The bulk resistance of a water saturated sandstone core sample with a radius of

Question

The bulk resistance of a water saturated sandstone core sample with a radius of 5 cm and length of 20 cm is 12,500 ohms. Using Archie's Law, calculate the range of porosity of the sample if the pore fluid conductivity is that of standard drinking water (0.5 - 1.0 mS/cm). Assume the m and a parameters for Archies equation are 2.0 and 1.0. Archies Law is Equation 1.6.

AQUIFER WATER PAQUIFER- specific resistivity of water saturated sand pwATER specific resistivity of pore water. For partly saturated material, F can be replaced by F/Sw (Sw-saturation degree fraction of water filled pore space) The formation factor F combines all properties of the material influenc- ing electrical current flow like porosity , pore shape, and diagenetic ce mentation -m

Explanation / Answer

Given, bulk resistance of sandstone = 12500 ohms

Length of aquifer = 20 cm and radius = 5

Specific resisitivity of sandstone, = RA/L

= (12500 X 3.14 X 52) / 20

= 49062.5 ohm cm

Given Conductivity range of water = 0.5 -1 mS/cm

Resistivity = 1/Conductivity

= 1 /( 0.5 X 10-3 ) and 1 / (1X 10-3)

= 2000 and 1000 ohm cm

Now we will calculate formation factor F for both the values

F1 = aquifer / water = 49062.5 / 2000 = 24.53

F2 = aquifer / water = 49062.5 / 1000 = 49.06

Now we will calculate the range of posrosity

Given F = a / m

   Given m=2, a=1

  m = a/F

12 = 1/F1 = 1/24.53 = 0.040766

1 = sqrt (0.040766) = 0.2019 = 20 %

Similarly, 22 = 1/49.062 = 0.02038

  2 = sqrt (0.02038) = 0.1427 = 14 %

Therefore the range of porosity for the aquifer = 20 -14 %

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.