picket plot paper

7/25/2019 Picket Plot Paper

1/9

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


2/9

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


3/9

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


4/9

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


5/9

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


6/9

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>'

picket plot paper

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