Critical Point and Saturation Pressure Calculations for Multipoint Systems (includes associated paper 8871 )

Abstract

Abstract Calculation of fluid properties and phase equilibria isimportant as a general reservoir engineering tool andfor simulation of the carbon dioxide or rich gasmultiple-contact-miscibility (MCM) mechanisms. Of particular interest in such simulations is thenear-critical region, through which the compositionalpath must go in an MCM process.This paper describes two mathematical techniquesthat enhance the utility of an equation of state forphase equilibrium calculations. The first is animproved method of estimating starting parameters(pressure and phase compositions) for the iterativesaturation pressure (bubble-point or dew-point)solution of the equation of state. Techniquespreviously have been presented for carrying out thisiterative solution; however, the previously describedprocedure for obtaining initial parameter values wasnot satisfactory in all cases. The improved methodutilizes the equation of state to estimate theparameter values. Since the same equation then isused to calculate the saturation pressure, the methodis self-consistent and results in improved reliability.The second development is the use of the equationof state to calculate directly the critical point of afluid mixture, based on the rigorous thermodynamic criteria set forth by Gibbs. The paper presents aniterative method for solving the highly nonlinearequations. Methods of obtaining initial estimates ofthe critical temperature and pressure also arepresented.The techniques described are illustrated withreference to a modified version of the Redlich-Kwong equation of state (R-K EOS); however, theyare applicable to other equations of state. They havebeen used successfully for a wide variety of reservoirfluid systems, from a simple binary to complexreservoir oils. Introduction MCM processes such as CO2 or rich gas miscibledisplacements (conducted at pressures below thecontact-miscible pressure) traverse a compositional path that goes through the near-critical region. Thishas been described in several papers. Simulationof an MCM process requires the use of an equation of state to describe the liquid- and vapor-phasesaturations and compositions. Fussell and Yanosikdescribed an MVNR (minimum-variableNewton-Raphson)method for solution of a version of theR-K EOS. They discussed some of the difficulties ofobtaining solutions to the equation of state in the near-critical region and showed that the MVNRmethod gave improved results.Experience with the MVNR method hasdemonstrated a need for an improved estimate ofinitial iteration parameters (pressure, phasecompositions)for an iterative solution of saturation(dew-point and bubble-point) pressures. It waslearned that the semitheoretical K-value correlationused for initial estimates usually gave satisfactoryresults when the fluid system contained significantamounts of heavy components (C7+) but was oftenunsatisfactory for fluid systems containing only lightcomponents. This type of system is exemplified bythe fluids in a dry gas-rich gas mixing zone or bymixtures rich in CH4, CO2, or N2.Experience also has demonstrated a need for direct calculation of the critical point. While the MVNRsolution technique discussed by Fussell and Yanosikexhibits improved convergence in the near-critical region, it often is difficult to obtain convergedsolutions of the equation of state at compositionswithin a few percent of the critical composition. SPEJ P. 15＾