Patchy Saturation Model Research Articles

A model combining patchy saturation and moisture-induced elastic weakening with application to ultrasonic monitoring under varying water saturation

SUMMARY Water is known to induce weakening on the static mechanical properties of rocks. However, injection-based operations such as EGS or EOR are commonly monitored through seismic methods involving dynamic moduli. It is therefore important to understand and quantify the effect of water-weakening on dynamic properties. In this study, we performed water injection tests on microporous carbonate rocks (two chalks from the Mons Basin) with ultrasonic monitoring of P-wave velocity and attenuation in order to observe the evolution of the rock moduli with varying water saturation. Our experimental results were interpreted through (i) a classical patchy saturation or PS model and (ii) the same model coupled with water weakening effect through modulus reduction induced by surface energy decrease induced by water in the fluid–rock system, called the WW-PS model. We show that the WW-PS model can better fit the experimental data than the PS model for both selected chalks, but also the previously published data for Sherwood sandstone. Therefore fluid–rock interaction needs to be taken into account when dealing with a fluid not in equilibrium with the host reservoir in fluid injection operations. An extension to reservoir scale modelling is proposed to emphasize the potential impact of water weakening at larger scales.

Hydrate Attenuation Characteristics Based on the Patchy-Saturation Model

At present, attenuation characteristics of hydrate applicable to the seismic frequency band are still controversial. In this study, the dispersion and attenuation characteristics of hydrate in different occurrence modes were defined from the mesoscale perspective, and the saturation of hydrate in the study area is estimated. Based on effective medium theory and cementation theory, the skeleton elastic modulus of the sedimentary layer was obtained in the present study. The variation of P-wave attenuation with hydrate saturation was obtained by the patchy-saturation theory. P-wave attenuation increased with saturation when hydrate occurred in the suspension mode. P-wave attenuation decreased with saturation when hydrate occurred in the particle-contact or cementation mode. The particle-contact mode and cementation mode hydrate made the P-wave attenuation peak shift to the right. The influence of the cementation mode on attenuation was greater than that of the particle-contact mode. The conclusions of this study are applicable to the frequency range of seismic exploration, thus solving the problems of hydrate saturation prediction and resource quantity calculation assessment in the study area.

Lithology and fluid discrimination using combined seismic attributes with the constraint of rock physics: a case study from W field, South Sumatra Basin

Reservoir characterization and fluid discrimination based on seismic reflection amplitude play important roles in seismic exploration industry. Stable fluid-sensitive attributes from seismic data can help reduce uncertainties of hydrocarbon prediction in interwell locations and increase the reliability of drilling plans. In this study, in combination with seismic AVO inversion impedance and the rock physics template analysis, we proposed a new attribute (DI) to discriminate the hydrocarbon-associated anomalies and predict the reservoir parameters including porosity and water saturation quantitatively in Upper Gumai formation of W field, South Sumatra Basin. The new attribute (DI) is constructed using a set of combined impedances derived from prestack seismic inversion with the constraint of rock physics. Numerical modelling based on patchy-saturated model was implemented to test the sensitivity and stability of the new attribute and results showed that the DI attribute can predict the existence of hydrocarbon-filled sands with less ambiguity. With known well log data in W field, a feasibility study including cross-plotting and histogram methods was carried out and concluded that the DI attribute contributes higher resolution in distinguishing the hydrocarbon-filled sands from the background trend. In the process of quantitative interpretation, the DI attribute shows a good regression relationship with porosity and water saturation properties within the hydrocarbon sands with the correlation coefficients reaching 92% and 85%, respectively. By using seismic AVO inversion impedance, combining the application of the DI attribute and Vp/Vs ratio for lithology and fluid contents discrimination was conducted to improve the reservoir prediction accuracy in the field. Application results show that low values of the DI attribute (<18,000 m/s.g/cc) was indicative of hydrocarbon-filled sands effectively while Vp/Vs ratio presented a higher resolution in separating wet sand, dry-sand from shale. By using the linear regression relationship derived from cross-plotting analysis with well data, we calculated the volumes of porosity and water saturation from DI attribute and successfully screened out the hydrocarbon accumulation distribution, which reveals the potential zones of exploration interest in South Sumatra Basin.

An Exact Expression for the Effective Bulk Modulus for Acoustic Wave Propagation in Cylindrical Patchy-Saturation Rocks

Abstract Hydrocarbon reservoirs often contain partially gas-saturated rocks that have attracted the attention of exploration geophysicists and geologists for many years. Wave-induced fluid flow (WIFF) is an effective mechanism to quantify seismic wave dispersion and attenuation in partially gas-saturated rocks. In this study, we focus on the local fluid flow induced by variations in fluids in different regions and present a new model that describes seismic wave propagation in partially gas-saturated rocks, namely, the cylindrical patchy-saturation model. Because the seismic wave velocity and attenuation oscillate at high frequencies, it is not ideal for studying dispersion and attenuation caused by WIFF. To avoid the high-frequency oscillation in the cylindrical patchy-saturated model, we use an approximation to the Newman function instead of the full Newman function to calculate the effective bulk modulus. We then calculate the P-wave velocity and attenuation of the proposed model and interpret the lab-measured data. The proposed model is an alternative patchy-saturation model that can explain the problem of high-frequency oscillation and low-frequency attenuation.

Continuous Recording of Viscoelastic Relaxation Processes at a Constant Ultrasonic Frequency Due To Wave‐Induced Fluid Flow in a Microporous Carbonate Rock

AbstractIn a set of water injection, imbibition and drying tests on the Obourg Chalk, relaxation processes induced by variations in water saturation were continuously recorded at a constant ultrasonic frequency, with a peak in attenuation concomitant to a velocity increase from a lower to an upper bound. This behavior is well described by standard viscoelastic models, considering a continuously changing relaxation frequency which at water saturation above 80% matches the frequency of our ultrasonic pulse generator. Using a patchy saturation model, we show that the heterogeneity in fluid distribution is responsible for this relaxation phenomenon which could be observed at the ultrasonic frequency, thanks to the very fine scale of the rock microstructure combining low permeability and high porosity. We believe that our detailed data set can feed new models or help improve existing ones for a better understanding of wave‐induced fluid flow processes in reservoir rocks.

Reflection coefficients of P‐waves in partially saturated fractured media

ABSTRACTWave‐induced fluid flow, an important mechanism in seismic wave attenuation, is considered in the amplitude variation with the offset technique. In a fractured marine carbonate reservoir, fractures and pores develop simultaneously, such that wave‐induced flow is an important mechanism in attenuation caused by the fluid flow between pores as well as between pores and fractures. However, these two types of attenuation are typically investigated separately or studies assume that the pores and fractures are dry or saturated by the same fluid. Rock pores are usually saturated by a mixture of two or more fluids, such that the fracture and pore filling fluids may be different. During variation with offset reservoir prediction and fluid identification, the influence that the porosity, fracture, and fluid have on the P‐wave reflection coefficient should be considered. The patchy saturation model can describe the seismic wave dissipation caused by the wave‐induced flow between pore fluids, whereas the Norris model can describe seismic wave dissipation caused by the fluid flow between fractures and pores. This study considers both the patchy saturation model and Norris model to calculate the amplitude variation with the offset P‐wave reflection coefficient under different conditions. Combining the saturation and Norris models forms a new model, which is regarded as a transversely isotropic medium with a vertical symmetric axis, and can be extended to any incident angle through the relaxation function and the high‐ and low‐frequency elastic limits of the stiffness tensor, where the complete effective stiffness tensor of the new model can be obtained. Finally, the amplitude variation with offset reservoir technology is used to determine the influence of model parameters on the reflection coefficient of P‐waves under different angles and frequencies, including fracture weakness, fluid saturation and pore fluid saturation.

Dual attenuation peaks revealing mesoscopic and microscopic fluid flow in partially oil-saturated Fontainebleau sandstones

SUMMARY We conducted stress–strain oscillation experiments on dry and partially oil-saturated Fontainebleau sandstone samples over the 1–2000 Hz band at different confining pressures to investigate the wave-induced fluid flow (WIFF) at mesoscopic and microscopic scales and their interaction. Three tested rock samples have similar porosity between 6 and 7 per cent and were partially saturated to different degrees with different oils. The measurement results exhibit a single or two attenuation peaks that are affected by the saturation degree, oil viscosity and confining pressure. One peak, exhibited by all samples, shifts to lower frequencies with increasing pressure, and is mainly attributed to grain contact- or microcrack-related squirt flow based on modelling of its characteristics and comparison with other experiment results for sandstones. The other peak is present at smaller frequencies and shifts to higher frequencies as the confining pressure increases, showing an opposite pressure dependence. This contrast is interpreted as the result of fluid flow patterns at different scales. We developed a dual-scale fluid flow model by incorporating the squirt flow effect into the patchy saturation model, which accounts for the interaction of WIFFs at microscopic and mesoscopic scales. This model provides a reasonable interpretation of the measurement results. Our broad-frequency-band measurements give physical evidence of WIFFs co-existing at two different scales, and combining with modelling results, it suggests that the WIFF mechanisms, related to pore microstructure and fluid distribution, interplay with each other and jointly control seismic attenuation and dispersion at reservoir conditions. These observations and modelling results are useful for quantitative seismic interpretation and reservoir characterization, specifically they have potential applications in time-lapse seismic analysis, fluid prediction and reservoir monitoring.

Experimental study on frequency‐dependent elastic properties of weakly consolidated marine sandstone: effects of partial saturation

ABSTRACTInvestigating seismic dispersion and attenuation characteristics of loosely compacted marine sandstone is essential in reconciling different geophysical measurements (surface seismic, well logging and ultrasonic) for better characterization of a shallow marine sandstone reservoir. We have experimented with a typical high‐porosity and high‐permeability sandstone sample, extracted from the Paleogene marine depositional setting in the Gulf of Mexico, at the low‐frequency band (2–500 Hz) as well as ultrasonic point (106 Hz), to investigate the effects of varying saturation levels on a rock's elasticity. The results suggest that the Young's modulus of the measured sample with adsorbed moisture at laboratory conditions (room temperature, 60%–90% humidity) exhibits dispersive behaviours. The extensional attenuation can be as high as 0.038, and the peak frequency occurs around 60 Hz. The extensional attenuation due to moisture adsorption can be dramatically mitigated with the increase of confining pressure. For partial saturation status, extensional attenuation increases as increasing water saturation by 79% with respect to the measured frequencies. Additionally, the results show that extensional attenuation at the fully water‐saturated situation is even smaller than that at adsorbed moisture conditions. The Gassmann–Wood model can overall capture the P‐wave velocity‐saturation trend of measured data at seismic frequencies, demonstrating that the partially saturated unconsolidated sandstone at the measured seismic frequency range is prone to be in the relaxed status. Nevertheless, the ultrasonic velocities are significantly higher than the Gassmann–Wood predictions, suggesting that the rocks are in the unrelaxed status at the ultrasonic frequency range. The poroelastic modelling results based on the patchy saturation model also indicate that the characteristic frequency of the partially saturated sample is likely beyond the measured seismic frequency range.

Analysis of wave dispersion and attenuation effects on seismic low-frequency reflections of a poroelastic layer

We investigated reflection dispersion characteristics of a poroelastic layer with patchy saturations in seismic low-frequency range. Frequency-dependent attenuation and dispersion of phase velocity were determined with varying fluid saturation, porosity, permeability and heterogeneity size, using analytical solutions of a generalised 1D White’s model proposed here, obtained by incorporating capillary forces into the patchy saturation model. Numerical predictions were employed in combinations with an approximation for the complex and frequency-dependent reflection coefficient from an attenuating thin layer embedded in a dissipative background medium, so as to give a deep insight into the impacts of velocity dispersion and tuning, as well as acoustic impedance contrast, on the seismic low-frequency reflections. Results from this study suggest that wave-induced fluid flow in poroelastic media might account for low-frequency reflection signature anomalies that are associated with fluid saturation in the pore space. We also observed that seismic reflection coefficients of a partially saturated layer can vary strongly versus frequencies, especially in low-frequency range where high attenuation and dispersion can take place due to fluid partial saturation. Analysis of the crossplots of the magnitude for reflection coefficients and dispersion showed that attenuation, dispersion and tuning are more sensitive to gas saturation, porosity, and heterogeneity size. Thus the crossplot provides a useful means for detecting changes in fluid saturation and rock properties.

Seismic numerical analysis for partially gas-saturated porous rocks by an extended local Rytov Fourier approximation based on the diffusion-viscous theory

The frequency-dependent attenuation and velocity dispersion of seismic responses are closely related to hydrocarbon reservoirs. To further investigate the characteristics of seismic responses caused by pore fluid-bearing reservoirs, the role of gas saturation is analyzed in seismic responses of sand reservoirs characterized by the patchy saturation model. To this end, a novel wave extrapolation method is developed based on the diffusive-viscous wave equation (DVWE) as well as a scheme for an extended local Rytov Fourier (ELRF) approximation within the extrapolation depth interval. Our proposed method considers the presence of fluid mixtures in the porous media, resulting in seismic attenuation and dispersion by the mechanism generally known as wave-induced fluid flow (WIFF). This method enables an accommodation for the lateral variations in slowness, diffusion coefficient and viscosity. Subsequently, the extrapolation is adopted to model the synthetic seismic data of a distributary channel model. During this modeling, a gas-water saturated sand reservoir embedded into one of the channels was used to comparatively analyze the distinct features on its seismic synthetic data. We exhibited the numerical simulation results using the proposed wave extrapolation method here and the traditional acoustic wave equation (AWE) method. A comparison of the simulation results, demonstrates that our proposed numerical method can depict the seismic dispersion and frequency-dependent attenuation as well as the phase delay effects associated with gas-water-saturated sand reservoirs. Furthermore, we compare the seismic responses by changing the gas saturations of the sand reservoir. The gas saturation of the reservoir has significant effects on the seismic characteristics of the numerical modeling data. The numerical modeling method improves our understanding of the mechanisms of seismic frequency-dependent characteristics associated with gas saturations and potentially contributes to better insights into gas reservoir indicators derived from seismic field data.

Reflection dispersion signatures due to wave-induced pressure diffusion in heterogeneous poroelastic media

ABSTRACTWe have studied the reflection dispersion signatures of a heterogeneously patchy saturated reservoir exhibiting attenuation and velocity dispersion in a seismic range of frequency. A modified patchy saturation model is employed to predict velocity dispersion and intrinsic attenuation behaviour associated with wave-induced pressure diffusion due to the presence of both mesoscopic and microscopic heterogeneities. Understanding the combined effects of microscopic squirt flow and wave-induced fluid flow related to mesoscopic heterogeneities on wave attenuation and associated dispersion would be important for determining the relative contribution of both of the interdependent energy loss mechanisms. The acoustic properties from the modified patchy saturation model were then employed in combination with an approximate expression for the frequency-dependent normal-incidence reflection coefficient of a dispersive reservoir rock, to give insights into the impacts of attenuation (and its associated velocity dispersion) and acoustic impedance contrast on the reflection dispersion characteristics. Analysis of the results indicates that the dispersion attribute of reflection coefficients and the associated cross-plot are more sensitive to fluid saturation and porosity than the magnitude of the reflection coefficient, and hence provide a promising approach to characterise fluid saturation and porosity in heterogeneous hydrocarbon reservoirs.

Spatiotemporal changes of seismic attenuation caused by injected CO2 at the Frio‐II pilot site, Dayton, TX, USA

AbstractA continuous active source seismic monitoring data set was collected with crosswell geometry during CO2 injection at the Frio‐II brine pilot, near Liberty, TX. Previous studies have shown that spatiotemporal changes in the P wave first arrival time reveal the movement of the injected CO2 plume in the storage zone. To further constrain the CO2 saturation, particularly at higher saturation levels, we investigate spatial‐temporal changes in the seismic attenuation of the first arrivals. The attenuation changes over the injection period are estimated by the amount of the centroid frequency shift computed by local time‐frequency analysis. We observe that (1) at receivers above the injection zone seismic attenuation does not change in a physical trend; (2) at receivers in the injection zone attenuation sharply increases following injection and peaks at specific points varying with distributed receivers, which is consistent with observations from time delays of first arrivals; then, (3) attenuation decreases over the injection time. The attenuation change exhibits a bell‐shaped pattern during CO2 injection. Under Frio‐II field reservoir conditions, White's patchy saturation model can quantitatively explain both the P wave velocity and attenuation response observed. We have combined the velocity and attenuation change data in a crossplot format that is useful for model‐data comparison and determining patch size. Our analysis suggests that spatial‐temporal attenuation change is not only an indicator of the movement and saturation of CO2 plumes, even at large saturations, but also can quantitatively constrain CO2 plume saturation when used jointly with seismic velocity.

Seismic wave attenuation in hydrate-bearing sediments based on the patchy saturation model in the Shenhu area, South China Sea

In the Shenhu area, South China Sea, a study on P-wave attenuation in the hydrate-bearing sediments has been developed based on the Biot-Squirt (BISQ) porous medium model. However, the BISQ model has been proven to be inappropriate for the attenuation characteristics at seismic frequencies. We have adopted the patchy-saturation model, which is being increasingly considered to be more suitable for attenuation analysis at seismic frequencies in porous media, to study P-wave attenuation in the hydrate-bearing sediments in the Shenhu area, South China Sea. The theoretical modeling indicates that the P-wave attenuation at seismic frequencies is observed to decrease when the sediments contain gas hydrates. In the case studies in the Shenhu area, the interval inverse [Formula: see text]-factors from seismic reflection data were estimated, and the results indicate good agreement with the theoretical modeling.

Measurement of Electrical Impedance and P-wave Velocity of a Low Permeable Sandstone Core During the Displacement of Saturated Brine by CO2 Injection

Evaluating and monitoring the CO2 behavior in the reservoir, understanding the mechanism of CO2 flow and distribution in the water-CO2 mixture state is essential. In this study, measurement of the complex electrical impedance (Z) and P-wave velocity (Vp) is conducted during the CO2 injection into the rock core under the reservoir condition. Specimen is low permeable sandstone and injection rate is ultra-low (in the low capillarity number (Cn) area) to high. In addition to measuring Z and Vp, differential pressure on the both sides of the specimen and CO2 saturation (SCO2) of the entire specimen are measured. The change of Z and Vp are observed according to the change of differential pressure and SCO2. After the injection test, SCO2 in cross-section of the specimen is estimated using Archie's law and Gassmann's equation (Patchy saturation model) to the experimental results.

Fluid Distribution Effects on P-wave Velocity of CO2/brine Saturated Rocks: A Comparison Study and Implications for CO2 Storage Monitoring Using Seismic Method

The evaluation of fluid saturation using P-wave velocity is affected by the fluid distribution at mesoscale significantly. Here we present the experimental results of two tests for measuring P-wave velocity under ultrasonic frequencies in two different rocks (one sandstone and one tuff, respectively) during CO2 displacing brine. Both tests were performed under a high injection pressure of 10 MPa in order to control CO2 in a supercritical state. The two rock samples display differences in rock heterogeneity. The sandstone sample shows obvious layered structures with high and low porosity layers, whereas the tuff sample shows a near homogeneous structure. During the dynamic fluid displacements tests, we used X-ray CT technique to image rock interior frequently and then calculated average CO2 saturation near the local wave propagation path. The results show very different saturation-velocity relationships for the two tests. The sandstone sample gives a relationship that is close to Gassmann-Hill limit, whereas the tuff sample gives a relationship located near the Gassmann-Wood limit. Meanwhile, X-ray CT images show the distribution of CO2 in the sandstone sample is more heterogeneous and larger fluid patches are developed in it during CO2 drainage. In contrast, the tuff sample shows the development of very small and dispersed CO2 patches and relatively well mixing state of CO2 and brine in the rock. We then use the random patchy saturation model to interpret the results theoretically. The results indicate that the characteristic patch size is in an order of tens of millimeters in the experiment using sandstone sample, whereas it is smaller than 0.1mm in the experiment using tuff sample. Whether the scale of the strong-contrast heterogeneity created by patchy CO2 saturation is significant to wave velocity is determined by the ratio of patch size and fluid diffusion length (A/L ratio), which is a function of wave frequency and hydraulic diffusion coefficient of the rock. If the scale of the heterogeneity is larger than the fluid diffusion length at a wave frequency, the strain field created by wave propagation cannot be relaxed during a half period and the media shows the stiffening effect–a higher velocity at macroscale. These suggest that one should pay attenuation to the effect of fluid distribution and degree of phase mixing when evaluating fluid saturation from P-wave velocity using seismic methods, if the reservoir develops significant large-scale heterogeneity. Furthermore, the velocity becomes insensitive to saturation changes when CO2 saturation becomes higher than approximately 0.2, if its changes follow the Gassmann-Wood relationship (with small A/L ratio at lower frequencies). In contrast, the velocity remains changing with CO2 saturation at higher CO2 saturation if the changes follow the Gassmann-Hill relationship (with large A/L ratio at higher frequencies). The changes suggest the selection of wave frequency is critical to validly monitor the saturation changes at higher CO2 saturations.

Modelling ultrasonic laboratory measurements of the saturation dependence of elastic modulus: New insights and implications for wave propagation mechanisms

Seismic time-lapse techniques are a valuable tool used to estimate the mobilization and distribution of stored CO2 in depleted reservoirs. The success of these techniques depends on knowing the seismic properties of partially saturated rocks with accuracy. It is commonplace to use controlled laboratory-scale experiments to determine how the fluid content impacts on their properties. In this work, we measure the ultrasonic P- and S-wave velocities of a set of synthetic sandstones of about 30% porosity. Using an accurate method, we span the entire saturation range of an air-water system. We show that the rocks’ elastic behaviour is consistent with patchy saturation and squirt flow models but observe a discontinuity at around 90% gas saturation which can be interpreted in two very different ways. In one interpretation, the responsible mechanism is frequency-dependent squirt-flow that occurs in narrow pores that are preferentially saturated. An equally plausible mechanism is the change of the mobile fluid in the pores once they are wetted. Extrapolated to seismic frequencies, our results imply that the seismic properties of rocks may be affected by the wetting effect with an impact on the interpretation of field data but would potentially be unaffected by the squirt flow effect. This provides strong motivation to conduct laboratory-scale experiments with partially saturated samples at lower frequency or, ideally, a range of frequencies in the seismo-acoustic range.

Frequency-Dependent Amplitude Versus Offset Variations in Porous Rocks with Aligned Fractures

The theory of frequency-dependent amplitude versus offset (AVO) was developed for patchy-saturated model. In this work, we consider this theory in the case of an anisotropic medium based on a fractured-sandstone model. Thus, building on viscoelastic theory, we introduce a method for the computation of frequency-dependent AVO that is suitable for use in the case of an anisotropic medium. We use both analytical methods and numerical simulations to study P-P and P-S reflection coefficients, and results suggest that dispersion and anisotropy should not be neglected in AVO analysis. Indeed, for class I AVO reservoirs, the reflection magnitude of P-wave increases with frequency, while the responses of class II AVO reservoirs suggest that phase reversal occurs as frequency increases positively. In the case of class III AVO reservoirs, reflection magnitude decreases as frequency increases positively, while in the offset domain, the presence of anisotropy can distort or even reverse AVO responses. Thus, when compared to reflection coefficients for P-wave, reflection magnitude features of S-wave are more complex. The frequency-dependent AVO responses reported in this study provide insights for the interpretation of seismic anomalies in vertical transverse isotropy (VTI) dispersive reservoirs.

4D reservoir characterization using well log data for feasible CO2-enhanced oil recovery at Ankleshwar, Cambay Basin - A rock physics diagnostic and modeling approach

In recent years, rock physics modeling has become an integral part of reservoir characterization as it provides the fundamental relationship between geophysical measurements and reservoir rock properties. These models are also used to quantify the effect of fluid saturation and stress on reservoir rocks by tracking the changes in elastic properties during production. Additionally, various rock physics models can be applied to obtain the information of rock properties away from existing drilled wells, which can play a crucial role in the feasibility assessment of CO2-enhanced oil recovery (EOR) operation at field.Thus, the objective of this study is to develop a rock-physics model of the Ankleshwar reservoir to predict the reservoir response under CO2-EOR. The Ankleshwar oil field is a mature field situated in Cambay Basin (Western India) that witnessed massive peripheral water flooding for around 40years. Since the field was under water flooding for a long term, reasonable changes in reservoir elastic properties might have occurred. To identify potential reservoir zone with significant bypassed (or residual) oil saturation, we applied the diagnostic rock physics models to two available wells from the Ankleshwar oil field. The results clearly indicate transitions from clean sands to shaly sands at the base, and from sandy shale to pure shale at the top of the reservoir pay zone, suggesting a different seismic response at the top when compared to the base of the reservoir in both the wells. We also found that clay content and sorting affects the elastic properties of these sands, indicating different depositional scenario for the oil sands encountered in the Ankleshwar formation. Nevertheless, the rock physics template (RPT) analysis of the well data provides valuable information about the residual oil zone, a potential target for CO2-EOR. Further, a 4D reservoir characterization study has been conducted to assess the seismic detectability of CO2-EOR, and we observed that the injected CO2 changes the Vp, Vp/Vs and P-wave impedance (PI) dramatically, suggesting a reasonable change in the seismic response of the reservoir, even if we consider patchy saturation model. Thus, it is highly advisable to conduct 4D/time-lapse seismic monitoring in this field for optimized production by CO2-EOR and the reservoir management.

Saturation scale effect on time‐lapse seismic signatures

ABSTRACTQuantitative interpretation of time‐lapse seismic signatures aims at assisting reservoir engineering and management operations. Time‐lapse signatures are thought to be primarily induced by saturation and pressure changes. Core‐flooding and reservoir flow simulations indicate that a change of the driving forces during dynamic fluid injection gives rise to a varying saturation scale. This saturation scale is yet another variable controlling the time‐lapse seismic signal. In this work, we investigate the saturation scale effect on time‐lapse seismic signatures by analysing simple modelling scenarios. We consider three characteristic saturation scales, ranging from few millimetres to metres, which may form during gas injection in an unconsolidated water‐saturated reservoir. Using the random patchy saturation model, we compare the corresponding acoustic signatures, i.e., attenuation, reflectivity, and seismic gather associated with each saturation scale. The results show that the millimetre saturation scale produces minimum attenuation and the same seismic signatures with those obtained from the elastic modelling. The centimetre saturation scale produces maximum attenuation, whereas the metre saturation scale causes highest velocity dispersion. The analyses of the time shift and amplitude change indicate that ignoring a time‐dependent saturation scale can result in biased estimation/discrimination of the saturation and the fluid pressure. In particular, the 4D signal can be strongly affected by the saturation‐scale change when the reservoir gas saturation is low and the effective pressure is high. In the presence of an increasing (decreasing) saturation scale during injection, interpreting an observed time shift and amplitude change using the Gassmann model will lead to underestimation (overestimation) of the change in gas saturation and fluid pressure. We show that including the effects of capillarity and residual saturation into the rock physics modelling can potentially reduce the interpretation uncertainty due to the saturation‐scale change.

Theoretical derivation of a Brie‐like fluid mixing law

ABSTRACTPrediction of the velocity of acoustic waves in partially saturated rocks is very important in geophysical applications. The need to accurately predict acoustic velocities has resulted in a widespread popularity of Brie's effective fluid mixing law. This empirical model together with Gassmann's formula are used routinely in fluid substitution problems in petroleum geophysics and seismic monitoring of carbon capture and storage. Most attempts to justify Brie's model have been focused on interpretation in terms of patchy saturation models and attaching meaning to the Brie parameter in terms of the patch size. In this paper, using a microstructural description of the rock and a parameter relating to capillary pressure, we calculate an effective fluid modulus that is very similar to Brie's law. The fluid mixing law we propose is independent of frequency and has a solid theoretical foundation. This proposed law produces analytically harmonic and arithmetic averaging at the endpoints. Our results indicate that Brie‐like behaviour may not necessarily be related to frequency‐ and patch‐size‐ dependent phenomena.