well testing of horizontal wells

7/29/2019 Well testing of horizontal wells

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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

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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

well testing of horizontal wells

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