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Transition Zone Analysis

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procedure and example of manual calcuation of SHF

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  • 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

    Capill

    ary

    Pre

    ssure

    , psi

    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