This document presents two novel techniques for generating accurate capillary pressure (Pc) curves from well log and core data. The first technique involves reservoir zonation based on pore size distribution, correlating irreducible water saturation (Swir) to reservoir quality index (RQI), and developing relationships between Pc endpoints and RQI. The second technique involves developing two Pc models - one relating normalized Pc and normalized non-wetting phase saturation using a modified Brooks and Corey model, and another relating normalized Pc and normalized non-wetting phase saturation. Both techniques were shown to accurately predict water saturation from well logs in different zones of a reservoir. The techniques can generate Pc curves without need for expensive laboratory measurements.

1. SPE-181305-MS
A Novel Technique for Generation of Accurate Capillary Pressure (Pc)
Curves from Conventional Logs and Routine Core Data and new Pc
Endpoint Functions after Considering the Sedimentary Environment and
Pore Throat Size Distribution Shape (PTSDS)
Mohsen FazelAlavi, Petrocarbon; Mina FazelAlavi, Kansas Geological Survey (KGS); and
Maryam FazelAlavi, Petrocarbon

2. Overview
 Reservoir zonation based on the linear relationship between FZI and 1/ (Swir.φ),
(Fazelalavi et al. 2014)
 Correlation of endpoints of Pc curves (Pe and Swir) with different rock properties
 Effect of pore size distribution on Pc curves
 1st Pc Model - Brooks and Corey model after modification
 2nd Pc Model – Normalized Pc (Pcn) relation with normalized non-wetting phase
saturation (Snwn)
 Sw prediction in well A3 by 1st Pc model
 Sw prediction in well A3 by 2nd Pc model
Slide 2
SPE-181305-MS • A Novel Technique for Generation of Accurate Capillary Pressure (Pc) Curves • Mina Fazelalavi

3. Slide 3
SPE-181305-MS • A Novel Technique for Generation of Accurate Capillary Pressure (Pc) Curves • Mina Fazelalavi
Reservoir Zonation
 FZI (core) and 1/(Swi*Phi) (log) are plotted vs. depth and zones with similar
pore size distribution are delineated (Fazelalavi et al. 2014)

4.  Best correlation is obtained when 1) reservoir rocks are classified 2) Swir is
correlated to Reservoir quality Index (RQI)
 Correlations of Swir with other rock properties such as k, FZI, DRT, HUs, and
Phi are more inferior relative to RQI. Table below shows R2 of Swir correlation
with different rock properties
Irreducible Water Saturation (Swir) Correlation
Reservoir Zone RQI k FZI Phi
1 0.85 0.85 0.72 0.34
2 0.87 0.82 0.67 0.04
3 0.95 0.93 0.89 0.08
4 0.86 0.84 0.67 0.24
5 0.88 0.87 0.82 0.13
6 0.91 0.86 0.91 0.02
Average 0.88 0.86 0.78 0.10

5. Slide 5
SPE-181305-MS • A Novel Technique for Generation of Accurate Capillary Pressure (Pc) Curves • Mina Fazelalavi
Swir Correlation with RQI
 Reservoir rock is first classified based on FZI and 1/(Sw*Phi), (Fazelalavi et al.
2014)
 Swir correlation with RQI is found: Swir = a*𝑅𝑄𝐼 𝑏
 A distinct Swir correlation is found for every zone of the reservoir
y = 0.031x-0.895
R² = 1
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.000 0.100 0.200 0.300 0.400
IrreducibleWaterSaturation,Fr
Reservoir Quality Index (RQI)
Zone 1
y = 0.022x-0.63
R² = 0.9955
0.000
0.050
0.100
0.150
0.200
0.000 0.050 0.100 0.150 0.200Swi,Fr
Reservoir Quality Index (RQI)
Zone 2

6. Slide 6
SPE-181305-MS • A Novel Technique for Generation of Accurate Capillary Pressure (Pc) Curves • Mina Fazelalavi
Relationship between Pc Entry pressure (Pe) and RQI
 A strong correlation exists between Winland R35 and RQI in each zone: R35= aRQIb
 Pore throat radius (Re) at entry pressure (Pe) is proportional to Winland R35: Re = C1*R35
 A function for Re in terms of RQI is found for each zone: Re = C1*a* RQIb
 Therefore, Pe can be expressed in terms of RQI for each zone: Pe = (2σ2cosθ) /(Re)

7. Residual Oil Saturation Correlation
Residual Oil saturation is needed for imbibition Pc curves
 When SCAL data is available:
Sor = e× RQIf
 When SCAL data is not available (Pentland et al. 2010) :
Sor = 0.012 Soi2 + 0.474 Soi

8. Effect of Pore Size Distribution on Pc Curves
Figure 19: Pore throat size distribution
– Single Modal
Figure 20: Capillary pressure curve by
mercury injection –Single Modal
One Pc equation accurately
predicts water Saturation in a
single modal pore size
distribution
Similar pore size distributions
are delineated by reservoir
zonation (Slide 3)
Constant C1 (Re = C1*a*
RQIb) depends on degree of
sorting
Irreducible water saturation
function based on RQI depends
on degree of sorting

9. 0
0
1
10
100
1000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Pc,psi
Sw, v/v
Pc Lab
Predicted Pc
Figure 21: Pore throat size distribution
in a carbonate Sample – Bi--Modal
In a bi-modal pore
size distribution, one
Pc equation can
predict water
saturation for all Pc
values
In this case, two
models are needed
Effect of Pore Size Distribution on Pc Curves
Figure 23: Core Capillary pressure –
Bi-Modal Sample and Pc Prediction by
a Single Model

10. Son
Swn
Lambda is obtained by plotting Pcn versus normalized water saturation (Swn) on log-log scale
1st Pc Model
Brooks and Corey Model after Modification

11. Slide 11
SPE-181305-MS • A Novel Technique for Generation of Accurate Capillary Pressure (Pc) Curves • Mina Fazelalavi
Well A3 – Zone 1: Correlation between Pcn and Swn
(Modified Brook and Core Model)
 Capillary pressure at log depth
was calculated from FWL and fluid
densities
 Pcn and Swn were calculated at
each depth and they were plotted
to obtain Lambda in Pc equations
 Lambda is the negative of the
reciprocal of slope

12. 2nd Pc Model- Drainage Pc curves
Pcn Relation with Normalized Non-wetting Phase Saturation (Snwn)
Pcn = Pc/Pe
Snwn= (1-Sw)/ (1-Swir) Eq.21
Pcn is plotted against Snwn and following equation is found:
Snwn = (1 – a ×Pe/Pc) × (1- (Pe/Pc) b) Eq.22
Combining the equations 21 & 22 and after rearranging result in:
Sw = 1 − (1 − Swir)× (1 – a × Pe/Pc)×(1- (Pe/Pc)b) Eq.24

13. Slide 13
SPE-181305-MS • A Novel Technique for Generation of Accurate Capillary Pressure (Pc) Curves • Mina Fazelalavi
Well A3 – Zone 5: Correlation between Pcn and Snwn (2nd Model)
 Capillary pressure at log depth
was calculated from FWL and
fluid densities
 Pcn and Snwn were calculated at
each depth and they were plotted
to obtain a and b in Eq. 22.
 Sw was predicted by Eq. 24

14. Slide 14
SPE-181305-MS • A Novel Technique for Generation of Accurate Capillary Pressure (Pc) Curves • Mina
2nd Pc Model-Imbibition Pc curves
Pcn Relation with Non-wetting Phase Saturation (Snwn)
Snwn = (1-Sw-Sor)/ (1-Swir-Sor)
Pcn is plotted against Snwn and following equations are found:
Snwn = (1 – a×Pe / (Pc+Pe)) × (1 – ((Pe / (Pc+Pe)) b) Eq.23
Combining the two equations and after rearranging result in:
Sw= 1 – Sor – (1−Swir−Sor)× (1 – a × Pe/ (Pc+Pe))× (1− ((Pe / (Pc+Pe))b) Eq. 25

15. Predicted Pc Curves Match with Laboratory Pc for different RQI

16. Slide 16
SPE-181305-MS • A Novel Technique for Generation of Accurate Capillary Pressure (Pc) Curves • Mina
Comparison of Predicted Sw by Model 1 and Model 2 with
Log Derived Sw

17. Slide 17
SPE-181305-MS • A Novel Technique for Generation of Accurate Capillary Pressure (Pc) Curves • Mina
Conclusion
 More accurate Pc curves are obtained once the reservoir rock is classified according to
the proposed method
 Swir is best correlated with RQI for Pc modeling
 Relationship between Swir with other rock properties are inferior relative to Swir to RQI
 A robust relationship between Winland R35 and RQI is confirmed
 A linear relationship between radius of pore throat at threshold pressure (Re) and
Winland R35 exists
 Based on the above statements, entry pressure is related to RQI
 Two Pc models are proposed which can be applied to each reservoir zone (both give
accurate results)
 Both models were used to derive Pc curves from log saturations which replicated log
saturations accurately
 The presented technique could eliminate or reduce the need for expensive lab Pc
measurements

18. Acknowledgements
The authors would like to thank Kansas Geological Survey, especially Cathy
Evans, for their support and Schlumberger for the use of Techlog software
Slide 18

19. Thank You
Slide 19