Rock Physics Modeling of the Unconsolidated Mahanadi Basin Sandstone in Deep Water off India’s Eastern Coast

Mukesh Gupta(1) and Ranjit Shaw(1)

(1) Schlumberger Data & Consulting Services, Mumbai (MGupta5@slb.com )

ABSTRACT

Recent gas discoveries in deepwater prospects of Mahanadi basin, offshore Eastern coast of India has created significant exploration interests amongst major Exploration and Production (E&P) companies operating in Indian subcontinent. Hydrocarbon bearing sands have been encountered in deep water channel-levee complex of Mio-Pliocene age showing very slow compressional as well as shear velocities in well measurements. The exploration model has been generally guided by direct hydrocarbon indicators (DHI) from seismic amplitudes as well as amplitude variation with offset (AVO) with varied levels of success. The area has seen both clean as well as shaly sand facies causing significant ambiguity in interpreting seismic amplitude and AVO attributes. Under this background, it is important to have a clear understanding of relationship between elastic properties of rock with reservoir petrophysical properties to develop a model for further exploration and development. Towards meeting this objective, we investigated theability of different classical rock physics models to predict the seismic velocities of deep water rocks of Mahanadi basin. We have used effective medium models and contact theories to explain the elasticproperties of sandstone from observed petrophysical data. Modeling results show that effective medium models over-predict the sonic velocities. On the other hand a simple contact theory satisfactorily predicts the observed elastic properties of the sand. Such a rock physics model, in turn, can be used for predicting shear velocity in old wells where these measurements are not available. Besides, it can be used to understand sensitivity of fluid as well as facies variation in the different parts of the basin belonging to the same geological age.

KEY WORDS: Rock physics modeling, contact theory, effective medium model, co-ordination number.

INTRODUCTION

Mahanadi basin is located in the northeastern part of eastern passive continental margin of India. Deepwater environment of Mahanadi basin comprises sediments ranging from Cretaceous to Miocene. Channel systems

transported clastics from the shelf environment in the north to deep basinal part to the south and forms isolated sandstone bodies within the channel levee complex (Singh et al., 2010).

For the present study, aiming at identifying a rock physics model that explains the observed elastic properties of the unconsolidated sands, we selected high porosity (28-36%) sands from a wet sand encountered at depth interval of 1690.5-1700.0 m in a well (Singh et al., 2010). Bulk density of this rock varies between 2050-2200 kg/m3, compressional velocity varies between 2000-2500 m/sec and shear velocity variation is between 600-800 m/sec (Figure 1).

These deep water sandstones show very slow seismic velocities on P and S sonic logs. Bulk and shear moduli of these rocks lie close to Hashin-Shtrikman (1963) lower bound (Figure 2a and b) which suggeststhese rocks to be very unconsolidated. We require an appropriate model to predict seismic velocity as a function of porosity, mineralogy and fluid-content in unconsolidated sediments as these are crucial for identifying deep water hydrocarbon prospects from seismic data. In this study we have tested two effective medium models: Kuster-Toksoz (1974) and Gal (1998),and a simple contact theory: Hertz-Mindlin (Mindlin, 1949) for modeling elastic moduli of the unconsolidated sandstone.

Figure 1. Density vs P-velocity (solid dots) and S-velocity (solid triangles) for a deepwater sandstone from Mahanadi basin (after Singh et al., 2010).

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Figure 2. Porosity versus elastic moduli of sandtone described in Figure 1 with Reuss lower bound and Voigt upper bound over-laid : a) bulk modulus b) shear modulus.

THEORY

We investigated two types of rock physics models, effective medium theory and contact theory to evaluate their usefulness in explaining observed elastic behavior of the unconsolidated sandstone. Of the effective medium theories, Kuster-Toksoz (1974) model considers rock constituents as individual inclusions and composes the effective elastic properties of rock. On the other hand, Gal et al. (1998) have used modified Hashin-Shtrikman upper bound to predict the elastic properties of porous rocks. Hertz-Mindlin contact theory predicts elastic moduli at highest porosity point which is followed by Hashin-Shtrikman model to predict moduli at reservoir porosities.

KUSTER-TOKSOZ (K-T) MODEL

Kuster-Toksoz (1974) model assumes the medium to beisotropic and linearly elastic. It can incorporate inclusions of various shapes using following equations.

?@AB � @CD

4AEFGHIE5

4AJK FG

HIE5L M NO?@O � @CDPCOQR

O6S (1)

?TAB � TCD ?IEFUED

VIJK FUEW

L M NO?TO � TCDXCORO6S YY, (2)

where @AB and TAB

are bulk and shear moduli of effective media, @C and TC are bulk and shear moduli of mineral. @O and TO are bulk and shear moduli of inclusions and NO represents volume fractions of inclusions. For spherical inclusions, PCO and XCO can be written as

PCO LAEFG

HIE

AZFGHIE

,YYXCO L IEFUE

IZFUE, and \C L IE

^

?_AEF`IED

?AEFaIEDb

GAL MODEL

Gal et al. (1998) used modified Hashin-Shtrikman upper bound to predict the effective elastic properties of a porous media as

@cde L @C f g ghij

JhkJEF jkg ghi

JElGHmE

, (3)

Tcde L TC f g ghij

mhkmEFn?jkg ghi D?JElnmED

omE4JElGHmE5

, (4)

where @cde and Tcde are effective bulk and shear moduli, @C and TC are mineral bulk and shear moduli. g is reservoir porosity and gp is highest porosity of rock. @pand Tp respectively represent the bulk and shear moduli of the rock at porosity gpb

HERTZ-MINDLIN (H-M) CONTACT MODEL

For a random packing of spheres, the effective bulk and shear moduli can be modeled using following equations (Mindlin, 1949).

@qr L 2sn?StgDnIn

S`unY?StvDn P<S

wx, (5)

Tqr L ytzv

y?atvD2wsn?StgDnIn

aunY?StvDn P<S

wxYQY (6)

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Figure 3. Results of elastic moduli prediction using different rock physics models. The solid curves represent predicted elastic modulus and solid dots represent the observed data. Prediction from K-T and Gal models are : a) bulk modulus b) shear modulus. Predictions from Hertz-Mindlin contact theory are: c) bulk modulus and d) shear modulus. CN represents coordination number.

where @qr andYTqr are effective moduli of the rock, C is coordination number defined as the total number of contacts a grain has with its neighbors, P is confining pressure, { and � are Poission’s ratio and shear modulus of solid grains. Elastic parameters for quartz, clay and brine used in this study are tabulated in Table-1.

Table 1. Elastic parameters used in rock physics modeling (Mavko et al., 1998).

Bulk modulus

(GPa)

Shear modulus

(GPa)

Bulk density (Kg/m3)

Quartz 36.0 44.0 2650 Shale 6.0 1.5 2500 Brine 2.7 0.0 1010

RUSULTS AND DISCUSSIONS

We used the following simple workflow to compare the validity of the three models used in this study in explaining the elastic behavior of the unconsolidated sandstone under investigation.

i) Elastic properties of grain are estimated through mixing of mineral modulus using Reuss (1929) model.

ii) Elastic moduli of rock skeleton (dry) are calculated through K-T, Gal and H-M models using petrophysical volumes and grain properties.

iii) Saturated rock bulk modulus is estimated using Gassmann (1951) model and fluid properties mentioned in Table 1. Shear moduli of saturated and dry rocks are considered equal, i.e., T|}~ L YT

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Figure 3 shows the predicted elastic moduli for different porosities for all the three models. Both K-T and Gal models over-predict the elastic moduli. H-M model explains the observed data for coordination number varying between 5 and 9 indicating loose contacts between the matrix grains. The accuracy of prediction of elastic moduli through H-M model can be determined from the cross-plot of measured and predicted elastic moduli shown in Figure 4. Correlation coefficient of 0.904 between observed and predicted bulk modulus and 0.943 for the shear modulus indicates satisfactory explanation of observed elastic properties by the Hertz-Mindlin contact theory.

Figure 4. Cross plot of measured versus modeled moduli using Hertz-Mindlin model. Solid dots represent bulk modulus and solid triangles represent shear modulus.

An analysis of mis-prediction of all the three models investigated in this study (Table 2) shows that difference between measured and modeled data is more for shear modulus compared to bulk modulus.

Table 2. Misprediction of elastic moduii by different rock physics models.

Rock physics model

Misprediction (%)

Bulk modulus Shear Modulus Hertz-Mindlin -09 - 06 -15 - 10 Kuster-Toksoz 68 - 78 93 - 95 Gal 58 - 65 95 - 98

CONCLUSIONS

The present study shows that Hertz-Mindlin contact model combined with Hashin-Shtrikman lower bound

closely predicts the elastic properties of deep water Mahanadi sandstone. On the other hand, effective medium theories significantly overpredict the elastic properties suggesting that seismic velocity of deep water Mahanadi sandstone member investigated under this study depend heavily upon contact conditions of grains e.g. coordination number, contact surface area, confining pressure etc. Thus, lateral changes in contact conditions due to any of these factors would play a major role on changing mechanical rock properties which may impact the reservoir performance during production.

ACKNOLEDGEMENT

We are thankful to Schlumberger Asia Services Limited for encouragement and technical support to do this work.

REFERENCES

Gal, D., Dvorkin, J., and Nur, A., 1998, A physical model for porosity reduction in sandstones, Geophysics, 63, 454-491.

Gassmann, F., 1951, Uber die Elastizitat poroser Medien, Vierteil Der Natur Gesellshaft, 96, 1-23.

Hashin, Z., and Shtrikman S., 1963, A variational approach to the elastic behavior of multiphase materials, J. Mech. Phy. Solids, 11, 127-140.

Kuster, G. T., and Toksoz, M. N., 1974, Velocity and attenuation of seismic waves in two-phase media, Geophysics, 39, 587-618

Mavko, G., Mukherji, T., and Dovorkin J., 1998, The Rock Physics Handbook, Cambridge University Press.

Mindlin, R. D., 1949, Compliance of elastic bodies in contact, ASME J. of App. Mech., 16, 259-268.

Reuss, A., 1929, Berechnung der Fliessgrenzen von Mischkridtallen auf Grund der Plastizitatsbedingung fur Einkristalle, Zeitschrift fur Angewandte Mathematik und Mechanik, 9, 49-58.

Singh, N., Bankhwal, S., Das, S., Waraich, R. S. and Mohan, S., 2010, Elastic impedance for gas sands discrimination and risk mitigation – A case study in deep water of Mahanadi Basin, 8th Biennial International Conference & Exposition on Petroleum Geophysics, Society of Petroleum Geophysicists, 274-279.

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