reservoir rock and fluid properties ii

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;

VPVP 2211

VPVP 22

(1)

(2)

At Time 1 --

At Time 2 --


Helium Porosimeter

In case of a porous plug:

VVVV pb 1

(3)

PPP TT 21 (4)

VPVVVPP pb 22121 (5)


Helium Porosimeter

Then the pore volume;

(6)

PPVP

VVV bp

21

22

1

VPP

VPV

b

21

22

1

1

(7)


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


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



i core measurement


i

n

i

ii

ah

h1

Areal Weighted Average Porosity

a

i

th



i core measurement


i

n

i

ii

aA

A1

Volumetric Weighted Average Porosity

a

i

th



i core measurement


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?


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


Fluid Saturations


Average 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

VV

Sp

o

o

VV

Sp

w

w

VV

Sp

g

g

Oil Saturation

Water Saturation

Gas Saturation


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


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

3. Weight of oil

4. Volume of oil


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


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

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

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


P

L

q A

Flowing fluid is 100% saturating the medium

L

PkAq

m Absolute permeability

Effective Permeability


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


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


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.


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


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


Two phase relative permeability behavior with respect to wetting phase saturation

krnw krw

Sw

1.0 1.0

Swmin Swmax

0 1


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)


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

Questions

Questions?

reservoir rock and fluid properties ii

Documents