HWK 2 solution

# HWK 2 solution - PGE 203 HWK 2 Solution Due at start of...

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PGE 203 HWK 2 Solution Due at start of lecture: Feb. 15 (1) Please derive the correct units constant for traditional U.S. units for Darcy's Law for elliptical flow shown below. ( 29 -14 2 2 f m 2 2 2 3 m f 4.45 ln md-ft 1.063195x10 ft lb 32.152231 lb -ft 144 in cp 1488 ft-s 86,400 s bbl 4.45 md cp lb day in ft lb -s 5.614583 ft 199.4 ln w e e w w e e w kh q B B q kh q B B μ μ Φ - Φ = - = Φ - Φ = - You should follow the example for radial liquid flow shown in the lecture notes to complete this. (2) Using the equation for radial flow in the notes and the equation you derived in part (1) please compute the flow rate through each system using the following data. o 2 2 30 md 25' =10 cp 4,000 psi 3,000 psi = -20 deg 0.9 1 STB/bbl The area drained by each is 1,743,611 ft For the circle, , 745' For the e wf o e e k h p p B A r r μ θ γ π = = = = = = = = ellipse, , 1290' if /3 Assume that 0.2' e w w A ab B a b r B π = = = = = For elliptical flow: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 199.4 ln 62.4 0.9 32.2 3,000 4,000 1290 0.2 sin 20 32.2 144 30 25 199.4 1 10 ln 1290/ 0.2 50.3 STB/day w e e w kh q B B q q μ Φ - Φ = - - + - -

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