PGE 323 Test #1 Open notes February 14, 2006 Pope 1. (30%) In homework#1, you did a mass balance for single-phase flow in a permeable medium using cylindrical coordinates. (a) Starting with the equation ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 r z t t t r z r z r r z z r r z r r z r z U r r U z r U t z r r U r r U z r U t θ +∆ θ θ +∆ +∆ θ+∆θ ∆θ∆ ∆ φρ- ∆θ∆ ∆ φρ = ∆θ∆ ρ + ∆θ∆ ρ + ∆ ∆ ρ ∆- ∆θ∆ + ∆ ρ + ∆θ∆ ρ + ∆ ∆ ρ ∆ show in detail how to get the differential mass balance equation ( 29 ( 29 ( 29 ( 29 r z 1 1 r U U U0 t r r z r θ φρ + ρ + ρ + ρ = ⇒∏ • θ (b) Starting with the mass balance from part (a) and assuming Darcy's law, derive the diffusivity equation for ideal gas in terms of pressure squared (neglect gravity). 2. (40%) Assume the solution for point sources and sinks applies to this problem. (a) Make a sketch showing how to model two vertical wells completed over different depths, which means the interval over which each well is perforated is different. Label
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This note was uploaded on 05/15/2011 for the course PGE 323 L taught by Professor Johns during the Spring '10 term at University of Texas.