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PGE 323
Final Exam
Open book and notes
May 11, 2006
Pope
1. (a) Write Darcy's law for threephase, three dimensional flow assuming a diagonal
permeability tensor but make no other assumptions.
(b) Does this general form of Darcy's law apply even if the fluid compositions change? Is
it valid if the temperature is not constant? Is it valid for unsteady state flow? Is it valid for
compressible flow?
(c) The coefficients in Darcy's law must be measured just as coefficients in other similar
equations such as Fourier's law must be measured. In particular, the relative permeability
of each phase must be measured. Explain the steady state method for measuring three
phase flow relative permeability in reservoir cores. Use both sketches and equations to
explain your answer. List all assumptions and simplifications used in this method.
2. (a) Derive a mass balance for twophase flow of oil and water in a permeable medium
using cylindrical coordinates. Assume an isotropic medium. Do not assume constant fluid
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