
Permeability ( 1 Darcy)
Pressure gradient (1 atm/cm)
q
L
dx
A
Types of Permeability
• Absolute Permeability
• Effective Permeability
• Relative Permeability
Absolute Permeability
Reservoir Rock and Fluid Properties, 2007
P
L
q A
Flowing fluid is 100% saturating the medium
L
PkAq
m Absolute permeability
Effective Permeability
Reservoir Rock and Fluid Properties, 2007
More than one fluid is saturating the medium. Only one of them is mobile (flowing)
L
PAkq
i
ii
m Effective permeability
P
L
qo
A
qg
qw
Relative Permeability
Reservoir Rock and Fluid Properties, 2007
More than one fluid is saturating the medium. At least two of them are mobile (flowing)
L
PAkq
i
rii
m Relative permeability
qo
P
L A
qg
qw
kk
ki
ri
Relative Permeability Two phase relative permeability behavior
kro krw
Sw 0 1
Permeability
From the Darcy’s Law equation, permeability is defined
Basic linear and radial flow can be derived
General classification of permeability
)/( dxdPA
qk
m
Classification Permeability Range
Very Low 1 mD
Low 1 – 10 mD
Medium 10 – 50 mD
Average 50 – 200 mD
Good 200 – 500 mD
Excellent 500 mD
Averaging Permeability
Parallel Flow
Arithmetic Average
k1
k2
k3
h1
Series Flow
Harmonic Average
h2
h3
L1 L2 L3
k1 k2 k3
i
ii
Ah
hkk
ii
i
HkL
Lk
/
Random Flow
Geometric Average
ihhhh
G kkkk1
321 .......321
Data Sources of Porosity & Permeability
Core analysis Discrete measurement on small scale Routine Core Analysis (RCA) and Special Core Analysis (SCAL)
Electrical and radioactive logs Provide average response Neutron, sonic, density log
Well Tests (for permeability)
It is important that all measurements from all sources are always reconciled and not to be used in isolation.
Solution 1:
Darcy’s equation for horizontal flow:
L
PPkAq
m21
P
L
q A
21 PPA
Lqk
m
Solving for permeability,
UNITS:
k= Darcy
q= cm3/sec
P= psi
A= cm2
m= cp
L= cm
Solution 1:
21 PPA
Lqk
m
darcy.
atmcm
cmcpsec
hr
hr
cc
k 0295032
2023600
1100
22
P= 3 atm
L= 20 cm A=22
q= 100 cm3/hr
md.k 529
Relative Permeability
Darcy’s law is considered to apply when the porous medium is fully saturated with a homogenous, single phase fluid.
In petroleum reservoirs, however, the rocks are usually saturated with two or more fluids, such as interstitial water, oil and gas. It is necessary to modify Darcy’s law by introducing the concept of to Effective Permeability to describe the simultaneous flow of more than one fluid.
In the definition of Effective Permeability each fluid phase is considered immiscible and completely independent, so that Darcy’s law can be applied to each phase individually.
Relative Permeability
Effective Permeability is a function of the
• revealing fluid saturation,
• the rock wetting characteristics, and
• the geometry of the pores of the rock
The effective permeabilities are generally normalized by the absolute permeability of the rock sample and called as Relative Permeability.
L
PAkq
o
oo
m
L
PAkq
w
ww
m
L
PAkq
g
g
g
m
Relative Permeability
More than one fluid is saturating the medium. At least two of them are mobile (flowing)
L
PkAkq
i
rii
m
Relative permeability
qo
P
L A
qg
qw
kk
ki
ri
Relative Permeability
Two phase relative permeability behavior with respect to wetting phase saturation
krnw krw
Sw
1.0 1.0
Swmin Swmax
0 1
Relative Permeability
kro krw
Sw
Oil-Water relative permeability behavior with respect to Water saturation
1.0 1.0
Swc 1-Sor 0 1
Example 3:
A cylindrical core sample with a length of 20 cm, a diameter of 4 cm and with porosity of 30 % is subjected to a linear flow test with water of 1 cp viscosity and its absolute permeability is estimated as 80 md. Later the experiment is continued
1.With the injection of oil with 3 cp viscosity until no more water production is observed at production end. At that point the water saturation left in the core is calculated as 25 % and the permeability is estimated as 55 md. And then,
2.With the injection of water again at 0.09 cc/sec, below data is collected until no more oil production is observed at production end.
Estimate the oil-water relative permeability characteristics of this core sample.
Solution 3:
P, atm
t, sec
Vo, cc
VW, cc
qo, cc/s
qw, cc/s
ko, md kw, md kro krw
3 10 0.30 0.60
3 10 0.20 0.70
3 10 0.05 0.85
3 10 0.01 0.89
3 10 0 0.9
o2
oo q59.1
)2)(3(
)20)(3(qk
w2
ww q53.0
)2)(3(
)20)(1(qk
L
PAkq
i
ii
m
Solution 3:
P, atm
t, sec
Vo, cc
VW, cc
qo, cc/s
qw, cc/s
ko, md kw, md kro krw
3 10 0.30 0.60 0.03 0.06 0.0477 0.0318 0.0005963 0.0003975
3 10 0.20 0.70 0.02 0.07 0.0318 0.0371 0.0003975 0.0004638
3 10 0.05 0.85 0.005 0.085 0.00795 0.04505 0.0000994 0.0005631
3 10 0.01 0.89 0.001 0.089 0.00159 0.04717 0.0000199 0.0005896
3 10 0 0.9 0 0.09 0 0.0477 0 0.0005963
o2
oo q59.1
)2)(3(
)20)(3(qk
w2
ww q53.0
)2)(3(
)20)(1(qk
L
PAkq
i
ii
m
MULTIPHASE FLOW
2.0 Introduction
2.1 Absolute & Effective Permeability
2.2 Relative Permeability
2.3 Hysterisis
2.4 Mobility
2.5 Fractional Flow
2.6 Buckley-Leverett & Welge methods
2.0 Introduction
Info on relative permeability is very important because it:
Affects fractional flow of fluids during displacement
Affects performance of a reservoir
Determine relative flow rates of each fluid
Predict production from a reservoir
2.1 Absolute & Effective Permeability
Absolute Permeability Rock permeability irrespective of the 100% saturated fluid type, k.
100% water saturated
100% oil saturated
Effective Permeability
If 2 fluids are present and flowing simultaneously. Defined for each fluid. Depend on each fluid saturation.
Effective Permeability to Water =
Effective Permeability to Oil = ok
wk
Effective Permeability Curve
Water Curve: kw = 0 at Swc kw = 1 at 100% water saturation Oil Curve: ko = 0 at Sw=1-Sor ko = k at 100% oil saturation
ko kw
Swc 1- Sor
Sw
k k
absolute permeability
0 1
0 0
So 1 0
2.2 Relative Permeability
It is a normalised measure of conductance of one phase in a multiphase system
Measure of the mutual interference between phases competing for the same pore space (values 0 – 1)
k
kk w
rw k
kk o
ro Water Relative Permeability
Oil Relative Permeability
Depends on each fluid saturation in the pore space.
Part of SCAL – conducted on a carefully preserved core samples
If lab data is not available, may use correlations (e.g. Corey coefficients)
Effective & Relative Permeability Curves
kro krw
Swc 1- Sor
Sw
1 1
0 1
0 0
So 1 0
ko kw
Swc 1- Sor
Sw
k k
absolute permeabilit
y
0 1
0 0
So 1 0
k’ro
k’rw
End point (indicator of
wettability)
Wettability effect on the curves
kro krw
Swc 1- Sor
Sw
1 1
0 1
0 0
So 1 0
kro krw
Swc 1- Sor
Sw
1 1
0 1
0 0
So 1 0
Water Wet Oil Wet
Effective & Relative Permeability Curves
Effective & Relative Permeability Curves
Questions
Questions?
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