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PERMEABILITY Flow of Liquids in Porous Media

PERMEABILITY Flow of Liquids in Porous Media. A. q. 2. L. 1. Linear Flow, Incompressible Liquid. 1-D Linear Flow System steady state flow incompressible fluid, q(0  s  L) = constant d includes effect of dZ/ds (change in elevation) A(0  s  L) = constant

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PERMEABILITY Flow of Liquids in Porous Media

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  1. PERMEABILITYFlow of Liquids in Porous Media

  2. A q 2 L 1 Linear Flow, Incompressible Liquid • 1-D Linear Flow System • steady state flow • incompressible fluid, q(0s  L) = constant • d includes effect of dZ/ds (change in elevation) • A(0s  L) = constant • Darcy flow (Darcy’s Law is valid) • k = constant (non-reactive fluid) • single phase (S=1) • isothermal (constant )

  3. A q 2 L 1 Linear Flow, Incompressible Liquid • Darcy’s Law: • q12 > 0, if 1 > 2 • Use of flow potential, , valid for horizontal, vertical or inclined flow

  4. q rw re Radial Flow, Incompressible Liquid • 1-D Radial Flow System • steady state flow • incompressible fluid, q(rws  re) = constant • horizontal flow (dZ/ds = 0   = p) • A(rws  re) = 2prh where, h=constant • Darcy flow (Darcy’s Law is valid) • k = constant (non-reactive fluid) • single phase (S=1) • isothermal (constant ) • ds = -dr

  5. q rw re Radial Flow, Incompressible Liquid • Darcy’s Law: • qew > 0, if pe > pw

  6. Flow Potential - Gravity Term •  = p - gZ/c • Z+ • Z is elevation measured from a datum •  has dimension of pressure • Oilfield Units • c = (144 in2/ft2)(32.17 lbmft/lbfs2)

  7. Flow Potential - Darcy’s Experiment • Discuss ABW, Fig. 2-26 (pg. 68) • Confirm that for the static (no flow) case, the flow potential is constant (there is no potential gradient to cause flow) • top of sand pack • bottom of sand pack

  8. Flow Potential - Example Problem • Discuss ABW, Example 2-8 (pg. 75) • Solve this problem using flow potential

  9. Permeability Units • Discuss ABW, Example 2-9 (pg. 79) • 2 conversion factors needed to illustrate permeability units of cm2 • cp  Pas • atm Pa

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