CSG Short Course

Reservoir Engineering

Brisbane, Friday 16th October 2010

Prof. George STEWART

Weatherford International

Heriot-Watt IPE

Casing

Tubing

Testing Valve(operated by

annulus pressure)

Drillstem

Testing

Assembly

Downhole

Memory

Surface

Recording

Packer(set by weight on

string)

PressureTransducer

Tailpipe

Figure 2.1.1

Choke

GasSurface Choke providesRate Control

Q

Test Separator

Well Test Surface Hardware

Oil

Orifice PlateFlow Measurement

qo

Test Rate Limited by

Separator Capacity

Fig 2.1.1b

Test Separator

Transient Well Testing

Buildup Analysis - Horner (Theis) Plot

BuildupAffectedby

WellboreStorage Intercept

ETR MTR LTR

p*pws

Nomenclature

due to D.

Pozzi (EPR)

Fig 2.1.3

4 k hπ

q Bs

µ

Semilog Analysislnt + tp ∆

∆t

Storage InterceptgivesskinfactorS

Affectedby

Boundariesslope = −

altered

zone

p

Unaltered

Permeability

k

Fig2.1.4a

Near Wellbore Altered Zone

pw

pw f

∆ps

k

rw rs re

wellbore

radius

altered zone

radius

external

radius

∆p = Incremental Skin Pressure Drop

s

ks

x Heated Bar

Thermocouples in thermowells

Inner B.C.

Linear Flow

t

FaceTemp.

Dynamic Temperature Distribution

∂ ∂T k T=

2q

kT

= −∂

Constant

heat

flux

T(t=0)

x

Transient Heat

Conduction Equation

i.e.

. . . specified

gradient

(2 kind BC)nd

t

Penetration Depth

Initial Temp.

T

Fig 2.1.9

∂

∂ ρ

∂

∂

T

x

k

C

T

xp

=2

q

AkT

xx

= −

=

∂

∂0

∂

∂

T

x

q

kAx=

= −

0

The Conduction

of Heat in Solids

by

H.S. Carslawand

J.C. Jaeger

Clarendon PressOxford1959

PanMesh

Finite Element

Numerical

Simulation

of

Diffusion Equation

Problems

FEM

Comprehens ive

Library of

Analyt ical

Solut ions

All Commercial

Heat Conduction

Codes are FEM

e.g. NASTRAND

Used to Solve

Perforation Completion

and RFT Probe

Problems

Foundation of

Many Transent Well

Testing Papers

Foundation of Many

Transient Well Testing

Papers

Sydney Opera House

t

p(r ,t)

pi

Well-Bore

Fig 2.2.2

ln r

tBore

Trans ient Deve lopment o f

the Format ion Pressure

Dis t r ibu t i on

p EirtDD

D

=

1

2 4

2

For

( )∆ pq

p EiDµ12

10 2194

2011= = = =

..

r

ti e r tD

D

Di D

2

41 4= =. .

Radius of Influence

qkhµ

π22 2

Arbitrarily chosen as defining the appreciable depth

of penetration of the pressure disturbance

r tk tci

t

= =44

αφµ

Classical depth of penetration formula in diffusional processes

Synonomous with depth of investigation

pt

SwDD= +

12

4ln

γ

Dynamic Formation

Dimensionless

Quasi-Steady-State

Dimensionless Skin

Addition of Quasi-Steady-State Skin Effect

Dimensionless

Pressure Drop

Dimensionless Skin

Pressure Drop

( )p t pq

khk tc r

Swf it w

= − + +

µπ φµ4

0 80908 22ln .i.e.

Additional (constant) pressure drop is given by:

Both S and q are presumed constant

Skin factor is a measure of completion efficiency

Different meaning in fractured systems

∆ pq

khSs =

µπ2

rD01 200

q

t = 10pD

4

t = 10D

4

∆

50

200

2 103

pwsD

5

0t pD

∆ t D

Pressure Build-Up in a Reservoir

Figure 2.5.2

10

∆p

p =d( p)∆

d( t)ln

. . . Local slope ofsemilog graph

Tangents to Curve(Obtained by Numerical

Differentiation)

Logarithmic Derivative

Ln p

Ln t

Ln t

Differentiation)

Plateau

ETR MTR LTR

Slug

TestingNote RisingLiquid Level

hCushion

Valve

Closed

GaugeRegisters

pi

Fig 6.11.1

p = ρgh

- assuming negligible friction and KE losses

q Adh

dt

A

g

dp

dt

w= =ρ

Field Units qA dp

dt

w= 9 86.ρ

Well with Rising Liquid Level

Field Units qdt

= 9 86.ρ

q : bbl/D

A : ft

: g/cc

p : psi

t : hr

2

ρ

w

- flow-rate obtained from the natural derivative of the pressure

Note form:

q Cdp

dt=

p q

Draw-down

VRD

Build-up

VRB

Slug

Schematic of Complete Slug Test including Shut-in

pi

pw

po

q

0ValveOpens

ValveCloses

Slug

Tes t

Fig 6.11.3Time, t

∆ t

Australian CSG (CBM) DST

rw = 0.3542 ft h = 14.1 ft φ = 0.02 Bw = 1.0038 µw = 0.736 cp cw =

3.177×10-6 psi-1 ct = 3.6468×10-6 psi-1 T = 93oF

85.2

66.1q = 101 bbl/d

Australian CSG (CBM) DST

pwf(tp) = 344.0 psia

pi = 386.1

psia

47

po = 272.8

psia

Log-Log Diagnostic of Final Buildup

US

k = 124 md

DP

k = 124 md

S = 6.83

Three rate points in history

Elapsed Time (hr)

pppp2222

pppp1111

Control Volume

X-sectional Area, A

Steady-State Realisation of a Naturally Fractured Reservoir

No Flow

C P

F r a c t u r e

N e t w o r k

kf = Bulk Average Fracture Network Permeability

( Continuum Theory ) Fig 10.1.1

q

A

k p p

L

fb=−

µ

2 1

WaterFlowOnly

CDP

Pressure Drawdown Profileof a Single Well

Only

DiscontinuousGas Flow

ContinuousGas Flow

After Airlie

500

400

300

Ca

pa

city

(scf/

ton

) Gas Storage Capacity450 scf/ton

InitialGas

Content355 scf/ton

InitialReservoir

CriticalDesorption

Langmuir Isotherm and Gas Desorption Calculations

200

100

0

Ga

s

Sto

rage

C

5000 1000 1500 2000

Pressure (psia)

ReservoirPressure

1,620 psia

DesorptionPressure632 psia Maximum Gas Recovery

230 scf/ton

Abandonment Gas Content125 scf/ton

Abandonment Pressure100 psia

Gas Recovery Factor

230355

= 0.648

After Airlie

Gas - Water Relative Permeability CurvesGas - Water Relative Permeability CurvesGas - Water Relative Permeability CurvesGas - Water Relative Permeability Curves

0.6

0.8

1

kkkkrrrr

m = 3.5 n = 2.0

krgo = 1.0 krw

o = 0.365

Swc = 0.365 Sgr = 0.3

0

0.2

0.4

0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7

SSSSwwww

kkkkrrrr

Fig 19.6.1

1.0

0.8

0.6

kr

Gas - Water Relative Permeability Curves

KC32KB24

KA12

Low kGroup

0.013 md ( = 0.0151)φ

0.14 md ( = 0.0158)φ

0.262 md ( = 0.0263)φ krw

2.5 in dia

0.4

0.2

05040 60 70 80 90 100

S (%)w

After Shedidand Rahman

Group

krg

2.5 in diacore plugs

Australian Coal

6

8

10

12

SGB

Gas Block Skin, SGB

rw = 0.35 ft

ka = 0.365k

k/k − 1 = 1.74

0

2

4

6

0 50 100 150 200 250 300

SGB

Radius of Gas Block Region, ra (ft)

a

k/ka − 1 = 1.74

w

a

a

GBr

rln1

k

kS

−=

Log-Log Diagnostic and Type Curve

p

∆ t

ETRWBS

MTR

singlephasegas

DP

DP

Radial Composite

twophase Transition

k k1

1µ µ=LNMOQP

k k2

2µ µ=LNMOQP

Radial Composite Behaviour in a

CBM System

∆ t e

∆ t e

pws

Semilog Plot

SecondSt raigh tLine

FirstStraightLine

Total(Pseudoradial)

Skin

Fig 16.3.3

slopek

→ 1

1µ

slopek

→ 2

2µ

2nd Australian CSG (CBM) DST

Rate steps: 70.8, 66.9, 63, 60.5, 57.5 bbl/d

rw = 0.1573 ft h = 10.3 ft φ = 0.02 Bw = 1.008 µw = 0.589 cp cw =

3.03×10-6 psi-1 ct = 2.03×10-4 psi-1 T = 113.6oF

Log-Log Diagnostic of Final Buildup

Five rate points in history

k h1 1

Region 2

k h2 2

Pressure Propagation in a Linear Composite System

Region 1

k h1 1 k h2 2k h2 2

Active Well

Koenig, R.A., Choi, S.K. and Meany, K.T.A.:“Dartbrook Coal Mine

Two-Phase Well Testing, Boreholes

DDH79, DDH81, DDH83, DDH84, DDH94, DDH106 and

DDH107”, ACPRC Report No. 068, CSIRO Petroleum Australia, May

1994

• Variation of permeability with depth was investigated by Koenig et al

• Injection, falloff and production tests carried out in six wells

• Depths in the range 180 – 292 m

• Wynn Upper A seam (4m interval)

• Trend of decreasing permeability with increasing effective stress apparent• Trend of decreasing permeability with increasing effective stress apparent

• Mean permeability from an interference test and laboratory measurements

also plotted

Durucan, S. And Edwards, J.S.:“The Effects of Stress and Fracturing on the Permeability

of Coal”, Mining Science and Technology, 3, 1986, 205-216

• The high sensitivity of coal permeability to effective stress is well known

3

1

σ∝k approximately

10000

1000

100

Permeability, k

*103

(md)

Laboratory Permeability versus Effective Stress

All Tests

Well DDH140

10

10 2 4 6

Effective Stress, (Mpa)σ

(md)

k = −756 3 06σ .

After Wold and Jeffreys

φ

φi = 1 +

p − pi

φiM

k

= φ 3

Palmer and Mansoori CBM Rock Mechanics Model

Recommended

by Mavor

- Based on Linear Elasticity

Code Porosity Cutoff

φ = 0.00001

Does not handle

permeability rebound

very sensitive to φi

k

ki =

φ

φi

M = E1 − ν

(1 + ν)(1 − 2ν)

K = M

3

1 + ν

1 − ν

E = Young’s Modulus ν = Poisson’s Ratio

Constrained Axial

Modulus

Bulk Modulus

Palmer and Mansoori Data for the San Juan Basin

Poisson’s Ratio, ν• Poisson’s ratio measured on core in the laboratory fall in a range 0.27 – 0.4

• Large scale Poisson’s ratio should be about a factor of 1.15 greater

• “Good” average, large scale ν = 0.39

Young’s Modulus, E

Elastic Parameters

• Young’s modulus has been determined in two ways

• Static core measurements

• Measurements of PV compressibility, c• Measurements of PV compressibility, cf

• cf = 1/(2Eφi)

• Core measurements

• Range of (3 – 7)×105 psi (Jones et al)

• Large scale modulus should be about 4 times smaller

• This gives Els (0.75 – 1.75)×105 psi

• Pore volume compressibility

• Average of several cf measurements lie in the range (23.3 –

96.9)×10-5 psi-1

• φi lies in the range 0.001 – 0.005

• Hence E = (1.72 – 7.15)×105 psi

• Mean of core and PV compressibility results E = (1.24 – 4.45)×105 psi

Choking Condition in Production (Drawdown)

rw = 0.26 ft h = 2.5 ft µ = 0.65 cp Bo = 1.005 ct = 3.003×10-3 psi-1

E = 500,000 psi ν = 0.25 n = 3

pi = 734 psia ki = 11.3 md φi = 0.001

Parameters from Mavor IFO Field Example (q = -96 bbl/d)

qcrit = 7 bbl/d

tp = 10 hr

CRD

Invasion of Natural Fractures

by Mud Solids

NTS

Candidate for UnderbalanceDrilling

High Fluid Loss whenDrilled Overbalance

15

20

25

30To

tal A

pp

are

nt

Sk

in,

Sa

Apparent Skin from Conventional Buildup Analysis

φi = 0.01

Effect of True Skin is Magnified

0

5

10

0 1 2 3 4 5 6 7 8

Tota

l A

pp

are

nt

Sk

in,

S

True Skin, S

Sσ = 1.3725

Well “Chokes”

Mavor Field Example Data (Unreduced)

Injection Falloff

pwf(tp) = 1504.56 psia

pw

(psia)

q = −96 bbl/d

Time (hr)

Mavor Field Example (Injection and Falloff)

Falloff period

(IFO)∆p(psi)

rw = 0.26 ft h = 2.5 ft m = 0.65 cp cw = 3.0×10-6 psi-1 Bw = 1.005

q = -96 bbl/d pwf(tp) = 1504.56 psia tp = 8.6458 hr

Elapsed Time, ∆t (hr)

Manual Match of Mavor Data

SDPP + NIWBS Model

(Hegeman)∆p(psi)

k = 11 md S = 4.5 φi = 0.0009 Cs = 3×10-5 bbl/psi

t = 0.075 hr Cf = -6900 psi

E = 5×105 psi ν = 0.25 n = 3

Elapsed Time, ∆t (hr)

tp = 8.6458 hr

5

6R

ate

, q

(

bb

l/d

)Production Forecast (Dewatering)

pi = 734 psia

pwf = 500 psia

Constant BHFP

k = 10.8 md S = 2 n = 2.466

3

4

0 200 400 600 800 1000

Flo

w-R

ate

, q

(

bb

l/d

)

Time, t (hr)

Mavor Field Example Analysed with 90o Fault Boundary Model

(No Stress Dependency)

φi changed from 0.001 to 0.01

Results from Nonlinear Regression

Cs = 1.789×10-4 bbl/psi τ = 0.0742 hr Cφ = -1000 psi

k = 30.63 md S = -0.0105 L1 = 24 ft L2 = 54.5 ft pi = 723 psia

Dewatering Transient Rate Based on Fault Model

Mavor Field Example

Wa

ter

13 bbl/d

SDPP Model predicted 4 bbl/d

Structure

• Formation Geometry

• Natural Fractures

• Faulting

• Folding

• Stress/Compression

Well

A

Well

C

Well

BPermeability

Facies Change

Channel

Sandstone Belt

Fault

Offset

Coal

Pinch

Out

Offset

Schematic Diagram of Coalbed Reservoir Geometry

Components that affect lateral continuity, cleat

properties, permeability, and porosity

CRB

Derivative L-L Diagnostic Derivative L-L Diagnostic

Apparent

Testing Strategy for CBM Wells

Buildup Following Production Falloff Succeeding Injection

IFO

k DP k DP

ApparentDP

Ideal SDPP Alone

Including Storage andBoundary Effect

ApparentDP

Buildup Identifies Presenceof Boundary Effects

In Falloff SDPP andBoundary Effects are Similarand Combine to Give Steep

Derivative Response

k DPik DPi

Strategy for Testing CBM (CSG) Wells

• In Australia Rising Liquid Level DSTs (Slug Tests) have largely been employed

• Objective has been to determine permeability, skin and pressure• Results have often indicated high skin the nature of which must be

clarified• Origins of skin are:

• Drilling (formation) damage• Stress effect on near wellbore permeability• Gas block due to gas desorption• Gas block due to gas desorption

• DST Test Results have revealed considerable complexity:• Faulting (boundary) effects• Radial composite behaviour• Reservoir compartmentalisation• Limited Entry

• Radial composite effect may be:• Formation damage inner region• Reservoir effect such as increasing kh away from the well• Linear composite• Gas block

Porosity Dilemma

• In CBM (CSG) wells it is difficult to obtain porosity from either logs or core data

• Well test interpretation requires a realistic φ value to correctly model the diffusional aspect of the pressure propagation

• Fortunately the determination of permeability does not involve porosity

• Effect of porosity on computed skin is weak because φenters a logarithmic term

• Operators have used a porosity which allows production data (dewatering) to be modelled

• This is not the value which should be used in the Palmer-Mansoori SDPP model

• Practitioners in the US have used φi = 0.001 in the SDPP model

• This is misleading!• Porosity can be determined in well-to-well interference

testing