Spe 26436 MS PDF
Spe 26436 MS PDF
Spe 26436 MS PDF
SPE 26436
Enhanced Reservoir Description: Using Core and Log Data
to Identify Hydraulic (Flow) Units and Predict Permeability in
Uncored Intervals/Wells
Jude O. Amaefule* and Mehmet Altunbay*, Core Laboratories; Djebbar Tiab*, U. of Oklahoma; David G. Kersey
and Dare K. Keelan*, Core Laboratories
SPE Member
Abstract
Understanding complex vanatlOns in pore geometry within
different lithofacies is the key to improved reservoir description
and exploitation. Core data provide information on various
depositional and diagenetic controls on pore geometry.
Variations in pore geometrical attributes in turn, define the
existence ofdistinct zones (hydraulic units) with similar fluid-flow
characteristics. Classic discrimination of rock types has been
based on subjective geological observations and on empirical
relationships between the log of permeability versus porosity.
However, for any porosity within a given rock type, permeability
can vary by several orders of magnitude, which indicates the
existence of several flow units.
Introduction
One of the most important existing and emerging challenges of
geoscientists and engineers is to improve reservoir description
techniques. It is well recognized that improvements in reservoir
description will reduce the amount of hydrocarbon left behind
pipe. Accurate determination of pore-body/throat attributes and
fluid distribution are central elements in improved reservoir
description.
Many reservoir description programs, though
detailed, have not included descriptions at the pore-throat scale.
Yet, pore-throat attributes control initiaVresidual hydrocarbon
distribution and fluid flow. Because they are readily available,
continuous sources of data, logging tool responses are often used
to draw inferences ahout lithology, depositional and diagenetic
sequences, and fluid content. These inferences are based on
empirical models utilizing cOITelations among tool responses,
rock and fluid properties. In many instances, unfortunately, the
correlation models can not be used globally because of the
influences of factors not fully considered by the models. Factors
include (a) the presence of potassium-feldspar, zircon, etc.
causing erroneously high calculated Vsh from the gamma ray; (b)
microporosity in kaolinite, chert, etc. leading to high apparent
water saturation calculations; and (c) siderite, pyrite, barite, and
smectite influencing the resistivity, density and neutron log
205
SPE 26436
logk
= a~ + b
(I)
Fundamental Theory
The hydraulic quality of a rock is controlled by pore geometry.
This, in turn, is a function of mineralogy (i.e., type, abundance,
morphology and location relative to pore throats) and texture (i.e.,
grain size, grain shape, sOlting, and packing).
Various
permutations of these geological attributes often indicate the
existence of distinct rock units with similar pore throat attributes.
Determination of these pore throat attributes is central to accurate
zoning of reservoirs into units with similar hydraulic properties.
The mean hydraulic unit radius (rmh) concept l2 is the key to
unraveling the hydraulic units and relating porosity, permeability
and capillary pressure.
rmh
= 2'
(3)
206
SPE 26436
. . . . . . . . . . . . . . ..
(4)
The mean hydraulic radius (rmh) can be related to the surface area
per unit grain volume (Sgy) and effective porosity (~e) as follows:
Sg,
~ (l ~~,)2
[z,:d
(6)
~~ [~J
-Fst S;v2
(l - ~ e)
(7)
Ji ~
[1
~'$~ [JF:~sJ
10gRQI
= log~z + 10gFZI
(12)
On a log-log plot of RQI versus ~z' all samples with similar F'Zl
values will lie on a straight line with unit slope. Samples with
different FZI values will lie on other parallel lines. The value of
the FZI constant can be determined from the intercept of the unitslope straight line at ~z = 1. Samples that lie on the same straight
line have similar pore throat attributes and, \hereby, constitute a
hydraulic unit.
Alternative relationships that yield FZI values similar to those
derived from Eq. 12 have also been developed from Eq. 7 as
follows.
If k (md), FZI (!-.1m) and
~e
= 1014 (FZI) -
')
(fraction), then
~~
(l - ~ e) 2
(13)
If ~R is defined as
~3
~R= (l_~)2'
(14)
then
k= 1014(FZI2)~R
(15)
(16)
= ResevoirQualityIndex
~ 0.0314
(8)
where k is in !-.1m2.
RQI(!-.Im)
..................... (11)
(5)
k =
RQI
~z
Ji
~ = 1014 (FZI) 2
~e
(9)
(_e_)- = 1014(FZI)2(~
')
l-~e
)2.
(17)
c\)
$z
log (:)
e
(10)
207
(18)
SPE 26436
'
.1.FZI
.1.<1> ?3 - <I> ?.1.k
( - - ) = O,5[(-) ( - ) + (-)
FZI
<I>
1- <I>
k
(20)
(21)
15 ...
Thus,
Y = mX,
where X
,
rill},
r;;:
208
(23)
SPE 26436
JF:
South America
Porosity and permeability data generated on a typical South
American clastic reservoir rock were used to compute RQI, <1>z'
and FZI. A log-log plot of RQI versus <1>z (Fig. 7) shows five
distinct hydraulic units within the cored interval. These units
were discriminated by the previously discussed statistical
techniques with the theoretical unit slope constraint.
Additionally, Fig. 8 shows the classical log k versus <1> plot after
the zonation process. 'The permeability response equations were
derived from Eq. 13. It is evident from this plot that permeability
is a nonlinear function of porosity, texture and mineralogy. The
differences between the hydraulic units was further verified by
water-oil capillary pressure data and cation exchange capacity
(CEC) per unit pore volume (Qy). It is evident on Fig. 9 that Qy
decreased with increasing FZI, thus manifesting the effect of clay
minerals on the rock's hydraulic quality.
West Africa
Fig. 16 shows the classical log k versus <1> plot for a typical data set
from the Niger Delta. Seven distinct hydraulic units were
established within the cored interval by utilizing the proposed
techniques. As previously observed, the permeability-porosity
relationship in the Niger Delta is also nonlinear and predictable
(Eq. 13). FZI ranged from 0.3 to well over 11 in these
depositionaVdiagenetic sequences. 'The variability of FZI in the
Niger Delta rocks appears to be both texturally and
mineralogically controlled.
Fig. 17 documents the intrinsic pore geometrical characteristics
and reflects the effect of geological attlibutes (Figs. 18A to 18C)
on hydraulic quality. For example, hydraulic unit 4 (FZI =4.83),
which is a fine-grained, moderately well-rounded and well-sorted
sand with a low clay content (l % kaolinite) (Fig. 18A), had the
following distribution of pore throat sizes: macro = 83%, meso =
2%, and micro = 15%. In contrast, a sample from hydraulic unit
5 (FZI =3.7), with a pore throat size distribution of macro =68%,
meso = 5%, and micro = 27%, is comprised of laminated, coarse
and fine grained sequences with angular, poorly sorted grains and
an intermediate clay content (5% kaolinite) (Fig. 18B). The worst
quality hydraulic unit (FZI = 0.4), which is comprised of
laminated, fine grained, well rounded, moderately sorted
sandstone sequences, had a high clay content (12% kaolinite and
chlorite) (Fig. 18C) and a pore throat size distlibution of macro =
22, meso = 29, and micro = 49%.
Porosity and pelmeability data determined at multiple net
overburden pressures were used to characterize the RQI stress
sensitivity of each hydraulic unit. RQI was correlated to net
overburden stress (a) by the following relationship:25
209
SPE 26436
RQI = EXP [
[l-EXP(-(--'
0'-0'. ] ]
= -RQl
-b.
,.. (24)
c
j
where bs = stress sensitivity factor, O'i = initial stress used for RQI i,
and c =stress constant (2000-4000 psi).
The stress sensitivity factor (b s) was further correlated to FZI,
which was computed from porosity and permeability at initial
stress conditions, to arrive at the following predictive relationship:
............. (25)
West Texas
For the Niger Delta clastic rocks, the RQI stress sensitivity (b s)
was correlated to FZI with the following parameters: Al = 1.39,
X =FZI, X o =FZImiu ' B 1 = 1.31, C 1 =0.96, D 1 =5.2, nl = 2.09,
with a coefficient of determination (R1 == .9999). In general, it was
established that rocks from the same hydraulic unit (similar FZI)
exhibited similar RQI stress sensitivities (b s)' bs decreased with
, increasing FZI. Additionally, rocks with abundant macropore
throats typically showed lower RQI stress sensitivities (b s < 0.05),
in contrast to microporosity-dominated rocks that showed higher
bs values (b s > 0.05).
The classical J function is not adequate for differentiating the
various hydraulic units. This is because the J function only
normalizes capillary pressure with respect to porosity,
permeability and tortuosity, but does not include the effect of
surface area. Eq. 26 confirms this observation.
P~
= ~ = ~ ~ = RQI = _1_
O'cose
r~$
rmll
Jiis"C
(26)
210
SPE 26436
Conclusions
A new. practical and theoretically-based technique has been
developed to identify and characterize units with similar pore
throat geometrical attributes (hydraulic units). This technique has
a wide variety of practical field applications for both cored and
uncored wells. These include:
Improved prediction of permeability and permeability
distributions from wireline logs in partially cored/uncored
intervals and adjacent wells
Improved well-to-well rock properties correlations for
refinement of petrophysical models
Forecasts reservoir rock quality (and formation damage
potential) in partially cored/uncored wells for improved
completions and enhanced recovery decisions
211
SPE 26436
5.
Stiles, J.H., Jr. and Hutfilz, J.M.: "The use of Routine and
Special Core Analysis in Characterizing Brent Group
Reservoirs, U.K. North Sea," SPE 18388 (1988).
6.
7.
8.
9.
Nomenclature
bs
c
Acknowledgments
The authors thank Core Laboratories Division of Western Atlas
International for permission granted for the publication of this
manuscript. Additional thanks are due to Cynthia Philipson for
technical editing and assistance in figure preparation and to
Shelley Barnett for dedicated efforts in the preparation of this
manuscript.
References
1.
2.
3.
4.
19. Testerman, J.D.: "A Statistical Reservoir-Zonation Technique," JPT (August 1962) 889-893; Trans., AIME.
212
SPE 26436
Parameter
Y
153.50
m2/g
2
19.79%
Y min
16.92 m /g
13.68
X min
0.10 !Jm
0.80 !Jm
R2
0.95
0.995
't
Sgv
FZI
SWR
rmh
Coarse grained
Fine grained
Texture
Weight %
(Wet Sieve)
W
Sgv
Y max
Surface Area
(NMR)
Mineralogy
L = Low
M= Medium
H = High
FZI = -==-----'-
Jiis'tS
gv
<l>
(%)
k (md)
RQI
FZI
Features
6436
7.9
21.87
0.522
6.090
6390
8.8
6.38
0.267
2.774
6417
10.1
2.23
0.148
1.313
6491
10.4
1.43
0.116
1.005
6454
8.3
0.37
0.066
0.732
6621
19.4
0.76
0.062
0.258
massive to faintly mottled; small anhydrite patches; faint allochem ghosts; healed fractures
213
10
SPE 26436
HU
. Cements
RQI
Pore Types
Other
6436
0.522
fine-med. crystalline
avg =0.06 mm
subhedral to euhedral
intercrystalline
6390
0.267
medium crystalline
avg =0.23 mm
subhedral to euhedral
intercrystalline
6417
0.148
finely crystalline
avg =0.04 mm
anhedral to subhedral
intercrystalline
microporosity
6491
0.116
finely crystalline
avg =0.05 mm
anhedral to subhedral
imercrystalline
possible pin-point
vugs
allochem molds
6454
0.066
bimodal crystalline
size: very finely and medium
crystalline
avg = 0.007 and 0.014 mm
anhedral to subhedral
intercrystalline
moldic microporosity
common dolomite-replaced
allochems
allochem molds
6621
0.062
anhydrite-healed fractures
minor sparry calcite
intercrystalline
microporosity
allochem molds
minor allochem ghosts
Upper Interval
l::J. Lower Interval
100-l.------------~.-------,........".
Clay
Mor hology
0.8
"E
m
0
z
10
+----+----4-----1-----l-----I
1.0
0.6
'0
~
CD
en
lIfI
CD
0.1
...
0.4
0.01
0.2
0.001 ....I-_-4-...........f-J4-.L.+---.--+-.,.--+""""'T..,.....--,--i~r---+--.,.--+-----.....
o 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
Porosity
Fig. 1.
0.5
Fig. 2.
214
1.5
2.5
FZI
100
100
\
I
.\
I,
\ \
\~
>-
\ "-..
..............
Plot either
- log RQl vs. log $z
or
- log k vs. log $R
or
log k/$ vs. log $z
FZ/ = RQ/@$z = 1
---
~ ---l:9
s:---r----.
Jk@$R=l
FZ/=
80
70
60
:<:
a.
:c
SO
40
= ~.~.
RQ/
k j ' $z,' RQ/o
2.5
FZI
= EXP(-b e
a-a
N
0\
~
VJ
0\
/
~
9
;l>
;l>
trJ
~
t"'"
lT1
~
,)
;l>
t"'"
(l-EXP(-(7
/eX
20
10
C/)
,./.
e;/
0::
30
.-
1.5
0.5
k
FZ/ = $@$z
10
f\)
90
Fig. 3.
10
14
12
Fig. 5.
;l>
~>-<:
~
....,
k_(a);$(a)
......
;;
compule
$
$z=q
CJ1
HU1
HU2
HU3
HU4
HU5
HUG
FZI
FZI
FZI
FZI
FZI
FZI
RQ/
= 4.00
= 2.00
= 1.50
= 0.75
= 0.50
= 0.25
10 ~---------.-----------~
ttl
t:1
= 0.314~
FZI
ttl
FZI
P
~
RQ/
trJ
:;:&j
C/)
$3
trJ
>-<:
$R = (1_$)2
;l>
zt:1
III
C
ec.>
a0::
Fig. 4.
I
0.1
7'
t:1
a0::
0.1
I /
/ 71'
7'
trJ
t"'"
;l>
0.01
0.01
0.01
'
0'
ci
Phl(z)
Fig. 7.
0.1
0.1
Phi(z)
Fig. 6.
I
0.01
....
....
10000
HU1
1000 +-J
0.9
HU2
HU3
HU4
HU5
IL-
I--<
tv
ttl
0.8
100
,.....
--3
~
0.7
:I:
E
0.6
"0
10
:::tl ttl
~ 0.5
:g
Q>
~
0-
0.3
0.2
0.01
0.1
0.001
I'
0.1
0.2
0.3
.,
>
Z
n
n
.-. ttl
I\)
I--<
.
~
... ... ..-. . """"-.-; .
fJ
[~
&
"
&
&
&
i
&
. ..
Fig. 9.
~
c:::
en
I--<
-<
0
>
:::tl
oZ
en
ttl
Z :::tl
--3
en
10
0.4
FZI, microns
Porosity, fraction
Fig. 8.
0.4
c::: :I:
0.4
0.1
>
Fig. 10.
I--<
~ :::tl
g ~
n--3 0-
~ ~
(j)
~ c:::
~ ~
ttl
ttl
> a
~ n
I--<
:::tl
-Z >
Z
c::: 0
Z
o a
:::tl 0
>
o --3
ttl
Z>
tri
:::tl
Fig. 11A.
Fig. lIB.
Fig. 12.
-<
>
~
en en
~~ tv~
~ ~
~
en
0\
en
rg
t'-J
0\
~
0\
9
Fig. 13.
Fig. 15.
Fig. 14.
>
s::
>
t'I1
'Tj
~~
~
>
~
C
Z
t:ti
>
1.0 , - - - - - - - - - - , r - - - - - - - - , - - - - - - - - - - - ,
100000
HU1
HU2
HU3
HU4
HU5
HUG
HU7
I\)
......L
--...J
10000
1000
I I
FZI
FZI
FZI
FZI
FZI
FZI
FZI
= 10.5
= 8.5
= 7.011
= 4.3
= 2.5
= 1.0
= 0.3
I~
t:ti
0.8
...............
0.7
0.6
0.5
"I
:g
:;
tj
'U
~-<
~
100
""'" ...... 1
'"
'II...
'f":\:
",
t'I1
:::'d
en
t'I1
",\
....... '<
",,\
Vi
-<
>
Z
41
tj
a.
0."
10
0.3
0.1
of!
0.05
f
0.1
0.15
0.2
I
0.25
0.3
0.0
0.35
Crossplot of Klinkenberg
permeability versus porosity
(West Mrican example).
In,
illt""'
>
Z
I '
1
Porosity, fraction
Fig. 16.
HU1
HU2
HU4
HU5
HUG
HU7
0.2
0;1
'"
/I:
10
I
100
Fig. 17.
......
12
0.9
,\\
I
10
0.8"\\
0.7
I \\\',
l-'
+:-
tt1
>-3
t;j
::r:
0.6
\'. '.
'\: I
Fig. 18A.
0.41
\\
0.31
0.2
0.1
'\:
,,\.
> Z
::r:
>
t"""
....... oorL
----=
-n Z
n
fJ 0tt1
---
, ..... <
::0 tt1
, I
~
III
II
!--
10000
Fig. 20.
i::ool-
100 I f - -
1000
.:.;;7"
2"
HU1
HU2
HU3
HU4
HU5
HU6
.r.
:::;;>'"""1
'C
E
~
~1
~
J~
10
l /.
,'"
ell
Q.
'/
0:1
0.1
tI'J
L...-
./V
l.? V
V
~ . /V
....-V
V
L.../
/" ~
V~
V V V
/:v l........v
V
J;;7o~
l--J...
....-
v:
V V
l/
~ V k-'
<9'
c,
?~
l-p
c,
0&
--
/0
o 0
+-----+--1
MU .)
= 1.01
1'".1
tt1
'i:l
~ ~ V~
~~~
A
if'
52
0.1
::0
0.01
0.01
0.1
0.2
0.3
0c,
J/ '/
0.001
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26
Porosity, fraction
Porosity, fraction
Fig. 21.
Fig. 22.
~ ~
tI'J
> a
~ n
t""" 0
- ::0
~
tI'J
-z z
>
c 0
Z t"""
n 0
::0 0
o a
tTl
>
>-3
>
~ >-3
::0 0
-<
>
t"""
(,I)
Fig. 18C.
(,I)
::0 C
V L( ~V
/'
::0
Z 0
tI'J
5.18
3.09
1.79
1.09
0.53
0.24
:1': t'
::0
S2 ~
FZl
FZl
FZl
FZl
FZl
FZl
tt1
n
>-3 0
10 I
100
>
'i:l
I\)
tt1
(,I)
Class Interval
1000 I
.......
ex>
(,I)
PclPd
Fig. 19.
::0
->-3 -<
0
0.5 1.5 %.5 3.5 4.5 5.5 1.5 7.5 1.5 1.5 10.5 11.5 12..5 13.5 14.5 15.5 >16
1000
100
10
'-"
(,I)
~ IV~
t"""
t"""
(,I)
e
0\
0\
15
SPE 26436
.1
PREDICT(O
POROSITY
r=-_-----'-''''l400
Pi'll (,..nstr'O'l)
PERI.lEABlllTY,md
FIRST PASS
s-
AND
ESER'VOIR OUAl..JTY
INDEX
SAMPLE WEll.
HYDRAULIC UNITS
HU1"BesIOvolity
HU 7-Wo"t Quality
60
Phi (lolol)
.1
ROI(d.L.nnin.d)
0.01
O.O~
10
(P"dk:l.d)10
~
Calculate permeability
FZI;
1014 (FZI) 2 _ _
>3_
(I -
q2
=t(iilc;iX7i)
I
Fig. 23.
10000 . . . , - - - - - . - - - - - - - - - - , - - - - - - , - - - - - - ,
HU1
HU2
HU3
HU4
HU5
HUG
1000
100
'C
FZl
FZI
FZJ
FZI
FZJ
FZJ
= 5.50
= 2.86
=1.91
= 0.92f----+--~,---t----:::;;;>""""'--i
= 0.43
= 0.22
+-----+---,t'-'-----7'!"'-=-~,..e_--+--::7"""--l
10 +---+--,~r---hoI17-!_-__::7i"'='----~
:g
a.
0.1
0.01
0.001
0.1
0.2
0.3
0.4
Porosity, fraction
Fig. 24.
Fig. 25.
219
Vc!
,.
1000.00
.-j.
:~:~l
_....... -
1--
I;~
10.00
..
-o
k-prwdicled. md
Z
....,
(een)
..,
a.
II
0.10
0.10
0.01
k.~.
Fig. 26.
1000.00
100.00
10.00
1.00
C
Z
trJ
en -
>
0.1
(core permeability)
10
100
Fig. 27.
Z 0
1000
I\)
I\)
trJ
- 0-<
....,
0.01
---
~ en
trJ
"-.-/
0.1
trJ
fJ
fffffittbV7
>
Z
C ::c:
l" >
-n Z
n
E
-0
17
::r::
10
......
0\
trJ
c:
"..
1.00
HYDRAULIC UNITS
HU 1_ Best Quolity
HU 7-Wo.....t Quality
IJ
PR06ABJUTY
c:
"
J:
."
INDEX
"tl
:::)
SAMPLE WEll.
Sw
E5E~~D OUAUTYI
O.D~(prwdletlld)IO
!
.,;
FlRST PASS
l!OI(dolonn"'...'
0.01
10
VI.
PREOiClUJ
PERUEABILlTY, rnd
;j
.17
10
'5
Phi
"il
.1. 17
Phi (_irK-)
rill
100.00
Phi(".utrnn)6Q
Ii(
Ptll(lutul}
14010
~-t~
--'-''''.''->-
--f-H++HH----
:2:
:5
CR
POROSITY
"i:l
trJ
en
-n otrJ
"i:l
....,
...., 0
"i:l ~
~ C
COMPARISON
~ ~
trJ
> a
~ n
l" 0
~ trJ
-Z >
Z
C 0
Z l"
o a
otrJ >
..,
Z
...., >
....,
trJ
-<
>
100
l'
en en
100
200
300
400
500
k.oodla~)
Fig. 28.
Fig. 29.
- - similarity line
;g
en
VJ
0\
l'
l'