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?