Reservoir Engineering: Continuum Approach

If the necessity for continuum approach emanates from the intrinsic uncertainty in describing in an exact manner the geometry of the internal solid surfaces that bound the flow domain inside a porous medium for the purpose of meaningful and efficient field-scale simulations; and in turn, instead of treating the problems at the pore level, if a different approach is adopted, which remains statistical in nature, towards deriving information regarding the motion of a system composed of many pores, then, are we not supposed to overlook the actual or internal pore structure of the medium (while regarding as a continuum)?

Towards describing various transfer phenomena at higher level (macroscopic level, where porous medium is treated as a continuum), are we not required to define appropriate transfer coefficients?

One for mass conservation (hydrodynamic dispersivity); and the other, for momentum conservation (permeability)?

If we do not have an appropriate transfer coefficient for mass conservation, in an oil recovery process, then, upon utilizing a zone of miscible fluid, how do we deduce the possibility of losing miscibility by dissipating the miscible fluid or by channeling or fingering through the miscible zone?

How do we know, whether, dispersion would remain to be detrimental or beneficial (if it prevents fingering through the miscible zone)?

Dr Suresh Kumar Govindarajan Professor [HAG] IIT-Madras 24-Feb-2025