Reservoir Engineering
If both porosity and permeability remains to be scale-dependent (depending on the size of the averaging volume), then, how about the notion of REV? Whether, the effect of heterogeneities on the scale of the averaging volume requires to be ignored? Does the notion of ‘Average Pressure’ NOT lead to Darcy’s Law? If so, then, does ‘average Pressure’ NOT correspond to ‘macroscopic pressure’ appearing in Darcy’s Law?
Whether the conceptualization on the application of averaging theorems to manipulate the average of microscopic pressure gradients (which allows Darcy’s equation to be written with all the variables defined directly in terms of averages of micro-scale quantities) towards obtaining the gradient of an average pressure essentially fail with spatially varying porosity and in the presence of gravity (leading to non-physical gravitational effects)?
Dr Suresh Kumar Govindarajan Professor [HAG] IIT Madras 24-Feb-2025
Dear Prof. Suresh Kumar Govindarajan
If both porosity and permeability remains to be scale-dependent, it is necessarily to assume that the sampled volume corresponds to a representative elementary volume (REV) is the only be tested.
In this case, the effect of heterogeneities of the scale on the averaging volume assume to be neglected.
Yes, the notion of ‘Average Pressure’ NOT lead to Darcy’s Law. Since. Darcy's law is an empirical linear relationship between the macroscopic filtration velocity and the macroscopic pressure gradient and not the "Average Pressure".
Averaging theorems to manipulate the average of more than one microscopic pressure reading at any well defined point on the flow line is only valid, while the averaging theorems to manipulate microscopic pressure gradients is different story.
Best regards...
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