Gassmann Model Research Articles

Joint measurement of cosmic-ray muons and seismic waves at laboratory scale

SUMMARY Current geophysical exploration methods face challenges in accurately determining gas saturation levels and elastic constants with adequate spatial resolution. Seismic wave velocity is a critical physical property in these techniques, but it introduces uncertainties because of its composite nature involving density and two elastic constants (e.g. bulk and shear modulus), which exhibit a trade-off relationship. We propose a novel approach that integrates cosmic-ray muon detection with seismic exploration to independently resolve P- and S-wave velocities into their constituent elastic constants and densities. First, we utilized a fluid substitution approach based on Gassmann's model to illustrate the benefits of incorporating density information in predicting gas saturation levels in pores. This supports the advantage of decomposing seismic wave velocity into density and two elastic constants. Second, to validate the applicability and performance of the proposed method, which involves separating seismic wave velocity into density and two types of elastic constants, muon and ultrasonic data were collected in laboratory experiments on two different targets: an acrylic block and an aluminium block. Upon muon observation, a relationship is established to convert muon flux into density length, considering the characteristics of the building housing the laboratory and the direction of muon arrival at specific positions within the building. Although there is potential for enhancing the accuracy of the derived physical properties such as density, bulk modulus, and shear modulus, the feasibility of this method has been successfully demonstrated at the laboratory scale.

Bayesian linearized inversion for petrophysical and pore-connectivity parameters with seismic elastic data of carbonate reservoirs

Abstract Carbonate reservoirs are important targets for promoting the oil and gas reserve exploration and production in China. However, such reservoirs usually contain the developed complex pore structures, which heavily affect the precision in seismic prediction of petrophysical parameters. As one of the most important parameters to characterize reservoir rock, pore-related parameters can not only describe the pore structure, but also be used to evaluate the oil/gas bearing capabilities of potential reservoirs. The conventional rock-physics models (e.g. Gassmann's model) are formulated assuming fully-connected pores, which is unable to accurately capture the geometrical complexity in real rocks. In order to characterize the influences of multiple pores on the elastic properties, this work presents a rock-physics modelling method for carbonates, wherein the percentage composition of connected pores is equivalently quantified as the pore-connectivity factor. The method treats the pore-connectivity factor as an objective variable to characterize the spatial variations of pore structure. Specifically, the method combines the differential equivalent medium theory and Gassmann's model, and derives a linearized forward operator to quantitatively link porosity, water saturation, and pore-connectivity factor to seismic elastic parameters. According to the Bayesian linear inverse theory, the simultaneous estimation of petrophysical and pore-connectivity parameters is achieved. To characterize the statistical variations with multiple lithofacies, the Gaussian mixture model is employed to quantify the prior distribution of the objective variables. The posterior distribution of the objective variables is analytically expressed with the linearized forward operator. Numerical experiments show that the accuracy of the proposed method in predicting elastic parameters is improved. Compared with the conventional Xu-White model and the varying pore aspect ratio method, the accuracy of predicted P-wave velocity increases by 10.29% and 1.33%, respectively, and the predicted S-wave velocity increases by 6.44% and 0.03%, in terms of correlation coefficient. The application to the field data validates the effectiveness of the method, wherein the porosity and water saturation results help indicating the spatial distribution of potential reservoirs.

Rational function neural networks for learning rock physics models from field data

Abstract Seismic wave velocity estimation is critical for understanding Earth's internal structure. Traditional rock physics models require careful physical assumptions and mathematical derivations, often facing challenges when applied to complex field data. Empirical formulas, while simple, lack a solid physical foundation. To address these limitations, we propose a data-driven approach using rational function neural networks (RafNN) for rock physics modelling. By analysing logging data, RafNN establishes a rational equation capturing the interdependencies among rock modulus, matrix stiffness, porosity, and fluid. The results show that RafNN accurately extracts the Gassmann's equation when the training data adheres to its constraints. Moreover, RafNN can derive general models from logging data that deviate from the Gassmann's equation. These data-driven models exhibit lower prediction errors while maintaining consistency with Gassmann's model. RafNN's adaptability to field data variability is a key advantage, facilitating better comprehension of the underlying mathematical and physical principles. Additionally, we explore the relationship between modulus, porosity, and compressibility, shedding light on the physical interpretation of RafNN models. Notably, RafNN derives analytical models directly from field data, reducing reliance on mathematical derivations and physical assumptions. Although further research is needed to understand the convergence theory of RafNN, this study presents a promising approach for data-driven rock physics modelling. It contributes to the exploration of Earth's heterogeneous structure and advances the field of seismic wave velocity estimation.

Modelling and validation of dry and saturated velocities in carbonates from Saudi Arabia – Part II

Ultrasonic compressional (P-wave) and shear (S-wave) velocity data, obtained from a set of 35 dry and water-saturated (carbonate) core samples, were presented as a first part to this study, in a separate paper by Bakhorji and Schmitt (2022). These carbonate samples were obtained from a prominent reservoir in Saudi Arabia.In this follow-up paper, the velocity measurements, obtained from these 35 core samples, were utilized to, firstly, predict and validate four appropriate rock physics models and to, secondly, derive empirical relationships relating the P- and S-wave velocities to the porosity and calcite content of the samples (over the effective pressure range from 5 MPa to 25 MPa). The derived empirical relationships were validated against the wireline P- and S-wave velocities assuming insitu reservoir pressure conditions. The empirical models predicted the P- and S-wave velocities accurately over the reservoir interval of interest. The shear strengthening / weakening effect, or the saturation effect on the shear moduli, was also modelled and is discussed further.The comparisons of the Biot, Gassmann, Mavko-Jizba-Biot (MJ-Biot) and Mavko-Jizba-Gassmann (MJ-Gassmann) model predictions, with the measured water-saturated P- and S-wave velocities, show that the squirt mechanism was not applicable for our samples. The Gassmann model consistently over-predicts the water-saturated S-wave velocities at low pressure, but closely fits the measured velocities at high pressures, whereas Biot over-predicts the water-saturated velocities in most of the studied samples. We conclude that Biot global-flow is most likely to be the principle dispersion mechanism in these samples.

Monitoring fluid saturation in reservoirs using time‐lapse full‐waveform inversion

AbstractMonitoring the rock physics properties of the subsurface is of great importance for reservoir management. For either oil and gas applications or CO2 storage, seismic data are a valuable source of information for tracking changes in elastic properties which can be related to fluids saturation and pressure changes within the reservoir. Changes in elastic properties can be estimated with time‐lapse full‐waveform inversion. Monitoring rock physics properties, such as saturation, with time‐lapse full‐waveform inversion is usually a two‐step process: first, elastic properties are estimated with full‐waveform inversion, then the rock physics properties are estimated with rock physics inversion. However, multiparameter time‐lapse full‐waveform inversion is prone to crosstalk between parameter classes across different vintages. This leads to leakage from one parameter class to another, which, in turn, can introduce large errors in the estimated rock physics parameters. To avoid inaccuracies caused by crosstalk and the two‐step inversion strategy, we reformulate time‐lapse full‐waveform inversion to estimate directly the changes in the rock physics properties. Using Gassmann's model, we adopt a new parameterization containing porosity, clay content and water saturation. In the context of reservoir monitoring, changes are assumed to be induced by fluid substitution only. The porosity and clay content can thus be kept constant during time‐lapse inversion. We compare this parameterization with the usual density–velocity parameterization for different benchmark models. Results indicate that the proposed parameterization eliminates crosstalk between parameters of different vintages, leading to a more accurate estimation of saturation changes. We also show that using the parameterization based on porosity, clay content and water saturation, the elastic changes can be monitored more accurately.

Probabilistic seismic petrophysical inversion with statistical double-porosity Biot-Rayleigh model

Petrophysical inversion quantitatively extracts reservoir properties from seismic data/attributes, which has gained increasing attention in assisting hydrocarbon reservoir exploration and evaluation. However, given complex reservoirs, its application is limited either due to the adopted rock-physics model or due to the computational demand. We have developed a semianalytic seismic petrophysical inversion method intended for complex reservoirs. The method incorporates the double-porosity Biot-Rayleigh (BR) model into the petrophysical forward operator, to take into account the heterogeneities within reservoir rocks. The inversion process combines statistical rock-physics modeling and Bayesian Gaussian mixture estimation, by which the analytical expression of the results can be achieved with limited computational cost. To better describe pore structure complexities, the inclusion content that constitutes a double-porosity medium of the BR model is considered an unknown variable, which favors the spatial variation of pore structures under complex lithofacies conditions. In addition, the method uses simulated annealing to estimate the inclusion content at a well location to obtain its prior information and takes advantage of the Monte Carlo simulation in rock-physics modeling to stabilize the inversion results. The method is tested and applied to the field data from a carbonate reservoir in southern China, the results of which show that the accuracy of the petrophysical parameters in terms of root-mean-square error are increased by as much as 12% compared with the method based on the Gassmann model.

Acoustic Dispersion in Low Permeability Unconventional Reservoir Rocks and Shales at In Situ Stress Conditions

Utilizing laboratory measurements on dry and fully brine-saturated well-lithified shale reservoir rocks and comparing them to log data and theoretical modeling, we find no statistically significant intrinsic dispersion from seismic to sonic and laboratory measurement frequencies due to fluid effects. Under in situ stress conditions, the Gassmann zero-frequency P-wave velocity prediction for a Permian basin sample was within 0.3% of the measured velocity on the brine-saturated sample at an ultrasonic frequency. At deviatoric stresses ranging from 1.7 to 70 MPa on the same sample, the percent error in the Gassmann P-wave velocity prediction ranges from 0.3 to 2.2%. These results are consistent with the lack of significant dispersion in the reported velocities and theoretical predictions in the Cotton Valley shale. Based on the Biot–Gassmann model, the characteristic frequency in both formations occurs at ~1010 Hz. Applying a squirt flow model also predicts transition to the high-frequency regime occurring at ~109 Hz for both formations. The comparison of the sonic log measurements for four different shale/tight rock formations to ultrasonic measurements taken from core samples under in situ stress conditions confirms these findings. To our knowledge, this is the first extensive comparison of the sonic log to ultrasonic core data measurements. For these rocks, there is no clearly observable or predicted significant dispersion due to fluid effects at in situ stress conditions within the frequency range for which measurements are made.

A seismic-properties and wave-propagation analysis for the long-term monitoring of supercritical geothermal systems

This study is focused on the modeling of the seismic response in a supercritical geothermal system subjected to a long-term cold and isothermal re-injection during 20 years of exploitation. The modeling aims to assess the usability of seismic-methods for monitoring supercritical geothermal reservoir. We use a synthetic data set for the analysis of the seismic properties of the reservoir: pressure and temperature evolution is derived from a previous numerical study of a two-dimensional supercritical reservoir with pure water as the pore fluid. We calculate the related variations in time of the seismic properties of the reservoir saturated-rock formation using the Burgers–Gassmann mechanical model to evaluate the effects of high temperature on the rock frame, and to account for fluid-properties variations. We observe that, at the analyzed pressure and temperature conditions, the seismic properties of the reservoir formation are mainly determined by the thermophysical characteristics of the pore fluid. During the long-term cold re-injection we observe a decrease in the compressional seismic velocity in the cooled area near the injection well, with a radius that increases in time. We use a 2D full-waveform propagation algorithm based on the Burgers–Gassmann model to calculate synthetic signals in a single-well acquisition layout, with a time step of half year. We observe that in the cool injection scenario the changes in the anomalous area can be seismically monitored, while in the case of isothermal injection, changes due to the re-injection are not seismically appreciable.

SEISMIC-DERIVED ROCK TRUE RESISTIVITY (Rt ) REVISITED. PART II: REFORMULATION USING WYLLIE’S TIME-AVERAGE MODEL

This paper is the second of a three-part presentation. As highlighted in the previous paper (Part I, Widarsono Mendrofa, 2006), the main objective of the study is to re-evaluate the potential of acoustic impedance as a source of resistivity data. This essentially came from the very idea of extracting information of resistivity (Rt ), data that plays a very important role in the determination of water saturation in reservoir, from seismic-derived acoustic impedance (AI).As observed in the past view years, there have been a lot of efforts devoted to the extraction of water saturation information from seismic. However, as Widarsono Mendrofa (2006) put it, most of the efforts were mainly based on pattern recognition activities with little attention was given to the theoretical aspects of relationships between seismic signals and water saturation. The work reported in this threepart presentation is concentrated more as re-establishing (a reformulation of works reported in Widarsono Saptono, 2003; 2004) the theoretical relationship between resistivity and acoustic impedance.In the Part I (Widarsono Mendrofa, 2006), a reformulation between the classical Gassmann acoustic velocity model and shally sand models of Modified Simandoux and Hossin is presented. In the reformulation, a new resistivity function of acoustic impedance has been established. In principle, whenever acoustic impedance data from seismic has been made available resistivity data for the determination of fluid saturation can be estimated.Despite the theoretical correctness of the resistivity function presented in the Part I, practicallity is not the function’s best aspect. In other words, the resistivity function is not an easy one to be used practically. Various parameters (e.g. matrix moduli) have to be assumed, since the data cannot easily measured even in the laboratory. This is indeed the main reason why gassmann model, and others such as Biot, has not been used much in day-to-day practices such as log interpretation for porosity determination.Being aware of such difficulties, in 1954 M.R.J. Wyllie et al proposed their “time average” model (named after its proportional averaging of pore fluid, rock matrix, and shale transit time values to represent transit time of a fluid-filled porous medium) for any practical uses related to P-wave velocity in porous media. Due to its simplicity, the model, as well as its subsequent modifications, has been used extensively since then in some areas especially in log analysis for porosity determination. Considering this simplicity aspect, this three-part study also adopted Wyllie “time average” model into its reformulation works. This Part II paper presents the formulation using Wyllie and the two shally sand models following the same manner that was adopted and presented in the Part I paper.Summarily, the objectives of the works presented in this paper are:- To establish a model/method to obtain formation rock true resistivity (Rt ) from seismic-derived acoustic impedance (AI),- To provide correction/modification onto previous works reported in Widarsono Saptono (2003, 2004), and- To provide a simpler alternative to the resistivity function yielded from the reformulation works presented in Part I paper (Widarsono Mendrofa, 2006)

4D petroelastic modeling based on a presalt well

After their initial discovery in 2006, followed by an accumulated production of over 2 billion barrels of oil equivalent, the presalt carbonate reservoirs of offshore Brazil are now candidates for time-lapse seismic analysis. Therefore, we have conducted a 4D feasibility study in a Brazilian presalt reservoir well, which is composed of two types of carbonate rocks: microbialite and coquina. We evaluated two petroelastic models to obtain the acoustic impedance (AI) and shear impedance (SI) needed to estimate potential time-lapse differences ([Formula: see text], [Formula: see text], and [Formula: see text]). For this, we used the Gassmann and Xu-Payne models, in which the latter considers the pore geometry of the rock in its equations. Our analysis of both models shows that changes in pressure and saturation are very similar, and we can conclude that, despite being a carbonate, the application of Gassmann’s model is sufficient for the 4D feasibility studies conducted in the deemed reservoir because it does not require pore space geometry parameters, as does the Xu-Payne model. The analysis of the time-lapse attributes provided us with a greater comprehension of the 4D scenarios modeled, some of which presented detectability of changes in the microbialite and coquina.

An evaluation of empirical and rock physics models to estimate shear wave velocity in a potential shale gas reservoir using wireline logs

Shear wave velocity (Vs) is essential for determining the elastic properties of rocks, which are useful for shale gas reservoir characterization. Many investigators have developed empirical models of varying form and complexity, and simplified rock physics models for the estimation of Vs using conventional well logs and/or laboratory measurements on core samples. Other investigators have developed rock physics models and used them to estimate velocities based on fundamental rock properties such as mineralogy, pore geometry and fluid saturations. The selection of a suitable model based on well logs is challenging, especially in cases where cores are not available. This study evaluates various relationships in the literature for the estimation of shear wave velocity applied to sandy shale and shale intervals of the Lower Goru Formation, Lower Indus Basin, Pakistan. Some inputs (e.g., compressional wave velocity) are directly taken from conventional log measurements, while others (e.g., petrophysical and elastic properties) are estimated using available log and the literature data. A statistical analysis has been used to quantify the difference between measured and predicted Vs. The results reveal that some empirical models can produce a coefficient of determination (R2) of roughly 0.8 when cross-plotted against measured Vs values, and R2 values can be further increased by 10%–20% if the coefficients are adjusted based on available Vs data. However, these models do not explicitly account for the mechanisms of velocity variations in sandy shale and shale due to pore geometry (aspect ratio), consolidation and fluid saturations in the manner that rock physics models do. The rock physics modeling conducted for this work demonstrated that the use of Biot's model (rather than Gassmann's model) for fluid substitution improved model performance for Vs estimation in gas-saturated sandy shale and shale of the Lower Goru Formation. Although statistical analysis showed this model to be slightly less accurate than the best empirical models (R2 of approximately 0.77), it is suggested that the rock physics model should be reliable when applied to a broader range of saturations and lithologies in the Lower Goru Formation. Also, using the rock physics approach, model input parameters can be optimized using Vp data, which represents a significant advantage over the empirical models which require Vs data for optimization. The modified rock physics model is thus deemed to be the best option available at present for the study area, and it is suggested that it should be appropriate for use in other settings – assuming that Vp data are available and sufficient knowledge regarding rock lithology is available.

Seismic properties in conductive and convective hot and super-hot geothermal systems

Seismic methods contribute to the exploration of geothermal areas and characterization of existing geothermal resources. Seismic velocity and attenuation depend on the pressure and temperature conditions of the geothermal systems, which are closely related to the properties of the rock frame and geothermal fluids. We calculate the seismic velocities and attenuation in terms of the subsurface distribution of the confining and pore pressures and temperature, assuming that the heat transfer from below is convective or conductive. The pore pressure is assumed hydrostatic. In hydrothermal systems the temperature is calculated assuming the boiling point condition at the specific pore pressure down to the reservoir. Beneath the reservoir it is assumed constant in convectively heated systems and following a constant temperature gradient in conductively heated systems. In Enhanced Geothermal Systems (EGS) conductive heat transfer and constant temperature gradient are assumed. We present three application examples, considering simplified subsurface models to describe the geothermal systems beneath the production wells. The seismic wave properties are calculated using the rock's mechanical Burgers model and the Arrhenius equation to take into account rock-properties-variability with temperature and the Gassmann model for fluid saturating the porous rocks.

Effect of CO2 on P- and S-wave velocities at seismic and ultrasonic frequencies

Time-lapse seismic is a widely used technology for monitoring the geological sequestration of carbon dioxide (CO2), consisting of mapping its movement in the subsurface and of demonstrating that the CO2 is safely stored in the reservoir (Xue and Ohsumi, 2004). In this work, the effect of CO2 on P- and S-wave velocities was investigated. Laboratory measurements were performed with Castlegate sandstone both at seismic frequencies (1–155 Hz), and at ultrasonic frequency (around 500 kHz). Different CO2 saturations between 2% and 10% were obtained by controlled depressurization of CO2-saturated water with which the sandstone sample had been saturated with. At seismic frequencies, the results of the experiments revealed that P-wave velocity is strongly reduced in the presence of free gas CO2 in the pore space, whereas at ultrasonic frequency, the P-wave velocity changed only slightly. Therefore, the presence of free CO2 gas increased significantly the P-wave dispersion between seismic and ultrasonic frequencies. The S-wave velocity, on the other hand, was hardly affected by the pore fluid at seismic frequencies. At seismic frequencies, P- and S-wave velocities were consistent with the Biot–Gassmann model. The P-wave velocity dispersion and corresponding attenuation were simulated by applying the Cole–Cole model. The transition frequency was found around 200 kHz.

Sensitivity of seismic properties to temperature variations in a geothermal reservoir

Geophysical characterization plays a key role for the definition of the deep structures of geothermal reservoirs and the consequent assessment and validation of the geothermal conceptual model. Seismic methods may provide a valuable contribution for this purpose. This involves a deep and reliable understanding of the sensitivity of seismic-wave propagation to physical and temperature variations, with complex interactions. We present the theory and sensitivity analysis based on rock's mechanical Burgers model including Arrhenius temperature equations, integrated with Gassmann model for fluid saturated porous rocks, pressure effects for bulk and shear moduli, as well as permeability and squirt flow effects. Assuming a temperature gradient model, the analysis applied at low seismic frequencies compares the interpretation of the sensitivity effects for different typical seismic elastic quantities, showing the different performance in relation to physical effects, including melting, supercritical conditions, and observability obtained in different temperature regions. With a quantification of the physical properties, the results of the study show that in deeper zones the main expected contributions in terms of variations in seismic velocity, moduli and seismic attenuation due to temperature come from melting transition, while in shallower porous fluid-saturated formations the trends are governed by pressure effects, with minor contributions of permeability and possible effects related to soft porosity. The new calculated elastic moduli are complex-valued and frequency-dependent, and temperature dependent through the fluid properties. In this complex scenario, not always the increments in the velocity and elastic wave moduli correspond to an increment in the temperature. Moreover, with mobility decreasing as a function of depth, the analysis shows that the shear quality factor is sensitive to permeability, which introduces moderate effects for velocity and attenuation of shear waves. The analysis applies to active exploration seismic and passive seismology.

Velocity dispersion and fluid substitution in sandstone under partially saturated conditions

The elastic moduli of four sandstone samples are measured at seismic (2−2000 Hz) and ultrasonic (1 MHz) frequencies and water- and glycerin-saturated conditions. We observe that the high-permeability samples under partially water-saturated conditions and the low-permeability samples under partially glycerin-saturated conditions show little dispersion at low frequencies (2−2000 Hz). However, the high-permeability samples under partially glycerin-saturated conditions and the low-permeability samples under partially water-saturated conditions produce strong dispersion in the same frequency range (2−2000 Hz). This suggests that fluid mobility largely controls the pore-fluid movement and pore pressure in a porous medium. High fluid mobility facilitates pore-pressure equilibration either between pores or between heterogeneous regions, resulting in a low-frequency domain where the Gassmann equations are valid. In contrast, low fluid mobility produces pressure gradients even at seismic frequencies, and thus dispersion. The latter shows a systematic shift to lower frequencies with decreasing mobility. Sandstone samples showed variations in Vp as a function of fluid saturation. We explore the applicability of the Gassmann model on sandstone rocks. Two theoretical bounds for the P-velocity are known, the Gassmann–Wood and Gassmann–Hill limits. The observations confirm the effect of wave-induced flow on the transition from the Gassmann–Wood to the Gassmann–Hill limit. With decreasing fluid mobility, the P-velocity at 2–2000 Hz moves from the Gassmann–Wood boundary to the Gassmann–Hill boundary. In addition,, we investigate the mechanisms responsible for this transition.

Influence of subsurface injection on time‐lapse seismic: laboratory studies at seismic and ultrasonic frequencies

ABSTRACTSeismic monitoring of reservoir and overburden performance during subsurface CO2 storage plays a key role in ensuring efficiency and safety. Proper interpretation of monitoring data requires knowledge about the rock physical phenomena occurring in the subsurface formations. This work focuses on rock stiffness and elastic velocity changes of a shale overburden formation caused by both reservoir inflation induced stress changes and leakage of CO2 into the overburden. In laboratory experiments, Pierre shale I core plugs were loaded along the stress path representative for the in situ stress changes experienced by caprock during reservoir inflation. Tests were carried out in a triaxial compaction cell combining three measurement techniques and permitting for determination of (i) ultrasonic velocities, (ii) quasistatic rock deformations, and (iii) dynamic elastic stiffness at seismic frequencies within a single test, which allowed to quantify effects of seismic dispersion. In addition, fluid substitution effects connected with possible CO2 leakage into the caprock formation were modelled by the modified anisotropic Gassmann model. Results of this work indicate that (i) stress sensitivity of Pierre shale I is frequency dependent; (ii) reservoir inflation leads to the increase of the overburden Young's modulus and Poisson's ratio; (iii) in situ stress changes mostly affect the P‐wave velocities; (iv) small leakage of the CO2 into the overburden may lead to the velocity changes, which are comparable with one associated with geomechanical influence; (v) non‐elastic effects increase stress sensitivity of an acoustic waves; (iv) and both geomechanical and fluid substitution effects would create significant time shifts, which should be detectable by time‐lapse seismic.

The impact of saturation on seismic dispersion in shales — Laboratory measurements

Previous studies found a significant increase of acoustic velocities between seismic and ultrasonic frequencies (seismic dispersion) for shales, which would have to be taken into account when comparing seismic or sonic field data with ultrasonic measurements in the laboratory. We have executed a series of experiments performed with a partially saturated Mancos shale and a Pierre shale I in which the influence of water saturation on acoustic velocities and seismic dispersion was investigated. The experiments were carried out in a triaxial setup allowing for combined measurements of quasistatic rock deformation, ultrasonic velocities, and dynamic elastic stiffness at seismic frequencies under deviatoric stresses. Prior to testing, the rock samples were preconditioned in desiccators at different relative humidities. For both shale types, we present and analyze the experimental results that demonstrate strong saturation and frequency dependence of dynamic Young’s moduli, Poisson’s ratios, and Thomsen’s anisotropy parameters, as well as P- and S-wave velocities at seismic and ultrasonic frequencies. The observed effects can be attributed to water adsorption and capillary pressure that are functions of several factors including water saturation. Water adsorption results in a reduction of surface energy and grain-contact stiffness. The capillary pressure affects the effective stress and possibly also the effective pore-fluid modulus, which may be approximated by Brie’s empirical model. Reasonable fits to the low-frequency seismic data are obtained by accounting for these two effects and applying the anisotropic Gassmann model. The strong increase in dispersion with increasing water saturation is attributed to local flow involving adsorbed (bound) water, but a quantitative description is yet to be provided.

The combined effects of pore structure and pore fluid on the acoustic properties of cracked and vuggy synthetic rocks

Many experimental observations show that the shear modulus of carbonate rocks changes in some cases upon fluid saturation. This observation is inconsistent with the presumption inherent to Gassmann's model that the shear modulus is independent of the fluid saturant. If the shear modulus change after saturation is ignored, the reliability of analyses of amplitude-versus-offset (AVO) and time-lapse seismology would be affected. So the elastic properties and velocities of saturated carbonates with complex pore structure are investigated. We made synthetic carbonate cores containing either void cracks or vuggy pores by first embedding predesigned aluminum foils or NaCl grains into the two-component matrix (carbonate cuttings and epoxy) and then leaching them out. We measured the ultrasonic P-and S-wave velocities of eight synthetic cores at different saturation conditions, and compared our measurements with theoretical predictions. The results indicate that changes in the shear modulus after saturation depend on both the pore structure and the pore saturant. Samples with cracks show shear stiffening because the viscous coupling is more active in narrow pores. Regardless of the pore structure, the shear moduli at kerosene saturation are larger than that at brine saturation, because the completely wetting kerosene provides a more shear-resistant solid-fluid boundary. The dynamic moduli changes with saturation increase as the secondary porosity increases. Gassmann's equation underestimates the velocities at shear stiffening and overestimates the velocities at shear weakening. The velocity deviation between Gassmann's prediction and experimental observations increases as the increase of shear modulus change.

Research on the equivalence between digital core and rock physics models

In this paper, we calculate the elastic modulus of 3D digital cores using the finite element method, systematically study the equivalence between the digital core model and various rock physics models, and carefully analyze the conditions of the equivalence relationships. The influences of the pore aspect ratio and consolidation coefficient on the equivalence relationships are also further refined. Theoretical analysis indicates that the finite element simulation based on the digital core is equivalent to the boundary theory and Gassmann model. For pure sandstones, effective medium theory models (SCA and DEM) and the digital core models are equivalent in cases when the pore aspect ratio is within a certain range, and dry frame models (Nur and Pride model) and the digital core model are equivalent in cases when the consolidation coefficient is a specific value. According to the equivalence relationships, the comparison of the elastic modulus results of the effective medium theory and digital rock physics is an effective approach for predicting the pore aspect ratio. Furthermore, the traditional digital core models with two components (pores and matrix) are extended to multiple minerals to more precisely characterize the features and mineral compositions of rocks in underground reservoirs. This paper studies the effects of shale content on the elastic modulus in shaly sandstones. When structural shale is present in the sandstone, the elastic modulus of the digital cores are in a reasonable agreement with the DEM model. However, when dispersed shale is present in the sandstone, the Hill model cannot describe the changes in the stiffness of the pore space precisely. Digital rock physics describes the rock features such as pore aspect ratio, consolidation coefficient and rock stiffness. Therefore, digital core technology can, to some extent, replace the theoretical rock physics models because the results are more accurate than those of the theoretical models.

Laboratory measurements of the effect of fluid saturation on elastic properties of carbonates at seismic frequencies

ABSTRACTA significant portion of the world's hydrocarbon reserves are found in carbonate reservoirs, yet analysis of the petrophysical properties of these reservoirs is associated with a number of challenges. Some of these challenges stem from physical and chemical interactions between the carbonate rock matrix and pore fluids, which can affect elastic properties of the rock. Hence, the study of the pore fluid effects on the elastic properties of carbonates is important for understanding a change of the field performance properties of а carbonate reservoir caused by fluid movements during hydrocarbon extraction in producing fields. In this laboratory study, we investigate the applicability of Gassmann's model for predictions of the elastic moduli of water‐ and hydrocarbon‐saturated Savonnières limestone and the influence of partial water saturation on elastic and anelastic properties of the rock. We present the results of two sets of laboratory experiments on the Savonnières oolitic limestone where we: (i) evaluate the effect of full water and n‐decane saturation on elastic moduli and attenuation at seismic (0.1 Hz–120 Hz) and ultrasonic (0.5 MHz) frequencies; and (ii) quantify the dependence of elastic moduli and extensional attenuation on water saturation at two seismic frequencies of 1 Hz and 10 Hz. We demonstrate that the change in the bulk modulus of limestone fully saturated either with n‐decane or water is in agreement with Gassmann's fluid substitution theory, whereas the shear modulus is noticeably reduced. The measurements with partial saturation show that the bulk modulus decreases with increasing water saturation to a lesser extent than the Young's and shear moduli. Our results show that extensional attenuation in the samples with closed boundaries is insignificant under dry and fully saturated conditions but is influenced greatly by the liquid content when saturation is between 0 and 20% or 95% and 100%.