saturation height function
DESCRIPTION
procedure and example of manual calcuation of SHFTRANSCRIPT
Transition Zone Analysis
Porosity Cross-Plots
End-point values for porosity logs are determined from
cross-plots of log response versus core porosity (NOB)
Density Log Calibration with Core Data
y = -1.7702x + 2.7103
0
0.5
1
1.5
2
2.5
3
0 0.1 0.2 0.3 0.4
Core Porosity at NOB
Bu
lk D
en
sit
y, g
/cc
Density Log
Sonic Log Calibration with Core Data
y = 126.52x + 49.905
0
20
40
60
80
100
120
140
160
0 0.1 0.2 0.3 0.4
Core Porosity at NOB
Tra
ns
it T
ime
, m
icro
-se
co
nd
Sonic Log
Shale Content Cross-Plots
min
minlog
SPSP
SPSPI
sh
SP
min
minlog
sh
I
In this case, use
Larionov – Older Rocks correlation
In this case,
Make a new correlation
Calibration of Well Logs
with Core Data
OWC
Oil Rim
Bottom Water
Cap Rock
If Capillary Pressure is Negligible
10
Sw
Swc
Initial Saturation Distribution
No transition zone
OWC
Oil Rim
Bottom Water
Cap Rock
If Capillary Pressure is Significant
10
Sw
Swc
Initial Saturation Distribution
Top transition zone O/w
Transition Zone
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
PcowA = Ah(w - o)g
Hence;
h = Pcow/ (w - o)g
OWCh
A
Pcow
SwSwc0 1
h
SwSwc 10
Example Calculation
Given:
Water density = 995 kg/m3
Oil density = 689 kg/m3
Acc. of gravity g = 9.8 m/s2
Oil
WaterWater
(A) h = 5 m
(B) h = 15 m
(C) h = 30 m
OWC
Oil
WaterWater
(A) h = 5 m
(B) h = 15 m
(C) h = 30 m
OWC
Pcow
psi
Sw
0 10
16
8
24
0.40.2 0.80.6
For point A: Pcow = 5x9.8x(995-689)/6900 = 2.2 psi
Swi = 0.88
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
• Defining reservoir rock facies
Objectives
• Checking validity of Sw values calculated from well logs
• Checking validity of OWC level
• Calibration of well logs with core data
• 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
k
Vcl
Swc in terms of k
log k
Swc
Transition Zone Analysis
Procedure, continued
Formulate suitable J-Functions from core data
J-Function vs Sw
J
Sw0 1
kPJ c
cos
Transition Zone Analysis
Procedure, continued
Convert J-Function to normalized J-Function
wc
wcww
S
SSS
1
*
J-Function vs Sw*
J
Sw*0 1
Jmax
Transition Zone Analysis
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
--- --- --- --- --- --- ---
--- --- --- --- --- --- ---
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
--- --- --- --- --- --- ---
--- --- --- --- --- --- ---
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
Procedure, continued
Calculate k, Swc and Sw* for every point above OWC
from log analysis results
wc
wcww
S
SSS
1
*
Transition Zone Analysis
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
--- --- --- --- --- ---
--- --- --- --- --- ---
3501.0 0.162 25 0.425 33.0 0.0284
3501.5 0.225 412 0.494 32.5 0.0970
--- --- --- --- --- ---
--- --- --- --- --- ---
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
Procedure, continued
Calculate h and (J cos) for every point above OWC
from log analysis results
h = height above OWC
kghJ ow )(cos
Transition Zone Analysis
Procedure, continued
Plot (J cos) versus Sw* and fit the best J-Function Curve
(J cos) vs Sw*
J cos
Sw*0 1-0.2
Jmax cos
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 J-
functions 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
Pc
Sw0 1Swc
kJPc
cos
Determine average and k for various
reservoir rock facies
Estimate Swc from transforms
Calculate Pc values from J, cos, and k
Plot Pc versus Sw
Assume several values for Sw* between 0 and 1
Calculate corresponding values of Sw
Determine J values from Sw*
Transition Zone Analysis Example
Given capillary pressure data
Sw 1 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
Pc, psi 0 5 10 15 20 25 30 40 50 60 70 80 90 100
0
5
10
15
20
25
30
35
40
45
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Water Saturation Sw
Ca
pill
ary
Pre
ss
ure
, ps
i
Sample A
Porosity = 18%
Permeability = 236 md
Swc = 24%
Transition Zone Analysis Example
Given k and Swc transforms
log k = - 28.56por2 + 21.14por - 4.6Vsh - 0.38
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
0 0.05 0.1 0.15 0.2 0.25 0.3
Porosity
Lo
g k
Vsh
0
0.1
0.2
0.3
0.4
y = 0.0192x2 - 0.1434x + 0.4555
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
-1 -0.5 0 0.5 1 1.5 2 2.5 3
Log kS
wc
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
Other data
Transition Zone Analysis Example
Calculated Jlab versus Sw*
Sw* 1 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
J 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
y = -38.494x5 + 105.36x4 - 108.03x3 + 53.181x2 - 15.649x + 3.63
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Sw*
J
Transition Zone Analysis Example
Calculated Jcos versus Sw* from log dataDepth Porosity Vsh Sw k Swc Sw* h J cos
ft subsea md 0 ft
2758 0.155 0.271 0.696 9.2 0.335 0.542 108 0.01713
2758.5 0.12 0.017 0.430 46.5 0.270 0.219 107.5 0.04357
2759 0.166 0.11 0.422 68.6 0.257 0.223 107 0.04479
2759.5 0.223 0.287 0.597 39.2 0.276 0.444 106.5 0.02907
2760 0.168 0.035 0.310 160.1 0.233 0.101 106 0.06738
2760.5 0.201 0.241 0.589 40.4 0.275 0.433 105.5 0.03080
2761 0.218 0.333 0.646 21.8 0.298 0.496 105 0.02162
2761.5 0.241 0.175 0.276 178.2 0.230 0.060 104.5 0.05851
2762 0.164 0.19 0.577 27.8 0.288 0.405 104 0.02788
2762.5 0.148 0.277 0.797 7.1 0.347 0.689 103.5 0.01476
2763 0.128 0.089 0.567 28.1 0.288 0.392 103 0.03142
2763.5 0.161 0.256 0.748 12.8 0.320 0.630 102.5 0.01882
2764 0.173 0.074 0.323 120.8 0.240 0.109 102 0.05550
2764.5 0.233 0.139 0.256 226.8 0.224 0.042 101.5 0.06521
2765 0.255 0.069 0.230 685.8 0.203 0.034 101 0.10785
2765.5 0.252 0.256 0.438 90.4 0.248 0.253 100.5 0.03919
2766 0.224 0.209 0.465 91.4 0.248 0.288 100 0.04159
2766.5 0.106 0.355 0.950 0.8 0.470 0.905 99.5 0.00563
2767 0.105 0.19 0.795 4.5 0.370 0.674 99 0.01335
2767.5 0.101 0.161 0.773 5.3 0.362 0.644 98.5 0.01469
2768 0.17 0.275 0.751 13.3 0.319 0.634 98 0.01785
2768.5 0.103 0.354 0.913 0.7 0.478 0.834 97.5 0.00523
2769 0.147 0.145 0.585 27.8 0.288 0.418 97 0.02747
2769.5 0.25 0.067 0.218 648.3 0.204 0.018 96.5 0.10119
2770 0.258 0.095 0.215 544.6 0.207 0.010 96 0.09082
2770.5 0.144 0.07 0.448 56.2 0.263 0.251 95.5 0.03885
2771 0.106 0.128 0.680 8.9 0.337 0.517 95 0.01792
2771.5 0.21 0.291 0.679 28.9 0.287 0.550 94.5 0.02283
2772 0.176 0.253 0.722 19.6 0.302 0.602 94 0.02043
2772.5 0.152 0.351 0.885 3.6 0.382 0.813 93.5 0.00937
2773 0.215 0.171 0.402 114.4 0.242 0.212 93 0.04417
2773.5 0.16 0.295 0.845 8.2 0.340 0.765 92.5 0.01364
2774 0.11 0.233 0.803 3.4 0.385 0.679 92 0.01053
2774.5 0.106 0.293 0.847 1.6 0.427 0.733 91.5 0.00732
2775 0.146 0.12 0.577 35.1 0.280 0.413 91 0.02905
2775.5 0.221 0.196 0.447 99 0.246 0.267 90.5 0.03944
2776 0.195 0.217 0.585 45.5 0.271 0.430 90 0.02831
2776.5 0.195 0.309 0.765 17.2 0.308 0.660 89.5 0.01731
2777 0.191 0.395 0.836 6.3 0.353 0.747 89 0.01052
2777.5 0.162 0.273 0.803 10.9 0.327 0.708 88.5 0.01495
2778 0.11 0.34 0.886 1.1 0.450 0.792 88 0.00573
2778.5 0.168 0.383 0.926 4 0.376 0.881 87.5 0.00879
2779 0.194 0.045 0.310 275 0.220 0.116 87 0.06745
2779.5 0.257 0.178 0.348 222.8 0.225 0.159 86.5 0.05244
2780 0.185 0.086 0.413 143.8 0.235 0.232 86 0.04937
2780.5 0.199 0.291 0.693 22.8 0.296 0.564 85.5 0.01884
2781 0.131 0.055 0.481 44.3 0.271 0.289 85 0.03219
2781.5 0.165 0.008 0.282 196.7 0.228 0.070 84.5 0.06007
Transition Zone Analysis Example
Transition zone plot
Transition Zone Analysis Example
Calculated (cos)res for various Sw* values
Sw* J cos J cos
0 0.0853 3.630 0.0235
0.1 0.0602 2.499 0.0241
0.2 0.0453 1.919 0.0236
0.3 0.0371 1.565 0.0237
0.4 0.0296 1.268 0.0233
0.6 0.0172 0.713 0.0242
0.8 0.0090 0.377 0.0239
1 0 0
0.0238Average
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
kghJ ow
cos
)(
For every point, determine height above
OWC (h)
Estimate k and Swc from transforms
Calculate corresponding values of Sw*
Calculate corresponding values of Sw Sw = Swc + Sw*(1 - Swc)
Oil
Water
OWC
h
Calculating Initial Water Saturation
From Capillary Equilibrium
Example
Density difference = 205 kg/m3
g = 9.8 m/s2
= 0.215
Vcl = 0.141
OWC at 1833 mss
( cos)res = 0.037 N/m
Transforms
Swc = 0.388 – 0.055 log k
log k = 14.5 - 5.8 Vcl
y = -1,2764x5 + 5,9212x4 - 10,565x3 + 9,1674x2 - 4,179x + 1
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 0,4 0,8 1,2 1,6
J-Function
Sw
*
Estimate Swi at depth = 1821 mss
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