SPWLA 49 th Annual Logging Symposium, May 25-28, 2008 1 THE EFFECT OF PORE GEOMETRYON THE DISTRIBUTION OF RESERVOIR FLUIDS INU.K. NORTH SEA OIL AND GAS FIELDSDean Gagnon 1 , 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 and Well 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 height above the free water level (FWL). Nowhere is this more important than in the transition zone. Electrical logs, core data and thin sections from fifteen North Sea fields were compared to understand how reservoir parameters determine the shape of the transition zone. These incl uded 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 FOIL Function, 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 the reservoir 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 oil fields, the ‘b’ constant is surprisingly invariable: with the shape of the transition zone described by the SwH Function being controlled almost entirely by the single 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’ value have 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 well as porosity and height above the FWL. Analysis confirmed that the pore geometry rather than porosity and 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 pore geometry 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 functions and 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 understood and 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 be mapped as it depends on numerous factors including porosity and the height above the loca l FWL. SwH functions are used in a field’s reservoir model to estimate Sw away from well locations so that hydrocarbons initially in place can be calculated. The error in reserves resulting from an equation that poorly describes t he reservoir can be significant. This study uses the FOIL 1 SwH function to compare reservoirs of different North Sea fields. The FOIL Function is an algorithm which is commonly used to determine 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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7/24/2019 Steve Cuddy Edinburgh Pore Geometry 2008
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.
7/24/2019 Steve Cuddy Edinburgh Pore Geometry 2008
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.
7/24/2019 Steve Cuddy Edinburgh Pore Geometry 2008
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.
7/24/2019 Steve Cuddy Edinburgh Pore Geometry 2008
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.
7/24/2019 Steve Cuddy Edinburgh Pore Geometry 2008
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).