A re-entrant resonator for the measurement of phase boundaries: dew points for {0.4026CH4 + 0.5974C3H8}

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Abstract

For a natural gas and, especially, retrograde condensates, it is important for exploration and production that the (liquid + gas) phase boundary be known along with the ratio of liquid-to-gas volumes within the (liquid + gas) two-phase region. These fluid properties can be measured by a plethora of methods and here we report a method based on the measurement of the resonance frequency of the lowest order inductive-capacitance mode of a re-entrant cavity capable of operating at temperatures up to 473 K and pressures below 20 MPa. This instrument has been used to measure, at T < 340 K, the dew pressures of {0.4026CH4 + 0.5974C3H8}. The measured dew pressures differ by less than 0.5 % from values obtained by interpolation of those reported in the literature, which were determined from measurements with experimental techniques that suffer from quite different potential sources of systematic error than the radio-frequency resonator used here. Dew pressures estimated from both NIST 14 and the Peng-Robinson equation of state lie within <±1 % of our results at temperature between (315 and 337) K while predictions obtained from the Soave Redlich Kwong cubic equation of state deviate from our results by 0.4 % at T = 315 K and these absolute differences increase smoothly with increasing temperature to be −2.4 % at T = 337 K.

Introduction

The optimal recovery of naturally occurring hydrocarbons mixtures depends on a knowledge of the physical properties of the porous media and fluid contained within, including its phase boundaries, density, and viscosity. Dew and bubble points can be determined experimentally or estimated with an equation-of-state; the latter requires as input temperature, pressure and chemical composition, which may be obtained from gas chromatography with a mass spectrometer. For retrograde condensates (or natural gas) the dew curve and ratio of liquid-to-gas volumes within the (liquid + gas) two-phase region, often referred to as the quality line, are the most significant thermodynamic properties for exploitation. For multi-component mixtures, for example, retrograde condensates, predicted dew pressures are often considered unreliable and must be measured.

Experimentally, dew curves are often determined by visual observation of the first onset of liquid. Often, but not always, the techniques used by industry to determine dew points have volumes of about 1 L. Although the results obtained from visual methods are renowned for suffering systematic errors that arise from blind regions and dead volumes, and these sources of error have, to a lesser or greater extent, been reduced by refinements to the method, the visual method is the most prevalent in the petroleum industry. Non-visual methods, that require small (<100 cm3) samples and are particularly suited to automation, have been developed to determine the presence of a phase transition. These include measurements of refractive index with fibre-optic cables [1], evanescent waves at GHz frequencies [2], and relative permittivity [3], [4], [5], [6], [7]. The latter, determined with a radio frequency re-entrant cavity, was previously used by Goodwin et al. [6], [7] to determine phase boundaries, and is the subject of this work. Dew points were detected from the variation in resonance frequency of the LC mode of the re-entrant cavity, where L is the inductance and C the capacitance, with respect to temperature decrements along pseudo isochores.

The operation of the re-entrant cavity is demonstrated with measurements of the dew pressure for {0.4026CH4 + 0.5974C3H8} at temperatures in the range (315 to 340) K. There are eight publications [8], [9], [10], [11], [12], [13], [14], [15] that report the phase behaviour of {(1  x)CH4 + xC3H8} at temperatures in the range (273 to 363) K. References [8], [9], [10], [11], [12], [13] report results obtained from (p, V, T, x) measurements, while [14] reports dew pressures obtained with a dual-sinker densimeter. May et al. [15] used a re-entrant cavity modified to optimise the determination of liquid drop-out-volume with a resonance at frequencies of GHz. The present results have been compared with literature values and estimates obtained from 3 equations of state: (1), National Institute of Standards and Technology, Standard Reference Database 14 version 4 [16]; (2), the Peng-Robinson cubic equation of state; and (3), the Soave–Redlich–Kwong cubic equation of state.

Section snippets

Apparatus and experimental

A schematic of the apparatus, shown in figure 1, includes the re-entrant resonator similar to that reported by Goodwin et al. [6], [7], a magnetically activated circulation pump, and a differential pressure gauge all of which are mounted within a circulated air thermostat and the temperature controlled to < ± 3 mK. The re-entrant cavity, shown schematically in figure 2, was designed to be both the geometry required to form the LC resonator and act as a pressure vessel capable of operating at

Working equations

The vector network analyser was used to measure the complex forward scattering transmission fraction S21, defined as the complex ratio of the voltage transmitted through the cavity to the voltage incident on it, for the lowest order non-degenerate LC mode. The measured real Re and imaginary Im components were fit to the theoretical expression for the resonance [22] of the re-entrant cavity given by:Re(S21)=2β1β2(1+β1+β2)(1+β1+β2)2+2Δff02Q2,andIm(S21)=-2β1β22Δff0Q(1+β1+β2)2+2Δff02Q2,where f0 is

Results and discussion

The measured gas to liquid (p, T) phase boundaries of {0.4026CH4 + 0.5974C3H8} are listed in table 1. The uncertainties, listed in table 1 at a confidence of 0.995 (k = 2), for the phase boundary temperature and pressure were obtained by combining in quadrature uncertainties arising from the determination of the phase boundary location (that is 0.25 times the step size) with uncertainties arising from dT/dx, dp/dx, dpd/dT, and the individual measurements of temperature, pressure and frequency. The

Acknowledgements

The authors thank the University of Canterbury for an Internal Research Grant that was used to purchase equipment and Schlumberger for financial support of Mohamed Kandil.

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