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H2O Sat Productivity Electrical Survey Logs Clean Shale .pdf


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Water Saturation & Productivity Estimates from Old Electrical Survey Logs of Clean & Shaly
Sections, Part3: Thin or Shielded Beds by Otis P. Armstrong P.E. Feb 17 2007
Abstract:
The analysis of thin beds with Electrical Survey (ES) logging tool is reviewed. Particular
concern is where two survey tools, Short Normal, (SN; AM=16”), and either Long Lateral,
(LL; AO=18’-8”) or Long Normal (LN, AM=64”) are available. Also an analytical method is
presented for low resistivity formations. Typically, thin beds are resistive formations too thin
for analysis by Long Normal (AM=64”). That is where thickness, e, is less than 1.1 times
AM, (72 inches) but thicker than 10% of AO, (22 inches). Resistive beds in this thickness
range may frequently be analytical using thickness and invasion correction charts. However,
the conventional method of estimating invasion diameter from both Normal and Lateral
charts cannot be applied due to a lack of accurate response by one deep tool. It is proposed
to apply a form of the porosity balance to determine invasion diameter and water saturation
using parametric equations related to the invaded, SN, and deep zones, LL or LN. The
proposed parametric plotted against invasion diameter are:
Invaded Zone Y
Y=(Ri/Rm){[z+(1-z)/10(PSP/-K)]/S1.6α}
It will be shown that Deep Zone Y
Y = (Rt/Rm)
these parametrics are H2O Sat at Zi
S ={(Ri/Rm)(Rm/Rt)[z+(1-z)/10(PSP/-K)]}1/1.6α
a pseudo Formation Formation Factor, F
Ft = {Ft/Fa}[Ri (1-2Z)2]/(Rz)
Factor and are valid
Invaded Zone Fluid R 1/Rz= z/Rw +(1-z)/Rmf
in both shaly and
Apparent to true F
Ft/Fa = 10[(α - 1)SSP/K]
clean sections. The
derivation of equations may be found in appendix 1 of this series.
12
RS-1 Yj = (Rt/Rm)j = [(Ri/Rm)]j{[zj+(1-zj)/10^(PSP/-K)]/S^1.6a}

10
8
6
Y(Rd/Rm)
Y(S=0.05)
Y(S=0.12)
Y(S=0.11)
Y(S=0.10)
F(Di/dh)

4
2
Di/dh
0
2

3

4

5

6

7

8

9

10

11

12

13

14

15

Background
Formations with R/Rmud greater than 10 may be analyzed using the Rocky Mountain
method and the simplified departure curves of Schlumberger B2 and B4. In other cases.
where both deep resistivity tools are responsive and R/Rmud < 10 may be analyzed by the
Lane Wells charts by Pirson’s method.

1

Water Saturation & Productivity Estimates from Old Electrical Survey Logs of Clean & Shaly
Sections, Part3: Thin or Shielded Beds by Otis P. Armstrong P.E. Feb 17 2007
However, if bed thickness is less than 64 inches, deep resistivity cannot be found with R64
and even then Normal bed thickness correction charts are given to a minimum of 1.1AM
(72inch R64 and 18” R16). In many instances only the 16 inch Normal and Lateral ES tools
can respond to thin beds. A practical minimal thickness range for response is likely to range
between 20 and 72 inches. Additional complications may be introduced by shielding effects
on the deep Lateral tool. Invasion diameter and resistivity for thin beds is determined by a
porosity balance between invaded and deep zones using Lane Wells charts for the two
available tool responses.
Another instance of ES log where this method applies is when a moderately thin bed (e<21
feet) is capped with a resistive top and the bed thickness exceeds 72 inches. In this case
the bed under the resistive cap is in the dead zone of the deep Lateral tool, but is responsive
to the Long Normal, AM=64 inches. Again, in this case only R64 and R16 are available for
interpretation. The same plotting technique is applied using invasion charts for wet and dry
resistivities.
The ES log is not analytical in two cases. Firstly when a dense caprock is over a lower
resistive short bed, e<64 inches, for then the bed is in the Lateral shielded zone and neither
can the Long Normal tool respond. The second case is of a thin sandwich zone, e<64
between two low porosity beds. Possibly a MicroLog survey would be helpful in such
instances, but this discussion is limited to all too frequent case where the ES Log was run
using the single sonde for SN, LN and LL.
The Method
Provided both deep and wet responses are available, this method solves the porosity balance
as a function of invasion diameter and water saturation, especially where R/Rmud < 10.
Both dry and shallow resistivity are used in the Lane Wells charts to determine Ri and Rt at
the four invasion diameters of Di/dh = 2, 5, 10, and 15.
A plot of the porosity balance is made in the form of:
(PSP/K)
)]}/Sw(1.6α)
Rt/Rmud = Y= {(Ri/Rmud)[Z + (1-Z)/(10

This identity can be seen in Doll’s Equation as applied to the invaded zone or as Tixler’s
Equations applied with the Schlumberger representation of flushed zone water saturation.
The equation was elaborated in Part 1 of this series as:

Sw = {(Ri/Rt)[Z + (1-Z)/(10(αSSP/K))]}(5/α8)
The pseudo porosity balance can be seen as follows: 1)apply the power term to Sw,
2)substitute PSP as αSSP , and 3)use identity of (Rmud/Rmud) on ratio of (Ri/Rt).

2

Water Saturation & Productivity Estimates from Old Electrical Survey Logs of Clean & Shaly
Sections, Part3: Thin or Shielded Beds by Otis P. Armstrong P.E. Feb 17 2007

Determination of Mixing Factor, Z
The mixing factor, Z, is more problematical but is empirically evaluated in terms of invasion
diameter Pirson2, pg 144 and Fig.21-7.
por
z
Por
Di/dh
interpor
z
Di/dh

>25%
0.15
>20
2
polate
25%
0.15
2

18-25%
0.10

as
21.5%
0.10
2.5

15-22%
0.075
20%->15%
3
given
18.5%
0.075
3

10->15%
0.05
15%->10%
5
below
12.5%
0.05
5

and < 10%
0.025
10%->5%
10

Fig.21-7
Fig.21-7
pg 144
pg 144

7.5%
0.025
10

A total of 4 sets of points will be plotted as:
Di/dh=2
Y2 = (Rt/Rm)2 = (Ri/Rm)2{[0.15+(0.85)/10(PSP/-K)]/Sw(1.6α)}
The
Di/dh=5
Y5= (Rt/Rm)5 = (Ri/Rm)5{[0.05+(0.95)/10(PSP/-K)]/Sw(1.6α)}
invasion
Di/dh=10
Y10 = (Rt/Rm)10 = (Ri/Rm)10{[0.025+(0.975)/10(PSP/-K)]/Sw(1.6α)}
charts are
Di/dh =15 Y15 = (Rt/Rm)15 = (Ri/Rm)15{[0.00+ 1/10(PSP/-K)]/Sw(1.6α)}
provided for
Di/dh of 2, 5, 10, and 15. In the case of very deep invasion, Di/dh =15, the mixing factor
will be taken as zero. The mixing factors on Ri/Rm would then be 0.15, 0.05, 0.025, and 0.0
respectfully.
Determination of Formation Factor, F
In the case of Shaly Formations, F calculates too low. Pirson developed a ratio to relate
apparent electrical Formation factor to the true Formation factor of an equivalent clean
formation. Pirsons’ ratio is universal, in that it equals 1 at zero shale, (alpha =1) and it may
be applied without any loss of functionality.
The Formation Factor is solved at enough invasion diameters to ascertain a correct invasion
diameter by matching to a realistic value of porosity using intercepted values of Sw and
Ri/Rmud for invasion diameter, which in turn determines value of Z in the equation pair:
2
1. Formation Factor Ft = {Ft/Fa}[Ri (1-2Z) ]/(Rz) &
2. Ft/Fa = exp[0.0307(α - 1)SSP]

This process is greatly simplified by solving for Sw at Y2, Y5, Y10, and Y15, and eliminating
values of Sw outside the range of zero to one.

Sw(Y2) = [(Ri/Rm)2{[0.15+(0.85)/10(PSP/-K)]/(Rt/Rm)2}]1/(1.6α)
Other values of Sw are solved in like manner.

3

Water Saturation & Productivity Estimates from Old Electrical Survey Logs of Clean & Shaly
Sections, Part3: Thin or Shielded Beds by Otis P. Armstrong P.E. Feb 17 2007
Since formation factor is uniform in radial, the invaded and deep zone F are identical, thus
the term, “Porosity Balance”. In some instances porosity balance refers a comparison of
porosity by electrochemical method and either nuclear or sonic methods. However in most
ES log suites there is no alternative porosity. Thus the only comparison that can be made is
between deep and shallow zones of the ES tool.
Results
The below example is 10
Yj = (Rt/Rm)j = [(Ri/Rm)]j{[zj+(1-zj)/10^(PSP/-K)]/S^1.6a}
The
from Pirson4.
Olmos sand lies below
the Lituola Taylorensis
un-conformity in Big
Foot Field of Frio Co.,
south central Texas.
It is listed as a
Y(Rd/Rm)
glauconitic
upper
Y(S=0.2)
Cretaceous
sand.
Y(S=0.22)
Y(S=0.25)
Pirson notes it being
3790Olmos R64-R16, Di/dh=x
Y(S=0.27)
one of the “most shaly
F(Di/dh)
1
oil producing sands
2
3
4
5
6
7
8
9
10 11 12 13 14 15
known”. In Pirson’s
figure 17, the zone is
listed between 3798.5 to 3785 feet (e=13.5ft), with Rm of 1.95, T=121F. No micro log was
run. A thin (e~2ft) dense lime cap at 3783 (R19=7), eliminates analysis with the Lateral, as
the bed lies zone within Lateral shielded zone, e<AO. The Log SP is -53mv. R16 is taken as
6.7 and R64 is picked at 6. Glauconitic sands are known for low resistivity pays, due to the
conductive properties of the potassium in these green sands. The Nacatoch sand (also
upper Cretaceous) has been mined at Arkansas outcrops for potassium content and used as
fertilizer.
Pirson does not give the SSP value nor does he give Rw. Alpha of 0.73 was assumed. On
this basis, maximum F is 7 at Di/dh of 5 and Sw of 0.22. The Olmos sand in this location
produces only after formation fracturing. Core analysis determined Sw of 0.65 on total
porosity. The Schlumberger method calculates Sw on effective porosity. This is postulated
as the reason for the difference in Sw values. Success with this example is encouraging.
This example is also a case where R16/R64 is close to one, 0.99. In which instance
Schlumberger chart D14 is not applicable but analysis by invasion charts as seen here
appears feasible.
Confirm pay by Tixier rule (Sch. D9 last par.): Sw<Rz/Rmf. Plotting this rule against Di/dh
indicates invasion diameter must exceed 3.5, based on core analysis of Sw=0.65. The very
low F at Di/dh is also in indicator that Di/dh exceeds 3.5.

4

Water Saturation & Productivity Estimates from Old Electrical Survey Logs of Clean & Shaly
Sections, Part3: Thin or Shielded Beds by Otis P. Armstrong P.E. Feb 17 2007

An example plot is given below: From Pirson p291. First intersection is at S=0.22,
Schlumberger method calc’s water at 38%, using Rxo. This determination is using the R64R16 invasion chart. Calculated F by this method is 26, vs 30% porosity by Schlumberger
with Rxo charts.
100
9245Wilcox R64-R16
Yj = (Rt/Rm)j = [(Ri/Rm)]j{[zj+(1-zj)/10^(PSP/-K)]/S^1.6a}

10

Y(Rd/Rm)
Y(S=0.04)
Y(S=0.05)
Y(S=0.07)
Y(S=0.22)
F(Di/dh)

1

0.1
2

3

4

5

6

7

8

9

10

11

12

13

14

15

The following graph is a plot of the Annova Chalk Formation from Pirson, p311. Pirson using
microtool, estimated Sw about 37% and F of 12.5, compared to Sw of about 30% and F of
8. Pirson states the zone contains 10% fracture. possibly giving a deep invasion.
10

Yj = (Rt/Rm)j = [(Ri/Rm)]j{[zj+(1-zj)/10^(PSP/-K)]/S^1.6a}

Y(Rd/Rm)
Y(S=0.16)
Y(S=0.28)
Y(S=0.27)
Y(S=0.30)
F(Di/dh)

1500Annova R19-R16
1
2

3

4

5

6

7

8

9

10

11

5

12

13

14

15

Water Saturation & Productivity Estimates from Old Electrical Survey Logs of Clean & Shaly
Sections, Part3: Thin or Shielded Beds by Otis P. Armstrong P.E. Feb 17 2007
Conclusion & Summary
The analysis of examples indicates the method is applicable to those instance where only
one pair of deep and shallow response is available from an ES log. The plotting method
solves for both Formation Factor, porosity balance and the invasion diameter for wells logged
without porosity tools. According to Hilchie, there numerous possibilities for hydrocarbon
exploitation if old well logs are properly reviewed. The method is particularly suited to high
porosity and or shaly formations.
References

1. Pirson, S.J., 1963 Handbook of Well Log Analysis, Prentice Hall Englewood NJ, p309-13
2. Pirson SJ, 1950, Elements of Oil Reservoir Engineering 1st Ed McGraw Hill NY pp 136-154,
Fig2.35 from Guyod. plenty of old ES logs
3. Pirson SJ, 1957, Formation Evaluation by Log Interpretation, p1-3, May-June World Oil
Pirson, SJ, Cira1957, Formation Evaluation by Log Interpretation, Dresser Industry,
Tulsa paper LE-32D several ES logs & Upper Cretaceous Olmos shaly formation w/Sw by
core anal.
4. Pirson, S.J., 1958 Oil Reservoir Engineering, McGraw Hill 2nd Ed, NYC, p137-302 Ri Method
259-264, Prediction productivity, pp279-282
5. Asquith G.B. 1982, Basic Well Log Analysis AAPG Tulsa pp187-194 upper Cretaceous example
& porosity methods for Sw in shaly formations.
6. Jordan CR, Cira1954, Chalk Rock Oil, Dresser Industry, Tulsa paper LZ-34-A, Another series of
ES logs in upper Cretaceous w/Core anal of SW
7. Guyod,H. Electrical Well Logging Fundamentals, Mostly reprints from World Oil & Oil Weekly
1944-1952 and one from O&GJ v.50No.31 Dec6/1952. Fig’s 10-6 & 3 & 6 regressed for bed
thickness correction pp 64, 139, 140 p39 p130-2 SP cf’s.
8. Guyod H. Electric Analogue of Resistivity Logging, Geophysics Vol.XXNo.3 July/1955 pp615629
9. Hilchie DW 1979 Old E.Log Interpretation, pre1958, AAPG reprint 2003 Tulsa
10. Wylie, M.R.J., 1963 The Fundamentals of Well Log Interpretation, 3rd Ed, 2nd ed 1957 p72,
Academic Press, NYC
11. Armstrong OP, 2003, The Shale Factor & Permeability in Latvia Geology”. Geol.Soc.Amer.
Nov.03 meeting presentation of carbonate k equation
12. Armstrong OP, 2001, Water Resistivity for Western Latvia Ordovician Zone, Informal paper
SPWL031, Taos NM, a review of shale methods
13. Meehan, D.N. Vogel E.L., 1982, Reservoir Engineering Manual using HP41 , Penwell Pub.,
Tulsa OK p7 ch13 another shale eval. method
14. de-Witte, AJ, (Mar4 & April 15, 1957), Saturation and Porosity from Electric Logs in Shaly
Sands, O&GJ, 55 ( A method of computing oil saturation and porosity in formations which
contain disseminated clay minerals, with simple Nomographs)

6


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