Derivative Library

EPS Derivative Diagnostic Library Horizontal Wells

Vertical Fractured Well Diagnostic ETR

MTR

p

Diagnostic

Model Fractured Well (InfCon)

Fractured Well (FinCon)

ETR 0s

p

0s

1/2s 1/2s

M T R

t

CRD

Diagnostic

Model

ETR

MTR

p

ETR

p

0s

M T R

1/2s

t

CRD

Diagnostic

Model

B2

ETR

p

MTR 0s

p

1s

t

CRD

Diagnostic

Model

B3

MTR

ETR

p

Model

p

t

CRD

Diagnostic

Model

ETR

MTR

0s 1/2s

LTR

Horizontal Well 0s

Model

2m m

0s

0s

Gas Cap Support (CPUB)

t

CRD or BU-MDH

Diagnostic

Model

ETR

1s

p

1/4s

Low Perm. Layer

0s

t

CRD

∆te

B10

BUF

Double Porosity and Dual Permeability Systems Diagnostic ETR

Diagnostic

Model

MTR

p

Finite Wellbore Radius

p

ETR

m

0s 1/2s

0s

0s

m/2

t

CRD

Diagnostic

Model

MTR

ETR

p

t

CRD

Diagnostic

Model

C4

M T R

ETR

p

t Diagnostic

Model

ETR

MTR

m

Diagnostic

Model

0s

p

CRD

Diagnostic p

MTR

2m

0s

t

CRD

Diagnostic

Model

p

M T 2m R m

0s

CRD

Diagnostic

Model

1/2s

t

CRD

Diagnostic

Model

MTR

p

MTR

p

1s

LTR

Closed Square

0s

8m M T p R m

t

CRD or BUD

Diagnostic

Model

E1

MTR

1s

MTR

BUF

Diagnostic

Model

LTR

45o Intersecting Faults

p 1/2s

0s

t

CRD or BUD

Diagnostic

Model

M T R

Rectangular Reservoir

p

0s

LTR

Rectangular Reservoir

1s

p

BUF

Diagnostic M T R

M T R

2m m

∆te

E4

W

D11

Diagnostic

Model

LTR

Offset Well CRD or BUD

t

Diagnostic MTR

Offset Well BUF

∆te

E6

p

MTR

LTR

p

-1s

t

Distant Gas Cap CRD or BU-MDH

Diagnostic

Model

ETR

Diagnostic

Model

0s

F1

Diagnostic p

0s

-1s

t

ETR

CRD or BU-MDH

Diagnostic

Model

MTR

p

0s

0s

F4

M T R

p 1/4s

t

t

CRD or BU-MDH

Diagnostic

Model

LTR

CPB

0s

CRD or BU-MDH

F6

t

CRD or BU-MDH

Model

ETR

M T R

0s 0s

Phase Redistribution "Humping"

Dual Porosity

t

I10

Diagnostic

Model Partially Communicating Fault

LTR

MTR

p

Model Linear Composite

LTR

0s 0s

0s

t

CRD

Diagnostic

Model

G1

MTR

t

CRD

Diagnostic

Model

G2

Linear Composite plus Barrier

LTR

Linear Composite

LTR 0s

p 0s

0s

t

CRD

Diagnostic

Model

G3

LTR

MTR

1s 1/2s

t

CRD

Diagnostic

Model

G4

Two Cell Compartmentalised

p

W

MTR

Two Cell Compartmentalised

LTR

p 1s

1s 0s

0s Well Offset

t

D6

CRD

Diagnostic MTR

CRD or BUD

t

G5

∆te

G6

BUF

Model

LTR

Channel Reservoir

p

L

W

Yeh Empirical Mod.

45o

∆te

D8

Diagnostic MTR

t

CRD

Diagnostic LTR

Model

p

Open-ended U Shape

p

1/2s 0s 0s

t

CRD

D 2m m P 0s D12

Model

Diagnostic

Homogeneous Reservoir

MTR

p L

0s

M T R

Diagnostic

120o Intersecting Faults 0s

ETR

0s

120

Diagnostic LTR

Model

Infinite-Acting

t

A1

CRD

Diagnostic ETR

Major and Minor Fault

p

1/2s

MTR

t

CRD

Diagnostic

Model

A2

Model Extreme Limited Entry

ETR

p

-1/2s

MTR

0s Tight Inner

t

CRD

t

CRD

Diagnostic

Model

A3

MTR

t

CRD

Diagnostic

Model

A4

Radial Composite

0s

ETR

p

MTR

CRD InfCon FinCon W L Lw LD m BUD BUF BU-MDH CPUB CBLB PRF

Logarithmic derivative Elapsed time in a drawdown Elapsed (shut-in) time in a buildup Agarwal equivalent drawdown time for a buildup Early time region Middle time region Late time region Derivative plateau Half slope Quarter slope Unit slope Negative half slope Negative unit slope False Flow Regime Constant rate drawdown Infinite conductivity Finite conductivity Channel width Distance to nearest boundary horizontal well length Dimensionless horizontal well length Ideal slope of semilog graph i.e. m = qµ(4πkh) Buildup under desuperposition Buildup functioned with Agarwal equivalent time Buildup without functioning or desuperposition Constant pressure upper boundary Constant pressure lower boundary Pseudo-radial flow

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Shale Lens

0s 0s

0s

~

Radial Composite

0s

0s

0s

ETR

p’ t ∆t ∆te ETR MTR LTR 0s 1/2s 1/4s 1s -1/2s -1s

Limited Entry

p

o

CRD

Model

MTR

0s

t

D10

Limited Entry and Radial Composite Systems

Model

LTR

3m

L

BUF

Channel Reservoir with Edge Water

1/2s

-1s

F5

Model

Strong Bottom Water (CPLB)

Nonintersecting Fracture

LTR

Distant Strong Aquifer CRD or BU-MDH

LTR

Gas Cap Support (CPUB)

t

Model

LTR

0s

F2

LTR

F3

p

Rectangular Reservoir

Constant Pressure Boundaries p

MTR

p 0s

Fractured Well (FinCon)

t

1/2s

0s E5

Small FCD

1s

0s

Diagnostic

Parallel Faults

p 1/2s

1s

p

t

Model

LTR

1/4s

HR

0s

0s

CRD

0s

m

D9

NWS

No Skin

IWS

Diagnostic

p

L

t

0s

0s

0s

Model

LTR

1/2s

E3

BUF

Diagnostic

Rectangular Reservoir

LTR

p

∆te

E2

Model

0s

1/2s

0s

Diagnostic

1/2s

∆te

Model

t

ETR

Model M T R

Zone

Dual Porosity Strata CRD

I8

ETR

1s

Parallel Faults

p

1/2s

D7

Diagnostic

Closed Square

LTR

LTR

Agarwal Overcorrection

Closed Reservoir Compartments Model

L

W 0s

t

Tight

0s

I6

Fractured Well (InfCon)

NWS

0s

p

1/2s

p

M T R

ETR

No Skin

IWS

0s

Model

L

Channel Reservoir 1s

p

CRD

1/2s

M T R

2m m

LTR

Model

I7

m

t

D4

L

W

D5

Diagnostic

1s

Model

Inf.-Acting

MTR

U-Shaped Faults

LTR

MTR

Diagnostic

L

p

0s CRD

t

Far Single Fault CRD

MTR

Diagnostic m m/2

0s

ETR

CRD

p

2m

Diagnostic

Semipermeable Barrier

t

NWS

LTR

t

Limited Extent (Baffle)

t

MTR

HR

0s

0s

D3

0s

C6

0s

D2

Single Fault

LTR

NWS

Phase Redistribution - the "famous spike"

1s I4

0s

Model Right Angle Faults

M T R

MTR

Partially Communicating Faults and Linear Composite Systems

LTR

4m

M T R

ETR

I9

m 0s

D1

Model

Matrix

t

p

L

Diagnostic

1s

Damage

Diagnostic

Single Fault

LTR

p

M T R

1/2s

Model

CRD

m

Horizontal Well

Model

p

Diagnostic

Semi-infinite Sealing Fault Systems

Dual Permeability

LTR

No Interporosity Skin

t

CRD

Model

H10

L

t

C5

0s

C3

High Perm Closed Layer

Infinite Low Perm. Layer

Dual-porosity (transient)

0s

0s

m/2

Reservoir Storage

1s Interporosity Skin CRD

CRD

0s 0s

p

Zone

Diagnostic

1/4s

High Perm. Zone

1s

C2

Tight

p

m

Dual-Porosity (sss)

0s

Dual Porosity Strata

CRD or BU-MDH

Conductive Fault

0s

Inf. Conductive Inner

C1

t

Model

MTR

t

Dual Porosity Strata H9

p

Strong Bottom Water (CPLB)

-1/2s

Agarwal Overcorrection B9

p

Diagnostic ETR

t

p

0s

CRD

NWS

Near Single Fault

Horizontal Well

0s

t

0s

Model

LTR

H8

LTR

I5

Horizontal Well

p

1/2s

M T R

Model

1s

Drain Hole

LD < 0.2

Diagnostic

Horizontal Well

LTR

H7

0s

t

Model

Diagnostic

2m m

Lw

H6

Diagnostic M T 2m R

0s

HR

Nonideal Wellbore Storage Homogeneous Reservoir

I2

0s

Model

Offset Position

t

CRD

I3

Horizontal Well

-1/2s

LD > 10

H5

CRD

LTR

1/2s

0s

Fractured Well (IC)

ETR

p

t

ETR

p

Natural Fractures plus Face Skin

NWS

1s

m

Diagnostic

MTR

0s Ideal Wellbore Storage Homogeneous Reservoir

2m

t

M T R

ETR

HR

11/2 Log Cycle

1s I1

Horizontal Well

Tight Matrix H4

Lw

with Storage and Skin

Diagnostic

hf

Model

2m 0s m

p

t

Limited Height Fracture IC

Diagnostic M T R

m

CRD

B8

xf

p

Fractured Well (InfCon)

0s

0s

1s

CRD

IWS

Model

p

Model

PRF

t

H3

Conductive Lens

Diagnostic M T R

CRD

p Acid Stimulation

MTR

0s

1/2s 1/2s

Diagnostic

Model

Lw

t

H2

0s

p

CRD

ETR

Apparent Quarter Slope

B7

ETR

t

1/4s 1/2s

Horizontal Well

"Geoskin"

Fractured Well (InfCon)

1/4s

LTR

p

1/2s B6

0s

Fractured Well (FinCon)

H1

ETR

No Flow Upper and Lower Boundaries

Diagnostic

0s

Thin Reservoir

1/2s

1/4s

Model

Model

MTR

0s

No Flow Upper and Lower Boundaries

Diagnostic p

0s

Diagnostic

Diagnostic ETR

Horizontal Well

Model

t

Horizontal Fracture

LTR

MTR

CRD

FCD < 10 CRD

B5

Model

p

Lw LD > 10

Diagnostic

t

0s 1/4s

0s

0s

Diagnostic

Horizontal Fracture

Horizontal Well

LTR

1/2s

t

B4

MTR

Model

p FCD > 10 CRD

1/4s

B1

Diagnostic

Model

Wellbore Storage Overlay

Conductive Inner

t

A5

Diagnostic MTR LTR m

Model Pinch-Out

p

CRD

Diagnostic

Model

MTR

Top

0s -1/2s

t

A6

CRD

p

1/2s

0s

h

Well Offset in a Channel

ETR

Botto m

A7

t

CRD

A8

t

CRD