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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 =
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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
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
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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
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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
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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
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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
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KAPP
A
1987-00
Slanted Well
in a Closed Rectangle