Basic Reservoir Engineering - Part I

8/16/2019 Basic Reservoir Engineering - Part I

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GEOPET BACHELOR PROGRAM IN

PETROLEUM ENGINEERING

BASIC RESERVOIRENGINEERING

3/18/2013 1Mai Cao Lân – Faculty of Geology & Petroleum Engineering - HCMUT


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Learning Objectives

At the end of this lecture, you should be able to understand the

fundamentals of reservoir engineering and do some basic

analyses/calculations as follows:

PVT Analysis

Special Core Analysis

Well Test Analysis

Production Forecast



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References

1. L.P.Dake (1978). Fundamentals of Reservoir Engineering,

Elsevier Science, Amsterdam.

2. L.P.Dake (1994). The Practice of Reservoir Engineering,

Elsevier Science, Amsterdam.

3. B.C.Craft & M.Hawkins (1991). Applied Petroleum

Reservoir Engineering,Prentice Hall, New Jersey.

4. T. Ahmed (2006). Reservoir Engineering Handbook , Gulf

Professional Publishing, Oxford.



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Outline

Key Concepts in Reservoir Engineering

Fundamentals of Oil & Gas Reservoirs

Quantitative Methods in Reservoir Characterization and

Evaluation.



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Part I


Key Concepts in

Reservoir Engineering


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Definition of Reservoir


In petroleum industry, reservoir fluids is a mixture ofhydrocarbons (oil and/or gas), water and other non-hydrocarboncompounds (such as H2S, CO2, N2, ...)


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Definition of Engineering

Engineering is the discipline or profession of

applying necessary knowledge and utilizing

physical resources in order to design and

implement systems and processes that realize a

desired objective and meet specified criteria.



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Engineering is the discipline and profession of







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Necessary Knowledge

Knowledge about oil & gas reservoirs

Reservoir Rock Properties & Behavior during the

Production Process

Reservoir Fluid Properties & Behavior during the

Production Process

Fluid Flows in Reservoirs



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Necessary Knowledge (cont’d)

Technical & Scientific Knowledge

Quantitative Methods for Reservoir

Characterization

Quantitative Methods for Reservoir

Evaluation



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Physical Resources

In-place Reservoir Resources

Reservoir’s energy source resulted from the

initial pressure & drive mechanisms during

production

Available flow conduits thanks to reservoir’s

characteristic properties such as permeability

distribution.



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Design and Implementation

Design and Implement an Oil Field Development Plan

Plan for producing oil & gas from the reservoirs in the

field: Exploit reservoir energy sources; Design

appropreate well patterns; Select suitable subsurface &

surface facilities ... during the lifecycle of the oil field



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Desired Objective

To Maximize the profit resulted from the

recovered oil & gas

To recover as much as possible oil & gas from

the reservoirs

To recover high-quality oil & gas



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Specified Criteria

Money associated with hired manpower,

facilities, technologies, ...

Time

Local regulations



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Oil Fields and Their Lifecycle



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Oil Fields and Their Lifecycle

A lifecycle of an oil field consists of the following stages:

Exploration

Appraisal

Development

Production

Abandonment



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Revenue Throughout LifeCycle



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Part II


Basic Properties and

Behaviors of

Oil & Gas Reservoirs


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Five Basic

Reservoir

Fluids

Black Oil

Criticalpoint

P r e s s u r e , p s i a

Separator

Pressure pathin reservoir Dewpoint line

% Liquid

Temperature, °F

P r e s s u r e

Temperature

Separator

% Liquid

Volatile oil

Pressure pathin reservoir

3

2

1

3

Criticalpoint

3

Separator

% Liquid


1

2Retrograde gas

Critical

point P r e s s u r e

Temperature

P r e s s u

r e

Temperature

% Liquid

2

1


Wet gas

Criticalpoint

Separator

P r e s s u r e

Temperature

% Liquid

2

1


Dry gas

Separator

Retrograde Gas Wet Gas Dry Gas

Black Oil Volatile Oil


Classification of Reservoir Fluids


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Used to visualize the fluids production path from

the reservoir to the surface

Used to classify reservoir fluids

Used to develop different strategies to produce

oil/gas from reservoir

Pressure-Temperature Diagrams



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Phase Diagrams

Single

Liquid

Phase

Region

CriticalPoint

P r e s s u r e , p s i a

InitialReservoir

State

% Liquid

Temperature, °F

Cricondentherm


Separator

Cricondenbar

Single

Gas

Phase

Region

Two-Phase

Region


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Black Oil

Black Oil

CriticalPoint

P r e s s u r e ,

p s i a

Separator


Dewpoint line

% Liquid

Temperature, °F



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Volatile-Oil

P r e s s u

r e

Temperature, °F

Separator

% Liquid

Volatile oil


2

1

3

Criticalpoint



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Retrograde Gas

3

Separator

% Liquid

Pressure path

in reservoir1

2Retrograde gas

Critical point

P r e s s u r

e

Temperature



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Wet Gas

P r e s s u r e

Temperature

% Liquid

2

1

Pressure path

in reservoir

Wet gas

Criticalpoint

Separator



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Dry Gas

P r e s s u

r e

Temperature

% Liquid

2

1

Pressure path

in reservoir

Dry gas

Separator



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Field Identification

Black

Oil

Volatile

Oil

Retrograde

Gas

Wet

Gas

Dry

Gas

Initial Producing

Gas/Liquid

Ratio, scf/STB

3200 > 15,000* 100,000*

Initial Stock-

Tank Liquid

Gravity, API

< 45 > 40 > 40 Up to 70 No

Liquid

Color of Stock-

Tank Liquid

Dark Colored Lightly

Colored

Water

White

No

Liquid

*For Engineering Purposes



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Laboratory Analysis

Black

Oil

Volatile

Oil

Retrograde

Gas

Wet

Gas

Dry

Gas

Phase

Change in

Reservoir

Bubblepoint Bubblepoint Dewpoint No Phase

Change

No

Phase

ChangeHeptanes

Plus, Mole

Percent

> 20% 20 to 12.5 < 12.5 < 4* < 0.8*

Oil

Formation

VolumeFactor at

Bubblepoint

< 2.0 > 2.0 - - -

*For Engineering Purposes



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0

50000

0 30

Heptanes plus in reservoir f luid, mole %

I n i t i a l p r o d

u c i n g

g a s / o i l r

a t i o ,

s c f / S T B

Dewpoint gas

Bubblepoint oil

Retrograde

gas

Volatile

oil

Wet

gas

Dry

gas

Blackoil


Field Identification


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34 Flui

Primary Production Trends

G O R

G O R

G O R

G O R

G O R

Time Time Time

TimeTime TimeTimeTime

TimeTime

No

liquid

No

liquid

Dry

Gas

Wet

Gas

Retrograde

Gas

Volatile

Oil

Black

Oil

A P I

A P I

A P I

A P I

A P I


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Exercise 1

Based on the phase diagrams of volatile oil

and retrograde gas, describe some

characteristic properties of these two

reservoir fluids

Name some applications of phase diagrams

in selecting surface facilities



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Basic Properties of Natural Gas


Equation-of-State (EOS)

Apparent Molecular Weight of Gas Mixture

Density of Gas Mixture

Gas Specific Gravity

Z-factor (Gas Compressibility or Gas Deviation

Factor)

Isothermal Compressibility

Gas Formation Volume Factor

Gas Viscosity


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Gas Equation-Of-State (EOS)


pV nZRT =Equation of State:

Quantity Description Unit/Value

p Pressure psia

V Volume ft3

n Mole Number lb-mol

Z Gas Deviation

Factor

dimensionless

T Temperature Rankine

R Universal Gas

constant

10.73

psia.ft3 /lb-mole. °R

Apparent Molecular Weight of a


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Apparent Molecular Weight of aGas Mixture


Normally, petroleum gas is a mixture of variouslight hydrocarbon (C1-C4). For example:

Component Mole Percent MolecularWeight

(lb/lb-mol)

Critical Critical

Pressure Temperature

(psia) (o

R) (1) (2) (3) (4)

C1 0.85 16.043 666.4 343.00

C2 0.04 30.070 706.5 549.59

C3 0.06 44.097 616.0 665.73

iC4 0.03 58.123 527.9 734.13 nC4 0.02 58.123 550.6 765.29

1

20.39 N

a i i

i

M y M =

= =∑


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Density of Gas Mixture


Gas density is calculated from the definition ofdensity and the EOS

3 pM= = (lb/ft )g a a

g

g

m nM p

V nZRT ZRT ρ =


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Gas Specific Gravity


The specific gravity is defined as the ratio of thegas density to that of the air

M= =

28.97

g a a

g

air air

M

M

ρ γ

ρ =


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Gas Deviation Factor (Z-factor)


Z-factor in the EOS accounts for the difference inthe behavior of natural gases in compared with idealgases.

; pr pr

pc pc

p T p T

p T = =

Z-factor can be expressed as: Z=Z(ppr,Tpr) where

; pc i ci pc i ci

i i

p y p T y T = =∑ ∑

ppr: pseudo-reduced pressureTpr: pseudo-reduced temperatureppc: pseudo-critical pressureTpc: pseudo-critical temperature


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Standing-Katz Chart


Step 1: Calculate pseudo-criticalpressure and temperature

Step 2: Calculate pseudo-reducedpressure and temperature:

Step 3: Use Standings-Katz chartto determine Z

; pr pr

pc pc

p T p T

p T = =

; pc i ci pc i ci

i i

p y p T y T = =∑ ∑

Dranchuk & Abou-Kassem


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Dranchuk & Abou-KassemCorrelation


7210.0;6134.0

1056.0;1844.0;7361.0

5475.0;05165.0;01569.0

5339.0;0700.1;3265.0

1110

987

654

321

==

==−=

=−==−=−==

A A

A A A

A A A

A A A

2 5 2 2 22

1 3 4 5 11 11

3 4 5

1 1 2 3 4 5

2

2

3 6 7 8

2

4 9 7 8

3

5 10

( ) (1 ) exp( ) 1 0

0.27 / ( )

/ / / /

0.27 /

/ /

( / / )

/

r r r r r r r r

r pr pr

pr pr pr pr

pr pr

pr pr

pr pr

pr

RF R R R R A A

p ZT

R A A T A T A T A T

R p T

R A A T A T

R A A T A T

R A T

ρ ρ ρ ρ ρ ρ ρ ρ

ρ

= − + − + + − + =

=

= + + + +

=

= + +

= +

=


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Exercise 2

Component yi Mi Tci,°R pci

CO2 0.02 44.01 547.91 1071

N2 0.01 28.01 227.49 493.1

C1 0.85 16.04 343.33 666.4

C2 0.04 30.1 549.92 706.5

C3 0.03 44.1 666.06 616.4

i - C4 0.03 58.1 734.46 527.9

n - C4 0.02 58.1 765.62 550.6



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Wichert-Aziz Correction Method

R , oε −= pc pc T T

2 2

, psia(1 )

pc pc

pc

pc H S H S

p T p

T y y ε =

+ −

Corrected pseudo-critical temperature:

Corrected pseudo-critical pressure:

( ) ( )( ) ( )2 2 2 2 2 20.9 1.6

0.5 4.0120 15 , H S CO H S CO H S H S y y y y y yε = + − + + −

Pseudo-critical temperature adjustment factor



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Exercise 3

Component Mole fraction

C1 0.76

C2 0.07CO2 0.1

H2S 0.07

Given the following real gas composition,

Determine the density of the gas mixture at 1,000psia and 110 °F using Witchert-Aziz correctionmethod.



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Sutton Correction Method

20.5

o

o

1 2, R/psia

3 3

, R/psiai

i

c ci i

i ic ci i

c

i

i c

T T J y y

p p

T K y

p

= +

=

∑ ∑

∑

Step1: Calculate the parameters J and K:

7 7

7 7

7 7 7

7

20.5

2 2

2 3

1 2

3 3

0.6081 1.1325 14.004 64.434

0.3129 4.8156 27.3751

c c J

c c

C C

J J J J C J C

cK C C C

c C

T T F y y

p p

F F F y F y

T y y y

p

ε

ε

+ +

+ +

+ + +

+

= +

= + − +

= − +

Step 2: Calculate the adjustment parameters:


S C i M h d ( )


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Sutton Correction Method (cont.)

K

J

K K

J J

ε

ε

−=

−=Step 3: Adjust the parameters J and K

J T p

J

K T

pc pc

pc

=

=2

Step 4: Calculate the adjusted pseudo-criticalterms


Correlations for Pseudo Properties


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Correlations for Pseudo Propertiesof Real Gas Mixture


Isothermal Compressiblity of


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Isothermal Compressiblity ofNatural Gas Mixture

1 d

d g

V c

V p= −

By definition, the compressibility of the gas is

1 1g

T

dzc

p z dp

= −

Isothermal pseudo-reduced compressibility:


or

1 1 d

d pr

pr g pc pr pr T

z

c c p p z p

= = −

Gas Isothermal Compressiblity Correlation by


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Gas Isothermal Compressiblity Correlation by

Matter, Brar & Aziz (1975)

2

1 0.27

1

pr

pr

r T

g

pr pr r

r T

dz

d c

p z T dz

z d

ρ

ρ

ρ

= −

+


( ) ( )4 2 2 4 21 2 3 4 8 8 82 5 2 1 exp pr

r r r r r r

r T

dzT T T T A A A

d ρ ρ ρ ρ ρ ρ

ρ = + + + + − −

3 521 1 2 43

5 6 73 4 53

;

0.27; ;

pr pr pr

pr

pr pr pr

A A AT A T A

T T T p A A A

T T T T T T

= + + = +

= = =

A1 0.3150624 A5 -0.61232032

A2 -1.04671 A6 -0.10488813

A3 -0.578327 A7 0.68157001

A4 0.5353077 A8 0.68446549

G F i V l F


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Gas Formation Volume Factor

, p T

g

sc

V B

V =

By definition, the gas FVF is

Combining the above equation with the EOS yields


30.02827 (ft /scf)

0.005035 (bbl/scf)

g

g

zT B

p

zT B p

=

=

Gas Viscosity Correlation Method by


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Gas Viscosity Correlation Method byCarr, Kobayashi and Burrows (1954)

Step 1: Calculate pseudo-critical properties and thecorrections to these properties for the presence ofnonhydrocarbon gases (CO2, H2S, N2)


Step 2: Obtain the (corrected) viscosity of the gas

mixture at one atmosphere and the temperature ofinterest

2 2 21 1uc N CO H S µ µ µ µ µ = + ∆ + ∆ + ∆

Step 3: Calculate the pseudo-reduced pressure and

temperature, and obtain the viscosity ratio (µg /µ1)

Step 4: Calculate the gas viscosity from µ1 and theviscosity ratio (µg /µ1)

Carr’s Atmospheric Gas Viscosity


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Carr s Atmospheric Gas ViscosityCorrelation


G Vi it R ti C l ti


55/90

Gas Viscosity Ratio Correlation


Standing’s Correlation for


56/90

Standing s Correlation for Atmospheric Gas Viscosity

( )

( )5 6

1

3 3

1.709 10 2.062 10 460

8.118 10 6.15 10 log

uc g

g

T µ γ

γ

− −

− −

= × − × − +

× − × ×


( )2 2

2 2

2 2

3 3

3 3

3 3

9.08 10 log 6.24 10

8.48 10 log( ) 9.59 10

8.49 10 log( ) 3.73 10

CO CO g

N N g

H S H S g

y

y

y

µ γ

µ γ

µ γ

− −

− −

− −

∆ = × × + × ∆ = × × + ×

∆ = × × + ×

2 2 21 1uc CO N H S µ µ µ µ µ = + ∆ + ∆ + ∆

Dempsey’s Correlation for Gas


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e psey s Co e at o o GasViscosity Ratio

2 3

0 1 2 3

1

2 3

4 5 6 7

2 2 3

8 9 10 11

3 2 3

12 13 14 15

ln g

pr pr pr pr

pr pr pr pr

pr pr pr pr

pr pr pr pr

T a a p a p a p

T a a p a p a p

T a a p a p a p

T a a p a p a p

µ

µ

= + + + +

+ + + +

+ + + +

+ + +


a0 = −2.46211820 a1 = 2.970547414a2 = −2.86264054 (10−1)a3 = 8.05420522 (10−3)a4 = 2.80860949a5 = −3.49803305

a6 = 3.60373020 (10−1)a7 = −1.044324 (10−2)a8 = −7.93385648 (10−1)a9 = 1.39643306a10 = −1.49144925 (10−1)a11 = 4.41015512 (10−3)

a12 = 8.39387178 (10−2)a13 = −1.86408848 (10−1)a14 = 2.03367881 (10−2)a15 = −6.09579263 (10−4)


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Exercise 4

A gas well is producing at a rate of 15,000 ft3/dayfrom a gas reservoir at an average pressure of 2,000psia and a temperature of 120°F. The specificgravity is 0.72.

Calculate the vicosity of the gas mixture using bothgraphical and analytical methods.



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Properties of Crude Oil


Oil density and gravity

Gas solubility

Bubble-point pressure

Oil formation volume factor

Isothermal compressibility coefficient of

undersaturated crude oils

Oil viscosity

These fluid properties are usually determined by laboratoryexperiments. When such experiments are not available,empirical correlations are used


60/90

Crude Oil Density


The crude oil density is defined as the mass of aunit volume of the crude oil at a specifiedpressure and temperature.

3 (lb/ft )oo

o

m

V ρ =

d l


61/90

Crude Oil Gravity


The specific gravity of a crude oil is defined as theratio of the density of the oil to that of water.

oAPI is usually used to reprensent the gravity ofthe crude oil as follow

3; 62.4 (lb/ft )oo ww

ρ γ ρ

ρ = =

141.5 -131.5o

o

API γ

=

The API gravity of crude oils

usually ranges from 47° API forthe lighter crude oils to 10° APIfor the heavier crude oils.

l k il d l


62/90

Black Oil Model


G S l bili R


63/90

Gas Solubility Rs


Rs is defined as the number of standard cubic feetof gas dissolved in one stock-tank barrel of crudeoil at certain pressure and temperature.

The solubility of a natural gas in a crude oil is a

strong function of the pressure, temperature, APIgravity, and gas gravity.


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Standing’s Correlation for R


65/90

Standing s Correlation for Rs


( )

1.2048

1.4 1018.2

0.0125 0.0009 460

x

s g

p

R

x API T

γ

= + ×

= × − × −

Ch t i ti f R i R k


66/90

Characteristics of Reservoir Rocks


Porosity

Permeability

In-situ Saturation

P it


67/90

pore bulk matrix

bulk bulk

V V V

V V φ −

= =

Porosity


P it


68/90

Porosity

Porosity depends on grain packing, NOT grain size

Rocks with different grain sizes can have the sameporosity

• Rhombohedral packing

• Pore space = 26 % of total volume• Cubic packing

• Pore space = 47 % of total volume



69/90

Rock Matrix and Pore Space

Rock matrix Pore space


P S Cl ifi ti


70/90

Pore-Space Classification

Total porosity

Effective porosity

Total Pore Space

Bulk Volume

pore

t

bulk

V

V

φ = =

Interconnected Pore SpaceBulk Volume

eφ =


bili


71/90

Permeability is a property of the porous

medium and is a measure of the capacity of

the medium to transmit fluids

Permeability



72/90


73/90

R l i P bili


74/90

Relative permeability is defined as the ratio

of the effective permeability to a fluid at a

given saturation to the effective permeability

to that fluid at 100% saturation

Relative Permeability



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Darcy’s Law


76/90

Darcy s Law

v: Velocity

q: Flow rate

A: Cross-section areak: Permeability

µ: Viscosity∆L: Length increment

∆p: Pressure drop

q

Direction of flow A

q k pv

A Lµ

∆≡ = − ×

∆


Fluid Saturation


77/90

Fluid Saturation

Fluid saturation is defined as the fraction of porevolume occupied by a given fluid

Phase saturations

Sw = water saturation

So = oil saturationSg = gas saturation

specific fluid

poreSaturation

V

V =


I Sit S t ti


78/90

In-Situ Saturation

Rock matrix Water Oil and/or gas


Exercise 5


79/90

Exercise 5

1. Pore volume occuppied by water

2. Pore volume occupied by hydrocarbon


Given the following reservoir data:

Bulk Volume Vb

Porosity

Water saturation Sw

Calculate:

Reservoir Drive Mechanisms


80/90

Reservoir Drive Mechanisms

Solution Gas Drive

Gas Cap Drive

Water Drive

Gravity drainage drive

Combination drive


Reservoir Energy Sources


81/90

Reservoir Energy Sources

Liberation, expansion of solution gas

Influx of aquifer water

Expansion of reservoir rock

Expansion of original reservoir fluids

Free gas

Connate water

Oil

Gravitational forces

Solution-Gas Drive in Oil Reservoirs


82/90

Solution-Gas Drive in Oil Reservoirs

Oil

A. Original Condition

B. 50% Depleted

Oilproducing

wells

Oilproducing

wells


Solution-Gas Drive in Oil ReservoirsF i f S d G C


83/90

Formation of a Secondary Gas Cap

Wellbore

Secondarygas cap


Gas Cap Drive in Oil Reservoirs


84/90

Oil producing well

Oilzone

OilzoneGas cap

Gas-Cap Drive in Oil Reservoirs


Water Drive in Oil Reservoirs


85/90

Oil producing well

Water Water

Cross Section

Oil Zone

Edgewater Drive


Water Drive in Oil Reservoirs


86/90

Oil producing well

Cross Section

Oil Zone

Water

Bottomwater Drive


Gravity Drainage Drive in OilR i


87/90

Reservoirs

Oil

Oil

Oil

Point A

Point B

Point C

Gas

Gas

Gas


Combination Drive in Oil Reservoirs


88/90

Combination Drive in Oil Reservoirs

Water

Cross Section

Oil zone

Gas cap


Pressure and Gas/Oil Ratio Trends


89/90

Pressure and Gas/Oil Ratio Trends

0 20 40 60 80 100

100

80

60

40

20

0

Gas-cap drive

Water drive

Solution-gas drive

R

e s e r v o i r p r e

s s u r e ,

P e r c e n t o f o r

i g i n a l

Cumulative oil produced, percent of original oil in place


Exercise 6


90/90

Exercise 6

1. How can we identify different reservoir drive

mechanisms?

2. Rank in descending order typical reservoir drivemechanisms in terms of efficiency

3. How does knowledge about reservoir drive mechanisms

help us in designing an oil field development plan?

Basic Reservoir Engineering - Part I

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