RESERVOIR ENGINEERING
In the classical Young-Laplace (YL) equation, the capillary pressure or the pressure difference over an interface between two fluids is expressed in terms of the surface tension and the principal radii of curvature (R1 & R2).
Upon applying YL equation to an oil-water (petroleum reservoir) system, whether each point on the oil-water interface has the same ‘geometry factor’ or, the ‘mean curvature of the interface’ (which depends on R1 & R2) @ equilibrium?
Can we prove the above point either by using the principle of minimum (surface) energy or by applying a force balance (by summing all forces to zero)?
Also, can it be shown experimentally (@ laboratory-scale) that for arbitrary, smooth surfaces and curves, the curvature @ any point may be defined - by assigning two radii of curvature, R1& R2, in two normal planes (which are again normal to each other and their line of intersection remains to be the surface normal @ the chosen point) that cut the interface along two principal curvature sections?
Using YL equation, can we defend that the ‘capillary pressure’ in a petroleum reservoir remains to be a function of (a) the saturation distribution of the contained fluids; (b) the saturation history; & (c) the wetting characteristics of rock-fluid system?
Whether Leverett’s dimensionless (J) function that correlates (a) porosity; (b) absolute permeability, (c) capillary pressure and (d) surface tension @ fluid interface really validates YL equation?
Or,
Calhoun’s inclusion of ‘contact angle’ (on Leverett J-Function) makes YL equation to be more meaningful for petroleum reservoirs?
Or,
Carman’s expression for capillary pressure (height of capillary pressure as a function of grain size & porosity) that depends on ‘surface area per unit bulk volume of the medium’ in addition to ‘interfacial tension’ and ‘porosity’ mimics the YL equation more closer?
Whether the plot of the capillary function J (Sw) against the wetting-phase saturation can ever yield a unique curve for a petroleum reservoir, in case, if the concerned geology is hypothetically assumed to be of clean unconsolidated sands?
Or,
not at all possible - under any circumstances in a (consolidated) petroleum reservoir that can be uniquely represented by a single J-Function curve?
Why is that the estimation of ‘relative permeability to the wetting phase’ – as a function of ‘fractional wetting phase saturation’; ‘capillary pressure’; and ‘displacement pressure’ - ends up with huge discrepancies – even, if we assume that the ‘capillary pressure’ tends to become equal to ‘displacement pressure’ upon ‘water saturation tending to become unity’ (with uniform pore size) – in the absence of introducing ‘resistivity index’?
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