Laboratory-scale liquefiers for natural gas: A design and assessment study

Exact knowledge of natural gas composition is essential in custody transfer to deter-mine the energy content of the delivery. However, for liquefied natural gas (LNG), a reliable composition determination is difficult. Here, we describe the design of a laboratory-scale reference liquefier that enables the validation and calibration of optical spectroscopy sensors by providing them with a sample of metrologically traceable composition. Hence, it is crucial to avoid fractionation of the sample during liquefaction. This is realized by supercritical liquefaction of a reference gas mixture in conjunction with a special vapor – liquid-equilibrium (VLE) cell. As this is a demanding high-pressure application, low-pressure condensation as liquefaction method was also assessed. Through experimental investigations and VLE calculations, preservation of the composition of the produced liquid sample during condensation was studied. We conclude that under optimized conditions, validation, and calibration measurements of optical sensors can be performed on condensed liquids, which, however, needs further confirmation.

spectroscopy probes feature the advantage of online in situ composition analysis by submerging the sensor directly into the LNG transfer line. In this regard, optical measurement principles such as Raman 6 and possibly Fourier-Transform Near-Infrared (FT-NIR) spectroscopy can be used. For validation and calibration measurements, these sensors must be submerged into a liquid LNG-like sample of well-known composition. To obtain such a sample, the cryostat design of the laboratory-scale reference liquefier described within this work is based on a metrologically proven cryogenic single-sinker densimeter, [7][8][9] where reference gas mixtures are liquefied using a supercritical liquefaction technique in conjunction with a special vapor-liquid-equilibrium (VLE) cell. The described design is particularly developed to assess the capabilities of the in situ optical composition measurement systems.
(We note that the type of liquefier described here can potentially be used for other types of sensors as well.) Recently, the development and validation results of a small-scale liquefier were presented. 10 The work demonstrated the performance of the liquefier and metrological traceability of the liquid composition in accordance with the requirements of ISO/IEC 17025. 11 Unlike the design presented in this work, the small-scale liquefier does not utilize supercritical liquefaction but condensation. Since condensation features advantages regarding structural ruggedness and procedural application, it may be conceivable to be adopted for the described liquefier or further measurement facilities. In order to assess the capabilities of condensation as liquefaction technique, comparative density measurements were performed on a laboratory scale using different liquefaction techniques to evaluate the impact on the composition of the liquefied sample.
Further, to understand more comprehensively the current stateof-the-art of predicted properties of LNG in the single phase and in the VLE region, we extend the existing uncertainty analysis of equations of state by a mechanism that propagates the uncertainty of the input parameters, typically temperature, pressure and composition.
Currently, the uncertainty of equations of state is typically expressed in terms of the error in the predictions of the relevant properties as compared with experimental data. 12 This contribution aids in more comprehensively characterizing the uncertainty of natural gas properties, which is helpful in the assessment of the performance of liquefaction techniques and applications of (liquefied) natural gas reference data.

| GENERAL CONSIDERATIONS AND LIQUEFACTION TECHNIQUES
The conceptual design of the laboratory-scale reference liquefier for natural gases presented in this work is the precursor for the detail engineering of an apparatus, which features preservation and hence metrological traceability in composition; in other words: the composition inside the measuring cell is the same as that of the feed gas. To achieve this preservation, several criteria must be fulfilled, which are determined by thermodynamic and process engineering requirements.
Additionally, for suitable validation and calibration measurements, the sensor probes need to be investigated with its field specifications, which implies particular design requirements. Raman and FT-NIR sensor probes are typically mounted to LNG pipelines with flanges that are fitted to a probe shaft of adjustable length for immersion into the homogeneous LNG stream; the characteristic design of such probes is shown in Figure 1. The optical measurement takes place at the tip of the probe shaft. For integration of usual sensor probes, the cryostat of the new reference liquefier has to be adapted to the existing type of mounting. This is important because after the completion of the validation or calibration routines, the sensor has to be installed in the field without further modifications. By this means, the validated/calibrated sensor can either be used for actual composition measurements or as a "gold standard" for comparative calibration measurements of further probes installed in the field.
The validation and calibration measurements have to be performed in the homogenous liquid phase, that is, the probe tip is immersed into a liquid sample of well-known composition. To realize this condition, gravimetrically prepared calibration gas mixtures 13 are liquefied, providing low uncertainties in composition of the reference sample. For the liquefaction of the reference gas, the cryostat of the liquefier must reach the respective temperatures, which are required for the transition from the gaseous into the liquid state. In this regard, equations of state (EOS) such as the GERG-2008 equation of state 12,14 can be used to predict the vapor-liquid phase boundary for specified mixtures and, henceforth, the saturated liquid temperature for a given pressure. Typically, LNG is transported and transferred at temperatures of about 110 K with pressures close to atmospheric pressure. Since very lean natural gases can be present in two phases at these conditions, even lower temperatures might be required depending on the mixture's composition. To reach these cryogenic conditions, the use of liquid nitrogen (LN 2 ) as coolant for the cryostat is required. With a boiling temperature of T b (101.325 kPa) = 77.36 K, 15 the components of the cryostat can be efficiently cooled to T = 90 K.
Liquefaction on a laboratory scale can be achieved in multiple ways by various filling and cooling procedures of a measurement system. For illustration, Figure 2 shows the vapor-liquid phase boundary of a typical LNG (coming from Norway) in a p, T-diagram. The homogenous liquid region and the homogenous vapor region are separated by the two-phase region where liquid and vapor coexist. Haynes 17 stated that the composition of the liquid should be slightly different from the prepared mixture, when there is a residual vapor volume F I G U R E 1 Schematic illustration of optical in situ probes with exemplary probe tips for Raman and FT-NIR spectroscopy sensors [Color figure can be viewed at wileyonlinelibrary.com] inside a measurement system. Due to the zeotropic behavior of natural gas mixtures, the compositions of liquid and vapor in the VLE are different. Although the overall composition of the fluid will not change in a closed system, any measurements of the liquid sample could provide distorted results, which are not metrologically traceable to the composition of the reference gas mixture. Even if the fluid is completely transferred into the homogenous liquid phase by traversing the two-phase region, a gradient in composition can remain without a homogenization of the mixture (e.g., by mechanical mixing) subsequent to the liquefaction. Accordingly, we recommend that the sample inside the measuring cell is not separating in two phases, neither during the liquefaction nor during the actual measurement. In doing so, maintaining the reference composition for the liquid sample can be ascertained. straightforward approach is to condense the mixture into the liquid phase by cooling the sample at ambient or slightly elevated pressure Figure 2). This process can be carried out in two ways regarding the sequence of filling and cooling. Either, the cryostat is filled with the sample at ambient temperature and subsequently cooled down at constant filling pressure, or the evacuated apparatus is being cooled down and then filled with the mixture as soon as the target temperature is reached. Both methods tolerate the formation of a VLE, which can lead to a residual change in composition of the liquefied sample. 17 The two-phase region can be effectively bypassed when applying a supercritical liquefaction procedure. [7][8][9] Here, the cryostat is filled beyond the cricondenbar at ambient temperature (point 1 in Figure 2), which is followed by cooling the cryostat to the target temperature at a supercritical pressure (1 À! 2). The pressure can then be reduced by venting substance from the system or by using a pressure adjustment cell. 18 When the pressure falls below the pressure of the cricondenbar, an inevitable phase transition from liquid to vapor will form, when fluid filled components exhibit temperatures above the saturated liquid temperature. This, for example, can be the pressure measurement or the filling line located outside of the cryostat or even tubing at elevated temperatures within the cryostat. To prevent an impact on the liquid sample under investigation, this phase transition and its related component fractionation must be considered accordingly. [7][8][9] Hence, by appropriately utilizing this supercritical liquefaction procedure, the composition of the feed gas can be maintained in the homogeneous liquid phase, which is exactly the primary task of a reference liquefier. But even when the reference mixture is liquefied without a change in composition, it must be ensured that sorption phenomena, stratification of the liquid sample and diffusion effects that also can lead to changes in the composition are mitigated accordingly. Regarding the requirements of the liquefier, however, the supercritical technique involves the system to withstand high pressures to be able to exceed the pressure of the cricondenbar which, for natural gas mixtures, typically is between 5.0 and 9.0 MPa.
Hence, to facilitate the supercritical liquefaction for most common LNG mixtures, a pressure rating of the liquefier of at least 10 MPa is recommended. In contrast, just a slight overpressure is required when condensing the sample. This implies that building a liquefier employing condensation as liquefaction technique can be less expensive.

| Basic design
The design of the core-apparatus as shown in Figure 3 is based on the cryogenic single-sinker densimeter developed and improved by Richter and colleagues, 7-9 that is, adopting the application of supercritical sample liquefaction in conjunction with a VLE-cell. [7][8][9] The apparatus involves a multi-layer vacuum insulation to reduce the heat flow from the environment into the cryogenic sections. The tip of the sensor probe is submerged into the measuring cell, which is suspended from an intermediate plate. This plate is attached to the base plate of the cryostat. A copper shield is installed at the intermediate plate to enclose the measuring cell and shield it from thermal radiation.
A so-called VLE-cell is connected to the measuring cell to realize the functional principle that was developed for the cryogenic singlesinker densimeter. 7 The VLE-cell is located at the same height as the intermediate plate. By forcing the phase boundary of the VLE to occur inside this cell, the phase transition, and the distorting impact on the composition of the liquid is removed from the measuring cell. In addition, the VLE-cell can be used to adjust the pressure of the entire system subsequent to filling the apparatus. For a detailed description of the application and functional principle, please see references. [7][8][9] As can be seen in Figure 3, the mounting flange of the pilot probe under study is attached to the base plate of the cryostat. The probe shaft is connected to the measuring cell using a special hollow screw, which is used to compress a set of gaskets into the measuring cell and around the probe shaft. This design enables a relatively easy assembly and disassembly of the sensor. Once the vacuum cylinder and the insulation shield are removed and the hollow screw is loosened, the probe can be simply pulled out of the cryostat. The setup of three independent ring-thermostats allows to set different target temperatures for the measuring cell, the VLE-cell and the intermediate shield, which is an essential precondition to utilize the supercritical liquefaction procedure. [7][8][9] The measuring cell is set to a temperature in the homogenous liquid region, while the VLE-cell is generally held at higher temperatures making sure that the liquid to vapor phase transition occurs inside this auxiliary cell. In contrast, the intermediate plate temperature is set $9 K below the temperature of the measuring cell. This temperature difference provides the measuring cell with passive cooling during steady-state operation. Therefore, no liquid nitrogen is required, and the temperature is solely controlled by the resistance heater, which results in only small temperature oscillations as small as few millikelvins. Furthermore, unwanted heat flows into the measuring cell can be trapped by targeted thermal bridging (e.g., by contacting the probe shaft with the intermediate plate, see Figure 3). Thereby, potential partial evaporation can be prevented when the state of the liquid sample is close to the saturated liquid line.
Realization of only small temperature oscillations is also important to maintain constant pressure. The reason is as follows: when the filling of the measuring system is completed during the overall liquefaction procedure (Point 2 in Figure 2), the sample inlet is closed with the apparatus becoming an isochoric system. Consequently, due to the low compressibility of the liquid phase, small fluctuations in temperature can give rise to substantial variations in pressure. If it is required to provide very stable pressures during validation or calibration measurements, it is also recommended to thermostatically control the piping outside the cryostat or to reduce the impact of variations in ambient temperature via thermal insulation. Moreover, well-controlled temperature and pressure conditions can prevent a potential distortion of the measured spectra of the optical sensors, which can show a relevant dependency on temperature and pressure. 19 Given this interrelationship, we recommend to perform calibration/validation measurements at field conditions. However, this requires the cryostat to cover a certain range in pressure and temperature including different modes of temperature control (e.g., rough to fine).

| Thermal design calculations
The dimensioning of the described reference liquefier is based on a thermal analysis. Using a parametric and simplified model for the core apparatus, all decisive heat flows between internal components and the environment were calculated depending on the set-point temperatures of the three ring-thermostats. 20 These calculations include not only the occurring heat flows but also the resulting temperature gradients along the intermediate shield and the measuring cell using an iterative method. Evaluating the temperature gradient along the intermediate shield is crucial to assess the passive cooling of the measuring cell as described further above. The temperature gradient along the measuring cell should be kept to a reasonable degree to avoid vortices inside the cell and to obtain a representative temperature measurement. This is especially relevant when measurements are carried out close to the saturated liquid line as vaporization of the sample has to be definitely avoided.
To assess the temperature range required for validation and calibration measurements, a parametric study has been performed with measuring cell temperatures ranging from 100 to 160 K. Accordingly, the temperature of the intermediate plate was set to temperatures of 91 to 151 K, while the temperature of the VLE-cell was varied within (20 to 110) K above the measuring cell temperature to account for different heat flow scenarios. The study showed that the temperature gradient along the intermediate shield is in the range of 5.5 to 7.5 K due to the heat input from the outer insulation cylinder, which was assumed to be at ambient temperature. The gradient along the measuring cell turned out to be within 10 to 20 mK, where the variation is Regarding the overall cooling demand, less than 50 W are required for the cryostat with the dimensions determined from the different scenarios. This relates to an approximate liquid nitrogen consumption of less than 30 dm 3 per day for steady-state operation. For the initial cooling of the cryostat from ambient temperature to the target temperatures, that is, the liquefaction of a gaseous sample, less than 25 dm 3 are required for all scenarios. These values refer to the dimensions we selected for the present cryostat concept; they will of course change with a variation of the design.
Depending on the sensor requirements regarding stability in temperature during calibration, it might be feasible to utilize a simplified insulation layout. Hence, in addition to the cryostat described above, two alternative designs were investigated within the scope of the thermal design calculations. First, active cooling of the intermediate shield could be dropped so that it solely serves as radiation shield. As a result, the measuring cell has to be actively cooled with liquid nitrogen, and the temperature gradient caused by larger heat flows increases significantly to 550 to 820 mK. Second, the cryostat can be further simplified leaving out the intermediate shield. For this setup, the calculated temperature gradient along the measuring cell exceeds 1,400 mK. Consequently, both designs should only be considered, if the corresponding gradients can be tolerated. When measurements are carried out in sufficiently subcooled liquid states, greater temperature gradients along the measuring cell might not be an issue. Nevertheless, we note that that the thermodynamic models used for calculation of the phase boundary is also subject to uncertainty, that is, this circumstance has to be taken into account within the design process of a liquefier.

| Experimental investigations
To realize the recommended supercritical liquefaction technique, which was developed to maintain the feed composition, 7-9 a quite elaborate apparatus has to be set up that can be expensive depending on the ultimate design and the selection of periphery. As discussed before and shown in Figure 2, another way of liquefaction is possible, namely via condensation. The development and first results of a facility for producing LNG samples based on this technique were recently reported by Walker et al. 10 Even though the optical pilot probes are typically able to withstand high pressures, 6,21 using condensation implies the advantage that no high-pressure technology is required.
For this procedure, however, at least a temporary fractionation of the mixture during the transition from gas to liquid (i.e., when crossing the two-phase region) will occur. Hence, for metrological purposes, the impact of the temporal fractionation on the composition of the liquid sample inside the measuring cell needs to be clarified. Predicting a change in composition based on this liquefaction technique for such a dynamic system with numerous input factors is yet not possible with the accuracy required for a reference liquefier. Hence, to assess the extent to which the feed gas composition is preserved for the liquefied sample, it is partially reevaporated and analyzed using gas chromatography. 10  Concerning the filling and cooling sequence, two scenarios were experimentally assessed. Firstly, the apparatus was evacuated and cooled to the target temperature prior to the actual filling that was conducted at a constant pressure. However, with a precooled system, the rapid liquefaction of the introduced sample impedes to fill at a constant pressure. In practice, the measured pressure fluctuated within ±0.05 MPa during the filling of the apparatus. Secondly, the system was pressurized at room temperature and then isobarically cooled to condense the sample during the temperature reduction.
Both approaches were tested at filling pressures of $0.3 and 1.0 MPa to consider a potential influence of the pressure during condensation.
This strategy is based on the circumstance that component fractionation in VLE amplifies at higher pressures due to the higher vapor density, even for systems of same volumetric vapor fraction.
The different condensation procedures, four in total, were each carried out at a measuring cell temperature of 110 K. The temperature of the densimeter's VLE-cell was at 250 K and, thus, well above the saturated vapor temperature so that the phase transition from vapor to liquid is located in the connection line between the measuring cell and the VLE-cell. At a temperature of 110 K, no direct reference densities are available; therefore, the data measured by Eckmann et al at 100 and 120 K 23 were fitted to a quadratic polynomial and then interpolated to obtain the densities at T = 110 K. To consider the nonlinear relationship between density and temperature, the interpolation was not carried out using absolute density values but relative deviations of the reference densities from the EOS-LNG equation of state, 22 which is capable of representing the temperature dependency of density with reasonable accuracy. 23 For each of the four fillings carried out in this work, density measurements at different pressures were performed. The pressure after each measurement was reduced by venting substance from the system since the functionality of the VLEcell for pressure control 7-9 is not available when only filled with gaseous sample.
As can be seen in Figure 5, the relative deviations of the experimental densities ρ exp from the interpolated reference densities ρ ref reveal that the condensation of sample into the precooled and evacuated measuring cell resulted in a slight decrease in density, which implies an enrichment of methane in the liquid phase. Nevertheless, the shift in experimental density is within the relative expanded uncertainty (k = 2) of the experimental reference densities of less than U(ρ)/ρ = 0.015%. 23 We note that the uncertainty in composition of the reference gas mixture is excluded in this combined uncertainty because exactly the same mixture sample was used for the F I G U R E 5 Relative deviations of experimental densities ρ exp at T = 110 K measured after condensation of the sample from reference densities ρ ref interpolated using experimental densities at T = (100 and 120) K measured after supercritical liquefaction of a binary (0.98017 methane +0.01983 iso-pentane) mixture. , filling to p = 1. condensation experiments within the present work as for the reference measurements by Eckmann et al. 23 Nevertheless, due to the consistency of the data, neither a change in composition caused by the condensation procedure nor a dependency on the filling pressure can be observed, which supports the findings of Walker et al. 10 The condensation procedure where the system was pressurized at ambient temperature, however, resulted in a stronger decrease in density clearly exceeding the uncertainty of the reference densities.
The change in composition can be estimated by iteratively changing the composition for the densities calculated with the EOS-LNG equation of state 22  in the VLE-cell being flushed into the measuring cell, accumulating the heavier components. Upon completion of the condensation, the VLEcell was completely filled with liquid. The density measurements subsequent to this liquefaction procedure using the same (0.98017 methane +0.01983 iso-pentane) mixture resulted in a significant increase in density in the range of 0.125% (see Figure 6) compared with the reference densities. 23 Again, using the EOS-LNG equation of state 22 for estimation, now an enrichment in iso-pentane amount fraction of 0.00047 would cause this observed increase in density. This magnitude is within the typical standard uncertainty of the optical spectroscopy measurements of at least 0.0010 amount fraction, 19 but would certainly become a relevant contribution to the combined uncertainty of the calibration measurement. In order to verify these findings for an actual use case, the same procedure was applied to a multicomponent mixture representing a typical LNG coming from Norway (see Table 1 for composition) at a measuring cell temperature of 135 K. Here, an increase in density of $0.127% compared with reference densities 8  In previous work, an uncertainty evaluation was described for a flash calculation. 26 The models used to describe the liquid and vapor phase properties were kept very simple. In this work, the GERG-2008 equation of state was used for the flash calculations. This calculation was implemented in the TREND 4.0 software. 16 The calculation is treated as a black box in this uncertainty evaluation. For the modeling of the liquefier, it is relevant to know the uncertainty of the difference x-z where z denotes the feed composition and x the liquid composition. The feed composition is taken as the composition of the reference gas mixture being liquefied. From this composition, the uncertainty is available.
The measurement model in this instance is primarily the GERG-2008 equation of state in combination with the algorithm used. A convenient way to perform an uncertainty evaluation using a measurement model that is in the form of an algorithm is the use of the Monte Carlo method from GUM Supplement 1 (GUM-S1) 25 or GUM Supplement 2 (GUM-S2). 27 The principal difference between the two methods is that the method of GUM-S1 is suited for an univariate measurement model, whereas that of GUM-S2 is suited for a multivariate measurement model. The difference x-z is an example of a multivariate measurement model, hence the Monte Carlo method of GUM-S2 should be used. In previous work, a simple example of using the Monte Carlo method in the combination with an iterative calculation has been given to calculate the VLE properties of a pure fluid using a simple cubic equation-of-state. 26 The Monte Carlo method can be implemented as follows 27  feed composition. Whereas it is relatively uncomplicated to assign a (multivariate) probability density function to a composition, it is not straightforward to sample from it. A composition can be best described as a vector (array) of fractions, which add to a constant. 28 Hence, the covariance matrix associated with this vector is singular, which causes difficulties in many algorithms for the generation of pseudo-random numbers. This problem has been known for a long time 29 and has been investigated by several authors. 30,31 The problem of the singular covariance matrix can be "solved" in several ways. Firstly, a composition can be generated from a submatrix of the covariance matrix, for example by leaving the amount fraction methane out, and calculating the amount fraction methane by difference. This is a rather naive solution to the problem but might work if the uncertainty associated with the amount frac- When using compositions with small (relative) standard uncertainties, it is expected that when using these to generate compositions, the generated compositions will have small deviations from the mean composition fed into the random number generator. In the naive case, the generated compositions will not satisfy the constraint that all amount fraction should add to a constant. The latter can be achieved by normalizing the compositions thus generated, using, for example, the procedure from ISO 6974-1. 28 The corrections made to the amount fractions will then be generally small. The standard uncertainties that are achieved by national metrology institutes (NMIs) in comparisons of national measurement standards ("key comparisons") [33][34][35] are a suitable basis for this uncertainty evaluation, as they are the best uncertainties achievable. They range from below 0.0010 for the amount fraction methane to 0.0050 for the amount fraction hexane.
We have used the described mechanism to explore how the uncertainty of the feed composition propagates in a flash calculation.
We did so for a number of different LNG-compositions. Temperature and pressure were kept constant but could have been included in the uncertainty evaluation as well. The results for one of the compositions (0.008 nitrogen, 0.918 methane, 0.057 ethane, 0.013 propane, 0.0017 iso-butane, 0.0015 n-butane, 0.0004 iso-pentane, and 0.0004 n-pentane) is shown in Table 2. The results are based on a rather small sample of the output distribution (M = 1,000), but this sample size is sufficient to reproduce the first two digits of the stated SD.  The investigations within this work showed that the phase transition within the connection line between measuring cell and VLE-cell did not seem to exert any influence on the investigations in this work.

| Evaluation of results
Here, we note that the inner diameter of the tubing with 1. in the respective liquefier are accurately known, we suppose that a state-of-the-art fundamental equation of state can be used to reliably estimate the composition of the liquid phase. This is particularly helpful when condensation is used for liquefaction but also here, the experimental setup impacts this consideration as the vapor fraction of the VLE across the liquefier has to be precisely known.

| CONCLUSIONS
In this paper, the conceptional development of a small-scale reference liquefier for cryogenic liquid mixtures such as LNG is described. The resulting design may serve as the precursor for the detail engineering of an apparatus that features traceability in composition, which is an essential prerequisite, for example, for the validation and calibration of optical composition measurement systems. To assess the capabilities of the in situ optical composition measurement systems often used in industrial oil and gas applications, the apparatus was specifically designed to adopt the field mounting solution of the sensor probes. The sophisticated design of the cryostat allows operation over wide temperature and pressure ranges in the liquid region enabling calibration/validation measurements close to field conditions.
Thermal calculations for a large combination of temperature set points of the measuring cell, the VLE-cell and the intermediate plate, were the major input to dimensioning the apparatus. As a result, a temperature gradient along the measuring cell of less than 20 mK can be achieved, which is certainly a good basis for calibration/validation measurements. If allowed by the technical specifications of the sensor regarding stability in temperature during calibration, we showed that the thermal design can be specifically simplified.
To confirm if condensation as liquefaction technique might be a reasonable alternative to supercritical liquefaction of a reference mixtures, density measurements of condensed liquids were carried out. The experimental densities were compared with reference densities of the same mixtures that were measured using a reference densimeter. 8,23 It was found that the change in composition of the liquid phase was only small when the sample was filled into the precooled and evacuated system. Here, the deviations from the reference data were within the experimental uncertainty of the reference densimeter. Thus, as for the studied circumstances it can be stated that the given condensation procedure is capable of liquefying gas mixtures without a relevant change in composition.
Nevertheless, we note that this result is not universally valid but needs to be proven with different experiments and especially fur-