Reservoir Engineering: Darcy’s Law
Since, Darcy’s law represents the simplified version of ‘fluid momentum conservation’ deduced from Navier-Stokes equation, how can the associated reservoir fluids be treated to be either ‘compressible’ or, even, ‘slightly compressible’?
Further, whether, reservoir pore fluids won’t get accelerated at all (at least in the vicinity of production well; or, due to reservoir heterogeneities)?
In other words, won’t the reservoir pressure fluctuate with high frequencies so that fluid acceleration becomes significant?
If so, how about the validity of Darcy’s law?
In addition, even, if the reservoir is considered to be homogeneous and isotropic, how about its resultant bulk modulus (reciprocal of compressibility) and shear modulus in the presence of brine (with a significant finite bulk modulus with negligible shear modulus), oil and gas?
Can the reservoir solid grains not have a significant shear deformation even under a large shear stress?
Given the nature of reservoir pore fluids (brine, oil and gas), whether, the fluid pressure be transmitted instantaneously (so that the fluid of interest could be assumed to be incompressible) in a petroleum reservoir?