Considering the relatively larger dimension along the horizontal fluid flow direction with reference to the reservoir thickness in the vertical direction,
the reservoir should mainly deform in the vertical direction – resulting from
(a) a huge decline reservoir pressure;
(b) production from a relatively larger vertical pay-zone thickness;
(c) reservoir formation with weakly consolidated rocks; or
(d) the depth of reservoir being relatively shallow.
If so,
whether Terzaghi’s (one-dimensional) differential equation
that describes the deformation process
resulting from the coupling of Darcy’s equation with a linear elastic stress-strain relation
through mass conservation equation
would remain valid for the cases (a), (b), (c) & (d)?
In other words,
whether the rate of compaction will still be linearly governed
by the rate at which oil/gas/water is produced from the reservoir - for the cases (a), (b), (c) & (d)?
Can we apply Biot’s assumptions of isotropy and a reversible elastic stress-strain relation
to capture the deformation associated with a typical sandstone reservoir
based on the extension of three-dimensional elasticity theory?
If so, how can we include - the variations in reservoir permeability and compressibility – resulting from the effects of the motion of the solid-grain matrix?
OR
Is it fine to describe the stress-strain relation using Geertsma’s poro-elasticity concept - despite the fact that the body forces that are generated during the migration of oil/gas/water within the reservoir and their associated boundary conditions at the pore-scale are quite different from the original approach of thermos-elasticity?
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