Course Pansystem Interpretation

Interpreting CBM Well Tests

Houston Feb 25th 2010

Prof George STEWART

Weatherford Geoscience

SPE GCS Reservoir Study Group

Weatherford Geoscience

Institute of Petroleum Engineering

Heriot-Watt University

3rd Australian CSG (CBM) DST

Rate steps: 34.6, 32.8, 31, 27.8, 27.2 bbl/d

rw = 0.1573 ft h = 7.96 ft φ = 0.02 Bw = 1.013 µw = 0.475 cp cw = 3.03×10-6 psi-1 ct = 2.03×10-4 psi-1 T = 134.6oF

Log-Log Diagnostic of Final Buildup

Interpretation Based on 90o Intersecting Faults

Five rate points in history

Radial Flow SL

Semilog Analysis of Final Buildup

L1 = 14.8 ft L2 = 20.8 ft

Hemi2

Radial

Flow

3rd QLD CSG DST

pi = 1446.9 psia

k = 3.53 md

S = 9.42

2nd NSW CBM Test

Classical Falling Liquid Level Slug Test

h = 23.2 ft φ = 0.01 rw = 0.1575 ft T = 71.6oF µw =

0.951 cp c = 1.59×10-5 psi-1 B = 10.951 cp ct = 1.59×10-5 psi-1 Bw = 1

NSW Falling Liquid Level (Slug) Test

540.4 psiapc

429 psiapi

Pressure Integral Log-Log Diagnostic Plot

I(p)

pi − po

pi = 429 psia pc = 540.4 psia Cs = 0.021 bbl/psi

pi = 254 psia

Diagrammatic Illustration of a Slump Block of Limited Volume

PotentialLeakage

Path

Only a possible geological explanation

This block is chargedup in pressure during

the injection

4

5

6

7

Skin

, S

σσ σσ

Stress Dependent Skin Contribution, Sσσσσ

rw = 0.35 ft h = 100 ft Bo = 1 µo = 1 cp

ct = 80.3×10-5 psi-1 φi = 0.005 ki = 15 md

E = 125000 psi ν = 0.39 n = 3

pi = 1500 psia

Skin calculated from BU following

0

1

2

3

0 100 200 300 400 500

Skin

, S

Well Flow-Rate, q (bbl/d)

Skin calculated from BU following

a period of production

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

Ss = 1.3725

Well “Chokes”

Stress Dependent Permeability and Porosity

(SDPP)

CBM Evaluation:

Injection Fall-Off Test Example: High Perm

Reservoir Analysis

Well Shut- In

Start

Pumping

13

Inflate

Packer

Formation Temp

Pumping

Steady-State Radial Flow with Pressure Dependent

Permeability and Porosity

D’Arcy’s Law:

( )( )

dr

dppku

prh2

q

A

qr

µ−==

π=

( ) ( )[ ]p1ph)p(hh ii φ−

==( ) ( )[ ]

( )[ ]p1

p1ph)p(hh ii

effφ−

φ−==

. . . Compaction of formation due to porosity change

( ) ( )[ ] ( )( )

dpp1

pk

q

p1ph2

r

dr ii

φ−µ

φ−π−=

Separating the variables:

h = h(p)eff

p

pi

h(p)ih(p )w

Stress Dependent Height Compaction

=−

−

h p p

p

i i

b g1

1

φ

φ

rw

re

r

pw . . . used in formulation of SDPP pseudopressure

− pb g1 φ

( ) ( )[ ] ( )( )∫∫ φ−µ

φ−π=

e

w

e

w

p

p

ii

r

r

dpp1

pk

q

p1ph2

r

dr

Integrating:

( )[ ]( )

( )( )∫ φ−

φ−

µ

π=

e

w

p

pi

iii

w

e dpp1

pk

pk

p1

q

hk2

r

rlni.e.:

ψφ

φp

k

k p

pdpi

i p

p

b

b g b gb g=

− ′

− ′′z1

1

Normalised Pseudopressure definition: Reservoir

Integral

k p

pdp

k p

pdp

k p

pdp

p

p

p

p

p

p

b

e

w

e

b

w′

− ′=

′

− ′−

′

− ′zz zb gb g

b gb g

b gb g1 1 1φ φ φ

Reservoir integral may be expressed as the difference

between two pseudopressures:

lnr

r

k h

qp pe i i

e w= −2π

µψ ψb g b gm rln

r qp p

w

e w= −µ

ψ ψb g b gm r

Inclusion of Skin and Conversion to Semi-Steady-State:

lnr

rS

k h

qp pe

w

i iw− + = −

3

4

2π

µψ ψb g b gm r

ppb

p

pb

p

k(p)

k(p )

1 (p)− φ

1 (p)− φdp

InputRock Mechanics

Parameters

E, , nν

Generate Pseudopressure

Functionby Quadrature

Palmer-MansooriModel

Generation of the

SDPP

Pseudo-Pressure

Function p

ψ(p)

(psia)

(psi)

ψ(p)

ψ(p)

mr

rSe

w

ln − +M P3

4

Well SSS Deliverability

ppw

ψ(p )w

rw

M P4

Well deliverability curve reflects the shape of the pseudopressure functionEffect of Skin is magnified at low wellbore pressure

mq

k hi i

=µ

π2

FlowingBottomholePressure(FBHP)

pw

pWell Deliverability Curve

Effect ofDecreasingReservoir

Single PhaseLiquid (Water)

0Flow-Rate, q

pw

AOF

ReservoirPressure

Similar to Gas Well Behaviour i.e. curved IPR

SDPP Case

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

SDPP Test Problem

pi = 1500 psia ki = 15 md φi = 0.005 E = 1.25×105 psi ν = 0.39 n = 3

ct = 80.3×10-5 psi-1 h = 100 ft q = 500 STB/D µ = 1 cp Bo = 1 tp = 10 hr

• Typical parameter values relevant to CBM (CSG)

• High total compressibility, ct• High total compressibility, ct

• Test Design in well test software used to generate synthetic data

• Test declared as oil but given water properties

• This artifice allows access to pseudopressure option in software

Note: setting ν = 0.5 reduces SDPP model to

radial homogeneous behaviour

φ - natural fracture (secondary) porosity


CRD

∆p

pi = 1500 psia ki = 15 md φi = 0.005 E = 1.25×105 psi ν = 0.39 n = 3 ct = 80.3×10-5 psi-1 h = 100 ft q = 500 STB/D

SDPP Model - CBM

p'

Ideal DP kh = 1500 md.ft

p' =d∆p

dln t

Handling of SDPP in Pansystem

Method 1

Rock mechanics and known

Generate and import pseudopressure function, (p)Analyse data as a liquid systemWhole test can be analysed conventionallySimilar procedure to gas well analysis

φ

ψi a priori

Method 2

SDPP pseudomodelFlow and shutin periods handled separatelyPseudopressure computed within modelRock mechanics variables become parameters in regression

Especially and n

Shutin period modelled as equivalent flow period Synthetic initial pressure required

φi

SDPP Pseudopressure

• In gas well testing pseudopressure [ m(p) ] allows interpretation

for k and S in the usual way on log-log or semilog plots

• This is not the case in the SDPP situation

• ki , φi and rock mechanics parameters (E, ν, n) are required to generate a pseudopressure

• SDPP pseudomodel allows all parameters to be included in the

nonlinear regression process (Quickmatch and Automatch)

• Pseudopressure is used to validate an interpretation once the • Pseudopressure is used to validate an interpretation once the

parameters have been identified

• Early work of Raghavan and Cinco showed that data generated

using a numerical model could be transformed to the liquid

solution using SDPP pseudopressure

• Hence the pseudopressure method can be used to generate

SDPP responses (if the above parameters are specified)

• The term φct in the accumulation term of the diffusivity

equation does, in fact, vary with pressure through φ• Is Agarwal pseudotime necessary?

SDPP Model - StressDependPerm

• Key feature is the embedding of the pseudopressure

calculation in the model

• This allows rock mechanics parameters to be estimated by

regression

• Constant rate model

• Wellbore storage can be added in well test software• Wellbore storage can be added in well test software

• Finite wellbore radius (FWBR) solution which can handle

negative skin

• Variable rate convolution not allowed

SDPP Model - StressDependPerm

Parameter List:

k, S, E, ν, n, qref, tp, φ, pref

• k and φ evaluated at pref

• Parameters in red must be specified and not selected as

iteration variables in nonlinear regression

• pref may be pi but not necessary

• Allows rock mechanics parameters to be determined by • Allows rock mechanics parameters to be determined by

regression, particularly the exponent, n

• Most common regression subset is k, S and n

• Usually the coal properties, E and ν, are known independently• tp = 0 defines drawdown or injection at constant rate

• tp > 0 defines buildup or falloff preceded by constant rate

• Constrained by DLL facility in well test software

• Buildup or Falloff treated as equivalent drawdown or buildup

• In this case q +ve for Falloff and -ve for Buildup

CRD

pi = 1500 psia ki = 15 md φi = 0.005 E = 1.25×105 psi ν = 0.39 n = 3

ct = 80.3×10-5 psi-1 h = 100 ft q = 500 STB/D rw = 0.35 ft µ = 1 cp B = 1

pwf

(psia)

Simulation of Constant Rate Production (Test Design)

SDPP Model - CBM

Time, t (hr)

pwf(tp) = 927.113 psia

Last Flowing Pressure required for Buildup Simulation


CRD

∆p

pi = 1500 psia ki = 15 md φi = 0.005 E = 1.25×105 psi ν = 0.39 n = 3 ct = 80.3×10-5 psi-1 h = 100 ft q = 500 STB/D rw = 0.35 ft µ = 1 cp B = 1

SDPP Model

∆p

(psi)

SDPP Model - CBM

p'

Homogeneous Model

SDPP Model

Production

Time, t (hr)

Method 1 - SDPP Pseudopressure Import

• Rock mechanics model assumed known i.e. E, ν, n and φi are specified a priori

• Normalised pseudopressure function generated and imported into well test software

• Test analysed in terms of transformed pressure• Stress dependent effect is implicitly backed off• Interpretation yields k and true skin, S• Interpretation yields ki and true skin, S• Any well test model can be used to interpret the transformed

data• No-flow boundary, vertical fracture and radial composite effects

have been observed in CBM tests• Main problem is defining the initial porosity, φi, to use in the

Palmer and Mansoori model• E = 500,000 psi and ν = 0.25 are “good” values for coal seams• Iteration is required to find stress dependence of permeability

Analysis of CRD using Normalised SDPP Pseudopressure

∆ψ(p)

Liquid Solution k = 15 md S = 0

Pseudopressure Transform of Figure 2.6

q = 500 STB/D

(psi)

Production

CBM Data

Time, t (hr)

Critical Conditions in Production (Drawdown)

• Condition where permeability at the sandface has reduced to zero• Sandface closure• Unique to production (drawdown)• Flow-rate, q, cannot be larger than the critical (specified fi , pi and kh)• Or fi must be greater than fi,crit for specified flow-rate, q

Critical Conditions in Production (Drawdown)

rw = 0.35 ft µ = 1 cp Bo = 1 pi = 1500 psia k = 15 md S = 0 ct = 80.3×10-5 psi-1

E = 500,000 psi ν = 0.25 n = 3

q = 500 bbl/d φi = 0.0025 h = 81 ft

Sandface

Closure

At h = 80 ft a simulation “crashes”

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

Rock Compressibility, cf (Pore Volume)

Palmer and Mansoori

i

fE2

1c

φ=

Van den Hoek

)21(3c

υ−=

Almost identical when ν = 0.39

i

fE

cφ

=

ct = cwSwc + co(1 - Swc) + cf or ct = cw + cf

ct should be updated if E, φ or ν are changed by regressioncf is not pressure dependent

Use of Effective Young’s Modulus, E′

( )( )

( )( )ν−ν+

ν−=ν

ν′φ

−−=

φ

−−=

φ

φ

211

1f

fE

pp1

M

pp1

i

i

i

i

i

Palmer and Mansoori

• Enter log porosity, φi, into Pansystem parameter set

• Calculate rock compressibility from accepted value of E

• Use effective E′ to achieve variation in SDPP model

• This maintains correct diffusivity in the simulation


CRB

tp = 10 hr

∆p

′ =+LNM

OQP

pd p

dt t

t

p

∆

∆

∆

b gln

∆p

(psi)


∆p = pws − pwf(tp)

Buildup Following Constant Rate Production

p'

µ = 1 cp q = -500 STB/D Bo = 1 ct = 80.3×10-5 psi-1 rw = 0.35 ft h = 100 ft

ki = 15 md φi = 0.005 E = 1.25×105 psia ν = 0.39 n = 3 pi = 1500 psia

NM QPd

t∆ln

Elapsed Time, ∆t (hr)

DP k = 15 md

∆p = pws − pwf(tp)

Injection Well Falloff

CRStp = 10 hr

′ =+LNM

OQP

pd p

dt t

t

p

∆

∆

∆

b gln

∆p

(IFO)pwf(tp) = 1719.58 psia

∆pFO

(psi)

µ = 1 cp q = -500 STB/D Bo = 1 ct = 80.3×10-5 psi-1 rw = 0.35 ft h = 100 ft

ki = 15 md φi = 0.005 E = 1.25×105 psia ν = 0.39 n = 3 pi = 1500 psia

p'

Ideal DP kh = 1500 md.ft

Equivalent Time, ∆te

Mavor Field Example Data (Unreduced)

Injection Falloff


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


0.1

1

10

tD*d

pD

/dtD

dp01/s1 = dp02/s2 = 0.1

After Van den Hoek

SPE 84289

Derivative Fingerprints for IFO

Shrinking Fracture Model

pD′

0.001

0.01

1E-3 1E-2 1E-1 1E+0 1E+1 1E+2

tD

tD*d

pD

/dtD

dp01/s1 = dp02/s2 = 0.1

dp01/s1 = dp02/s2 = 0.3

dp01/s1 = dp02/s2 = 0.5

dp01/s1 = dp02/s2 = 0.7

dp01/s1 = dp02/s2 = 0.8

dp01/s1 = dp02/s2 = 0.9

dp01/s1 = dp02/s2 = 0.95

tD

Total Compressibility, ct

ct = cf + cw

cE

f

i

=−3 1 2ν

φ

b g

φi = 0.001 ν = 0.25 E = 5×105 psiFor coal :

cf = 3×10-3 psi-1 i.e ct = 3.003×10-3 psi-1

. . . very high rock compressibility

Determination of Initial Reservoir Pressure, pi

IFO

k = 11.3 md

Semilog (Horner) Graph

S = 4.5pws

(psia)

Extrapolated pressure, p* = 734 psia

Horner Time Function

tp = 8.6458 hr

DP k = 11.3 md

Permeability Range in IFO Data

∆p(psi)

DP k = 26 md


tp = 8.6458 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


tp = 8.6458 hr

400

500

600

700

Pseudopre

ssure

, y

(p)

(p

sia

)

Field Example Pseudopressure Function

ki = 11.3 md φi = 0.001 pi = 734 psia

E = 500,000 psi ν = 0.25 n = 3

0

100

200

300

500 600 700 800 900 1000

Pseudopre

ssure

, y

(p)

(p

sia

)

Pressure (psia)

Falloff Log-Log Diagnostic Based on Pseudopressure

Mavor Field Example

∆ψ(p)(psia)


Falloff Semilog Analysis Based on Pseudopressure

Mavor Field Example

ψ(p)

(psia)

k = 10.15 md S = 0.079 pi = 754 psia

Horner Time Function tp = 8.6458 hr

(psia)

DP k = 11.3 md

Revised Permeability Range in IFO Data

Cs = 0∆p(psi)

DP k = 54 md

φi = 0.001 E = 5×105 psi ct = 3×10-3 psi-1

Cs = 0 “False” Plateau

tp = 8.6458 hr


Improved Match with n Increased to 4.5

SDPP + NIWBS Model

∆p(psi)

ki = 7 md φi = 0.001 S = 13 Cφ = −7900 τ = 0.075 hr Cs =

3.0×10-5 psi-1 E = 5.0×105 psi ν = 0.25 n = 4.5


tp = 8.6458 hr

Permeability Range of Revised Model

DP k = 7 md

∆p(psi)

DP k = 70 mdki = 7 md φi = 0.001 S = 13 Cs = 0

E = 5.0×105 psi ν = 0.25 n = 4.5

Wellbore storage removed, extended FO

50


tp = 8.6458 hr

SDPP + NIWBS Model

k = 10.8 md S = 2.0 n = 2.466

Minimisation of χχχχ2

Nonlinear Regression for Three Parameters

∆p(psi)

φi = 0.001 Cf = -7900 t = 0.075 hr

Cs = 3×10-5 psi-1 E = 5×105 psi ν = 0.25

χχχχ2 based on pressures only 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

RH+NIWBS

(No Stress Dependency)

DP k = 26.4 md

φ = 0.001

Cs = 2.131×10-5 bbl/psi τ = 0.0876 hr Cφ = -11000 psi

k = 28.4 md S = -1.477 L1 = 175 ft L2 = 80 ft pi = 719 psia

DP k = 26.4 md

Results from Nonlinear Regression

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

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

Resolution of Lack of Uniqueness Problem

• Carry out a production test

• On drawdown the stress effect will be much stronger

• Choking may occur

Course Pansystem Interpretation

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