Saturation Height Function

Transition Zone Analysis

Porosity Cross-Plots End-point values for porosity logs are determined from cross-plots of log response versus core porosity (NOB) Sonic Log Calibration with Core Data

Density Log Calibration with Core Data

160 Transit Time, micro-second

3

Bulk Density, g/cc

2.5 2 1.5 y = -1.7702x + 2.7103 1 0.5 0

140

y = 126.52x + 49.905

120 100 80 60 40 20 0

0

0.1

0.2 0.3 Core Porosity at NOB

Density Log

0.4

0

0.1

0.2 0.3 Core Porosity at NOB

Sonic Log

0.4

Shale Content Cross-Plots I SP 

SPlog  SPmin SPsh  SPmin

In this case, use Larionov – Older Rocks correlation

 log   min I   sh   min

In this case, Make a new correlation

Calibration of Well Logs with Core Data

If Capillary Pressure is Negligible Initial Saturation Distribution Cap Rock

Oil Rim

OWC

0

Bottom Water

Swc

1

Sw

No transition zone

If Capillary Pressure is Significant Initial Saturation Distribution Cap Rock

Oil Rim

Top transition zone O/w

Transition Zone OWC

0

Bottom Water

Swc

1

Sw

Transition Zones Shape of (Sw vs depth) curve is similar to capillary pressure curve Oil-water capillary pressure Pcow = Po - Pw

At equilibrium: Forceup = Forcedown

A

PcowA = Ah(w - o)g

h OWC

Hence; h = Pcow/ (w - o)g

Pcow

h

0

Swc

Sw

1

0

Swc

Sw

1

Example Calculation 24

Oil

(C) h = 30 m (B) h = 15 m (A) h = 5 m

OWC

16

Pcow psi 8

Water 0

0

Oil density = 689 kg/m3

0.6

0.4

0.8

1

Sw

Given: Water density = 995 kg/m3

0.2

For point A: Pcow = 5x9.8x(995-689)/6900 = 2.2 psi

Swi = 0.88

Acc. of gravity g = 9.8 m/s2 For point A: Pcow = 15x9.8x(995-689)/6900 = 6.5 psi Swi = 0.39 For point A: Pcow = 30x9.8x(995-689)/6900 = 13 psi Swi = 0.24

Transition Zone Analysis Objectives • Checking validity of Sw values calculated from well logs • Checking validity of OWC level

• Calibration of well logs with core data • Defining reservoir rock facies

• Estimating ( cos) for various reservoir rock facies • Calculating capillary pressure curves for reservoir conditions

Transition Zone Analysis Procedure For each rock facies, formulate suitable transforms for: k in terms of  and Vcl

Swc in terms of k

Vcl

k

Swc



log k

Transition Zone Analysis Procedure, continued Formulate suitable J-Functions from core data J-Function vs Sw

Pc J  cos 

k



J

0

Sw

1

Transition Zone Analysis Procedure, continued Convert J-Function to normalized J-Function J-Function vs Sw*

S w  S wc S  1  S wc * w

Jmax J

0

Sw *

1

Transition Zone Analysis Procedure, continued Calculate k, Swc and Sw* for every point above OWC from log analysis results TVDSS



Vcl

Sw

k

Swc

Sw*

3422.0

0.232

0.091

0.200

621

0.199

0.001

3422.5

0.241

0.077

0.213

487

0.207

0.007

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---

---

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---

3501.0

0.162

0.175

0.598

25

0.301

0.425

3501.5

0.225

0.107

0.601

412

0.212

0.494

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3533.0

0.208

0.096

0.967

270

0.225

0.957

3533.5

0.182

0.124

0.989

85

0.262

0.985

OWC

0.197

0.115

1.000

152

0.244

1.000

S w  S wc S  1  S wc * w

Transition Zone Analysis Procedure, continued Calculate h and (J  cos) for every point above OWC from log analysis results TVDSS



k

Sw*

h

J cos

3422.0

0.232

621

0.001

112.0

0.4040

3422.5

0.241

487

0.007

111.5

0.3461

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---

3501.0

0.162

25

0.425

33.0

0.0284

3501.5

0.225

412

0.494

32.5

0.0970

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3533.0

0.208

270

0.957

1.0

0.0025

3533.5

0.182

85

0.985

0.5

0.0008

OWC

0.197

152

1.000

0

0

h = height above OWC

k J cos   h(  w  o ) g 

Transition Zone Analysis Procedure, continued Plot (J  cos) versus Sw* and fit the best J-Function Curve (J  cos) vs Sw*

J  cos

-0.2

Jmax  cos

0

Sw *

1

Transition Zone Analysis Procedure, continued Calculate  cos for each reservoir facies at several values of Sw* ( cos)res = (J  cos) / J Calculate the average value of ( cos)res Calculate the reservoir J-function for each reservoir facies using the average value of ( cos)res Jres = Jlab (J  cos) /( cos)res for each Sw* value

Transition Zone Analysis Procedure, continued Compare the curves of laboratory and reservoir Jfunctions versus Sw*

Estimate the value of  for each reservoir rock facies if  is known Calculate the coefficient of J-function for use in Petrel model

Use the reservoir J-function to formulate a transform relating Sw* to Jres or a selected function of Jres

Reservoir Capillary Pressure Curves Use the value ( cos)res to calculate required capillary pressure curves for various facies from their normalized J-Functions Determine average  and k for various reservoir rock facies

Pc  J cos 

 k

Estimate Swc from transforms Assume several values for Sw* between 0 and 1

Calculate corresponding values of Sw Determine J values from

Sw*

Pc

Calculate Pc values from J,  cos,  and k

Plot Pc versus Sw

0

Swc

Sw

1

Transition Zone Analysis Example Given capillary pressure data 0.871 0.729 0.612 0.521 0.453 0.389 0.342 0.301 0.273 0.257 0.244 0.241 0.240 5 10 15 20 25 30 40 50 60 70 80 90 100 45 40

Capillary Pressure, psi

Sw 1 Pc, psi 0

Sam ple A Porosity = 18% Perm eability = 236 m d Sw c = 24%

35 30 25 20 15 10 5 0 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Water Saturation Sw

1

Transition Zone Analysis Example Given k and Swc transforms 3.5

2

log k = - 28.56por + 21.14por - 4.6Vsh - 0.38

3 2.5

0.7

0.1

0.6

0.2

2

2

y = 0.0192x - 0.1434x + 0.4555

0.5

0.3

1.5

Swc

Log k

Vsh 0

0.4

1 0.5

0.4 0.3 0.2

0 0.1

-0.5

0

-1 0

0.05

0.1

Other data

0.15 Porosity

0.2

0.25

0.3

-1

-0.5

0

0.5

1

1.5

2

2.5

Log k

Oil-water contact elevation = -2866 ftss Reservoir oil density o = 764 kg/m3 Reservoir water density w = 982 kg/m3 Acceleration of gravity g = 9.8 kg/m2

3

Transition Zone Analysis Example Calculated Jlab versus Sw* Sw* J

1 0

0.83 0.643 0.489 0.37 0.28 0.196 0.134 0.08 0.043 0.022 0.005 0.001 0 0.55 1.10 1.65 2.19 2.74 3.29 4.39 5.49 6.58 7.68 8.78 9.88 10.97 4.5 y = -38.494x 5 + 105.36x 4 - 108.03x 3 + 53.181x 2 - 15.649x + 3.63

4 3.5 3 2.5 J 2 1.5 1 0.5 0 0

0.1

0.2

0.3

0.4

0.5 0.6 Sw*

0.7

0.8

0.9

1

Transition Zone Analysis Example Calculated Jcos versus Sw* from log data Depth Porosity ft subsea 2758 0.155 2758.5 0.12 2759 0.166 2759.5 0.223 2760 0.168 2760.5 0.201 2761 0.218 2761.5 0.241 2762 0.164 2762.5 0.148 2763 0.128 2763.5 0.161 2764 0.173 2764.5 0.233 2765 0.255 2765.5 0.252 2766 0.224 2766.5 0.106 2767 0.105 2767.5 0.101 2768 0.17 2768.5 0.103 2769 0.147 2769.5 0.25

Vsh

Sw

0.271 0.017 0.11 0.287 0.035 0.241 0.333 0.175 0.19 0.277 0.089 0.256 0.074 0.139 0.069 0.256 0.209 0.355 0.19 0.161 0.275 0.354 0.145 0.067

0.696 0.430 0.422 0.597 0.310 0.589 0.646 0.276 0.577 0.797 0.567 0.748 0.323 0.256 0.230 0.438 0.465 0.950 0.795 0.773 0.751 0.913 0.585 0.218

k md 9.2 46.5 68.6 39.2 160.1 40.4 21.8 178.2 27.8 7.1 28.1 12.8 120.8 226.8 685.8 90.4 91.4 0.8 4.5 5.3 13.3 0.7 27.8 648.3

Swc 0 0.335 0.270 0.257 0.276 0.233 0.275 0.298 0.230 0.288 0.347 0.288 0.320 0.240 0.224 0.203 0.248 0.248 0.470 0.370 0.362 0.319 0.478 0.288 0.204

Sw* 0.542 0.219 0.223 0.444 0.101 0.433 0.496 0.060 0.405 0.689 0.392 0.630 0.109 0.042 0.034 0.253 0.288 0.905 0.674 0.644 0.634 0.834 0.418 0.018

h ft 108 107.5 107 106.5 106 105.5 105 104.5 104 103.5 103 102.5 102 101.5 101 100.5 100 99.5 99 98.5 98 97.5 97 96.5

J  cos 0.01713 0.04357 0.04479 0.02907 0.06738 0.03080 0.02162 0.05851 0.02788 0.01476 0.03142 0.01882 0.05550 0.06521 0.10785 0.03919 0.04159 0.00563 0.01335 0.01469 0.01785 0.00523 0.02747 0.10119

Transition Zone Analysis Example Transition zone plot

Transition Zone Analysis Example Calculated (cos)res for various Sw* values Sw* 0 0.1 0.2 0.3 0.4 0.6 0.8 1

J  cos 0.0853 0.0602 0.0453 0.0371 0.0296 0.0172 0.0090 0 Average

J 3.630 2.499 1.919 1.565 1.268 0.713 0.377 0

 cos 0.0235 0.0241 0.0236 0.0237 0.0233 0.0242 0.0239 0.0238

Using a value of 0.025 N/m for res: res = 18

Calculating Initial Water Saturation From Capillary Equilibrium Required items are: ( cos)res

Sw* as function of J

k and Swc transforms

For every point, determine height above OWC (h)

Oil

Estimate k and Swc from transforms h

J

h(  w   o ) g k  cos  

OWC Water

Calculate corresponding values of Sw*

Calculate corresponding values of Sw Sw = Swc + Sw*(1 - Swc)

Calculating Initial Water Saturation From Capillary Equilibrium Example Transforms

y = -1,2764x 5 + 5,9212x 4 - 10,565x 3 + 9,1674x 2 - 4,179x + 1 1

Swc = 0.388 – 0.055 log k

0,9 0,8

Density difference  = 205 kg/m3

g = 9.8

m/s2

 = 0.215

Sw*

log k = 14.5  - 5.8 Vcl

0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 0

Vcl = 0.141 OWC at 1833 mss ( cos)res = 0.037 N/m

Estimate Swi at depth = 1821 mss

0,4

0,8

J-Function

1,2

1,6

Calculating Initial Water Saturation From Capillary Equilibrium Example, continued From transforms: k = 199 md and Swc = 0.262 Height above OWC h = 12 m J = 0.611

Hence; Sw* = 0.176 Sw = 0.262 + 0.176(1 – 0.262) = 0.392