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HORIZONTAL WELL TESTING

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Gauge Placement inHorizontal Wells

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D

D

D

D

D

D

D

D

tp

zp

yp

xp

=

+

+

2

2

2

2

2

2

pBq

hkp xD =

00708.0

tLc

kett

xD =

2

4

637.2

Solve using Greens Functions,

subject to boundary conditions

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=D D

D

t x

xDDDDD

DD

D dtdxSSSba

p0

0321

2

1

)..(2

+=

=D

DD

D

n D

DD t

an

axn

axnS

2

22

0

1

1 exp)cos()cos(21

+=

=D

DD

D

m D

DD

tb

m

b

ym

b

ymS

2

22

0

1

2 exp)cos()cos(21

+=

=D

DD

D

l D

DD t

h

l

h

zl

h

zlS

2

22

0

1

3 exp)cos()cos(21

LxxD =

LaaD =

y

xD

k

k

L

yy =

y

xD

k

k

L

bb =

z

xD

k

k

L

zz =

z

xD

k

k

L

hh =

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Horizontal Model Response

1E-3 0.01 0.1 1 10 100 10001

10

100

Without Wellbore Storage

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Horizontal WellFlow Regimes

Wellbore Storage Early (vertical) Radial Flow

Early (intermediate) Linear Flow

Elliptical Flow

Late (Horizontal) Radial Flow

Boundary Dominated Flow

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Wellbore Storage

Pressure:

Derivative:

t

qB

Cpw = 24

1

t

qB

Cpw

= 24

1

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Early Radial Flow

1E-3 0.01 0.1 1 10 100 10001

10

100

Early Radial

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Vertical Radial Flow

+

=

rc

tkk

Lkk

Bqp

wt

zy

ezy

868.0227.3log6.162

2

Pressure:

Derivative:

ezy Lkk

Bq

p

6.70'

=

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Early (Intermediate) Linear Flo

1E-3 0.01 0.1 1 10 100 10001

10

100

Early Linear

1/2

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Intermediate Linear Flow

( )dcezytye

SSLkkBq

ckt

hLqBp ++=

2.141128.8

Pressure:

Derivative:

tye ck

t

hL

qB

p

064.4'

=

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1E-3 0.01 0.1 1 10 100 10001

10

100

1/3

Elliptical Flow

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Elliptical Flow

Semi-log Pressure Derivative

35.0

7241.0

=

Dy

x

D

wD

Dt

k

k

dt

dpt

35.0

' 7241.0

= t

kkCpy

xEFw

35.0

2

B893.7

=

et

h

h

EFLc

k

hk

qC

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Late (Horizontal) Radial Flo

1E-3 0.01 0.1 1 10 100 10001

10

100

Late Radial

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Late Radial Flow

( cezyet

yx

yxSLkk

Bq

Lc

tkk

hkk

Bq

p ++

=

2.141

303.2log

6.1622

Pressure:

Derivative:

hkk

Bqp

yx

6.70' =

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Boundary Dominated Flow

1. Pseudo-steady state

2. Steady State

Note:

Both similar to vertical well

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ANALYSIS PROCESS

1. Segmented Analysis2. Modeling (Regression)

3. Integrated Approach

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Plot both pressure and derivative on log-log

Select reservoir model.

Make initial estimates of reservoir parameters;kx, ky, kz, Sd, Le, height of well from base

Run reservoir model to match actual pressure

Refine model by adjusting parameters above un

a good mach is attained

Evaluate confidence on the final parameter resu

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Use both methods whenever possible

Segmented and Modeling

Segmented analysis will help to identify the

magnitude of reservoir parameters

Modeling will help to fine tune the reservoir

parameter estimates