well test interprétation _ ifp
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Link on Names and Curves D. Bourdet
WELL TEST INTERPRETATION MODELS
WELLBORE MODELS
• Wellbore storage and Skin
• Infinite conductivity fracture
• Finite conductivity fracture
• Partial penetration • Horizontal well
RESERVOIR MODELS
• Double porosity, restricted interporosity flow
• Double porosity, unrestricted interporosity flow
• Radial composite • Linear composite • Double permeability,
same skin S1=S2 • Double permeability,
partial penetration S1=∞
BOUNDARY MODELS
• Sealing fault • Channel • Channel closed at one
end • Intersecting faults • Closed system
centered • Closed channel • Closed with
intersecting faults • Constant pressure
boundaries
Link on Names and Curves D. Bourdet
Shapes
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆ p'&
∆ p
∆t
∆ p'&
∆ p
∆t
∆ p'&
∆ p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t∆ p
'&∆ p
∆t∆ p
'&∆ p
∆t∆ p
'&∆ p
Link on Names and Curves D. Bourdet
Shapes
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆ p'&
∆ p
∆t
∆ p'&
∆ p
∆t
∆ p'&
∆ p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t∆p
'&∆p
∆t∆p
'&∆p
∆t∆p
'&∆p
Link on Names and Curves D. Bourdet
Shapes
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
Link on Names and Curves D. Bourdet
Wellbore storage and Skin
1. Wellbore storage, C 2. Radial, kh and S
∆t
∆p' &
∆p
kh
C
1
S
∆t
∆p' &
∆p
∆t
∆p' &
∆p
∆t
∆p' &
∆p
kh
C
1
S
Link on Names and Curves D. Bourdet
Infinite conductivity fracture
1. Linear, xf 2. Radial, kh and ST
∆t
∆p' &
∆p
kh, S1/2
xf
∆t
∆p' &
∆p
∆t
∆p' &
∆p
∆t
∆p' &
∆p
kh, S1/2
xf
Link on Names and Curves D. Bourdet
Finite conductivity fracture
1. Bi-linear, kf wf 2. Linear, xf 3. Radial, kh and ST
∆t
∆p'&
∆p
1/2kfwf
kh, ST
xf
1/4
∆t
∆p'&
∆p
∆t
∆p'&
∆p
1/2kfwf
kh, ST
xf
1/4
Link on Names and Curves D. Bourdet
Partial penetration
1. Radial, hw and Sw 2. Spherical (mobility ↑ ), kV 3. Radial, kh and ST
∆t
∆ p' &
∆p -1/2
hw, Swkh, ST
kV
∆t
∆ p' &
∆p
∆t
∆ p' &
∆p
∆t
∆ p' &
∆p -1/2
hw, Swkh, ST
kV
Link on Names and Curves D. Bourdet
Horizontal well
1. Radial vertical, kV and Sw 2. Linear (mobility ↓ ), L 3. Radial, kh and ST
∆t
∆p' &
∆p
1/2
LkV, Sw
kh, ST
∆t
∆p' &
∆p
∆t
∆p' &
∆p
∆t
∆p' &
∆p
1/2
LkV, Sw
kh, ST
Link on Names and Curves D. Bourdet
Double porosity, restricted interporosity flow
1. Radial fissures, kh 2. Transition (storativity ↑ ), ω and λ 3. Radial fissures + matrix, kh and S
∆t
∆ p'&
∆ p
kh, Sωωωω
λλλλ
∆t
∆ p'&
∆ p
∆t
∆ p'&
∆ p
∆t
∆ p'&
∆ p
kh, Sωωωω
λλλλ
Link on Names and Curves D. Bourdet
Double porosity, unrestricted interporosity flow
1. Transition, λ 2. Radial fissures + matrix, kh and S
∆t
∆p' &
∆p
λλλλ
kh, S
∆t
∆p' &
∆p
∆t
∆p' &
∆p
∆t
∆p' &
∆p
λλλλ
kh, S
Link on Names and Curves D. Bourdet
Radial composite
1. Radial inner, k1h and Sw 2. Transition (mobility ↑ or ↓ ), r 3. Radial outer, k2h and ST
∆t
∆p'&
∆p
r
k2h, STk1h, Sw
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
r
k2h, STk1h, Sw
Link on Names and Curves D. Bourdet
Linear composite
1. Radial inner, k1h and Sw 2. Transition (mobility ↑or ↓ ), L 3. Radial total, (k1h+k2h)/2 and ST
∆t
∆p' &
∆p
(k1+k2)h/2,ST
k1h, Sw L
∆t
∆p' &
∆p
∆t
∆p' &
∆p
∆t
∆p' &
∆p
(k1+k2)h/2,ST
k1h, Sw L
Link on Names and Curves D. Bourdet
Double permeability, same
skin S1=S2
1. No crossflow 2. Transition (storativity ↑ ), ω,
κ, λ (kV) 3. Radial, kh1+kh2 and ST
∆t
∆p' &
∆p
ωωωω, κκκκ kh, ST
λλλλ
∆t
∆p' &
∆p
∆t
∆p' &
∆p
∆t
∆p' &
∆p
ωωωω, κκκκ kh, ST
λλλλ
Link on Names and Curves D. Bourdet
Double permeability, partial penetration S1= ∞∞∞∞
1. Radial, k2h2 and S2 2. Transition (mobility ↑ ), λ (kV) 3. Radial, kh1+kh2 and ST
∆t
∆p' &
∆p
λλλλ
k2h2, Sw
kh, ST
∆t
∆p' &
∆p
∆t
∆p' &
∆p
∆t
∆p' &
∆p
λλλλ
k2h2, Sw
kh, ST
Link on Names and Curves D. Bourdet
Sealing fault
1. Radial, kh and S 2. Transition (mobility ↓ ), L 3. Hemi-radial
∆t
∆ p' &
∆p
L
kh, S
∆t
∆ p' &
∆p
∆t
∆ p' &
∆p
∆t
∆ p' &
∆p
L
kh, S
Link on Names and Curves D. Bourdet
Channel
1. Radial, kh and S 2. (Hemi-radial, L1) 3. Linear, L1+L2
∆t
∆p' &
∆p 1/2
kh, S
L1L1+L2
∆t
∆p' &
∆p
∆t
∆p' &
∆p
∆t
∆p' &
∆p 1/2
kh, S
L1L1+L2
Link on Names and Curves D. Bourdet
Channel closed at one end
1. Radial, kh and S 2. Linear, L1+L2 3. Transition (mobility ↓ ), L3 4. Hemi-linear
∆t
∆ p' &
∆p
1/2
kh, S
1/2
L1+L2
L3
∆t
∆ p' &
∆p
∆t
∆ p' &
∆p
∆t
∆ p' &
∆p
1/2
kh, S
1/2
L1+L2
L3
Link on Names and Curves D. Bourdet
Intersecting faults
1. Radial, kh and S 2. (Hemi-radial, L1) 3. Linear, L1+L2 4. Fraction of radial, θ
∆t
∆p' &
∆p
L1+L2
1/2
kh, S
L1θθθθ
∆t
∆p' &
∆p
∆t
∆p' &
∆p
∆t
∆p' &
∆p
L1+L2
1/2
kh, S
L1θθθθ
Link on Names and Curves D. Bourdet
Closed system centered
1. Radial, kh and S 2. Pseudo steady state, A (or
Average pressure p , and A)
∆t
∆p'&
∆p
1
kh, SA
P-
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
1
kh, SA
P-
Link on Names and Curves D. Bourdet
Closed channel
1. Radial, kh and S 2. Linear, L1+L2 3. Pseudo steady state, A (or
Average pressure p , and A)
∆t
∆p'&
∆p
1/2
kh, S
L1+L2
1
P-
A
∆t
∆p'&
∆p
∆t
∆p'&
∆p
∆t
∆p'&
∆p
1/2
kh, S
L1+L2
1
P-
A
Link on Names and Curves D. Bourdet
Closed with intersecting faults
1. Radial, kh and S 2. Linear, L1+L2 3. Fraction of radial, θ
4. Pseudo steady state, A (or Average pressure p , and A)
∆t
∆ p'&
∆ p
1/2
kh, S L1+L2
AθθθθP
-
∆t
∆ p'&
∆ p
∆t
∆ p'&
∆ p
∆t
∆ p'&
∆ p
1/2
kh, S L1+L2
AθθθθP
-
Link on Names and Curves D. Bourdet
Constant pressure boundaries
1. Radial, kh and S 2. Transition (mobility ↑ ), L
∆t
∆p' &
∆p
-1kh, S
L
∆t
∆p' &
∆p
∆t
∆p' &
∆p
∆t
∆p' &
∆p
-1kh, S
L
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