Course Pansystem Interpretation

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Transcript of 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
HeriotWatt 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 = 3.03×106 psi1 ct = 2.03×104 psi1 T = 134.6oF
LogLog 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 = 1.59×105 psi1 B = 10.951 cp ct = 1.59×105 psi1 Bw = 1
NSW Falling Liquid Level (Slug) Test
540.4 psiapc
429 psiapi
Pressure Integral LogLog 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 = 80.3×105 psi1 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 FlowRate, 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 FallOff Test Example: High Perm
Reservoir Analysis
Well Shut In
Start
Pumping
13
Inflate
Packer
Formation Temp
Pumping
SteadyState 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 SemiSteadyState:
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
PalmerMansooriModel
Generation of the
SDPP
PseudoPressure
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)
0FlowRate, 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 = 80.3×105 psi1 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
Stress Dependent Permeability and Porosity
CRD
∆p
pi = 1500 psia ki = 15 md φi = 0.005 E = 1.25×105 psi ν = 0.39 n = 3 ct = 80.3×105 psi1 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 loglog 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 = 80.3×105 psi1 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
Stress Dependent Permeability and Porosity
CRD
∆p
pi = 1500 psia ki = 15 md φi = 0.005 E = 1.25×105 psi ν = 0.39 n = 3 ct = 80.3×105 psi1 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• Noflow 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)• Flowrate, q, cannot be larger than the critical (specified fi , pi and kh)• Or fi must be greater than fi,crit for specified flowrate, q
Critical Conditions in Production (Drawdown)
rw = 0.35 ft µ = 1 cp Bo = 1 pi = 1500 psia k = 15 md S = 0 ct = 80.3×105 psi1
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 = 3.003×103 psi1
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
Stress Dependent Permeability and Porosity
CRB
tp = 10 hr
∆p
′ =+LNM
OQP
pd p
dt t
t
p
∆
∆
∆
b gln
∆p
(psi)
pwf(tp) = 927.113 psia
∆p = pws − pwf(tp)
Buildup Following Constant Rate Production
p'
µ = 1 cp q = 500 STB/D Bo = 1 ct = 80.3×105 psi1 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 = 80.3×105 psi1 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
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 = 3.0×106 psi1 Bw = 1.005
q = 96 bbl/d pwf(tp) = 1504.56 psia tp = 8.6458 hr
Elapsed Time, ∆t (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
1E3 1E2 1E1 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 = 3×103 psi1 i.e ct = 3.003×103 psi1
. . . 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
Elapsed Time, ∆t (hr)
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 = 3×105 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
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 LogLog Diagnostic Based on Pseudopressure
Mavor Field Example
∆ψ(p)(psia)
Elapsed Time, ∆t (hr)
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 = 3×103 psi1
Cs = 0 “False” Plateau
tp = 8.6458 hr
Elapsed Time, ∆t (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 =
3.0×105 psi1 E = 5.0×105 psi ν = 0.25 n = 4.5
Elapsed Time, ∆t (hr)
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
Elapsed Time, ∆t (hr)
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 = 3×105 psi1 E = 5×105 psi ν = 0.25
χχχχ2 based on pressures only tp = 8.6458 hr
Elapsed Time, ∆t (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
wR
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 = 2.131×105 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 = 1.789×104 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 LL Diagnostic Derivative LL 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