Homework_6 - (c) Derive an equation for the velocity...

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PGE 323 Homework#6 due April 17, 2006 Pope 1. This problem is analogous to the linear two-phase flow problem in Chapter 3 except rather than assume linear flow, assume radial flow in a cylindrical coordinate system. Assume there is an injection well in the center of a cylindrical reservoir of constant thickness h and no dip. (a) Derive a water mass balance for two phase flow of water and oil assuming radial flow and no mass transfer between the water and oil. (b) Assume constant fluid and rock properties and write the equation in terms of water saturation and fractional flow.
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Unformatted text preview: (c) Derive an equation for the velocity (dr/dt) of a front of constant water saturation (analogous to the Buckley-Leverett equation for linear flow derived in the course notes). (d) Integrate this differential equation to get the relationship between r, t and Sw using the same initial condition. (e) Make the solution from part (d) non-dimensional and write it in such as way that it is functionally the same as the linear solution so that you can use the same spreadsheet as posted for linear water floods to do calculations for a radial water flood....
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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.

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