If the dryframe moduli are known, from either measurements or theoretical calculations, the effect of pore water on velocities can be modeled using the gassmann theory. Gassmann, schlossstrasse 6, 18225 kuhlungsborn, germany. Kuster and toksoz developed a theory based on wavescattering theory for. Sensitivity analysis of gassmanns fluid substitution. It was assumed that the target zone is at a depth of 2. Read sensitivity analysis of gassmanns fluid substitution equations. 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. The unjacketed core compressibility in a porous rock is the change in pore volume due to change in pore pressure for constant differential pressure. 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. Gassmanns equation 1 estimates the saturated bulk modulus ksat through the bulk. Consider a porous medium whose connected pore space is saturated with a singlephase viscous fluid. On this basis, it was possible to get the input values needed to compute the gassmann equations table 2.
Gassmanns equation and fluidsaturation effects on seismic velocities. The gassmann equation gassmann, 1951 is commonly used to predict the effect of changes in. Therefore,fluid substitution on well log data was performed using the gassmanns model. 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. In the case of disconnected or cracklike pores, however, this assumption may be violated.
Then, substituting 12 back into either 10 or 11 gives one form of the result commonly known as gassmanns equation for the bulk modulus. The sensitivity of v p on gassmann equation parameters is attained by performing monte carlo simulations. We investigate the suitability of gassmann s equation for a co2 sequestration project with 1600 tons of co2 injected into highporosity, brinesaturated sandstone. Gassmann is the eponym for the gassmann triple and gassmanns equation. 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 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. Biot theory almost for dummies university of houston. The velocity of sound in a rock is related to the elastic properties of the rockfluid mixture and its density, according to the wood, biot, and gassmann equations.
Exact results for generalized gassmanns equations in composite. A distinction between stable and unstable stratification is required for the formulation of thermal dissipation in numerical modelling. 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. Current modelling delivers negative dissipation rates for stabl. When applying gassmanns equation in situations where too many phases.
Each parameter was modeled as a random variable, whose probability density function pdf corresponds to a gaussian function, characterized by a mean value. Leibniz institute of atmospheric physics, kuhlungsborn, germany. Uncertainty analysis of velocity to resistivity transforms. Gassmann s equations gassmann s equations relate the bulk modulus of a rock to its pore, frame, and fluid properties. 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. Elastic velocities of watersaturated sandstones depend primarily on porosity, effective pressure, and the degree of consolidation.
Numerous assumptions are involved in the derivation and application of gassmanns equation. Gassmann s equation gassmann s equations provide a simple model for estimating 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. 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. Pdf gassmanns fluid substitution equations belong to the most popular approaches to calculate velocities for.
Gassmanns equation how does the constant c 1 depend on the fluid bulk modulus in a region of partial melt. Gassmanns equation is suited for fluid substitution in a homogeneous medium. Effective porosity for gassmann fluid substitution fuyong yan, dehua han and qiuliang yao, rock physics lab, university of houston. Crains petrophysical handbook modeling gardners equation. New york had the highest population of gassmann families in 1880. In 1880 there were 14 gassmann families living in new york. The biotgassmann equations match observations well for unconsolidated gas sands. This parameter affects how the saturated bulk modulus of a rock is related to the drained frame modulus and the pore fluid compressibility.
Lee abstract the velocity ratio of watersaturated sediment derived from the biotgassmann theory depends mainly on the biot coef. On the applicability of gassmann model in carbonates. Gassmann showed that the shear modulus is independent of fluid content. Exact results for generalized biotgassmann equations for. For a given porosity, points with low values practical gassmann fluid substitution in sandshale sequences rob simm. Gs is the gassmann selfsimilar model, and gs dt is the model with a depthtrend. 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. Stanford exploration project, report 102, october 25, 1999, pages 187192. The first step in the use of gassmann equation consisted on the definition of input values.
A triple porosity scheme for fluidsolid substitution. Velocity ratio and its application to predicting velocities by myung w. The gassmann equation is the most common way of performing a fluid substitution model from one known parameter. 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. 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 fluid substitution process. Velocity ratio and its application to predicting velocities. Gassmanns equation for predicting saturation and porosity effects in carbonate rocks. Data shows that we have examined the applicability of the gassmanns equation for the heavy oil saturated samples. Gassmann and krief have both developed models relating compressional and shear acoustic velocities to bulk moduli of the solids and contained liquids. Apr 03, 2015 an understanding of rock physics is crucial for the interpretation of avo anomalies. Gassmanns equation for fluid substitution petrowiki.
Seismic pore space compressibility and gassmanns relation. This occurred mainly in older wells where the operator had financial constraints or thought the uphole potential was limited. Aug 25, 2017 gassmann with the symmetry of voigts class nr. The equations and software implementations rokdoc version 5. 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. The gassmann family name was found in the usa, the uk, and canada between 1880 and 1920. This assumes that the chemical interactions between the fluids and the solids are always the same or have the same consequences for rigidity. 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. A look into gassmanns equation search and discovery. In this study, we have analyzed the complexity of pore structure and its interaction with pore fluid. Weappliedknownmethods, including rock physics, depth trends, structural information, and uncertainty analysis. In particular, problems arise in automated analysis in which results are usually taken at face value. Geometrically speaking, the coefficients, and define a pair of straight lines. He also showed that the bulk modulus of the various components are related by the following equation.
Global stochastic inversion for characterization of a. Modeling the sonic log response from biotgassmann equations an alternate and more rigorous approach is the biotgassmann equation set. Pdf different forms of gassmann equation and implications. Gassmanns derivation is based on the following assumptions for a porous. To estimate the effect of the pore fluid on the elastic properties, the gassmann fluid. May 01, 2006 read sensitivity analysis of gassmanns fluid substitution equations. Substitution in gas bearing reservoirs to define velocity profiles application of gassmann and krief models digital formation, inc. Three porosity models total porosity, effective porosity, and a movable fluid model are compared from a simulator to seismic sim2seis modelling perspective. An understanding of rock physics is crucial for the interpretation of avo anomalies. Since co 2injected reservoirs have two different pore fluids i. Tran and others published different forms of gassmann equation and implications for the estimation of rock properties find.
Table 2 input values used to compute the gassmann equations. 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. 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. Practical gassmann fluid substitution in sandshale sequences. The biot gassmann equations match observations well for unconsolidated gas sands.
Rock types homogeneous, isotropic heterogeneous, isotropic gassmanns theory works only for the microscopically homogeneous rock e. Numerical examples biotgassmann and wyllie equations. Download limit exceeded you have exceeded your daily download allowance. This was about 22% of all the recorded gassmanns in the usa. 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. Fluid substitution in a shaley sandstone reservoir at seismic. Summary by describing the influence of the pore fluids on seismic properties, we attempt to provide a comprehensive understanding of gassmanns equation. The fraction of total volume occupied by fluid is the porosity, which is assumed to be uniform on some appropriate length scale.
Characterizing fluid contacts by joint inversion of seismic p. 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. Fluid substitution in carbonate rocks based on the gassmann. A look into gassmanns equation nawras alkhateb, chorus heavy oil consortium, department of geoscience, university of calgary nawras. Stanford exploration project, report 102, october 25, 1999, pages 187. The gassmann equation, first described by fritz gassmann, is used in geophysics and its. Fluid substitution in carbonate rocks is more difficult than it is in clastic rocks for two reasons. However, nowadays, many additional seismic attributes have been introduced by the seismic interpreters, which aid in the visualization of subsurface geological structures, facies, and. The scattering coefficients used here are exact results obtained previously for scattering from a spherical inclusion of one biot material imbedded.
Background resistivity model from seismic velocities. Assuming linear elasticity and the rocks to be isotropic and homogeneous. Background resistivity model from seismic velocities dieter werthmuller 1, anton ziolkowski, and david wright abstract we developed a methodology to estimate resistivities fromseismic velocities. 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. 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. The specific surface area is an important parameter related to water retention in reservoir rocks. 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. 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. 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. Estimation of co2 saturation during both co2 drainage and. The pore space compressibility of a rock provides a robust, modelindependent descriptor of porosity and pore fluid effects on effective moduli. At insitu conditions, pore fluids are often multiphase mixtures.
Even at a modest porosity of 15%, changes can be substantial. Fluid substitution in carbonate rocks based on the. Shaley sandstone is heterogeneous at a seismic scale. 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. Comparison of the modified biotgassmann theory and the. View enhanced pdf access article on wiley online library html view download pdf for offline viewing. 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. Geological survey scientific investigations report 20085196, 14 p. Pdf application of gassmanns equation for laboratory data from. Recent measurements of poroelastic constants and effective medium theories are used to estimate how the.
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. 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. 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. Modelling the seismic responses of amangihydrocarbon field.
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. Bulk modulus and density of the fluid are k f and,respectively. The bulk modulus of a saturated rock is given by the low frequency gassmann theory gassmann, 1951 as a tutorial on gassmann fluid substitution. A comparison of the krief and gassmann equation general. The most gassmann families were found in the usa in 1920. Fluid substitution in a shaley sandstone reservoir at. 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 this study, porosity concepts in gassmanns fluid substitution model are examined and their implications for quantitative 4d seismic studies are discussed. Predictions of the gassmann theory depend on the bulk and shear moduli of the dry samples, which are known from ultrasonic measurements, and the. K f and k b are the bulk moduli of the porefluid and the mineral in the rock frame. In this work, we carry out quantitative analysis of timelapse seismic by using rock physics and seismic modelling tools. K 0 lines is an indicator of relative rock stiffness, or rock compliance xu and white, 1995. 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.
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