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 siliciclastic sedimentary rocks. Consider a porous medium whose connected pore space is saturated with a singlephase viscous fluid. Recent measurements of poroelastic constants and effective medium theories are used to estimate how the. Each parameter was modeled as a random variable, whose probability density function pdf corresponds to a gaussian function, characterized by a mean value. For rocks saturated with fluids, the gassmann equation is proved effective in estimating the exact change in seismic velocity or rock moduli upon the changes in properties of pore infill.
Tran and others published different forms of gassmann equation and implications for the estimation of rock properties find, read and cite all the research you need. Even at a modest porosity of 15%, changes can be substantial. Estimation of co2 saturation during both co2 drainage and. Numerous assumptions are involved in the derivation and application of gassmanns equation. Sensitivity analysis of gassmanns fluid substitution. The biot gassmann equations match observations well for unconsolidated gas sands. This occurred mainly in older wells where the operator had financial constraints or thought the uphole potential was limited. The gassmann family name was found in the usa, the uk, and canada between 1880 and 1920. Global stochastic inversion for characterization of a. The bulk modulus of a saturated rock is given by the low frequency gassmann theory gassmann, 1951 as a tutorial on gassmann fluid substitution. Exact results for generalized biotgassmann equations for. A look into gassmanns equation nawras alkhateb, chorus heavy oil consortium, department of geoscience, university of calgary nawras.
Numerical examples biotgassmann and wyllie equations. The specific surface area is an important parameter related to water retention in reservoir rocks. K f and k b are the bulk moduli of the porefluid and the mineral in the rock frame. Download gassmanns fluid substitution carry out calculations and generate graphs with seismic velocity changes using an automatic plotting mode and employing the gassmanns equation method. A triple porosity scheme for fluidsolid substitution. Fluid substitution in carbonate rocks is more difficult than it is in clastic rocks for two reasons. Gassmann, schlossstrasse 6, 18225 kuhlungsborn, germany. Pdf gassmanns fluid substitution equations belong to the most popular approaches to calculate velocities for.
Gassmann s equation gassmann s equations provide a simple model for estimating the. The analysis usually quoted for addressing this problem in regions of partial melt have normally used some type of classical effective medium theory, which is most appropriately used for systems in which the inclusions are both. Read fluid substitution in carbonate rocks based on the gassmann equation and eshelbywalsh theory, journal of applied geophysics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available. Read sensitivity analysis of gassmanns fluid substitution equations.
In this work, we carry out quantitative analysis of timelapse seismic by using rock physics and seismic modelling tools. Stanford exploration project, report 102, october 25, 1999, pages 187. Since co 2injected reservoirs have two different pore fluids i. The volume average equation can be used to model density in a water sand, but this equation does not match observations for velocities in a gas sand. The gassmann equation, first described by fritz gassmann, is used in geophysics and its relations are receiving more attention as seismic data are increasingly used for reservoir monitoring. This was about 22% of all the recorded gassmanns in the usa. The sensitivity of v p on gassmann equation parameters is attained by performing monte carlo simulations. This assumes that the chemical interactions between the fluids and the solids are always the same or have the same consequences for rigidity. Gassmanns equation for predicting saturation and porosity effects in carbonate rocks. Shaley sandstone is heterogeneous at a seismic scale. New york had the highest population of gassmann families in 1880. Equation 11 shows that the solution is obtained by matrix multiplication of the righthand side of the equations 1 and 2 by a matrix entirely created from the coefficients of the and terms in these equations. On this basis, it was possible to get the input values needed to compute the gassmann equations table 2. Modeling the sonic log response from biotgassmann equations an alternate and more rigorous approach is the biotgassmann equation set.
The gassmann equation gassmann, 1951 is commonly used to predict the effect of changes in. Geological survey scientific investigations report 20085196, 14 p. Fluid substitution in carbonate rocks based on the gassmann. Exact results for generalized gassmanns equations in composite. In 1880 there were 14 gassmann families living in new york. The gassmann equation, first described by fritz gassmann, is used in geophysics and its. A distinction between stable and unstable stratification is required for the formulation of thermal dissipation in numerical modelling. Geometrically speaking, the coefficients, and define a pair of straight lines. When applying gassmanns equation in situations where too many phases. Background resistivity model from seismic velocities dieter werthmuller 1, anton ziolkowski, and david wright abstract we developed a methodology to estimate resistivities fromseismic velocities. In order to monitor injected carbon dioxide co 2, simultaneous measurements of seismic velocity and electrical resistivity are employed during the drainage co 2 injection and imbibition water injection processes of a berea sandstone. View enhanced pdf access article on wiley online library html view download pdf for offline viewing. Velocity ratio and its application to predicting velocities. The first step in the use of gassmann equation consisted on the definition of input values.
May 01, 2006 read sensitivity analysis of gassmanns fluid substitution equations. The scattering coefficients used here are exact results obtained previously for scattering from a spherical inclusion of one biot material imbedded. Download gassmann s fluid substitution carry out calculations and generate graphs with seismic velocity changes using an automatic plotting mode and employing the gassmann s equation method. K 0 lines is an indicator of relative rock stiffness, or rock compliance xu and white, 1995. Fluidproperty discrimination with avo crewes research report volume 2001 405 the density effects of the saturated rock can be computed quite accurately with the volume average equation as. Since porosity, density and moduli including k d, k m and g d of a core are known or measured before the core flooding experiment, we can obtain v p based on eqs and after computing the values of k f and. Gassmann s equations assume that the shear modulus of the saturated rock is the same as the shear modulus of the dry rock, for all saturating fluids. November 2003 title contents benefits introduction gassmann equation in shaley formation wyllie time series equation linking gassmann to wyllie adding a gas term to wyllie equation krief equation examples conclusions benefits. The pore space compressibility is also the direct physical link between the dry and fluidsaturated moduli, and is therefore the basis of gassmann s equation for fluid substitution. Effective porosity for gassmann fluid substitution fuyong yan, dehua han and qiuliang yao, rock physics lab, university of houston.
Substitution in gas bearing reservoirs to define velocity profiles application of gassmann and krief models digital formation, inc. The pore space compressibility is also the direct physical link between the dry and fluidsaturated moduli, and is therefore the basis of gassmanns equation for fluid substitution. Assuming linear elasticity and the rocks to be isotropic and homogeneous. To study the difference between shaley sandstone effective elastic moduli calculated by mean porosity as a homogeneous medium, and those calculated directly from the subvolumes of the volume as a heterogeneous medium, computational experiments are. Therefore,fluid substitution on well log data was performed using the gassmanns model. In particular, problems arise in automated analysis in which results are usually taken at face value. Some implications in feasibility studies of timelapse seismic reservoir monitoring, journal of applied geophysics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. In the case of disconnected or cracklike pores, however, this assumption may be violated. Crains petrophysical handbook modeling gardners equation. The gassmann equation is the most common way of performing a fluid substitution model from one known parameter. Gassmanns equation for fluid substitution petrowiki. Apr 03, 2015 an understanding of rock physics is crucial for the interpretation of avo anomalies. Current modelling delivers negative dissipation rates for stabl.
The equations and software implementations rokdoc version 5. An understanding of rock physics is crucial for the interpretation of avo anomalies. A direct result of gassmann s equations is that the shear modulus for an isotropic material is independent of pore fluid, and therefore remains constant during the fluid substitution process. A direct result of gassmanns equations is that the shear modulus for an isotropic material is independent of pore fluid, and therefore remains constant during the. 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. To estimate the effect of the pore fluid on the elastic properties, the gassmann fluid. Jul 01, 2014 read fluid substitution in carbonate rocks based on the gassmann equation and eshelbywalsh theory, journal of applied geophysics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Gs is the gassmann selfsimilar model, and gs dt is the model with a depthtrend.
Table 2 input values used to compute the gassmann equations. Fluid substitution in carbonate rocks based on the. A look into gassmanns equation search and discovery. The most gassmann families were found in the usa in 1920. Gassmann showed that the shear modulus is independent of fluid content. Characterizing fluid contacts by joint inversion of seismic p. Practical gassmann fluid substitution in sandshale sequences. Seismic pore space compressibility and gassmanns relation. Gassmann s equations gassmann s equations relate the bulk modulus of a rock to its pore, frame, and fluid properties. Gassmanns equation are not well understood, in general practice, no constraints are placed on input parameters and there is no quality control of the results. With respect to elasticity all directions perpendicular to z are equivalent transversely isotropic symmetry, love 1944, page 160 and the elasticity is determined by five constants c1, c2. Gassmanns equation 1 estimates the saturated bulk modulus ksat through the bulk. It was assumed that the target zone is at a depth of 2.
For a given porosity, points with low values practical gassmann fluid substitution in sandshale sequences rob simm. Gassmann and krief have both developed models relating compressional and shear acoustic velocities to bulk moduli of the solids and contained liquids. Pdf application of gassmanns equation for laboratory data from. A comparison of the krief and gassmann equation general. Kuster and toksoz developed a theory based on wavescattering theory for. He also showed that the bulk modulus of the various components are related by the following equation. Weappliedknownmethods, including rock physics, depth trends, structural information, and uncertainty analysis. The biotgassmann equations match observations well for unconsolidated gas sands. Gassmanns equations assume that the shear modulus of the saturated rock is the same as the shear modulus of the dry rock, for all saturating fluids. Uncertainty analysis of velocity to resistivity transforms. Background resistivity model from seismic velocities. Gassmann s equation 6 pore fluid does not interact with the solid to soften or harden the frame interaction is inevitable and in many of our samples significantly alters rock properties a common application of gassmann s equation is performed to differentiate lithology driven ava anomalies from fluid driven anomalies.
Gassmanns equation 6 pore fluid does not interact with the solid to soften or harden the frame interaction is inevitable and in many of our samples significantly alters rock properties a common application of gassmanns equation is performed to differentiate lithology driven ava anomalies from fluid driven anomalies. Velocity ratio and its application to predicting velocities by myung w. On the applicability of gassmann model in carbonates. The pore space compressibility of a rock provides a robust, modelindependent descriptor of porosity and pore fluid effects on effective moduli. Aug 25, 2017 gassmann with the symmetry of voigts class nr. Gassmanns derivation is based on the following assumptions for a porous. At insitu conditions, pore fluids are often multiphase mixtures.
Gassmann is the eponym for the gassmann triple and gassmanns equation. Gassmanns equation is suited for fluid substitution in a homogeneous medium. Bulk modulus and density of the fluid are k f and,respectively. Modelling the seismic responses of amangihydrocarbon field. Pdf different forms of gassmann equation and implications. Summary by describing the influence of the pore fluids on seismic properties, we attempt to provide a comprehensive understanding of gassmanns equation. Here we test the validity of gassmann equation using two published sets of ultrasonic measurements for a model nanoporous medium, vycor glass, saturated with two different fluids, argon and nhexane. Biot theory almost for dummies university of houston.
Lee abstract the velocity ratio of watersaturated sediment derived from the biotgassmann theory depends mainly on the biot coef. Leibniz institute of atmospheric physics, kuhlungsborn, germany. All web surfers are welcome to download these notes, watch the youtube videos, and to use the notes and videos freely for teaching and learning. Tran and others published different forms of gassmann equation and implications for the estimation of rock properties find. We investigate the suitability of gassmann s equation for a co2 sequestration project with 1600 tons of co2 injected into highporosity, brinesaturated sandstone. Rock types homogeneous, isotropic heterogeneous, isotropic gassmanns theory works only for the microscopically homogeneous rock e. However, nowadays, many additional seismic attributes have been introduced by the seismic interpreters, which aid in the visualization of subsurface geological structures, facies, and. Gassmanns equation and fluidsaturation effects on seismic velocities. Then, substituting 12 back into either 10 or 11 gives one form of the result commonly known as gassmanns equation for the bulk modulus. Three porosity models total porosity, effective porosity, and a movable fluid model are compared from a simulator to seismic sim2seis modelling perspective.
Gassmanns equation how does the constant c 1 depend on the fluid bulk modulus in a region of partial melt. The gassmann equation gassmann, 1951 is commonly used to predict the effect of changes in the fluid type on. Predictions of the gassmann theory depend on the bulk and shear moduli of the dry samples, which are known from ultrasonic measurements, and the. In this study, porosity concepts in gassmanns fluid substitution model are examined and their implications for quantitative 4d seismic studies are discussed. Download limit exceeded you have exceeded your daily download allowance. The fraction of total volume occupied by fluid is the porosity, which is assumed to be uniform on some appropriate length scale.
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