Reservoir Engineering
Deviations from Original Darcy’s Law
1. What was the need for Muskat to replace original hydraulic gradient by pressure gradient?
2. What was the need for Wyckoff to separate Darcy’s original constant of proportionality into permeability (rock property) and viscosity (fluid property)?
3. How about permeability depending on gas pressure, i.e., depending on fluid property (Knudsen-effect/Slippage-effect/Klinkenberg-effect) as well?
4. How about the significance of deviation of Darcy’s law @ very low fluid velocities – associated with consolidated, confined oil and gas reservoirs?
Whether fluid would require a definite threshold gradient in order to shear and to begin flowing?
Would it also influence reserve forecast?
5. How about the application of Darcy’s law for non-Newtonian fluids (where, viscosity remains a function of applied shear rate)?
6. How about non-Darcy flow or post-Darcy flow associated with the non-linear variation of flow velocity with respect to the applied pressure gradient (which has a significant influence on well performance)?
7. In radial flow, the cross sectional area to flow increases, which causes a decrease in fluid velocity for any, given constant flow rate. Whether Darcy’s law remains valid for non-uniform fluid flow having varying cross sectional area?
Even with radial flow, how about the flow analysis with wellbore storage and boundary effects?
8. Whether Darcy’s law be applied in the vicinity of injection or production well, where, the stream lines become curvilinear?
9. Whether Darcy’s law be applied to a reservoir, where, the well is not drilled to the entire thickness of the reservoir?
10. Whether Darcy’s be applied to a reservoir that includes reservoir thermodynamics (phase changes associated with temperature/pressure variation: non-isothermal conditions) as well, on top of considering reservoir fluid dynamics?
11. Can Darcy’s law take into account any pore-scale detail?
Then, what is the very purpose of applying continuum-scale using the concept of REV?
12. Can Darcy’s law explicitly take into account capillary (IFT) and wettability (contact angle) effects?
Does Darcy’s law take into account fluid-fluid interaction and fluid-solid interaction?
13. Can Darcy’s be applied for a fluid system having a significant and varying compressibility?
14. What was the need for Darcy to deduce an explicit equivalent momentum conservation equation – for characterizing fluid flow through a porous medium - than directly applying Navier-Stokes equation?
Suresh Kumar Govindarajan
Professor (HAG) IIT Madras
https://home.iitm.ac.in/gskumar/
https://iitm.irins.org/profile/61643 26-July-2024
Convective mixing in porous media: a review of Darcy ...
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National Institutes of Health (NIH) (.gov)
https://www.ncbi.nlm.nih.gov › articles › PMC10725412
by M De Paoli · 2023 · Cited by 7 — A possible strategy to model flows in porous media consists of taking the average of relevant quantities (velocity, concentration and pressure ..
Pore Scale - an overview
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ScienceDirect.com
https://www.sciencedirect.com › topics › pore-scale
Pore Scale. A pore-scale refers to phenomena at the microscopic level, specifically at the level of individual pores, in comparison to macroscopic phenomena ...
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