Measurement Uncertainty in the Laboratory
-
Upload
deepblue09 -
Category
Documents
-
view
73 -
download
3
description
Transcript of Measurement Uncertainty in the Laboratory
![Page 1: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/1.jpg)
Core Analysis Uncertainty andRock Typing
SPWLA Carbonate Workshop
Abu Dhabi
February, 2010
Gary Potter
Houston
![Page 2: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/2.jpg)
Is Rock Typing the Same asFacies?
• Facies are a body of rock with specifiedcharacteristics (from Wikipedia)
![Page 3: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/3.jpg)
Is Rock Typing the Same asFacies?
• Facies are a body of rock with specifiedcharacteristics (from Wikipedia)
• Types of facies
– Lithofacies - based on lithology (sandstones,siltstones etc)
– Microfacies - based on micro fabric
– Ichnofacies - based on burrow forms
– Electrofacies - based on electric log responses
– Seismicfacies - based on velocity response
![Page 4: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/4.jpg)
Rock Type
• Rock types that have been classified according totheir petrophysical properties, especially propertiesthat pertain to fluid behavior within the rock, such asporosity, capillary pressure, permeabilities, irreduciblesaturations or saturations. (from Schlumberger Oilfield Glossary)
![Page 5: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/5.jpg)
Rock Type
• Rock types that have been classified according totheir petrophysical properties, especially propertiesthat pertain to fluid behavior within the rock, such asporosity, capillary pressure, permeabilities, irreduciblesaturations or saturations. (from Schlumberger Oilfield Glossary)
• Rock Types are categorized by propertiesimportant to HC storage and flow.
![Page 6: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/6.jpg)
Scale
(after Worthington)
WellLog
BeddingScale
Core PlugScale
StratumScale
PoreScale
HomogeneousStratum
HeterogeneousStratum
HomogeneousRock Fabric
HeterogeneousRock Fabric
![Page 7: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/7.jpg)
Pore Scale Controls
![Page 8: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/8.jpg)
How are Rock Types Determined
• Porosity and Permeability
– Considers pore throat size
![Page 9: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/9.jpg)
How are Rock Types Determined
• Porosity and Permeability
– Considers pore throat size
• Capillary Pressure
– Considers interconnection and distribution ofpore throats with storage
![Page 10: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/10.jpg)
How are Rock Types Determined
• Porosity and Permeability
– Considers pore throat size
• Capillary Pressure
– Considers interconnection and distribution ofpore throats with storage
• Relative Permeability
– Includes wettability
![Page 11: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/11.jpg)
Rock Types by Porosity and
Permeability
• K-Phi Cross Plot
0.01
0.10
1.00
10.00
100.00
1000.00
0 10 20
Air
Perm
eab
ilit
y,
md
Core Porosity, %
![Page 12: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/12.jpg)
Rock Types by Porosity and
Permeability
• K-Phi Cross Plot
• Winland
– Log (R35) = .732+ .588Log(K) - .864Log(Φ)
0.01
0.10
1.00
10.00
100.00
1000.00
0 10 20
Air
Perm
eab
ilit
y,
md
Core Porosity, %
![Page 13: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/13.jpg)
Rock Types by Porosity and
Permeability
• K-Phi Cross Plot
• Winland
– Log (R35) = .732+ .588Log(K) - .864Log(Φ)
• Pittman– Pittman Log (R10) = .459 + .500Log(K) - .385Log(f)
– Pittman Log (R20) = .218 + .519Log(K) - .303Log(f)
– Pittman Log (R30) = .215 + .547Log(K) - .420Log(f)
– Pittman Log (R35 )= .255 + .565Log(K) - .523Log(f)
– Pittman Log (R40) = .360 + .582Log(K) - .680Log(f)
– Pittman Log (R50) = .778 + .626Log(K) – 1.205Log(f)
0.01
0.10
1.00
10.00
100.00
1000.00
0 10 20
Air
Perm
eab
ilit
y,
md
Core Porosity, %
![Page 14: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/14.jpg)
Rock Types by Porosity and
Permeability
• K-Phi Cross Plot
• Winland
– Log (R35) = .732+ .588Log(K) - .864Log(Φ)
• Pittman– Pittman Log (R10) = .459 + .500Log(K) - .385Log(f)
– Pittman Log (R20) = .218 + .519Log(K) - .303Log(f)
– Pittman Log (R30) = .215 + .547Log(K) - .420Log(f)
– Pittman Log (R35 )= .255 + .565Log(K) - .523Log(f)
– Pittman Log (R40) = .360 + .582Log(K) - .680Log(f)
– Pittman Log (R50) = .778 + .626Log(K) – 1.205Log(f)
• Rock Quality Index
0.01
0.10
1.00
10.00
100.00
1000.00
0 10 20
Air
Perm
eab
ilit
y,
md
Core Porosity, %
e
kRQI
0314.0
![Page 15: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/15.jpg)
Rock Types by Porosity and
Permeability
• K-Phi Cross Plot
• Winland
– Log (R35) = .732+ .588Log(K) - .864Log(Φ)
• Pittman– Pittman Log (R10) = .459 + .500Log(K) - .385Log(f)
– Pittman Log (R20) = .218 + .519Log(K) - .303Log(f)
– Pittman Log (R30) = .215 + .547Log(K) - .420Log(f)
– Pittman Log (R35 )= .255 + .565Log(K) - .523Log(f)
– Pittman Log (R40) = .360 + .582Log(K) - .680Log(f)
– Pittman Log (R50) = .778 + .626Log(K) – 1.205Log(f)
• Rock Quality Index
All from equating Poiseuille’s and Darcy’s equation
0.01
0.10
1.00
10.00
100.00
1000.00
0 10 20
Air
Perm
eab
ilit
y,
md
Core Porosity, %
e
kRQI
0314.0
![Page 16: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/16.jpg)
Poiseuille`s/Darcy`s equation
relates Pore Throat to K & Phi
• Poiseuille’s Equation for a tube
L
PA
rq
8
2
![Page 17: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/17.jpg)
Poiseuille`s/Darcy`s equation
relates Pore Throat to K & Phi
• Poiseuille’s Equation for a fracture
L
PA
dq
12
2
![Page 18: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/18.jpg)
Poiseuille`s/Darcy`s equation
relates Pore Throat to K & Phi
• Poiseuille’s Equation for a tube
• Darcy’s Equation
L
PA
rq
8
2
L
PAkq
![Page 19: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/19.jpg)
Poiseuille`s/Darcy`s equation
relates Pore Throat to K & Phi
• Poiseuille’s Equation for a tube
• Darcy’s Equation
• Combined
L
PA
rq
8
2
L
PAkq
8
2rk
![Page 20: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/20.jpg)
Poiseuille`s/Darcy`s equation
relates Pore Throat to K & Phi
• Poiseuille’s Equation for a tube
• Darcy’s Equation
• Combined with porosity
L
PA
rq
8
2
L
PAkq
8
2rk
8
2rk
![Page 21: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/21.jpg)
Poiseuille`s/Darcy`s EquationRelates Pore Throat to K & Phi
kr
8
Solve for radius
![Page 22: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/22.jpg)
Poiseuille`s/Darcy`s EquationRelates Pore Throat to K & Phi
kr
8
Solve for radius Similar to RQI
e
kRQI
0314.0
![Page 23: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/23.jpg)
Poiseuille`s/Darcy`s EquationRelates Pore Throat to K & Phi
kr
8
log5.0log5.0452.0log kr
Logrithm
Solve for radius Similar to RQI
e
kRQI
0314.0
![Page 24: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/24.jpg)
Poiseuille`s/Darcy`s EquationRelates Pore Throat to K & Phi
kr
8
log5.0log5.0452.0log kr
Logrithm
Solve for radius
Compare to Winland and Pittman equations
Winland Log (R35) = .732+ .588Log(K) - .864Log(Φ)
Pittman Log (R10) = .459 + .500Log(K) - .385Log(f)
Similar to RQI
e
kRQI
0314.0
![Page 25: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/25.jpg)
Lab Performance in Measuring K
and Phi
Internal Core Lab Quality Assurance Program
• Twenty- three (23) locations
• Some 3200 total points of data for evaluation
• Over 2 year(s) involved in each data series
• Updated program as existed for 8 years
![Page 26: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/26.jpg)
RCAL QA/QC Plugs - materials &plan
Twenty-four (24) total samples
Twelve (12) 1.0” diameterTwelve (12) 1.5” diameter
Porosity Ranges: 2.0 – 23.0%
Kinf Ranges: 0.0001 – 1050 mD
Grain Den. Ranges: 2.599 – 2.858 g/cc
![Page 27: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/27.jpg)
QA/QC Results - assessmentcriteria
• “Experienced-based acceptabledeviations” ofThomas & Pughused forperformanceassessments
• Prelim resultscompared tomean of limited“standard”measurements
Table 1: Maximum acceptable deviation in standard core plug analysis
Meancoefficient
Experience- Statistically- of
Measurement based derived1
variance, %
Porosity +/-0.5 Por% +/-0.23% 0.67
Grain density +/-0.01 g/cm3
+/-0.0093 g/cm3
0.13
Air permeability:0.01 - 0.1 md +/-30% +/-21% 8.0
0.1 - 1.0 md +/-25% +/-21% 8.01.0 - 50 md +/-15% +/-13% 5.0
50 md - 1 darcy +/-15% +/-8% 3.0
1A single measurement made on the same sample that falls outside
the specified limit is 99% likely to be in error, assuming that both testsare performed with the same standard deviation
Taken from:Thomas, D.C. and Pugh, V.J.: "A Statistical Analysis of the Accuracyand Reproducibility of Standard Core Analysis", The Log Analyst,March-April, 1989, 71-77. (journal version of SCA 8701)
![Page 28: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/28.jpg)
Core Labs` QA Experience
MeasurementThomas & PughExperience Error
Internal CoreLab QA
Porosity 0.50 Por% 0.20 Por%
Permeability
<0.001 md -- 26%
0.01 - 0.1 md 30% 12%
0.1-1.0 md 25% 8
1.0-50 md 15% 7
50 md- 1 darcy 15% 7
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.1 0.2 0.3
3S
tdD
ev
,P
or%
Porosity, %
Measurement Error vsPorosity
0
20
40
60
80
100
0.0001 0.001 0.01 0.1 1 10 100 1000
3R
el
Std
Dev
,%
Permeability, md
Measurement Error vsPermeability
![Page 29: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/29.jpg)
Impact on K&Phi Crossplot
y = 0.0194e0.4433x
0.001
0.010
0.100
1.000
10.000
100.000
1000.000
10000.000
0.00 10.00 20.00 30.00
Perm
eab
ilit
y,
md
Porosity, %
Porosity-Perm Cross Plot
Series1
Expon.(Series1)
y = 0.0194e0.4433x
y = 0.0232e0.4422x
0.001
0.010
0.100
1.000
10.000
100.000
1000.000
10000.000
100000.000
0.00 10.00 20.00 30.00
Perm
eab
ilit
y,
md
Porosity, %
Error Hi Perm vs Low Porosity
Series1
Series2
Series3
Expon. (Series1)
Expon. (Series3)
y = 0.0194e0.4433x
y = 0.016e0.4447x
0.001
0.010
0.100
1.000
10.000
100.000
1000.000
10000.000
100000.000
0.00 10.00 20.00 30.00
Perm
eab
ilit
y,
md
Porosity, %
Error Low Perm vs Hi Porosity
Series1
Series2
Series3
Expon. (Series1)
Expon. (Series2)
MeasurementThomas & PughExperience Error
Internal CoreLab QA
Porosity 0.50 Por% 0.20 Por%
Permeability
<0.001 md -- 26%
0.01 - 0.1 md 30% 12%
0.1-1.0 md 25% 8
1.0-50 md 15% 7
50 md- 1 darcy 15% 7
![Page 30: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/30.jpg)
Impact in Pitman/Winland curves
0.001
0.01
0.1
1
10
100
1000
10000
0 10 20 30 40
Perm
eabili
ty,
md
Porosity, %
Winland R35 Type Curves
150mm
20mm
3mm
0.3mm
0.02mm
![Page 31: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/31.jpg)
Impact in Pitman/Winland curves
0.001
0.01
0.1
1
10
100
1000
10000
0 10 20 30 40
Perm
eabili
ty,
md
Porosity, %
Winland R35 Type Curves
3mm
Perm*0.92
Perm*1.08
![Page 32: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/32.jpg)
Impact in Pitman/Winland curves
0.1
1
10
100
0 10 20 30 40
Perm
eabili
ty,
md
Porosity, %
Winland R35 Type Curves
3mm
Perm*0.92
Perm*1.08
![Page 33: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/33.jpg)
Using Leverett J-Function
• J-Function used to normalize capillary pressurefor different K and f within a rock type
• J-Function data that does not group indicatesdifferent rock type
• J-Function
k
J
rPc
coscos2
![Page 34: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/34.jpg)
Leverett J-Function
• J-Function used to normalize capillary pressurefor different K and f within a rock type
• J-Function data that does not group indicatesdifferent rock type
• J-Function
k
J
rPc
coscos2
cos
2166.0k
P
Jc
![Page 35: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/35.jpg)
J = 0.08691(Sw*)-1.11195
0.01
0.1
1
10
0.01 0.1 1
Sw*, (Sw-Swir)/(1-Swir)
J
Laboratory Pc vs Swdata for 6 samples.
Sw converted to Sw*
• Sw* at Pc max (140 psi) = 0, therefore not plotted on log scale
• Correlate Sw @ Pc max vs Rock Quality parameter (e.g., RQI)
• Determine J from interval K, f, Pc (or Height above FWL); Predict Sw*
• Predict Swir (140) for Rock Quality of interest; de-normalize Sw*
Sw* = (0.08691/J)(-1/-1.11195)
Swir = Sw at max Pcof test; in this example,max Pc = 140 psi
Leverett J Function vs Sw*
![Page 36: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/36.jpg)
J = 0.08691(Sw*)-1.11195
0.01
0.1
1
10
0.01 0.1 1
Sw*, (Sw-Swir)/(1-Swir)
J
Laboratory Pc vs Swdata for 6 samples.
Sw converted to Sw*
• Sw* at Pc max (140 psi) = 0, therefore not plotted on log scale
• Correlate Sw @ Pc max vs Rock Quality parameter (e.g., RQI)
• Determine J from interval K, f, Pc (or Height above FWL); Predict Sw*
• Predict Swir (140) for Rock Quality of interest; de-normalize Sw*
Sw* = (0.08691/J)(-1/-1.11195)
Swir = Sw at max Pcof test; in this example,max Pc = 140 psi
Leverett J Function vs Sw*
![Page 37: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/37.jpg)
Lab Measurement error in Capillary
pressure
0
50
100
150
200
250
300
350
400
450
0.00 0.20 0.40 0.60 0.80 1.00
Pc,p
si
Sw, fraction
CENTRIFUGE GAS/WATER PcRepeatability Testing
Originaltest1stRecheck
![Page 38: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/38.jpg)
Lab Measurement error in Capillary
pressure
0
50
100
150
200
250
300
350
400
450
0.00 0.20 0.40 0.60 0.80 1.00
Pc,p
si
Sw, fraction
CENTRIFUGE GAS/WATER PcRepeatability Testing
Originaltest1stRecheck
0
50
100
150
200
250
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Cap
illa
ryP
ressu
re,p
si
Water Saturation, fraction
CoreLab IF
Average Sw
Pc COMPARISONUnconfined Centrifuge
gas/water
Note, these data werere-evaluated 1-20-10using Forbes (TblCrv
![Page 39: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/39.jpg)
After Owens & Archer, JPT, July 1971
0.001
0.01
0.1
1
0 0.2 0.4 0.6 0.8 1
Sw
Re
lati
ve
Pe
rme
ab
ilit
y,fr
ac
tio
n
0º
47º
90º
138º
180º
Contact Angle
WW
OW
• Same core plug (Torpedo Sand; Ka = 571 md)
• Swi = 0.20 for all tests
• Steady-State (Penn State) method
• Oil treated to change wettability
Relative Permeability includesWettability
![Page 40: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/40.jpg)
Unsteady-State RelativePermeability Error
• Pore volume major factor
• In JBN analysis
– Smoothness of data critical
– Knowing dead volumes and detectingbreakthrough very important
– Experience indicates• Effective Perm +/- 5% of value
• Saturation +/- 10% saturation unit
• Variability decreases as floodout is approached
![Page 41: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/41.jpg)
Steady-State RelativePermeability Error
• X-ray saturation data
– +/- 1.2% saturation % units
– At least 1 million photons used (Poisson’sstatistics)
• Effective permeability data
– Typically +/- 2% of value
– Low flow rate, +/-10 – 50% of value
![Page 42: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/42.jpg)
Error bounds on RelativePermeability
0.001
0.01
0.1
1
0 0.2 0.4 0.6 0.8 1
Rela
tive
Perm
eab
ilit
y,
fracti
on
Water Saturation, fraction
Krw WaterIncreasingKro Water Increasing
Water Kr LCL
Water Kr UCL
![Page 43: Measurement Uncertainty in the Laboratory](https://reader034.fdocuments.us/reader034/viewer/2022050711/55cf93c6550346f57b9e5456/html5/thumbnails/43.jpg)
Conclusion
• Rock type is used to group rocks that havecommon storage and flow properties
• Rock typing is mostly based on pore size
• Rock properties measurement variabilitieshave no impact on rock typing
• Rock typing uses porosity, permeability,capillary pressure, and relative permeability