PGE 323 Homework#6 due April 18, 2008 Pope 1. Derive a mass balance on the gas for three dimensional, three phase flow of gas, oil and water in a reservoir using Cartesian coordinates. Assume immiscible flow without any mass transfer between the phases so the gas, oil and water have a fixed composition. Use the same formal procedure as in the class notes and show all detailed steps. 2. By definition, a Black Oil is oil that can be modeled with just two pseudo components: a solution gas pseudo-component and a stock oil pseudo-component. The gas pseudo-component partitions between the gas phase and the oil phase as a function of pressure. The conventional way of representing that relationship is to plot the solution gas-oil ratio Rs in SCF of solution gas per STB of oil as a function of pressure. You studied such PVT data in PGE 312 and saw examples in the textbook "The Properties of Petroleum Fluids" by William McCain. The gas pseudo-component is conserved because it is equivalent to the number of moles of gas (divide by 379 SCF/lbmole). Derive a mass balance on the
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