spe pc paper final-rev3

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

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


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)

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


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*𝑅𝑄𝐼𝑏

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

Irre

du

cib

le W

ate

r Sa

tura

tio

n, F

r

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 0.200Sw

i, Fr

Reservoir Quality Index (RQI)

Zone 2


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)

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

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

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

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


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

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


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

SPE-181305-MS • A Novel Technique for Generation of Accurate Capillary Pressure (Pc) Curves • Mina

Fazelalavi

2nd Pc Model-Imbibition Pc curvesPcn 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

Predicted Pc Curves Match with Laboratory Pc for different RQI


Fazelalavi

Comparison of Predicted Sw by Model 1 and Model 2 with

Log Derived Sw


Fazelalavi

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

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

Thank You

Slide 19

spe pc paper final-rev3

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