picket plot paper
TRANSCRIPT
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A Review, of Current Techniques for Determination
Of
Water Saturatio'n From Logs
Abstract
G.
R
PICKETT
MEMBER
AIME
The basic saturation and log response equations are
reviewed. It is concluded, that conventional saturation cal
culations account for lithology and rock-type changes,
but
that they are susceptible to uncertainties in water resistiv
ity (R
w
),
true resistivity, porosity and cementation factor
(m). It is shown that resistivity-apparent porosity plots are
useful in wells with
minimum
petrophysical data. Knowl
edge of
R M
m, the slope
of
the sonic log-porosity relation
or the, slope and intercept of the neutron log-porosity
relation are not necessary, provided they are constant.
d-
vantages and limitations are illustrated with exam Dies. It
is concluded that Rwa-depth plots are useful wher; Rw is
unknown and lithology varies, provided m is
known
for
all lithologies involved. ROB SO relations may be useful
for determining water saturation when only a few porous
intervals of
-
constant rock type are present, and when
either
Rw
or formation factor (but not bOth) are unknown.
Finally, an example is reviewed to illustrate that, ojten, no
one of the above techniques by itself m(lY be diagnostic,
and also to emphasize the need to utilize all available
data.
Introduction
The
determination
of
fluid saturations is still one
of
the
prime functions
of
the petrophysical engineer. Although
this problem has been continuously faced in day-to-day
evaluation work since the advent of petrophysics, it still
presents technically challenging problems. If is realized
that hydrocarbon saturation is the quantity
of
real ili
erest. However, with few exceptions, the problem resolves
mto determination
of
water saturation as defined
by
the
following relationships:1
(1)
(2)
F
=
cp-m
(3)
A
~ i t g ~ n a l m a n u s c ~ i p t
received
in
Society
of Petroleum Engineers office
1146) , 966. ReVIsed manuscript received
Aug. 1,
1966.
Paper
(SPE
D was presented
at
SPE
Rocky
Mountain Regional Meeting held in
o f ~ i ~ i n ~ i [ t Way . 2 ~ - 2 4 196,6. @Copyright 1966
American
Institute
*
e a :urIDcal,
and Petroleum
Engineers, Inc.
M
. PreseGntly assIstant
professor
of geophysics.,
Colorado
School of
lnes,
olden,
Colo. '
lReferences given at end of p a p e r ~
NOVEMBER
SHELL
OIL CO.
DENVER
COLO.
where
810 =
the fractional
part of
the pore volume filled
with water of resistivity Rw
1 = resistivity index
n =
saturation exponent
R
t = true formation resistivity
F
=
formation resistivity factor*
Cp
= fractional porosity
m
=
c e ~ e n t a t i o n
exponent.
Historically, the approach to this problem has been to
determine resistivity index 1 from borehole measurements,
and from
I
to calculate
Sw
using either
an
assumed value
for
n or one established from laboratory' experiments.
A
discussion
of
the validity
of
laboratory determined values
of n
is beyond the scope
of
this paper. t will be assumed
that the appropriate value for
n
is known, and this paper
will discuss recent experience with
the
following tech
niques
for
determining
I: (1)
conventional saturation cal
culations,
(2) Ra
vs CPA plots,
(3)
Rwa plots,
and (4)
SO VS
RD. relations.
Conventional Satur,ation Calculations
The
time-honored process
for
making water saturation
calculations involves
the
following steps:
(1)
porosity, is
obtained from a core
or
a porosity log (sonic, neutron
or
density log); 2) formation factor is calculated from Eq. 3
using
an
estimated
m or
one obtained from 'laboratory
measurements or from resistivity measurements in 100
per cent water-bearing intervals; (3)
I
is calculated from
Eq. 2 using a true resistivity
R
t
obtained from
an
appro
priate resistivity device
F
as calculated from Eq. 3
and
an
estimated
Rw or
one obtained
from
a water recovery
in a nearby zone
or
another well,
or
one calculafed from
the
SP
log; and (4) S10 is calculated from Eq.
1
using the
I
calculated from Eq. 2 and n.
This technique has the advantages
of
being well estab
lished and, therefore, relatively easily discussed with man-
agement and other log analysts.
t
also has the advantage
of accounting
for
changes in rock types and lithologies
*An equation of
the
form F =
At/J-m
is s@metimes
used.
For FJurposes
of this report the
form
given
by E'q. 3 is used. The choice of forms
will
not
have a significant effect Qip
the
conclusiop.s reached
in this
paper,
1425
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through the use of Eqs. I through 3
.It
has the major dis
advantage of being susceptible to errors in a number of
quantities which are
med
in the three equations. In the
author's experience, the principal culprits leading to sig
nificant errors in water saturation are uncertainties in
knowledge of water resistivity, errors in the determination
of porosity and errors in determination of
R
I
On occa
sion, errors
in
determination
of
the quantity m
can
also
lead to significant errors in ~ a t e r saturation determina
tion.
To
minimize these errors in water saturation estimates,
a
number of
cross checks on the calculated water satura
tions sometimes can be used. These cross checks usually
consist of comparing the calculated water saturations with
fluid saturations measured in cores,
by
making the calcu
lated water saturations equal 100 per cent water in what
are believed _ o be water-bearing intervals, by comparing
the calculated water saturations with fluid recoveries
from
drill-stem or production tests and by making _ alculated
fluid saturations compatible with shows
or
lack
of
shows
in cutting samples.
Apparent Resistivity
ys Apparent
Porosity
Plots
Another method for estimating resistivity index
I
con
sists of making a log-log plot
of
apparent resistivity vs ap
parent
porosity-. The technique
is
based on manipulation
of Eqs. 2
and
3to obtain
log R
t = -
m log
+
log R O
+
log I
(4)
Eq. 4 shows that a log-log plot
of R
t
vs porosity will
exhibit a straight line of slope minils m
for
zones with
constant water resistivity and constant
1
I f this type of
plot (Fig.
1)
is
made for
a long series
of
intervals, a lin
ear
group of
points can usually be found to define the
100 per cent water-saturated intervals. Then, for a fixed
porosity, any points on the plot whiCh fall at higher re
sistivities have
I's
equal to the ratio
of
their resistivities
to the resistivity on the water-bearing line at that porosity.
Eq. 4 shows that
it
is not necessary to ]mow
R,vor m
in advance to estimate water saturation. In fact, they are
defined, respectively, by extrapolation
of
the water-bear
ing portion
of
the plot to
100
per cent porosity and by
the slope of the water-bearing portion
of
the
plot.
The term apparent resistivity vs apparent porosity" was
chosen for this technique because apparent resistivities
can be
used (to determine saturation
but not
necessarily
R
1V
providing they are proportional to true resistivities
100
I
Rw
'
02
=H=if l
. I .
= = t = - ~ - : - H
r r ttn
\--
- - \ - -
Log RI '
-m
log Ii log
Rw
+ log I: ~ f t t _
I
- ; L ~
I I
I
s::
,-H-
I I ~ 7 5 i i
y
r b..
% ~ I mJni
-1.
~ ~ ' - -
I
7
r
l
/ Y 4 , . . < ~ - j - - - t + , :r
:1
0
-
t
/4 /0
I 1
I - ~ -
fl\l(11\I1:
I I t t l ~
& 10
I
I
I
Hili
0.1
10
100
R
t
Fig. l ~ - S c h c n w t . i c diagram, resistivil.y vs porosity plot.
1-1:':6
and because the technique
is
also applicable to measure
ments which allow either the calculation
of
porosity ex
plicitly or the derivation of a quantity from a log which
is proportional to porosity.
For
example, for the sonic log
the appropriate response equat ion can usually be ex
pressed in the following form:
2
=
:"t.n
+
B
(5)
In Eq. 5,
, ~ t
is the response of the sonic log in microsec
onds per foot, ~ t l n is the va:ue of
6 t
at zero porosity (ma
trix , ~ t )
and
B
is
slope of the linear relation between I ~ t
and
porosity. Solution
of
Eq. 5 for porosity
and
sub
stitution in Eq. 4 leads to:
log R
t
= -m log
6. t - 6 t
lll
+
m log B
+
log
R
II)
+
log
I "
(6)
Eq. 6 shows
that
a log-log
plot of R
t
vs ,6.t-
6 t
ln
(Fig.
2)
is
also linear with a slope of - tn, and further
shows that
I
can be calculated from such a plot -even if
the values
of B,
R1V
or
m are unknown. In fact, the
slope
of
the water-bearing line defines
m.
The
use of a plot of a reciprocal function of resistivity
vs
, ~ t
has also been described:' This method does not re,.
quire a knowiedge ofR
w
or ,6.t
m
, but
does require a knowl
edge of m. The technique was apparently first advocated by
A. T. Hingle
of
Magnolia Petroleum Co.
Similarly, the corresponding equations for using the
resistivity log with the neutron log or with the compen
sated density log are:
log R
t
=
m
me
j )ND
+n+-IogRw
+
log1
(7)
and
log R
t
= -em
log
(DLD-E-Fps)
+mlogF Pf-p, )
logR
1V
logl, 8)
where
ND
=
C+ Dlog
(9)
and
DLD
=
E + Fpb
(10)
. are the response equations of the neutron and density
(compensated) devises'l r ~ s p e c t i v e l y .
Inspection of Eqs. 6 through 8 shows that the resistiv
ity-sonic log combination
can be
expected to
be one
of
the most diagnostic log combinations for this method
(since the slope
of
the plot for water-bearing intervals is
1 0 0 E f f f f i l ~ ~ ~
og
R,
' -m
Log (81
~ m ) + m Log B + Log
Rw
+ Log I
0-
x
: - ~ ~ ~ ~ - 4 - ~ ~ - - - - - J ~ I - r 1 4 -
1 - - - \ - - \ - - l - - H - \ - ~ ~ ~ ~ ~ - t t H - - - r I ' , 75 \ -
m ' - y
-
R
t
1.0
I
, ~ ,
4
.
100
Fig. 2-Schematic
diagram,
resistivity vs ( ~ t - ~ t l n ) plot.
JOURNAL
OF
PETROLEUM TECHNOLOGY
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117 , that the resistivity-neutron combination can
also
be
expected to be one of the most diagnostic (since
the 10Karithm
of
resisti,yity
can.
be directly plotted vs tool
and that
the resistivity-compensated density
omparison is probably the least useful (since constants
and
F
in the density log -response equation must be known
to define the water-bearing plot).
Fig. 3 is
an
example
of
the application
of
the technique.
ith the resistivity-sonic log combination to a several
thousand foot
sand-silt-shalesequence.
This well was a
wildcat and neither
Rw
nor the sonic log porosity re.lation
was known in the section of interest. Intervals A,
Band
C shown on Fig. 3 had good gas shows and were obvious
ly hydrocarbon-bearing, although volumetric reserves were
too small to
make
the well commercial. Intervals D and E
were much thicker but lacked clear-cut gas shows. The
plot indicates that Interval D had greater than 50 per cent
hydrocarbon saturation,
but
that Interval E had less than
50 per cent
hydrocarbon
saturation. Intervals D
and
E
were both thick enough to be of
more
interest. Interval
D, therefore, was opened
and
produced gas. This interval
was later abandoned since the gas flow could
not be
con
trolled, but
the
example shows
how such an
interval can
be distinguished even
in
the absence of water resistivity
and definitive sonic log-porosity information.
Fig. 4 is an example where the
method by
itself was
not diagnostic. If the water-bearing
trend is
taken as shown
by the dashed line, then the two points of interest (A and
B are indicated
to
have
about
30
per
cent hydrocarbon
saturation. However, a core which was taken through
100
D
o 0
6
1
1
~ ~ r
Q ~
L.I-
0 . . 2 . . ~
0
~ ~ ~
~
~ ~ o i --
0
00
~
J
i'---
r
-...
Sw 100
.. -
+
I
fT
Ft
1 '
==R - j - r -
...
~ I = m t t .
1
I i , II
10
100
1000
Fig. 3 -R
a
vs (At-Arm)'
Wildcat
No. 1.
...... '
. ,
1 1 ~ - - ~ ~ ~ - L U i ~
__ - L ~ L l ~ ~ i l ~ I ~ ~ __ - L J ~ ~
10 100 1000
RA (lL)
Fig. 4-
R
a vs At -A t
m
, Wildcat No.2;
NOVEM' .ER,
1966
some of the intervals represented by points
on
the dashed
line had
residual
oil saturations of
about
20 per cent. I f
the water-bearing line is shifted so as to make the dashed
line represent a hydrocarbon saturation of 20 per cent,
then Points A and B are indicated to have a
hydrocarbon
saturation of 45 per cent.
The
extrapolation
of
this new
water-bearing trend to a 100 per cent porosity indicates
an
Rw
of
0.05
ohm-m
at
bottom
hole. Later,
the
fluid re
coveries from this formation yielded a water resistivity of
0.03 ohm-m. This would indicate a water-bearing trend
(solid line)
and
would now
make
the hydrocarbon satura
tions
for
Points A arid B
about
55 per cent.
These
re
sults imply that some residual oil was lost from the cores
representing points' on the dashed line in bringing the
cores to the surface, and that the actual in situ residual
oils were about 30 per cent. Intervals A and B were later
completed
for
a marginal oil well. .
Fig. 5
is an
exani.ple where . his. technique by itself
failed completely. Flow meter tests established that Inter
vals A, Band C were producing only water,
but
that In
tervals D and E were producing gas. The plot indicates
no apparent contrast in apparent resistivity index between
the gas- and water-producing i n t ~ r v a l s . Comparison of
the density log and spnic log responses
in
.the section con
taining these zones indicated the presence of two signifi
cantly different sonic log-porosity relations.
When
these
two relations were accounted for, the plot shown
in
Fig.
6 was then obtained. Intervals D and E again represent
the gas-producing zones, arid Points A, Band C the wa
ter-producing zones. The
apparent
porosity-resistivity plots
1 0 0 t ~ ~ ~ E ~ ~ ' ~ f = f = f ' ~ l - ~ ~ ~ ~ ~ ~ ~ - I ~ ~ ~ ~ ~ ~ t ~
I
--+----
I-
r- I r -'
1 -1--1- -1 H - _ I +...
~ = - - - _ ~ - = - = =
==A,s,
_
l T E R ' I - + ~ I ' - ' + +
1
I
____ . __ :-""1' -
- - ; ; - ~ . +
__
D , _ E + _ ,
- - - t ' - I - 1-,-
-------
---
- - - - -- -
1- - - - -
. ---- i r ------f----I--+---+-I-H-t-I
10
100
1000
Fig. 5 -Ra
VB (At-At ,) , Wildcat No.3.
100
-
-I-+-
~
= ~ : H c
-
A, B, C. - WATER PROD.
-
D, E, - GAS PROD
~
..........
~
r .
..........
~
~
el -
E
0
A
V>
10
0
o 0
0-6
~
'-.-
C't'
~
~
Sw
50
.....
- Sr 0 1 0 ~ ;
I
10
100
1000
Fig. 6 -R
a
vs son ie
Wildcat No.3.
1427
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indicate' that Intervals D and E have gas saturations great
er than 50 per cent, while Intervals A,
Band
C have gas,
saturations greater than 50 per cent. The solid curve was
drawn to represnt the 100 per cent water-bearing
inter:
vals, and extrapolation
of
this trend to 100 per cent poros
ity indicates an Rw
of
0.09 ohm-m at bottom hole, which
agrees with the resistivity of the produced water.
These examples were chosen specifically to illustrate
that the apparent porosity-resistivity plotting technique
is
not a panacea but that, as in all petrophysical techniques,
use should be made
of
all available data; Experience had
indicated that this technique
is
a most powerful one, and
has proven diagnostic in the majority
of
cases where an
independent verification of the interpretation arrived at
could be obtained.
Its principal advantages are (1) a knowledge of Rill
and m
is
not needed;
(2)
if the sonic-resistivity log com
bination is used, the slope of the sonic log-porosity rela
tion does not have to be known, providing there is. only
one slope in effect in the section plotted; (3) if the nu
tron-resistivity log' combination is used, the constants in
the neutron response equation do not have to be known;
(4)
a great amount of section can be quickly evaluated
for significant hydrocarbon saturations without the time
consuming process of calculating water saturations
by
use
of
Eqs. 1 through 3; and
(5)
once the plot has been made,
parameters such as D.tm and m can be easily varied with
out tedious recalculations.
, The technique, therefore,
is
particularly useful for a
quick evaluation of long sections in wells where there is a
minimum of petrophysical data. Also, useful information
concerning petrophysicai relations can often be derived
from these plots in addition to delineating the hydrocar
bon zones.
Fig. 7
is
a plot from a carbonate section which indi
cated no resistivity anomalies of consequence and an av
erage trend which extrapolated to
a
value of. Rw that
agreed with the resistivity of waters produced in other
wells in the area. However,
the
section for which this plot
is
made was completed for one of the better oil wells in
the area.
Fig. 8 shows a plot of the same
data'
plus additional
points from zones of lower porosity. Fig. 8 indicates that
there is a significant resistivity anomaly in the intervals
which pf.oduced the oil and, further,the water saturations
decrease precipitously at a porosity corresponding to a
(D.t -
,D.t
m
between 4 and 6 microsecl ft. The water-bear
ing trend established in this way for the lower porosity
100
E
10
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Rwa =
I Rw
(13)
of
wavs
depth are useful evaluation techniques
Rw
is unknown and where lithology may vary so
The
technique is especially useful for evaluating a long
of
intervals where
Rw is
believed to be constant.
of the Rwa for one interval to the
for a second interval is equal to the ratio of the I's
of
Rw is
constant. Therefore, the
of
application for this technique
is
to plot
vs depth for intervals which are believed to be
of
the
Rwa's
R,oa
within the section used. It follows
if
all the ratios are unity, the interval has a constant
f the Rwa for
R,oa of
four or
For values
of
the Rwa ratios be
four, the method merely. indicates that
of
the intervals contain hydrocarbons.
- GAMMA RAY
. - ~
..
CALIPER
100
SONIC
LOG
.6t
in
mierosee/ft
70
D5T 1
Ree 6000'
Oil
SAND
R
WA
=4.10
1
SAND
K
wA
=1.78
\
@
40
Fig. 1o shows
an
example of the application of this
technique to a section in which the lithology varies from
dolomite to sand. Sqmple descriptions had indicated that
Intervals A, Band C (Fig. 10) were sandstones. R ,a's of
4.1, 3.0 and 1.8 were calculated for these three intervals,
respectively. This indicated the presence of some hydro
carbons in at least Intervals A and B. f Interval C were
completely
w a f e r ~ b e a r i n g
Interval A had to have at least
35 per cent hydrocarbon saturation (if n
=
2 and Interval
B had to have at least 2 per cent hydrocarbon satura
tion. Since hydrocarbon shows had been observed
in
In
terval C, these inferred that hydrocarbon saturations for
Intervals A
an
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7/25/2019 Picket Plot Paper
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after flushing with a wetting fluid. There are two situa
tions where initial-residual relations may be
of
particular
use: (1) where Rw
is
unknown and there are not enough
porous i n t ~ r v a l s to apply an Ra vs apparent porosity plot,
but where formation factor F can be determined, and (2)
where
R ,
is known but where porosity or F cannot be de
termined.
I t
foHows that if a relation between
So
and
R
o
can be
established for a reservoir of interest and if
ROR
in the
zone flushed by
mud
filtrate adjacent to the borehole can
be measured, then So (hydrocarbon saturation in the un
invaded formation) could be estimated from the
S
vs R""
relation.
This technique was applied successfully to a reservoir
where none of the other techniques previously discussed
had proven successful. Conventional water saturations
were not diagnostic because
water resistivity changes by
a factor
as
high as four between adjacent well locations,
with the fresher waters associated with the water saturat
ed locations
and
the saltier waters with the oil-bearing lo
cations.
R,va
plots and
R
vs
apparent porosity plots were
not applicable because the formatioll only contains one or
two porous zones. However, capillary pressure work had
established a relatively definite So vs Ros relation which
was verified by log calculations in wells
where Rw
was
measured from produced fluids (Figs.
11
and 12). The
technique was applied in the following manner.
1.
Ros was estimated from the equation
(14)
where
Ros
is residual oil saturation in the flushed zone ad
jacent to
the
borehole,
Rm
is
mud
filtrate resistivity and
R . ~ o is flushed Zone resistivity (obtained in this case from
the MicroLaterolog).
2. The average curve shown in Fig. 11 was entered
with the calculated
ROB
and
So
was estimated.
This evaluation technique has been used as the basis
for
an
I8-well recompletion program and, as of this date,
the m.ethod has been successful in e v ~ r y case. This
is
an
example
of
the first situation mentioned above.
Tixier used an
So
vs
R08
relation_ in a different way in
his Rocky
Mountain
interpretation technique.
5
From
Eqs.
14 1, 2 and 3, it can be shown that:
Rw (I-Rost
Rill (1-S,,)
(15)
so that
if
Rw
and a relation between
So
and
Ros
are known,
70
60
50
o-'?
40
en
o
0::
30
20
10
1/1,30
~ -
r7fl
7 l / ~ 0
; ; 0
I .
lZ'----- o g o o ~ ~ O C
d
o 8
o ~ o
000
I
l?
8
0
V
g
c>'