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Test_1.2009 - PGE 323L Test#1 Open notes Pope 1(10 Darcy's...

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PGE 323L Test#1 Open notes February 26, 2009 Pope 1. (10%) Darcy's law for multiphase flow in a permeable medium can be written as follows: ( 29 rj j j j j k u k P g D = - μ r r where j can be any phase such as water, oil or gas. (a) Is Darcy's law valid for unsteady state flow? (b) Is Darcy's law valid for compressible flow? (c) Is Darcy's law valid for an anisotropic permeable medium? (d) Is Darcy's law valid if all three phases are flowing simultaneously? 2. Assume single phase flow of a gas at residual water saturation. (a) 20% Derive a mass balance for the gas in cylindrical coordinates (b) 15% Derive a diffusivity equation for the gas assuming a diagonal permeability tensor (c) 5% The diffusivity equation has the gas density in it. What is the most common method that reservoir engineers use to model the gas density? 3. (a) 15% Explain when you would use the solution for line sources and sinks and when you would uses the solution for point sources and sinks. Your explanation should include sketches illustrating examples. Your sketches should include pathlines, isopotential
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