Homework _6.key

Homework _6.key - PGE 323 Homework#6 KEY May 2 2006 Pope 1...

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PGE 323 Homework#6 KEY May 2, 2006 Pope 1. Accumulation mass = mass in - mass out ( 29 ( 29 ( 29 w w w w w w w w t t t r r r 2 r rh S S 2 rh u 2 rh u t +∆ +∆ π ∆ φρ - φρ = - π ρ - π ρ (a) Dividing by r r t ∆ ∆ and taking the limits gives the mass balance: ( 29 ( 29 w w w w S r u 2 h 2 h t r r φρ ρ π π = - Α ssuming constant φ and ρ w gives: ( 29 w w ru S 2 h 2 h t r r G G π π φ = - Use definition of fractional flow w w u f u = to get: ( 29 w w ruf S 2 h 2 h t r r G G π π φ = - q 2 hru cons tan t = π = ( 29 w w qf S 1 2 h t r r G G - π φ = w w S f q t 2 h r r G - = π φ (b) Mass balance in terms of water saturation: w w w w S df S q t 2 h r dS r G - = π φ w S Sw dr t Sw dt r G = - w w w w S f q t S 2 h r S r G G G - = π φ (c) The velocity of a front of constant water saturation is:

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Homework _6.key - PGE 323 Homework#6 KEY May 2 2006 Pope 1...

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