This paper deals with the development of a general algorithm for phase envelope construction. It extends the pressure-temperature diagram construction method of Michelsen to the generation of phase envelopes on pressure-composition, temperature-composition and composition-composition diagrams. The bubble point and dew point curves are traced in one pass, and an estimate of the critical point is also given. The loci of mixtures having a point is also given. The loci of mixtures having a constant vapor-liquid split (e.g. 25% vapor mole fraction or volume fraction) can also be generated. The algorithm selects internally the primary variables and the points on the diagram to enhance the convergence.
Results are presented for simple mixtures, typical reservoir oil-CO2 mixtures and a gas condensate. Problems associated with a discontinuity in the phase envelope because of a three-phase region are also presented, and it is shown how an analysis of the Gibbs energy surface can help in discarding unrealistic results.
Phase equilibrium diagrams or phase envelopes are very desirable in the study of reservoir fluids. Pressure-composition and composition-composition Pressure-composition and composition-composition (e.g. ternary) diagrams are particularly useful in the design of gas injection processes. They are usually the form under which laboratory data are reported. Pressure-temperature diagrams are required in the design of pipelines or surface facilities (e.g. separators), and temperature-composition (An grams find application in separation processes.
In the past, the generation of the phase envelope on pressure-temperature, pressure-composition and temperature-composition diagrams involved a series of bubble point and dew point calculations. Several difficulties are inherent to this approach:
Near the critical point, it is not clear whether a bubble point or dew point should be computed.
The tracing of the dew point curve is tedious due to the presence of a lower dew point and an upper dew point.
The specification of variables has to be done manually. For example, in the construction of
pressure-temperature diagrams, one usually pressure-temperature diagrams, one usually specifies the pressure and computes the dew point temperature near the cricondentherm, and specifies the temperature and computes the bubble/ dew point pressure near the cricondenbar.
A general algorithm for phase envelope construction was first investigated by Asselineau et al. Their formulation involved the simultaneous solution of 2n+4 equations for each point on the phase envelope, where n is the number of components in the system. A more efficient algorithm for pressure-temperature diagram construction was later pressure-temperature diagram construction was later given by Michelsen. This formulation involves the simultaneous solution of n+1 equations for each point on the phase envelope. To enhance the convergence, this algorithm selects internally the set of primary variables and the step size to the subsequent point on the diagram. The initial guess for this point is obtained by extrapolation. The bubble point and dew point curves are traced in one pass, and the critical point curves are traced in one pass, and the critical point, cricondentherm and cricondenbar are estimated point, cricondentherm and cricondenbar are estimated from interpolation. The loci of mixtures having the same mole fraction of vapor-liquid split (e.g. 25% vapor mole fraction) can also be generated.
The present work involves the extension of Michelsen's algorithm to the construction of pressure-composition, temperature-composition and pressure-composition, temperature-composition and composition-composition diagrams along the lines of Asselineau et al. The loci of mixtures having the same mole fraction or volume fraction of vapor-liquid split can also be traced. These diagrams are very useful in the study of reservoir fluids, the matching of experimental phase behavior data, and the design of different recovery schemes, pipelines and surface facilities. The algorithm was applied to a binary system, typical reservoir oil-CO2 mixtures, and a gas condensate.
