As the title, where can I find a relation describing the compressibility and permeability of sedimentary rocks? I am trying to use it as a first guess of initial condition in numerical modeling of sedimentary formations (many layers).
Thank you.
Dear Johnny
You may have a look at Reservoir Geomechanics book of Mark Zoback, 2007 chapter 11.
Well,
The proportionality constant in Darcy's law depends on the porous medium and the quality of the liquid, ie, k is a function of the medium and the liquid. If we keep ∆h, ∆l constant and make two attempts first using the same sand, liquid and water, and in the second we use the sugar solution, we find that the value of v will be greatly reduced On the second attempt it up on the first attempt.
Experiments have shown that if the porous medium contains regular spherical granules, the radius of d affects the value of v and shows that v Darcy speed is proportional to:
- Directly with a square radius of porous medium granules. - directly with the specific weight of the liquid Ɣ = ρ γ
- And inversely with the kinematic viscosity of liquids (μ) and that the stability of the hydraulic tilt.
We can write these relationships as follows:
V α d2
V α ρ g
V α 1 / μ
According to Darcy notes: V α dh / dl
السابقة Past relations of proportionality lead us to another version of Darcy law:
V α [d2 ρ g / μ] dh / dl
V = [C d2 g / μ] dh / dl …… .1
Where C is a proportionate constant and depends on the properties of the porous medium that affect the flow such as the irregularity of the radius of the particles of the formation of the medium and the irregular distribution and degree of rotation and compacting conditions.
equation 1 with the Darcy equation 2: V = K dh / dl …… .2
► Deduce equation 3: K = [(Cd2 g) / μ] …… 3
Μ Since μ, ρ depends only on the liquid, that is, each is a function of the liquid only.
Cd2 depends only on the media, ie, it is a function of the medium, from which we deduce equation - 4 ..... k = Cd2 -------4
- From equation 4 in equation 3 we find that K = (k ρ g) / μ
► where k expresses specific or intrinsic permeability
► If we refer to K with hydraulic conductivity, it is better to call k permeability.
It should be noted that some references use the term permeability coefficient instead of the term hydraulic conductivity hydraulic conductivity.
Permeability is a function of the medium only and has an area of m2 and the term is used in petroleum industries where there are gas, oil, and water in a mixture flow system and when measurements in square meters k will be very small, so petroleum engineers have defined the permeability unit, Darcy. If we replace the value of K according to the equation (= (k ρ g) / μ K) and place it in the Darcy equation (V = Ki), the Darcy law becomes.
V = (k g) / μ. dh / dl
Regards
Dear Faisal
Thank you for your suggestion, I did not find a relationship of rock compressibility and permeability in the book.
Dear Bayan
Thank you for your answer. But I did not see the role of rock's compressibility or storage.
Well,
Rock's compressibility; Indirectly obtained with the amount of C constant which depends on the properties of the porous medium that affect the flow and the particles of the media and the compacting conditions.
Regards
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