A Comparison of Three Equation-of-State Compositional Simulators

Abstract

The compositional equation of state formulations by Coats (C), Nghiem, Fong, and Aziz (NFA), and Young and Stephenson (YS) are compared for both immiscible (IM) and multiple contact miscible (MCM) problems. Coats formulation has the largest computer memory requirements and computation times. Nghiem, Fong, and Aziz's formulation requires the least memory, and Young and Stephenson's formulation is generally the fastest. Introduction Beginning in the late 1950's, several mathematical models were developed to study the effects of compositional changes on oil recovery. Jacoby and Berry developed a tank-type model which used vapor-liquid equilibrium (VLE) and composition-dependent densities and viscosities. Constant pressure, linear, one-dimensional, (1-D) models were then developed by Welge, et al. and Attra to study the displacement of oil by gas injection. Pressure effects were included in a radial, 1-D model by Kniazeff and Naville; introduced in linear models by McFarlane, et al.; and improved upon by Price and Donohue. Roebuck, et al. added water as a flowing phase and Price and Donohue. Roebuck, et al. added water as a flowing phase and presented the first formulation applicable to higher dimensions. presented the first formulation applicable to higher dimensions. Formulations by Culham, et al., Gondouin et al., Van Quy, et. al., Tsutsumi, MacDonald, Nolen, and Kazemi et al. also contributed various items such as dispersion or more rigorous methods for computing VLE. In all of the preceding formulations, the VLE, densities, and viscosities were computed from independent correlations. Many times these correlations would not predict consistent critical points and, hence, oscillatory behavior was sometimes observed, in the critical region. Fussell and Fussell overcame this difficulty by using a cubic equation of state (EOS) to determine both the VLE and the densities which were then used to compute the viscosities. Since 1980, three more EOS formulations have been presented: Coats developed a fully implicit formulation; Nghiem, Fong, and Aziz modified the Kazemi, et al formulation to include an EOS; and Young and Stephenson presented a formulation similar to, but more general and efficient than presented a formulation similar to, but more general and efficient than Fussell and Fussell's. The C, NFA, and YS formulations represent state-of-the-art, VLE, compositional simulators. The primary objective of this study is to compare the last three EOS formulations. The comparisons are analogous to those made for black oil simulators - except we focus here on run characteristics rather than characteristics of the solution. A secondary purpose of this work is to provide detailed, standard, run-time data for other programmers. provide detailed, standard, run-time data for other programmers. We compare the formulations in terms of computer storage, accuracy, number of iterations, and computation time, for both immiscible and multiple contact miscible cases. Great care was taken to make the comparisons on a consistent basis. The C formulation was implemented only in 1-D; the YS and NFA formulations were implemented in both 1-D and two-dimensional (2-D) areal geometries. EQUATIONS The formulations model the flow of two hydrocarbon phases: oil and gas; and an aqueous phase. Each hydrocarbon phase is composed of Nc hydrocarbon components (which may include non-hydrocarbons such as CO2, N2, or H2S, but not water) and the aqueous phase is entirely water. p. 123

Effects of CO2 Solubility in Brine on the Compositional Simulation Of Co2 Floods

“…A complete data set for the simulations is available elsewhere. 18 Continuous Injection of CO 2 , The continuous injection of CO 2 into a formation with a high oil saturation was expected to yield the smallest effects of CO 2 solubility in brine. The recovery curves in Fig.…”

An Equation-of-State-Based Reservoir Model Incorporating Continuous-Mixture Thermodynamics

“…Let the combination of these two streams be denoted by M and F. See Computations All computations were performed on a Digital DEC 3100 workstation. First of all, the pseudocomponent simulator performance was verified with published literature (Thiele et al, 1983) before incorporating the continuous thermodynamics concept. The model problem involved a three-component in-place oil comprising methane, butane, and decane in a hypothetical one-dimensional reservoir into which a mixture of methane and butane (mole ratio 0.68:0.32) is injected at a specific rate.…”

“…The water phase is immobile. We used the same physical properties, equation of state (EOS), assumptions, and solution method (IMPES) as the authors (Thiele et al, 1983). The only difference in the methods is that Thiele et al used the Lohrenz and Bray method (Lohrenz et al, 1964) to compute phase viscosities while we used pure component viscosities at the reservoir temperature and pressure obtained from Muskat (1949) along with a molecular weight and mole fraction mixing rule.…”