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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 Assumptions 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 Assumptions • 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 Assumptions • 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 TermSI •  = p - gZ • Z+ • Z is elevation measured from a datum •  has dimension of pressure • In SI Z is measured in m, both  and p are in Pa, ρ is in kg/m3 and g is 9.81 m/s2 • The second term can also be written as S.G * 9810 Pa where S.G. is specific gravity w.r.t. water

  7. Flow Potential - Gravity TermField • In Field units: •  = p – Z ρ g / conversions = p – Z (S.G.) c • Z+ • Z is elevation measured from a datum • Both  and p are measured in psi • Z is measured in ft, • ρ is in lbm/ft3 and g is 32.7 ft/s2 conversions are complicated • S.G. is specific gravity with respect to water and is dimensionless • c is 0.433 psi/ft

  8. 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

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

  10. 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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