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CHINESE JOURNAL OF GEOPHYSICS Vol.51, No.3, 2008, pp: 639644
DISCRIMINATING GAS AND WATER USING MULTI-ANGLEEXTENDED ELASTIC
IMPEDANCE INVERSION
IN CARBONATE RESERVOIRS
PENG Zhen-Ming1,2, LI Ya-Lin2, WU Sheng-Hong2, HE Zhen-Hua3,
ZHOU Yong-Jun2
1 School of Opto-Electronic Information, University of
Electronic Science and Technology of China,
Chengdu 610054, China
2 Sichuan Geophysical Company, CNPC Sichuan Petroleum, Chengdu
610213, China
3 State Key Laboratory of Oil and Gas Reservoir Geology and
Exploitation, Chengdu University of
Technology, Chengdu 610059, China
Abstract AVO response for carbonate reservoirs is weaker than
the clastic reservoirs. So it is very hard to
discriminate fluid in carbonate reservoirs using elastic
impedance (EI), even under the optimal incident angle.
In this paper, a novel method is proposed for discriminating
fluid using multi-angle extended elastic impedance
(MEEI) inversion in carbonate reservoirs. We established the
fluid-bearing patterns and effective criterions for
discriminating gas and water by calculating MEEI of target
layers using the known well data. MEEI inversion of
real seismic data shows that we can judge whether the reservoir
is good or bad or is gas-bearing or water-bearing
by observing EEI change trend with various incident angles. The
efficiency of the proposed method is validated
by the practical application of real seismic data in Sichuan
basin.
Key words Extended elastic impedance, Multi-angle analysis,
Fluid criterions, Fluid discrimination, Carbonate
reservoirs
1 INTRODUCTION
The concept of elastic impedance (EI) was first introduced by
Connolly (1999)[1], which is suitable for fluiddiscrimination and
lithology prediction for various reservoirs because it includes
more abundant informationof lithology and fluid than acoustic
impedance (AI). Recently, a great quantity of research work for EI
hasbeen done by scientists in China and abroad. In order to
overcome the drawback of incident angle restrictionand the rapid
variation of inversion results with incident angle which gives rise
to difficulties for interpretation,Whitcombe et al.[2,3] deduced
the expression of the extended elastic impedance (EEI) by modifying
the originalequation of the EI established by Connoly, which makes
it more suitable for fluid discrimination and lithologyprediction.
They calculated the distribution map of lithology impedance and
fluid impedance using EEI in anoil field of North Sea and obtained
the distinct imaging map of their channel system. Duffaut et al.[4]
introducedthe shear wave elastic impedance (SEI) to solve the
problem for lithology prediction with converted waves.Ezequiel[5]
presented a formulation of P-to-S converted waves elastic impedance
(PSEI) under arbitrary incidenceangles and used to distinguish fizz
water from commercial gas for predicting area distribution. From
2003, thegeophysical circles in China[615] began to pay attention
to this subject, presented a series of concepts andtheories such as
Ray-path elastic impedance (REI), Generalized elastic
impedance(GEI), Zoeppritzt elasticimpedance(ZEI), etc., and a
quantity of research and analysis works have been done in the areas
of its practicalapplications.
The authors consider that EEI is effective for lithology
discrimination of clastic reservoirs by analyzing andcomparing the
results of the above methods and computed the real seismic data.
However, various case studiesshow[1417] that AVO response for
carbonate reservoirs is weaker than the clastic reservoirs.
Difficulties wereencountered when we discriminated fluid for
carbonate reservoirs under the optimal incident angle according
tothe literature [3] because all EEI values indicate low value
abnormity for gas-bearing or water-bearing reservoirs,
E-mail: [email protected]
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640 Chinese J. Geophys. Vol.51, No.3
even under the optimal incident angle. We can effectively
predict reservoirs, but it is beyond its capabilities touse the
above-mentioned method for evaluating the reservoir quality and
discriminating gas- or water-content.On the basis of the EEI
theory, we computed the multi-angle extended elastic impedance
(MEEI) of targetlayers and observed its varying trend with various
incident angles. In our experiments, we found that the
MEEIresponses indicate the significant difference for gas-bearing
or water-bearing reservoirs by combining loggingdata (P- wave,
S-wave and density) of drilled wells with the results of well log
interpretation. It is provedthat using MEEI inversion to
discriminate fluid for carbonate reservoirs is effective and
feasible and effectivecriterion for discriminating gas and water
was established in this paper. The efficiency of the proposed
methodsis validated by the application of real data in Sichuan
basin.
2 THE DEFINITION OF ELASTIC IMPEDANCE AND EXTENDED ELASTIC
IMPEDANCE
Elastic impedance (EI) is established on the basis of simplified
equation of Aki-Richards[18]. If just considerthe incident angles
less than 30, then
R() = A+B sin2 , (1)
where A =12
(vpvp
+
), B =
vp2vp
4(vsvp
)2(vsvs
)2
(vsvp
)2(
), and vp,vp, vs,vs, , donate
the average value and difference of compressional (P-wave)
velocity, shear wave velocity and density in adjacentformation,
respectively.
Connolly[1] constructed an equation for calculating reflectivity
similar to acoustic impedance as follows
R() =EIi+1 EIiEIi+1 + EIi
12EIEI
12ln(EI), (2)
where EI is called as elastic impedance. Comparing Eq.(1) and
(2) and by simple computation, EI expressionscan be written as
follows
EI() = v(1+sin2 )
p v(8K sin2 )s
(14K sin2 ), (3)
where vp is P-wave velocity, vs is S-wave velocity, is density
and K =
[(vsivpi
)2+(vsi+1vpi+1
)2]/2 is the average
value of the square of the ratio of P to S velocity. is the
incident angle of P-wave. The main problems incalculating EI using
Eq.(3) is that its value dramatically decreases with incident
angle, which probably losesome information for analyzing elastic
impedance at near and far angles, for example, the difference of
fluid orlithology change.
Therefore, in order to eliminate the effects, Whitcombe et
al.[3] deduced a new formula of EI by normalizingthe original EI
equation, as follows
EI() = 00
[(
0
)a(
0
)b(
0
)c], (4)
where 0, 0, 0 are constant coefficient, which donate average
value of vp, vs, in reservoir intervals, respectively., , are vpi ,
vsi , i and at different depth, respectively, and
a = 1 + sin2 , b = 8K sin2 , c = 1 4K sin2 . (5)Although Eq.(4)
can remove the effect of dramatic EI decrease with incident angle
and keep the same
orders of magnitude with post-stack acoustic impedance, the
reflectivity R() are probably larger than 1 con-flicting with the
real seismic recorder. Thus, Whitcombe[3] further modified the EI
equation, and replaced sin2 by tan ( is theoretical incident angle
being expanded, which changes between 90 and 90), scaled the
re-flectivity R() by multiplication by cos. The so-called extended
elastic impedance (EEI) can be formulatedas
EEI() = 00
[(
0
)p(
0
)q (
0
)r], (6)
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Peng Z M et al.: Discriminating Gas and Water Using Multi-Angle
Extended Elastic Impedance Inversion 641where
p = cos+ sin, q = 8K sin, r = cos 4K sin. (7)
EEI value calculated by Eq.(6) not only eliminates the effect of
EI dramatic decrease with incident angle,but also controls the
reflectivity within [1,1] and is more suitable to real seismic
recorder and beneficial todirectly detect lithology and fluid.
3 MEEI WELL MODEL AND FLUID CRITERION FOR CARBONATE
RESERVOIRS
Fluid detection using EEI needs to build the fluid
discrimination model according to the prior information.In general,
the relationship between EI and water saturation at fixed incident
angle is adopted and then theinterpretation scheme is determined.
However, these methods have two disadvantages: one is that it is
difficultto predefine a reasonable incident angle; the other is
that the multi-angle information of pre-stack seismic datais lost
under the fixed incident angle. In the study we found that the EEI
inversion results of target layers showlow value abnormity under
the gas-bearing or water-bearing conditions in fixed incident angle
(for example,16), and it is hard to discriminate the gas and water
in reservoir. Some literatures also introduce the approachto
partition gas and water boundary by EI inversion for the limited
partial stack seismic section at near andfar incident angle and the
cross-plot analyses are done for inversion results and data samples
are artificiallyclassified for gas or water. However, this method
is probably affected by various artificial factors, because
thesedata are not completely divided, and cause the large
interpretation error.
This paper presents a new model for discriminating fluid using
multi-angle extended elastic impedance,(MEEI), in which the change
trend of EEI with incident angles is observed continuously by
calculating a seriesof EEI within the efficient range of incident
angles for reservoir zone. Then the corresponding fluid
criterionsare determined by prior information of fluid-bearing (for
example, log interpretation results). The analyses oflogging data
(P-wave velocity, S-wave velocity and density) from several wells
show that the proposed method canconstruct an efficient
fluid-bearing pattern for carbonate reservoirs. Fig. 1 shows EEI
varying with the incidentangle (theoretical angle ) of gas-bearing
and water-bearing reservoirs of well X6. This well was interpreted
asgas-bearing layer at 43844386 m and 44714480 m depth and as
water-bearing layer at 44884511 m. Wecan see from the figure that
EEI value increases with the incident angle decreasing for
water-bearing reservoirsand EEI value decreases with the incident
angle increasing for water-bearing reservoirs, while it changes
slowlyfor gas-water-bearing. To further verify the regularity and
obtain a consistent conclusion, the same analysesare also done for
the other wells in this area. Fig. 2 shows that EEI values for
gas-bearing and water-bearinglayers of well X4 and X5 are
consistent with Fig. 1. The EEI change trend of gas-bearing layer
in well X1 isalso basically consistent.
The calculation of real data from several wells shows that MEEI
analysis is effective for discriminating gasand water in carbonate
reservoirs and its response is obvious. Comparing with acoustic
impedance, EEI also
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642 Chinese J. Geophys. Vol.51, No.3
shows low value for gas-bearing or water-bearing reservoirs.
However, MEEI for the different fluid in reservoirinterval show the
different responses as follows: (1) EEI increases with the increase
of incident angle for water-bearing case; (2) EEI decreases with
increasing incident angle for gas-bearing case; (3) EEI changes
slowly withthe increase of incident angle for gas-water-bearing
case.
In practice application, gas-bearing cases of a few wells show
inconsistent result with the above fluidcriterion, in which EEI
increases with incident angle increasing. It is caused by absence
of S-wave velocity inthis well and using Castagna equation to fit
it. Because the relationship between P-wave and S-wave velocityis
not linear, it causes the uncertainty of calculating results.
Generally, according to Castagna equation, P-wave and S-wave
velocity at most layers are correlative. However, practice shows
that those zones with poorcorrelation between vp and vs are just
the places for favorable reservoir bodies. Therefore, the results
and theiraccuracy will be affected due to the absence of S-wave
velocity in fluid discrimination using MEEI inversion.
For the sake of analyzing problem, the label of the abscissa is
the theoretical angles (not the actual incidentangle) in Fig. 1 and
Fig. 2, which change within 0 90. The relationship between the
actual incident angleand the theoretical angles is monotonic
increasing or decreasing, and we aim at observing the EEI change
trendwith incident angle for gar-bearing or water-bearing
reservoirs rather than numerical value of actual incidentangles. It
will not affect the result of analyzing problem, although the
theoretical angles are not converted tothe actual incident
angles.
4 CASE STUDY AND RESULTS ANALYSIS
MEEI analyses are conducted for logging data and the gas and
water criterions are established by forwardcalculation based on the
above approaches, then the real seismic data can be inversed for
angle trace gatherswith pre-stack NMO and pre-stack time migration.
In the study area, MEEI inversion was tested for two 2-Dseismic
line across gas well and water well, respectively.
Figure 3 and 4 are the results of MEEI inversion and fluid
detection for real 2-D line across typical gaswell and water well,
respectively. Fig. 3a, 3b, and 3c are the EEI inversion sections at
gas-bearing reservoirintervals of inline 450 (across well X4) with
various actual incident angles (5, 13, and 21), where navy
bluecolor donates the low EEI value. We can see from the regions
marked as red ellipses in the figures that thecolor of inversion
results within gas-bearing reservoir interval deepens gradually
with incident angles increasing,indicating that EEI values decrease
with incident angles increasing. The EEI inversion results of
reservoirintervals of inline 557 (across well X6, interpreted as
water-bearing layer in logging ) under various actualincident
angles (5, 15 and 25) are shown in Fig. 4a, 4b, and 4c. Similarly,
we can see from the regions markedas purple ellipses in the figures
that the color of inversion results within water-bearing reservoir
interval lightensgradually with incident angles increasing,
indicating that EEI values increase with incident angles
increasing.
The inversion results of real seismic data are all consistent
with fluid discrimination criterion establishedin this paper.
Moreover, model-based inversion of MEEI was realized for the 3-D
working area of 100 m2.Consistency verification has been done by
using 3 wells of the 6 wells drilled in the area as constraining
conditionsand taking the others as the unknown wells, the resultant
consistency ratio is 100%. The test results show thatthe proposed
method based on MEEI for discriminating fluid is efficient and
feasible.
5 CONCLUSIONS
The fluid discrimination criterions are established by analyzing
logging data at reservoir intervals andforward calculation in this
paper. The test results for real 3-D seismic data show that it is
an effective approachto discriminating gas and water in carbonate
reservoirs using MEEI inversion and is better than EEI
inversionunder the fixed incident angle or EEI cross-plot analysis
between near and far angles. Although the presentmethod is used to
detect fluid in carbonate reservoirs, it also has referential
significance to lithology identificationin sand-shale formation or
clastic reservoirs.
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Peng Z M et al.: Discriminating Gas and Water Using Multi-Angle
Extended Elastic Impedance Inversion 643
The actual incident angles is (a) 5, (b) 13, (c) 21. The actual
incident angles is (a) 5, (b) 15, (c) 25.
ACKNOWLEDGMENTS
Authors would like to express their gratitude to Sichuan
Geophysical Company of CNPC Sichuan Petroleumfor permitting to
publish this project. This work has been supported by the
Aeronautic Science Foundation ofChina (20060112116), Research Fund
for the Doctoral Program of Higher Education of China
(20070614016)and National Natural Science Foundation of China
(60572092).
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