steve cuddy edinburgh pore geometry 2008
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SPWLA 49th
Annual Logging Symposium, May 25-28, 2008
1
THE EFFECT OF PORE GEOMETRY
ON THE DISTRIBUTION OF RESERVOIR FLUIDS IN
U.K. NORTH SEA OIL AND GAS FIELDS
Dean Gagnon1 , Steve Cuddy
2 , Fabrizio Conti
2 , Craig Lindsay
2
1
Nexen Petroleum UK Ltd.,
2
Helix RDS
Copyright 2008, held jointly by the Society of Petrophysicists andWell Log Analysts (SPWLA) and the submitting authors.
This paper was prepared for presentation at the SPWLA 49 th
Annual Logging Symposium held in Edinburgh, Scotland, May 25-28, 2008.
ABSTRACT
The accurate determination of hydrocarbons initially
in place requires a thorough understanding of how
water saturation (Sw) varies as a function of heightabove the free water level (FWL). Nowhere is this
more important than in the transition zone.
Electrical logs, core data and thin sections fromfifteen North Sea fields were compared to understand
how reservoir parameters determine the shape of the
transition zone. These included pore geometry as
well as the rock quality and reservoir fluid parameters
contained in the Leverett J-Function.
The water saturation vs. height (SwH) function
selected for this research is the so-called FOILFunction, that relates the bulk volume of water to
height using only two constants ‘a’ and ‘b’ in the
form BVW=aH b
. Comparison of the Leverett J-Function with the FOIL Function showed that all thereservoir parameters relating to rock quality and
reservoir fluids are found within the ‘a’ constant of
the FOIL Function. Although the fields studied
ranged from multi-Darcy gas fields to milli-Darcy oilfields, the ‘b’ constant is surprisingly invariable: with
the shape of the transition zone described by the SwH
Function being controlled almost entirely by thesingle constant ‘a’.
The constant ‘a’ is found to be predominantly
dependent on reservoir pore geometry. Thin section
analysis showed that the fields with a low ‘a’ valuehave well connected evenly spaced pores, lack pore
throat bridging, blocking and grain coating clays and
have simple pore pathways. This explains how the
water saturation is a function of connectivity as wellas porosity and height above the FWL. Analysis
confirmed that the pore geometry rather than porosityand permeability determine the shape of the transition
zone.
A new pore geometry (PG) index is proposed that is
correlated to the FOIL ‘a’ constant. This index can be
used to make predictions about the quality of poregeometry within a reservoir and the shape of the SwH
function. This PG index is successful in explaining
how fields with very different porosity and
permeability can have very similar SwH functionsand why poorer quality reservoir intervals do not
necessarily have higher water saturations. The revised
SwH function provides a robust method for picking
the FWL even in fields where the actual fluid contact
is unclear or was not penetrated.
The new index better describes pore geometry and
allows the hydrocarbon distributions to be understoodand represented more accurately in the 3D reservoir
model.
INTRODUCTION
Background
Accurate determination of hydrocarbons initially in place requires a saturation vs. height (SwH) function
to describe how water saturation varies with height
above the free water level (FWL).
Water saturation (Sw) determined from interpretation
of log data can only represent the reservoir within a
few feet surrounding the well bore. Sw cannot bemapped as it depends on numerous factors including
porosity and the height above the local FWL.
SwH functions are used in a field’s reservoir model to
estimate Sw away from well locations so thathydrocarbons initially in place can be calculated. The
error in reserves resulting from an equation that
poorly describes the reservoir can be significant.
This study uses the FOIL1 SwH function to compare
reservoirs of different North Sea fields. The FOIL
Function is an algorithm which is commonly used todetermine water saturations in North Sea reservoirs
(Cuddy 1993). It was developed using log data from
the Southern North Sea and has since found wider
1 The term FOIL refers to free oil (or gas) above the
FWL. Free water exists below the FWL.
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SPWLA 49th
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2
application throughout the United Kingdom
Continental Shelf (UKCS). The function has a simple
form and is largely independent of porosity and
permeability. It calculates the Bulk Volume of Water
(BVW) as a function of height (H) above the FWL.Alternatively, it can be used to calculate BVW as a
function of Capillary Pressure (Pc). BVW is the
product of water saturation and porosity. The FOILFunction is derived from the Leverett J-Function and
has the form:
b
w aH S BVW =Φ= Equation 1
where:BVW = bulk volume of water (v/v)
Ø = porosity (v/v)
Sw = water saturation (v/v)H = height above the free water level (ft)
a = constant (dimensionless)
b = constant (dimensionless, negative value)
The function describes how BVW varies as a function
of height above the FWL. The function tells us that at
a particular depth in the net reservoir BVW is fixed
with hydrocarbon filling the remaining pore space.
Once the function has been derived water saturation
can be calculated re-arranging equation 1:
Φ=
b
w
aH S Equation 2
The main strengths of the FOIL Function are that it
does not require permeability and is mostly
independent of lithology. However, if a reservoir
interval contains different geological units or litho-facies with distinct and coherent porosity–
permeability relationships, then separate FOIL
Functions should be constructed to provide a morerobust description of the reservoir (Amabeoku et al.
2005). The predictions the function makes with
regard to pore and pore throat geometry were
investigated through thin section observations.
The FWL is the datum from which the FOIL Function
bases its calculations as it represents the depth where
the capillary pressure is zero. In the absence ofdrilling fluids it is the depth where water andhydrocarbon would vertically separate in a large
borehole. In water-wet reservoirs the FWL is below
the lowest occurrence of hydrocarbons. The FWL isthe depth predicted by the interception of the
formation fluid pressure gradients.
The aim of SwH functions is to estimate the water
content throughout the reservoir as accurately as
possible. The advantage of the FOIL Function is that
it contains the BVW term which is especially
appropriate to 3D modelling (Worthington 2002)
Study Objectives
This study had five main objectives:
• Relate pore and pore throat geometry as seen in
thin sections to FOIL Functions from log data.
• Gain an understanding of how and why the FOILFunction works by carrying out FOIL analysis on
fields with differing depositional environments
and hydrocarbon composition.
• Derive the FOIL Function from the Leverett J-
Function and capillary pressure versus height
relationship in order to determine which rock andfluid parameters are contained within the
function’s constants.
• Validate the method by analysis of core capillary
pressure, porosity and permeability data.
• Determine the sensitivity of the FOIL Functionconstant ‘a’ to variations in the rock and fluid
parameters that compose it.
Data Available
Data from fifteen UK North Sea fields (250 wells)
were used in this study. Electrical logs and
conventional core (porosity and permeability) data
were available from eleven fields. Thin section and
capillary pressure data were respectively availablefrom three and two of these fields. Capillary pressure
and conventional core data were also available fromfour additional fields.
The fields with log data used in the study are listed in
Table 1. They were selected as they represent a range
of reservoir fluids, depositional environments and porosity vs. permeability (poroperm).
The poroperm distribution for the eleven fields withlog and core data is shown in Figure 1: where average
permeability increases with average porosity as
expected. Average permeability spans fourlogarithmic cycles: from 0.1 mD to 2 D (Darcy).
Porosities range from 8 to 32 Porosity Units (PU).
THIN SECTION ANALYSIS
Thin sections from three of the study fields (Fields E,
F, and K) were described with emphasis placed on the
geometry of pores and pore throats. The descriptions
were quantified where possible in order to facilitate
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SPWLA 49th
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3
the comparison between samples. This quantification
was based on visual observation and estimation of
relative percentages.
The limitations of describing a 3-dimensional poresystem from 2-dimensional thin-sections are well
documented. For the purposes of this study,
comparative evaluation of thin sections from differentreservoirs provided fit for purpose quantification of
pore network properties.
Fields E, F, K have similar porosity but substantially
different permeability as seen in Figure 1. This can be
explained by differences in pore throat attributes.
Pore throat attributes include pore throat shape,
radius, pore coordination number (number of outlets per pore), general connectivity (defined as the
arithmetic mean of the pore coordination number for
the entire measured volume) and quantity/type ofthroat blocking (flow impeding) minerals. Generally,
if samples have the same porosity, any differences in permeability can be explained by differences in
connectivity and amount of flow impeding materialwithin the connecting pore pathways.
Fields E and F have very similar pore and pore throat
attributes. Figure 2 (Field E) and Figure 3 (Field F)
display complex pore shapes which are evenlydistributed, have a smooth pore wall texture and lack
pore lining materials, though minor amounts of quartz
overgrowths, pyrite crystals and grain coating claysdo occur. Most often the pore throat radii are only
moderately smaller than the adjoining pore’s
maximum dimension and the majority of pores areconnected via short non–tortuous pore pathwayswhich have a curved geometry. Overall the
connectivity between pores is excellent and most
pores have an average coordination number of 4.
Field K shown in Figure 4 has a much different pore
and pore throat character. Pore shapes are distributed
between complex and simple geometric shapes. Porewalls have a rough texture and are lined with detrital
grain coating clays. Pore lining, bridging, and filling
authigenic clays (platy chlorite and illite, wispy illite)
are common. Most pores are found in isolated groups
with good internal connectivity but very poor inter– group connectivity. Internal connectivity is
characterized by short curved pathways with three to
four outlets per pore, where as inter–group
connectivity is via long narrow tortuous pathways.
These observations suggest that good reservoirs arecharacterised by well connected evenly spaced pores,
minor throat obstructing material and simple pore
throat pathways. Conversely, low quality reservoirs
are characterised by isolated groups of pores
connected via long tortuous pathways that contain an
abundance of pore throat obstructing material.
FOIL FUNCTION METHODOLOGY
A FOIL Function can be determined for a well or
entire field from either log or core data. This sectiondescribes the steps involved in constructing a FOIL
Function for a field using log data. FOIL Functions
were determined from electrical logs for eleven fieldslocated throughout the UK North Sea. The fields
included both gas and oil accumulations in different
types of clastic reservoirs from different depositional
environments. The broad spectra of fields were
chosen in order to assess the robustness of thefunction. Table 1 lists the fields, their fluid type and
depositional environment.
The BVW for each well was calculated as the product
of the water saturation and porosity curves. This was plotted against the height above the FWL. Only data
away from conductive bed boundaries were includedin order to minimise the effect of shoulder bed effects
on the resistivity logs.
The FOIL Functions were calculated by plotting the
logarithm (base 10) of BVW (x-axis) against thelogarithm of the true vertical height (y-axis) above the
FWL. Then a free linear regression was used to
compute the FOIL Function parameters. This processworks because the form of the FOIL Function can
also be stated as:
a H b BVW 101010 logloglog += Equation 3
which is the form of the straight-line equation y = mx
+ c, where parameter ‘b’ (m) has a negative value.
Since the FOIL Function can be written in the form of
a straight line the ‘a’ value is the y-intercept and the
‘b’ value is the slope of the line. The FOIL Functions
calculated for the study fields are shown in Figure 5.
The FOIL ‘a’ and ‘b’ parameters were calculated
from logs for the eleven study fields as listed in Table
1. A log-log plot of BVW against height above theFWL is shown in Figure 6.
It is noticeable that all the fields share a similar ‘b’
parameter (slope) and the main difference between
the SwH Functions is due the variation of ‘a’
(intercept) between the fields.
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4
FOIL FUNCTION ANALYSIS
The FOIL Function can be derived from the Leverett
J-Function and capillary pressure versus height
relationship as described by Cuddy (1993).
ΦΦ−
= *)(
cos β
ρ ρ ϑ ασ
K H g BVW
hw
Equation 4
Re-arranging this into the form of the FOIL Function
(Equation 1) gives:
β β
ρ ρ
ϑ ασ 1
1
)(
cos −
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ Φ
−Φ= H
K g BVW
hw
Eq. 5
Comparison with Equation 1 gives constants ‘a’ and‘b’ of the FOIL Function:
( )( )
β
ρ ρ
ϑ ασ
1
cos⎟⎟ ⎠
⎞⎜⎜⎝
⎛ Φ
−Φ=
K ga
hw
Equation 6
β
1−=b Equation 7
where:σ = interfacial tension (dyne/cm)
K = permeability (cm2)
Ø = porosity (fraction)
ϑ = contact angle (degrees)
g = acceleration of gravity (m/sec2)ρw = density of the water phase (g/cm3)ρg = density of the hydrocarbon phase (g/cm3)α = dimensionless constantβ = dimensionless constant
It is noticeable that all parameters associated withrock quality and reservoir fluids are contained in
parameter ‘a’. This is consistent with the empirical
observation from Figure 6.
In order to compare the FOIL Functions between
fields they were recomputed using a common ‘b’value (slope). This was done by calculating the
average ‘b’ value for the fields and using this to re-compute a forced regression ‘a’ value for each field
as listed in Table 1. The average ‘b’ value used was -
0.41. The ‘a’ value for each field calculated from the
average ‘b’ value is herein referred to as the forced’a’ value.
The ‘b’ of the FOIL Function is invariant to scale as it
is a dimensionless unit of measurement which is
consistent with the Leverett J-Function which itself is
dimensionless. Consequently, the same ‘b’ value is
calculated: regardless of whether the scale of the y-axis represents height (H) above the FWL in feet or
metres, or it represents capillary pressure (Pc).
Sensitivity analysis of Equation 5 confirmed that
BVW is largely independent of porosity and
permeability for the typical porosity range seen in theeleven fields of Table 1. Equation 5 was shown to be
dependent on the reservoir parameters such as
hydrocarbon and water densities. However these
parameters vary little in a given field.
RESERVOIR QUALITY
We define the ‘quality’ of a reservoir by its value ofwater saturation at a certain height above FWL and
given porosity: with lower Sw being considered betterquality reservoir. The computed water saturation
derived from the FOIL Function at 200’ above theFWL and assuming a porosity of 20 PU is listed for
each field in Table 1.
The quality of a reservoir can be defined by the value
of its forced ‘a’ parameter. Figure 7 shows reservoirquality increasing towards the top-right corner of the
cross-plot. Water saturations vary from 6 Saturation
Units (SU) in high quality reservoirs (Field G) to 36SU in low quality reservoirs (Field I). Notice that the
FOIL parameter ‘a’ varies much more between these
fields compared to the FOIL parameter ‘b’.
THE PORE GEOMETRY INDEX
We define the Pore Geometry (PG) Index as
Φ
−=
log
7log _
K IndexPG Equation 8
The PG Index is similar to (K/Ø)0.5 which Leverett
proposed in 1941 with the dimension of mean pore
radius. The Leverett J-Function represents a sand pack as a bundle of capillary tubes with different pore
radii. Just as core plugs are a bundle of capillary tubes
with an average pore radius, hydrocarbon reservoirs
consist of a number of facies with different porosity-
permeability characteristics. So long as these faciesare in communication, over geological time, the
whole reservoir can be considered as having a mean
pore radius.
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The constant ‘7’ was found to give the best
correlation coefficient between the values of PG
index and FOIL ‘a’ parameters from regression of log
and core data: respectively figures 8 and 11. This
constant is also a convenient scaling factor.
When the PG Index is a constant for a particular field,
Equation 4 shows that BVW is constant at givenvalue of height (H) above FWL. Therefore, any
formation with a similar PG Index will have
comparable BVW values for a given H and hencesimilar pore throat geometry. The PG Index is plotted
against the forced FOIL parameter ‘a’ in Figure 8.
Using PG to Understand Reservoir Quality
Figure 1 shows that Fields D and G have high
average porosity and permeability with Field D
having significantly better properties. Surprisingly,the computed water saturations are twice in Field D
compared to Field G, for the same height above theFWL and porosity. This can be explained by the
better (lower) values of PG Index and forced FOIL‘a’ parameter for Field G.
The PG Index can also be used to explain the
apparent inconsistency seen in Field L. Two zones
that are thought not to be in communication have the porosity and permeability values shown in Table 2.
Zone 1 has much higher permeability and porositycompared to Zone 2. However, Zone 2 has lower
water saturations. This is explained by the PG Index
being better (lower) in this zone.
Using PG to Predict Reservoir Permeability
Using the average ‘b’ value (-0.41), the forced ‘a’
parameter can be determined by FOIL analysis ofelectrical logs. The forced ‘a’ parameter can provide
an estimate of the PG Index which in turn is related to
the average field permeability by using Equation 8.
Therefore, the PG Index allows the prediction of
reservoir mean permeability from electrical logs that
measure only porosity and water saturation.
Formation pressures and core are not required for thisgross field permeability estimate.
Picking the FWL using the FOIL Function
The FWL can be determined from logs by plotting
BVW vs. true vertical depth sub sea (TVDSS) in log-log space and solving for the parameter ‘a’ and the
depth of the FWL. Only net data away from
conductive bed boundaries should be included.
Although the parameter ’b’ is not strictly a constant it
can be assumed to be -0.41 for this purpose. Solving
for two unknowns ‘a’ and FWL is more precise
compared to ‘a’, ‘b’ and FWL.
As the FOIL ‘a’ parameter represents the intercept of
the FOIL function with the y-axis, the FWL can be
determined from this intersect when the y-axis has theunits of TVDSS.
CORE ANALYSIS
The findings on the relationship between Bulk
Volume of Water (BVW) and Pore Geometry Index
(PG) derived from log data were validated by means
of core data. The database available included core porosity, permeability and capillary pressure (Pc)
measurements.
The study was focussed on 102 core plugs from six
reservoirs in the North Sea region. These represent avariety of depositional environments, including a
Permian Aeolian Sand, a Triassic Distal FluvialDelta, a Jurassic Marine Fan Conglomerate, two
Jurassic Shallow Marine Sands and a Palaeocene
Turbidite. The variety of lithological and textural
features made the database suitable for validation of
the method.
The database included all main types of core Pc
measurements: Air-Brine Porous Plate, Air-MercuryInjection and Air-Brine Centrifuge. All porosity and
permeability measurements were executed at ambient
conditions. Similarly, all core Pc measurements wereconverted to Air-Brine Pc at laboratory conditions. In
addition all core data were quality controlled and poor
data discarded from the database.
The porous plate data was considered free of artefactsassociated with loss of capillary contact with the
porous plate which can result in pessimistic water
saturation for a given capillary pressure. The ultra-centrifuge data was considered coherent and
consistent. All centrifuge capillary pressure data were
derived by modelling the raw production data. The
model employed for the datasets utilised appeared fit
for purpose. Mercury intrusion produces a verydetailed description of the capillary properties of a
pore system, however, data derived from capillary
pressures equivalent to greater than the maximum
reservoir closure are not relevant for saturation heightmodelling – these were excluded from the QC
dataset.
The QC core data at laboratory conditions were used
to generate cross-plots of Bulk Volume of Water vs.
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Capillary Pressure (BVW vs. Pc) in log-log space.
Regressions were generated for 102 core plugs,
having all Pc values expressed in pounds per square
inch (psi). Figure 9 shows one core plug for each of
the six reservoirs. Figure 10 shows the results for all102 regressions.
The regressions provided the FOIL parameters foreach core plug: intercept ‘a’ and slope ‘b’. Also,
porosity and permeability measurements on each core
plug allowed the evaluation of the PG index, asdefined in Equation 8. As a result, values of FOIL
parameters ‘a’ and ‘b’ were compared to values of PG
for 102 core plugs. Figures 11 and 12 show the cross-
plots used for such comparisons.
The cross-plot of Figure 11 shows the FOIL ‘a’
parameter to be a consistent function of the Pore
Geometry (PG) index: over a large range of ‘a’ values(0.1-1). The regression shows a high correlation
coefficient (R 2=0.86) and provides a useful functionapplicable to a variety of clastic reservoir rocks and
depositional environments.
The applications of the correlations between the PG
index and the FOIL ‘a’ and ‘b’ parameters are
important. Figure 13 shows the results of a ‘blind
test’ done to verify the method. In this example core porosity, permeability and Pc data were available
from one well (Well X) and wireline logs plus core
porosity and permeability were available from asecond well (Well Y). Both wells encountered the
same reservoir facies: Permian Aeolian Sand.
The core data available from Well X were used to predict permeability in Well Y. The method is
described here briefly and details are provided in
Appendix 1. As a first step, the core data from Well X
were used to derive the FOIL function’s parameters‘a’ and ‘b’ plus the function relating ‘a’ to the PG
index. As a second step, the FOIL function was used
to calculate a continuous ‘a’ profile in Well Y usingthe BVW profile calculated from logs.
The continuous ‘a’ profile was converted to
continuous PG and then to a continuous permeability
profile, using total porosity computed from logs.Tracks 5 and 6 in Figure 13 show the comparison
between predicted continuous permeability (K_PG)
and core permeability (PERM_CORE) in logarithmic
and linear scales respectively. An excellent match between the two set of data is observed over most of
the hydrocarbon column, except for the top and basewhere the resistivity log is affected by polarization
effects (highly deviated well).
The comprehensive core database also allowed the
investigation of the correlation between the FOIL ‘b’
parameter and PG. Figure 12 shows such a
correlation, where ‘b’ exhibits a narrow range of
values: (-0.2 to -0.6). The FOIL ‘b’ parameter wasfound to have a median (P50) value equal to -0.37,
with an uncertainty range of ±37%. Despite its low
correlation coefficient (R 2=0.20), the regression onthe cross-plot of Figure 12 provides a means of
estimating ‘b’ from the Pore Geometry (PG) index.
The functions obtained from Figures 11 and 12
provide a means of estimating the FOIL parameters
‘a’ and ‘b’ from conventional (lab) core porosity and
permeability.
In conclusion, the analysis of core data supports the
findings from logs. The strong correlation between
FOIL ‘a’ and PG was confirmed to be consistent for avariety of depositional environments. The range of
values of the FOIL ‘b’ parameter was confirmed to benarrow, with a median value of -0.37, very close to
the average value derived from logs (-0.41).
The availability of core porosity, permeability and Pc
data allows the identification of field specific
functions: ‘a’=f(PG) and ‘b’=f(PG). These provide a
reliable link between SwH height and porosity- permeability, with important applications for
saturation-height and permeability modelling. Ideally
every reservoir facies should be characterised with itsown ‘a’, ‘b’ and PG parameters.
Two functions were derived from regressions on coredata from a variety of clastic fields:
PGea41.001.0 ⋅= Equation 9
and
17.003.0 −−= PGb Equation 10
These equations are applicable to a variety of North
Sea clastic reservoirs and can be used to calculate preliminary saturation-height functions in absence of
core Pc data using just conventional core porosity and permeability. They provide values of ‘a’ and ‘b’ thatare applicable to FOIL functions where BVW is
expressed as a function of capillary pressure at
standard (lab) conditions and in psi units. Conversely,
they could be used to estimate permeability if the
FOIL parameters were known and a porosity profilewas available from logs.
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Amaefule (1988) developed a method for identifying
and characterising formation zones having similar
hydraulic characteristics. The technique is based on a
modified Kozeny-Carman relationship and the
concept of mean hydraulic radius. Amaefule proposed a parameter called the flow zone indicator
(FZI) which has many useful applications in
formation evaluation. FZI was calculated for each ofthe core database elements and reviewed for
correlations with the FOIL function exponents.
Although correlations exist, the PG Index produced better correlations with respect to modelling
saturation height behaviour in the transition zone, the
objective of this study.
The core analysis focused on a variety of clastic North Sea fields that exhibit a range of poroperm,
depositional environment and geological age.
Preliminary work on a North African fluvial-glacialsands and Saudi dolomites suggest that they may also
follow the same trend especially for PG and the FOIL‘a’ parameter.
CONCLUSIONS
This study investigated electrical logs and core data
from fifteen North Sea clastic fields with different
porosity and permeability characteristics, depositionalenvironments and geological age. The overall
objective was to understand how reservoir parameters
determine the shape of the transition zone.
The FOIL Function was found to be a simple but
robust SwH function that allows an accuratedetermination of hydrocarbons initially in place.Based on log or core data, it does not require
permeability or knowledge of Leverett J parameters at
reservoir conditions.
Comparison of the Leverett J-Function with the FOIL
Function (equation 1) showed that most of the
reservoir parameters relating to rock quality andreservoir fluids are in the FOIL ‘a’ constant.
The ‘b’ constant was found to be a function of pore
geometry, but to a much lesser extent than the ‘a’
constant. Observation of the reservoirs in this studysuggest that ‘b’ is similar between fields and the
shape of the transition zone described by the SwH
Function is controlled almost entirely by the single
constant ‘a’. This was confirmed from core data.
The ‘b’ constant is independent of scale and is thesame whether it is derived from core plugs, electrical
logs or on the field scale. Consequently the median
value of the ‘b’ constant derived from core data can
be used for the computation of the forced ‘a’ constant
from logs. This is believed to be more accurate than
the average ‘b’ value derived from log data.
Observations of thin sections indicate that the FOILfunction is dependent on the geometry of the pore
throats; wide non-tortuous short pore pathways with
little flow impeding mineralogy produce the bestquality FOIL shape as determined by the constant ‘a’.
The constant ‘a’ is found to be predominantlydependent on reservoir pore geometry and explains
how the water saturation is a function of connectivity
as well as porosity and height above the FWL.
Analysis confirmed that the pore geometry has a
major influence on the shape of the transition zone.
As the FOIL ‘a’ parameter represents the intercept of
the FOIL function with the y-axis in log-log space, itsdependence on scale confirms that the FWL can be
determined from this intersect when the y-axis has theunits of true vertical depth subsea (TVDSS). If ’b’ is
assumed to be relatively constant then the picking ofthe FWL is more precise with only 2 unknowns.
Therefore the revised SwH function provides a robust
method for picking the FWL even in fields where it is
unclear or was not penetrated.
One method of defining the ‘quality’ of a reservoir is
the value of water saturation at a known porosity and
height above FWL, where the lower the Sw the better.The quality of reservoirs can be compared through the
comparison of FOIL ‘a’ values.
A new Pore Geometry (PG) Index is proposed that
correlates to the FOIL ‘a’ constant. This index can be
used to make predictions about the quality of pore
geometry within a reservoir and the shape of the SwH
Function. This PG Index is successful in explaininghow fields with very different porosity and
permeability can have very similar SwH functions
and why poorer quality reservoir intervals do notnecessarily have higher water saturations.
The PG Index depends upon the ‘mean pore radius’
of the reservoir and is a single value for the field
provided it has been in pressure/fluid communicationover geological time. The PG Index has been shown
here to be a useful tool for predicting the shape of the
transition zone as a function of average porosity and
permeability in the reservoir.
The investigation of core data convincingly supportsthe findings obtained from logs. The strong
correlation between FOIL ‘a’ and the PG Index was
confirmed to be consistent for a variety of
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depositional environments. Also, the range of values
for the FOIL ‘b’ parameter was found to be very close
to the range of values obtained from electrical logs.
Using an average FOIL ‘b’ parameter the PG Indexallows the prediction of reservoir mean permeability
from electrical logs that measure only porosity and
water saturation. Formation pressures and core are notrequired for this gross permeability estimate for the
field. Conversely, this research provides a means of
estimating the FOIL shape of the transition zone from porosity and permeability in the absence of Pc data.
Preliminary work on a North African fluvio-glacial
sand and a Saudi dolomite suggests that they follow
the same trend for the PG Index and the FOIL ‘a’ parameter.
ACKNOWLEDGEMENTS
The Authors would like to thank Helix RDS for theuse of their data and resources, and also to the
University of Aberdeen, Geology Department, fortheir guidance.
REFERENCES
AMABEOKU, M.O. et al., 2005. Incorporating
hydraulic units concepts in saturation-height
modelling in a gas field: 2005 SPE Asia Pacific Oiland Gas Conference – Proceeding, pp. 609.
AMAEFULE J.O. et al., 1993 – Enhanced reservoirdescription: using core and log data to identifyhydraulic (flow) units and predict permeability in
uncored intervals/wells: SPE 68th Annual technical
Conference, Houston, Texas 3-6 October 1993.
CUDDY, S., 1993. The FOIL function - a simple,
convincing model for calculating water saturations in
Southern North Sea gas fields: Transactions of the34th Annual Logging Symposium of the Society of
Professional Well Log Analysts, H1-17, Calgary,
Canada., 1993, BP Exploration.
LEVERETT, M.C., Capillary behaviour in poroussolids: Trans AIME (1941), Vol. 142.
WORTHINGTON, P.F., LOVELL, M. and
PARKINSON, N., 2002, Application of saturation-height functions in integrated reservoir description:
AAPG Methods in Exploration Series, 13, pp. 89.
ABOUT THE AUTHORS
Dean Gagnon is Geoscientist with Nexen Petroleum
UK Ltd. and holds a M.Sc.in Integrated Petroleum
Geoscience from Aberdeen University. Before joining Nexen he worked with a CBM Solutions Ltd. and
Tahera Corporation.
Steve Cuddy is a Principal Petrophysicist with Helix
RDS and holds a Ph.D. in Petrophysics from
Aberdeen University. Before joining Helix RDS heworked for Schlumberger and BP for 10 and 15 year
respectively.
Fabrizio Conti is the Petrophysics Team Leader for
Helix RDS and holds a B.Sc. in Geology from MilanUniversity. Before joining Helix RDS he worked for
Schlumberger and ENI UK Ltd.
Craig Lindsay is Principal Core Specialist with Helix
RDS and holds a B.Sc. in Geology from LiverpoolUniversity. Before joining Helix RDS he worked for
Core Laboratories Ltd. and Gearhart Industries.
NOMENCLATURE AND DEFINITIONS
BVW Bulk volume of water (v/v).The product of Sw and Phi.
FOIL SwH function describing a variation of the
free oil (gas) with heightFWL Free water level (feet).
Depth of zero capillary pressure
FZI Flow zone indicatorH Height above the FWL (feet)Pc Capillary pressure (psi)
PG Pore Geometry Index
Phi Effective Porosity (PU)
Sw Water saturation (SU)SwH Water saturation vs. height function
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TABLES
FieldFluidType
DepositionalEnvironment
Av.Porosity
(v/v)
Av.Perm(mD)
FOILa FOIL b
FOILForced
a PG
Sw at200’(v/v)
A Oil Palaeocene Turbidite 0.217 27.94 0.3110 -0.3107 0.4693 8.360 0.270
B Oil Devonian Lacustrine 0.140 7.19 0.3242 -0.3561 0.5221 7.190 0.300
C Oil Palaeocene Turbidite 0.191 21.20 0.3520 -0.3732 0.4066 7.893 0.234
D Gas Palaeocene Turbidite 0.324 2207.89 0.2897 -0.4351 0.2520 7.470 0.145
E Oil U. Jurassic Turbidite 0.214 570.04 0.2744 -0.5196 0.1835 6.329 0.106
F Gas Permian Aeolian 0.202 341.78 0.2669 -0.3956 0.2441 6.438 0.140
GGas
Conden. L. Cret. Turbidite 0.239 847.65 0.1045 -0.4054 0.1115 6.552 0.064
H Oil M. Jurassic Deltaic 0.134 3.24 0.4309 -0.4073 0.5183 7.422 0.298
I Oil Palaeocene Turbidite 0.214 23.94 0.6686 -0.4391 0.6292 8.385 0.362
J Gas Permian Fluvial 0.086 0.17 0.4492 -0.4746 0.3223 7.268 0.185
K Gas Permian Aeolian 0.135 0.87 0.4154 -0.3526 0.5408 8.121 0.311
Table 1: UKCS fields with electrical log data analysed in this study
Zone
Av.
porosity(v/v)
Av. Perm'
(mD)
Forced
FOIL a FOIL b PG Sw (v/v)
1 0.172 15.75 0.2350 -0.4225 7.584 0.135
2 0.089 0.59 0.0900 -0.3216 6.881 0.052
Table 2: Zone Parameters for Field L (Permian Aeolian Gas Sand)
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FIGURES
Field A B C D E F G H I J K
Legend
0 .
0 0
0 .
0 5
0 .
1 0
0 .
1 5
0 .
2 0
0 .
2 5
0 .
3 0
0 .
3 5
0.01
0.1
1
10
100
1000
10000
P e r m e a b i l i t y ( m D )
Porosity (V/V)
Figure 1: Porosity vs. Permeability for eleven fields in the Study
Figure 2: Field E Thin Section. Pores are evenly spaced throughout sample. Pore edge geometry ranges from
convex (60%) and straight (30%) to concave (10%). Quartz composes 90% of pore walls with remainder beingfeldspar. Pore walls are mostly smooth (95%) and there is minor (< 5%) pore lining or pore throat bridgingmineralization visible. The sample is loosely compacted and does not show any pore occlusion due to cementation.
There is minor secondary porosity associated with degraded feldspars. The majority of pore throats (60%) are of asimilar size to the pores they connect. Pore pathways are short, non-tortuous and visibly free of flow impedingmaterials. Overall connectivity is excellent.
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Figure 3: Field F Thin Section. Visible porosity is dominated by primary intergranular pores (13.5%) with minor
secondary dissolution pores (2.0%). Primary pores are large and well connected and there is consistent pore distributionthroughout the sample. There are very few simple geometric pore shapes (10%), most pores have complex shapes(98%) and are joined together via short pore throats that are often only slightly smaller in diameter than the maximum
dimension of the adjoining pore. They are mostly clay free, smooth walled and free of blocky authigenic cements.Pore lining ferroan dolomite rhombs are the only obstacles to fluid flow. Secondary pores are associated with degradedK-feldspar and rock fragments. Secondary porosity is often isolated due to relic grain boundaries being coated by k-feldspar or clay. Trace microporosity is associated with kaolinite and illite.
Figure 4: Field K Thin Section. Most pores have complex shapes (63%) with the remainder having simple
geometric shapes (37%). Pore edge geometry ranges from convex (50%) and straight (30%) to concave (20%). Pore
walls are rough (95%) and there is abundant pore lining and pore throat bridging mineralization. The majority of pore
throats (95%) have a much smaller diameter than the adjoining pores. Pores are contained within isolated groups. Poregroups have good internal connectivity; however connectivity between groups is via long tortuous pathways.
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Field A B C D E F G H I J K
Legend
0 . 0
0 0
0 . 0
2 0
0 . 0
4 0
0 . 0
6 0
0 . 0
8 0
0 . 1
0 0
0 . 1
2 0
0 . 1
4 0
0 . 1
6 0
0 . 1
8 0
0 . 2
0 0
0
50
100
150
200
250
300
350
400
450
500
H e i g h t a b o v e t h e F W L ( F e e t )
Bulk Volume of Water (V/V) Figure 5: FOIL Functions from Logs for the Study Fields (linear scales)
0 .
0 1
0 .
1
0 .
2
1
10
100
500
H e i g h t a b o v e t h e F W L ( F e e t )
Bulk Volume of Water (V/V)
Figure 6: FOIL Functions from Logs for the Study Fields (log scales)
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Field A B C D E F G H I J K
Legend
0 .
0
0 .
1
0 .
2
0 .
3
0 .
4
0 .
5
0 .
6
0 .
7
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
W a t e r S a t u r a t i o n ( V / V ) a t 2 0 0 ' P h i = 2 0 p . u .
Forced 'A' Parameter
Figure 7: Relationship between Force ‘a’ and Water Saturation
5 6 7 8 9 1 0
0.05
0.1
1
2
F o r c e d ' A ' P a r a m e t e r
PG - Pore Geometry
Figure 8: Relationship between forced ‘a’ and PG on the Field Scale
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0.10
1.00
10.00
100.00
1000.00
0.010 0.100 1.000
Bulk Volume of Water [v/v]
C a p i l l a r y P r e s s u r e [ p s i ]
NS Triassic Distal Delta Sand
NS Jurassic Marine Fan Conglomerate
NS Permian Aeolian Sand
NS Jurassic Shallow Marine Sand (1)
NS Jurassic Shallow Marine Sand (2)
NS Palaeocene Turbidite
Figure 9: BVW vs. Pc for 6 Core Plugs from 6 different N.S. clastic reservoirs
1
10
100
1000
0.01 0.1 1
Bulk Volume of Water [v/v]
C a p i l l a r y P r e s s u r e [ p s i ]
Figure 10: BVW vs. Pc for 102 Core Plugs from 6 different N.S. clastic reservoirs
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y = 0.01e0.41x
R
2
= 0.86
0.01
0.10
1.00
10.00
4 6 8 10 12 14 16 18 20
Pore Geometry Index
F O I L
a
ALL
NS Triassic Distal Fluvial Delta Sand
NS Jurassic Marine Fan Conglomerate
NS Permian Aeolian Sand
NS Jur assic Shallow Mar ine Sand (1)
NS Jur assic Shallow Mar ine Sand (2)
NS Palaeocene Turb idite
Expon. (ALL)
Figure 11: Foil ‘a’ vs. PG for 102 core plugs from 6 N.S. clastic reservoirs
y = -0.03x - 0.17
R2 = 0.20
-2.0
-1.8
-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
4 6 8 10 12 14 16 18 20
Pore Geometry Index
F O I L
b
ALL
NS Triassic Dis tal Fluvial Delta Sand
NS Jurassic Marine Fan Conglomerate
NS Permian Aeolian Sand
NS Jur assic Shallow Marine Sand (1)NS Jur assic Shallow Marine Sand (2)
NS Palaeocene Turb idite
Linear (ALL)
Figure 12: Foil ‘b’ vs. PG for 102 core plugs from 6 N.S. clastic reservoirs
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Figure 13: Permeability prediction in Well Y using Pc data from offset Well X
APPENDIX 1
Details of Permeability prediction in Well Y using Pc data from offset Well X (Figure 13)
Step 1 Core porosity, permeability and Pc from well X were used to derive the functions:
BVW=0.135*(Pclab)^(-0.275) the FOIL Function with Pclab in [psi] and
a=0.01*e^(0.41*PG) the relationship between ‘a’ and PG.
The FOIL Function was used to calculate the Sw profile named ‘SWE_PC_OFF’ in well Y, to be
compared to the Sw profile from the Archie equation (SWE):SWE_PC_OFF=[0.135*(H*0.42*72/50)^(-0.275)]/PHIE
Where: H = height above FWL [ft], 0.42 = differential fluid gradient [psi/ft], 72/50 = conversion
factor from gas/brine at reservoir conditions to air/brine at lab conditions and PHIE = continuous
effective porosity calculated from logs in well Y.
Step 2 The FOIL Function was used to solve a continuous ‘a’ profile (not displayed in Fig. 13) in well Yusing BVW calculated from logs (BVW=SWE*PHIE) as input:
a=BVW*(H*0.42*72/50)^0.275
Step 3 Function ‘a’=f(PG) from step 1 was re-arranged to solve PG (not displayed in Fig. 13) in well Y:
PG=ln(a/0.01)/0.41.
Step 4 Equation 8 was used to solve for continuous permeability using the continuous PG (from Step 3)
and total porosity calculated from logs (curve PHIT) as input: K_PG=10^(PG*log10(PHIT)+7).
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