Reservoir Engineering: Assumptions of Darcy’s Law
Under what circumstances, ALL the following conditions remain valid in a petroleum reservoir?
(a) Darcy’s law representing the classic macroscopic scale expression of the conservation of momentum for a low Reynolds number, single-phase, steady fluid flow with insignificant fluid inertia flowing in a porous solid remains valid for describing multi-dimensional multi-phase fluid flow through a petroleum reservoir too;
(b) The reservoir fluids in the mixing zone at a displacement front will not encounter any rapidly fluctuating rock properties and fluid saturations;
(c) oil and water never gets mixed;
(d) absolutely, there will be no exchange of fluid masses between water, oil and gas;
(e) there will be no phase changes associated with reservoir fluids;
(f) the fluids in the reservoir are @ constant temperature;
(g) the fluids in the reservoir are in a state of thermodynamic equilibrium;
(h) the capillary pressure jump between the phases remains neglected;
(i) the fluid pressures in the phases remain equal;
(j) The use of non-linear constitutive relations such as relative permeabilities and capillary pressure are assumed to be only local functions of saturation; while its dependence on other non-linear parameters like saturation-history and composition-dependent rock wettability and fluid viscosities remain neglected;
(k) the mass of rocks located above (seal) the top of the reservoir creates pressure, which is considered to remain unchanged during the production life of reservoir;
(l) both the top and bottom of the reservoir (thickness zone) remains absolutely impermeable and completely take in the load of overlying rocks so that the rock pressure gets exactly balanced by the stress in the reservoir formation solid-skeleton network and the pressure in the fluid;
(m) changes not only in porosity but also in permeability - due to both changes in pore pressure and changes in effective stress remain neglected;
(n) the reservoir fluid flow remains no more based on length-scale averaging that would accommodate the effects associated with spatially heterogeneous reservoir geological units and the non-linearities inherent in the multi-phase fluid flow;
(o) the state of fluid flow within an individual pore will not be described;
(p) the reservoir characterization will not take into account the actual curvilinear path of the fluid particle with continuously varying fluid velocity and acceleration scenario;
(q) the reservoir characterization will not take into account either weak or strong inertia, leaving aside the turbulent effect;
(r) the reservoir rock is supposed to be isotropic, and, in addition, the porous medium remains averaged over the ensemble homogeneous;
(s) Although, Darcy’s empirical relation does not include the tensor form of the absolute permeability; and thus, the experimental/field validation of multi-dimensional permeability remains beyond the scope of Darcy’s law; it will still be assumed to be applicable for describing complex fluid flow through a petroleum reservoir.
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