Calculation Of Phase Envelopes Research Articles

Phase envelope calculations of synthetic gas systems with a crossover equation of state

We describe, in this work, a procedure for the calculation of the phase envelope of multi-component systems using a crossover Equation of State (EoS) based on the renormalization group theory and two different algorithms. The first algorithm utilizes pressure and temperature as natural variables, while the second uses volume and temperature. Our comparison shows that the second method is more suitable to a crossover EoS, as it avoids solving for the volume roots of the EoS, which is computationally intensive and potentially hampers the widespread use of such models in engineering applications. Moreover, we compare the simulated phase envelopes with the experimental data of 30 synthetic natural gas mixtures. The results indicate that the crossover SRK EoS has a similar performance to the classical model. Although larger deviations are observed for the representation of the bubble and dew-point curves, the crossover EoS yields a superior description of the critical points.

Calculation of phase envelopes of fluid mixtures through parametric marching.

Two-dimensional cross-sections of the phase envelopes of fluid mixtures—in particular isotherms, isobars, and isopleths—are often computed point-by-point by incrementing a so-called marching variable and solving the equilibrium conditions at each step. The marching variable is usually pressure, temperature, or a mole fraction, depending on the application. These isolines, however, can have rather complicated shapes, so that a simple unidirectional “sweep” of the marching variable often gives merely a part of the desired isoline. It is then necessary to restart the sweep with different initial values, or to switch to another marching variable. This, however, makes it difficult to compute complete isolines automatically, without human interference. We propose here a new marching technique through which it is possible to follow isolines of arbitrary shape and thus to compute complete isolines, as long as they are contiguous.

Characterization, Pressure–Volume–Temperature Properties, and Phase Behavior of a Condensate Gas and Crude Oil

The oil reservoirs are underground and have the oil and gas contained in the porous rock at high temperatures and pressures. Only 5–20% of the oil is withdrawn in primary production. Further recovery can be achieved by injecting carbon dioxide (CO2) that displaces and dissolves part of the remaining oil; this process is called enhanced oil recovery. Although the characterization and fractionation of petroleum are well-known and studied, each oil sample represents a unique multicomponent system; therefore, an individual study of the sample is required. Real samples of condensate gas (CG) and light crude oil (LCO) were collected and analyzed for density, viscosity, atmospheric distillation and fractionation, and aiming characterization. Synthetic visual and non-visual methods for high pressure were successfully applied for bubble point measurements of the systems composed of supercritical CO2 and CG or LCO. Phase envelope calculations were developed on the basis of pseudo-components obtained by atmospheric ...

Differential equations for the calculation of isopleths of multicomponent fluid mixtures

An isoplethic phase envelope is a locus of two-phase equilibria where one of the phases is kept at constant composition. The thermodynamic conditions for such a phase envelope are expressed as a set of first-order ordinary differential equations in which molar concentrations appear as central variables instead of mole fractions. The resulting formalism is applicable to multicomponent mixtures, well-suited for machine calculations, and allows a very rapid calculation of phase envelopes with arbitrary equations of state.Application to the formalism to pure fluids yields simple differential equations that are analoga of Clapeyron's equation, but permit the calculation of orthobaric densities.

Present status of the group contribution equation of state VTPR and typical applications for process development

For the development and design of industrial processes the reliable knowledge of thermophysical properties, in particular phase equilibria is most important. Assuming that 1000 components are of technical interest, vapor-liquid equilibrium data for approximately 500,000 binary systems are needed to fit all required binary interaction parameters. Due to the fact that the measurement of all needed properties is nearly impossible, the process engineer depends on factual data banks.Besides the different phase equilibria, the Dortmund Data Bank as worldwide largest factual data bank for thermophysical properties contains nearly all worldwide available pure component, excess and transport properties. Although more than 66,300 binary VLE data sets for non-electrolyte systems are currently stored in the DDB, in total up to now VLE data for only 13,540 different binary systems are available. The reason is that some systems are very popular and were measured very often, e.g. ammonia – water, ethanol-water and so on. When the 1000 most important components are considered, VLE data for only 8635 binary systems are available. This means for only 1.73% of the systems the required binary interaction parameters can be fitted. Since the assumption of ideal behavior for the missing binary systems can be very erroneous and measurements are very time consuming, predictive group contribution models can be successfully applied to estimate the missing thermophysical properties.To cover sub- and supercritical conditions, group contribution equations of state have to be applied. They automatically take into account both phases and can be used up to high pressures and supercritical conditions. This allows for example the calculation of phase envelopes. Furthermore, the introduction of Henry coefficients for gaseous compounds is not required. At the same time, enthalpies, heat capacities, densities and so on can be predicted. Today the most sophisticated group contribution equation of state is the volume translated Peng-Robinson group contribution equation of state VTPR. In this paper, typical applications of VTPR for process development are shown and new parameters for 24 additional group combinations are given.

Density Marching Method for Calculating Phase Envelopes

Different methods have been proposed in the literature for the calculation of phase envelopes of mixtures. The phase envelopes of even simple mixtures have at least two stationary points on the P–T plane [∂P/∂T = 0 at the point of maximum pressure (cricondenbar) and ∂T/∂P = 0 at the point of maximum temperature (cricondentherm)]. Even more stationary points exist for complex mixtures. Therefore, a monotonic variation of either pressure or temperature cannot be used to trace the full phase envelope. Different methods have been proposed in the literature to help choose the right variable at the right location of the phase envelope to automatically trace the entire phase envelope. Although most methods work well for simple mixtures, many of them do not work well with wide-boiling mixtures or with mixtures that exhibit open-ended dew lines. In this article, we compare phase envelopes with space curves and show that the use of an independent variable helps trace complex phase envelopes automatically. It is sho...

An efficient algorithm for the calculation of phase envelopes of fluid mixtures

The criteria of fluid phase equilibrium can be expressed in terms of derivatives of the Helmholtz energy density, which takes component densities (concentrations) as its natural variables. The resulting formulation is very symmetric, avoids shortcomings of other approaches, and leads to a very efficient computer algorithm for the calculation of phase envelopes of multicomponent mixtures.The new algorithm does without inverting the equation of state (calculate the density from pressure and temperature) at each iteration step, and thus achieves a significant acceleration of phase diagram computations with noncubic equations of state. The estimation of initial values for the iteration is reduced to a 1-dimensional search problem even for multicomponent mixtures.

Phase behavior of a near-critical reservoir fluid mixture

In this paper, the phase behavior of a naturally occurring reservoir fluid mixture has been experimentally studied in the near-critical region. The computer-controlled ROP (France) high-pressure PVT system equipped with video camera-monitor-recorder system and an on-line Anton-Paar fluid density meter was used in the experimental work. The measurements involve the compressibility factor of the compressed fluid, the bubble/dew point locus in the near-critical region, the mixture critical point, the liquid volume fraction in the two-phase region, and the density of the liquid/vapor phase. The volume-translated Soave-Redlich-Kwong equation of state proposed by Peneloux and Rauzy (1982) [Peneloux, A. and Rauzy, E., 1982. A consistent correction for Redlich-Kwong-Soave volumes. Fluid Phase Equilibria, 8: 7–23] was selected to test its performance in the near-critical region. The C 7 +-fraction of the reservoir fluid was characterized by the procedure proposed by Pedersen et al. (1984) [Pedersen, K.S., Thomassen, P. and Fredenslund, Aa., 1984. Thermodynamics of petroleum mixtures containing heavy hydrocarbons. 1. Phase envelope calculations using Soave-Redlich-Kwong equation of state. Ind. Eng. Chem., Process. Des. Dev., 23: 163–170].

Prediction of high-pressure multicomponent phase equilibria using a perturbed hard chain equation of state

A model based on the Perturbed Hard Chain Theory (PHCT) applicable for asymmetric mixtures where molecules differ significantly in size and shape, which are typical for supercritical extraction processes is used to predict the phase behavior at high pressure of multicomponent mixtures. The high-pressure vapor-liquid equilibrium (VLE) and phase envelope calculations for multicomponent mixtures presented in this paper are based on the predictive procedures for the pure component properties, and for the binary interaction parameters. No higher-order interaction parameters have been used. The model gives satisfactory results as far as predictivity of phase equilibrium is concerned.

Phase equilibria and critical points in n-alkanes + CO 2 OR + N 2 systems

In this work, phase envelopes and critical points of multicomponents mixtures were calculated. Newton-Raphson algorithm is used for solving the system of non-linear equations in the phase envelope calculations. This algorithm and the method proposed by R.A. Heidemann for calculating critical points are used with the Peng-Robinson cubic equation of state.

Thermodynamics of petroleum mixtures containing heavy hydrocarbons. 1. Phase envelope calculations by use of the Soave-Redlich-Kwong equation of state

Analytical data for various North Sea oils and gas condensates have been measured. The data include compositional measurements, TBP analyses, molecular weights, PNA analyses and specific gravities of most fractions. In addition, some dew and bubble points have been measured for each mixture establishing a few points on the phase envelopes. The corresponding phase envelopes are computed with the SRK (Soave-Redlich-Kwong) equation of state. Different methods of representing the heavy components by subfractions and different methods for computing the properties of the subfractions (T /SUB c'/ P /SUB c'/ and ..omega..) are compared. It is found that the phase envelopes can be accurately represented if the TBP residue (C/sub 21/+) is split into approximately 20 subfractions and the C/sub 6/-C/sub 20/ interval is treated as one subfraction for each carbon number. A logarithmic dependence of the mole fraction against carbon number may be assumed for the residue. The best results are obtained by using the Cavett relations for T /SUB c/ and P /SUB c/ of the subfractions and the Lee-Kesler relations for ..omega... The results are improved when the paraffinic, naphthenic, and aromatic parts of each subfraction are treated separately rather than lumped. No ''matching'' or ''tuning'' to experimentalmore » phase equilibrium data is needed.« less

Calculation of phase envelopes and critical points for multicomponent mixtures

Abstract An algorithm for the construction of complete vapour—liquid phase envelopes, capable of accurately determining the critical points and maxima in temperature and pressure is described. Recently developed methods for direct calculation of critical points are critically examined, and a computationally more convenient formulation is suggested.

Gapless, granular; Three-color screens for color photography

An isoplethic phase envelope is a locus of two-phase equilibria where one of the phases is kept at constant composition. The thermodynamic conditions for such a phase envelope are expressed as a set of first-order ordinary differential equations in which molar concentrations appear as central variables instead of mole fractions. The resulting formalism is applicable to multicomponent mixtures, well-suited for machine calculations, and allows a very rapid calculation of phase envelopes with arbitrary equations of state.Application to the formalism to pure fluids yields simple differential equations that are analoga of Clapeyron's equation, but permit the calculation of orthobaric densities.

Heat of evaporation of liquid air

An isoplethic phase envelope is a locus of two-phase equilibria where one of the phases is kept at constant composition. The thermodynamic conditions for such a phase envelope are expressed as a set of first-order ordinary differential equations in which molar concentrations appear as central variables instead of mole fractions. The resulting formalism is applicable to multicomponent mixtures, well-suited for machine calculations, and allows a very rapid calculation of phase envelopes with arbitrary equations of state.Application to the formalism to pure fluids yields simple differential equations that are analoga of Clapeyron's equation, but permit the calculation of orthobaric densities.