Gassmanns equation for fluid substitution petrowiki. Seismic modelling e l b of unconventional reservoirs c i t m. The next step was the calculation of the compressional and shear wave velocities for brine saturated samples using. Gassmann s equation calculates fluidsaturation effects on the bulk modulus of a porous medium using the known bulk moduli of a the solid matrix, b the frame, and c the pore fluid. Given the importance of the effectivepressure coefficient. 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. Focus article contd seismic modelling continued from page 54 continued on page 56 ig u re2. Numerous assumptions are involved in the derivation and application of. To do this, note first that equation 2 can be rewritten as. Identifying patchy saturation from well logs short note. Summary by describing the influence of the pore fluids on seismic properties, we attempt to provide a comprehensive understanding of gassmanns equation. Conversely, the gassmann equations for fluidsolid substitution gassmann, 1951. Download gassmanns fluid substitution carry out calculations and generate graphs with seismic velocity changes using an automatic plotting mode.
Equation 7 gives the undrained bulk modulus of fluidsaturated porous material as function of the bulk. Pdf gassmanns fluid substitution equations belong to the most popular approaches to calculate velocities for rocks saturated with one fluid. Geological survey scientific investigations report 20085196, 14 p. Supporting information for american chemical society. In this section, we will derive a new rock physics template based on the pore space stiffness approach. For a given porosity, points with low values practical gassmann fluid substitution in sandshale sequences rob simm. Extended solid gassmann substitution, as proposed by ciz and shapiro 2007, extended the anisotropic gassmann equation brown and korringa, 1975 to calculate elastic modulus of reservoir rock. Application of gassmanns equation for laboratory data from. 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. The simple asperitydeformation model is useful to explain the physics of porous and cracked media under confining and porefluid pressures. Equation 7 was first derived by 10, however, as shown above this equation can also be derived from the more general and earlier biots poroelasticity theory. Crains petrophysical handbook modeling biot gassmann.
Gassmanns equation fluid substitution relates the elastic moduli of fluidsaturated rock k s, m s to those of dry porous rock k d, m d. A constitutive equation and generalized gassmann modulus for multimineral porous media jose m. Presently, the applicability of gassmanns equation to carbonate rocks is unresolved. On this basis, it was possible to get the input values needed to compute the gassmann equations table 2.
Consider a porous medium whose connected pore space is saturated with a singlephase viscous fluid. A look into gassmanns equation nawras alkhateb, chorus heavy oil consortium, department of geoscience, university of calgary nawras. 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. Thus, it is only proper to call equa tion 7 as the biotgassmann equation. The gassmann equation gassmann, 1951 is commonly used to predict the effect of changes in the fluid type on the acoustic property of a. R ar vp br vs cr d, the akirichards equation says that the reflectivity at angle is the weighted sum of the v p, v s and density reflectivities. Gassmann s equation may not be directly applicable for amplitude variation with offset avo modeling due to the violation of its assumptions low permeability, highly compressible mineral components, invasion and dispersion, the high sensitivity to input parameters which may be in error, the variations in rock frame porosity and compressibility between gas and brine saturated rocks. The gassmann equation is the most common way of performing a fluid.
Deriving the gassmann equation we can combine these two fundamental equations to arrive at the simplest form of the gassmann equation. Despite the popularity of gassmanns equations and their incorporation in most. Numerous assumptions are involved in the derivation of gassmanns equation. Gassmann s 1951 equations relate the bulk and shear moduli of a saturated isotropic porous, monomineralic medium to the bulk and shear moduli of the same medium in the drained case and shows.
Asymptotic gassmann model for unconsolidated sediments containing water and gas hydrate without free gas. K 0 lines is an indicator of relative rock stiffness, or rock compliance xu and white, 1995. 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. Gassmanns equation and fluidsaturation effects on seismic velocities. The sensitivity of v p on gassmann equation parameters is attained by performing monte carlo simulations. Each parameter was modeled as a random variable, whose probability density function pdf corresponds to a gaussian function, characterized by a mean value. 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.
The solution, as well as equivalent solutions for three nuclides and the general case, are known as bateman 1910 equationssolutions. In the case of disconnected or cracklike pores, however, this assumption may be violated. The first step in the use of gassmann equation consisted on the definition of input values. The well logs can be used with other software to calculate synthetic. These include, for instance, terzaghi law, gassmann equation and the static approach leading to the concept of effective stress, much used in soil mechanics. Solving this first order differential equation for n. Prestack pro getting started guide sharp reflections. The program generates well logs with vp, vs and density. Comparison of the modified biotgassmann theory and the. 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.
The coupon code you entered is expired or invalid, but the course is still available. This state of partial saturation where equation 3, together with gassmanns equations, is applicable for calculating the rocks elastic moduli is. 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. A constitutive equation and generalized gassmann modulus for. S chm atp s nof h k b d w l porosity and mineral end members. Ciz and shapiro, 2007 assume that the inclusions are interconnected with each other, and therefore, the stress or. In particular, problems arise in automated analysis in which results are usually taken at face value. Effective porosity for gassmann fluid substitution fuyong yan, dehua han and qiuliang yao, rock physics lab, university of houston. The unjacketed core compressibility in a porous rock is the change in pore volume due to change in pore pressure for constant differential pressure. Apr 02, 2018 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. Gassmann s equation gassmann s equations provide a simple model for estimating the.
Global stochastic inversion for characterization of a. A gassmannconsistent rock physics template cseg recorder. Thus, gassmanns theory results in an independence of the rocks shear modulus from the pore fluid type berryman, 1999. Fluidseis users guide a matlab fluid substitution program.
A look into gassmanns equation search and discovery. Modeling the sonic log response from biot gassmann equations an alternate and more rigorous approach is the biot gassmann equation set. The fraction of total volume occupied by fluid is the porosity, which is assumed to be uniform on some appropriate length scale. Uncertainty in fluid substitution using gassmanns equation. Testing gassmann fluid substitution in carbonates where k sat, k d and k g are respectively saturated, dry and grain bulk moduli, and. Bulk modulus and density of the fluid are k f and,respectively. The pore space compressibility of a rock provides a robust, modelindependent descriptor of porosity and pore fluid effects on effective moduli. It was assumed that the target zone is at a depth of 2. In the approach presented here, we have solved the gassmann equation in petrophysical terms, and defined a gas term for the wyllie timeseries equation that rigorously accounts for gas. Table 2 input values used to compute the gassmann equations. This parameter affects how the saturated bulk modulus of a rock is related to the drained frame modulus and the pore fluid compressibility. This assumes that the chemical interactions between the fluids and the solids are always the same or have the same consequences for rigidity. Pdf application of gassmanns equation for laboratory data from.
Then, substituting 12 back into either 10 or 11 gives one form of the result commonly known as gassmanns equation for the bulk modulus. Sensitivity analysis of gassmanns fluid substitution. Gassmann is the eponym for the gassmann triple and gassmanns equation. Reporting class iv type avo anomaly in deep waters of indian. Porous material is isotropic, elastic, monomineralic, and. The akirichards equation any other angle is modelled with the akirichards equation, a linearized form of the zoeppritz equations which is written and is the basis of virtually all avo methods.
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. 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. The specific surface area is an important parameter related to water retention in reservoir rocks. Ravazzoli4 abstract we derive the timedomain stressstrain relation for a porous medium composed of n. Effects of co2 injection on the seismic velocity of sandstone. Then, substituting 12 back into either 10 or 11 gives one form of the result commonly known as gassmann s equation for the bulk modulus. General equation of gassmanns relation 12, 1619 for saturated rock is as follows. Fluisseis can be used to calculate only fluid properties, dry rock properties or calculate the undrained rock properties.
Recent measurements of poroelastic constants and effective medium theories are used to estimate how the. Seismic pore space compressibility and gassmanns relation. Simultaneous linear equations mathematics resources. 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. In this study, all the brinesaturated measurements have been normalized to fluid properties at constant pore pressure of p p3. Isotropic, homogeneous, elastic, monomineralic medium. One form of gassmann s equation that clearly emphasizes the fluid saturation effects is given by 2 2 1 1 dry. Practical gassmann fluid substitution in sandshale sequences. Gassmann s equation how does the constant c 1 depend on the fluid bulk modulus in a region of partial melt.
As shown by russell and smith 2007, equation 2 allows us to model k dry at different porosities. Numerous assumptions are involved in the derivation and application of gassmanns equation. Effective pressure or what is the effect of pressure. In order to get effective bulk modulus, a range of gk can be used to find the best fit between modeled and. In this study, we have analyzed the complexity of pore structure and its interaction with pore fluid.
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