Gassmann Model Research Articles

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.

Prediction of crack density in porous-cracked rocks from elastic wave velocities

The stability of structures that are built over rock is affected by cracks in the rock that result from weathering, thawing and freezing processes. This study investigates a new method for determining rock crack densities using elastic wave velocities. The Biot–Gassmann model, which consists of several elastic moduli and Poisson's ratio, was used to determine a theoretical equation to predict the crack density of rocks. Ten representative specimens were extracted from ten boreholes to highlight the spatial variability. Each specimen was characterized using X-Ray Diffraction (XRD) analysis. The specimens were carved into cylinders measuring 50mm in diameter and 30mm in height using an abrasion process. A laboratory test was performed to obtain the elastic wave velocity using transducers that can transmit and receive compressional and shear waves. The measured compressional wave and shear wave velocities were approximately 2955m/s–5209m/s and 1652m/s–2845m/s, respectively. From the measured elastic wave velocities, the analyzed crack density and crack porosity were approximately 0.051–0.185 and 0.03%–0.14%, respectively. The calculated values were compared with the results of previous studies, and they exhibit similar values and trends. The sensitivity of the suggested theoretical equation was analyzed using the error norm technique. The results show that the compressional wave velocity and the shear modulus of a particle are the most influential factors in this equation. The study demonstrates that rock crack density can be estimated using the elastic wave velocities, which may be useful for investigating the stability of structures that are built over rock.

Laboratory seismic monitoring of supercritical CO2 flooding in sandstone cores using the Split Hopkinson Resonant Bar technique with concurrent x‐ray Computed Tomography imaging

ABSTRACTAccurate estimation of CO2 saturation in a saline aquifer is essential for the monitoring of supercritical CO2 injected for geological sequestration. Because of strong contrasts in density and elastic properties between brine and CO2 at reservoir conditions, seismic methods are among the most commonly employed techniques for this purpose. However the relationship between seismic (P‐wave) velocity and CO2 saturation is not unique because the velocity depends on both wave frequency and the CO2 distribution in rock. In the laboratory, we conducted measurements of seismic properties of sandstones during supercritical CO2 injection. Seismic responses of small sandstone cores were measured at frequencies near 1 kHz, using a modified resonant bar technique (Split Hopkinson Resonant Bar method). Concurrently, saturation and distribution of supercritical CO2 in the rock cores were determined via x‐ray CT scans. Changes in the determined velocities generally agreed with the Gassmann model. However, both the velocity and attenuation of the extension wave (Young's modulus or ‘bar’ wave) for the same CO2 saturation exhibited differences between the CO2 injection test and the subsequent brine re‐injection test, which was consistent with the differences in the CO2 distribution within the cores. Also, a comparison to ultrasonic velocity measurements on a bedded reservoir rock sample revealed that both compressional and shear velocities (and moduli) were strongly dispersive when the rock was saturated with brine. Further, large decreases in the velocities of saturated samples indicated strong sensitivity of the rock's frame stiffness to pore fluid.

Sensitivity of flow and elastic properties to fabric heterogeneity in carbonates

ABSTRACTCarbonate rocks are heterogeneous at various levels from deposition to diagenesis. Any existing depositional heterogeneity becomes more complex when carbonate rocks are in contact with polar fluids. Our experiments on carbonate rocks show that change in textural heterogeneity leads to heterogeneity in the distribution of storage and flow properties that may govern changes in saturation patterns. This would be akin to any carbonate reservoir with a mix of heterogeneous and homogeneous facies within a formation and their control on saturation distribution in response to a standard imbibition process. Associated with the saturation pattern heterogeneities, the resultant elastic property distributions also change. We quantify this heterogeneity and its effects on flow and seismic properties based on a few textural extremes of fabric heterogeneity in samples that can exist in any typical carbonate reservoir system. Our measurements show that textural heterogeneity can lead to anisotropy in permeability and in acoustic velocities. Permeability anisotropy measurements varied between 40% and 100% while acoustic velocity anisotropy measurements varied between 8% and 30% with lower values for homogeneous samples respectively. Under similar conditions of the saturation experiment (spontaneous imbibition at the benchtop and undrained pressure imbibition at 1000 psi), the imbibing brine replaced 97% of the pore volume in a homogeneous sample (porosity 20% and permeability 2.6 mD) compared to 80% pore volume in a heterogeneous sample (porosity 29% and permeability 23.4 mD). Furthermore, after pressure saturation, a change of +79% in the bulk modulus and ‐11% in the shear modulus is observed for homogeneous samples in comparison to +34% in the bulk modulus and −1% in the shear modulus for heterogeneous samples, with respect to the dry state moduli values of the samples. We also examined the uncertainties associated with Gassmann models of elastic properties due to variations in fluid saturations.Our results provide significant information on the saturation and, with it, modulus variations that are often ignored during fluid substitution modelling in time‐lapse seismic studies in carbonate reservoirs. We show that the bulk modulus could vary by 45% and the shear modulus by 10% between homogeneous and heterogeneous patches of a reservoir after a water flooding sequence for secondary recovery. Our findings demonstrate the need to incorporate and couple such fabric‐controlled saturation heterogeneities in reservoir simulation and in seismic fluid substitution models.

Experimental Verification of the Petroelastic Model in the Laboratory – Fluid Substitution and Pressure Effects

The poroelastic model is a major component in the workflows for the interpretation of time-lapse (or 4D) seismic data in terms of fluid repartition and/or pressure variation during the exploitation of reservoirs. This model must take into account both the fluid substitution effect and the pressure variation effect on the measured seismic parameters (velocities, impedance). This paper describes an experimental verification in the laboratory of this model. Regarding fluid substitution, Biot- Gassmann model is the most popular model. This model assumes that the shear modulus is independent of the nature of the saturating fluid, as long as this latter is not viscous and give the expression of the variations of the bulk modulus of the rock due to fluid substitution as function of the parameters of the rock frame and of the saturating fluids. The experimental validation, dealing with these two items, demonstrates on various samples of sandstone and limestone that the shear modulus of the rock is independent of the not too viscous saturating fluid. This is verified even with viscous fluids (viscosity as large as 10<sup>4<sup/> cP) if the differential pressure, that is to say the difference between the confining pressure and the pore pressure, is high (closure of the mechanical defects); the bulk modulus of the crystal constituent of mono-mineral rocks (limestone, clean sandstone) is close to tabulated values; under fixed differential pressure but variable pore and confining pressures, the variation of the rock bulk modulus can be explained by the nonlinearity of the fluid bulk modulus. These three types of experimental results constitute unambiguous corroborations of Biot-Gassmann theory. Regarding pressure effects, the relevant parameter is the differential pressure <i>P<i/><sub><i>diff<i/><sub/> = <i>P<i/><sub><i>c<i/><sub/> – <i>P<i/><sub><i>p<i/><sub/>, that is to say the difference between the confining pressure P<sub><i>c<i/><sub/> and the pore pressure P<sub><i>p<i/><sub/>. More precisely, this means that P-wave and S-wave velocities only depend on the differential pressure <i>P<i/><sub><i>diff<i/><sub/> = <i>P<i/><sub><i>c<i/><sub/> − <i>P<i/><sub><i>p<i/><sub/>, and not in an independent way on P<sub><i>c<i/><sub/> and on P<sub><i>p<i/><sub/>. Increasing the differential pressure P<sub><i>diff<i/><sub/> tends to stiffen the rock by closing the mechanical defects (grain contacts, microcracks, microfractures...). The consequence on velocities and attenuations is variable according to the relative abundance of these mechanical defects in the rock sample. Limestones are often weakly pressure dependent, whatever the pressure level. This is due to the ease with which mechanical defects can be cemented by carbonate crystals. Consolidated sandstones are often sensitive to the differential pressure P<sub><i>diff<i/><sub/> and the unconsolidated geomaterials (sands) are very pressure sensitive. The pressure dependence of the velocities is often well approximated by a power law. The exponent of this power law, often called the Hertz exponent, is a good way to quantify the pressure sensitivity of the rock velocities.

SATI algorithm — the calculation of stress aligned HTI stiffness tensor for sandstone reservoir from wireline data

I present an algorithm that uses cross-dipole wireline data only in order to estimate the HTI stiffness tensor for sandstone formations under in-situ asymmetric lateral (azimuthal) stress conditions. The algorithm is based on the generalization of terms “excess compliance” and “fracture weakness” developed within the linear slip interface theory for fractured rocks and is applied here to describe the effect of grain contacts in loose sandstones. I introduce the term “plane of weakness” being oriented (aligned) orthogonal to the minimal horizontal principal stress direction in order to describe the overall effective weakness of sandstone caused by the different principal stresses. For the quantification of this phenomenon I use the anisotropic Gassmann model. As a result I am able to calculate a HTI stiffness tensor for the interval length of a saturated sandstone formation and the respective Thomsen’s parameters. The input data required for these calculations have to be provided by wireline logging and will consist of porosity, density, P-wave velocity, fast and slow shear wave velocities and oil-water saturation ratio. The algorithm in its current form is applicable to sandstone reservoirs only. Its limitation is based on two assumptions, which state that all the measured anisotropy is induced by the present stress in sandstone and that the unstressed sandstone would be nearly isotropic. From a technical viewpoint this algorithm can be implemented fairly easily in data acquisition and interpretation software relying on correct estimation of anisotropy parameters. It is also cheap because it does not require any additional measurements apart from the cross-dipole logging.

Evolution of Compressional Wave Velocity during CO2Hydrate Formation in Sediments

While the acoustic wave-based survey is considered to be one of the most effective and promising means for monitoring the behavior of particulate/discrete geomaterials, the P-wave velocity has scarcely been used to monitor the long-term behavior of CO2 sequestered sediments or to understand the characteristics of CO2 hydrate formation in sediments. Furthermore, there are still only limited reliable laboratory results quantifying the P-wave velocity change in sediments that results from CO2 hydrate formation and accumulation processes. This study presents experimental measurements on the evolution of P-wave velocity as CO2 hydrate saturation increases in unconsolidated sediment. The measured data are compared with the simple yet robust asymptotic Gassmann model to estimate CO2 hydrate saturation (volume fraction of hydrate in pore space) in sediments. Given that in situ techniques to measure acoustic waves are well-established for the exploration of deep oceanic sediment, the methodology presented in this ...

Time-lapse seismic modeling assisted by numerical reservoir simulation of water and gas flooding scenarios in oil reservoirs

In this project, we link fluid flow simulation results to time-lapse seismic through rock physics and modeling. Our goal is to examine the main effects of permeability barriers on seismic response using fluid flow simulations to generate pressure and saturation fields. To explore this problem, we have carried out water and gas injection numerical experiments in a simple reservoir model which has vertical and horizontal variations of porosity as well as permeability barriers. In each experiment, we change the barrier permeability values. By using fluid substitution theory, Gassmann and patchy models, and Batzle and Wang's empirical relationship we model the main seismic parameters, such as acoustic impedance and compressional velocity. After that, we generate synthetics seismograms and some contrast sections to compare the seismic images prior and after fluid injection events in subsequent time periods to analyze possible differences in the seismic parameters due to changes in barriers properties. The results show that barriers can increase fluid pore pressure changing the bulk modulus in the regions with barriers. The results also show that water flow does not have significant impact on seismic response when the barrier is present. On the other hand, gas flow and the degree of impermeability of the barrier can help us to understand how the barriers act on the seismic response and thus to reduce uncertainty. Finally, this paper presents a methodology to examine barriers effects on seismic response.

Shear wave velocity prediction using improved effective medium model

Seismic prospecting and evaluation of the rock mechanical properties require knowledge of shear-wave (S-wave) velocity. However, frequently the S-wave logs are not available, especially in past years. Prediction of S-wave velocity is still attracting researchers? attention because of its importance in petroleum exploration and engineering application. A new rock physics model of clay-sand mixture is developed based on Self-Consistent Approximations (SCA) and Gassmann model. The model assumes that total pore space consists of two parts: (1) pores from sand grains and (2) pores from clays. The elastic moduli of clay-fluid mixture and sand-pore mixture are obtained by SCA. The clay-fluid mixture first fills up the total porosity, then replace the matrix (sand grains), taking the form of structure clay. The model can explain the distinctive changing relations between clay content and compressional velocity of the sand-clay mixture observed by Marion. The model can be applied to predict compressional and shear wave velocities of the rock using conventional logs such as acoustic velocity, density and gamma ray logs. Parameters of the sand clay mixture model are chosen according to the fitness between predicted and measured compressional wave velocity. After that, we use the improved model to predict shear wave velocity, and the computational results indicate that the predicted shear wave velocities agree well with the measured velocities. The reliability of the shear wave velocity estimation can be validated by the predicted and measured compressional wave velocities fitness.

Generalization of Gassmann equations for porous media saturated with a solid material

Gassmann equations predict effective elastic properties of an isotropic homogeneous bulk rock frame filled with a fluid. This theory has been generalized for an anisotropic porous frame by Brown and Korringa’s equations. Here, we develop a new model for effective elastic properties of porous rocks — a generalization of Brown and Korringa’s and Gassmann equations for a solid infill of the pore space. We derive the elastic tensor of a solid-saturated porous rock considering small deformations of the rock skeleton and the pore infill material upon loading them with the confining and pore-space stresses. In the case of isotropic material, the solution reduces to two generalized Gassmann equations for the bulk and shear moduli. The applicability of the new model is tested by independent numerical simulations performed on the microscale by finite-difference and finite-element methods. The results show very good agreement between the new theory and the numerical simulations. The generalized Gass-mann model introduces a new heuristic parameter, characterizing the elastic properties of average deformation of the pore-filling solid material. In many cases, these elastic moduli can be substituted by the elastic parameters of the infill grain material. They can also represent a proper viscoelastic model of the pore-filling material. Knowledge of the effective elastic properties for such a situation is required, for example, when predicting seismic velocities in some heavy oil reservoirs, where a highly viscous material fills the pores. The classical Gassmann fluid substitution is inapplicable for a configuration in which the fluid behaves as a quasi-solid.

Vp ∕ Vs ratio versus differential stress and rock consolidation — A comparison between rock models and time-lapse AVO data

The compressional to shear wave velocity ratio [Formula: see text] is an important parameter in seismic amplitude versus offset (AVO) analysis, and this parameter plays a key role especially for lithology and fluid prediction methods. The P-wave velocity is a key parameter in traditional pressure prediction methods, because overpressure often results in a velocity reduction. However, for AVO-based pore pressure prediction methods, one expects that the [Formula: see text] ratio also is a key parameter. The Hertz-Mindlin geomechanical model predicts a constant [Formula: see text] ratio as the differential stress changes in a dry package of identical spheres. Ultrasonic core measurements show increased [Formula: see text] ratios as the differential stress decreases, especially for unconsolidated wet sands. Thus, one is likely to assume that the [Formula: see text] ratio is dependent on rock consolidation. By combining the Hertz-Mindlin model with the Gassmann model, we show how to obtain a sim-ple rock-physics framework including both the differential stress and the degree of rock consolidation. We use the number of grain-to-grain contacts (coordination number) to represent the rock consolidation. For two field examples, we calibrate this consolidation parameter to in-situ stress conditions, then compare the predicted [Formula: see text] ratios for the overpressured reservoir conditions with observed time-lapse AVO changes. The correspondence between modeled and AVO-estimated [Formula: see text] ratios is good within the assumed accuracy of the real time-lapse AVO changes. In both cases, we observe an increase in the [Formula: see text] ratio as the differential stress decreases. In the first case, a pore pressure increase of [Formula: see text] is measured, whereas the other case shows a pressure increase of approximately [Formula: see text]. The first reservoir represents a low-to-medium-consolidated sandstone reservoir of 33% porosity on average, whereas the second reservoir is a more consolidated sand with similar porosities (30%).

Elastic behaviour of North Sea chalk: A well‐log study

ABSTRACTWe present two different elastic models for, respectively, cemented and uncemented North Sea chalk well‐log data. We find that low Biot coefficients correlate with anomalously low cementation factors from resistivity measurements at low porosity and we interpret this as an indication of cementation. In contrast, higher Biot coefficients and correspondingly higher cementation factors characterize uncemented chalk for the same (low) porosity. Accordingly, the Poisson's ratio–porosity relationship for cemented chalk is different from that of uncemented chalk.We have tested the application of the self‐consistent approximation, which here represents the unrelaxed scenario where the pore spaces of the rock are assumed to be isolated, and the Gassmann theory, which assumes that pore spaces are connected, as tools for predicting the effect of hydrocarbons from the elastic properties of brine‐saturated North Sea reservoir chalk. In the acoustic impedance–Poisson's ratio plane, we forecast variations in porosity and hydrocarbon saturation from their influence on the elastic behaviour of the chalk. The Gassmann model and the self‐consistent approximation give roughly similar predictions of the effect of fluid on acoustic impedance and Poisson's ratio, but we find that the high‐frequency self‐consistent approach gives a somewhat smaller predicted fluid‐saturation effect on Poisson's ratio than the low‐frequency Gassmann model. The Gassmann prediction for the near and potentially invaded zone corresponds more closely to logging data than the Gassmann prediction for the far, virgin zone. We thus conclude that the Gassmann approach predicts hydrocarbons accurately in chalk in the sonic‐frequency domain, but the fluid effects as recorded by the acoustic tool are significantly affected by invasion of mud filtrate.The amplitude‐versus‐angle (AVA) response for the general North Sea sequence of shale overlying chalk is predicted as a function of porosity and pore‐fill. The AVA response of both cemented and uncemented chalk generally shows a declining reflectivity coefficient versus offset and a decreasing normal‐incidence reflectivity with increasing porosity. However, for the uncemented model, a phase reversal will appear at a relatively lower porosity compared to the cemented model.

Study on the Biot-Stoll model for porous marine sediments

The Biot-Stoll model is useful for analyzing the acoustic wave propagation in porous marine sediments. However, the practical application of the model is not easy, because 13 physical parameters are required to apply it, and the physical phenomena in this model are difficult to understand. In this study, equivalent circuits for the plane longitudinal wave propagation in porous media are proposed for easy understanding of the physical phenomena. Also, practical approximated equations for the longitudinal wave velocity and attenuation are proposed to simplify practical application of the Biot-Stoll model. Then, simpler models, such as the Wood model, the Gassmann model, and the Biot-Stoll model without frame moduli can be used within limited ranges of frequency and porosity to approximate the exact Biot-Stoll model. Therefore, the ranges of frequency and porosity applicable to some simple acoustic models are obtained to simplify practical application of the Biot-Stoll model.

A Numerical Study of Acoustic Wave Propagation in Partially Saturated Poroelastic Rock

AbstractBased on the Biot theory we use a high‐order staggered finite‐difference algorithm to carry out numerical experiments on wave propagation in a rock sample partially saturated by multi‐phase fluids with random fluid distributions. The ultrasonic source frequencies are 25, 50, 75kHz and 100kHz, respectively. The first modeling sample is homogeneous isotropic sandstone partially filled with two phase pore fluids (water and gas), which are defined by their different elastic characteristic parameters of saturation, viscosity, compressibility, and density, respectively. We assume that the two different pore‐fills occupy different macroscopic regions and the wavelength of acoustic wave is much larger than the scale of these regions. The result shown that the P‐wave velocity and attenuation change with fluid saturations (water and gas) and central frequencies of the acoustic source. These numerical results are qualitatively in agreement with the White and Gassmann's models. The second modeling sample is partially filled with 3 phase pore fluids (water, oil, and gas). We keep the saturation of water with a constant and change the saturations of oil and gas. Under these conditions, the velocity of P‐wave shows an increasing trend with the increasing saturation of oil. The snapshot of the acoustic wave field shows that the energy of P‐wave is converted into several kinds of slow P‐waves and S‐waves which occur at the interfaces between water, oil and gas. These modeling results have great significance in seismic exploration and acoustic well logging interpretations.

Optimal use of PP and PS time‐lapse stacks for fluid–pressure discrimination

ABSTRACTThe combined use of time‐lapse PP and PS seismic data is analysed for optimal discrimination between pressure and saturation changes. The theory is based on a combination of the well‐known Gassmann model and the geomechanical grain model derived by Hertz and Mindlin. A key parameter in the discrimination process is the opening angle between curves representing constant changes in PP and PS reflectivity plotted against pressure and saturation changes. The optimal discrimination angle in the pressure–saturation space is 90° and this is used to determine optimal offset ranges for both PP and PS data. For typical production scenarios, we find an optimal offset range corresponding to an angle of incidence of 25–30°, for both PP and PS data. For gas we find slightly different results. This means that conventional survey parameters used in marine multicomponent acquisition should be sufficient for the purpose of estimating pressure and fluid saturation changes during production.

Frequency-Dependent Seismic Anisotropy of Porous Rocks with Penny-Shaped Cracks

Porous reservoirs with aligned fractures exhibit frequency-dependent seismic anisotropy because of wave-induced fluid flow between pores and fractures. To relate the elastic properties of porous rocks with aligned fractures at low frequency, we use the linear slip model of fractures and anisotropic Gassmann fluid substitution. We combine this low-frequency anisotropic Gassmann model with a dispersion relationship, based on a penny-shaped crack model of fractures, to account for frequency-dependent anisotropy.The combined model is validated using experimental measurements of angle-dependent wave velocities of synthetic porous sandstone with aligned disc-shaped cracks. For the low-frequency anisotropic Gassmann model, the agreement between the measured and predicted velocities is reasonably good for both 5-wave velocities, but P-wave anisotropy is overestimated by approximately 25%. This quantitative difference can be explained by fluid diffusion effects occurring at the relatively high frequencies used in the experiment (100 kHz), which are not accounted for by the low-frequency assumption of anisotropic Gassmann theory. The predictions of the combined frequency-dependent model, which considers this effect, give very good agreement with measured velocities.

Fluid substitution in laminated sands

Petrophysicists and geophysicists do “fluid substitution” to estimate the density and sonic velocity of porous rocks at saturation conditions such as fully hydrocarbon-saturated or “fizz-bearing” with fluids such as gas, condensate, and oil. However, the Gassmann model implementation in many commercial packages sometimes yields implausible results for the compressional sonic velocity in laminated sand-shale sequences. In particular, the counterintuitive phenomenon of fluid effects increasing with computed shale fraction is often observed, as in the gas-bearing interval of a well drilled with oil-based mud shown in Figure 1. DTC FLUSUB (Gassmann fluid substitution) is the result of substituting DTC WET to the observed water saturation SW. As expected (Brie et al., 1995) the modeled fluid effect is larger than the difference between the wet and the observed log DTC OBS. The observed fluid effects reach a maximum in the cleanest sand with the highest porosity, but the model predicts a maximum in shaley sand with low porosity. Figure 1. Gassmann equation breakdown in laminated sequence. Normal practice is to specify a shale cutoff above which the computed fluid effects are ignored. This is an unsatisfactory workaround because the choice of cutoff is arbitrary, and results are counterintuitive even below the cutoff. Resolution and depth mismatches between wireline logs and the observation that the Gassmann equation does not apply in shale are frequently cited as reasons for these phenomena, but do not explain the modeled results in Figure 2. Figure 2. Model showing Gassmann equation breakdown. This model was generated from regional density, velocity, and porosity trends. A sand reservoir was defined by an abrupt transition at the base and a linear transition to shale over the top 100 ft. The clean part of the sand is not assumed totally free of clay. Sands in the study area are known to include some detrital …

Experimental verification of the anisotropic Gassmann model for fluid substitution in fractured reservoirs

Porous reservoirs with aligned fractures exhibit frequency dependent seismic anisotropy due to wave induced fluid flow between pores and fractures. We model this frequency dependent anisotropy by combining the low-frequency anisotropic Gassmann model with the Hudson et al. model for frequency dependent properties of a porous material with penny-shaped cracks. The predictions of the anisotropic Gassmann model are compared with experimental measurements of elastic wave velocities as function of angle for a synthetic sample with aligned disc-like cracks. The properties of the host rock and fracture compliances are obtained from P, SV, and SH velocities measured on the dry sample. The dry fractured porous rock properties serve as input to anisotropic Gassmann fluid substitution model, which is used to compute the saturated rock properties. The stiffnesses of the saturated fractured porous rock are used to calculate the angular dependent compressional and shear wave velocities. The predicted velocities are then compared to the measured velocities. The agreement is reasonably good for both S-wave velocities, but P-wave anisotropy is overestimated by about 25%. This discrepancy can be explained by the fact that the low frequency assumption of the anisotropic Gassmann model does not account for the fluid diffusion effects occurring at relatively high frequencies used in the experiment (100 KHz). A combination of the low frequency anisotropic Gassmann model with the Hudson et al. frequency dependency accounts for fluid diffusion effects and results in an excellent agreement for P- as well as S- waves.

Underground gas storage: estimating gas column height and saturation with time lapse seismic

Seismic monitoring is often used to check hydrocarbon movements during production. On the site of Céré-la-Ronde, an underground water-bearing gas storage facility developed by Gaz de France, a methodology has been implemented for estimating gas column height and saturation with time lapse seismic. The methodology is based on the Gassmann model, on the measurement of time-shifts and on the computation of a specific seismic function. The time-shifts obtained by cross-correlation techniques are used to derive the residual time-shift Δ t induced by the presence of gas within the reservoir. A specific function is used to estimate both the gas bubble extension and the gas time thickness H t . It is shown that knowledge of H t and Δ t and the use of a Gassmann model can lead to an estimation of the gas saturation. The methodology has been applied successfully on conventional seismic profiles as well as on vertical seismic profiles (VSP). The results obtained with seismic data are in good agreement with those obtained by logging (sonic and neutron logs) but with a lateral investigation, which is much larger than the one given by logging techniques. In our field example, the gas anomaly has been checked over a distance of 300 m with VSP data and over 2 km with surface seismic data.

A generalized Biot–Gassmann model for the acoustic properties of shaley sandstones1

We obtain the wave velocities of clay‐bearing sandstones as a function of clay content, porosity and frequency. Unlike previous theories, based simply on slowness and/or moduli averaging or two‐phase models, we use a Biot‐type three‐phase theory that considers the existence of two solids (sand grains and clay particles) and a fluid. The theory, which is consistent with the critical porosity concept, uses three free parameters that determine the dependence of the dry‐rock moduli of the sand and clay matrices as a function of porosity and clay content.Testing of the model with laboratory data shows good agreement between predictions and measurements. In addition to a rock physics model that can be useful for petrophysical interpretation of wave velocities obtained from well logs and surface seismic data, the model provides the differential equation for computing synthetic seismograms in inhomogeneous media, from the seismic to the ultrasonic frequency bands.