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Abstract This paper uses the effective media theory to estimate the heterogeneous distribution, the bulk and formation compressibility in the reservoir, in function of rock elastic properties, such as, the volumetric moduli (K) and shear (µ) vs. depth, by means of field available data, such as geophysical logs (density and sonic). Results from four (4) naturally fractured carbonated reservoir are shown and from one sand reservoir counting on log information for validation. Introduction In the oil Mexican industry, mainly in the reservoir simulation, and in other similar areas, knowledge in properties formation is most needed, as in compressibility. It is common to use averages of such properties or use correlation from other fields, data reported in literature, or in the best of the cases samples are sent to the laboratory for an on time compressibility evaluation, despite the effort theoretical and experimental tools are currently needed to determine and forecast compressibility representative values Due to the above in this paper an original geomechanic survey is presented, letting us know the rock mechanic properties. Taking into account both, well predominant lithologies and the rock matrix elastic properties, Model GG (1) is used (Garcia - GarcÍa), requiring little well information and without any additional investment to forecast bulk and formation compressibility. A specific case, can consider lithology unawareness; thus, elastic properties are deduced with the same data (fracture-matrix) of study material. The elastic rock properties. The elastic rock properties depend on geological formation conditions such as pressure, temperature, time and other environment conditions. Additionaly, rocks are highly heterogeneous and isotropic materials, thus these elastic properties can vary in big extent areas at different depths. Currently, the oil industry counts onsonic FWS(2) logs to predict rock elastic properties, unfortunately these tools are quite expensive, and only in very especial cases, are available in Mexican fields, on the other hand, it is usually counted ondensity and sonic logs.
- North America > United States (0.46)
- South America > Brazil (0.28)
- Europe > Norway > Norwegian Sea (0.24)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Sandstone (0.35)
Inclusionbased formulations allow an explicit description of pore geometry by viewing porous rocks as a solid matrix with embedded inclusions representing individual pores. The assumption commonly used in these formulations that there is no fluid pressure communication between pores is reasonable for liquidfilled rocks measured at high frequencies; however, complete fluid pressure communication should occur throughout the pore space at low frequencies. A generalized framework is presented for incorporating complete fluid pressure communication into inclusionbased formulations, permitting elastic behavior of porous rocks at high and low frequencies to be described in terms of a single model. This study extends previous work by describing the pore space in terms of a continuous distribution of shapes and allowing different forms of inclusion interactions to be specified. The effects of fluid pressure communication on the elastic moduli of porous media are explored by using simple models and are found to consist of two fundamental elements. One is associated with the cubical dilatation and governs the effective bulk modulus. Its magnitude is a function of the range of pore shapes present. The other is due to the extensional part of the deviatoric strain components and affects the effective shear modulus. This element is dependent on pore orientation, as well as pore shape. Using sandstone and granite models, an inclusionbased formulation shows that large differences between high and lowfrequency elastic moduli can occur for porous rocks. An analysis of experimental elastic wave velocity data reveals behavior similar to that predicted by the models. Quantities analogous to the open and closed system moduli of GassmannBiot poroelastic theory are defined in terms of inclusionbased formulations that incorporate complete fluid pressure communication. It was found that the poroelastic relationships between the open and closed system moduli are replicated by a large class of inclusionbased formulations. This connection permits explicit incorporation of pore geometry information into the otherwise empirically determined macroscopic parameters of the GassmannBiot poroelastic theory.
- North America > United States (0.73)
- North America > Canada (0.68)
- Geology > Geological Subdiscipline > Geomechanics (0.68)
- Geology > Rock Type > Sedimentary Rock (0.51)
- North America > United States > West Virginia > Appalachian Basin > Berea Sandstone Formation (0.89)
- North America > United States > Pennsylvania > Appalachian Basin > Berea Sandstone Formation (0.89)
- North America > United States > Ohio > Appalachian Basin > Berea Sandstone Formation (0.89)
- (2 more...)
ABSTRACT: We test a number of empirical models, such as the Wyllie time average and Raymer?s velocity-porosity equation, as well as physic based effective-medium models, such as the self-consistent and differential effective medium theory, against three published datasets. Two of these datasets are velocity measurements in artificial composites made of metal particles embedded in epoxy resin in a range of particle concentration. The third dataset is velocity in water-saturated carbonate. We find that for certain ranges of inclusion concentration and porosity, the empirical equations (Wyllie?s and Raymer?s) fail. At the same time, an effective-medium model, such as DEM, appears to be consistently valid if the aspect ratio is selected appropriately and then held constant for the entire concentration or porosity range. This aspect ratio can be found by calibrating the theory to the data at a single data point and then holding it constant in the entire concentration/porosity range. The intention of this work is to set a consistent rigorous foundation for modeling of the elastic properties of sediment with inclusions, such as carbonate, with the ultimate goal of consistent interpretation of log and seismic data for rock properties and texture. 1. INTRODUCTION A composite with isotropic matrix and randomly embedded and oriented inclusions is isotropic. Theories for the effective elastic moduli of such a composite are of two general types: (1) upper and lower bounds and (2) exact solutions. The narrowest bounds are due to Hashin and Shtrikman (1963). Mal and Knopoff (1967) obtained effective properties for a two-phase medium with the assumptions that the matrix is solid, the inclusions are spherical, much smaller than the wavelengths of the propagating waves, and that interactions between inclusions are negligible. Kuster and Toksöz (1974a) derived theoretical expressions for long wavelengths based on scattering theory. Both spherical and oblate spheroidal inclusions were considered in their calculations. When comparing experimental data for the case of a liquid matrix with solid inclusions, Kuster and Toksöz (1974b) concluded that the observed data could be fit either by their model or by the Reuss (1929) lower bound appropriate for the elastic moduli of a suspension. More recent are the differential effective medium theory (DEM) and self consistent methods (SC). DEM (Bruggeman, 1935; Walsh, 1980; Norris, 1985; Avellaneda, 1987; Berryman, 1992) assumes that a composite material may be constructed by making infinitesimal changes in an already existing composite. It is relevant to modeling the elastic properties of a porous medium with inclusions in a wide porosity range. SC uses mathematical solutions for the deformation of isolated inclusions, but the interaction of inclusions is approximated by replacing the background medium with as-yet-unknown effective medium (Mavko, et al., 1998). Berryman (1992) proposed three single scattering approximations for estimating the effective elastic properties of composite materials: (a) the average Tmatrix approximation; (b) the coherent potential approximation; and (c) DEM. Devaney and Levine (1980) proposed another model based on a self consistent formulation of the multiscattering theory. Their approach assumed that the inclusions are spherical and that the wavelengths are longer than the size of the inclusions.
- Geophysics > Seismic Surveying (1.00)
- Geophysics > Borehole Geophysics (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Reservoir geomechanics (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management > Open hole/cased hole log analysis (0.94)
Using fused glass beads, we have constructed a suite of clean sandstone analogs, with porosities ranging from about 1 to 43 percent, to test the applicability of various composite medium theories that model elastic properties. We measured P and Swave velocities in dry and saturated cases for our synthetic sandstones and compared the observations to theoretical predictions of the HashinShtrikman bounds, a differential effective medium approach, and a selfconsistent theory known as the coherent potential approximation. The selfconsistent theory fits the observed velocities in these sandstone analogs because it allows both grains and pores to remain connected over a wide range of porosities. This behavior occurs because this theory treats grains and pores symmetrically without requiring a single background host material, and it also allows the composite medium to become disconnected at a finite porosity. In contrast, the differential effective medium theory and the HashinShtrikman upper bound overestimate the observed velocities of the sandstone analogs because these theories assume the microgeometry is represented by isolated pores embedded in a host material that remains continuous even for high porosities. We also demonstrate that the differential effective medium theory and the HashinShtrikman upper bound correctly estimate bulk moduli of porous glass foams, again because the microstructure of the samples is consistent with the implicit assumptions of these two theoretical approaches.
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Sandstone (1.00)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Exploration, development, structural geology (0.68)
- Reservoir Description and Dynamics > Reservoir Characterization > Reservoir geomechanics (0.68)
Rock physics aims to characterize rock properties based on the behavior of seismic waves propagating through them. This requires consideration of how the composition of a rock dictates its stress-strain relationship and thus seismic response. The effect of pore fluids is of particular interest due to its applicability to the hydrocarbon industry. In a standard seismic interpretation workflow rock physics is used to relate impedance and elastic parameters derived from seismic data to specific rock properties. This constrains what seismic data is physically capable of resolving and the non-uniqueness associated with a specific interpretation. A material is linearly elastic if its stress-strain relationship is governed by Hooke's Law, The fourth order elasticity or stiffness tensor requires 34 terms to specify the stress strain relationship for an arbitrary homogeneous material.
- Information Technology > Knowledge Management (0.40)
- Information Technology > Communications > Collaboration (0.40)