Reservoir Engineering
The definition of an ideal porous medium as the carrier of the pore-fluids pertains to an unconsolidated sand; and it essentially represents a medium, which consists of an innumerable voids of varying pore-sizes and pore-shapes comprising ‘pore-spaces’ or interstices between the individual solid particles of sand. Further, each pore remains connected by the constricted channels to other pores, the whole forming a completely inter-connected network of openings, which from the channels through which the contained pore-fluid might flow. This kind of a complete multiple inter-connection of the minute opening that characterizes an ideal porous medium definitely differentiates the concept of ‘fluid flow through a porous medium’ from that of ‘fluid flow through pipelines’ (which remains associated with the traditional hydrodynamics or classical hydraulics).
In addition, in an ideal porous medium, we have to deal with flow channels composed of multiply connected minute pores, defined by discontinuous impermeable boundaries, and characterized by a complex pore-geometry.
As a result, it is not feasible to deduce a well-defined boundary condition to describe fluid flow @ pore-scale. And, it requires a relatively bigger-scale in order to investigate the problem associated with fluid flow through a porous medium. Otherwise, we could have very well applied Navier-Stokes Equation (NSE) itself –as the momentum conservation equation - for characterizing fluid flow through a porous medium @ pore-scale. Hence, Hendry Darcy required an explicit (equivalent) momentum conservation equation in order to characterize fluid flow through a porous medium. However, Darcy’s can no more be applied @ pore-scale, while, it remains applicable only @ Darcy-scale, which requires the concept of continuum, where, the fundamental dependent variables of interest are supposed to vary smoothly as well as continuously.
Hence, upon using Darcian approach, the pore-scale details remain ruled-out, because, we are supposed to deduce only an average value over that concerned REV (and, we should not directly get into the pore-scale details).
Also, since, the fundamental dependent variables of interest are supposed to vary smoothly and continuously, any form of reservoir heterogeneity needs to be dealt with utmost care (because, the reservoir heterogeneity may essentially introduce steep gradients in variables of interest or may introduce discontinuity, which will violate the fundamental assumption associated with the calculus).
Now, as far as Petroleum Reservoir Engineering (PRE) is concerned, the concept of a porous medium pertains to a “consolidated sandstone” (as against the unconsolidated sand). And that too, the concept of a porous medium in PRE remains associated only with a confined reservoir, with a reservoir pressure nearly 100 – 1000 times greater than the atmospheric pressure (and unlike an unconfined aquifer as conceptualized by Darcy, where, the pressure at the upper boundary equals to unit atmosphere).
Does the definition of a porous medium in the context of petroleum reservoir engineering deserve a special attention?
Suresh Kumar Govindarajan
Professor (HAG) IIT-Madras
https://home.iitm.ac.in/gskumar/
https://iitm.irins.org/profile/61643
19-July-2024
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