Basic Reservoir Engineering - Mai Cao Lan

GEOPET BACHELOR PROGRAM INPETROLEUM ENGINEERING

BASIC RESERVOIR

ENGINEERING

5/2/2013 1Mai Cao Lân – Faculty of Geology & Petroleum Engineering - HCMUT

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


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.


Outline

Key Concepts in Reservoir Engineering

Fundamentals of Oil & Gas Reservoirs

Quantitative Methods in Reservoir Characterization and

Evaluation.


Part I


Key Concepts in

Reservoir Engineering

Definition of Reservoir


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

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.



Engineering is the discipline and profession of






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


Necessary Knowledge (cont’d)

Technical & Scientific Knowledge

Quantitative Methods for Reservoir

Characterization

Quantitative Methods for Reservoir

Evaluation









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.









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









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









Specified Criteria

Money associated with hired manpower,

facilities, technologies, ...

Time

Local regulations


Oil Fields and Their Lifecycle


Oil Fields and Their Lifecycle

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

Exploration

Appraisal

Development

Production

Abandonment


Revenue Throughout LifeCycle


Part II


Basic Properties and

Behaviors of

Oil & Gas Reservoirs

Five Basic Reservoir Fluids

Black Oil

Criticalpoint

Pre

ss

ure

, p

sia

Separator

Pressure pathin reservoir Dewpoint line

% Liquid

Temperature, °F

Pre

ss

ure

Temperature

Separator

% Liquid

Volatile oil

Pressure pathin reservoir

3

2

1

3

Criticalpoint

3

Separator

% Liquid


1

2Retrograde gas

Critical

pointPre

ss

ure

Temperature

Pre

ss

ure

Temperature

% Liquid

2

1


Wet gas

Criticalpoint

Separator

Pre

ss

ure

Temperature

% Liquid

2

1


Dry gas

Separator

Retrograde Gas Wet Gas Dry Gas

Black Oil Volatile Oil


Classification of Reservoir Fluids

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


Phase Diagrams

Single

Liquid

Phase

Region

CriticalPoint

Pre

ssu

re,

psia

Initial Reservoir

State

% Liquid

Temperature, °F

Cricondentherm


Separator

Cricondenbar

Single

Gas

Phase

Region

Two-Phase

Region

Black Oil

Black Oil

CriticalPoint

Pre

ssu

re,

psia

Separator


Dewpoint line

% Liquid

Temperature, °F


Volatile-Oil P

ressu

re

Temperature, °F

Separator

% Liquid

Volatile oil


2

1

3

Criticalpoint


Retrograde Gas

3

Separator

% Liquid


1

2Retrograde gas

Critical point

Pre

ssu

re

Temperature


Wet GasP

ressu

re

Temperature

% Liquid

2

1


Wet gas

Criticalpoint

Separator


Dry GasP

ressu

re

Temperature

% Liquid

2

1


Dry gas

Separator


Field Identification

Black Oil

Volatile Oil

Retrograde Gas

Wet Gas

Dry Gas

Initial Producing Gas/Liquid Ratio, scf/STB

<1750 1750 to 3200

> 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


Laboratory Analysis

Black Oil

Volatile Oil

Retrograde Gas

Wet Gas

Dry Gas

Phase Change in Reservoir

Bubblepoint Bubblepoint Dewpoint No Phase Change

No Phase

Change Heptanes Plus, Mole Percent

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

Oil Formation Volume Factor at Bubblepoint

< 2.0 > 2.0 - - -

*For Engineering Purposes


0

50000

0 30Heptanes plus in reservoir fluid, mole %

Init

ial p

rod

uc

ing

gas/o

il r

ati

o, scf/

ST

B

Dewpoint gas

Bubblepoint oil

Retrograde

gas

Volatile

oil

Wet

gas

Dry

gas

Black

oil


Field Identification

34Flui

ds & Fluid

Primary Production TrendsG

OR

GO

R

GO

R

GO

R

GO

R

Time Time Time

TimeTimeTimeTimeTime

TimeTime

No

liquid

No

liquid

Dry

Gas

Wet

Gas

Retrograde

Gas

Volatile

Oil

Black

Oil

A

PI

A

PI

A

PI

A

PI

A

PI

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


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

Gas Equation-Of-State (EOS)


pV nZRTEquation 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 Gas Mixture


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

Component Mole PercentMolecular Weight

(lb/lb-mol)

Critical Critical

Pressure Temperature

(psia) (oR)

(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

20.39N

a i i

i

M y M

Density of Gas Mixture


Gas density is calculated from the definition of density and the EOS

3pM= = (lb/ft )

g a ag

g

m nM p

V nZRT ZRT

Gas Specific Gravity


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

M= =

28.97

g a ag

air air

M

M

Gas Deviation Factor (Z-factor)


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

;pr pr

pc pc

p Tp 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 yT

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

Standing-Katz Chart


Step 1: Calculate pseudo-critical pressure and temperature

Step 2: Calculate pseudo-reduced pressure and temperature:

Step 3: Use Standings-Katz chart to determine Z

;pr pr

pc pc

p Tp T

p T

;pc i ci pc i ci

i i

p y p T yT

Dranchuk & Abou-Kassem Correlation


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

AA

AAA

AAA

AAA

2 5 2 2 221 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

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


Wichert-Aziz Correction Method

R , o pcpc TT

2 2

, psia(1 )

pc pc

pc

pc H S H S

p Tp

T y y

Corrected pseudo-critical temperature:

Corrected pseudo-critical pressure:

2 2 2 2 2 2

0.9 1.60.5 4.0120 15 ,H S CO H S CO H S H Sy y y y y y

Pseudo-critical temperature adjustment factor


Exercise 3

Component Mole fraction

C1 0.76

C2 0.07

CO2 0.1

H2S 0.07

Given the following real gas composition,

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


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 TJ y y

p p

TK y

p

Step1: Calculate the parameters J and K:

77

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 cJ

c cC C

J J J J C J C

cK C C C

c C

T TF y y

p p

F F F y F y

Ty y y

p

Step 2: Calculate the adjustment parameters:


Sutton Correction Method (cont.)

K

J

KK

JJ

Step 3: Adjust the parameters J and K

J

Tp

J

KT

pc

pc

pc

2

Step 4: Calculate the adjusted pseudo-critical terms


Correlations for Pseudo Properties of Real Gas Mixture


Isothermal Compressiblity of Natural Gas Mixture

1 d

dg

Vc

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

dpr

pr g pc

pr pr T

zc c p

p z p

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

dc

p z T dz

z d


4 2 2 4 2

1 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

3 521 1 2 43

5 6 73 4 53

;

0.27; ;

pr pr pr

pr

pr pr pr

A AAT A T A

T T T

pA A AT 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

Gas Formation Volume Factor

,p T

g

sc

VB

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

zTB

p

zTB

p

Gas Viscosity Correlation Method by Carr, Kobayashi and Burrows (1954)

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


Step 2: Obtain the (corrected) viscosity of the gas mixture at one atmosphere and the temperature of interest

2 2 21 1uc N CO H S

Step 3: Calculate the pseudo-reduced pressure and temperature, and obtain the viscosity ratio (g/1)

Step 4: Calculate the gas viscosity from 1 and the viscosity ratio (g/1)

Carr’s Atmospheric Gas Viscosity Correlation


Gas Viscosity Ratio Correlation


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


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

2 2 21 1uc CO N H S

Dempsey’s Correlation for Gas Viscosity 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

lng

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


a0 = −2.46211820a1 = 2.970547414 a2 = −2.86264054 (10−1) a3 = 8.05420522 (10−3) a4 = 2.80860949 a5 = −3.49803305a6 = 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)

Exercise 4

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

Calculate the vicosity of the gas mixture using both graphical and analytical methods.


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 laboratory experiments. When such experiments are not available, empirical correlations are used

Crude Oil Density


The crude oil density is defined as the mass of a unit volume of the crude oil at a specified pressure and temperature.

3 (lb/ft )oo

o

m

V

Crude Oil Gravity


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

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

3; 62.4 (lb/ft )oo w

w

141.5-131.5o

o

API

The API gravity of crude oils usually ranges from 47° API for the lighter crude oils to 10° API for the heavier crude oils.

Black Oil Model


Gas Solubility Rs


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

The solubility of a natural gas in a crude oil is astrong function of the pressure, temperature, API gravity, and gas gravity.

Gas Solubility Rs


Standing’s Correlation for Rs


1.2048

1.4 1018.2

0.0125 0.0009 460

x

s g

pR

x API T

Characteristics of Reservoir Rocks


Porosity

Permeability

In-situ Saturation

pore bulk matrix

bulk bulk

V V V

V V

Porosity


Porosity

Porosity depends on grain packing, NOT grain size

Rocks with different grain sizes can have the same porosity

• Rhombohedral packing

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

• Pore space = 47 % of total volume


Rock Matrix and Pore Space

Rock matrix Pore space


Pore-Space Classification

Total porosity

Effective porosity

Total Pore Space

Bulk Volume

pore

t

bulk

V

V

Interconnected Pore Space

Bulk Volumee


Permeability is a property of the porous

medium and is a measure of the capacity of

the medium to transmit fluids

Permeability


When the medium is completely saturated

with one fluid, then the permeability

measurement is often referred to as specific

or absolute permeability

Absolute Permeability


Effective permeability is a measure of the

fluid conductance capacity of a porous

medium to a particular fluid when the

medium is saturated with more than one

fluid

Effective Permeability


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


Oil

Water

Gas

k

kk eo

ro

k

kk ew

rw

k

kk

egrg

Calculating Relative Permeabilities


Darcy’s Law

v: Velocity

q: Flow rate

A: Cross-section area

k: Permeability

: Viscosity

L: Length increment

p: Pressure drop

q

Direction of flowA

q k pv

A L


Fluid Saturation

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

Phase saturations

Sw = water saturation

So = oil saturation

Sg = gas saturation

specific fluid

pore

SaturationV

V


In-Situ Saturation

Rock matrix Water Oil and/or gas


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

Solution Gas Drive

Gas Cap Drive

Water Drive

Gravity drainage drive

Combination drive


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

Oil

A. Original Condition

B. 50% Depleted

Oil producing

wells

Oil producing

wells


Solution-Gas Drive in Oil ReservoirsFormation of a Secondary Gas Cap

Wellbore

Secondarygas cap


Oil producing well

Oilzone

OilzoneGas cap

Gas-Cap Drive in Oil Reservoirs


Oil producing well

Water Water

Cross Section

Oil Zone

Water Drive in Oil ReservoirsEdgewater Drive


Oil producing well

Cross Section

Oil Zone

Water

Water Drive in Oil Reservoirs Bottomwater Drive


Gravity Drainage Drive in Oil Reservoirs

Oil

Oil

Oil

Point A

Point B

Point C

Gas

Gas

Gas


Combination Drive in Oil Reservoirs

Water

Cross Section

Oil zone

Gas cap


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

Reservo

ir p

ressu

re,

Percen

t o

f o

rig

inal

Cumulative oil produced, percent of original oil in place


Exercise 6

1. How can we identify different reservoir drive

mechanisms?

2. Rank in descending order typical reservoir drive

mechanisms in terms of efficiency

3. How does knowledge about reservoir drive mechanisms

help us in designing an oil field development plan?


Material Balance Equation (MBE)


An Overview of MBE

Generalized Material Balance Equation

MBE for Typical Oil and Gas Reservoirs

Applications of MBE

An Overview of MBE


First developed by Schilthuis in 1936, MBE is

considered to be a tool for:

estimating initial hydrocarbon in place

predicting future reservoir performance

predicting ultimate reservoir recovery

under certain type of driving mechanisms

Fundamentals of MBE


MBE is derived using the following assumptions:

Reservoir

Bulk

Volume

Volume of

Rock Matrix

Pore

VolumeConstant

The pore volume is fully occuppied by existing fluid components (oil, gas, water)

The reservoir is homogenuous and isotropic (zero-dimensional)

General MBE (GMBE)


GMBE is an MBE that can be applied to

all reservoir types;

MBE for a particular type of reservoir

can be derived from the GMBE by

removing nonexistent terms.

Tank Model


INITIAL OIL

INITIAL GAS-CAP GAS

REMAINING OIL

CURRENT GAS-CAP GAS

RELEASED GAS

INJECTED GAS

NET WATER INFLUX

EXPANDING CONATE WATER

EXPANDING ROCK MATRIX

INJECTED WATER

Initial Condition Current Condition

ROCK (MATRIX)

CONATE WATER

Derivation of GMBE


Volume ofInitial Oil

Volume of Initial Gas Cap

Volume of Remaining Oil

Volume of Expanding Rock Matrix

Volume of Remaining Free Gas

Volume ofWater Influx

Volume ofRock Matrix

Volume of Conate Water

Volume ofExpanding

Conate Water

Volume ofInjectedWater

Volume of Injected Gas

Acronyms in GMBE


GMBE: Final Formulation


( ) ( ) (1 )1

( )

w wi ftit ti g gi ti e inj w inj g

gi wi

p t p si g p w

c S cNmBN B B B B m NB p W W B G B

B S

N B R R B W B

( )t o si s gB B R R B

ti oiB B

Where:

Exercise 7

1. Derive the equation for the pore volume of the reservoir

2. Derive the equations for water and rock matrix

expansions

3. Derive the equation for the initial gas in the reservoir

4. Derive the equation for the remaining free gas in the

reservoir


Fluid Flows in Reservoirs


Properties of Reservoir Fluids in Motion

Flow Regimes

Flow Geometry

Fluid Flow Equations

Properties of Reservoir Fluids


Classification Criteria: Isothermal Compressibility

or

Slightly Compressible Fluids

Reservoir Fluids

Incompressible Fluids

Compressible Fluids

dp

dV

Vc

1

dp

dc

1

Incompressible Fluids


Volume and density do not change with pressure

0; 0 0l

Vc

p p



Small changes in volume or density with changes in pressure

ppc

refrefeVV

!!2!11

21

n

xxxe

nx For small x: xex 1

ppcVV refref 1



refo

o

oppc

BB

ref

1

refooo ppcref

1

Compressible Fluids


A compressible fluid has compressibility ranging from 1.E-3 to 1.E-4

1 1g

zc

p z p

g

pM

zRT

gsc scg

c g c sc

p zB T

T p

Flow Regimes


Classification Criteria: Changes in pressure with time

Pseudosteady-State Flow

Flow Regimes

Steady-State Flow

Unsteady-State Flow

Steady-State Flows


Pressure does not change with time

0

t

p

Unsteady-State Flows


Pressure derivative with respect to time is a function of both space and time

),( tft

px

Pseudo-Steady Flows


Pressure declines with a constant rate

const.

t

p

Flow Geometry


The shape and boundaries of a reservoir has a significant effect on its flow geometry.

Linear Flow

Flow Geometry

Radial Flow

Hemispherical Flow Spherical Flow

Radial Flow


Fluids move toward the well from all directions

Linear Flow


Flow paths are parallel and the fluid flows in a single direction

Spherical Flow


A well with a limited perforated interval could result in spherical flow in the vicinity of the perforations

Hemispherical Flow


A well which only partially penetrates the pay zone coud result in hemispherical flow

Wellbore

Flow lines

Side view

Fluid Flow Equations


Describing the flow behavior in a reservoir

Depending on the combination of variables

recently presented (types of fluids, flow regimes, …)

Developed by combining Darcy’s transport

equation with the conservation of mass and various

equations of state

Darcy Law


Velocity of a homogeneous fluid in a porous medium is proportional to the pressure gradient, and inversely proportinoal to the fluid viscosity.For a radial flow system, Darcy’s transport equation is given by

r

pk

A

qv

Pseudo-Steady State Radial Flow of Slightly Compressible Fluids


75.0ln

00708.0

w

eo

wfr

o

r

rB

ppkhQ

Pseudo-Steady State Radial Flow of Compressible Fluids


75.0ln1422w

e

wfr

g

r

rT

pmpmkhQ

p

dpZ

ppm

0

2)(

Where the real-gas pseudo pressure m(p) is defined as:

For 2000 ≤ pwf ≤ 3000 psi:

Pressure Squared Approximation for Compressible Fluid Flow Equations


75.0ln1422

22

w

e

r

g

r

rZT

ppkhQ

wf

2

22

wfr

avg

ppp

For pwf<2000 psi:

and are determined at the average pressure

Zavgp

Average Pressure Approximation for Compressible Fluid Flow Equations


75.0ln1422w

egg

r

g

r

rBT

ppkhQ

wf

2

wfr

avg

ppp

For pwf>3000 psi:

Average Z, g are calculated at the average pressurepavg.

Exercise 8


The PVT data from a gas well in the Anaconda Gas Field is given below:

p (psi) mu (cp) Z

0.0 0.01270 1.000

400.0 0.01286 0.937

800.0 0.01390 0.882

1200.0 0.01530 0.832

1600.0 0.01680 0.794

2000.0 0.01840 0.770

2400.0 0.02010 0.763

2800.0 0.02170 0.775

3200.0 0.02340 0.797

3600.0 0.02500 0.827

4000.0 0.02660 0.860

4400.0 0.02831 0.896

The well is producing at a stabilized

bottom-hole flowing pressure of 2800

psi. The wellbore radius is 0.3 ft. The

following additional data is available:

k=65 md, h=15 ft, T=600 °R,

Pr = 4400 psi, re=1000 ft,

1. Calculate the gas flow rate in

Mscf/day

2. Draw the graph of m(p) vs p

Numerical Integration


Trapezoidal Method

Constant-Termial-Rate Solution


kt

rcEi

kh

qBpp t

i

29486.70

Exponential Integral


duu

exEi

x

u

)(

Approximation of Ei Function


2 3 2 3 81 2 3 4 5 6 7

1

2

2

3

3

4

5

6

2

7

0.01

( ) ln(1.781 )

0.01 3.0

( ) ln( ) [ln( )] [ln( )]

0.33153973

0.81512322

5.22123384 10

5.9849819 10

0.662318450

0.12333524

1.0832566 10

x

Ei x x

x

aEi x a a x a x a x a x a x a x

x

a

a

a

a

a

a

a

a

4

8 8.6709776 10

Exercise 9


An oil well is producing at a constant flow rate of 300 STB/day under unsteady-

state flow conditions. The reservoir has the following rock and fluid properties

Bo=1.25 bbl/STB, =1.5cp, ct=12 x 10-6 psi-1

ko=60 md, h=15 ft, pi=4000 psi,

= 15%, rw=0.25 ft,

1. Calculate the pressure at radii of 0.25, 5, 10, 50, 100, 500, 1000, 1500,

2000, and 2500 ft, for 1 hour. Plot the results as:

• pressure versus the logarithm of radius

• pressure versus radius

2. Repeat question 1 for t=12 hours and 24 hours. Plot the results as

pressure versus logarithm of radius

Part III


Data Analysis Methods In

Reservoir Engineering

Overview of Data Analysis in Reservoir Engineering


PVT Analysis


The objective of PVT Analysis is to

estimate essential properties and

predict behaviors of reservoir fluids

during production

PVT Analysis Tools


Wax & Asphaltene Deposition

PVT ANALYSIS

SAMPLING SPECIAL STUDYGAS CONDENSATEBLACK OIL

Effect of Injection Gas on Fluid Properties

Quality check

Effect of Injection Chemical on Fluid

Properties

Compositional analysis

Constant Composition Expansion

Viscosity Test

Quality check

Separator Test

Differential Vaporisation Test

Subsurface

Open hole

Case hole

Surface

Separator

WellheadCompositional

analysis

Constant composition expansion

Quality check

Constant Volume Depletion

Basic PVT Data for Black Oil


Oil Formation Volume Factor


Solution Gas Oil Ratio


Oil Viscosity


Oil Formation Volume Factor

Oil Formation Volume Factor at 200 F

1.000

1.100

1.200

1.300

1.400

1.500

1.600

0 1000 2000 3000 4000 5000

Pressure, psig

Oil F

orm

ati

on

Vo

lum

e F

acto

r b

bl/stb

Above bubble point pressure, Bo increases as pressure decreases. Why?

Below bubble point pressure, Bo decreases as pressure decreases. Why?


Oil Density at 200 F

0.700

0.710

0.7200.730

0.740

0.750

0.760

0.7700.780

0.790

0.800

0.810

0.8200.830

0.840

0.850

0 1000 2000 3000 4000 5000

Pressure, psig

Oil D

en

sit

y,g

/cc

Oil Density

Above Pb, the oil density decreases. Why?

Below Pb, the oil density increase. Why?

The reduction of mass is minimal compare to oil volume decrease


Solution Gas Oil Ratio at 200 F

0

50

100

150

200

250

300

350

400

450

500

550

600

0 1000 2000 3000 4000 5000

Pressure, psig

So

luti

on

Gas O

il R

ati

on

scfl

/stb

Above bubble point pressure,Rs is constant. Why?

Below bubble point pressure,Rs decreases as pressuredecreases. Why?

It will continue to vapouriseuntil no gas come out fromthe oil at the atmosphericpressure.

Solution Gas Oil Ratio


Exercise 10

1. Explain why above the bubble point pressure (Pb), Bo

increases as pressure decreases whereas below Pb, Bo

decreases as pressure decreases.

2. Explain why above Pb, the oil density decreases as

pressure decreases whereas below Pb, it increases as

pressure decreases.

3. Explain why above Pb, Rs is constant whereas below Pb, it

decreases as pressure decreases.

Well Test Analysis


The objective of well test analysis is to

interprete data obtained from well tests

for the ultimate purpose of identifying

reservoir characteristics such as

dynamic pressure behavior in

reservoirs, permeability, reservoir

boundaries, wellbore storage, etc ...

Wellbore Storage


Skin Factor - Formation Damage


Skin Factor

500

1000

1500

2000

1 10 100 1000 10000

Distance from center of wellbore, ft

Pre

ssu

re, p

si

s = +5

s = -2

s = 0

Types of Well Tests


Drawdown Tests

Buildup Tests

Isochronal Tests

Modified Isochronal Tests

Inteference Tests

Types of Well Tests


Types of Test


Types of Test


Type of Test


Interference Test


Diffusivity Equation


Well Test Analysis Techniques

MDH Analysis

Horner Analysis

Pressure Derivative Based Techniques

Type Curves Analysis

Numerical Simulation


Constant-Terminal-Rate Solution

294870.6 t

i

c rQBp p Ei

kh kt

Log Approximation to the Ei-Function

2162.6 log 3.23 0.87wf i

t w

QB ktp p s

kh c r

bmxy

249.48 10 t wc r

tk

Finite Acting Radial FlowMDH analysis


Problems with Drawdown Tests

It is difficult to produce a well at a strictly constant rate;

Even small variations in rate distort the pressure

response.

Buildup Test - Pressure Response

ttp

t0

tp + t

0

Buildup Test - Superposition

s869.023.3rc

klogtlog

kh

qB6.162

s869.023.3rc

klogttlog

kh

qB6.162pp

2wt

1010

2wt

10p10iws

Pressure Response for a Buildup Test

10162.6 logp

ws i

t tqBp p

kh t

y = mx + b

Finite Acting Radial FlowHorner analysis


Estimating Skin – Horner Plot


1 0

21.1513 log 3.23

hr wf t

t w

p p ks

m c r

P1hr: Pressure after 1 hr shut-in

Pwf|t=0: Flowing well pressure immediately before shut-in

Type Curve Analysis: Data Set


Dimensionless Variable


Type Curve Analysis: Unmatched Overlay


Type Curve Analysis: Matched in Pressure


Type Curve Analysis: Matched in Both Pressure & Time


Type Curve Analysis: Extraction of Type Parameters


Pressure Match: Extracting kh

From the expression of dimensionless pressure

one defines the pressure match Mp

Mp is read as the value of pD matching a specific value of Δp. Then


Skin Match: Extracting S

One reads the value of Ms on the matching type curve:

Then

with CD calculated from its dimensionless expression:


Agarwal’s Type Curves


First introduced by Agarwal et al. (1970), a type curve is a graphical representation of the theoretical solution to the flow equation with the following dimensionless groups:

pQB

khPD

2.141t

rc

kt

wt

D 2

0002637.0

w

Dr

rr

QB

khpPD

2.141log)log(log

22

0002637.0log)log(log

rc

kt

r

t

tD

D

Type-Curve Methods


Type-Curve Methods


Gringarten’s Type Curves


Dimensionless groups for Drawdown Tests:

ddD pQB

khP

2.141t

C

kh

C

t

D

D

0002951.0

Dimensionless groups for Buildup Tests:

buD pQB

khP

2.141 e

D

D tC

kh

C

t

0002951.0

p

e

t

t

tt

1



For the wellbore storage dominated period, the graph PD vs tD/CD is a unit-slope straight line:

1

D

D

D

D

DD

C

td

Pd

C

tP



For the Infinite Acting Radial Flow period, one has:

s

D

D

DD eC

C

tP 2ln80907.0ln

2

1

Bourdet’s Pressure Derivative


Bourdet et al. (1983) defined pressure derivative as:

D

D

DD

C

td

PdP '

Bourdet’s Pressure Derivative Method


For the wellbore storage dominated period, the graph PD vs tD/CD is a unit-slope straight line:

D

D

D

DDD

C

t

C

tPP

'' 1

xyWS

D

D

D

DDWS

C

tx

C

tPy

;'


For the Infinite Acting Radial Flow period, one has:

s

D

D

DD eC

C

tP 2ln80907.0ln

2

1

2

11

2

1 ''

D

DD

D

DD

C

tP

C

tP

2

1IARFy

Bourdet’s Pressure Derivative Method


Physical Pressure Derivative (using Finite Difference method):

11

11 )()('

ii

ii

t

dddd

tt

tptp

td

pdp

i

Bourdet’s Pressure Derivative

11

11)()(

'

ii

ii

ieee

ee

te

bubu

tt

tptp

td

pdp

Exercise 11

Using the reservoir and welltest data to:


DataParam Value Unit

0.25

ct 4.2E-06 psi

B 1.06 bbl/STB

rw 0.29 ft

2.5 cp

h 107 ft

Q 174 bbl/STB

tp 15 hrs

Draw p vs te graph in

log-log scale

Draw p’ vs te graph in

log-log scale

Calculate the wellbore

storage factors C and CD.

Exercise 11 (cont’d)


0 3086.330.00417 3090.570.00833 3093.81

0.0125 3096.550.01667 3100.030.02083 3103.27

0.025 3106.770.02917 3110.010.03333 3113.25

0.0375 3116.490.04583 3119.48

0.05 3122.48

0.0583 3128.960.06667 3135.92

0.075 3141.170.08333 3147.64

0.09583 3161.950.10833 3170.680.12083 3178.390.13333 3187.120.14583 3194.24

0.1625 3205.960.17917 3216.680.19583 3227.89

0.2125 3238.370.22917 3249.07

0.25 3261.790.29167 3287.210.33333 3310.15

0.375 3334.340.41667 3356.270.45833 3374.98

0.5 3394.440.54167 3413.90.58333 3433.83

0.625 3448.050.66667 3466.260.70833 3481.97

0.75 3493.690.8125 3518.63

0.875 3537.340.9375 3553.55

1 3571.751.0625 3586.23

1.125 3602.951.1875 3617.41

1.25 3631.151.3125 3640.86

1.375 3652.851.4375 3664.32

1.5 3673.811.625 3692.27

1.75 3705.521.875 3719.26

2 3732.232.25 3749.71

2.375 3757.192.5 3763.44

2.75 3774.653 3785.11

3.25 3794.063.5 3799.8

3.75 3809.54 3815.97

t Pws(hrs) (psi)

t Pws(hrs) (psi)

t Pws(hrs) (psi)

t Pws(hrs) (psi)

The End


GEOPET BACHELOR PROGRAM PETROLEUM ENGINEERING

Basic Reservoir Engineering - Mai Cao Lan

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