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PGE 323.Test_3(2008)

# PGE 323.Test_3(2008) - calculations are needed to make...

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PGE 323 Test#3 Open Notes May 2, 2008 Pope 1. Assume the three-phase flow of gas, oil and water into a vertical well can be modeled as radial flow in a cylinder of thickness h around the production well and the fluids can be modeled with the Black Oil model as described in the course notes and used in homework#6. (a) (30%) Derive a one-dimensional radial flow mass balance on the gas pseudo- component. Show and explain all of the detailed steps in the derivation. (b) (20%) Write Darcy's law for this problem and then use it with the mass balance to derive the diffusivity equation. 2. (50%) This problem is similar to problem 3 of homework #6. Assume gas is displacing oil in a reservoir at residual water saturation and all of the assumptions used to derive Buckley-Leverett theory apply. (a) Sketch the gas and oil relative permeability curves and the corresponding fractional flow diagram. Label and explain the residual saturations on these sketches. No
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Unformatted text preview: calculations are needed to make these sketches and you do not need to use the same data as used in the homework problem. (b) Show and explain in detail how to calculate the displacement sweep efficiency at exactly 1.5 pore volumes using the sketches you made in part (a) and the Welge method you used in homework#6. Assume the initial gas saturation is zero. (c) Make a sketch of the gas saturation profile at 1.5 pore volumes. (d) Make a sketch of the oil production rate (q o ) versus pore volumes that is consistent with your fractional flow sketch. Again, no calculations are needed to make this sketch, but it should be qualitatively consistent with your fractional flow diagram. (e) Sketch the displacement sweep efficiency versus pore volumes for your example and for two other examples with widely different mobility ratios to show how it changes with mobility ratio....
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