Surface tension and critical point measurements of methane + propane mixtures

Highlights

• Validating and extending surface tension data for methane + propane mixtures.

• Determining suitability of surface tension models for hydrocarbon mixtures.

• Extending critical point literature data for methane + propane mixture.

Abstract

Surface tension predictions of hydrocarbon mixtures at vapour-liquid equilibrium are crucially important and used in the design of many unit operations in the production of liquefied natural gas (LNG). Predictive models for surface tension are not well tested for hydrocarbon mixtures at high pressures due to the limited data available at relevant conditions. A differential capillary rise apparatus consisting of a high-pressure sapphire equilibrium cell was constructed and used to measure the surface tension of methane + propane mixtures along three isotherms T = (272.23, 285.51 and 303.34) K at pressures up to 9 MPa. The capillary diameters were calibrated using pure saturated propane at 271 K, and the technique was validated by measurements of pure ethane. The measured surface tensions were compared with the available data and the predictions of various models, including the Parachor method and Linear Gradient Theory: both were able to describe the data within their uncertainty. However, the default surface tension model for hydrocarbon mixtures implemented in the widely-used software package REFPROP 9.1 gave poor predictions; this was rectified through the implementation of the Parachor method in a beta-version of REFPROP 9.2. Critical points were also measured from observations of critical opalescence and the disappearance of the bulk interface. The measured mixture critical points were consistent with, and extended, literature values for this binary system. The measured critical points differed by between 0.5 and +27 K from predictions made with the GERG-2008 equation of state (EOS) and between −5 and +10 K for the Peng-Robinson EOS.

Introduction

Natural gas is a multicomponent mixture comprised principally of hydrocarbons. As part of the extraction and purification processes used to prepare this major energy source for safe transport and storage, it is often found as a mixture of vapour and liquid phases. The interaction of these phases is governed by the surface tension of the mixture. Surface (or interfacial) tension is due to the existence of imbalanced intermolecular forces at the liquid/vapour interface. Surface tension is a key thermodynamic property of central interest to the natural gas industry affecting, for example, multiphase flow, separation efficiencies of scrubber columns, the efficacy of heat transfer and the nucleation of new phases [1], [2], [3], [4]. Natural gas production facilities operate across a wide range of temperature and pressures. The accurate prediction of surface tension for natural gas at these operating conditions can be difficult, especially when approaching the mixture’s critical point.

Methods of predicting surface tension as a function of temperature, pressure and phase compositions are therefore essential to engineers designing and operating natural gas plants. Models for predicting surface tension are generally empirical and comprised of two components. The first component provides predictions of the phase compositions and densities based on vapour liquid equilibrium (VLE) calculations usually made with an equation of state (EOS). The second component then links the surface tension to the properties of the liquid and vapour phases, usually in an empirical way. The models used to predict surface tension for pure components are well tested and include the Parachor method [5], [6] and variations of Guggenheim-Katayama equations [7], [8] such as those by Mulero et al. [3]. The models available to predict surface tensions in mixtures include the Parachor model [9], the critical-scaling model of Moldover and Rainwater [10] and the Linear Gradient Theory [11]. These models for predicting mixture surface tensions are typically based on some method of combining the pure component surface tension values. Binary mixture data are used to test and validate the models for predicting the surface tension of mixtures. Validating and/or improving the accuracy of these predictive models thus requires high quality surface tension measurements of mixtures.

The methane (1) + propane (2) system is one of the most important binary mixtures for the description of natural gas systems. However, experimental surface tension values for binary mixtures of methane and propane are restricted to the work done by Weinaug and Katz [9] and Haniff and Pearce [12]. Weinaug and Katz [9] used the single capillary rise method to measure surface tension for methane and propane mixtures. These measurements were conducted isothermally at temperatures between T = (258.15 and 363.15) K starting with pure propane and by increasing the methane fraction over the range p = (0.29 to 8.48) MPa until the surface tension values were too low for accurate measurement. The work by Haniff and Pearce [12] used laser-light scattering to determine the surface tension while approaching the critical temperature for one mixture (z₁ = 0.62, z₂ = 0.38) across the range T = (302.75–312.35) K. The phase compositions and densities for the surface tension calculation presented by Weinaug and Katz [9] and Haniff and Pearce [12] were derived from the phase equilibrium data of Sage et al. [13]. There has been substantial improvement since the work done by Sage et al. [13], in the accuracy with which the phase compositions and densities of the methane + propane system can be described [14]. Thereby it should be possible to significantly improve upon the description of the system’s surface tension as determined by these authors, and in addition, continue those surface tension measurements up to the critical point.

Static surface tension measurements are typically classified into microbalance techniques, capillary pressure measurements, capillary and gravity force equilibrium measurements and forced droplet distortion measurements. Microbalance techniques such as Wilhelmy plate [7], [15], du Noüy Ring [16] and du Noüy-Padday rod [17] are traditionally used for low pressure systems involving liquid-air interfaces and are not easily implemented for use in high pressure systems. Surface tension for high pressure and temperature systems can be measured using the pendant drop [1], [18], [19], [20], sessile drop [21], capillary rise [22], [23], [24], [25], [26], [27], laser light scattering [12], [28], [29], spinning drop [30] and drop weight volumes methods [12], [31]. The advantages and disadvantages of these methods depend on the accuracy, sensitivity and range of surface tension measurements required. The drop volume and the laser light scattering methods are extremely sensitive to any vibrations around the system which can make obtaining reliable measurements difficult [12], [31]. The pendant/sessile drop method and spinning drop method have limitations based on the Bond number (ratio of gravitational to surface tension forces over the length scale of the droplet). Accurate results for the standard pendant or sessile drop method are generally limited by Bond number (Bo > 0.2) and, typically, systems with lower surface tension values produce low Bond numbers and unstable drops [20], [32]. Variations to the typical pendant drop methodology can produce higher accuracy results at lower Bond numbers [32]. The spinning drop method can in principle deliver high accuracy measurements of low surface tensions but requires a large density difference between the phases and is still generally limited to measurements at high Bond numbers due to limitations in maximum rotational speed [33]. The capillary rise method is well-tested and capable of measuring a range of surface tension values limited only by the diameters of the capillaries, at high pressures and over a wide range of temperatures, with low sensitivity to vibrations. The differential capillary rise method [34], in which two capillaries are used to determine the surface tension as used in this work eliminates the uncertainties associated with determination of the bulk liquid level. An additional benefit of the capillary rise method, which involves the use of a visual equilibrium cell, is that it facilitates determination of the mixture critical point through two independent methods: the estimation of the zero surface tension condition and the observation of critical opalescence.

This paper presents (i) an experimental setup and method that allows the measurement of surface tension up to the critical point, (ii) the calibration and validation of the setup with pure hydrocarbon fluids, (iii) surface tension and critical point data for methane and propane mixtures, and (iv) the comparison of the experimental data obtained with predictive models used by industry. The results obtained helped identify a significant problem with the implementation of a surface tension model in a widely-used software package, which has now been rectified. The critical point data collected can be compared to the EOS-predicted critical point and thereby test the performance of the EOS.