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Related to bulk modulus: Poisson's ratio, Young's modulus, Shear modulus
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The time constants for dissolution and aeration have a strong influence on the instantaneous amount of separated air, which in turn determines the value of the effective bulk modulus of the air/oil mixture.
Parameter Value Coal elastic modulus 2813 E (MPa) Matrix elastic modulus 8439 [E.sub.s] (MPa) Poisson's ratio v 0.34 Coal density [[rho].sub.c] 1250 (kg/[m.sup.3]) Air density (kg/[m.sup.3]) 0.717 Facture stiffness 4800 [K.sub.f] (MPa) Dynamic viscosity 1.84 x [10.sup.-5] u (Pa x s) Bulk modulus K (MPa) 5400 Matrix width [a.sub.0] (m) 5 x [10.sup.-6] Frack width [b.sub.0] (m) 0.005 Parameter Parameter Coal elastic modulus Adsorption pressure E (MPa) constant [P.sub.L] (MPa) Matrix elastic modulus Adsorption volume constant [E.sub.s] (MPa) [V.sub.L] ([m.sup.3]/kg) Poisson's ratio v Adsorption pressure strain [[epsilon].sub.L] Coal density [[rho].sub.c] Initial matrix porosity.
In the context of acoustics, the bulk modulus of unit cell [B.sub.A] is an important parameter of sound propagation [11].
Poisson's ratio (a) is related to the bulk modulus and the shear modulus as calculated by Hill as follows:
Parameters Values Poisson's ratio v 0.33 Elastic modulus E 3.35 GPa Internal friction angle [phi] 30[degrees] Compressive strength [f.sub.c] 40 MPa Tensile strength [f.sub.t] 3 MPa Homogeneity index m 1000, 20 Parameters Values Initial permeability [k.sub.0] 3 x [10.sup.-18][m.sup.2] Initial porosity [[phi].sub.0] 0.05 Residual porosity [[phi].sub.r] 0.01 Water dynamic viscosity 3.55 x [10.sup.-4] Pa x s Bulk modulus of water [[beta].sub.1] 2.5 x [10.sup.9] Pa Biot coefficient [alpha] 0.8 TABLE 3: Parameters for the numerical calculation.
Given the problems mentioned above, the influences of temperature, effective stress, and rock fracture on bulk modulus and Biot's coefficient were investigated in this study aiming at experimentally quantifying the influence.
The bulk modulus and density of the fluid change as the gas becomes trapped into the oil during the strut operation.
The grain size dependence of Young's modulus and the bulk modulus observed here in the case of a bcc metal (tungsten) can be related to studies that have given similar results for nanocrystalline fcc metals.
As presented in Table 1, the values of bulk modulus of our calculation are very close to experimental value (115 GPa).
Furthermore, the bulk modulus of the third layer ranges between 0.99 GPa and 15.94 GPa.
As seen in Equations (1), (2), (3), (4), the bubble radius and pressure are both impacted by the fuel property parameters of (i) density, (ii) viscosity, (iii) surface tension, (iv) vapor pressure, (v) Bulk modulus, (vi) solubility, and (vii) Volatility of gases.
I[[bar.[lambda]].sub.0] and [[bar.[mu]].sub.0] are the Lame elastic constants of the spacetime continuum: [[bar.[mu]].sub.0] is the shear modulus and [[bar.[lambda]].sub.0] is expressed in terms of [[bar.[kappa]].sub.0], the bulk modulus: