ch-1 data used in well testing

8/9/2019 CH-1 Data Used in Well Testing

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Internal


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What Is A Well Test?

• A tool for reservoir evaluation andcharacterization

– Investigates a much larger volume of thereservoir than cores or logs

– Provides estimate of permeability under in-situ conditions

– Provides estimates of near-wellborecondition

– Provides estimates of distances toboundaries

Internal


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How Is A Well Test Conducted?qq = 0

t

q

t

p

Internal


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Well Test Applications

• Exploration

• Reservoir engineering

• Production engineering

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Well Test Objectives

• Define reservoir limits

• Estimate average drainage area

pressure• Characterize reservoir

• Diagnose productivity problems

• Evaluate stimulation treatmenteffectiveness

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Types of Well Tests

q

Single-Well Multi-WellInternal


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Development of the

Diffusivity Equation

Internal


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The Diffusivity Equation

• Describes the flow of

–

A slightly compressible fluid – Having constant viscosity

– In a porous medium

– At constant temperature

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The Continuity Equation

21

vAvAm

(A v)1 (A v)2

Internal


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Equation of State for a Slightly

Compressible Liquid

oppcoe

Internal


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Flow Equation - Darcy’s Law

or, in differential form,

L

pkAq

xpku xx

Internal


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The Diffusivity Equation

t

p

k

c

r

pr r r

1t

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Data Used in Well Testing

Internal


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Formation Volume Factor

surf

resoV

VB

Internal


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Viscosity

dyv

v + dv

dy

dv A

F

Internal


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Fluid Compressibility

p

Vln

p

V

V

1

c oo

oo

Internal


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Porosity

Internal


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Permeability

pALqk

Internal


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Pore Compressibility

p

ln

p

1

cf

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Net Pay Thickness

h = h1 + h2 + h3

Shale

Sand

h3

h2

h1

Internal


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Net Pay Thickness

Case 1 Case 3

Case 4Case 2Internal


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SaturationsH2O

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Wellbore Radius

r w

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Total Compressibility

ggwwoof t cScScScc

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Radial Flow andRadius of Investigation

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Radial Flow and

Radius of InvestigationInstructional Objectives

1. Calculate radius of investigation at a

given time or time required to reach a

given radius of investigation.

2. Describe the effects of reservoirproperties on radius of investigation.

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Radial Flow Reservoir Model

Bulkformation

hr w

r Internal


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Ei-Function Solution

kt

r c948

Eikh

qB

6.70pp

2t

i

x

u

duu

exEi

Internal


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Ei-Function Graph

0

1

2

3

4

5

6

7

0.001 0.01 0.1 1 10 100

-x

- E i (

- x

)

Ei-function

Log approximation

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Short-Time Approximation for


i p p

10948 2

kt

r ct Applies when

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Long-Time Approximation to


kt r c

kh Bq p p t i

2

101688log6.162

Applies when 01.0948 2

kt

r ct

Internal


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Pressure Profile During Drawdown

t = 0

Distance from center of wellbore, ft

P r e s s u r e ,

p s i

2000

1000

1200

1600

1800

1400

1 10 1000100 10000

t = 10000 hrs

t = 0.01 hrs

t = 1 hr

t = 100 hrs

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Pressure Profile During Buildup

Distance from center of wellbore, ft

P r e s s u r e , p s i

2000

1000

1200

1600

1800

1400

1 10 1000100 10000

t = 0.01 hrs

t = 1 hr

t = 100 hrs

t = 10000 hrs

t = 0

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Radius of Investigation

Equations• Radius of investigation for a given time

t:

• Time required to reach a given radius of

investigation r i:

ti

c948ktr

k

r c948t

2it

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Wellbore Storage

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Wellbore Storage

Instructional Objectives• Define wellbore unloading

•

Define afterflow• Calculate wellbore storage (WBS)

Coefficient for wellbore filled with A

single-phase fluid

• Calculate WBS coefficient for rising

liquid level

Internal

Fluid-Filled Wellbore -


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Fluid-Filled Wellbore -

Unloading

R a t e

Time

Bottomhole

Rate

Surface Rate

wbwb

sf w

cV

Bqq

dt

dp

24

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Fluid-Filled Wellbore - Afterflow

R

a t e

Time

Bottomhole

Rate

t=0

Surface Rate

wbwb

sf w

cV

Bqq

dt

dp

24

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Rising Liquid Level

R a t e

Time

Bottomhole

Rate

t=0

Surface Rate

cwb

wb sf w

g

g

A

Bqq

dt

dp

144

615.5

24

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ch-1 data used in well testing

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