Talk:Darcy's law

Reason for Peak Oil Category

One of the major arguments for Peak Oil is that energy companies will find it increasingly difficult to extract oil from reservoirs.

This is predicated on the understanding that an underground oil field consists of oil co-existing with permeable rock. Once the pressure inside the reservoir drops and electric pumps are used to speed up extraction, lower viscosity oil will be extracted.

Thicker oil passing through permeable rock takes time to get through, hence the reason why Darcy's Law is included as a Peak Oil category. --One Salient Oversight 00:48, 22 Mar 2005 (UTC)

huh? "Once the pressure inside the reservoir drops and electric pumps are used to speed up extraction, lower viscosity oil will be extracted."

Isn't ALL oil pumped from reserviors?

No. TastyCakes 04:37, 9 November 2006 (UTC)

thicker means higher viscosity.

Darcy's law has nothing to do with viscosity, which only tenuously has something to do with peak oil... I could maybe see the label in the permeability article, since that is the only way Darcy's Law is related to viscosity. --kris 03:22, 22 Mar 2005 (UTC)

Viscosity is a factor in darcy's law, it just seems to have been folded in with "K" here, possibly because it's being done for water where viscosity is 1.. some unit I forget. I agree though, its link to peak oil is tenuous at best. TastyCakes 04:44, 9 November 2006 (UTC)

Article generalization

This whole article has been written from a hydrology standpoint. I have rewritten a bunch of it in a more generalized form, that is one where fluids other than water are involved (as is frequently the case when using Darcy's law in oil field applications). TastyCakes 05:20, 9 November 2006 (UTC)

Article consistency

In the additional forms section an expression of Darcy's Law common to 'petroleum engineering' uses small 'q' for total discharge (units of volume per unit time). At the start of the article small 'q' is defined as flux, and large 'Q' as total discharge (units volume per unit time).

I can't even see what new information that extra equation for petroleum engineers give to the article. I vote for removal or rewrite of that particular section. Berland 07:45, 29 January 2007 (UTC)

For the sake of clarity, could the petroleum engineering version of the equation be given a large 'Q' too? jac 15:09, 11 January 2007 (UTC)

I'd support that. I also made an article concerning that a few weeks ago, groundwater discharge (which I'm yet to integrate into other articles). I'm not 100% sure about petroleum engineers, however I know the civil/hydro engineers stick to the same 'q' vs 'Q' conventions as hydrogeologists.+mwtoews 00:40, 12 January 2007 (UTC)

This article needs serious revision, to make it both correct and consistent with other articles. First, by not including gravity in the generalized form, the article oversimplifies the Darcy equation. I will fix this if I have time. Definately stick to the q=flux Q=flow rate. Also, put in references to other hydrogeology books to supporrt the generalized forms. Luckymonkey 17:02, 19 February 2007 (UTC)

No, gravity is (or can be) included, in $\Delta P$, in the equation $q=-\kappa /\mu \Delta P$. It is a vector equation, and $\kappa$ possibly as a tensor if anisotropy is to be considered. Berland 17:33, 19 February 2007 (UTC)

Porosity

I think the symbol for porosity should be $\phi$, not n, as in the porosity arcticle. Berland 07:25, 17 January 2007 (UTC)

I know I've seen both, but I forget who uses what (different disciplines have different notations). You might add a sentence to the article saying "Foo engineers use "x" to denote porosity, and bar engineers use "y"." Lunch 18:31, 17 January 2007 (UTC)

Unfortunately, there are many conventions used for the "symbol for porosity" (such as $n$, $\phi$, $\beta$). For the sake of consistency with the porosity article, I suggest using the same φ symbol, as Berland suggested, and perhaps add the sentence about the different conventions in the porosity article. Fetter and Domingo and Schwartz use $n$, while Dingman uses $\phi$. Personally, I'm a fan of $\phi$ for porosity, and $n$ for Manning's roughness coefficient.+mwtoews 19:40, 17 January 2007 (UTC)

I changed to $\phi$. Berland 07:39, 29 January 2007 (UTC)

Derivation

I believe there was a mistake in the derivation section, namely that in the application of the proportional but opposite viscous resisting force, a negative sign was omitted, which prevents the algebraic manipulation into the following step. I will make the change, but hope someone with better knowledge will check this. SselemanLuos (talk) 21:20, 13 January 2009 (UTC)

I think you are absolutely right. --Johnsarelli (talk) 11:09, 14 January 2009 (UTC)

I think there is a mistake: The pressure gradient is not a dimensionless quantity but should have the units Pa/m. Maybe it would be easier to use the pressure head psi=P/(rho*g) hydraulic potential whose gradient is dimesionless indeed. — Preceding unsigned comment added by Markus.mueller.1.g (talk • contribs) 10:54, 13 December 2010 (UTC)

Tensor permeabilities

There's no discussion of anisotropic permeabilities; in this case, the permeability term, k, is a tensor. Please could someone add some information on how this tensor and the resulting equation are to be interpreted?

The section 'In 3D' encompasses this, though it is not explicitly mentioned that $\kappa$ there is a tensor/3 by 3 matrix. --Berland 21:16, 29 July 2007 (UTC)

How does the term $k_{i}$ in the derivation section relate to the permeability tensor? Are you assuming isotropy, so that $k_{i}$ is the $i$-th element of the diagonal? It would help to state that in the derivation section, and also to change $k_{i}$ to $\kappa _{i}$. Thanks. Eerb (talk) 20:42, 24 November 2009 (UTC)

What about Hagen-Poiseuille?

Aren't the two laws quite related? Beryllium-9 (talk) 09:53, 29 June 2011 (UTC)

flow through other kinds of porous medium?

It would be useful to see a related link to other kinds of porous medium, specially thin (in flow direction) PM. 174.112.104.110 (talk) 18:26, 28 January 2012 (UTC)

Navier-Stouks

It would be nice to see derivation from Navier-Stouks or at least reference to some paper — Preceding unsigned comment added by 91.228.20.50 (talk) 14:39, 23 March 2012 (UTC)

Reynold's number

The article defines Re for porous media as Re = ρ.v.d₃₀/μ  ; v is defined as specific discharge and d₃₀ as representative grain diameter (often taken as 30% grain size ...) - I am paraphrasing here. I have two comments about that:
1) specific discharge is effectively equal to flux, q, as defined earlier. I then propose that we use only one term and keep symbols consistent.
2) d₃₀ cannot be "a representative grain diameter". I propose we drop the ₃₀ in the equation, but keep the description as is explaining that representative can be the d₃₀ or d₅₀. Also d₃₀ or d₅₀ can be measured in various ways, not necessarily via sieving so the mentioning the methodology is out of context.
So, I propose to have:
The Reynolds number (a dimensionless parameter) for porous media flow is typically expressed as
Re = ρ q d / μ
where ρ is the density of water (units of mass per volume), q is the flux (units of length per time), d is a representative grain diameter for the porous media (with units of length), and μ is the viscosity of the fluid. The representative grain diameter is often taken as the d₅₀ (i.e. median grain size) or the d₃₀ (i.e. the size of where 30% of the grains are smaller).--85.116.189.149 (talk) 14:38, 5 February 2013 (UTC)

Formula question

In the first discussion of the formula the author states: length over which the pressure drop is taking place (m). There is no m in the formula!! There is an "L" in the denominator. I can't believe I'm the only one who noticed this! — Preceding unsigned comment added by Siragrossman (talk • contribs) 19:08, 7 August 2013 (UTC)

First, there are many authors to this any any article on Wikipedia. The "m" you are seeing in the text is the common abbreviation for metre, the SI unit of the length variable, L. Units don't usually appear in the formula, but are in parenthesis after explanation of each variable. +mt 05:00, 8 August 2013 (UTC)

Assessment comment

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Comment(s)

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I'd like to thank the author for putting the article together. However, the article would benefit from a serious revision. The most important correction is to explicitly include gravity, by using the vertical z coordinate in the main formula, and by replacing the sketch with the one having the pipe at a slope or a vertical pipe. The explanation that gravity can be included within P is not correct, because when the gravity part is added P ceases to be pressure. A further correction concerns the role of Darcy's law in the fundamental equations of porous media flows. Darcy's law provides the relationship between the resistance of the porous material to fluid flow and the fluid velocity (averaged over the Representative Elementary Volume of the porous material). In other words Darcy's law is a parameterisation (valid for small Reynolds numbers) not the fundamental equation itself. Depending on a particular application the fundamental equation may contain just the Darcy's equation or also some other terms such as acceleration or Brinkman's term. Such equations are not 'Additional forms of Darcy's law' as stated in the article. They are various versions of momentum equation which use Darcy's law to parameterise the resistance (i.e. drag or skin friction) term. The Brinkman's correction term accounts for the viscous resistance within the fluid flowing through the porous material, not for the porosity of grains. The article should reference at least one classical textbook such as Bear, Jacob, 1979, Hydraulics of groundwater: New York, McGraw-Hill, 569p. Average58 17:57, 3 June 2007 (UTC) Average58

Last edited at 17:57, 3 June 2007 (UTC). Substituted at 12:49, 29 April 2016 (UTC)

Petroleum engineering and multiphase flow

The symbol k for absolute permeability is widespread in the petroleum industry, and the petreoleum industry includes a large number of people. We also use pressure and gravity as separate terms in the equations. The original version of Darcy's equation is deficient even for single phase flow for our (the reservoir engineers) use, and we always use multiphase (et least two-phase) flow equations as developed by Muskat et al. I have written a significant expansion and contribution on multiphase equations that I am thinking to implement in this article. How widespread is the use of hydraulic conductivity parameter, and how widespread is the use of the symbol K for this parameter? My general impression is that there are no strict standard on use of symbols and units in Wkipedia articles. The impression is that the author of article or pargraph in question explains his selection of symbols and list his choice of units. Can you estimate how many articles in Wikipedia that contain kappa as symbol for permeability? — Preceding unsigned comment added by Frode54 (talk • contribs) 03:04, 22 December 2016 (UTC)

There are no strict standards on the use of symbols, but it is nice when there is consistency between articles. As for changing the symbol κ (kappa) to k, I think I now agree that is is more widespread and support changing it. (Hydraulic conductivity is pretty much always K, as I've never seen any other forms). How about we let this suggestion sit here for about another week to see if anyone wants to weight in on the topic. If there's no further discussion or objection, then please proceed to change the symbol. Other articles that I'm aware of include Permeability (earth sciences), Darcy (unit), Relative permeability, and Fluid flow through porous media (possibly more), which I'd advise to change too. +mt 04:04, 22 December 2016 (UTC)

Update: I've updated most instances of kappa to lower k, as discussed above. +mt 03:13, 27 October 2018 (UTC)

Logical soundness of the derivation from Navier-Stokes

Is there any other references showing the supposed derivation from the Navier-Stokes equations. It is not entirely clear where the additional equation for the linear "viscous resisting force" comes from, since, judging from the two equations, it would also mean that $\nabla ^{2}u_{i}+\varphi k_{ij}^{-1}u_{j}=0$. The whole procedure seems overdetermined. PolyconvexPoster (talk) 17:29, 18 November 2024 (UTC)