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Acta Geodaetica et GeophysicaA Quarterly of the Hungarian Academyof Sciences ISSN 2213-5812Volume 48Number 3 Acta Geod Geophys (2013) 48:347-361DOI 10.1007/s40328-013-0023-7

Discrimination of fizz water and gasreservoir by AVO analysis: a modifiedapproach

Perveiz Khalid & Shahid Ghazi

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Acta Geod Geophys (2013) 48:347–361DOI 10.1007/s40328-013-0023-7

Discrimination of fizz water and gas reservoir by AVOanalysis: a modified approach

Perveiz Khalid · Shahid Ghazi

Received: 1 December 2012 / Accepted: 14 May 2013 / Published online: 4 June 2013© Akadémiai Kiadó, Budapest, Hungary 2013

Abstract Amplitude versus offset response is analogous to variation in P-wave velocity re-sulting from different pore fluid saturations. However, the input parameters of fluid mixturessuch as fluid modulus and density are often estimated using volume average method, and theresulting estimates of fluid effects can be overestimated. In seismic frequency band, the vol-ume average method ignores the heat and mass transfers between the liquid and gas phases,which are caused by pore pressure perturbations. These effects need to be accounted for theinterpretation of the seismic events and forward modeling of fizz water reservoirs. The con-ventional model is corrected in present study by considering the thermodynamic propertiesof the fluid phases. This corrected model is then successfully applied on a gas producingfield in the North Sea. AVO response, based on the corrected model is highly affected bypressure related variations in bulk modulus of multi-phase formation fluid. Velocity pushdown effect appears, as the free gas saturation generates stronger AVO response than ob-tained by a conventional AVO model. The, present research reveals that such response ishelpful to discriminate fizz water from commercial gas, to detect primary leakage of gas(CO2 or CH4) from geological structures and to model free gas effects on seismic attributes.

Keywords Conventional model · Thermodynamic properties · Fizz water · Gas reservoir ·AVO analysis

1 Introduction

Differentiation of formation fluids and their saturation is one of the important tasks in explo-ration geophysics. For this purpose, many techniques have been used, for example, velocity

P. KhalidLab. Fluides Complexes, UPPA, CNRS, BP1155, 64013 Pau Cedex, France

P. Khalid · S. Ghazi (�)Institute of Geology, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistane-mail: ghazigeo6@gmail.com

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Fig. 1 Typical effect of gas (orliquid) saturation on P-wavevelocity of a reservoir rock. Atshallow conditions, minimumvalue of VP is attained atSg ≈ 7 % (Kg/Kl ≈ 8 × 10−3).At deep conditions minimumvalue of VP is shifted to high gassaturation Sg ≈ 13 %(Kg/Kl ≈ 5 × 10−2). This shiftshows the pressure effects onfluid properties

modeling (Wang et al. 1990), amplitude attenuation (Cadoret et al. 1998), amplitude varia-tion with offset (AVO) analysis (Hilterman 2001), elastic inversion for shear and compres-sional impedances (Gonzaléz 2006), fluid factor (Smith and Gidlow 1987). Interestingly,all the above mentioned techniques are functions of three fundamental parameters of rock-fluid system: effective density (ρeff ), shear velocity (VS ) and compressional velocity (VP ).Only VP and ρeff are directly analogous to the fluid properties (density, ρf and modulusof incompressibility, Kf ). The fluid modulus or inverse of the compressibility of the fluidhas no impact on VS , even so, VS depends on the fluid density to a certain extent (Mavkoet al. 2009). Furthermore, the effect of fluid viscosity, rock permeability and mixing inho-mogeneities are additional parameters influencing the seismic velocities (Barton 2007) butare beyond the scope of this paper.

Since the last four decades, AVO analysis has become a prominent and useful techniqueto predict fluid effects on the seismic properties of saturated (or partially saturated) rocks,as a direct indicator of hydrocarbons (Batzle and Han 2001; Fahmy and Reilly 2006) and inreducing dry holes risk (Han and Batzle 2002). The bulk properties of saturated rocks aresensitive to the properties of fluids present within the pores of these rocks. Pore fluid natureand saturation can change AVO response significantly (Batzle et al. 1995). The P-wave re-flection coefficient (RPP ) from a reflection interface is a function of P-wave velocity (VP ),S-wave velocity (VS ), the effective density of rock-fluid composite (ρeff ) and the incidentangle of the seismic waves (θ )

RPP = f(VP ,VS,ρeff , θ). (1)

From (1), the reflection response of a fluid (oil, water or gas) saturated rock can be eas-ily calculated. However, the quantitative description of effects of fluid saturation especially,when the fluid is gas with small saturation, on seismic response is one of the most im-portant challenges in seismic exploration and time-lapse (4D) monitoring. The saturatedVP exhibits a very characteristic saturation dependent behavior at in-situ temperature andpressure conditions and with burial depth (Fig. 1). The apparition of a free gas phase ina reservoir filled with oil or water has for effect to considerably decrease VP , which of-ten produces a strong impedance contrast with overlying/underlying rock layer. Experi-ments show, if liquid is replaced by free gas, VP decreases sharply and continuously ina narrow interval of gas saturation (Sg) 5–10 % to minimum value. Then it increases

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linearly but very slowly, and further increase in Sg reaches up to dry value. In case ofshallow gas reservoir conditions with high difference between bulk moduli of water andgas (e.g., Kg/Kl < 10−2 where Kl and Kg stand respectively for bulk modulus of liquidand gas phase), the point of minimum is shifted towards lower values of Sg . However, indeep gas reservoirs, the difference between Kg and Kl values is very small. This mini-mum is shifted towards higher gas saturation mainly due to the density effect (Domenico1974). However, this behavior of VP is less pronounced when the phase distribution isspatially heterogeneous (patchy) at the scale of seismic wavelength (Cadoret et al. 1995;Toms et al. 2006).

This poor sensitivity of VP to Sg is generally modeled by using a poroelastic model,for example Gassmann (1951) under adiabatic condition (i.e., no transfer of heat betweenfluid and rock-forming minerals at the passage of seismic waves). Recent study argued thatthis adiabatic condition is not valid in surface seismic frequency band (Khalid 2011). InGassmann’s model the effective bulk modulus of saturating two-phase fluid (liquid and gas)is approximated by the harmonic (or Reuss) average of the liquid and gas bulk moduli.This averaging procedure is often referred to as Wood’s average (Wood 1930). In the aboveGassmann-Wood model with homogeneous fluid distribution pattern, the P-wave velocityand impedance of porous rocks saturated with different liquid and gas phases (such as waterand gas in shallow reservoirs) are almost insensitive to gas saturation, except for low gas sat-urations (Fig. 1). Nevertheless, the exact measurements of the low-gas saturation effects onseismic attributes remain questionable (Gomez and Tatham 2007). The exploration industryneeds to have a reliable method to estimate the effective bulk modulus and the density ofthe multi-phase (oil and gas or water and gas) pore fluids due to very strong influence of thepore fluid properties on seismic response. This is true in particular when pore pressure (P )drops below the bubble point pressure of the fluid (Pb) at any temperature (T ) where dis-solved gases come out of solution and appear as free gas. Batzle and Wang (Batzle and Wang1992) proposed a widely accepted set of empirical relationship to overcome this problem.However, these correlations are unable to properly account value of Kf when gas appearsas free gas.

Khalid (2011) proposed a simple rigorous method (see Appendix), based on thermody-namic principle and follows the black oil simulation with proper account of heat and masstransfers between the phases during pressure perturbations, to estimate two-phase fluid bulkmodulus and sound velocity under adiabatic conditions. It has been successfully applied todifferent types of reservoir fluids including gas-water, CO2-water, gas-oil and gas conden-sates (Khalid 2011). The aim of this paper is to extend this method to estimate AVO responseof low gas-saturated reservoirs. In present research, conventional and modified methods areapplied on real data set, taken from a gas producing field of the North Sea to analyze theeffectiveness of the method.

2 Sensitivity of seismic properties to partial gas-saturation

Pore fluid properties can influence reflection response of its host rock. The response ofdifferent gases in the absence of a rock matrix that affects seismic response is investigated.

2.1 Seismic response of gases

Reservoir gases are mixtures of various hydrocarbon and non-hydrocarbon gases. Seismicresponses of these reservoir gas mixtures are much different than those of the pure individ-ual gases (Han and Batzle 2004). The bulk moduli of incompressibilities of the reservoir

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Fig. 2 (a) Bulk modulus and(b) density of common reservoirgases methane (C1), ethane (C2),propane (C3), butane (C4) andpentane (C5) as a function ofreduced pressure at T = 0.9Tc ofeach gas. Data is taken from NIST(http://webbook.nist.gov/chemistry/)

gases, including hydrocarbon and non-hydrocarbon, are 10–103 times smaller than those offormation water and oil (Whitson and Brulé 2000). Similarly, the densities of these gasesvary from gas-like to liquid-like forms depending on the in-situ T and P conditions. Fig-ure 2 shows the density and the adiabatic bulk moduli of some common reservoir gases as afunction of T and P , calculated by using NIST data set. For the sake of comparison, theseparameters are plotted against reduced pressure (Pr = P/Pc , where Pc is critical pressure ofeach gas) and reduced temperature (Tr = T/Tc , where Tc is critical temperature) of each gas.A very sharp noticeable change in both Kf and ρf of each gas, at Pb , shows phase transitioneffect. Kf and ρf can vary more than one order of magnitude across the liquid-gas phaseboundaries (at bubble point conditions). From Fig. 2a, it is also clear that lighter gases havehigher values of bulk modulus whereas heavier gases have lower values of bulk modulus.Moreover, lighter gases have low density values as compare to heavier gases (Fig. 2b).

2.2 Seismic response of fluid mixtures

Newton-Laplace equation is commonly used to calculate the adiabatic bulk modulus of fluid,if measurements of density and acoustic velocity in the fluid are available. This equation is,

Kf = ρf V 2P , (2)

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where ρf = Slρl +Sgρg is the fluid density and VP is the acoustic velocity in the fluid in theabsence of rock (Sl and Sg are the saturations of liquid and gas, ρl and ρg are the densities ofliquid and gas phases respectively). In the absence of these measurements, the bulk modulusof fluid mixture is estimated by using some volume average method. The most commonlyused method is proposed by Wood (1930).

2.2.1 Wood’s average

In this averaging method, a mixture of liquid and gas treats the liquid and gas as two separatephases. Thus, the effective modulus of the fluid mixture (Kf ) is taken as an isostress averageof the phase moduli weighted by their volume fraction:

Kf = [Sl/Kl + Sg/Kg]−1. (3)

In (3), Kl and Kg are the adiabatic bulk moduli (reciprocal of the adiabatic compressibil-ities) of liquid and gas phases respectively. Wood’s approximation holds if two essentialassumptions are satisfied. First, the liquid and the gas phases are homogeneously distributedat microscopic scale within the pore space. This saturation state is referred to as uniformsaturation. The second assumption is that the liquid and the gas phases remain frozen orunrelaxed at the passage of the seismic wave (Khalid 2011). The term frozen means no heatand mass transfer between liquid and gas phases at the passage of low frequency seismicwaves. The characteristic frequency that delineates the relaxed and unrelaxed frequencyregimes is obtained by comparing the acoustic time scale—that is, the reciprocal of seismicfrequency—to the relaxation time of the process L2/D, where D is the diffusion coeffi-cient and L the heterogeneity length scale. When this relaxation time is much larger thanthe seismic wave period, i.e., when the seismic frequency f is much larger than the char-acteristic frequency fc ∼ D/L2, then the rock/fluid system can be considered as unrelaxedwith respect to the mechanism of interest. Maximum attenuation is expected when fc andthe sampling frequency f lie in the same range. For f much smaller than fc , the elastic andseismic properties tend to be at their relaxed (low-frequency) limit.

2.2.2 Thermodynamic approach

Khalid et al. (2009) and Khalid (2011) showed clearly with the help of different reservoirfluid mixtures that (3) over-estimates the adiabatic modulus at given temperature and pres-sure conditions. A new method, which follows the black oil model, proposed by Khalid et al.(2009) and Nichita et al. (2010) is adopted to calculate two-phase adiabatic bulk modulus inquasi-static or relaxed limit with the consideration of heat and mass transfer effects betweenliquid and gas phases i.e.,

Kf =[K−1

T − α2P T V

CP

]−1

. (4)

Where, KT is the isothermal bulk modulus in GPa, routinely measured in PVT laboratorymeasurements or black oil simulations (McCain Jr 1990). CP is the apparent total heat ca-pacity in J/kg/K, αP is the thermal expansion coefficient at constant pressure in Pa−1, V isthe total volume of liquid and gas phases at in-situ conditions in m3/mol and T is the forma-tion temperature in Kelvin. The detailed derivation of (4) is given in Appendix. Relaxed andfrozen (unrelaxed) moduli, calculated by (4) and (3) respectively; differ strongly from eachother, especially in low gas-saturation (Fig. 3). A very large difference between (3) and (4)appears when dissolved gas starts to come out of solution. This happens when the pressureof the fluid mixture falls below the bubble point pressure of that mixture.

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Fig. 3 Effective fluid modulusof a gas-oil mixture taken fromStenby et al. (1996) at T = 344 Kand Pb = 29.8 MPa. Doublearrow shows the bigdiscontinuity between Wood’svalue and thermodynamics

3 Methodology for AVO analysis

Zoeppritz equations or their approximations are widely used for AVO analysis of an isotropicand homogeneous elastic media. In this work the exact Zoeppritz equations are used becausethe terms for far offsets or large angles contain fluid saturation information. Fluid substitu-tion is one of the principle steps in AVO modeling.

3.1 Fluid substitution models

Conventionally, for low frequency seismic modeling, Gassmann (1951) fluid substitutionmodel is frequently used to express the relationship among the bulk modulus of the fluid-saturated rock (Ksat), the bulk modulus of the drained rock (Kdry), the rock-forming mineral(Km) and to the adiabatic bulk modulus of the saturating fluid (Kf ) without referring toany specific pores geometry. Gassmann derived Ksat under quasi-static assumption in thesimplest form is:

Ksat = Kdry + α2M−1, (5)

where α = 1−Kdry/Km is the Biot’s coefficient or coefficient of effective stress and is alwaysless than 1 in real porous media. It is a complex function of porosity, clay content, poregeometry, grain size, mineral composition etc. (Hilterman 2001; Russell et al. 2003). Themodulus

M = φ

Kf

+ α − φ

Km

(6)

is defined as the pressure needed to force fluid into formation without changing volume andφ is rock porosity. In reality, solid mineral is incompressible, i.e., Km → ∞ or Km � Kf ,therefore, the second term of (6), is much smaller than the first term, thus can be neglected.This leads to a linear form of (5). The linear approximation of Ksat valid for high porosities(φ > 15 %; Han and Batzle 2004; Zinszner and Pellerin 2007) is

Ksat ≈ Kdry + α2

φKf . (7)

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The fluid contribution in effective bulk modulus of saturated rock is represented by secondterm of right hand side, known as pore modulus and is controlled by porosity. The termα2/φ, called gain function, is an increment of bulk modulus because of fluid saturation.The value of this gain function for different sands is in the range of 1.8–3.0. The importantdiscovery of the Gassmann’s equations is that the rock shear modulus is independent of thenature and amount of saturating pore fluid, thus

μsat = μdry = μ. (8)

However, (8) does not hold for carbonate rocks (Baechle et al. 2005). The seismic velocitiesin saturated porous rocks are

VP =(

Ksat + 4μ/3

ρeff

)1/2

, (9)

VS = (μ/ρeff )1/2, (10)

where

ρeff = (1 − φ)ρm + φρf , (11)

is the effective density of the saturated rock (ρm and ρf being the mineral and fluid densities,respectively). Seismic velocities are estimated by the following two approaches:

3.1.1 Gassmann-Wood (GW) model

The seismic properties of two-phase fluid saturated rocks under frozen phases assumptionor unrelaxed state are modeled conventionally by using Gassmann-Wood (GW) model. InGassmann fluid substitution equations, the effective bulk modulus of the two-phase (liquidand gas) fluid is approximated by the saturation-weighted harmonic average of the liquidand gas bulk moduli as given in (3).

3.1.2 Gassmann-thermodynamics (GT) model

Our current understanding is that heat and mass transfer take place between the differentfluid phases when pressure varies at the passage of the seismic wave or during productionstages, thus liquid and gas phases are in relaxed state (Khalid 2011). At very low frequency,pore pressure has sufficient time to equilibrate the transition effects after the passage of seis-mic waves, therefore, the fluid and rock frame may consider in relaxed state. The effectivefluid modulus is then calculated by using (4) and injected in (5).

4 Results

The conventional Gassmann-Wood and modified Gassmann-thermodynamic fluid substitu-tion models are applied on a well log data from the Dutch sector of North Sea. The sonic,density, gamma ray, resistivity and porosity logs are acquired for this well. Based on gammaray log, density and sonic logs, the interval from 4095 m to 4176 m (81 m) is marked as reser-voir (Fig. 4). The reservoir is mainly sandy in character with an average porosity φ ≈ 0.20.The top of the reservoir is marked as shale-sand contact whereas the base of the reservoir is

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Fig. 4 Logs data used in this study from North Sea

Table 1 Density and bulkmodulus of rock componentsused in this study

Quartz Water Gas

Density (kg/m3) 2650 1000 180

Modulus (GPa) 37 2.25 0.06

marked as sand-shale contact. The seismic parameters of the cap rock are: VP = 4685 m/s,VS = 2340 m/s, ρeff = 2250 kg/m3. Because of the non-availability of shear sonic log data,VS is derived using the established empirical relations (e.g., Han 1986). The gas distribu-tion is homogeneous in water at pore scale at in-situ temperature and pressure conditions(T = 402 K and P = 31 MPa).

4.1 Rock physics parameters

The rock physics parameters (elastic modulus and densities) of rock components used inthis study are given in Table 1. Kdry and μ for well-consolidated rocks can be measured inlab. However, in case of unconsolidated rocks, these measurements turn more complicateddue to non-linearity in elasticity and time-dependent properties (Gardner et al. 1965). In thepresence of well log data, Kdry and μdry can be easily deduced from (5) and (9). The Kdry

and μ are estimated from those parts of sonic log data where there is full water-saturation.

4.2 Effective fluid modulus

Kf of this water-gas mixture in unrelaxed and relaxed states are calculated by using (3)and (4), respectively. The percentage difference in Kf computed by both approaches (�Kf )is plotted (Fig. 5) at various values of Sl . At P > Pb , gas is fully dissolved into water,

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Fig. 5 Percentage difference inKf of water-gas mixture atT = 402 K and P = 31 MPacalculated by Wood andthermodynamic method

Fig. 6 P-wave velocity of thereservoir layer saturated withwater-gas mixture at T = 402 Kand P varies below Pb

(=31 MPa) modeled by usingGassmann-Wood (GW) andGassmann-thermodynamics (GT)approach. Double arrows markthe discontinuities inGassmann-thermodynamics VP

at the appearance of free gas veryclose to the bubble point pressure

and Wood and thermodynamic Kf are identical. However, when dissolved gas starts toappear as a free gas, at the crossing of Pb , the relaxed Kf decreases dramatically (up to40 % that of the single phase liquid). On the other hand, Wood values vary much moresmoothly and continuously with pressure or liquid saturation. The difference between Woodand thermodynamic fluid moduli is important at low gas saturations. At high gas-saturation,�Kf is large in percentage but the values of Kf are very small as compared to Kdry and willhave negligible effect on saturated rock properties.

4.3 Seismic velocities

The VP , VS and ρeff of saturated sands are computed as functions of water-saturation byusing (5)–(11). The Wood and thermodynamic Kf calculated in previous subsection are in-jected in Gassmann’ equations to compute Ksat by (5) and the corresponding VP by (9). Theresults for VP as a function of liquid saturation are depicted in Fig. 6. Since we are interestedin low gas saturation, near to liquid/gas phase boundary, therefore, liquid saturation axis islimited to 0.85. Very small amount of gas reduces VP dramatically because gas reduces Kf

significantly and has direct effect on VP via Ksat . Additional gas does not reduce VP signifi-cantly because further change in Kf is nominal. The difference between both approaches is

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Fig. 7 (a) Vertical profiles ofP-wave acoustic impedances forbackground sand, low gassaturation and high gassaturation, (b) zero-offsetsynthetic seismic traces for highgas saturation, (c) GT based lowgas saturation, (d) GW based lowgas saturation, (e) backgroundsand

calculated to be maximum at the appearance of free gas and decreases with increase in Sg .The gas sand has a P-wave velocity of approximately 3750 m/s and the background sand(water sand) about 4000 m/s. Fluid has no effect on shear modulus; therefore, change in VS

due to gas is only because of change in effective density of saturated rock. The density ofthe background sand is 2270 kg/m3, and of the gas sand is 2100 kg/m3. The drop in effectivedensity is merely 7.5 % from water sand to gas sand.

4.4 Zero-offset synthetic modeling

A three layer model is used to apply the above described models. It is important to assesshow phase transition and transfer (heat and mass) affect seismic signatures of partially sat-urated reservoirs. The normal (zero-offset) seismic traces are known to be very sensitive toVP and ρeff . 1D zero-offset synthetic seismograms are generated for sands with 100 % wa-ter saturation (background sands), low gas saturation (Sg ≈ 1 %) and gas sand (Sg ≈ 70 %)by convolving reflectivity series with a zero-phase Ricker wavelet of 30 Hz dominant fre-quency. The top and bottom shale layers have higher P-wave velocities than the sandwichedsand layer. Depending on whether GW or GT method is used for velocity or impedance mod-eling, very different seismograms are expected for the same low gas-saturations. Figure 7shows the vertical profiles of P-wave acoustic impedance (IP = VP ρeff ) for various gas sat-uration, the synthetic seismograms for background sand, gas sand and fizz water computedby using both GW and GT approaches. Clearly reflections at reservoir boundaries are verystrong when calculated by using GT velocity model instead of GW model, especially at lowgas-saturation (Sg ≈ 1 %). The reflection amplitudes calculated by GW model at low gas-saturation look identical to those of background sand (Fig. 7). Another interesting feature isthe velocity pushdown effect at the sand-shale interface obtained when using the GT modelunder the assumption of constant thickness (Fig. 7).

4.5 Gas saturation effect on AVO response

The expected AVO response of low gas saturated reservoir is estimated by using the mod-eled velocities and densities. The exact Zoeppritz equations are used to compute RPP as a

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Table 2 Seismic velocities and densities used for synthetic AVO modeling

VP (m/s) VS (m/s) ρeff (kg/m3)

GT GW

Background sand 4000 4000 2475 2270

Low gas 3780 3870 2476 2267

High gas 3810 3812 2552 2135

Fig. 8 P-wave reflectioncoefficient versus incident anglefor background sand, lowgas-saturation and highgas-saturation computed on thebase of GW and GT velocitymodels

function of incident angle for background sand, low gas-saturation and high gas-saturation.The AVO intercept (A) and gradient (B) are estimated. The input VP , VS and ρeff values atvarious gas saturations are listed in Table 2. The AVO curves for background sand, gas sand,and fizz water are plotted in Fig. 8 by using GW and GT velocity models as input. It is clearthat RPP increases with increase in offset and behaves as class III reservoir. The intercept‘A’ changes from −0.0745 to −0.1342 and gradient ‘B’ changes from −0.1394 to −0.1581when water is replaced by gas. AVO intercept and gradient show effective attributes to dis-tinguish gas saturation.

4.6 Impedance cross-plot

Estimation of the acoustic impedance of P-wave and velocity of shear wave from the seis-mic data will increase our ability to discriminate gas saturation and fluid phases. The mod-eled acoustic impedance of P-wave is plotted against the acoustic impedance of S-wave(IS = VSρeff ) in Fig. 9. The results suggest that for fizz water (low gas saturation), GT-based IP /IS values are smaller than those of from GW. IP /IS cross-plot values based onGassmann-Wood model are very similar to that of from back ground sand (fully water satu-rated) thus make it difficult to distinguish between background sand and fizz water. However,IP /IS cross-plot values based on Gassmann-thermodynamic approach suggests that low gassaturation can be easily distinguishable from high or commercial gas saturation and background sand. Gas values are much different than fizz water. This is because of change ineffective density as discussed in previous section.

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Fig. 9 Cross plot of P-waveacoustic impedance versusS-wave acoustic impedance forbackground sand, fizz water andgas sand

5 Discussion

The influence of gas saturation and the liquid/gas phase transition effects on the seismicproperties of saturated sand were determined. Gassmann fluid substitution equations wereused with combination of Wood’s or thermodynamic approaches to estimate fluid modulusin relaxed (under thermodynamic equilibrium) and unrelaxed (frozen phases) states whenpore pressure is below than the bubble point pressure of the formation fluid. VP is commonlyused to interpret fluid saturation and fluid types in reservoirs. The abrupt reduction in VP

with the appearance of first few percent of gas saturation controls the seismic response, andmakes it difficult to distinguish gas-saturated sand from fizz water (or low gas-saturatedsand). Our modified method based on thermodynamic principles may helpful to resolve thisissue.

AVO analysis is a promising technique to detect low gas-saturation effects on seismicattributes. However, the use of AVO analysis is very delicate as its success is subject tocorrect description of seismic properties of multi-phase fluid mixtures. Therefore, realisticgas, water or oil, and rock properties must be used to evaluate fluid mixture effects on seis-mic properties of reservoir rocks. The heat and mass diffusion associated with the phasetransitions (from single-phase liquid to two-phase liquid and gas) have significant effectson seismic and elastic parameters in terms of sharp decrease in bulk modulus and P-wavevelocity of partially-saturated rocks. The phase transition effects on saturated bulk modulusand VP are much larger at low gas saturation than at higher gas saturation. An appropriateaccount of these effects shows that a small amount of free gas gives rise to very large AVOanomalies.

The analysis for the North Sea gas-producing field reveals that the saturated P-wavevelocity is over-estimated by the conventional Gassmann-Wood’s approach because of ig-noring the transfers. The conventional model is therefore corrected by considering the ther-modynamic properties of the fluid phases. Modified (GT based) AVO enhanced the visibilityof the calculated reflectivity almost by order of 2 than the conventional (GW based) AVOat the same gas saturation. These enhanced AVO anomalies will be very helpful to interpretseismic events, reservoir monitoring, to detect primary leakage of gases from geologicalstructures such as CO2 sequestration, and to model free gas effects on seismic attributes.

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Variation in normal reflectivity at the top and bottom of a reservoir and the variation intravel time at the bottom of the reservoir before and after the appearance of free gas are twophysically meaningful attributes which are observable directly on seismic sections and canprovide information about fluid saturation. The results show that a velocity pushdown onseismogram, generated based on Gassmann-thermodynamic models is an indicator of theappearance of the free gas but this velocity pushdown is not as enhanced as we expectedto become a low and high gas saturation discriminator (�VP ≈ 210 m/s at low Sg and�VP ≈ 250 m/s at high Sg). However, the IP versus IS cross-plots may helpful to distinguishlow gas saturation from high gas saturation. We suggest performing complete AVO analysisof P-converted-S (PS) velocities, as the far-offset PS data may be helpful to distinguish lowand high gas saturations.

6 Conclusions

Conventional rock physics model, Gassmann-Wood overestimates the P-wave velocity ofpartially saturated reservoir, especially in the zone where gas saturation is very small(<5 %). Gassmann-thermodynamic velocities generate stronger AVO responses than thoseobtained by a conventional AVO model especially in vicinity of bubble point pressure of theformation fluid. The present research reveals that such response is helpful to discriminatefizz water from commercial gas, to detect primary leakage of gas (CO2 or CH4) from geo-logical structures and to model free gas effects on seismic attributes. Further investigationswith large data set, are required to construct IP/ARE trend. The pressure effects on fluid androck properties should also include in seismic modeling.

Acknowledgements The authors would like to acknowledge NLOG—Netherlands Oil and Gas Portal forproviding data. We are grateful to Daniel Broseta (University of Pau, France), Dan Vladimir Nichita (Univer-sity of Pau, France), Jacques Blanco (Physeis Consultant) and Farrukh Qayyum (dGB Earth Sciences, TheNetherlands) for valuable discussions and review of this manuscript.

Appendix: Relaxed two-phase compressibilities calculated from an equation of state(EOS)

This appendix describes the method used in this paper to compute the isothermal and adia-batic (or isentropic) bulk moduli of thermodynamically-equilibrated (or relaxed) co-existingliquid and gas phases using an equation of state (EOS) and expressions for the enthalpiesof the liquid and gas phases (Whitson and Brulé 2000). These moduli, labeled respectivelywith subscript T for isothermal and S for adiabatic, are related by the following formula,valid both in single-phase and in the two-phase regions

Kf =[K−1

T − α2P T V

CP

]−1

. (A.1)

In (A.1), V is the total volume (V = Vl + Vg in two-phase conditions), αP =1/V (∂V/∂T )P is the isobaric thermal expansivity, and CP the isobaric heat capacity. (Inthese partial derivatives, the overall mixture composition is kept unchanged.) In the one-phase region, αP , CP and the isothermal bulk modulus

KT = 1/βT = [−1/V (∂V/∂P )T

]−1(A.2)

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are easily obtained from an EOS. In (A.2), βT is the isothermal compressibility of the fluid.In the two-phase region, βT and αP are obtained numerically by determining phase compo-sitions from a phase-split (flash) calculation and then computing the phase volumes Vl andVg at fixed temperature and neighboring pressures (to obtain βT ), and at fixed pressure andneighboring temperatures (to obtain αP ).

Similarly, the two-phase heat capacity CP is obtained as the derivative with respect totemperature of the enthalpy of the two-phase system. The enthalpies of the liquid and gasphases are the sum of an ideal term and a departure term directly related to the equation ofstate. The only ingredients needed for calculating the departure terms are the phase com-positions obtained by the flash calculation and the phase volumes. The ideal terms are thecombination (weighed by the molar fractions) of the ideal enthalpies, whose values hadobtained from Reid et al. (1988). The two-phase CP is obtained numerically from the two-phase enthalpies calculated at two neighboring temperatures.

The EOS used for the aqueous fluids is the Peng-Robinson modified by Soreide andWhitson (1992) EOS. This EOS provides accurate phase compositions. The molar volumeof the liquid (aqueous) phase is calculated by using the following relation

Vl(T ,P ) = VH2O(T ,P )xH2O + Vj (T )xj , (A.3)

where VH2O is the molar volume of pure water at given T and P , and Vj is the apparentpartial molar volume of the non-aqueous component j . We have used the values of Vj de-duced from the density measurements by Hnedkovsky et al. (1996). The molar volume ofthe non-aqueous phase is obtained by using the Lee and Kesler (1975) equation for thecompressibility factor.

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