Journal of Scientific Research and Reviews Vol. 1(2), pp. 015 - 019, August 2012
Available online at http://www.wudpeckerresearchjournals.org
2012 Wudpecker Research Journals
ISSN 2277 0690
Review
Using of compressional-wave and shear-wave
velocities ratio in recognition of reservoir fluid contacts
case study: A Southwest Iranian oil field
*M Bahremandi , M Mirshahani and M Saemi
Research Institute of Petroleum Industry (RIPI), West Bldv, Azadi Sport Complex, Tehran, Iran.
Rock mechanics department, faculty of engineering, Tarbiat modares university, Tehran, Iran.
Accepted 27 July 2012
The Vp to Vs ratio is a key parameter for lithology and fluid prediction. In an oil layer, compressional
wave velocity decreases and shear wave velocity increases. The increase of shear wave velocity is due
to the decrease of density and the decrease of compressional wave velocity is due to the decrease of
bulk modulus of reservoir rocks; therefore the Vp/Vs ratio will decrease in oil sections. This ratio can be
used for determination of fluid type and OWC in oil reservoirs. A field example in southwest of Iran is
given to identify fluids type (water and oil) using the Vp/Vs ratio from well logs. The results have shown
that shear wave velocity increases and compressional wave velocity decreases when the water
saturated points become oil saturated points in the studied intervals. The results are compared results
from petrophysical interpretation.
Key words: Velocity, SW Iran, oil-water contact, Vp/Vs and well logs data.
INTRODUCTION
Elastic properties of rocks are discussed by specifying
the compressional velocity (Vp), the share wave velocity
(Vs) and the density (ρ). It is useful to know the
corresponding parameters: Compressional modules (M),
bulk modulus (k) and rigidity modulus (µ). The wave
velocity is defined by the elasticity parameter, M and
density, ρ. Effect of elasticity on velocity is much greater
than the effect of density. The basic equation is Vp =
0.5
(M/ρ) . For P-wave, the appropriate value of M is K + 4
/3µ or λ+ 2µ, while for S-wave the appropriate equation is
Vs = (µ/ ρ)0.5 (Cardona et al., 2001; Domenico, 1976).
Compressional wave velocity data are very useful in
identifying lithology, porosity and pore fluids in
petrophysical evaluations. Shear wave velocity data are
also useful for mineral identification and porosity
decreases and shear wave velocity increases and so
these can be used in identifying fluids type in porous
reservoir rocks. In this paper, the technique of Vp/Vs is
presented as fluid identification tool and field examples
*Corresponding author Email: [email protected]
are presented to show how the Vp/Vs crossplot can
distinguish between water and oil (or gas) saturated
zones (Ensley, 1985; Johnston and Christenson, 1993).
Wave velocity in rocks
Rocks with equal matrixes may have different responses
in sonic logs. In fact porosity and the type of fluid in pores
are factors that control the travel time in a rock. The
heuristic time average equation is often used to relate the
velocity, V and porosity , known as equation (1); it
assumes the travel time per unit path length in fluid filled
porous rock is the average of the travel times per unit
path length in the matrix 1/Vm and in the fluid 1/Vf:
1/V = /Vf + 1 – /Vm …………………...(1)
where:
V
wave velocity;
Vf
fluid velocity;

effective formation porosity.
Bahremandi et al.
The saturating fluids affect wave velocity. Wave velocity
shows a significant decrease when the saturating fluids
water or oil is replaced by gas (Wyllie et al., 1956)
16
Solution of any of these equations for one variable requires
the other two variables being known. Equations (4) or (6)
can be solved or porosity with assumption of known fluid
velocity and matrix velocity Tatham, (1976).
Vp-Vs ratio
Identification of fluid using Vp-Vs crossplot
Another useful quantity is: Vp-Vs Ratio. Compressional
wave velocity decreases and shear wave velocity
increases with the increase of light hydrocarbon
saturation, so combining shear wave and compressional
wave velocities will give new parameter Vp/Vs. This
parameter is more sensitive to fluid nature than P-wave
or S-wave alone. The ratio between compressional to
shear wave velocity is:
Vp/Vs = [(λ+ 2µ)/ ρ]0.5 / (µ/ρ)0.5
0.5
= [(λ+ 2µ)/µ]
= [(k + 4/3µ)/µ]0.5=[(1–)/(0.5 – )]0.5 ……….(2)
Where;
Vp
compressional wave velocity;
Vs
shear velocity;
λ
Lame’s parameter;
µ
rigidity modulus;

Poisson ratio (vary from 0.0 to 1.0);
k
Bulk modulus of rock.
The compressional velocity will always be greater than
the shear velocity in a given medium.
If  is 0.25, the Vp/Vs ratio equals to 3. It is worth
noting that for most consolidated rock materials, Vp/Vs is
between 1.5 and 2 and  is between 0.1 and 0.33. The
Vp/Vs ratio for sandstones varies between 1.66 and 1.81
and for carbonates between 1.81 and 1.98. As shear
deformation cannot be sustained in liquid (µ= 0) shear
waves will not propagate in liquid material at all (Crampin,
1985; Georgy, 1976).
From velocity equations, it is clear that shear wave
velocity is more affected by rigidity modulus than
compressional wave velocity.
Equation (1) can take the following form for P-wave:
1/Vp = /Vpf + 1 – /Vpm………………...(3)
or
Tp = Tpf+ (1 – ) Tpm……………….(4)
and for shear wave the form:
1/Vs = /Vsf + 1 – /Vsm…………….…..(5)
or:
Ts = Ts+ (1 – ) Tsm……………..…(6)
where Tp is P-wave transit time and Ts is S-wave
transit time. Velocity (Vp or Vs) in the Equations (3 and 6)
is a function of three variables; fluid velocity, Vf, porosity, 
and matrix velocity, Vm.
Equations (3and 6) can be solved for fluid velocity
instead of formation porosity with the assumption of
known porosity and matrix velocity. P-wave velocity in
water is greater than that in oil and in gas. Consequently
recorded P-wave velocity is sensitive to fluid change from
water to oil or gas. Shear velocity is more sensitive than
P-wave to fluid type.
This sensitivity difference is attributed to the fact that
S-wave depends mainly on rigidity modulus, µ parameter
while Vp depends on  and µ parameters. In an oil layer,
compressional wave velocity decreases and shear wave
velocity increases. The increase of shear wave velocity is
due to the decrease of density and the decrease of
compressional wave velocity is due to the decrease of
bulk modulus of reservoir rocks; therefore the Vp to Vs
ratio, Vp/Vs, will decrease and it is more sensitive to
change of fluid type than Vp or Vs separately. (Hamada,
2004).
Following Table 1 resumes travel time T for S-wave
and P-wave in most reservoir rocks. Vp/Vs crossplot is
constructed using these matrix constant in µs/m
(Domenico, 1984). Tp – Ts crossplot is preferred
rather than the form of Vp/Vs crossplot. It is technically
easier; values are taken directly from records to the
crossplot.
Figure 1 is Vp/Vs in µs/m. The three lines are limestone
water base line, dolomite water base line and sandstone
water base line in a reservoir with porosity between 13%
till 16%. For a specific case, e.g. sandstone line, points
lie on the sandstone line or above (in case of ρf > 1 g/cc)
are water points, the point lie below sandstone line are oil
points or gas points.
Light hydrocarbon or gas will cause a decrease in
shear travel time and an increase in compressional travel
time with respect to water point. This will shift the water
point to southwest corner of the cross plot, defined as
gas arrow effect in the crossplot. Gas points will show
more departure from sandstone water base line than oil
points and more shifted to the left of greater shear travel
times. This technique can be applied for limestone or
dolomite reservoir rocks. The use of Vp/Vs crossplot can
be useful for fluid identification for given reservoir rock
(same porosity and same matrix) especially in gas
reservoir (Sinha and Plana, 2001;
17
J. Sci. Res. Rev.
Table 1. Shear and compressional waves travel time.
Rock type
Limestone
Dolomite
Sandstone
Water
Tp (µs/m)
142
130.5
159
567
Ts (µs/m)
270
238
258
infinite
Figure 3. Vp/Vs crossplot for water zone in a limestone Fm.,
W#04, SW of Iran.
Figure 1. Vp/Vs crossplot to predict fluid type in different lithologys
Figure 4. Vp/Vs crossplot for oil zone in a limestone Fm.,
W#06, SW of Iran.
Figure 2. Vp/Vs crossplot for oil zone in a limestone Fm., W#04,
SW of Iran.
Soudra, 2002; Sun et al., 2000).
CASE STUDY
Following are certain examples of Vp/Vs application as
Figure 5. Vp/Vs crossplot for water zone in a limestone Fm.,
W#06, SW of Iran.
fluid identification tool in a field, Southwest of Iran. All
data for shear and compressional waves were acquired
from well logs (Petrophysical tools). Producing well has
Bahremandi et al.
18
OWC
Figure 6. Vp/Vs crossplot for oil zone in a Sandstone Fm.,
W#06, SW of Iran.
Figure 8. The oil-water contact of well w#04 has recognized
using integration of reservoir pressure data and the ratio of
sonic logs.
indicates that the unit is water.
Figure 7. Vp/Vs crossplot for oil zone in a Sandstone Fm.,
W#06, SW of Iran.
been tested to indicate fluid nature of different sections.
All data are obtained from regions where porosity is
between 13% and 16 %. Figure 2 shows Vp/Vs crossplot
for Asmari Formation in a well (W#04) in this field SW of
Iran. These data are obtained from an oil-producing unit
(above of oil water contact). The points shown in this
figure indicate very clearly that it is an oil zone. Figure 3
is the Vp/Vs crossplot for the same well but below the oil
water contact. The Vp/Vs crossplot points shown in
Figure 3 indicate that the unit is a water section.
Vp/Vs crossplot has been applied in well W#06
producing from two sections in a well; Asmari Formation
as a limy reservoir and Bourghan member (Kazhdumi
Fm.) as a sandy reservoir. Figure 4 is the Vp/Vs crossplot
in Asmari, which is oil producing (above the OWC). The
points lie below the line and this indicates an oil zone.
Figure 5 is the Vp/Vs cross plot for water section (below
the OWC) in that formation. The points shown in the
figure are shifted to the right and close to water line. This
Figure 6 is the Vp/Vs crossplot in Bourghan member
above the OWC. The points indicate that there is an oil
zone in this section. Finally Figure is the Vp/Vs crossplot
in the same member below the OWC. The points confirm
that this unit is a water-bearing unit.
Figure 8 indicates the variations of Swlog, prosity and
the ratio of Vp/Vs in individual tracks. Measured reservoir
pressure data was processed and depth of 2860 meter
has detected as OWC (green line). The comparison
between measured data and the ratio of sonic logs shows
a very good match and its reveals that our procedure has
a good capability in determining of reservoir fluid
contacts.
CONCLUSION
Ts-Tp (Vp/Vs) crossplot can be used as a tool to identify
fluid type for the same formation. It has been used in a
field with different fluid types (oil and water). This
technique assumed that the section has the same
porosity and it has the same lithology (for example 15%
porosity in limestone formations). In the studied intervals,
crossplots have shown that in oil zones shear wave
velocity increases and compressional wave velocity
decreases (Ts decreases and Tp increases). These
crossplots have been compared with petrophysical
analysis and there was a good correlation between them.
It is recommended to introduce it as an additional tool in
19
J. Sci. Res. Rev.
identifying fluid nature of new sections.
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