PERMEABILITY Flow of Liquids in Porous Media .

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 ) L q A 1 2

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

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 q re rw

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

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)

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

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

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