HW_7(2008) - dimensional scaling group (Peclet number) and...

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PGE 323 Homework#7 due April 28, 2008 Pope 1. Assume a solvent is completely miscible with a multicomponent oil and displaces it in a three dimensional permeable medium at residual water saturation. (a) Derive a mass balance on any component i in the oil. How does this equation differ from the equivalent mass balance for a non-porous medium given in Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena (b) Derive a diffusivity equation using Darcy's law and Fick's law and Cartesian coordinates. (c) Make sketches of the produced concentration of component i versus pore volumes for different values of the Peclet number. Explain these curves physically in terms of the variables in the Peclet number. Explain why it is useful to describe the results with a non-
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Unformatted text preview: dimensional scaling group (Peclet number) and pore volumes rather than time, distance, velocity, etc. 2. (a) Use Buckley-Leverett theory for two-phase flow of oil and water in a permeable medium to describe and explain how an unsteady state relative permeability experiment is done and some of its limitations when using actual reservoir core, brine and oil. Make sketches of the fractional flow diagram, saturation profiles and relative permeability curves to support your explanation. Assume the oil viscosity is 0.8 cp and the water viscosity is 0.5 cp. (b) These limitations are eliminated if the steady state method is used. Explain why. What data are measured and how are they used to determine the steady state values of relative permeability?...
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