Research and application of seismic porosity inversion method for carbonate reservoir based on Gassmann’s equation

Carbonate rocks frequently exhibit less predictable seismic attribute–porosity relationships because of complex and heterogeneous pore geometry. Pore geometry plays an important role in carbonate reservoir interpretation, as it influences acoustic and elastic characters. So in porosity prediction of carbonate reservoirs, pore geometry should be considered as a factor. Thus, based on Gassmann’s equation and Eshelby–Walsh ellipsoidal inclusion theory, we introduced a parameter C to stand by pore geometry and then deduced a porosity calculating expression from compressional expression of Gassmann’s equation. In this article, we present a porosity working flow as well as calculate methods of every parameter needed in the porosity inverting equation. From well testing and field application, it proves that the high-accuracy method is suitable for carbonate reservoirs.

Consistent experimental investigation of the applicability of Biot-Gassmann’s equation in carbonates

Carbonate formations are characterized by multiscale heterogeneities that control their acoustic response and flow properties. At the laboratory scale, carbonate rocks do not indicate a strong correlation between P- and S-wave velocities and porosity. The velocity disparities between carbonates of similar mineralogy and porosity result from different microstructures derived from their sedimentary facies and subsequent diagenetic transformations. The still-discussed applicability of Biot-Gassmann’s equation for fluid substitution in carbonate rocks remains another key issue. We have developed an integrated experimental workflow that allows a consistent checking of the applicability of Biot-Gassmann’s equation and provides key geologic and microstructural information to understand the petroacoustic signature of carbonate rocks. The defined approach is based on the phase-velocity measurements performed in liquid-saturated conditions using polar and nonpolar fluids. It allows the identification of the whole set of parameters required by Biot-Gassmann’s equation including the bulk modulus of the solid matrix. This approach is implemented on samples representative of two different carbonate formations deposited in lacustrine and marine environments, respectively. The obtained results demonstrate the applicability of Biot-Gassmann’s equation for the two studied carbonate families and indicate the link between their petroacoustic signature and diagenetic history.

SINGULAR VALUE SELECTION AND GENERALIZED CROSS VALIDATION IN MULTI-FREQUENCY SEISMIC DIFFRACTION TOMOGRAPHY FOR CO2 INJECTION MONITORING

ABSTRACT. Regardless of whether the cause of the greenhouse effect is anthropogenic, carbon dioxide (CO2) exacerbates global warming because it contributes directly to the increased temperature of the planet. In a geologic context, CO2 can occur in conjunction with porous oil reservoirs...Keywords: seismic diffraction tomography, reservoir monitoring, Gassmann’s equation, CO2 injection RESUMO. Independentemente se a causa do efeito de estufa é antropogênico, o dióxido de carbono (CO2) agrava o aquecimento global porque contribui diretamente para o aumento da temperatura do planeta. Em um contexto geológico, o CO2 pode ocorrer em conjunto com reservatórios de petróleo porosos.Palavras-chave: tomografia sísmica de difração, monitoramento de reservatórios, equação de Gassmann, injeção de CO2.

Seismic petrophysics: Part 2

In Part 1 of this tutorial in the April 2015 issue of TLE, we loaded some logs and used a data framework called Pandas to manage them. We made a lithology-fluid-class (LFC) log and used it to color a crossplot. This month, we take the workflow further with fluid-replacement modeling based on Gassmann's equation. This is just an introduction; see Wang (2001) and Smith et al. (2003) for comprehensive overviews.

Estimating Brown-Korringa constants for fluid substitution in multimineralic rocks

Brown and Korringa extended Gassmann’s equations for fluid substitution in rocks to allow for arbitrarily mixed mineralogy. This extension was accomplished by adding just one additional constant—replacing the mineral bulk modulus with two less intuitive constants. Even though virtually all rocks have mixed mineralogy, the Brown and Korringa equations are seldom used because values for the constants are unknown. We estimate plausible values for the Brown-Korringa constants, based on effective medium models. The self-consistent formulation is used to describe a rock whose mineral and pore phases are randomly distributed ellipsoids—a plausible representation of randomly mixed mineral grains, as with dispersed clay in sandstone. Using the self-consistent model, the two constants are predicted to be nearly identical, justifying the use of an average mineral modulus in Gassmann’s equations. For small contrasts in mineral stiffness, the Brown-Korringa constants are approximately equal to the Voigt-Reuss-Hill average of the individual mineral bulk moduli. In a second approach, a multilayered spherical shell model is used to describe a rock where a particular solid phase preferentially coats grains or lines pores. In this case, the constants can differ substantially from each other, demonstrating the need for the Brown-Korringa equation. A third model represents weak pore-lining or pore-filling clay within an arbitrary pore geometry. The clay-fluid mix can be replaced exactly with an average fluid or “mud.” When the nonclay minerals have similar moduli, then the replacement of the clay-fluid mix causes the Brown-Korringa equation to revert to Gassmann’s equation.

Effects of fluid changes on seismic reflections: Predicting amplitudes at gas reservoir directly from amplitudes at wet reservoir

The equations for fluid substitution in a sample with known porosity and the mineral’s and pore-fluid’s elastic moduli are well-documented. Discussions continue on how to conduct fluid substitution in practical situations where more than one fluid phase is present and the porosity and mineralogy are not precisely defined. We pose a different question: If we agree on a fluid substitution method, and also agree that at partial saturation the bulk modulus of the “effective” pore fluid is the harmonic average of those of the components, can we conduct fluid substitution directly on the seismic reflection amplitude? To address this question, we conducted forward modeling synthetic exercises: We systematically varied the porosity, clay content, and thickness of the reservoir and assumed that the properties of the bounding shale are fixed. Next, we used a velocity-porosity model to compute the elastic properties of the dry-rock frame and applied Gassmann’s equation to compute these properties in wet rock as well as at partial gas saturation. After that, we generated prestack synthetic seismic reflections at the top of the reservoir at full saturation and at partial saturation, and related one to the other. We found that within our assumption framework, there is an almost linear relation between the intercepts of the P-to-P reflectivity for the wet and gas reservoir. The same is true for the gradients. We have provided best-linear-fit equations that summarize these results. We applied this technique to field data and found that we can approximately predict the seismic amplitude at a gas reservoir from that measured at a wet reservoir, given that all other properties of the rock remain fixed. The solution given here should be treated as a method, meaning it should be tested and modified for various rock types and textures.

AVA inversion of the top Utsira Sand reflection at the Sleipner field

Amplitude variation with angle (AVA) inversion is performed on the top Utsira Sand reflector at the Sleipner field, North Sea, Norway. This interface is of particular interest because of the accumulation of [Formula: see text] injected from a point deeper in the Utsira Sand. The focus is on the postmigration processing of angle gathers together with the actual inversion procedure. The processing treats amplitude extraction, offset-to-angle mapping, and global scaling in detail. Two algorithms are used for the inversion of AVA data, one that assesses uncertainties and one fast least-squares variant. Both are very suitable for this type of problem because of their covariance matrices and built-in regularization. In addition, two three-parameter approximations of the Zoeppritz equations are used. One is linear approximation and the other is quadratic. The results show significant signals for all three elastic parameters, but the substitution of brine by [Formula: see text] using Gassmann’s equation indicates that the contrasts in S-wave impedance and density are overestimated. For the contrasts in P-wave impedance the results are in agreement with the fluid substitution. A simple sensitivity analysis shows that the offset-to-angle mapping and the damping factor in the inversion are the most plausible explanations of the discrepancy.

Variation of unjacketed pore compressibility using Gassmann’s equation and an overdetermined set of volumetric poroelastic measurements

Gassmann’s original equation provides a means to relate bulk elastic parameters of a porous material with the compressibility of the pore fluid. The original analysis assumed microhomogeneity and isotropy, which assumed that pore compressibility was equal to grain compressibility. Although subsequent theoretical arguments have shown that Gassmann’s original assumption is violated for most rocks and that pore compressibility need not equal grain compressibility, few experimental studies have compared the two compressibilities; the assumption that pore compressibility equals grain compressibility is still commonly made. We measured hydrostatic poroelastic constants of Berea sandstone and Indiana limestone under drained, undrained, and unjacketed conditions over a range of confining and pore pressures to test the assumption that pore compressibility equals grain compressibility. These two rocks were chosen because they havesimilar values of porosity but different elastic behaviors: Berea sandstone is nonlinearly elastic, especially at low effective stresses, but Indiana limestone is linearly elastic at nearly all stresses. At low effective stresses below [Formula: see text], the pore compressibility for Berea sandstone does not equal grain compressibility but approaches fluid compressibility. Even at higher effective stresses, pore compressibility for Berea sandstone does not equal bulk grain compressibility but approaches a value approximately two to three times the bulk grain compressibility. In contrast, pore compressibility for Indiana limestone does seem to be equal to grain compressibility except perhaps at low effective stresses below [Formula: see text]. The difference between pore compressibilities of these two rocks is likely from the presence of more compliant clay minerals mixed with quartz grains with more microcracks in the Berea sandstone as compared to the well-cemented Indiana limestone.