Reservoir Rock and Fluid Properties II.pdf

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


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)


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


Porosity Measurement Tools

Helium Porosimeter Boyle’s law: Under isothermal conditions;

At Time 1 -At Time 2 --

P1V 1 

PV P V  P V 2

2

2


(1)

2

(2)

Helium Porosimeter In case of a porous plug:

V



 V 1  V b V p

P P  P V  V 1



2

1



(3)

PT1  PT 2 

  b V p


(4)

PV 2

(5) 2

Helium Porosimeter Then the pore volume;

  V P 2 2     V p V b V 1 P1 P2     V P 2 2  V 1   P 1  P2     1

V


b

(6)

(7)

Saturation (Imbibition) 1. Weigh dry core sample

Wd

2. Measure bulk volume

Vb

Water in

3. Saturate the sample 4. Weigh saturated core sample

5. Calculate pore volume

Ww

W Vp w



Vacuum

W d water

6. Calculate porosity ( Assuming density of water = 1)

W W    w

d

V

b

water



W W  w

V

d

b


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 1     F

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.

TL  TM 1     TF

TL  TM  TF  TM

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.

n

a 

 i 1

i

n

a is the mean porosity i is the porosity of the i th core measurement n the number of measurements

Thickness weighted Average Porosity n

a

 h  h i 1

i i

i


Areal Weighted Average Porosity

n

a

 A  A i 1

i

i

i


Volumetric Weighted Average Porosity n

a

 h A  h A i 1

i i

i

i

i


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?


Fluid Saturations Defined as the fraction of pore volume occupied by a given fluid



S w, o , g 

Vw,o, g V pore space

S w  water saturation S o  oil saturation S g  gas saturation S h  So  S g

   

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, Pct Reservoir Rock and Fluid Properties, 2008

Fluid Saturations


Fluid Saturations


Fluid Saturations


Average Fluid Saturations


Fluid Saturations


Fluid Saturations


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

Oil Saturation

Vo  So V V  S V V  S V

p

Water Saturation Gas Saturation Reservoir Rock and Fluid Properties, 2008

w

w

p

g

g

p

Saturations 1.

2.

3.

Mass of water collected from the sample is calculated as

M



V

w

w

Mass of oil removed from the core is computed as the mass of liquid less weight of water

M

o

 MLMw

Oil volume is computed as

V 4.

w

o



Mo

o

Oil Saturation can then be determined with the formula

S V V o

o

S S S o

w

g

p

1


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


Solution 2 1. Weight of water 2. Weight of liquid

W

w



W W L

V

w

or

w

 1 x 3  3.0 gm

W d  20.0  14.0  6.0 gm

3. Weight of oil 4. Volume of oil

W  W W o

L

w

 6.0  3.0  3.0 gm

3.0  4.0cc V o  W o o  0.75 Reservoir Rock and Fluid Properties, 2008

Solution 2, continued 5.

Bulk volume of the core plug

5.

Pore volume of the core plug

6.

7. 8.

Water Saturation

Vb  πr L  2

3       30 . 40 0 . 26  7 . 9 cm V p Vb

Vw   Sw

Oil Saturation Gas Saturation

V

p

Vo   So V

S

g

 1

2.54 2 6  30.40cm 2

p

3.0  0.38 7.9 4.0  0.51 7.9

S  S   1  0.38  0.51  0.11 o

w


3

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 Air

OIL









WATER

 < 90

SOLID (ROCK)

FREE WATER

OIL

Oil

WATER

WATER

WATER

 > 90

SOLID (ROCK)

OIL GRAIN

GRAIN

OIL RIM BOUND WATER

FREE WATER Ayers, 2001

Effective & Relative Permeability Curves


Rock Compressibility
















LESSON OUTCOME 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 First introduced by Darcy in 1856 while investigating the flow of water through sand filters for water purification.

h h Q  KA 1

2

L

Constant of proportionality and for viscous fluids;

K

k

permeability

m viscosity

Permeability  Darcy’s Law

kAP Q mL Q  flowrate in cm3 /sec A  cross sectional area of flow in cm 2 P  pressure difference across ther sample, atmos. m  viscosity in centipoise L  length of sample in cm. k  permeability in Darcy

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 Taking viscosity as a variable

Qk

A  h1  h 2  mL

Poiseuille equation for laminar pipe flow

r P Q 8mL 4

r = radius of pipe of length L

Carmen Kozeny equation for flow in packed beds

 d 23  1 dP  u  ' 2  k 1     m dL  

k’ = shape factor d = particle size There is a very strong relationship between porosity and permeability

Permeability  Comparing equations.

Q P k A mL

Darcy

Carmen Kozeny

 d 23  1 dP Q  u  ' 2  k 1     m dL A  

It is not surprising therefore that there is a strong relationship between permeability and porosity

k

d 2 3 k 1    '

2

Porosity vs Permeability

Porosity is independent of grain size. Porosity is generally unaffected by grain size but permeability increases with increasing grain size.

Porosity vs Permeability The better sorted the sand, the higher are both the porosity and 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 106 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 L that:

q

A

dx

kA dp q m dx

Flow rate (1 cm3/s) Cross sectional area (1 cm2) Viscosity of flowing fluid (1 cp) Permeability ( 1 Darcy) Pressure gradient (1 atm/cm)

Types of Permeability • Absolute Permeability • Effective Permeability

• Relative Permeability

Absolute Permeability P

Flowing fluid is 100% saturating the medium

q A

kA P q m L Reservoir Rock and Fluid Properties, 2007

L Absolute permeability

Effective Permeability P More than one fluid is saturating the medium. Only one of them is mobile (flowing)

A

k i A P qi  mi L


qg qo qw L Effective permeability

Relative Permeability P More than one fluid is saturating the medium. At least two of them are mobile (flowing)

A

k ri A P qi  mi L


qg qo qw L Relative permeability

k ri 

k k

i

Relative Permeability Two phase relative permeability behavior

kro

krw

0

Sw

1

Permeability  From the Darcy’s Law equation, permeability is defined

qm k A(dP / dx)

 Basic linear and radial flow can be derived  General classification of permeability 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

Series Flow

Arithmetic Average

Random Flow

Harmonic Average h1



h3

k2

k1

k2

k3

L2

L3

k3

kA

kh   h

i i i



kG  k1 k2 k3 .......

h2

k1

Geometric Average

L1

kH

L   L /k i

i

i

h1

h2

h3

1  hi

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: P Darcy’s equation for horizontal flow:

kA P1  P2  q mL

Solving for permeability,

qmL k A P1  P2 

q A

L UNITS: k= Darcy

A= cm2

q= cm3/sec

m= cp

P= psi

L= cm

Solution 1: P= 3 atm

qmL k A P1  P2 

q= 100 cm3/hr A=22

L= 20 cm

 cc  1hr   100 hr  3600 sec   2cp 20cm     k  0.0295darcy 2 2  2 cm 3atm 





k  29.5md

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 ko A P qo  mo L

k w A P qw  mw L

qg 

k g A P

mg L

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.

Relative Permeability P More than one fluid is saturating the medium. At least two of them are mobile (flowing)

A

k ri kA P qi  mi L

qg qo qw L Relative permeability

k ri 

k k

i

Relative Permeability Two phase relative permeability behavior with respect to wetting phase saturation 1.0

1.0

krnw

Swmin

krw

0

Sw

1

Swmax

Relative Permeability Oil-Water relative permeability behavior with respect to Water saturation 1.0

1.0

kro

krw

0

Swc

Sw

1-Sor

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:

k i A P qi  mi L qo ( 3 )( 20 ) ko   1.59qo 2 ( 3 )( 2  ) P, atm

 t, sec

Vo, cc

VW, cc

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

qo, cc/s

qw ( 1 )( 20 ) kw   0.53qw 2 ( 3 )( 2  ) qw, cc/s

ko, md

kw, md

kro

krw

Solution 3:

k i A P qi  mi L qo ( 3 )( 20 ) ko   1.59qo 2 ( 3 )( 2  )

qw ( 1 )( 20 ) kw   0.53qw 2 ( 3 )( 2  )

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

3

10

0

0.9

0

0.09

0

0.0477

0.0000199 0.0005896 0

0.0005963

MULTIPHASE FLOW 2.0 2.1 2.2 2.3 2.4 2.5 2.6

Introduction Absolute & Effective Permeability Relative Permeability Hysterisis Mobility Fractional Flow 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

 If 2 fluids are present and flowing simultaneously. Effective Permeability  Defined for each fluid.  Depend on each fluid saturation.

Effective Permeability to Water = Effective Permeability to Oil =

ko

kw

Effective Permeability Curve absolute permeability k

ko

0

k

Water Curve: kw = 0 at Swc kw = 1 at 100% water saturation

kw

Oil Curve: ko = 0 at Sw=1-Sor ko = k at 100% oil saturation

0

Swc 0 1

1- Sor 1

Sw So

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)

Water Relative Permeability   

kw k rw  k

Oil Relative Permeability

ko k ro  k

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 End point (indicator of wettability)

absolute permeabilit y

k

k

1

1 k’ro

ko

kw

0

0

0

Swc 1

Sw So

0

krw

0

1- Sor

Swc 0 1

k’rw

kro

0 1

1- Sor 1

Sw So

0

Wettability effect on the curves Water Wet

Oil Wet 1

1

kro

krw

0

0

Swc 0 1

kro

krw

0

0

Swc

1- Sor 1

Sw So

1

1

0

0 1

1- Sor 1

Sw So

0



Questions

Questions?

Reservoir Rock and Fluid Properties II.pdf

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