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Analyzing Waterflood Patterns

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Water Flooding A-Z

Frontal Advance Theory

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Water Flooding A-Z

Frontal Advance Theory

Water Oil

Swi

Sor

Piston - like displacement

Connate water

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Water Flooding A-Z

Frontal Advance TheorySaturations below th e bubblepoint

Below the bubblepoint, a free gas saturation exists inthe pore spaces.

As the reservoir pressure increases to a level above thebubble point, gas will go back into solution with the oil.

The more depleted the reservoir, the longer the timeto fill-up, and therefore, the longer the time to waterfloodresponse.

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Water Flooding A-Z

Fractional Flow Equation

We have to study the front.


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Water Flooding A-Z


The fractional flow equation is a model used todetermine the water fraction of the total fluid flow at a

particular location and time in a linear reservoirwaterflood.

It determine the location and time for a fractional flow:distances against the saturation (front) after specific date:

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Water Flooding A-Z

Fractional Flow EquationDip angle

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Water Flooding A-Z


Capillary pressure term(usually ignored)

Gravity term

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Water Flooding A-Z


The actual magnitude of capillary forces andis small and difficult to accurately determine , if not impossibleto evaluate; therefore, it is usually omitted from the equation.


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Water Flooding A-Z

Fractional Flow EquationHorizontal reservoir

Please note that

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Water Flooding A-Z

Fractional Flow Equation If the reservoir is horizontal, the fractional flow equation

is simplified because we can ignore gravity and capillary pressure.

This equation is evaluated for a point in the reservoir at a point in time. This explicitly defines a water saturation.

Taking the water saturation and entering the relative permeability curves provides k ro and k rw.

Oil and water viscosities for the average reservoir pressure are obtained from laboratory data or correlations.

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Water Flooding A-Z

Fw is function of the saturation.Ko/kwViscosities ratio are almost constantIn the fractional flow equation, the ratio of therelative permeabilities in the equation is the ratio ata given/specific saturation-that is, at one point in thereservoir.

However, in the mobility ratio equation, the waterpermeability is that in the water-contacted portion of the reservoir, and the oil permeabil ity is that in theoil bank-that is, at two different and separated pointsin the reservoir. (End points)


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Water Flooding A-Z

Fractional Flow of Water is Affected by:


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Water Flooding A-Z

Oil-Water Relative Permeability

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0

20

400 1006020 80

Water Saturation (%)

R e l a

t i v e

P e r m e a

b i l i t y

( % )

100

60

80

Water k rw @ S or

Oil

Two-Phase Flo wRegion

IrreducibleWater

Saturation

k ro @ S wi

Residual OilSaturation

Fractional Flow Curves

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Water Flooding A-Z

Information From the Fractional Flow Curvef w=1

f W

S wi 1-S or

f WF

Fraction of water flowing at theflood front

S wS w at theflood front

Average r eservoi r water saturationat breakthrough

Tangent poin t

1

00

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Water Flooding A-Z

Information From the Fractional Flow CurveSeveral important pieces of information can be derived from thefractional flow curve. By drawing a straight line tangent to thefractional flow curve, starting at f w = 0 and S w = S wi,1) At the tangent point, the corresponding S w is the water

saturation at the flood front.2) The corresponding f

wis the fraction of water flowing

at the flood front.3) The water saturation value where the tangent line

intersects (f w = 1.0) is the average water saturation inthe reservoir at breakthrough .

Note: This is for a single-layer system.4) Displacement efficiency (E) at breakthrough is calculated

from:


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Water Flooding A-Z

Example 2: Fractional Flow Curve

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Water Flooding A-Z

Example 2 Solution

Fractional Flow Curve1. S w = 55%

2. f w = 82.5%

3. = 63%

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Analyzing WaterfloodPatterns

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Mobility

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Significance of Mobili ty Ratio Mobility, as taken fro m Darcys equation is

the permeability of the rock to that fluiddivided by the viscosity of the fluid.

Water mobility i s

Oil mobility is

Mobility is a function of saturation.

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Significance of Mobili ty Ratio

Mobility ratio is d efined as a ratio of t hemobility of th e displacing fluid to thedisplaced fluid.

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Mobility Ratio

Water relative permeability is taken at average water saturationbehind the flood front while oil relative permeability is taken at oilsaturation ahead of the front . Mobility ratio calculated this way issometimes referred to as end-point mobility ratio.

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Mobility Ratio Effects

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Mobility Ratio Mobility ratio has a controlling infl uence on

the areal sweep efficiency of a waterflood.

The mobility of th e water must be suf ficientlylow and that of the oil sufficiently high toprovide a reasonably h igh areal sweepefficiency and thus economically viableimproved oil recovery.

In general, sweep efficiency and oil recoverydecrease as mobility ratio increases.

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Significance of Mobili ty Ratio

Mobility ratio is a key element in t he design ofa waterflood. It is the principal indicator usedto determine sweep efficiency.

Often waterflooding pattern performance isrepresented graphically as a functio n ofmobility ratio.

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A mobil ity ratio greater than unity, M > 1 iscalled an unfavorable mobility ratio.

Water can flow throu gh the rock better than oil.The water behind the front moves faster thanthe oil ahead of the front . As a result, the waterdoes not disp lace the oil as efficiently as itadvances towards the product ion well.

Significance of Mobility Ratio

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A mobil ity ratio less than uni ty, M < 1, is cal leda favorable mobilit y ratio.

Oil flows more easily thr ough the formationthan water. The water moves more slowly than

the oil leading to high er water saturationsbehind the front. As a result, the water sweepsthe oil towards the pro ducer more efficientlyresulting in imp roved oil recovery.

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Significance of Mobility Ratio

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Fluid Displacement inPiston-Like Manner

1 - S or

Water

S wi

Oil

Distance

W a t e r

S a t u r a t

i o n

0

1

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Fluid Displacement inPiston-Like

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dx = ((q * t)/( * A)) *

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WaterfloodPerformance Efficiencies Recovery effic iency

ER = E v ED= E A E I ED

ER = Recovery efficiencyED = Displacement efficiencyEv = Volumetric efficiencyEA = Areal efficiencyEI = Vertical efficiency

Calculation of recovery efficiency is difficult because each factoris complex. However, understanding what affects each factor isimportant to understanding waterflooding. 38

Displacement Effic iency

Displacement efficiency is defined as thefraction of oil which water will displace in thatportion of the reservoir invaded by water.

This is represented in the figure shown above.

There are several methods for determining thedisplacement sweep efficiency.

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Laboratory Work

Laboratory work with core samples can beused to estimate displacement effic iencyfor a reservoir .

Laboratory w ork and conclusionsdeveloped from laboratory results oftenrepresent ultimate displacement effic iencyand should be used with caution.

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Performance Efficiencies

Displacement efficiency (E D)

is the value of water saturation at the point wherethe tangent line to the fractional flow curve has avalue f w = 1.0. (See Frontal Advance Theory,information from the fractional flow curve.) 41

Linear Flow Models

In a previous chapter, fractional flow andfrontal advance concepts w ere developed.This model can be used to determinedisplacement efficiency using thefollowing equation.

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Linear Flow Models The displacement effici ency of a waterflood

is maximized by minimizing the fractionalflow of water as a function of w atersaturation (shift the curve to the right handside).

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ExampleDisplacement Efficiency Calculation

Given a fractional flow curve, determinethe displacement effic iency of the system.

S wi is 0.20.

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Example

Displacement Efficiency Calculation1.0

0.8

0.6

0.4

0.2

00 0.2 0.4 0.6 0.8 1.0

f w

Sw45

Example: SolutionDisplacement Efficiency Calculation

Step 1 Draw a tangent to the curve starting from

the S wc (or S wi) value.Step 2 Determine the value of the average

saturation at breakthrough, S wb t , at theintersection of the tangent on f w = 1.0 line.

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Example: Solut ionDisplacement Efficiency Calculation

Step 3 Calculate displacement effic iency.

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Areal Sweep Efficiency (E A)

E A

Water invadedarea

Producer

Injector

Areal Sw eep Effi ci ency (E A)

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Areal Sweep Efficiency Defined as the fracti on of reservoir area

which the injected water contacts. The areal sw eep efficiency changes wit h

time before and after breakthrough.

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Areal Sweep Efficiency (E A)

Fraction of the horizont al plane of thereservoir that is behind the flood front at apoint in time

Factors affecting E A Mobility ratio Well spacing Pattern geometry Areal heterogenei ti es

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Areal Sweep Efficiency

MobilityRatio = 1.43

Water Flooding:

ArealSweep

Efficiency65%

70.5% 82.2%

Water Invaded Area

Oil-Containing Area

ArealSweep

Efficiency82.8%

87.4% 95.6%

Water Invaded

Area

Oil-Containing Area

Mobility

Ratio = 0.4

Water

Breakthrough

Water Breakthrough

WOR = Instantaneous Producing Water-Oil Ratio

Production Well

Injection Wells

Area Under Observation

A smaller mobility ratio improvesareal sweep efficiency.

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Mobility Ratio

Dip Angle

Formation Connectivity

Fractures

Areal Permeability Distribution

Barriers

Flood Pattern

Injection Rate

Factors Affecting Areal Sweep Efficiency

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Areal Sweep Efficiency Craigs SPE Monograph 3 cont ains

published design charts and correlationsfor areal sweep effic iency of a wide rangeof patterns.

Laboratory experiments have been conducted to

determine the areal sweep efficiency of various patterns for different mobility ratios. These resultsand correlations are discussed at length by Craig inChapter 5 of the SPE Monograph Vol. 3.

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Pattern geometry in fluences arealsweep effic iency

Correlations exist for common patterngeometries as a function of mobilityratio.

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x

xx

x

x

0.1 1.0 10

100

90

80

70

60

50

B r e a k

t h r o u g

h

A r e a l

S w e e p

E f f i f i e n c y ,

%

Mobility Ratio

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Areal Sweep Efficiency Af terBreakthrough

Reciprocal of Mobility Ratio

% A

r e a

S w e p

t

0.1 0.2 0.4 0.6 0.8 1.0 2.0 4.0 6.0 8.0 10.050

60

70

80

90

100Vd

Vd: displaceable volume

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Vertical Sweep Efficiency

INJECTION PRODUCTION

E I =

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Vertical (invasion) sweep effic iency isdefined as the cross-sectional area contactedby injected water divided by the cross-

sectional area enclosed in all layers behindthe furthest w aterflood front.

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Vertical Sweep Efficiency Vertical sweep effic iency is infl uenced most

significantly by: Mobility ratio Vertical variation of ho rizontal

permeabilities

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Water injected into st ratified reservoirs willpreferentially invade layers of highestpermeability.

The water front w ill also f low wit h a greater

velocity thro ugh these layers. The high permeability layers w ill break through

sooner than less permeable layers causing arapid increase of water cut i n the producin gwell.

As a resul t, the economic water cu t l imit maybe reached before less permeable layers haveresponded to the waterflood. 60


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Mathematical Models of VerticalSweep Efficiency

Permeability variation Dykstra and Parsons developed an ideal

model that uses a computed coefficient ofpermeability variation , V. This term is aquantitative indicator of the degree ofreservoir heterogeneity.

This model: Dykst ra Parsons and Stilesmethods.

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Volumetric Sweep Efficiency

Volumetric effici ency is defined as theproduc t of t he pattern areal sweepefficiency and the vertical sw eep

efficiency.

(15)

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Vertical Variation of Horizontal Permeability

Capillary Pressure

Mobility Ratio

Injection Rate

Factors Affecting Vertical Sweep Efficiency

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Performance predictionsMethods

A. AnalogyB. Empirical TechniquesC. Analyti cal ApproachesD. Material Balance ConsiderationsE. Simulation Studies

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Analogy In the early stages, prior to suffi cient reservoir

and producti on data, analogy is t he mainmethod.

An analogous reservoir in the near -by area canprovide a road map provided si milarity betweenthe two reservoirs is established or assumed.

Similarity should be established in reservoircharacterization, oil properties, oil -water r elative

permeability relationship, and pre-flood recoverymechanism.

Scaling will be required; both PV and OOIP basisare utili zed.

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Empirical Techniques

Many empirical techniques have been proposed inthe waterflood literature.

They are based on the expectation that waterfloodsin reservoirs with similar geological and depositionalsettings would tend to behave similarly.

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Analytical Techniques

Methodo logy: Most o f the analyticalmethods estimate volume of cumulativeoil recovery as a function of cumulativewater injection.

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Methods Stiles (1949) Buckley and Leverett

Dykst ra and Parsons (1950) Craig, Geffen, and Morse

Analytical Techniques

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MBAL options

Material Balance

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Simulation Technique

The best tool for designing a waterflood project. The model is based on i ntegration of all the

available static and dynamic data.

The reliability of the resulting predicti ons isdependent upon simil arity between the reservoirmodel and the real reservoir.

The degree of reliability imp roves if the reservoirsimulation mod el is validated, through t heprocess of history matching , prior to its used as apredictor.

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