Eor Ior Course t Ahmed

8/23/2019 Eor Ior Course t Ahmed

1/298

12/1/20

Dr. Tarek Ahmed

Tarek Ahmed & Associates Ltd

www.TarekAhmedAssociates.com

[email protected]

Principals of

Secondary & Enhanced Oil Recovery

Professor Emeritus of Petroleum EngineeringMontana Tech of the University of Montana

11/21/2011 2006Tarek Ahmed & Associates, Ltd. All

Rights Reserved

OUTLINE

1. Introduction and Review of Basic Reservoir Engineering

2. Stages of Oil Recovery

3. Factors to Consider When Planning an IOR

4. Introduction to Secondary Recovery Methods

5. Enhanced Oil Recovery Methods6. Equations of State and Compositional Modeling

7. Simulation

8. Team project: Developing and the Nameless Field

11/21/2011 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved
http://www.tarekahmedassociates.com/http://www.tarekahmedassociates.com/


2/298

12/1/20

Segmented Stages of Oil Recovery

Three Stages:

1.Primary Recovery2.Secondary Recovery3.Tertiary (Enhanced) Oil Recovery


Rights Reserved

11/21/2011

Primary Oil Recovery:describes the production of hydrocarbons under the natural driving mechanismspresent in the reservoir without supplementary help from injected fluids such asgas or water.

Secondary Oil Recovery:1. Refers to the additional recovery that results from the conventional

methods of water injection and immiscible gas injection.2. Usually, the selected secondary recovery process follows the primary

recovery but it can also be conducted concurrently with the primaryrecovery.

3. Before undertaking a secondary recovery project, it should be clearlyproven that the natural recovery processes are insufficient; otherwisethere is a risk that the substantial capital investment required for asecondary recovery project may be wasted.

Tertiary (Enhanced) Oil Recovery:is that additional recovery over and above what could be recovered by primaryand secondary recovery methods. Various methods of enhanced oil recovery(EOR) are essentially

2006Tarek Ahmed & Associates, Ltd. All Rights Reserved


3/298

12/1/20

Segmented Stages of Oil Recovery

Gas Injection

(Pressure Maintenance)

Micellar-Polymer

ASP Polymer

Others

Artificial Lift

Primary Recovery

Natural Flow

Secondary Recovery

Water Flood

Tertiary Recovery

Thermal Miscible Flood Chemical

Steam

In-situ Combustion Huff-and-Puff

Hot Water

SAGD

CO2

Lean Gas

LPG

. N2

Air

Enriched Gas

E

OR

ImprovedOilRecovery

(IOR)


EOR Assessment & Approach

1. Screening & Field Selection

2. Cost estimates

3. Go or No-Go

4. Experimental program and qualitative simulation

5. Pilot Study, Tracer Survey, and monitoring program

6. economic evaluation7. Go or No-Go

8. Matching pilot data and quantitative simulation

9. Decision making Go or No-Go

10. Full Field simulation and Implementation



4/298

12/1/20

IOR/EOR questions

miscible

immiscible

chemical

polymer

1- What is the anticipated phase behavior between reservoir fluid and injectant ?

2- What is Sorm?

3- what is the mobility of phases ?

4- will process be first contact or multi-contact?

1- What is the remaining oil saturation after H2O, i.e. Sorw ?

2- what is Sorg to immiscible gas?

3- Aquifer? Gas cap? Size? Strength?

1- What is the design of the chemical slug to reduce ? Sorm ?!!!

2- To what extend will chemical interact with clays in the formation through

adsorption?

3- what is the salinity of the reservoir water and how it will impact the

effectiveness of the slug ?

4- How will mobility control of the oil bank and chemical bank accomplished ?

1- What is the polymer concentration necessary to provide mobility the control?

2- What is % of the polymer slug that will be adsorbed on the reservoir rock ?

1- What are the anticipated thermal losses in the wellbore, to cap and base rock?

2- Can the thermal front be controlled in the reservoir?Thermal


EOR Target45% OOIP

EOR Target90% OOIP

Primary25% OOIP

Primary5% OOIP

Secondary30% OOIP

Heavy OilsLight Oils

Target for different crude oil systems



5/298

12/1/20


Residual Oil !!!!What Does That Mean? and Why?

A. Wettability

B. Capillary Forces

C. Heterogeneity of the Reservoir

2006Tarek Ahmed & Associates, Ltd. All

Rights Reserved


6/298

12/1/20

2006Tarek Ahmed & Associates, Ltd. All Rights Reserved11/21/2011

Initial Reservoir Condition at Equilibrium


Initial Reservoir Condition at Equilibrium


7/298

12/1/20

11/21/2011

Wettability

Consider the Displacement in a Single Pore

11/21/2011

Displacement in Multiple Channels

Capillary forces cause water toMove ahead faster in low permeability

channel

Gas displaces oil fromHigh permeability channels


8/298

12/1/20


Thread of the oil gets smaller at restricted pointsA &B; where oil film subsequently breaks

Target Setting for Recovery Factors

1) Tertiary EOR can Contribute by 7-15% Increase in Ultimate Recovery, i.e.P+S+T 45-65%. However, Vast Majority of Fields are below 40%.

2) How realistic is Setting a Target for RF > 70%? Can we do Better ?

3) The Key: a More Proactive Longer-Term minded ReservoirManagement Approach; that includes:

a) Understanding the HEALTH and Behavior of reservoir by analyzingEarly production data

b) Identify boundaries, un-drained and upswept areas

c) Improve fluid distribution mapping (avoid Average So) throughout thelife of the Field

d) May Require New Techniques

e) Very Important that you Start Planning VERY EARLY



9/298

12/1/20

Oil Recovery

Flow Rate

Tertiary

Secondary

Primary

Time

Oil Recovery Categories

? ?

Timing to Start Injection!


For any IOR process, important issues to consider

A. Movable Oil or Residual OilB. Time to start project, secondary or TertiaryC. Economics of the projectD. Given the reservoir rock and fluid properties; can the selected

process be used in the chosen reservoir, i.e. screening ?

Time

Rate

Primary Secondary Tertiary

? 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved


10/298

12/1/20

1

First Step for

A Successful for IOR Flood

Performing a Screening Test


Rights Reserved

Process Crude Oil Reservoir

N2 & Flue Gas >35 API

40%

Formation: SS or carbonate with few fractures

h: Relatively thin unless formation is dipping

K: Not Critical

D: >6000 ft

T: Not Critical

High Pressure GasInjection

>23 API

30%

Formation: SS or carbonate with min fractures

h: Relatively thin unless formation is dipping

K: Not Critical

D: >4000 ft

T: Can have a significant effect on MMP

Miscible CO2 >22 API

20%

Formation: SS or carbonate

h: Relatively thin unless dipping

K: Not Critical

D: MMP=f(D,T)

Chemical (ASP;micellar, etc)

>20 API

35%

Formation: SS preferred

h: Not Critical

K: >10md

D: 15 API

50%

Formation: SS but can be used in carbonates

h: Not Critical

K: >10 md

D:


11/298

12/1/20

Questions and Issues

1. How much oil remains at the end of primary and where is it? Volumes remaining in selected patterns

Sor in selected Flow patterns

2. What factors control or limit recovery? Reservoir quality (k,, etc) Field maturity (current pressure, free gas,etc) Operational effectiveness (availability of H2O/gas, capacity of surface

facilities, handling water production,..etc)

3. How can we improve recovery?

4. Plans after Secondary? EOR? Timing?

5. Sorm ? (Sor)res = f[ (Sor)core , M, V] ?


Rights Reserved

Brief Review of

Reservoir Engineering


Rights Reserved


12/298

12/1/20

1

What is the Original-Oil-in-Place? What Tools are Used?

1. A geological/petrophysical study is the key in

understanding and answering the question

2. Supplemented by mathematical formulations; that

include:

- Material Balance Equation MBE

- Decline Curves Analysis

- Type Curves Analysis

OOIP from Volumetric & MBE calculations !!!!!!!are they the same?


Rights Reserved

1- Material Balance Equation

OilZone

Gas Cap

ZoneOilofVolume

CapGasofVolume

mP

P

P N

G

R

Unknowns: N mRP



13/298

12/1/20

1

2- Decline Curves

b> 1 !!

When can be applied?


3- Type Curves?

qDd



14/298

12/1/20

1

Where is the current Oil-in-Place?

1. How the CURRENT oil saturation is distributed in the

reservoir; i.e. available oil for IOR Process?

2. Knowing the distribution is the Key for a successful IOR

3. Project.

4. The objective is to target remaining movable oil


Rights Reserved

Adjustments to theRemaining Oil Saturation

To account for:

1. The water influx zone

2. The expansion of the gas cap

3. Combined effect of water influx & gas cap expansion4. Shrinking of the gas cap

5. The gas migration to form a secondary gas cap


Rights Reserved


15/298

12/1/20

1

volumepore

volumeoilremainingoS

oi

op

wioB

B

N

NSS

11

Pore Volume P.V = 7758 A h

NBoi= (P.V) (1 Swi)

However; how this oil saturation is distributed in thereservoir?

wi

oi

S

BNVP

1).(

wi

oi

op

o

S

BN

BNNS

1


orwwi

wpe

WIZSS

BWWVP

1.

orwwi

wpe

wi

oi

orworwwi

wpe

op

o

SS

BWW

S

BN

SSS

BWWBNN

S

11

1

1- Oil Saturation Adjustment to Water Influx



16/298

12/1/20

1

2- Oil Saturation Adjustment Gas Cap Expansion

orgwi

gi

g

oi

GIZSS

B

BBNm

VP

1

1

.

111

1

1

gi

g

orgwi

oi

wi

oi

org

orgwi

gi

g

oi

op

o

B

B

SS

BNm

S

BN

S

SS

B

BBNm

BNN

S


3- Oil Saturation Adjustment toGas Cap Expansion & Water Influx

orwwi

wpe

orgwi

gi

g

oi

wi

oi

orwwi

orwpe

orgwi

org

gi

g

oi

op

o

SS

BWW

SS

B

BmNB

S

NB

SS

SWW

SS

SB

BmNB

BNN

S

11

1

1

11

1



17/298

12/1/20

1

oagrwi

org

gi

g

oigpc

BSS

SB

BBNmBG

LostOil)1(

])1([

Oil saturation adjustment for shrinking gas-cap:The volume of oil lost as a result of oil migration to thegas cap can also be calculated from:

Where:Gpc= Cumulative gas production from the gas cap, scfBg= Gas FVF, bbl/scf

You Must Consider:Migration of oil to the Gas Cap !!


Secondary gas capLost Residual Oil

Oil saturation adjustment inGravity Drainage Reservoirs



18/298

12/1/20

1

)1(

]1

[])([

P.V)( SGCgcorgwi

gc

wi

oi

gPPsPsi

SSS

SS

BNBRNRNNRN

SGC

SGC

P.V)(1

P.V)(

wi

oi

orgop

o

SBN

SBNNS

So Adjustment for Gravity Drainage

Secondary gas cap pore volume; gives:

Adjust the saturation equation to account for the migration of the evolvedgas to the secondary gas cap, to give:


Important Comment

In these types of reservoirs, the gravity effects result inmuch lower producing gas-oil ratios than would beexpected from reservoirs producing without the benefitof gravity drainage. This is due to the upstructuremigration of the gas and consequent higher oilsaturation in the vicinity of the completion intervals of theproduction wells which should be used when calculatingthe oil relative permeability kro.



19/298

12/1/20

1

FACTORS TO CONSIDER

The following reservoir characteristics must be consideredwhen determining the suitability of a candidate reservoir forIOR flood:

1. Wettability2. Fluid properties3. Lithology and rock properties4. Heterogeneity of the Reservoir5. Reservoir depth6. Fluid saturations

7. Reservoir Uniformity and Pay Continuity8. Primary reservoir driving mechanisms


1- WettabilityWettability is one of the most important rock properties that must beconsidered and accounted for when planning an IOR project.Wettability significantly effects and controls the success or thefailure of the injection fluid. Waterflooding option is generally notconsidered appropriate in Oil Wet Reservoir Systems

2- Fluid PropertiesThe physical properties of the reservoir fluids have pronounced effectson the suitability of a given reservoir for further development by

immiscible fluid injection. The viscosity of the crude oil is consideredthe most important fluid property that affects the degree of success ofan IOR project.The oil viscosity has the important effect of determining the mobilityratio that, in turn, controls the sweep efficiency.



20/298

12/1/20

2

3- Lithology and Rock Properties

Reservoir lithology and rock properties that affect flood ability and success are:

Porosity Permeability (impact of thief zones) Clay content Net thickness

Tight reservoirs or reservoirs with thin net thickness possess water-injection problemsin terms of the desired water injection rate or injection pressure. The governingrelationship:

kh

ip winj

The above relationship suggests that to deliver a desired daily injectionrate ofiwin a tight or thin reservoir, the required injection pressuremight exceed the formation fracture pressure.

To deliver a desiredinjection rate


4- Heterogeneity of the ReservoirThe reservoir existing directional permeability and orientation ofnatural/induced fractures can be effectively utilized when selecting theflooding pattern to improved the EUR. Efforts (conducting traditional welltesting, pulse testing, tracer surveys,etc) should be placed to properly

characterize the heterogeneity of the reservoir as a first preliminary step indesign a waterflood project.

Ky >>> Kx

Ky Ky

Kx Kx



21/298

12/1/20

2

Injection-well Hydraulic Fracture Orientation

Improves sweep efficiency


5- Reservoir DepthI. Maximum injection pressure will increase with depth. However, The

costs of lifting oil from very deep wells will limit the maximum economicwateroil ratios that can be tolerated, thereby reducing the ultimaterecovery factor and increasing the total project operating costs.

II. a shallow reservoir imposes a restraint on the injection pressure that canbe used, because this must be less than fracture pressure. In waterfloodoperations

There is a critical pressure (approximately 1 psi/ft of depth) that, ifexceeded, permits the injecting water to expand openings along fractures orto create fractures. This results in the channeling of the injected water or thebypassing of large portions of the reservoir matrix. Consequently, anoperational pressure gradient of 0.75 psi/ft of depth normally is allowedto provide a sufficient margin of safety to prevent pressure parting.



22/298

12/1/20

2

6- Fluid Saturations

In determining the suitability of a reservoir for waterflooding, ahigh oil saturation that provides a sufficient supply ofrecoverable oil is the primary criterion for successful floodingoperations. Note that higher oil saturation at the beginning of floodoperations increases the oil mobility (through Kro) that, in turn,gives higher recovery efficiency.


7- Reservoir Uniformity and Pay Continuity

Substantial reservoir uniformity is one of the major physicalcriterions for successful waterflooding. For example:

I. Thief zone will cause rapid channeling, high WOR, andbypassing will develop. This zone must be located andshut off

II. These thief zones will contain less oil than the other layers,and their flooding will lead to relatively lower oil recoveriesthan other layers.



23/298

12/1/20

2

8- Primary Reservoir Driving Mechanisms

Six driving mechanisms basically provide the natural energy

necessary for oil recovery:

I. Rock and liquid expansionII. Solution gas driveIII. Gas cap driveIV. Water driveV. Gravity drainage driveVI. Combination drive


Driving Mechanism Oil Recovery Range

Rock & liquid expansion 37 %

Solution Gas drive 530 %

Gas Cap 2040 %

Water drive 35 75%

Gravity drainage


24/298

12/1/20

2

I. SOLUTION GAS DRIVE


Rights Reserved



25/298

12/1/20

2

II. GAS-CAP DRIVE

11/21/2011



26/298

12/1/20

2

Size of the Gas Cap

Oil recovery

OilZone

Gas Cap

ZoneOilofVolume

CapGasofVolumem


Managing Gas Cap Drive reservoirs



27/298

12/1/20

2

III. WATER DRIVE


IV. Gravity Drainage Drive

Factors that affect ultimate recovery from gravity drainage reservoirsare:1- permeability in the direction of dip2- dip of the reservoir3- reservoir producing rates4- oil viscosity5- relative permeability characteristics (lab does not consider it)11/21/2011

2006Tarek Ahmed & Associates, Ltd. All Rights


28/298

12/1/20

2

To maximize the oil recovery by gravity segregation; Qo

should not exceed a Critical Maximum oil Rate to allow

gas migration


Secondary gas capLost Residual Oil

What is the Maximum Oil Rate to EnsureCounter Flow?

qo



29/298

12/1/20

2

This calculated value of qo represents the maximum oil rate that should not

be exceeded without causing the gas to flow downward.Where:

qo = oil production rate, bbl/dayo = oil density, lb/ft

3g = gas density, lb/ft

3A = cross-sectional area open to flow, ft2

k = absolute permeability, md = dip angle.

o

goro

o

Akkxq

)sin()(1083.76

Production should not exceed a critical maximum rate ofgravity drainage .The maximum rate of gravity drainage isdefined as the rate at which complete counter-flow exists

and mathematically by the following expression:

Comment; can be unrealistic 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved

Class Problem:An oil reservoir is produced under gravity drainage drivingmechanism with the following fluid and reservoircharacteristics:Oil density = 49 lb/ft2

Gas density = 8 lb/ft2Oil viscosity = 2.3 cpCross sectional area = 24,000 ft2K= 120 md

Kro = 0.85Dip angle = 60 degree

Calculate the maximum oil rate that should not beexceeded for counter flow



30/298

12/1/20

3

Reservoir Pressure and GOR Trends


11/21/2011

Understanding your Reservoir Driving

Mechanisms


Rights Reserved


31/298

12/1/20

3

11

1/

A

BG

A

BW

A

ppS

cScmBN

A

BWW

A

BBBBNm

A

BBN ginjinjwinji

wi

fwiw

oiwpegigigtitit

with:

A = Np [Bt+ (Rp Rsi) Bg]

DDI + SDI + WDI + EDI+ WII+ GII= 1.0

Most efficient 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved

MBE is an Essential Tool; dont forget to use

1/

A

BWW

A

BBBBNm

ABBN wpegigigtitit

A = Np [Bt+ (Rp Rsi) Bg]

A

BWW wpe

A

BWW wpe



32/298

12/1/20

3

Parameters to Consider When Selecting

Optimum Time to Start an IOR Project

1. Reservoir oil viscosity

2. Cost of injection equipment.

3. Productivity of producing wells.

4. Effect of delaying investment

5. Oil saturation

6. Free gas


1- Reservoir oil viscosity.Fluid injection should be initiated when the reservoir pressure reaches itsbubble-point pressure since the oil viscosity reaches its minimum value at thispressure. The mobility of the oil will increase with decreasing oil viscosity,which in turns improves the sweeping efficiency.

pb

0

Rs

Bo

o



33/298

12/1/20

3

ob

o

pb

oil

Effect of oil viscosity on mobility ratio

os

s

rsw

o

roo

kk

:Best

&


11/21/2011

2- Cost of injection equipment.at higher pressures, the cost of injection equipment increases. Therefore,a low reservoir pressure at initiation of injection is desirable.

3- Productivity of producing wells.A high reservoir pressure is desirable to increase the productivity of producing wells,which prolongs the flowing period of the wells, decreases lifting costs, and mayshorten the overall life of the project.

4. Effect of delaying investment on the time value

of $$.

A delayed investment in injection facilities is desirable from this standpoint.



34/298

12/1/20

3

11/21/2011

5- Oil Saturation

The principal requirement for a successful fluid injectionproject is that sufficient oil must remain in the reservoirafter primary operations ; e.g. starting waterflood at ahigher pressure.

High residual oil saturation after primary recovery is essential not onlybecause there must be a sufficient volume of oil left in the reservoir, but alsobecause of relative permeability considerations. A high oil relativepermeability, i.e., high oil saturation, means more oil recovery with lessproduction of the displacing fluid.


I. High So improved mobility; i.e. higher kroII. High So required to develop an oil bankIII. High So required to improve sweep efficiencies

Questions:A. Average Remaining Oil Saturation; What does it mean?B. How you identify areas with high So?

C. How you select areas for infill drilling?

Distribution of the remaining So is aMAJOR Problem



35/298

12/1/20

3

volumepore

volumeoilremainingoS

oi

op

wioB

B

N

NSS

11

Pore Volume P.V = 7758 A h

NBoi= (P.V) (1 Swi)

wi

oi

S

BNVP

1).(

wi

oi

op

o

S

BN

BNNS

1

How this oil saturation is distributed in the reservoir;

where is the Movable Oil?

MBE on a well-by-well basis !However; Simulation is a key answer


6- Effect of Free gas saturation.

A. In water injection projects. It is desirable to have initialgas saturation, possibly as much as 10%. This willoccur at a pressure that is below the bubble pointpressure (probably unrealistic)

B. In Miscible or Immiscible gas injection projects; zerogas saturation in the oil zone is desired. This occurswhile reservoir pressure is at or above bubble-pointpressure.



36/298

12/1/20

3

Effect of trapped gas on waterflood recovery

Initial Oil Soi

Free Gas Sgi

Initial Water Saturation Swi

Free Gas Sgi


No trapped gas


Free Gas Sgi

Oil Bank Initial Oil Soi

Sorw



37/298

12/1/20

3

With Trapped Gas


Free Gas Sgi

Oil Bank Initial Oil Soi

Trapped Gas SgtShrw


Rights Reserved

Shrw

Sorw



38/298

12/1/20

3




39/298

12/1/20

3

Coefficients Equation (14-1) Equation (14-2)

a1 0.030517211 0.026936065

a2 0.4764700 0.41062853

a3 0.69469046 0.29560322

a4 -1.8994762 -1.4478797

a5 -4.1603083 x 10-4 -3.0564771 x 10-4

gi

gigigigtS

aSaSaSaaS 534

2

321

gtgtgtgtor S

a

SaSaSaaS

53

5

2

321


Class problem

An oil reservoir is being considered for furtherdevelopment by initiating a waterflooding project.The oilwater relative permeability data indicatethat the residual oil saturation is 35%. It isprojected that the initial gas saturation at the start

of the flood is approximately 10%. Calculate theanticipated reduction in residual oil,Sor , due tothe presence of the initial gas at the start of theflood.



40/298

12/1/20

4

The waterflood recovery can possibly be improved if a so-calledoptimum gas saturation is present at the start of the flood.This optimum gas saturation is given by:

15 2.1

16 6.035 2.0

90 2.063 4.0001867.0

w

wi

o

o

o

op tg

SS

BkS

(Sg)opt= Optimum gas saturation, fraction

So, Swi = oil and initial water saturations, fraction

o,w= oil and water viscosities, cpk = Absolute permeability, md

Bo = Oil formation volume factor, bbl/STB

= Porosity, fraction11/21/2011 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved

The above correlation is not explicit and must be used in conjunction

with the material balance equation (MBE). The proposed methodologyofdetermining (Sg)opt is based on calculating the gas saturation as afunction of reservoir pressure (or time) by using both the MBE and theproposed expressions. When the gas saturation as calculated by the twoequations is identical, this gas saturation is identified as (Sg)opt.

Pressure

Psi

Bo

BBL/STB

ocp

MBE

So Sg= 1- So - Swi (Sg)opt

1925 1.333 0.600 0.700 0.000 --

1760 1.287 0.625 0.628 0.072 0.119

1540 1.250 0.650 0.568 0.132 0.122

1342 1.221 0.700 0.527 0.173

15 2.1

16 6.035 2.0

90 2.063 4.0001867.0

w

wi

o

o

o

op tg

SS

BkS



41/298

12/1/20

4

But; there is a problem

Variable Bubblepoint Pressures !!!

11/21/2011

Oil

Gas


o

o

g

gt

S

o

o

news

B

VolumePoreS

B

VolumePoreSR

B

VolumePoreS

R

g

o

o

g

SnewS

B

B

S

SRR

oi

op

wioB

B

N

NSS

11

Sg



42/298

12/1/20

4

Again; Important Equations

11/21/2011

Sg = 1 So - Swi

oi

oPwio

wi

oi

op

o

wi

oi

oi

wi

B

B

N

NSS

S

BN

BNNS

S

BN

B

SN

1)1(

1

1VolumePore

)1(volume)(pore


Class Problem:The Big Butte Field is a solution gas-drive reservoir that is under considerationfor a waterflood project. The volumetric calculations of the field indicate that theareal extent of the field is 1612.6 acres. The field is characterized by thefollowing properties:oThickness h = 25 ftoPorosity = 15%oInitial water saturation Swi = 20%oInitial pressure pi = 2377 psiResults from the MBE in terms of cumulative oil production Np as a function ofreservoir pressure are given below:

Pressure

Psi

Np

MMSTB

2377 0

2250 1.10

1950 1.76

1650 2.64

1350 3.3



43/298

12/1/20

4

Pressure

psi

Bo

Bbl/STB

Rs

scf/STB

Bg

bbl/scf

2377 1.706 921 --

2250 1.678 872 0.00139

1950 1.555 761 0.00162

1650 1.501 657 0.00194

1350 1.448 561 0.00240

1050 1.395 467 0.00314

750 1.336 375 0.00448

450 1.279 274 0.00754

The PVT properties of the crude oil system are tabulated below:

Assume that the waterflood will commence when the reservoirpressure declines to 1650psi; find:1- the pressure that is required to dissolve the evolved gas.2- the pressure that is required to dissolve the trapped gas.


11/21/2011

Simulation is the key

I. Calculations should be performed forseveral assumed times and the netincome for each case determined.

II. The scenario that maximizes the profit andperhaps meets the operators desirable goalis selected.



44/298

12/1/20

4

Fundamentals of

Waterflooding


Rights Reserved

11/21/2011

Considerations & Requirements

When

Planning Onshore or Offshore IOR Project


Rights Reserved


45/298

12/1/20

4

Considerations When Planning an

IOR Flood

1. Purpose of the flood

2. Onshore or Offshore

3. Defining the Aquifer

4. Permeability Consideration, kx,ky, and kz

5. Optimum Time to Start the Flood

11/21/2011


Rights Reserved

Consideration #1: Purpose for Onshore or Offshore; same:

A. Maintaining the reservoir pressureB. supplementing partial/strong natural water drive !!!C. Displacing oil

AquiferAquifer

Oil Oil

Offshore; What do you know about the reservoir?



46/298

12/1/20

4

Consideration #2: Offshore vs. Onshore Field Development

Time

Oil Rate

Offshore:Discovery well cannot produced atcontinuous basissince the offshore

production facilitiesare not in existence

Onshore:

Discovery well istied back to thenearest productionfacilities andproduced at highrate at continuousbasis


Aquifer

Aquifer

Oil Oil

Offshore Appraisal StageNo Continuous Flow

Minimum information?

Major question deals with the aquifer(strength, communication, etc)



47/298

12/1/20

4

Onshore:

Discovery well is tied back to the nearest production facilities and

produced at high rate at continuous basis to provide a positive cash flowfrom day one. The most important advantage; however, it permits toobserve and evaluate the reservoir under dynamic conditions.Continuous production creates a pressure sink at the discovery well whichpropagates radically and vertically throughout the formation. Withsubsequent appraisal/development well is drilled, the conducting of DSTand RFT will provide with the degree of areal and vertical communications

that are ESSENTIAL in:

A. Planning a secondary recovery and scale of the processB. Estimation of the strength of the natural driving

mechanism


Offshore:

Appraisal wells can not produced at continuous basis since theoffshore production facilities are not in existence. Perhapsadequate data may be collected with each appraisal well;however, it might be the lowest quality because they arecollected under purely STATIC conditions. No adequate dataare collected under DYNAMIC CONDITIONS (few thousandsbbl during DST) to allow:

A. Degree of the areal and vertical communications withinthe formation

B. Strength and type of the natural driving mechanism



48/298

12/1/20

4

Consideration #3: The Aquifer Problem (Basel or Edge):

A. Degree of communication; radial and vertical

B. Degree of communication with Aquifer!!!C. Strength of the Aquifer

Aquifer Aquifer

Basel Waterflood

Aquifer

Oil

Edge Waterflood


Consideration #4: Permeability:

1. With high K, large oil accumulations can be developed with relativelyfew wells; with more importantly fewer production platforms in offshorereservoirs

2. Offshore Platforms usually have finite lifetime which leads to the fact thatmaximizing oil recovery (function of k, tight or permeable) is required

before any significant mechanical deterioration occurs. Decision is

based on:

3. Value of remaining recoverable oil vs. cost of platform refurbishingSelection of flood pattern and infill drilling locations are very strongfunction of permeability distribution



49/298

12/1/20

4

11/21/2011

Consideration #5: Time to Initiate the Flood

A. Start the flood above Pb; at Pb or below Pb ?B. Effect of oil viscosity on mobility ratioC. Effect of trapped gas on waterflood recovery


Mobility Ratio M:

11/21/2011

w

o

Sro

Srw

o

w

wi

wBT

k

kM

M

Fluiddisplaced

Fluiddisplacing

ob

o

p

b

oil

Effect of oil viscosity on mobility ratio



50/298

12/1/20

5

The magnitude of the reduction and mobilization of residual oil saturation and

improving the sweep efficiency by any IOR process is controlled by thefollowing two major factors:

1) Capillary Number NC ; Question is: how to increase?

2) Mobility Ratio M, Question is: how to reduce it?

Controlling Parameters for a

Successful IOR Process


L

pok

cN

w

o

ro

rw

oro

wrw

displaced

displacing

k

k

k

kM

)/(

)/(

Critical Nc

beforeor

afteror

S

S

)(

)(

1.0

0

1) Effect of NC on residual oil saturation

L

pok

cN

Increase p/L

is the only practical way of increasing NC

Range ofWaterflood



51/298

12/1/20

5



2) Effect of Mobility Ratio on Sweep Efficiency

w

o

ro

rw

oro

wrw

displaced

displacing

k

k

k

kM

)/(

)/(


52/298

12/1/20

5

I. Objective: provide the injection fluid with themaximum possible contact with the crude oil system

II. Strategies: convert existing production wells toinjection wells, or drill infill injection wells

III. Factors that need to be considered:

Reservoir heterogeneity and directional permeability

Direction of formation fractures

Availability of the injection fluid (gas or water)

Desired and anticipated flood life Maximum oil recovery

Well spacing, productivity, and injectivity

Flooding Patterns


Injection Wells Placement Requirements:

1.Take advantage of directional permeability,fractures, dip,etc

2.Provide sufficient fluid injection rate to yield thedesired production rate

3.Maximize recovery with minimum production of

the injected fluid4. In most cases, require a minimum of new wells

(usually; the target field has been developed)



53/298

12/1/20

5

16 wells per section (1 sq-mile)

5280 ft

Well Spacing

40-acre for oil wells160-320 ac for gas wells

Leases are divided into square miles and quarter square miles


Essentially four types of well arrangements are used in fluidinjection projects:

Irregular injection patternsPeripheral injection patternsRegular injection patternsCrestal and basal injection patterns

106 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved


54/298

12/1/20

5

Could be caused by:

a) a planned, irregular pattern of vertical wells

b) irregular surface or subsurface topology

c) inclined wells

d) faulting

e) localized variations in porosity or

permeability

1- Irregular Injection Patterns


2- Peripheral Injection Patterns

In peripheral flooding, the injection wells are located at theexternal boundary of the reservoir and the oil is displacedtoward the interior of the reservoir, as shown below

108

injector

Producer



55/298

12/1/20

5

Forms of Peripheral and Central Flooding Patterns 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved

1. Relatively small number of injectors compared with producers.Generally yield maximum oil recovery with minimum producedwater.

2. Significant water Production can be delayed until only the last rowof producers remains.

3. Results from peripheral flooding are more difficult to predict thanother patterns.

4. For a successful peripheral flood, k must be large enough topermit the movement of the injected water at the desired rate

over the distance of several well spacing from injection wells tothe last line of producers.

5. Because of the unusually small number of injectors compared withthe number of producers, it takes a long time for the injectedwater to fill up the reservoir gas space. The result is a delay in thefield response to the flood

6. Injection rates are generally a problem because the injectionwells continue to push the water greater distances.

Characteristics of the Peripheral Flood:



56/298

12/1/20

5

3- Regular Injection Patterns

Due to the fact that oil leases are divided into square miles and quarter

square miles, fields are developed in a very regular pattern. A wide variety ofinjection-production well arrangements have been used in injection projects.The most common patterns are:

a) Direct line drive.b) Staggered line drive.c) Five spot.d) Seven spot.e) Nine spot.

111 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved

3- Regular Injection Patterns

Seven-SpotDirect LineDrive

Staggered Line Drive

The patterns termed inverted have only one injection well perpattern. This is the difference between normal and inverted wellarrangements. 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved


57/298

12/1/20

5

113

A. Direct line drive.The lines of injection and production are directly opposed to each other.The pattern is characterized by two parameters:

a = distance between wells of the same typed = distance between lines of injectors and producers.

B. Staggered line drive.The wells are in lines as in the direct line, but the injectors and producersare no longer directly opposed but laterally displaced by a distance of a/2.

C. Five spot.This is a special case of the staggered line drive in which the distancebetween all like wells is constant, i.e., a = 2d. Any four injection wells thusform a square with a production well at the center.

D. Seven spot.The injection wells are located at the corner of a hexagon with a production

well at its center.E. Nine spot.This pattern is similar to that of the five spot but with an extra injection welldrilled at the middle of each side of the square. The pattern essentiallycontains eight injectors surrounding one producer.


4- Crestal and Basal Injection PatternsIn Crestal Injection, as the name implies, the injection is through wellslocated at the top of the structure. Gas injection projects typically usea crestal injection pattern. Traditionally; a combination of Crestal andBasal Injection (injection at the bottom of the structure) are used toimprove sweep efficiency. Many water-injection projects use basalinjection patterns with additional benefits being gained from gravitysegregation.



58/298

12/1/20

5

SWEEP EFFICIENCIES

Areal Sweep Efficiency EA

Vertical Sweep Efficiency EV

Displacement Sweep Efficiency ED

11/21/2011


Rights Reserved

Recovery Performance

Recovery Performance of an IOR Flood is based

On:

1. Displacement Efficiency ED

2. Areal Sweep Efficiency EA3. Vertical Sweep Efficiency EV

Implicitly input to simulation modelsin a form of a number of

Zonation or layering system



59/298

12/1/20

5

Cumulative Oil Production:NP= Ns EA EVED

Recovery Factor:RF=(NP/Ns) = EA EVED

Volumetric Sweep Efficiency:Evol = EA EV


Oil Recovery Equations for AnyIOR Process

The displacement efficiency EDis the fraction of movable oilthat has beendisplaced from the swept zone at any given time orpore volume injected. Because an immiscible gasinjection or waterflood will always leave behindsome residual oil, ED will always be less than 1.0.

oi

ooiD

SSSE



60/298

12/1/20

6

Areal Sweep Efficiency:

The areal sweep efficiency EAis the fractional area of the pattern that is swept by thedisplacing fluid. The major factors determining areal sweep are:

a) Fluid mobilitiesb) Pattern typec) Areal heterogeneityd) Total volume of fluid injected

AreaTotalAEA

ASwept AreaA


11/21/2011

Line Drive

Kx

Ky

5-Spot

Kx

Ky



61/298

12/1/20

6

The vertical sweep efficiency EV

is the fraction of the vertical section of the pay zone that is contacted byinjected fluids. The vertical sweep efficiency is primarily a function of:

a) Vertical heterogeneityb) Degree of gravity segregationc) Fluid mobilitiesd) Total volume injection

Vertical Sweep Efficiency

AreaSectionCross

AEV

The problem isits defined by the USER;5,10,,25-layer system !!!!

A

k1

k2

k3

k4

A


11/21/2011

Volumetric Sweep Efficiency = EA EV

Volumetric Sweep Efficiency

EV

EA

Sweptarea

Swept area



62/298

12/1/20

6

Displacement Sweep Efficiency

Areal Sweep Efficiency

Vertical Sweep Efficiency


In general, reservoir heterogeneity has moreinfluence than any other factor on theperformance of a secondary or tertiary injectionproject. The most important two types ofheterogeneity affecting sweep efficiencies (EVand EA) are:

The Reservoir Vertical Heterogeneity; andThe Reservoir Areal Heterogeneity.



63/298

12/1/20

6

Vertical Heterogeneity

Stratification is by far the most significant parameterinfluencingthe vertical sweep and in particular its degree of variation in thevertical direction; i.e. permeability variation V

Water injected into a stratified system will preferentially enter thelayers of highest permeability (thief zone s are major problems)and consequently, a significant fraction of the less-permeable zoneswill remain unflooded.

Operators spend millions of dollars coring, logging, and drilling

appraisal wells, all of which permits direct observation of verticalheterogeneity. Therefore, if the data are interpreted correctly, itshould be possible to quantify the vertical sweep EV quiteaccurately; however; determining optimum number of layers forsimulation could be a problem (fine to coarse)


Areal HeterogeneityAreal heterogeneity includes areal variation in formationproperties and geometrical factors; such as:

1. position and nature of sealing faults2. boundary conditions due to the presence of an aquifer

or gas cap.3. direction of fractures4. Principle axis of permeability kx & ky5. Porosity, permeability, and net thickness variations

Areally, matters are much more uncertain since methods ofdefining heterogeneity are indirect



64/298

12/1/20

6

11/21/2011

All three efficiency factors (i.e., ED, EA,

and EV) are variables that increase duringthe flood and reach maximum values atthe economic limit of the injection project.


11/21/2011

Simple Equation: NP= Ns EA EVED ; What is the problemthen?

Understanding Sweep EfficienciesAnd Oil Recovery

EV

EA

Sweptarea

Swept area

!!!offunctionsare,, sVAD SEEE



65/298

12/1/20

6

I. DISPLACEMENT EFFICIENCY


Rights Reserved

I. DISPLACEMENT EFFICIENCYDisplacement efficiency is the fraction of movable oil that has been recovered fromthe swept zone at any given time. Mathematically, the displacement efficiency isexpressed as:

floodofstartatoilofvolume

volumeoilremainingfloodofstartatoilofvolume DE

oi

oi

o

o

oi

oi

oi

oi

o

o

oi

oi

D

B

S

B

S

B

S

B

SVolumePore

B

SVolumePore

B

SVolumePore

E

wi

wwi

oi

ooiD

S

SS

S

SSE

1

)1()1(

Assuming constant Bo

wi

wiwD

S

SSE

1

average remaining oil &water saturation in the swept area



66/298

12/1/20

6

11/21/2011

Class Problem

A saturated oil reservoir is under consideration to be waterflooded

immediately after dril ling and completion. Core analysis tests indicatethat the initial and residual oil saturations are 70 and 35%, respectively.Assuming that Bo will remain constant throughout, calculate:

1- The displacement efficiency when the oil saturation is reducedto 65, 60, 55, 50, and 40%

2- Maximum displacement efficiency that can be achieved during theproject life

3- The displacement efficiency under miscible displacement with an

estimated Sorm of 10%;


11/21/2011

Last example shows that ED will continually increase withincreasing water saturation in the reservoir. The problem, ofcourse, lies with developing an approach for determiningthe increase in the average water saturation in the sweptarea as a function of cumulative water injected (or injectiontime), i.e:

Buckley and Leverett (1942) developed a well establishedtheory, called the frontal displacement theory, which providesthe basis for establishing such a relationship. This classictheory consists of two equations:

1. Fractional flow equation2. Frontal advance equation

wi

wiwD

S

SSE

1



67/298

12/1/20

6

Fractional flow equation

Based on:

1) Water Cut fw

2) Darcys Equation


Rights Reserved

11/21/2011

wo

t

w

ow

ww

ff

q

q

qq

qf

1

Water and Oil Cut



68/298

12/1/20

6

11/21/2011

L

ppkAq

ppkA

Lq

pkA

xq

pkA

xq

x

pkA

q

P

p

L

)(

)(

21

12

0

2

1

Darcys Equation


L

p1 p2

11/21/2011

sing

x

pkAq

Darcys Equation & Water Cut


sin:FlowOil oo

o

oo

gx

p

kA

q

sin:FlowWater www

ww gx

p

kA

q


69/298

12/1/20

6

11/21/2011

sinowwoo

owo

w

ww gx

p

x

p

kA

q

kA

q

woc ppp :PressureCapillary

x

p

x

p

x

p woc

twotww qfqandqfq 1

o

w

w

o

c

to

o

w

k

k

gx

p

q

Ak

f

1

sin1


Developing the Fractional Flow Equation:

Step 1:

Step 2:

Step 3:

11/21/2011

o

w

w

o

c

to

o

w

k

k

x

p

q

Ak

f

1

sin433.0001127.01

o

w

rw

ro

c

wo

ro

w

k

kx

p

i

Akk

f

1

sin433.0001127.0

1

Noting that the relative permeability ratios kro/krw=ko/kwand the totalflow rate qtis essentially equal to the water injection rate, i.e. iw= qt,

the density difference = (wo) in g/cm3



70/298

12/1/20

7


o

w

w

o

c

to

o

w

k

k

gx

p

q

Ak

f

1

sin1

FOCUS FOCUS FOCUS

fo = 1 - fw

That is at ANY POSITION IN THE RESERVOIR,i.e. ANY DISTANCE FROM THE INJECTION WELL

11/21/2011

o

s

rs

ro

c

so

ro

s

k

k

x

p

i

Akk

f

1

sin433.0001127.0

1

the density difference = (so) in g/cm3


Water, Gas, or Solvent Injection:


71/298

12/1/20

7

11/21/2011

The effect capillary pressure is usually neglectedbecause the capillary pressure gradient is generallysmall and thus,

o

w

rw

ro

ow

wo

ro

w

k

k

i

Akk

f

1

sin433.0001127.0

1

o

D

rD

ro

oD

Do

ro

D

k

k

iAkk

f

1

sin433.0001127.01

Similarly for ANY Type of Displacing Fluid:

the density difference (wo) in g/cm3


The shape of the water cut versus water saturation curve is

characteristically S-shaped, as shown below

Gas-OilOil-Water


72/298

12/1/20

7

fo= 1 fwThe above expression indicates that during the displacement of oil bywaterflood, an increase in fwat any point in the reservoir will cause aproportional decrease in fo and oil mobility. Therefore, the objective is toselect the proper injection scheme that could possibly reduce the waterfractional flow. This can be achieved by investigating the effect of:

1. the injected water viscosity2. formation dip angle, and3. water-injection rate on the water cut.

o

w

rw

ro

o

w

rw

ro

owwo

ro

w

k

k

G

k

k

i

Akk

f

1

1

1

sin433.0

001127.0

1


In general; any influences that cause the fractional flow curve to shiftupward (i.e., increase in fwor fg) will result in a less efficient displacementprocess. It is essential, therefore, to determine the effect of various componentparts of the fractional flow equation on the displacement efficiency:

Sw

fw

reason

i.e:1. Water & Oil viscosities2. Wettability3. Injection rate iw4. Updip or downdip injection

o

w

rw

ro

o

w

rw

ro

ow

wo

ro

w

k

k

G

k

k

i

Akk

f

1

1

1

sin433.0001127.0

1


We need to increase G!


73/298

12/1/20

7

Sw

fw

o

w

rw

ro

ow

wo

ro

w

k

ki

Akk

f

1

sin433.0001127.0

1

We want to reduce fw


1- Effect of Water Viscosity

o

w

rw

ro

ow

wo

ro

w

k

k

i

Akk

f

1

sin433.0001127.0

1

w = 0.5 cp

w = 10 cpw = 5 cp

w = 2 cpw = 1 cp

Objective is to reduce fw



74/298

12/1/20

7

2- Effect of Oil Viscosity offw

o

w

rw

ro

ow

wo

ro

w

kk

i

Akk

f

1

sin433.0001127.0

1



3- Effect of Wettability




75/298

12/1/20

7

4- Combined Effect of Wettability and Oil Viscosity

o

w

rw

ro

ow

wo

ro

w

k

k

i

Akk

f

1

sin433.0001127.0

1


5- Effect of Dip Angle & Injection Rate

o

w

rw

ro

ow

wo

ro

w

k

k

i

Akk

f

1

sin433.0001127.0

1

Y

iX

fw

w

1

sin1

a) Injection Well is Located Downdip:sin() is positive when injecting downdip indicating a more efficient performance

is obtained. This improvement is due to the fact that the term [Xsin()/iw] willalways remain positive, which leads to a decrease (downward shift) in the fwcurve.

Injection Rate:The fractional flow equation also reveals that a lower water-injection rate iw isdesirable since the nominator{1 [X sin()/iw]}will decrease with a lowerinjection rate iw, resulting in an overall downward shift in the fwcurve.

Sin() > 0



76/298

12/1/20

7

b) Injection Well is Located Updip:sin() is negative. When the oil is displaced downdip (i.e., injection well is locatedupdip), the term [X sin()/iw]will always remain negative and, therefore, thenumerator of fractional flow equation will be 1+[X sin()/iw], i.e.:

Y

iX

fw

w

1

sin1

o

w

rw

ro

ow

wo

ro

w

k

k

i

Akk

f

1

sin433.0001127.0

1

Injection Rate:which causes an increase (upward shift) in the fwcurve. It is beneficial, therefore,when injection wells are located at the top of the structure to inject the water at ahigher injection rate to improve the displacement efficiency.


Sin() < 0

Y

iX

f

w

w

1

sin1

Sin() > 0



77/298

12/1/20

7

Water Cutfw>1 !!!!! How and Why?


Water Cutfw>1 !!!!!!!! How?Counter Flow IN THE RESERVOIR

11/21/2011

Y

i

C

fw

w

1

1

Y

iXf

w

w

1

sin

1

Sin() < 0

o

w

rw

ro

ow

wo

ro

w

k

k

i

Akk

f

1

sin433.0001127.0

1

Sin() < 0


Rights Reserved

iwis lowif

(C/iw)> Y fw> 1


78/298

12/1/20

7

11/21/2011

Class ProblemUse the relative permeability as shown in the next slide to plot thefractional flow curve for a linear reservoir system with the following

properties:Dip angle = 0Absolute permeability = 50 mdBo = 1.20 bbl/STB, Bw = 1.05 bbl/STBo = 45 lb/ft3; w = 64.0 lb/ft3Cross-sectional area A = 25,000 ft2

Perform the calculations for the following values of oil and waterviscosities:w = 0.5, 1.0, 5, and 10 cp with a constant o = 5 cp


Sw

Kr



79/298

12/1/20

7

11/21/2011

Class Problem:

The linear system in last example is under consideration

for a waterflooding project with a water injection rate of1000 bbl/day.; which has the following characterization:Absolute permeability = 50 mdBo = 1.20 bbl/STB, Bw = 1.05 bbl/STBo = 45 lb/ft3; w = 64.0 lb/ft3Cross-sectional area A = 25,000 ft2

The oil viscosity is considered constant at 1.0 cp.Calculate and PLOT the fractional flow curve for the

reservoir dip angles of: 10, 20, and 30, assuming:

updip displacementdowndip displacement


11/21/2011

Surface and Reservoir Water CutIn waterflooding calculations, the reservoir water cut fw and the wateroilratio WORare both traditionally expressed in two different units: bbl/bbl andSTB/STB. The interrelationships that exist between these two parametersare conveniently presented below:

Qo = oil flow rate, STB/day qo = oil flow rate, bbl/dayQw = water flow rate, STB/day qw = water flow rate, bbl/dayfws = surface water cut, STB/STB fw= reservoir water cut, bbl/bbl

WORs = surface wateroil ratio, STB/STBWORr= reservoir wateroil ratio, bbl/bbl



80/298

12/1/20

8

11/21/2011

Surface and Reservoir Water CutIn waterflooding calculations, the reservoir water cut fw and the wateroilratio WORare both traditionally expressed in two different units: bbl/bbl and

STB/STB. The interrelationships that exist between these two parametersare conveniently presented below:

1) Reservoirfwr ReservoirWORrRelationship:

1)(

)(

o

w

o

w

ow

wwr

q

q

q

q

qq

qf

1

r

rwr

WOR

WORf

wr

wr

wr

rf

f

f

WOR

1

11

1

2) Reservoir fwr Surface WORs Relationship

ow

o

w

w

o

w

ooww

ww

ow

wwr

BBQ

Q

B

Q

Q

BQBQBQ

qqqf

)(

)(

osw

swwr

BWORBWORBf

)1(

)11

( wrwwro

wr

w

osfB

fB

fB

BWOR


11/21/2011

3) ReservoirWORr Surface WORsRelationship:

o

w

o

w

oo

ww

o

wr

B

BQ

Q

BQ

BQ

q

qWOR

)(

)(o

wsrB

BWORWOR )(

w

orsB

BWORWOR

4) Surface fws Surface WORs Relationship:

1)(

)(

o

w

o

w

ow

wws

Q

Q

Q

Q

QQ

Qf

1

s

sws

WOR

WORf

5) Surface fws ReservoirfwRelationship:

o

w

w

ows

Bf

B

Bf

11



81/298

12/1/20

8

11/21/2011

The fractional flow equation, as discussed in the previous

section, is used to determine the water cut fw at any pointin the reservoir, assuming that the water saturation at the

point is known. The question, however, is how to

determine the water saturation at this particular point.

The answer is to use the frontal advance equation. The

frontal advance equation is designed to determine the

water saturation profile in the reservoir at any give time

during water injection.


Frontal Advance Theory


Rights Reserved


82/298

12/1/20

8

11/21/2011

Frontal Advance Equation

Buckley and Leverett (1942) presented what is recognized as the basic equation fordescribing two-phase, immiscible displacement in a linear system. The equation is derivedbased on developing a material balance for the displacing fluid as it flows through anygiven element in the porous media:

Volume entering the element Volume leaving the element = change in fluid volume

Consider a differential element of porous media, as shown below, having adifferential length dx, an area A, and a porosity . During a differential timeperiod dt, the total volume of water entering the element is given by:


11/21/2011

Consider a differential element of porous media, as shown above, having a differentiallength dx, an area A, and a porosity . During a differential time period dt, thetotal volume of water entering the element is given by:

Volume of water entering the element = qtfwdt

The volume of water leaving the element has differentially smaller water cut fw- dfwand given by:

Volume of water leaving the element = qt (fw dfw) dt

Subtracting the above two expressions gives the accumulation of the water volumewithin the element in terms of the differential changes of the saturation dfw:

qt fwdt qt (fw dfw) dt=A(dx) (dSw)/5.615Simplifying:

qtdfwdt=A (dx) (dSw)/5.615

fw=qw/qt



83/298

12/1/20

8

11/21/2011

Sww

winj

Sw

Sww

ww

Sw

dS

df

A

Wx

dS

df

A

tix

615.5

:or

615.5

The Frontal Advance Equation


11/21/2011

Water Saturation at the Front SwfExperimental core waterflood data confirmed that there is a distinct front, orshock front, at which the water saturation abruptly increases from Swc to Swf.Behind the flood front; there is a gradual increase in saturations from Swfup tothe maximum value of 1-Sor. Therefore, the saturation Swf is called the watersaturation at the front or alternatively as the water saturation of the stabilizedzone.

Swc

Swf

1-Sor

SwcStabilized Zone

Non-Stabilized Zone



84/298

12/1/20

8

11/21/2011

Welge (1952) showed that by drawing a straight line from Swc (or from Swi ifitis different from Swc) tangent to the fractional flow curve, the saturationvalue at the tangent point is equivalent to that at the front Swf. Thecoordinate of the point of tangency represents also the value of the water

cut at the leading edge of the water front fwf.

Important to Remember:fwfis the water cut at the front(Leading Edge)

Important to Remember:Swfis the water saturationat the front (Leading Edge)


11/21/2011

From the above discussion, the water saturation profile at any giventime t1 can be easily developed as follows:

Step 1. Ignoring the capillary pressure term, construct the fractionalflow curve, i.e. fwvs. Sw.

Step 2. Draw a straight-line tangent from Swito the curve.

Step 3. Identify the point of tangency and read off the values ofSwf

and fwf.

Step 4. Calculate graphically the slope of the tangent as (dfw/dSw)Swf.

Step 5. Calculate the distance of the leading edge of the water frontfrom the injection well by applying:

Water Saturation Profile

Swfw

wwSwf

dS

df

A

tix

1615.5



85/298

12/1/20

8

11/21/2011

Step 6. Select several values for water saturation Sw greaterthan Swf and determine (dfw/dSw)Swby graphically drawing atangent to the fwcurve at each selected water saturation

Step 7. Calculate the distance from the injection well to each selectedsaturation by applying:

Sww

wwSw

dS

df

A

tix

1615.5


11/21/2011

Step 8. Establish the water saturation profile aftert1, days by plotting

results obtained in step 7.

Step 9. Select a new time t2 and repeat steps 5 through 7 togenerate a family of water saturation profiles as shown schematicallybelow

Swc

Swf

1-Sor

Swc

Water saturation profile as a function of time and distance

t2tnt1



86/298

12/1/20

8

11/21/2011

NOTICE

When constructing the water saturationprofile, it should be noted that there isno water saturation with a value lessthan Swfexists behind the water theleading edge of the water bank.


11/21/2011

Important Approach:Some erratic values of (dfw/dSw)Sw might result whendetermining the slope graphically at different saturations. Abetter way is determine the derivative mathematically byrecognizing that the relative permeability ratio (kro/krw) can beexpressed by:

wSb

rw

ro eak

k

Notice that the slope b in the above expression has a negative

value.The above expression can be substituted in fractional flowequation, to give:

wSb

o

w

w

ea

f

1

1



87/298

12/1/20

8

11/21/2011

The derivative of (dfw/dSw)Sw may be obtained mathematically bydifferentiating the above equation with respect to Sw, to give:

2

1

w

w

bS

o

w

bS

o

w

Sww

w

ea

eba

dS

df

Sww

ww

SwdS

df

A

tix

615.5

2

1

615.5)(

w

w

bS

o

w

bS

o

w

wSw

ea

eba

A

tix


11/21/2011

Class Problem:Given the following data is available for a linear-reservoir system:

Sw 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75

kro/krw 30.23 17.00 9.56 5.38 3.02 1.70 0.96 0.54 0.30 0.17 0.10

Oil formation volume factor Bo = 1.25 bbl/STB

Water formation volume factor Bw = 1.02 bbl/STB

Formation thickness h = 20ft

Cross-sectional area A = 26,400 ft.

Porosity = 25%

Injection rate iw = 900 bbl/day

Distance between producer and injector L = 600 ft.Oil viscosity o = 2.0 cp

Water viscosity w = 1.0 cp

Dip angle = 0

Connate water saturation Swc = 20%

Initial water saturation Swi = 20%

Residual oil saturation Sor = 20%

Calculate and plot the water saturation profile after 60, 100, 120, 200 and 240 days.



88/298

12/1/20

8


Rights Reserved

Understanding the Frontal Advance

Theory & its Applications

11/21/2011

Swfw

wBTw

dS

dftiVP

AL

.

615.5

iBT

Sw fw

w

BTwiBT QVP

dS

df

VPtiW ).(.

Swfw

w

iBTiBT

dS

dfVP

WQ

1

.4- P.V Injected at B.T

2- Time to B.T:

3- Cum. Water Injected at B.T:

Swfw

ww

BT

dS

dfi

VPt

1.


1- at B.T:

Swfw

wBTwSwf

dS

df

A

tiLx

615.5)(


89/298

12/1/20

8

11/21/2011

Class Problem:

Using the data given in last class problem, calculate:

time, to breakthroughcalculate cumulative water injected at breakthroughcalculate total pore volumes of water injected at B.T


11/21/2011

Average Water Saturation at B.T



90/298

12/1/20

9

11/21/2011

Average Water Saturation at B.Tlet us exam the following important expression:

iBT

Swfw

w

iBT QVP

dS

dfVPW .

1).(

If the tangent to the fractional flow curve is extrapolated to fw= 1 with acorresponding water saturation of Sw

*, then the slope of the tangent can be

calculated numerically as:

wiwSwfw

w

SSdS

df

*

01

iBTwiwBTiBT QVPSSVPW ..

Combining the above two expressions,gives:

iBTwiwiBT

QVPSSVPW .. *

Or:


11/21/2011

One more time, Key Definitions

Important to Remember:Swfis the water saturation at thefront (Leading Edge)

Important to Remember:Average water Saturationat B.T

Important to Remember:fwfis the water cutat the front (LeadingEdge) wf

wf

bS

o

w

bS

o

w

wiwBT

eba

ea

SS

2

1



91/298

12/1/20

9

11/21/2011

There are two important points that must be considered when determiningaverage water saturation at SwBT and cumulative water injected at B.T :

Point 1. When drawing the tangent, the line must be originated from the

initial water saturation if it is different from the connate watersaturation.

Swf

wf

wf

bS

o

w

bS

o

w

wiwBT

eba

ea

SS

2

1


11/21/2011

Point 2. When calculating cumulative water injected at B.T; the ArealSweep Efficiency EAand Vertical Sweep Efficiency EV must beaccounted for, as:

VBTABTwiwBTiBT EESSVPW .

VBTABTiBTiBT EEQVPW .



92/298

12/1/20

9

11/21/2011

At BreakthroughIt should be noted that the average water saturation in the swept areawould remain constant with an average SwBTuntil breakthrough occurs. Atthe time of breakthrough, the flood front saturation Swf reaches the

producing well and the water cut increases suddenly from zero to fwf. Atbreakthrough, Swfand fwfare designated as SwBTand fwBT.


Average water saturation

11/21/2011

After BreakthroughAfter breakthrough, the water saturation and the water cut atthe producing well gradually increases with continuousinjection of water. Traditionally, the produced well isdesignated as well 2 and, therefore, the water saturation andwater cut at the producing well are denoted as Sw2and fw2,respectively.

1 2 2006Tarek Ahmed & Associates, Ltd. All Rights Reserved


93/298

12/1/20

9

Waterflooding Performance

Performance Calculations are divided into two

Stages:

A. To Breakthrough

B. After Breakthrough


Rights Reserved


Recovery Performance to Breakthrough

Step 1. Draw tangent to the fractional flow curve as originated from Swianddetermine:1) Point of tangency with the coordinate (Swf, fwf) and slope of the line

2) Average water saturation at breakthrough by extending the tangentline to fw= 1.0, or by applying:

wf

wf

bS

o

w

bS

o

w

wiwBT

eba

ea

SS

2

1

2

1

wf

wf

bS

o

w

bS

o

w

Sw fw

w

ea

eba

dS

df


94/298

12/1/20

9


Step 2. Calculate pore volumes of water injected at breakthrough byusing:

)(

)(

1wiwBT

Swf

w

w

iBT SS

dS

dfQ

wf

wf

Sb

o

w

Sb

o

w

iBT

eba

ea

Q

2

1

Or equivalently:


Step 3. Assuming EAand EVare 100%, calculate cumulative waterinjected at breakthrough by applying:

wiwBTiBT SSVPW . iBTiBT QVPW .

Step 4. Calculate the displacement efficiency at breakthrough by applying

wi

wiwBT

DBTS

SSE

1

Step 5. Calculate cumulative oil production at breakthrough from

DBTSBTpENN

Step 6. Assuming a constant water injection rate, calculate time tobreakthrough from :

w

iBT

BTi

Wt

WP = 0


95/298

12/1/20

9


Step 7. Select several values of injection time less than the breakthrough time,i.e. ttBTand set:

Winj = iw tQo = iw/Bo

WOR =0Wp =0

o

inj

o

wp

B

W

B

tiN

Step 8. Calculate the surface water-oil ratio WORs exactly at breakthroughby using

11

wf

w

os

fB

BWOR

It should be pointed out that ALL calculations abve are based onthe assumption that Sgi =0, EA and EVare 100%.

Recovery Performance After

Breakthrough


Rights Reserved


96/298

12/1/20

9

11/21/2011

when the water saturation at the producing well reaches any assumed valueSw2after breakthrough, the fractional flow curve can be used to determine:

I. Producing water cut fw2II. Average water saturation in the reservoirIII. Cumulative water injected in pore volumes, i.e. Qi



Saturation around wellbore at the Production wellSw2


97/298

12/1/20

9

Step 1:Assume a value of Sw2 greaterthan Swfand draw a tangent to fwcurve. the point of tangency corresponds to the well producingwater cut fw2, as expressed in bbl/bbl.

Step 2: The saturation at which the tangent intersects fw= 1 is the averagewater saturation Sw2 in the swept area. Mathematically, the averagewater saturation is determined from:

2

222

1

Sww

w

www

dS

df

fSS

2

2

2

2

22

1)1(

w

w

bS

o

w

bS

o

ww

ww

eba

eaf

SS

Or:


Performance after B.T:

11/21/2011

Step 3: The reciprocal of the slope of the tangent is defined as the cumulativepore volumes of water injected Qi at the time when the watersaturation reaches Sw2 at the producing well, or:

2

2

2

1

w

w

bS

o

w

bS

o

w

i

eba

ea

Q

2

1

Sww

w

i

dS

dfQ

Remember, the b

is negative

Step 4: The cumulative water injected when the water saturation at theproducing reaches Sw2 is given by:

PwVAwiwinj WBEESSVPW )(. 2



98/298

12/1/20

9

11/21/2011

Step 5: Fora constant injection rate iw, the total time t to injectWinjbarrels of water is given by:

w

inj

i

Wt


11/21/2011

PVAwiwinj WEESSVPW )(. 2

2

2

2

2

2

11

1

)().(

w

w

w

bS

o

w

bS

o

w

bS

o

w

wiwVAinj

eba

ea

eba

SSEEVPW

For Spreadsheet Calculations & Working Equations

21

12

wSb

o

w

w

ea

f

2

2

2

2

22

1)1(

w

w

bS

o

w

bS

o

ww

ww

eba

eaf

SS

wf

wf

bS

o

w

bS

o

w

wiwBT

eba

ea

SS

2

1



99/298

12/1/20

9

11/21/2011

Class problem:

Using the data given in last class problem for the linear reservoir system,calculate the following when the water saturation at the producing wellreaches 0.70 (i.e., Sw2 = 0.7):

a. reservoir water cut in bbl/bblb. surface water cut in STB/STBc. reservoir wateroil ratio in bbl/bbld. surface wateroil ratio in STB/STBe. average water saturation in the swept areaf. pore volumes of water injectedg. cumulative water injected in bbl

Assume that the areal and vertical sweep efficiency are 100%, i.e., EA =

1.0 and EV = 1.0.Just in case its hard for you to go back; sa

Eor Ior Course t Ahmed

Documents

Transcript of Eor Ior Course t Ahmed