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PGE 323.Final.2008 (1) - PGE 323 Final Examination Open...

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PGE 323 Final Examination Open Notes May 12, 2008 Pope 1. A slight generalization of the standard Black Oil equations allows for the oil pseudo component to partition between the gas and the oil phases in addition to the usual partitioning of the gas pseudo component between the gas and oil phases. By analogy to R s in SCF of gas per STB of oil, we can define r o in STB oil per SCF of gas. Both depend on pressure and temperature. This is called the modified Black Oil model and is used by reservoir engineers worldwide when they use Black Oil reservoir simulators. This makes the Black Oil model equivalent to a standard pressure-composition diagram for a binary hydrocarbon mixture at reservoir temperature such as you studied in thermodynamics where the two components might have been methane and n-heptane. (a) 10% Derive a mass balance on the oil pseudo component for the modified Black Oil model defined above. Assume three-phase flow of oil, gas and water in a one- dimensional, linear reservoir with no mass transfer of the hydrocarbons to the water phase. (b) 5% Insert Darcy's law in the appropriate form into the mass balance for the oil pseudo component to get the modified Black Oil diffusivity equation. (c) 5% List all of the assumptions needed to derive the diffusivity equation in part (b). Indicate yes or no whether the following were assumed to derive it: incompressible fluids
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