PNG410-lecture___4

PNG410-lecture___4 - LECTURE 4 ROCK PROPERTIES PERMEABILITY...

This preview shows pages 1–5. Sign up to view the full content.

LECTURE – 4 ROCK PROPERTIES – PERMEABILITY

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Permeability Porosity is fluid-bearing capacity of rock, permeability is the fluid conducting property Assume rock is made up of a bundle of capillary tubes Fluid flow in each tube is governed by Poiseulle’s law: Consider the flow of two parallel layers of fluid: Law of viscosity: Tangential force (perpendicular to direction of dx) required to maintain a velocity difference dv between the layers is directly proportional to dv and A and inversely proportional to dx: P+ P P Capillary tubes Q v v+dv dx F y A Separation of layers = dx Area of contact = A dx dv A F y
Poiseulle’s Law Now consider a cylindrical volume of fluid inside the capillary X - direction X=0 (center line); X=r (wall of the capillary) P + D P P Next we integrate the above and in order to evaluate the constant of integration, we assume that at x=r, v = 0 (no slip) dx dv L x dx dv A x P F y D 2 ) ( 2 dx x L P dv 2 D 2 ) ( 2 2 2 x r L P v D

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Poiseulle’s Law (cont’d) This is the velocity at a radius x within the tube Volumetrically, v is the velocity of fluid flowing between the layer x and x+dx. Therefore: Where dA is the cross-sectional area of the annular region between x and x+dx The Incremental flow rate: Integrating between the bounds x=0 and x=r yields: 2 ) ( 2 2 2 x r L P v D dA v dQ dx x dA x A 2 2 dx x x r L P dQ D 2 2 ) ( 2 2 2 L P r Q 8 4 D
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern