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

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LECTURE – 4 ROCK PROPERTIES – PERMEABILITY
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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
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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
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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
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