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BASIC LOGS UNLOCK COMPLEX CARBONATE PORE PROPERTIES
Stefan Calvert,BG Group PLCand Gene Ballay,Independent Consultant
Copyright 2011, held jointly by the Society of Petrophysicists and Well Log
Analysts (SPWLA) and the submitting authors.
This paper was prepared for presentation at the SPWLA 52 ndAnnual LoggingSymposium held in Colorado Springs, Colorado, United States, May 14-19,
2011.
ABSTRACT
Many carbonate fields exhibit a high degree of
heterogeneity and structural complexity leading to
challenges in understanding the production performance.
In many cases only triple combo data is available due to
cost and/or operational considerations.
It is generally recognised that an understanding of the
complex micritic pore structure properties of carbonates
is essential to the development of an understanding of
formation properties that impact on production; such as
the effective (flowing) porosity, water saturation either
from resistivity logs and/or saturation height functions,
permeability, relative permeability, wettability and
recovery factors.
Carbonate rock typing from logging data is generally
considered to lie within the realms of NMR and image
log analysis that is calibrated to core data. The
characterisation of the different porosity types present in
carbonates are driven by pore size variation (micro,
meso and macro) which have wide variations in poro-
perm characteristics for samples with the same total
porosity. Similarly, the complex and heterogeneous pore
structures can result in associated problems quantifying
hydrocarbon saturations due to non-Archie resistivity
water saturation relationships.
The application of the Thomeer technique has provided
insights and better production estimates. Integration of
core derived Thomeer parameters with basic logs has
delivered a robust and readily implementable reservoir
property framework. The density-neutron logs canprovide a direct measure of threshold entry pressure thus
allowing simple and reliable rock typing using the basic
logging suite. The resultant rock typing significantly
improved the formation evaluation description for the
full field reservoir modelling.
INTRODUCTION
In many cases the data available to examine field
heterogeneity is limited to only triple combo data due to
cost and/or operational considerations. Core data
therefore is especially valuable to investigate the
possible explanations.
An understanding of the complex micritic pore structureproperties of carbonates was found to be key to the
describing the formation properties that impacted on
production. The study field undertook a petrophysical
re-evaluation based on several factors:
Discrepancies between the fluid distributions based
on the reservoir model predictions and production
volumes implying that the in place volumes and
production characteristics were not understood.
Realisation that textural variations and fractures
within the carbonate formations were prolific and
should be captured in the petrophysical model.
Poor agreement between log and core data.
Geology
The study field consist of three main units: Alternates,
that rapidly alternate from limestone to shale. The A
zone, a tight limestone and shale unit forms ephemeral
local seals for the B zone. The B zone is 50m thick with
excellent continuity and quality. The top 10-15m of B
unit contains the best reservoir rock. The A zone is
~50m thick and comprises 10m zone of tight limestone
with thin marl/shale beds, overlain by moderate quality
limestone reservoir. The tight zone acts as a local
baffle between the gas cap primarily in A zone, and the
oil column which largely resides in the B zone.
The oil column is approximately 20m thick (xx37-
xx57m TVDSS) with a gas cap and a 40-60m water leg.
The gas column is typically 50m thick, but locally
exceeds 130m. The free water level is at xx62m
TVDSS.
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THOMEER MODEL
Thomeer (1960) introduced a pore geometrical factor to
assist the description of saturation-height as defined by
capillary pressure curves. The premise being that
reservoir quality is driven by rock fabric and thereforesaturation-height function must reflect the rock fabric.
Thomeers method (1960) is based on fitting hyperbola
to the logarithm of capillary pressure (Pc) and bulk
volume occupied (BV = !T* Sw, !T= total porosity andSw= water saturation):
[log(BV/BV")] * [log(Pc/Pd)] = log(e-G)
(BV/BV") = e-G*[log(Pc/Pd)]
where Pd is the threshold capillary pressure, BV" is the
bulk volume at infinite pressure (close to !T) and G is
the Thomeer pore geometrical factor.
The advantages of Thomeers formulation are:
Independent from permeability, K
Can be superimposed for multiple pore volumes
Texturally representative
Facies are separable
Permeability, K and irreducible water saturation,
Swircan be predicted as follows
Swir= [eG*log(Pd_macro)
] / !T
where Pd_macro is the threshold capillary pressure of themacro pores. Permeability, K can be calculated using the
Thomeer (1983) or Clerke (2008) methods respectively:
KThomeer= 3.8068 * (BV"_macro/Pd_macro)2* G-1.3334
KEd_Clerke= 10(a + b * log(214/P
d_macro) + c *
!
T)
where a, b and c are the appropriate fitting constants.
Micritic Carbonates
Micritic carbonates typically consist of two or three
separable pore volumes related to the pore size; micro
(5!m). The
Thomeer model is most effective when hyperbolae are
superimposed therefore each pore size can be fitted and
summed to describe the whole pore system:
BVT= BVmacro+ BVmeso+ BVmicroBVi= 10^{-Gi*(log(BV"_i)+[log(Pc)-log(Pd_i)]}
where i is micro, meso and macro respectively.
POROSITY AND SHALE VOLUME
The density-neutron crossplot was used to compute
shale volume, Vsh, assuming linear response equations:
( )( )
( )( )
( )( )
( )( )!
!"
#
$$%
&
'
''
'
'
!!"
#
$$%
&'
'''
'
=
LimeWater
LimeKao
LimeNWaterN
LimeNKaoN
LimeWater
Lime
LimeNWaterN
LimeNN
shV
((
((
))
))
((
((
))
))
__
__
__
_
where !N= neutron porosity, !N_Lime= limestone neutron
porosity, !N_Water = water neutron porosity, !N_Kao =
kaolinite neutron porosity, " = bulk density, "Lime =
limestone bulk density, "Water= water bulk density, "kao
= kaolinite bulk density. Note that XRD data shows the
shale is almost entirely kaolintie in the form of dickite.The fluid parameters were fixed to that of the formation
water ("water=!N_water=1) that provided an excellent match
with XRD data even within the hydrocarbon intervals
and provided a stable solution within the inversion.
The volumes of limestone, Vlime, dolomite, Vdolo, and,
effective porosity, !e were calculated using a material
balance matrix inversion method:
!!!
"
#
$$$
%
&
'
('
('
=
!!!
"
#
$$$
%
&
(((
(((
sh
kaoNshN
kaosh
doloee
doloNdoloeNeflNe
dolodoloeefle
V
V
V
VV
VV
VV
1
_
lim
_lim_lim_
limlim
))
**
)
))))
***)
( )( )
( )( ) !
!"
#
$$%
&
'
'+
'
'(=
waterNkaoN
claydryNkaoN
waterkao
claydrykao
Sh
__
____2
3
1
))
))
**
**)
ShSheT V !!! "+=
where limestone, dolomite, kaolinite and dry clay
density are "lime, "dolo, "kao and "dry_clay respectively
likewise limestone, dolomite, clay and dry clay neutron
porosity are !N_lime, !N_dolo, !N_kao and !N_dry_clay
respectively. Hydrocarbon density, "hc was chosen
appropriately for the oil and gas legs then solved
iteratively for the unknowns. Grain density, "matrix was
calculated by:
( ) ( ) ( )( )
She
hcxoWaterxoekaoSh
Matrix
V
SSV
!!
"!+""!"!
=
#
$$#$$$
1
1
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where Sxo is calculated using the Archie equation
assuming Rmf=Rw,
n
mTxo
mf
xo
R
aRS
1
!
!
"
#
$
$
%
&=
'
where a = 1, m = 2, n = 2. The effective porosity, !e
calculated here is not used in anyway apart from to
calculate total porosity, !T. Effective porosity was
calculated from the rock typing and capillary pressure
model detailed below.
WATER SATURATION
Formation and flushed zone water saturations were
calculated using the dual porosity method, Petricola andWatfa (1995). Rw, m and n values were based on Rw
analysis and SCAL results from two wells.
Effective and total formation and invaded water
saturations were calculated using equation 3, Petricola
and Watfa (1995):
( )
( ) ( )
( )micro
micro
micro
macro
micro
marcom
macro
mircom
micro
T
w
n
w
R
R
S
!
!!
!
!
!
+
+
+
+
"##$
%&&'
(
=
1
)(
1
)(1
1
1
)T
microwe
wT
SS
!
!! +"=
where m(micro) and m(macro) were taken to be the
minimum and maximum measured Archie m values
respectively.
IRREDUCIBLE WATER SATURATION AND
RESIDUAL OIL SATURATION
Irreducible water saturation, Swir, and residual oilsaturation, Sor, were fitted to total porosity derived from
SCAL data.
Swir=1*e-a
!
T
Sor=1*e-b
!
T
Maximum recoverable oil = (1- Swir- Sor)
where a and b are the appropriate fitting constants.
CAPILLARY PRESSURE AND ROCK TYPING
The hyperbolae for each plug of nearly 90 plugs were
plotted on the bulk volume occupied against capillary
pressure plot (Figure 1). A histogram of the threshold
entry pressures for the macro pores, Pd_macro, (Figure 2)provided the classification of the rock types (Table 1).
It is interesting to know that at the basic level, the Lucia
(1995) classes are also based upon variations in
displacement pressure, which Lucia then relates to
crystal size (and poro-perm crossplot position). Thomeer
(1983), however, has the enhanced capability of being
able to simultaneously address multiple pore systems.
Gaussian fits to each of the rock types enabled P10, P50
and P90 estimates to be developed (Figure 1). The
average and standard deviation of Pd, BV", G parameters
for each pore space were analysed to produce the BVP10, P50, P90 data fits.
Rock TypeCapillary Pressure
Range (psia)
0 275
Table 1.Rock typing pressure classes
An observation was made that the P10-90 range of eachPd, BV", G parameter was ~0.5 times the parameter
average. This was utilised to generate the P10 and P90
from the P50 parameters.
The Pd, BV", G fitting parameters were analysed to
develop relationships that allowed the prediction of the
parameters from known/measured inputs !Tand Pd_macro
were taken forward (Figure 3).
(macro and micro) Pd= a * !T-b
(meso) Pd= a * Pd_macro-b
(macro) BV#= c * Pd_macrod(meso and micro) BV#_i= c * !T
d
G_i= e
where i is micro, meso and macro respectively and a to e
are the appropriate fitting constants.
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P10 parameters were calculated as = 1.5 * parameter and
P90 parameters were calculated as = 0.5 * parameter.
Effective porosity, !e is defined as the macro pore space
as this is the only pore space considered to contribute to
flow in this reservoir.
!e= (BV#_macro/BVT) * !T
SATURATION HEIGHT IMPLEMENTATION
Implementation of the saturation height model required
linking Pd_macroto log data allowing log based rock types
calibrated to the capillary pressure data thus allowing
delivering textural representative K, !eand Swestimates.
Most log datasets contained only LWD gamma ray,
resistivity, density and neutron logs. Advanced logswere restricted to a small number of vertical wells.
Density-neutron log separation was been observed to
indicate rock quality irrespective of pore fluid thus
establishing a relationship between density-neutron
porosity separation and Pd_macro(Figure 4):
!density= (2.71 - "b) / 1.71
!dif= !density- !neutron
Pd_macro= a*10-b.
!dif
where a and b are the appropriate fitting constants. Thevariations in mineralogy (calcite dolomite, kaolinite)
were linked to the rock quality variations. High kaolinite
and/or dolomite found in the poorer facies but due to the
close values of the photoelectric factor for example both
~3B/e, a photoelectric factor method was unsuitable for
implementation.
In combination with !T from density-neutron logs and
height above free water level the capillary pressure, Sw
(BV/!T), !e, Swirand K could be calculated.
Wireline implementation and comparison with SCAL
data was performed on a number of wells with therelevant core data sets (Figure 5). Note the log based
rock typing (curves) are most well fitted to SCAL data
(stars) and that the log based rock typing is never more
that one rock type incorrect.
Permeability
The relationship between !T and K is compared with
Pd_macro and permeability, K. Note that the stronger
correlation is between Pd_macro and K (Figure 6). An
improved relationship is established by combining !Tand Pd_macro(green) compared with Pd_macroalone (black)
to predict K (Figure 7). P10 and P90 estimates were also
given (Table 2).
KClerke= 10[d + e * log(Pd_macro) + f * log(
!T)]
Parameter P10 P50 P90
d 0 -0.6 -1.2
e -0.59 -0.59 -0.59
f 7.3 7.3 7.3
Table 2.Permeability fitting parameters
Lucia (1995) also notes the strong correlation between
Pd_macro and K specifically that pore throat size, the
largest of which is reflected in the displacement
pressure, is more important than is the porosity. The
Thomeer analyses approach presented here is an
improvement on the usual Lucia model in that it
recognizes simultaneous multiple pore size modes.
Absolute fluid permeabilities were measured as part of
the relative permeability tests at residual oil saturation
and irreducible water saturation. Crossplotting fluid
permeabilities with core Klinikenberg permeability
demonstrated that only simple power trends wererequired (Figure 8). Note that the magnitude of the
Klinkenberg correction is smaller, as permeability
becomes larger.
Relative Permeability
The objective of relative permeability analysis is to
describe the fractional flow of the fluids produced at any
given water saturation observed. In combination with
the rock typing it was possible to estimate fluid fractions
based on fitted parameters by extending Clerkes (2007)
fitting method for oil curves in a water/oil system to all
fluids in the three phase system present in this case.
In addition the concave relative permeability
behaviour observed could be fitted and is due to the
micritic nature of the rock. Fitting concave curves was
possible using exponents
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By normalising water/oil saturation between the residual
oil/trapped gas to irreducible water/residual oil, fitting
parameters were obtain for each of the sample-fluid pair
curves and fractional flow curves (Figure 9). These
fitting parameters were analysed to obtain predictive
trends with absolute permeability (Figure 10).
Permeability thickness and fractional flow could be
derived to assist with production volume and rates
estimates.
Oil/Gas
( )( )( )
( ) ( )[ ]
( ) ( )[ ]gasoilgasoilgasoil
gasoil
Sdoilgas
b
gggasoil
orgt
orwgg
KrKrFF
cecKr
SaKr
SS
SSS
gg
!!+=
"!+=
!=
""
""
=
!
__
_
_
_
1
1
1
1
1
Water/Oil
( )( )
( ) ( )[ ]
( ) ( )[ ]oilwateroilwateroilwater
oilwater
Shwateroil
f
soilwater
orwir
wirws
KrKrFF
gegKr
SeKr
SS
SSS
s
!!+=
"!+=
!=
""
"
=
!
__
_
_
_
1
1
1
1
where SSand Sggare the normalised saturation, Sgtis the
trapped gas saturation, Kris the relative permeability to
the respective fluids, FF is the fractional flow to the
respective fluids and ! are the respective fluid
viscosities and, a to h are the appropriate fitting
functions of the form:
a=x*Ky
a = x*log(K)+y
CONCLUSIONS
The use of an appropriate capillary pressure model
enabled the petrophysical characterisation of a micritic
carbonate field. It was observed that the difference in
density and neutron porosity values was related tothreshold entry pressure of the macro pore system. In
combination it was possibly to extend the water
saturation and permeability calculations to all wells with
triple combo logs in the field.
The Thomeer analyses approach presented here is an
improvement on the usual Lucia model in that it
recognizes simultaneous multiple pore size modes. The
approach also extends Clerkes methods.
The revised approach assisted the understanding of the
hydrocarbon distribution within the field and thus well
planning and recoverable volumes. As a consequence of
the improved description of the matrix behaviour, there
was recognition of the significance of fracture flow to
production.
Production and well test permeability values were an
order of magnitude greater than the maximum
permeability values calculated from the matrix. Fracture
mapping and image analysis was therefore required and
gave rise to the re-processing of the seismic volume for
fracture attributes and an integrated study of fracture
from core and image logs.
ACKNOWLEDGMENTS
The authors wish to thank BG Group for permission to
publish this work. Dr. Tim Pritchard, Head of
Petrophysics (BG Group) is gratefully acknowledged for
reviewing the text and discussing the results.
REFERENCES
Ballay, G., 2008, Monte Carlo modelling with Excel,
GeoNeurale. (Gene.Ballay@gmail.com)
Bateman, R.M., and Konen, C.E., 1977, "The Log Analystand the Programmable Pocket Calculator, Part II -
Crossplot Porosity and Water Saturation", The Log
Analyst, November-December 1977.
Batzel, M., and Wang, Z., 1992, Seismic properties of pore
fluids, Geophysics., 57, 1396-1408.
Clerke, E.A., Mueller III, H.W., Phillips, E.C.,
Eyvazzadeh, R.Y., Jones, D.H., Ramamoorthy, R., and
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Srivastava, A., 2008, Application of Thomeer Hyperbolas
to decode the pore systems, facies and reservoir properties
of the Upper Jurassic Arab D Limestone, Ghawar field,
Saudi Arabia: A Rosetta Stone approach, GeoArabia,
Vol. 13, No. 4, p.113-160
Clerke, E.A., 2007, Permeability and microscopic
displacement efficiency of M_1 Bimodal pore systems in
Arab-D Limestone, SPE 105259
Crain, E.R., 1986, "The Log Analysis Handbook, Volume
1: Quantitative Log Analysis Methods", PennWell, ISBN
0-87814-298-3 (v.1).
Kewen, L. and Horne, R.N., 2002, Experimental
verification of methods to calculate relative permeability
using capillary pressure data, SPE 76757
Lucia, F.J., 1995, Rock-fabric/petrophysical classification
of carbonate pore space for reservoir characterization,
AAPG Buletin no.79 v.9, pp1275-1300.
Petricola, M.J.C., and, Wafta, M., 1995, Effect of micro
porosity in carbonates: Introduction of a versatile saturation
equation, SPE 29841
Schlumberger Chartbook, 2009, Schlumberger.
Thomeer, J.H.M., 1983, Air permeability as a function of
three pore-network parameters, Journal of Petroleum
Technology, April, p. 809-814.
Thomeer, J.H.M., 1960, Introduction of a pore
geometrical factor defined by a capillary pressure curve,
Petroleum Transactions, AIME, v. 219, T.N. 2057, p. 354-
358.
ABOUT THE AUTHORS
Stefan Calvert is a Principal Petrophysicist currently
working in Brisbane and for the last seven years withBG Group Plc. Prior to BG he spent four years working
as a Research Petrophysicist for Reeves Wireline
Technologies Ltd (now Weatherford). His interests
include unconventional reservoirs, horizontal well log
interpretation, induction logging, cased hole nuclear
logging, carbonates and thin bed evaluation. Stefanholds a BSc in Physics, an MSc in Geophysics and a
PhD in Petrophysics from UK universities. He has also
published papers with the SPWLA, SPE and EAGE.
Stefan is current President of the FESQ and member of
SPWLA, SPE, IOP and PESGB. Stefan jointly holds a
patent for cased hole density log hydrocarbonevaluation. Outside of work Stefan enjoys swimming,
scuba diving, hiking, snowboarding and travelling.
Gene Ballay served in the U.S. Army as a microwave
repairman and in the U.S. Navy as an electronics
technician, and he is a USPA parachutist and a PADI
dive master. He holds a PhD in theoretical physics with
double minors in electrical engineering/mathematics,
has taught physics in two universities and heldpetrophysical engineering assignments in Houston,
Texas; Anchorage, Alaska; Dallas, Texas; Jakarta,
Indonesia; Bakersfield, California; and Dhahran, Saudi
Arabia.
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Figure 1. Bulk volume occupied against capillary pressure.
Figure 2. Pore throat radius distribution.
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Figure 3. The Pd, BV", G fitting parameters relationships with known inputs !Tand Pd_macro.
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Figure 4. Core threshold entry pressure to wireline density neutron porosity difference calibration crossplot.
Capillary pressure data was available for four wells each represented in a different colour.
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Figure 5. Example log with wireline predicted threshold entry pressure (blue curve) and rock type (magenta curve)
compared to core threshold entry pressure (blue star) and rock type (magenta star).
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Figure 6. Core total porosity (green) and core threshold entry pressure (blue) crossplot with core permeability.
Figure 7. Permeability prediction comparing Clerke (2007) {green} and Thomeer (1983) {black} methods.
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Figure 8.Crossplot of fluid permeabilities with core Klinikenberg permeability.
Figure 9.Fitting parameters to fractional flow curves, gas-oil example. Note that one sample has a concave shape.
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Figure 10.Relative permeability fitting parameters predictive trends with absolute permeability.