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Exam2Key(2006) - PGE 331 Exam 2 Key Open book notes Read...

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PGE 331 Exam 2 Key Open book, notes. Read each problem carefully and show all work, including units. One hour time limit. Indicate your class unique number on the first page below your name: 19320 10-11 am 19325 1- 2 pm 1. Derivations. (5 points each). Begin with the following conservation equation. 1 r d dr k ρ μ ρ δπ δρ = 0 1 The symbols have the meanings that we used in class. The permeability k is constant in all cases. Answer or derive the following: a. What type of conservation equation is this? What are the assumptions involved? This is a steady-state, microscopic conservation equation for a single phase fluid in one- dimensional radial coordinates. The phase need not be slightly compressible. b. Write Eq. 1 for the special case of an incompressible fluid with constant viscosity. For incompressible flow the density is constant. Eq. 1 becomes 1 r d dr r dp dr = 0 c. Derive the right side of Eq. 7-56 in the text. The viscosity is constant. Cancel out the mobility terms from Eq. 1 to give 1 r d dr k ρ μ ρ δπ δρ = 0 = 1 ρ δ δρ ρ δπ δρ 0 = ρ δ δρ δπ δρ + δπ δρ δρ δρ 0 = ρ δ 2 π δρ 2 + δπ δρ 2 δρ δπ 1
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0 = δ 2 π δρ 2 + δπ δρ 2 1 ρ δρ δπ 0 = δ 2 π δρ 2 + δπ δρ 2 χ which is the equation.
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