PGE 323L HW_2 - PGE 323L HW#2 due Pope 1 Assume the...

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PGE 323L HW#2 due February 19, 2009 Pope 1. Assume the solution for point sources and sinks applies to this problem. Consider a very simple problem where there is just one point source of flow rate q located at (0,0,0) and one point sink with flow rate -q located at (1000,0,0) in an isotropic reservoir. (a) Write the particular equations for the potential function and the three components of the velocity vector. (b) Starting with the potential function from part a, now write an equation for the pressure drop between the source and sink taking the "well radius" around each point to be R. Solve this equation for the flow rate q. (c) Write and equation for the velocity along the shortest pathline between the source and sink. Show how you could use this equation to calculate the breakthrough time. Make a 3D sketch of the pathlines at breakthrough. (d) Suppose a tracer is injected continuously at the source and its concentration measured
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