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It is well-known that one should be cautious with the use of composition-independent K-value correlations for phase equilibria at high pressures. The first limitation is the correlation's inability to predict convergence of the dew and bubble curves at the mixture's critical point or at a closed phase envelope. Rather, these two curves extend indefinitely beyond the critical temperatures and pressures of all the species in the mixture. However, even at low pressures, where these correlations are usually applied, results can be misleading. This paper presents some practical examples where correlations fail. In the calculation of three-phase flash equilibria one cannot use the same correlation for the K-values between the vapor phase and the liquid, hydrocarbon-rich phase, and the K-values between the vapor phase and aqueous phase. Use of the same correlation provides two linearly dependent equations, making it impossible to obtain a unique solution. The solution of this three-phase flash problem by bisection provides trivial roots, indicating different values of the aqueous and hydrocarbon-rich phase fractions but a unique value for the vapor fraction. The compositions of both liquid phases are clearly identical. A physically sound assumption for the solution of this three-phase flash equilibria problem is that hydrocarbons are insoluble in the aqueous phase. However, the solution of this case for a test ternary of n-heptane, n-decane and water ( C 7 C 10 H 2 O ) led to distinct multiple roots that satisfy the material balance constraints. Up to 67 roots were found for a system of 40% n-heptane, 20% n-decane and 40% water at 70 psia and 350 °F (a fairly low pressure). Physical properties of the phases evaluated using these roots can be substantially different; therefore, this assumption could lead to serious problems in reservoir engineering calculations. A second assumption of no-solubility of water in the hydrocarbon-rich phase also provides linearly independent equations. However, no simultaneous roots could be found for the test system under study for the same pressure and temperature and various combinations of these two variables. |
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