s; K is bulk modulus
, GPa; [G.sub.1] is elastic modulus of Kelvin bulk, GPa; [G.sub.2] is elastic modulus of Maxwell bulk, GPa.
being p the pressure, V the volume, [beta] the fluid bulk modulus
, [Q.sub.i] the flow rate through the generic port i-th (positive if ingoing), [omega] and [phi] respectively the angular speed and the position of the shaft.
where G, v, and K are the shear modulus, Poisson's ratio, and bulk modulus
of coal, respectively, [alpha] and [beta] are the Biot coefficients of matrix and fracture, [[epsilon].sub.s] is gas sorption strain, and [P.sub.mmix] and [P.sub.fmix] are the pore pressure in fractures and matrix.
where [[rho].sub.w] is water density and [[kappa].sub.w] is the bulk modulus
. Based on the standard theories, the variational form of (4) can be got as
The effective bulk modulus
and the amendment formula of resonance frequency were established.
The formula for bulk modulus
(B) and shear modulus (G) is as follows:
where [[beta].sub.1] represents the water bulk modulus
and [q.sub.1] represents the vector of water seepage velocity; the first and second terms of equation (9) are the change of water quantity due to water pressure and water flux flowing out, respectively.
However, altering the temperature not only changes stress but also modifies the physical properties of rock, including the rock bulk modulus
and thermal expansion coefficient.
The Bulk Modulus
of the material was calculated from confined compressive test.
The article presents the results of studying the bulk microstructure and measuring both sonic velocities [c.sub.L] and [c.sub.T] and elastic modules, bulk modulus
K and shear modulus G, of epoxy-nanocarbon composites with different types of carbon nanofillers--graphite nanoplatelets (GNP) and multiwall carbon nanotubes (MWCNT).
The entrapped gas within the oil has been reported to increase the volume of the mixed fluid, and thereby lead to reduced fluid bulk modulus
and fluid density [7,16].
First, the samples were submitted to isotropic compression and dilatation tests to determine the bulk modulus