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Unformatted text preview: PGE 323 Test#2 key March 24, 2003 Pope 1. (40%) Two oil wells are drilled and produced in the same reservoir. The distance between the wells is 500 m. Assume that the solution of the radial diffusivity equation for line sources and sinks and a slightly compressible fluid apply to this problem. Well 1 produces at the constant rate of 10 m 3 /D and well 2 produces at the constant rate of 20 m 3 /D. (a) Starting from the basic solution for transient flow, use superposition to write an equation for the reservoir pressure at any location during the transient flow period and the pressure at r w of well 1 during this same time period. ) kt 4 r c ( Ei kh 4 q P ) t , r ( P 2 t i - - = - - + - - - = ) kt 4 r c ( Ei D m 20 ) kt 4 r c ( Ei D m 10 kh 4 P ) t , y , x ( P 2 2 t 3 2 1 t 3 i For the pressure at any location x,y r 1 = x 2 + y 2 r 2 = (x-500m) 2 + y 2 For the pressure at well 1 r 1 =r w 2 r 2 = (500 m) 2 (b) At time t p , well 1 is shut in for a build up test. Use superposition to write an equation for the shut-in pressure taking into account that well 2 is still producing oil....
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