  The paper is devoted to the derivation of a combined system of motion
equations for solid and fluid in isotropic tight oil/gas sandstone media
through volume averaging theorems (VAT). Based on the features of the media,
four physical assumptions are proposed as the foundation for our derivation.
More precisely, volume averaging theorems are applied to the micro-scale motion
equations for both the solid and the fluid as well as to the stress-strain
relations, resulting in a combined system of macro-scale equations for the
tight oil/gas sandstone media. It is worth noting that the four assumptions may
not be satisfied in the whole region. Nevertheless, since the characteristic
diameter for applying VAT ranges between $10^{-6}$ meters and dozens of meters,
we may split the entire domain into several sub-domains such that the four
physical assumptions are satisfied in each sub-domain. By choosing a proper
characteristic diameter of an averaging volume, we derive a formula for the
fluid average pressure in terms of the divergence of the average displacement
from the continuity equation of the fluid. As a result, the motion equations
derived in this paper are simpler than the Biot equations, and are more
suitable for inversion of porous medium parameters. When the fluid is gas and
the compressional wave is considered, the derived motion equations can be
simplified to the diffusive-viscous wave equation. Moreover, the explicit
relationship between the coefficients in this equation and medium parameters is
very important for gas detection in tight gas sandstone.
