### Pore Fluid and Elastic Properties of Rock

A soft sand sample of 35% porosity The dry-rock density is 1.722 g/cm3 Fluid bulk modulus 2.5 GPa; density 1 g/cm3 1.2 1.4 1.6 1.8 2.0 2.2 10 20 30 Velocity (km/s) Pressure (MPa) Dry Sandstone

get price### [PDF] The relationship between dry rock bulk modulus and

Geology There are various approaches to computing dry rock bulk modulus as a function of porosity and, from this, inferring velocity and density changes due to reservoir fluid change as a function of porosity. One such approach is the pore space stiffness method. A second approach is the critical porosity model (Mavko and Mukerji, 1995).

get price### ROCK PHYSICS MODELING OF AN UNCONSOLIDATED SAND

Hertz-Mindlin theory estimates bulk modulus accurately but overpredicts shear modulus, which was adjusted applying slip-factor correction, and as such it was used as a final model for Hoover sands. From the log data at Hoover field, the equation is derived for dry frame properties as a function of porosity and shaliness.

get price### The relationship between dry rock bulk modulus and

To model dry rock bulk modulus at different porosities, we can use pore space stiffness, the inverse of the dry rock space compressibility at a constant pore pressure, written: pore space stiffness, and porosity. dry rock bulk modulus, mineral bulk modulus,, where : 1 1 = = = = = + φ φ φ φ K K K K K K dry m dry m

get price### Change of bulk and shear moduli of dry sandstone with

and µ1A defined as the effective moduli of the rock with all the pores except those with aspect ratio a. KA* is the static bulk modulus of the empty rock (Toksoz, et al., 1976), but because of the lack of such data it is usually taken to be the dynamic bulk moduli of the dry rock. The expression for Ei is given in appendix B. Given that the

get price### [PDF] The relationship between dry rock bulk modulus and

There are various approaches to computing dry rock bulk modulus as a function of porosity and, from this, inferring velocity and density changes due to reservoir fluid change as a function of porosity. One such approach is the pore space stiffness method. A second approach is the critical porosity model (Mavko and Mukerji, 1995). Using the clean sandstones at different pressures from a dataset

get price### Change of bulk and shear moduli of dry sandstone with

and µ1A defined as the effective moduli of the rock with all the pores except those with aspect ratio a. KA* is the static bulk modulus of the empty rock (Toksoz, et al., 1976), but because of the lack of such data it is usually taken to be the dynamic bulk moduli of the dry rock. The expression for Ei is given in appendix B. Given that the

get price### A modeling solution for predicting (a) dry rock bulk

Feb 01, 1999 It is essential to input rock-matrix and fluid parameters that reflect in situ conditions. The physical parameters of the rock matrix and fluids required to do the modeling are (a) density of the matrix, (b) bulk modulus of the matrix, (c) shear modulus of the rock, (d) salinity of brine, (e) API gravity of oil, (f) gas–oil-ratio, (g) solution-gas specific gravity, and (h) gas specific gravity.

get price### (PDF) Calibration of Minerals’ and Dry Rock Elastic Moduli

Calibration of Minerals’ and Dry Rock Elastic Moduli in Sand-Shale Mixtures. June 2018; The ratio of the rock frame bulk modulus to mineral bulk modulus 𝜅𝑓𝑟𝑎𝑚𝑒⁄𝜅0 is

get price### Velocities of deepwater reservoir sands

Here G(φ) is the gain function, which is a dry rock frame property. Figure 9 shows dry and brine-saturated bulk mod-ulus at high pressure. Data show that dry bulk modulus increases significantly with decreasing porosity: 2.0 GPa at porosity of 35% to 7.0 GPa at porosity of 24%. The brine saturation causes a sig-nificant increase of bulk modulus.

get price### Practical Gassmann fluid substitution in sand/shale sequences

rated bulk modulus K sat: (3) In turn, the bulk modulus of the new rock requires knowl-edge of the mineral modulus K 0, the fluid modulus K f and the pore space stiffness K φ (Mavko and Mukerji, 1995; Avseth et al., 2005): (4) with (5) The pore space stiffness K φ is related to porosity, mineral modulus, and the dry rock bulk modulus K d by (6)

get price### Rock Mechanics

For unconsolidated materials (e.g. dry sand) the Engineering Classiﬁcation of Rock and Rock Masses! 33!! Determining the modulus of elasticity E t50! Plotting E Weakest link principle = overall strength of a rock not determined by bulk properties, but by strength of weakest link ! Rock

get price### (PDF) Using Mindlin theory to model friction-dependent

Often in granular rock-physics. The dry effective bulk modulus of a random sphere packing is ob- modulus of the solid sand grains are approximately 39.5 GPa and.

get price### Abstract: Reservoir Characteristics of a Quaternary

where K sat = saturated bulk modulus, K 0= bulk modulus of the minerals, K fl = bulk modulus of pore fluid, K*= bulk modulus of porous rock frame, and φ = porosity. P wave velocity (Vp) can be calculated once ‘K sat’ is calculated for desired fluid saturation using Gassmann’s equation.. Where G = shear modulus; ρ B = bulk density; K sat = saturated bulk modulus.

get price### Bulk modulus Wikipedia

The bulk modulus (or ) of a substance is a measure of how resistant to compression that substance is.It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume. Other moduli describe the material's response to other kinds of stress: the shear modulus describes the response to shear, and Young's modulus describes the response to linear stress.

get price### Exploring The Friable Sand Theory With Python 3.6 Rock

Aug 08, 2017 and are the ‘dry’ rock bulk and shear moduli respectively at critical porosity, .P is the effective pressure (i.e., the difference between the overburden pressure and the pore pressure). and are the shear modulus and Poisson’s ratio of the solid phase respectively, and is the coordination number (the average number of contacts per grain) and can be determined at any given porosity, .

get price### Estimate shear velocity based on dry P-wave and shear

Dry bulk and shear modulus p 1. 3b Figure 3. Dry bulk (Kd) and shear (µ) modulus ratio for consolidated rock (3a) and deep-water sands (3b) from Gulf of Mexico as function of differential pressure. For consolidated sandstone (Han, 1986), the ratio of dry a bulk and shear modulus of individual sample tend to be

get price### Gassmann's equation for fluid substitution PetroWiki

Aug 31, 2016 This case uses a dry bulk modulus calculated with the mineral modulus of 40 GPa, D = 2, and a water modulus of 2.8 GPa. The water saturation effect was calculated for three mineral moduli of 65, 40, and 32 GPa. Results show that for the same K d and K f, bulk modulus increment ΔK because of fluid saturation increases with increasing mineral

get price### A modeling solution for predicting (a) dry rock bulk

The velocity of sound in porous, fluid-saturated rocks can be predicted using the Biot-Geertsma-Gassmann (BGG) and shear-wave velocity equations. However, two of the needed input parameters, the bulk modulus ( K<SUB>b</SUB>) of the empty, porous rock and the shear modulus ( μ) of the rock are very difficult to obtain in situ. In the past, these values were typically chosen a priori and input

get price### Estimate shear velocity based on dry P-wave and shear

Dry bulk and shear modulus p 1. 3b Figure 3. Dry bulk (Kd) and shear (µ) modulus ratio for consolidated rock (3a) and deep-water sands (3b) from Gulf of Mexico as function of differential pressure. For consolidated sandstone (Han, 1986), the ratio of dry a bulk and shear modulus of individual sample tend to be

get price### Velocities of deepwater reservoir sands

Here G(φ) is the gain function, which is a dry rock frame property. Figure 9 shows dry and brine-saturated bulk mod-ulus at high pressure. Data show that dry bulk modulus increases significantly with decreasing porosity: 2.0 GPa at porosity of 35% to 7.0 GPa at porosity of 24%. The brine saturation causes a sig-nificant increase of bulk modulus.

get price### Exploring The Friable Sand Theory With Python 3.6 Rock

Aug 08, 2017 and are the ‘dry’ rock bulk and shear moduli respectively at critical porosity, .P is the effective pressure (i.e., the difference between the overburden pressure and the pore pressure). and are the shear modulus and Poisson’s ratio of the solid phase respectively, and is the coordination number (the average number of contacts per grain) and can be determined at any given porosity, .

get price### Rock Mechanics

For unconsolidated materials (e.g. dry sand) the Engineering Classiﬁcation of Rock and Rock Masses! 33!! Determining the modulus of elasticity E t50! Plotting E Weakest link principle = overall strength of a rock not determined by bulk properties, but by strength of weakest link ! Rock

get price### Extended poroelastic impedanceExtended poroelastic

The Batzle-Wang equations were used to calculate the properties of the gas and brine fluid components. The effective bulk modulus of the porous, fluid-filled sandstone was computed from the dry-rock bulk modulus using the Gassmann equation, which can be found

get price### (PDF) Using Mindlin theory to model friction-dependent

Often in granular rock-physics. The dry effective bulk modulus of a random sphere packing is ob- modulus of the solid sand grains are approximately 39.5 GPa and.

get price### Rock Physics Rock Science

and are the ‘dry’ rock bulk and shear moduli respectively at critical porosity, .P is the effective pressure (i.e., the difference between the overburden pressure and the pore pressure). and are the shear modulus and Poisson’s ratio of the solid phase respectively, and is the coordination number (the average number of contacts per grain) and can be determined at any given porosity, .

get price### Abstract: Reservoir Characteristics of a Quaternary

where K sat = saturated bulk modulus, K 0= bulk modulus of the minerals, K fl = bulk modulus of pore fluid, K*= bulk modulus of porous rock frame, and φ = porosity. P wave velocity (Vp) can be calculated once ‘K sat’ is calculated for desired fluid saturation using Gassmann’s equation.. Where G = shear modulus; ρ B = bulk density; K sat = saturated bulk modulus.

get price### Bulk modulus Wikipedia

The bulk modulus (or ) of a substance is a measure of how resistant to compression that substance is.It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume. Other moduli describe the material's response to other kinds of stress: the shear modulus describes the response to shear, and Young's modulus describes the response to linear stress.

get price### Fundamentals of Concrete

Gs(ssd) = (1 + Absorption) x Gs(dry). For example, a sample of sand having an absorption of 5% and a specific gravity of 2.63 has a bulk specific gravity saturated surface dry that is computed as follows: Gs(ssd) = (1 + 0.05) x 2.63 = 2.76. BULK VOLUME The volume of a granular material including the volume of the solid

get price### International Journal of Physical and Human Geography

The bulk modulus is also referring to the measure of rock’s resistance to change in volume. When porosity increase in the rock that lead to decrease the rock's resistance to change in volume and thus decrease its bulk modulus. This makes the bulk modulus a good porosity indicator especially in stiffer rocks like carbonates.

get price### Acoustic and petrophysical properties of mechanically

dry are the dry unconsolidated sand bulk and shear moduli. K is the bulk modulus of mineral. φ is the porosity. φ c is the critical porosity. μ is the shear modulus of solid mineral. K HM and μ HM are the dry rock bulk and shear moduli calculated from equations (1)–(3). The K dry and μ dry can be transformed to water saturated

get price### Seismic rock physics SEG Wiki

Jun 01, 2017 Rock-physics models output dry-rock frame moduli: bulk modulus Rock-physics templates for the Soft Sand model. (a) The template by itself, showing how we expect / and to vary with water saturation and porosity ). (b) The template (gray) plotted with the data (green). (c) The template (blue) has been recalculated by changing the rock matrix

get price### ROCK PHYSICS CHARACTERIZATION OF ORGANIC-RICH

Bulk Modulus of Component X Volume of Kerogen Modulus (Bulk or Shear) Inverse of Modulus (Compressibility or Shear Compliance) n Coordination Number Dry Rock Inverse Modulus Pore-Fill Inverse Modulus Pe Effective Pressure PSP Pore-Structure Parameter . vii Compressional Velocity Shear Velocity . viii

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