well Models.pdf

8/11/2019 well Models.pdf

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1

KAPP

A

1987-00

Well Test Analysis

Well Models


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2

KAPP

A

1987-00

Well models


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3

KAPP

A

1987-00

Line Source Solution (Theis)

0 .000264 k t

c trw2

pD = kh

141.2 qBp tD =


4/24

4

KAPP

A

1987-00

Wellbore Storage and Skin

C= qB

24m

tD =0.000264

kt

ctr

w

2 p

D =

kh

141.2 qBp CD =

0.8937 C

cthr

w

2 S

Specialized plot : p vs t

Unit slope


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6/24

6

KAPP

A

1987-00

Changing Wellbore Storage

Decreasing wellbore storage

Initial WBS

Final WBS

In tight gas wells, the compressibility decreases with the pressure

build-up, and wellbore storage decreases.

Unit slope


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7

KAPP

A

1987-00

Fractures

Impermeable

Boundaries

Single Vertical Fracture intersecting the wellbore

Wellbore

xf

In low permeability reservoirs a frac jobmay improve the flow into the wellbore


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8

KAPP

A

1987-00

High Conductivity Fractures

Infinite Conductivity -

No Pressure Drop along

the fracture

Uniform Flux -

Uniform Production perunit length of fracture

X f

Infinite Conductivity and Uniform Flux Vertical Fracture


9/24

9

KAPP

A

1987-00

Infinite Conductivity and

Uniform Flux Vertical Fracture

Specialized Analysis :

Early Time Linear Flow

pD = kh

141 .2 qBp CD =

0.8937C

c thXf2 S

Xf =

4.064qB

mh

kct

2000 ft fracture

tk t

c XDf t f=0000264 2.

unit slope


10/24

10

KAPP

A

1987-00

Infinite Conductivity and

Uniform Flux Vertical Fracture

Specialized Analysis :

Early Time Linear Flow

pD = kh

141 .2 qBp CD =

0.8937C

c thXf2 S

Xf =

4.064qB

mh

kct

200 ft fracture

tk t

c XDf t f=0000264 2.

unit slope


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11

KAPP

A

1987-00

Finite Conductivity

Vertical Fracture

The flow inside the fracture is no longer neglected,

and at early time we may observe a bilinear flow

kf ; w

k ; xf

The ratio kf.w/k.xfcharacterizes the bilinear flow


12/24

12

KAPP

A

1987-00

Finite Conductivity

Vertical Fracture

When the fracture effect dominates

we may observe linear flow

k ; xf

This linear flow is later dominated by radial flow


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13

KAPP

A

1987-00

Finite Conductivity

Vertical Fracture

Model # 1 Wellbore storage constant C =0

Model # 2 Wellbore storage constant C =0.001

unit slope


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14

KAPP

A

1987-00

Finite Conductivity

Vertical Fracture

Model # 2 low fracture conductivity kfw = 98000 md ft ~ unit slope

Model # 1 high fracture conductivity kfw = 1000000 md ft ~ unit slope

unit slope

~ unit slope


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15

KAPP

A

1987-00

Limited Entry

Spherical or hemi-spherical Flow : p proportional to 1

t


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16

KAPP

A

1987-00

Partially Penetrating Well

Specialized Analysis

p vs 1/sqrt(t )

Dimensionless Leading Parameters as per Homogeneous Model

plus Anisotropy, Total Vertical Drainage, Perforated Interval and Placement

m =2452 .91qB ct

kr kz unit slope


17/24

17

KAPP

A

1987-00

Horizontal Well

Dimensionless Leading Parameters as per Homogeneous Model

plus Anisotropy, Total Vertical Drainage, Horizontal contribution and Placement

kh Early = h w kzk r

Early Time Radial Flow


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18

KAPP

A

1987-00

Horizontal Well

Intermediate Linear flow


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19

KAPP

A

1987-00

Horizontal Well

khLate = krh

Late Time Radial Flow


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20

KAPP

A

1987-00

Horizontal Well

Horizontal well pressure behaviour

Sealing upper and lower

boundaries

Constant pressure upper

or lower boundaries

unit slope

unit slope


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21

KAPP

A

1987-00

Fractured horizontal well


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22

KAPP

A

1987-00

Horizontal Well with anisotropy


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23

KAPP

A

1987-00

Slanted Well

Three models :

-fully or partially penetrating

-at any angle

-in infinite or closed reservoir


24/24

KAPP

A

1987-00

Slanted Well

in a Closed Rectangle

Documents

well Models.pdf