Why does the concept of "turbulence" NOT finding a place in the design of gas well fracturing treatments associated with a porous medium?
Actually Required: Turbulence concept while designing gas well fracturing treatments as emphasized by Cooke.
Minimum Requirement: Laminar flow with inertial effects as emphasized by Geertsma.
What is currently followed: Laminar based diffusivity equation.
Using diffusivity equation for describing fluid flow through a complex heterogeneous reservoir, and then, discussing so much on optimization and uncertainty - why is it so?
Yes, we were NOT able to move forward after Darcy's momentum equation in 1856 that is used to describe fluid flow through a porous medium at the macroscopic scale. I mean, till date, we DO NOT have an equation that can describe fluid flow through a porous medium at the microscopic scale.
In other words, I AM NOT SUPPOSED to look at any details of a porous medium at the microscopic scale, when we talk about Darcy's approach.
It can be noted that the concept of microscopic-scale based Navier-Stokes equation can well be applied for a porous medium conceptualized as a bundle of parallel capillary tubes - which is highly idealistic - with reference to the actual complicated pore geometry associated with a typical porous medium. The problem becomes further complicated with a fractured reservoir having multiple continuum.
Given this fact, Is it fair for us to introduce the concept of "nano-Darcy" associated with a shale gas reservoir OR the mobility of nano-particles associated with chemical EOR?
Is it possible to mathematically merge nano- and macro- scales together - associated with the concept of nano-Darcy OR nano-particles?
Appreciate your time and energy.
Thanks in anticipation.
Regards,
Suresh Kumar.
I have done a lot of work with flow through fractured media. I developed my analysis having access to measured data. I'm an engineer and developed the software working closely with geohydrologists who understood the physical processes. The results were quite successful, as confirmed by subsequently drilling wells and taking samples. The processes in question do not fit with the concept of turbulence, rather they follow the patterns of diffusion and dispersion. To model these processes, I developed a Hamiltonian (not a Lagrangian) particle tracking code, PTRAX, as well as an entire system of domain building tools. Lagrangian particle tracking is much too slow to be practical. Here's a link to a write up:
http://dudleybenton.altervista.org/projects/Ptrax/ParticleTracking.html
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