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What petrophysics provides for the reservoir model
Steve Cuddy
Outline
• What petrophysics provides for the geomodel
• Log QC and repair
• Depth – how to fix the most important measurement
• Saturation vs. height modelling
• Net vs. Pay cut-offs
• The importance of the correct upscaling
• Differential geomodels
What the Geomodel Requires from the Petrophysics
Required to initialise a 3D static and dynamic reservoir model with the water and hydrocarbon volumes i.e. water saturation
Petrophysics supplies porosity, permeability, fluid contacts, net flag
Quality Control and Log Repair Logs should be quality controlled
- Poor data should be corrected
- Data gaps filled
- Synthetic logs considered in wells without complete logs
There area several petrophysical packages that do this
Based on mathematics of Fuzzy Logic
- Geolog
- Interactive Petrophysics
- Petro-Predict (free Baker Hughes software)
- Code freely available
e.g. porosity = 22 pu
The Principles of Fuzzy Logic • Extension of Classical logic to handle the “grey scale”
• Asserts that there is useful information in the fuzziness
• Fuzzy logic ‘finds’ relationships in multi-dimensional data
• These relationships are then used to QC and repair logs
• Doesn’t accept certainty. Any interpretation is possible, only some are more likely than others
Probability
80% 20% 30% 10%
Advantages of Fuzzy Logic
• Self-calibrating
- No parameters to pick or Xplots to make
• Not worried about the input of poor data
- Uses fuzziness to identify the best data
• Works with an unlimited number of inputs - Electrical logs, core data, drilling data, mud logging data
• Works even if some of those inputs are missing
• Updates hundreds of wells in minutes
Case Study Washouts shown on Caliper and Drho log Where recorded and synthetic logs overlay this confirms log quality Poor logs and gaps can be replaced by synthetic logs
Borehole Conditions
Recorded Logs
Repaired Logs
Repaired Density Log
Repaired Neutron Log
Log Interpretation
Oil Water
Sandstone
Shale
Neutron
Density
Neutron
Density
Neutron
Density
Recorded Recorded
Repaired Repaired
The Free Water Level (FWL) FWL is the horizontal surface of zero capillary pressure
Hydrocarbon Water Contact (HWC)
The HWC is the height where the pore entry pressure is sufficient to allow hydrocarbon to start invading the formation pores This depends on the local porosity & permeability It is a surface of variable height The FWL is much more important than the HWC
0 Water Saturation 1
Hei
ght
abo
ve F
WL
Hydrocarbon Water Contact Free Water Level
Tells us how water saturation varies as a function of the height above the Free Water Level (FWL)
Tells us how the formation porosity is split between hydrocarbon and water
Tells us the shape of the transition zone
Used to initialize the 3D reservoir model
Saturation Height Function
0 Water Saturation (%) 100
Hei
ght
abo
ve F
WL
(Fee
t)
FWL >
Water
Hydrocarbon
The Bulk Volume of Water (BVW)
Bulk Volume of Water = Porosity x Water Saturation
B V W = % volume of water in a unit volume of reservoir
This is what is measured by electrical logs by core analysis
𝐵𝑉𝑊 = 𝑎𝐻𝑏
Where:
𝐵𝑉𝑊= Bulk Volume Water (Sw*Phi)
𝐻 = Height above FWL
𝑎, 𝑏 = Constants
The Fractal Water Saturation vs. Height Function
• Derived from the fractal nature of reservoir rocks • Based on the bulk volume of water • Independent of facies type, porosity and permeability • Two parameters completely describe the reservoir
Bulk of Volume of Water Free Water Level >
Deriving Water Saturation from the Swh Function
𝑆𝑤 =𝐵𝑢𝑙𝑘 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
𝑃𝑜𝑟𝑜𝑠𝑖𝑡𝑦
S𝑤 =𝑎𝐻𝑏
𝑃𝑜𝑟𝑜𝑠𝑖𝑡𝑦
Where:
𝐻 = Height above FWL
𝑎, 𝑏 = Constants
• The fractal Swh function gives the hydrocarbon water contact as a function of porosity
Hydrocarbon water contact
Water Saturation (%)
Hei
ght
abo
ve F
WL
(Fee
t)
5pu
• Required for zonal averaging and upscaling
• Net Reservoir – The portion of reservoir rock which is capable of storing hydrocarbon
- Relatively easy to pick - Can be based on a porosity and/or shale cutoff • Net Pay – “The portion of reservoir rock which will produce
commercial quantities of hydrocarbon” - SPWLA - Very difficult to pick
Net Reservoir Flag
Net Reservoir Cut-off
Net reservoir porosity cut-off
Free Water Level
Net reservoir is defined as the rock capable of holding hydrocarbon
The net cut-off is required for averaging porosity and water saturation in the reservoir model
The net reservoir cut-off varies as a function of height above the FWL
The Net reservoir cut-off varies as a function of height above the FWL
Reservoir high above the FWL has low saturations of capillary bound water and hydrocarbon enters the smaller pores
Reservoir just above the FWL, with higher porosities, contains high saturations of capillary bound water and there is a no room available for hydrocarbons
Net Reservoir Cut-off
Net
Porosity 25 pu 0
Sand Shale Gas
FWL
Depth is the most important measurement True vertical depth subsea can be +/- 30 feet.
Example of two wells that don’t intercept the FWL
BVW trend identifies the FWL Normalises depths between wells
Depth control
0 Bulk Volume of Water (v/v) 0.25 1
0,7
50
Dep
th (
ftTV
Dss
)
10
,35
0'
Well 1
Well 2
FWL
Comparison between resistivity and fractal derived water saturations
Swept zone showing residual oil saturations
By-passed hydrocarbon
The resistivity log is incorrect in thin beds, close to bed boundaries and where there are conductive shales
The Differential Geomodel
Irreducible Water Saturation (Swirr) Is the lowest Sw that can be achieved in a core plug
This is achieved by flowing hydrocarbon through a sample or spinning the sample in a centrifuge
0 Water Saturation (%) 100
Hei
ght
abo
ve F
WL Swirr ?
Swh profile
This depends on the drive pressure or the centrifuge speed
Sw therefore depends on the height above the free water level
A minimum Swirr does not exist
The transition zone extends indefinitely
The fractal Swh function defines Swirr as a function of height and porosity
Upscaling
From ½ foot to the cell size of the reservoir model Net flag required Sw-Height functions (SWHF) are used to initialize the 3D reservoir model. It is essential that the SWHF predicted water saturations upscale accurately
This is done by integrating the Sw-Height function
Unlike other parameters, such as porosity, water saturation must be pore volume averaged
Upscaling Water Saturations
21
2211
SwSwSw
= average water saturation Sw
= average porosity
Sw = average bulk volume of water
“A function that predicts BVW from height is especially appropriate to this application” Paul Worthington
Upscaling Permeability Log and core permeabilities represent typically 2 feet
To be used in a reservoir model the predicted permeabilities must upscale correctly
They must have the same dynamic range as the core data
Least square methods regresses towards the mean
Fuzzy logic preserves the dynamic range
Core Permeability Predicted Permeability
0.01 (mD) 1000 0.01 (mD) 1000
Core permeability upscaling
Core distribution Linear Regression Fuzzy logic prediction
Frequency Histogram of CORE.CKHL_NCWell: 15 Wells
Range: All of WellFilter: CKHL_NC>0.001
0.0
0.2
0.4
0.6
0.8
1.0
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.0
01
0.0
1
0.1 1
10
10
0
10
00
Wells:
1. 2/5-12. 2/5-12A3. 2/5-13Z4. 2/5-175. 2/5-26. 2/5-37. 2/5-48. 2/5-69. 2/5-8B10. 2/5-911. 2/5-H0112. 2/5-H0213. 2/5-H0414. 2/5-H1815. 2/5-H34
Statistics:
Possible values 1123Missing values 0Minimum value 0.00109Maximum value 2159.16626Range 2159.16517
Mean 59.71616Geometric Mean 2.78804Harmonic Mean 0.02935
Variance 15340.71661Standard Deviation 123.85765Skewness 6.10523Kurtosis 80.35227Median 5.14044Mode 100.00000
1123
1122
0 1
Frequency Histogram of PERM.KFLWell: 15 Wells
Range: All of WellFilter: CKHL_NC>.001
0.0
0.2
0.4
0.6
0.8
1.0
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.0
01
0.0
1
0.1 1
10
10
0
10
00
Wells:
1. 2/5-12. 2/5-12A3. 2/5-13Z4. 2/5-175. 2/5-26. 2/5-37. 2/5-48. 2/5-69. 2/5-8B10. 2/5-911. 2/5-H0112. 2/5-H0213. 2/5-H0414. 2/5-H1815. 2/5-H34
Statistics:
Possible values 1120Missing values 0Minimum value 0.00015Maximum value 926.65411Range 926.65397
Mean 64.44684Geometric Mean 3.08146Harmonic Mean 0.01087
Variance 14082.12021Standard Deviation 118.66811Skewness 2.73982Kurtosis 12.40389Median 7.58578Mode 100.00000
1120
1094
26 0
Frequency Histogram of PERM.KLINWell: 15 Wells
Range: All of WellFilter: CKHL_NC>.001
0.0
0.2
0.4
0.6
0.8
1.0
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.0
01
0.0
1
0.1 1
10
10
0
10
00
Wells:
1. 2/5-12. 2/5-12A3. 2/5-13Z4. 2/5-175. 2/5-26. 2/5-37. 2/5-48. 2/5-69. 2/5-8B10. 2/5-911. 2/5-H0112. 2/5-H0213. 2/5-H0414. 2/5-H1815. 2/5-H34
Statistics:
Possible values 1120Missing values 0Minimum value 0.00016Maximum value 3626.16382Range 3626.16366
Mean 45.29200Geometric Mean 0.96455Harmonic Mean 0.01464
Variance 44699.46287Standard Deviation 211.42247Skewness 9.67622Kurtosis 121.92938Median 1.20226Mode 6.30957
1120
1088
19
13
North Sea field case study
Permeability frequency plots
- Colour represents data from 15 cored wells
Regression permeability techniques are poor at the extremes and therefore
will be incorrect when upscaled
Fuzzy logic predicted permeability matches the core distribution
0.001 mD 1000
Conclusions • Petrophysics supplies porosity, permeability, fluid contacts, net flag
• Sw is derived from a Sw height function (fractal function)
• Log QC and repair using Fuzzy Logic
• Depth Control using the Free Water Level
• Net reservoir is defined as rock capable of holding hydrocarbon
• Swirr doesn’t exist
• Correct upscaling is vital
• Differential geomodels give useful insights
Questions?
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