Reservoir Engineering: Fluid Flow
1. In describing fluid flow through a petroleum reservoir (diffusivity equation), why do we have only divergence of diffusive flux; and not the divergence of summation of diffusive and advective fluxes together (as it is supposed to be)?
2. Are we 'precisely' using the rate of change of the product of density and porosity, i.e., the stored quantity per unit volume?
3. Given water, oil and gas (three-phases having extreme fluid compressibility) in a petroleum reservoir; and in the absence of an explicit continuity of fluxes between water, oil & gas; how could we physically as well as mathematically ensure the conservation of both mass as well as momentum?
4. Since a petroleum reservoir remains characterized not only by multi-dimensional fluid flow; but also by multi-phase fluid flow, the concept of flow potential for each phase can be defined as against the concept of hydraulic head used for single-phase fluid flow. During this process, if we replace hydraulic conductivity, fluid density and acceleration due to gravity by mobility (a ratio between permeability and viscosity); are we not supposed to use Darcy flux as a function of potential gradient (and not strictly as a pressure gradient)?
If not, whether potential gradient and pressure gradient have no distinction in a petroleum reservoir?
Are we strictly treating both Darcy flux and the potential gradients as vectors?
How would Darcy flux vector remain to be collinear with the potential gradient, if the reservoir formation remains to be cross-bedded?
5. Is there a way to deduce all the values of reservoir permeability associated with a second order tensor?
Why do we always assume the permeability tensor to remain to be symmetric despite the reservoir being heterogeneous and anisotropic?
OR
Do we at least consider the (minimum) three orthogonal reservoir coordinate directions that would transform the permeability tensor into a diagonal matrix?
Are we really taking into account the off-diagonal terms of the permeability tensor, when the reservoir coordinate directions remain not aligned with the three Cartesian coordinate directions (such as found in cross-bedded deposits that have bedding planes which remain not parallel to the geological strata and thereby leading to the existence of non-zero off-diagonal terms)?
Under what circumstances, the reservoir permeability could be expressed as a scalar and in turn, an identity matrix?
6. In a petroleum reservoir, would it remain feasible for water, oil and gas flow to remain parallel to the bedding?
Even, if it is so, whether, all the geological layers would have a common pressure drop and length – irrespective of the reservoir pore fluid types (water/oil/gas)?
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