Equation For Fluid Substitution Research Articles

Pore pressure prediction based on rock physics theory and its application in seismic inversion

Formation overpressure seriously affects drilling and downhole operation. Accurate prediction on the formation pore pressure can not only reduce the probability of drilling accidents, but also quantitatively evaluate the original formation pressure of underground pore space, which provides an important reference for site selection of carbon sink projects using underground space resources such as CO2 geological storage. It is therefore necessary to set up a widely applicable method that is based on rock physics theory and conforms to the characteristics of rock mechanics and fluid mechanic. This method is suitable for both logging prediction and seismic inversion of pore pressure. The traditional method of predicting pore pressure based on P-wave velocity has multiple solutions, and the prediction based on S-wave velocity which is not sensitive to fluid has new significance. Based on the Hertz-Mindlin petrophysical model that considering pressure variation and the Gassmann fluid substitution equation that addresses the change in fluid saturation, this paper firstly derived rock physical formulas for predicting pore pressure in logging, and then derived the intrinsic power function relationship between the effective pressure (Pe) and S-wave velocity (Vs) as well as S-wave impedance (Is). Based on this, a set of geophysical methods integrating S-wave velocity prediction, pore pressure prediction in well and seismic inversion is finally established. The efficacy of this method has been well validated, with an average error of 2.35% in S-wave velocities prediction, 4.5% in single-well pore pressure prediction. The results of seismic inversion of pore pressure are consistent with the phenomenon of overpressure development in actual working area. This method can be further extended to other areas, providing invaluable reference for underground operation such as oil and gas exploration and CO2 geological storage.

Estimation of in situ stresses from PP-wave azimuthal seismic data in fracture-induced anisotropic media

Horizontally transverse isotropy (HTI) induced by vertical or subvertical aligned fractures is common for unconventional fractured porous shale oil or gas reservoirs. Compared with the unfractured rocks, the seismic response characteristics of PP-wave azimuthal amplitudes are usually disturbed by the fractures and the in situ stresses. Knowledge of fracture properties, as well as in situ stresses, is required to optimize horizontal well planning and hydraulic fracturing during production, and the seismic inversion for in situ stresses from the PP-wave azimuthal amplitude data in fracture-induced anisotropic media is an essential step. Using the linear-slip theory and the effective stress law, we derive the fluid-saturated effective elastic stiffness tensors parameterized by background elastic moduli, the effective stress coefficient of isotropic host rocks, fluid modulus, porosity, and fracture parameters based on the anisotropic Gassmann’s fluid substitution equation. Combining the perturbations in saturated stiffness tensors and scattering theory, we formulate the reflection coefficient equation of PP-wave data as a function of background porosity-related stress parameter and two (i.e., normal and shear) fracture weakness parameters. Following Bayes’ rule, we estimate the porosity-related stress parameter and fracture weaknesses using the inversion method of azimuthal Fourier coefficients. Finally, we compute the effective horizontal and vertical in situ stresses using the estimated elastic moduli, porosity-related stress parameter, and fracture weaknesses. Synthetic and real data sets demonstrate that our proposed inversion approach based on the derived reflection equation provides us another way to obtain reasonable estimates of in situ stresses in a complex-fractured porous shale reservoir.

Nonlinear inversion of seismic amplitude variation with offset for an effective stress parameter

Effective stress estimates play important roles in reservoir characterization, for instance, in guiding the selection of fracturing areas in unconventional reservoirs. Based on Gassmann’s fluid substitution model, we have set up a workflow for nonlinear inversion of seismic data for dry rock moduli, fluid factors, and a stress-sensitive parameter. We first make an approximation within the fluid substitution equation, replacing the porosity term with a stress-sensitive parameter. We then derive a linearized reflection coefficient as a function of a stress-parameter reflectivity and reexpress it in terms of elastic impedance (EI). An amplitude-variation-with-offset (AVO) inversion workflow is set up, in which the seismic data are transformed to EI, after stacking within five incidence angle ranges; these are then inverted to determine the stress-sensitive parameter. The two-step process involves two inversions with significantly different properties. The first is a model-based least-squares inversion to estimate EI; the second is a more complex nonlinear inversion of the EI for a set of unknowns including the stress-sensitive parameter. Motivated by an interest in hybridizing AVO and full-waveform inversion (FWI), we set the latter step up to resemble some features of a published AVO-FWI formulation. The approach is subjected to synthetic validation, which permits us to analyze the response and test the stability of the workflow. We finally apply the workflow to real data acquired over a gas-bearing reservoir, which reveals that the approach generates potential indicators of fluid presence and stress prediction.

Wave-velocity dispersion and rock microstructure

Porosity, fluid type and rock texture significantly affect acoustic wave propagation, since velocity dispersion and attenuation in fluid saturated rocks are mainly caused by wave-induced local fluid flow between microcracks and intergranular pores. We analyze P-wave velocity dispersion as a function of porosity to obtain information about the rock microstructure. The P-wave velocities in water-saturated rocks are predicted from measurements in gas-saturated rocks, using the Gassmann fluid substitution equation (the relaxed state). The dispersion is estimated from the difference between this predicted velocity and the measured one, where the latter corresponds to the unrelaxed state. We evaluate the wave dispersion as a function of porosity for 112 carbonates, 128 sandstones and 56 volcanic rocks, including our measurements for 86 tight rocks, showing that dispersion increases with porosity in the low porosity range, but decreases in the high porosity range. The dispersion peak occurs at a porosity of approximately 15%. Double-porosity poroelasticity modeling based on the local fluid-flow mechanism confirms this behavior. The microcrack radius has a peak in the porosity range 15–19% for all the lithologies from our collection, while the behavior of microcrack porosity is less evident. The dispersion peak may reveal the characteristics of lithological units, in particular porosity, fluid type and rock microstructure.

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.

Seismic inversion for fluid bulk modulus based on elastic impedance

Beginning with the simplification of Gassmann's fluid substitution equation, we propose a simplified bulk modulus of saturated rock in terms of fluid bulk modulus and porosity. Using relationship between reflection coefficients and scattering function, we derive a linearized PP-wave reflection coefficient as a function of fluid bulk modulus and modified porosity, and we also present the corresponding elastic impedance, which is useful for modeling how fluids affect seismic reflection amplitudes. The accuracy of derived reflection coefficient is confirmed in the case of maximum incidence angle being around 30°. Using the derived reflection coefficient and EI, we establish an inversion approach to estimate fluid bulk modulus and porosity from observed seismic data, which involves 1) the estimation of EI from partially stack seismic data, and 2) the extraction of fluid bulk modulus from estimated EI datasets. The extraction of fluid bulk modulus is implemented using a nonlinear inversion approach. Using the derived elastic impedance we compute the gradient of energy residual with respect to model vector directly, which allows us to implement the nonlinear inversion stably. Synthetic tests confirm the stability and robustness of the proposed inversion approach, and applying the inversion approach to a real dataset we obtain meaning results of fluid bulk modulus that are valuable for fluid identification in reservoirs.

Seismic anisotropy of a fractured rock during CO2 injection: a feasibility study

Fluid substitution plays the key role in reservoir characterization, leading to enhance understanding of the influence of fluids on seismic parameters. In general, fluid substitution tool assumes that the Earth is as an isotropic medium, which may not represent the practical field situation. Nevertheless, anisotropic fluid substitution provides important insights into the processes that control the anisotropic seismic response of a fractured rock when subjected to CO2 injection for enhanced oil recovery and its geological sequestration. Here, we examine the influence of fluid substitution in a porous yet fractured reservoir for quantitative interpretation of seismic data. This investigation involves anisotropic Gassmann’s equation and linear slip theory for fluid substitution in a transversely isotropic media with a horizontal axis of symmetry (HTI). We present a synthetic case by conceptualizing a double-layered half-space model with upper layer as shale and bottom layer as HTI sandstone, representing an Indian mature reservoir. The effects of variation in background porosity and fracture weaknesses on anisotropic (Thomsen’s) parameters, acoustic parameters including amplitude variation with angle have also been discussed. We observe that brine and oil sands to be associated with the highest elastic moduli, while CO2 sands exhibit contrasting trend. It is noteworthy that CO2 is more sensitive to fracture weakness when compared to the other reservoir fluids such as hydrocarbons and brines, as P-wave moduli (as much as 37.1%) and velocity (as high as 12.2%) reduces significantly with the increase in fracture weakness. Further, Gassmann’s assumption is validated as we noticed unchanged values in shear-wave moduli and shear-wave splitting parameter (γ) for various fluid types.

Characterizing fluid contacts by joint inversion of seismic P-wave impedance and velocity

In the past, seismic exploration technique was mainly used for gathering information about subsurface rock structures and fluids by analyzing the travel time, reflection amplitude, and phase variations. However, nowadays, many additional seismic attributes have been introduced by the seismic interpreters, which aid in the visualization of subsurface geological structures, facies, and lithologies. This research aims to identify the pore fluids in the reservoir using post-stacked seismic data without requiring well log data. Gassmann’s equation, a well-known equation for fluid substitution, has been used for fluid substitution in this research. To test the proposed technique, a three-layer geological anticline model has been used. The third layer of the model represents a reservoir which is saturated with water, except its top part which is fully saturated with petroleum. Fluid identification is achieved by using fluid density, velocity changes, and acoustic impedance (AI). P-wave velocity and AI are measured from post-stacked seismic data and its inversion, from which the saturated rock density and compressional modulus (M) are calculated. Using this information, saturated rock density and compressional modulus are inverted for fluid velocity and density, respectively, to identify the pore fluid.

Brown and Korringa constants for heterogeneous thinly layered poroelastic media

AbstractMacromechanical characterization of a layered poroelastic package treated as a homogeneous (upscaled) medium is presented. The characterization is based on the knowledge of the poroelastic properties of the package's constituents. Specifically, we provide closed‐form expressions for the sum of the fourth‐order average elastic compliances tensor of the solid frame and pore space compressibility 1/Kϕ, previously defined in Brown and Korringa's extended formulation of the Gassmann's fluid substitution equations. These constants allow, thus, to perform fluid substitution on an upscaled composite consisting of poroelastic layers. Each layer within the layered package is assumed to have isotropic symmetry, uniform porosity, and single pore‐filling fluid and composed of several homogeneously distributed mineral phases such that each layer is approximately Gassmann consistent; however, the fluid and mineral phases as well as the porosity may vary from one layer to the next along the package. In addition, we obtain insights into the sensitivity of and 1/Kϕ when an approximate fluid substitution operation is used. Moreover, it is shown that the of the upscaled medium can have transverse isotropy symmetry. The degree of anisotropy is controlled by the volume fractions of individual layers and the contrast of elastic properties between the layers. The results for and 1/Kϕ are compared to those obtained by Berryman and Milton (BM) for a two‐phase isotropic composite. At a limiting case of an effectively isotropic medium, this paper's results coincide with those of BM.

Effect of pore geometry on Gassmann fluid substitution

ABSTRACTAlthough there is no assumption of pore geometry in derivation of Gassmann's equation, the pore geometry is in close relation with hygroscopic water content and pore fluid communication between the micropores and the macropores. The hygroscopic water content in common reservoir rocks is small, and its effect on elastic properties is ignored in the Gassmann theory. However, the volume of hygroscopic water can be significant in shaly rocks or rocks made of fine particles; therefore, its effect on the elastic properties may be important. If the pore fluids in microspores cannot reach pressure equilibrium with the macropore system, assumption of the Gassmann theory is violated. Therefore, due to pore structure complexity, there may be a significant part of the pore fluids that do not satisfy the assumption of the Gassmann theory. We recommend that this part of pore fluids be accounted for within the solid rock frame and effective porosity be used in Gassmann's equation for fluid substitution. Integrated study of ultrasonic laboratory measurement data, petrographic data, mercury injection capillary pressure data, and nuclear magnetic resonance T2 data confirms rationality of using effective porosity for Gassmann fluid substitution. The effective porosity for Gassmann's equation should be frequency dependent. Knowing the pore geometry, if an empirical correlation between frequency and the threshold pore‐throat radius or nuclear magnetic resonance T2 could be set up, Gassmann's equation can be applicable to data measured at different frequencies. Without information of the pore geometry, the irreducible water saturation can be used to estimate the effective porosity.

Fluid substitution in carbonate rocks based on the Gassmann equation and Eshelby–Walsh theory

Fluid substitution in carbonate rocks is more difficult than it is in clastic rocks for two reasons. Firstly, the rock physics modeling uncertainties in carbonate rocks, this is due to the difficulty of accurately acquiring the moduli of carbonate rocks' solid matrix because the experimental data on carbonate rocks have not been as thoroughly studied as silici-clastic sedimentary rocks. Secondly, due to the complex pore systems of carbonate rocks, it is very difficult to model pore geometry of carbonates, and hence hard to assess how the elastic properties change as fluid saturation changes based on the traditional Biot and Gassmann theories. In order to solve these problems, we present a new fluid substitution equation of carbonate rocks using the Gassmann equation and Eshelby–Walsh theory (GEW) in this paper. Then, the specific procedures of how to calculate the moduli of carbonate rocks' solid matrix and how to measure the effect of pore geometry in fluid substitution based on the new fluid substation equation were illustrated by experimental testing about 12 carbonate rock samples in different fluid saturation scenarios and logging data. Finally, we further compared the new fluid substitution method with the conventional Gassmann fluid substitution based on the experimental data. The results verified that the new method is more accurate and reliable in the fluid substitution of complex carbonate rocks. • Providing a method to calculate the compressive coefficient of a solid rock matrix • Analyzing the influence of solid rock matrix compressive coefficient • Analyzing the influence of pore systems on fluid substitution quantitatively • This fluid substitution method is relatively convenient, practical and reliable. • This method can acquire a more reliable result especially in carbonate rocks.

Physical modelling and the poroelastic model with application to fluid detection in a VTI medium

In this paper, both poroelasticity theory and pre-stack inversions have been combined to generate a flexible way to derive an effective fluid factor, which is then used to identify the presence of the hydrocarbon in weakly anisotropic VTI reservoirs. The effective fluid factor has been derived by using an approximate fluid substitution equation for anisotropic VTI media. The approximate equation provides a means of performing fluid substitution for elastic moduli along the vertical symmetry axis of a VTI medium with fewer elastic moduli. The effective fluid factor can be used to analyse the sensitivity of seismic attributes to fluid content. In order to examine the effectiveness of the effective fluid factor, an anisotropic physical model has been constructed. The rock properties of artificial sandstone used as a reservoir building material are properly selected by using an empirical model and Gassmann's equation. An effort is made to ensure the physical modelling data represent the `true' response of different fluid-filled sands. The fluid detection method is then applied to interpret the inverted seismic impedance obtained from physical modelling seismic data with some known gas-sands and wet-sands. The results shows that the interpretive resolution of seismic fluid detection has been dramatically improved by using the effective fluid factor. In addition, more information on lateral changes in fluid content can be distinguished. This study has demonstrated the potential of this method in detecting different fluid content in weakly anisotropic VTI reservoirs.

Estimation of CO2 saturation during both CO2 drainage and imbibition processes based on both seismic velocity and electrical resistivity measurements

SUMMARY In order to monitor injected carbon dioxide (CO2), simultaneous measurements of seismic velocity and electrical resistivity are employed during the drainage (CO2 injection) and imbibition (water injection) processes of a Berea sandstone. Supercritical CO2 (10 MPa at 40 o C) was injected into a water-saturated Berea sandstone in the drainage stage and monitored via simultaneous measurements. After the injection of supercritical CO2, fresh distilled water was injected into the CO2-injected sandstone during the imbibition stage. Electrical resistivity and P-wave velocity measurements acquired during the drainage and imbibition stages were employed to evaluate CO2 saturations (SCO2) based on the resistivity index and the Gassmann fluid-substitution equations, respectively. Comparing estimated values for SCO2 saturation against those from volume-derived SCO2, based on analysis on injected and drained fluid volumes in the drainage process, we conclude that Gassmann‐Brie and resistivity index are suitable for the evaluation based on P-wave velocity and electrical resistivity, respectively. Rt-based estimation properly tracks the variation in SCO2 even when SCO2 is large (>0.15), while Vp-based estimation is sensitive to the variation in SCO2 when SCO2 is small ( 0.1), while properly estimating SCO2 when SCO2 is small (<0.1). Monitoring the CO2 imbibition process confirms residual CO2 saturation within the sample.

Joint petrophysical inversion of electromagnetic and full-waveform seismic data

Accurate determination of reservoir petrophysical parameters is of great importance for reservoir monitoring and characterization. We developed a joint inversion approach for the direct estimation of in situ reservoir petrophysical parameters such as porosity and fluid saturations by jointly inverting electromagnetic and full-waveform seismic measurements. Full-waveform seismic inversions allow the exploitation of the full content of the data so that a more accurate geophysical model can be inferred. Electromagnetic data are linked to porosity and fluid saturations through Archie’s equations, whereas seismic data are linked to them through rock-physics fluid-substitution equations. For seismic modeling, we used an acoustic approximation. Sensitivity studies combined with inversion tests show that seismic data are mainly sensitive to porosity distribution, whereas electromagnetic data are more sensitive to fluid-saturation distribution. The separate inversion of electromagnetic or seismic data is highly nonunique and thus leads to great ambiguity in the determination of porosity and fluid saturations. In our approach, we used a Gauss-Newton algorithm equipped with the multiplicative regularization and proper data-weighting scheme. We tested the implemented joint petrophysical inversion method using various synthetic models for surface and crosswell measurements. We found that the joint inversion approach provides substantial advantage for an improved estimation of porosity and fluid-saturation distributions over the one obtained from the separate inversion of electromagnetic and seismic data. This advantage is achieved by significantly reducing the ambiguity on the determination of porosity and fluid saturations using multiphysics measurements. We also carried out a study on the effects of using inaccurate petrophysical transform parameters on the inversion results. Our study demonstrated that up to 20% errors in the saturation and porosity exponents in Archie’s equations do not cause significant errors in the inversion results. On the other hand, if the bulk modulus and density of the rock matrix have a large percentage of errors (i.e., more than 5%), the inversion results will be significantly degraded. However, if the density of the rock matrix has an error of less than 2%, the joint inversion can tolerate a large percentage of errors in the bulk modulus of the rock matrix.

Smooth regression to estimate effective porosity using seismic attributes

Abstract Data mining is very important to characterize complex geological structures, where a large variety of geophysical and petrophysical variables are typically involved and interrelated. In this paper we apply smooth regression for data analysis, by means of the Gamma test (a revolutionary estimator of the noise in a data set) to aid in the construction of Artificial Neural Network (ANN) models to predict effective porosity (φe) using seismic attributes. As a result, we obtain the best combination of seismic attributes to estimate φe. We briefly describe the Gamma test, its benefits in model identification and model building. The first validation of the Neural Network based on leave-one-out was poor. Therefore, we generate a complementary set of synthetic data (from the original well-log data), varying the effective porosity and applying the Gassmann's equation for fluid substitution to obtain resulting velocities and densities. The complete procedure is repeated including the new synthetic well-logs and the best suited selection of seismic attributes is used to train a new ANN producing a better validation and more accurate results. The advantage of smooth regression over other techniques is that it tells us how well we can predict φe using any model. This information saves time during training of the ANN and also sets a lower bound for the mean squared error to prevent over-training.

Approximate fluid substitution for vertical velocities in weakly anisotropic VTI rocks

Despite the prevalence of elastic anisotropy in rocks, most models used routinely for wave propagation, imaging, and rock physics assume an isotropic Earth. The main reason for using isotropic approximations is that we seldom measure enough parameters to characterize the stiffness tensor of a rock completely. Fluid substitution is an important example: because of an incomplete knowledge of the stiffness tensor, often we choose isotropic equations over their anisotropic form. Assuming weak anisotropy, we derive an approximate form of the anisotropic fluid-substitution equation for seismic waves propagating along the symmetry axis of a transversely isotropic medium. The approximation takes the form of the usual isotropic calculation, with a simple first-order correction proportional to the Thomsen anisotropic parameter [Formula: see text], thus requiring only three elastic constants. Because [Formula: see text] can be either greater than or less than zero in a VTI medium, we can explain why isotropic fluid substitution sometimes overpredicts or underpredicts the full anisotropic result. Numerical simulations show that the approximate equation is valid for anisotropic medium with absolute value of [Formula: see text] as high as 0.3.

Ultrasonic properties of granular media saturated with DNAPL/water mixtures

We present the results of four experiments investigating the ultrasonic properties of granular materials partially saturated with trichloroethylene (TCE), a dense non‐aqueous contaminant. P‐wave velocity measurements were made under in situ effective stress conditions using a pulse transmission cell at ≈250 kHz. Two synthetic samples and two natural aquifer cores were fully saturated with water and then subjected to an axial injection of TCE. The resulting measurements show reductions in P‐wave velocity of up to 15% due to contaminant saturation. A theoretical model combining Gassmann fluid substitution and Hill's equation was used to estimate the effects of DNAPL saturation; this model underpredicted observed reductions in velocity at high TCE saturations. A linear relationship, expressed in terms of volumetric contaminant fraction, provided an excellent empirical fit to the laboratory measurements.

Rock property- and seismic-attribute analysis of a chert reservoir in the Devonian Thirty-one Formation, west Texas, U.S.A.

In west Texas, fractured-chert reservoirs of Devonian age have produced more than 700 million barrels of oil. About the same amount of mobile petroleum remains in place. These reservoirs are characterized by microporosity; they are heterogeneous and compartmented, which results in recovery of less than 30% of the oil in place. In this case study the objective was to use cores, petrophysical logs, rock physics, and seismic attributes to characterize porosity and field-scale fractures. The relations among porosity, velocity, and impedance were explored and also reactions among production, impedance, and lineaments observed in 3D attribute volumes. Laboratory core data show that Gassmann’s fluid-substitution equation works well for microporous tripolitic chert. Also, laboratry measurements show excellent linear correlation between P-wave impedance and porosity. Volumetric calculations of reflector curvature and seismic inversion of acoustic impedance were combined to infer distribution of lithofacies and fractures and to predict porosity. Statistical relations were established between P-wave velocity and porosity measured from cores, between P-wave impedance and producing zones, and between initial production rates and seismic “fracture lineaments.” The strong quantitative correlation between thick-bedded chert lithofacies and seismic impedance was used to map the reservoir. A qualitative inverse relation between the first [Formula: see text] of production and curvature lineaments was documented.

Sensitivity analysis of Gassmann's fluid substitution equations: Some implications in feasibility studies of time-lapse seismic reservoir monitoring

Here, we discuss the sensitivity of the seismic response to uncertainties in the physical parameters of the reservoir rock. For this purpose, a probabilistic sensitivity analysis of Gassmann's fluid substitution equations using a Monte Carlo approach was carried out. We represented uncertainties related to each parameter as probability density functions to evaluate the contribution of each parameter uncertainty to the variance of the seismic response ( V p), calculated by means of the Monte Carlo approach. We show that uncertainties related to grain density ( ρ gr), dry shear modulus ( G d) and dry bulk modulus ( K d) contribute more significantly on the variance of V p, if all parameters are uncorrelated. This outcome changes, when physical dependencies are represented as correlations in the Monte Carlo sampling of some of the parameters. In this sense, correlations distribute more evenly the contributions to uncertainty in V p. On the other hand, we also evaluated scenarios of fluid substitution, in which fluid 1 is replaced by fluid 2, with the corresponding variations in seismic response. In this case, V p2 is the P-wave velocity of rock saturated with a fluid 2. If V p2 were forecasted from an initial set of parameters of the rock saturated with fluid 1 ( V p1, V s1, etc.) the uncertainties related to V p1, V s1 and K gr would contribute more significantly to the variance of V p2. From these three initial parameters, the most important contributions come form V p1 and V s1. Concomitantly, we evaluated the contribution of possible variations in fluid phase density and bulk modulus and of a pore pressure perturbation (4MPa) for several scenarios of connate and injection fluids on the variance of V p. We did this for several values of initial differential pressure. Results indicate that the contribution of the elastic piezosensitivity and possible changes in the fluid phase properties depend not only on the initial differential pressure, but also on the type of fluids involved in substitution process. We conclude that sensitivity information, limited in this case to Gassman's equations, can be used as a tool to improve feasibility studies in time-lapse seismic reservoir monitoring and as a priori qualitative knowledge. The latter can guide the inversion process or help to diminish the uncertainties due to poorly constrained inversion schemes.

A rock physics strategy for quantifying uncertainty in common hydrocarbon indicators

We present a strategy for quantifying uncertainties in rock physics interpretations by combining statistical techniques with deterministic rock physics relations derived from the laboratory and theory. A simple example combines Gassmann’s deterministic equation for fluid substitution with statistics inferred from log, core, and seismic data to detect hydrocarbons from observed seismic velocities. The formulation identifies the most likely pore fluid modulus corresponding to each observed seismic attribute and the uncertainty that arises because of natural variability in formation properties, in addition to the measurement uncertainties. We quantify the measure of information in terms of entropy and show the impact of additional data about S-wave velocity on the uncertainty of the hydrocarbon indicator. In some cases, noisy S data along with noisy P data can convey more information than perfect P data alone, while in other cases S data do not reduce the uncertainty. We apply the formulation to a well log example for detecting the most likely pore fluid and quantifying the associated uncertainty from observed sonic and density logs. The formulation offers a convenient way to implement deterministic fluid substitution equations in the realistic case when natural geologic variations cause the reference porosity and velocity to span a range of values.