An Experimental and Modelling Investigation on the Water Content of CO2and CO2-rich Mixtures Using the Differential Scanning Hygrometry (DSH) Method

Monitoring humidity downstream to conditioning facilities and during transportation is essential for avoiding hydrate deposition. However, water inline monitoring under high pressure is still challengingintheCCSindustry.Thisstudypresentsanexperimentalandmodellinginvestigation for enhancing field monitoring and model predictions. Measurements are performed using the Differential Scanning Hygrometry (DSH). This novel analytical approach has been successfully tested for measuring dew/frost temperatures for carbon dioxide, CH 4 +CO 2 , and CO 2 -rich mixtures in equilibrium with hydrates, free water and ice. Moreover, the DSH method has been applied for direct HP equilibrium temperature measurements. Also, this work compares three modified versions of the classical SRK EoS with the Multi-Fluid Helmholtz Energy Approximation (MFHEA). This evaluation includes Huron-Vidal and the EMS mixing rules and the cubic-plus association (CPA) approach. A thorough fitting process was carried out and, overall, comparisons with the experimental data showed that SRK+EMS yielded results as satisfactory as sCPA.


Introduction
As global warming concerns grow, a worldwide appeal for immediate action to reduce greenhouse gas (GHG) emissions unfolds.The emission gap between nations, reliance on petrochemicals in all industrial sectors, and the difficulty in estimating the carbon footprint in complex and highly specialized production chains delay the implementation of practical solutions.In this context, carbon capture, storage and utilization (CCSU) emerge as the most readily available option for reducing those emissions while promoting a smooth and efficient transition into alternative energy sources.However, transporting and processing carbon dioxide and CO 2 -rich mixtures are challenging for many industrial processes.The unavoidable presence of water and the necessity of handling such mixtures over a wide range of operational conditions raises concerns about hydrate formation and corrosion suppression.
As discussed in many publications, there are several instrument technologies currently available for the measurement of water content in fluid phases, including capacitance sensors, quartz crystal microbalance (QCM), electrolytic cells, CaC 2 -GC, fibre optic sensor, Karl Fischer titration, chilled mirror, chilled surface acoustic wave sensor and Tuneable Diode Laser Absorption Spectrometer (TDLAS) [17,18,11,22].Despite that, one can recognize that there is still plenty of room for new developments and improvements in water content determination.The range of applicability is vast and indeed goes beyond natural gas conditioning and processing plants, potentially including CCS facilities, gas and supercritical fluid pipeline transportation and many other processes that handle natural gas components and permanent gases, among others.
Recently, Burgass et al. [6] have introduced an alternative approach to water determination.Instead of introducing new materials or analytical fundamentals, the new method relies on an analytical procedure which prescinds calibration requirements.The method tracks water content variations in the fluid phase resulting from frost/dew formation on a surface in direct contact with the stream.Because of that, it was named Differential Scanning Hygrometry (DSH).
This paper presents results for experimental frost temperatures and their corresponding water content in CO 2 and CO 2 -rich mixtures in equilibrium with water, ice or hydrates at temperatures between 229.05 and 289.65 K and pressures up to 50 MPa.Measurements were carried out using the DSH methodology and compared with literature data published by several authors.In addition, pressurized measurements of frost and hydrate dissociation temperatures for under-saturated CO 2 have been performed.Also, this study compares three modified versions of the classical Soave-Redlich-Kwong (SRK) cubic equations of state (CEoS) with the Multi-Fluid Helmholtz Energy Approximation (MFHEA) for calculating water concentrations.A thorough regression procedure has been carried out for the advanced (Huron-Vidal) and the asymmetric (Edmonds-Moorwood-Szczepanski) mixing rules, as well as for the cubic-plus association SAFT hybridization (CPA) approach.

Material and Methods
Table 1 presents the specification of pure components used for the measurements carried out in this work.Additional tests were performed for several mixtures whose compositions are given in Tables 2 and 3. Also, certified Spectra-Seal® standards supplied by BOC Ltd, as described in Table 4, were employed for validation purpose and for performing the pressurized measurements at under-saturated conditions.

Experimental Apparatus
The quasi-static method previously described was used to establish equilibrium conditions between the test fluids and water, ice or hydrates [25,6], as shown in Figure 1.The experimental cell comprises a temperature-controlled, variable volume equilibrium cell and a heated line and valve through which gas equilibrated with water, ice, or hydrates passes toward the analytical device.Downstream, a flow meter monitors the gas flow rate controlled by the heated valve.The equilibrium cell is a 300 mL Titanium piston vessel rated to 69 MPa.A jacket connected to a temperature-controlled circulator (Lauda Proline RP 870 Edition X) surrounds the equilibrium cell.The circulator can control the temperature of the fluid pumped through the jacket within ± 0.1 K of the set point and can be used at temperatures between 203.15 and 373.15 K.This temperature is measured using a Platinum Resistance Temperature probe (PRT) located in the jacket.
Temperature differences between the jacket and the fluid compartment were measured using a reference probe mounted inside the cell.This reference probe was calibrated against a certificated platinum resistance probe issued in accordance with the National Measurement Accreditation Service (NAMAS) Accreditation Standard and NAMAS Regulations.
A strain gauge transducer mounted on the lower end of the cell is used for pressure measurements.This strain transducer was checked for uncertainty using a Budenberg dead weight tester.The stated uncertainty of the pressure transducer is 0.03 MPa.Additionally, barometric pressures were measured for each test using a barometer supplied by Greisinger (model GPB 3300).
Because of the low water content and the possibility of water naturally adsorbing on the internal tube surface, tubing line segments between the exit of the quasi-static equilibrium cell and the gas flow meter, including the heated line, were comprised of 1/8" OD electropolished stainless steel Siltek supplied by Thames Restek UK Ltd.This treated tubing is corrosion resistant and fast to adsorb/desorb water, reaching equilibrium conditions much faster than untreated stainless steel.Moreover, it adsorbs much less water, which minimises the influence of water adsorption/desorption in the results.

Differential Scanning Hygrometry (DSH) setups
The DSH methodology records variations in the water concentration in the fluid phase around its saturation points to determine dew/frost temperatures at constant pressures.A DSH experimental set-up comprises: A) Cooling section: normally a tubing segment equipped with a temperature probe where the dew/frost formation will take place; B) Hygrometer sensor: to record the water content variations in the flowing gas phase during the procedure.
The sample gas flows through the cooling section at a constant rate, in continuous contact with the chilled surface, where a PRT probe is used to monitor temperature.After leaving the cooling section, a hygrometer sensor measures the water content of the vapour phase.
During the development of this new methodology, different technologies were tested for cooling the tubing element to promote dew/frost formation and for monitoring fluid phase humidity variations during this process: The main features of these different set-ups are illustrated in Figure 2. Configuration 1 represents the original arrangement described by Burgass et al. [6].In this case, the cooling section comprises an electropolished U-tube submerged in a thermal circulator bath (model Proline RP 870 Edition X manufactured by Lauda) filled with pure ethanol.The Proline RP870 circulator works in temperature ranges from 203.15 to 472.15 K, with a resolution of 0.01 K and stability of ± 0.01 K.The Manalytical MicroView ® Mini Hygrometer moisture analyzers supplied by Moisture Control & Measurements (MCM) Ltd were used for water monitoring.This capacitive hygrometer is silicon-based and operates at a controlled temperature (319.15K), and two portable versions, with operational ranges from 1 to 1000 and 1 to 6000 ppm, respectively, were used.
For measurements above atmospheric conditions, a digital pressure transducer (model GS4200-USB supplied by ESI Technology Ltd) and a precision back-pressure regulator (model EB1LF1 supplied by Equilibar) were used in an alternative arrangement, as depicted in Figure 2(b).In this case, two situations are possible: P/T conditions inside the U-tube during the measurement might lead to the formation of hydrates or dew/frost.If no hydrates are expected, the experimental procedure remains the same as described by Burgass et al. [6].Otherwise, the U-tube loop is closed and remains pressurized at sub-cooled conditions for 24 hours to promote hydrate formation.After that, the loop is open again, the gas is allowed to flow, and the second part of the analytical procedure is carried out.
In order to optimize the time of response and to demonstrate the flexibility of the DSH methodology, the thermal bath was replaced by a thermoelectric cooler (a three-stage Peltier).This modification corresponds to the Configuration 2. In this case, the tubing segment was embedded in an aluminium rectangular block, which was in direct contact with the cold side of the thermoelectric device.An enhanced heat transfer between surfaces was obtained by applying Dow Corning 340 heating compound on the contacting surfaces.A PT 100 single Platinum sensor (diameter = 6mm, L = 25 mm, 1/10 DIN, 3 wire, mineral insulated, supplied by Peak Sensors Ltd) was placed in a well in the aluminium block, in thermal contact with the chilled tube and the Peltier module.A DC power supply (CPX400DP dual 420 Watt supplied by Aim and Thurlby Thandar Instruments) delivered electric current to the thermoelectric Peltier module.A PID controller interface was developed in the LabView ® version 2019 to perform data acquisition (from the water sensor and the dew point) and temperature control in the cooling section.
Following the recent findings by Løkken et al. [18], the possibility of reducing the duration of analysis was the motivation for replacing the capacitive hygrometer with a QCM sensor manufactured by Suto Itec Co. Ltd.This device is supplied in a measuring chamber that was submitted to an electropolished treatment by Thames Restek prior to the tests.For data acquisition, the sensor was connected to an RQCM unit supplied by Maxtec, inc., that returned the oscillating frequency of the microbalance.
As a typical result, Figure 3 (a) displays temperature readings and the respective water sensor outputs.The initial and final stable readings are used as baselines (red line) to determine the saturation point.The DSH methodology is based solely on recording water concentration variations, which eliminates the necessity for calibration procedures.Figure 3 (b) shows the results for a long-term operation with set-up configuration 2 (Peltier + capacitive water sensor).The repetition of the cooling-heating temperature cycles characterizes this continuous monitoring process.Because of the fast response of the thermoelectric cooler devices, one can attain very low temperatures in only a few minutes, which leads to fast and reliable cycled operation.The Labview ® interface developed for controlling the temperature in the cooling section and recording the Hygrometer output signal also allowed the automatic repetition of cooling-heating cycles.Thus, for a given T and P conditions, the water determination has been carried out for several hours, during which up to 25 frost points were typically measured.One of the primary concerns in measuring frost temperatures is the potential formation of supercooled water [32,24].To mitigate this risk, this cycled operation has been adopted.
Figures 3 (c) and (d) illustrate outputs for configuration 3 (Peltier + QCM-based hygrometer) under different heating rates.It was observed that QCM frequently returned upward or downward baselines.Despite that, this arrangement also showed noteworthy repeatability and stable operation applicable to water monitoring.
For all described set-ups in this work, a good agreement has been observed either by comparison with certified water standards, other analytical methods (particularly from two Tuneable Diode Laser Spectrometer (TDLAS) sensors supplied by Yogokawa model 5200 and Endress+Haussen UK available for comparison), or data from the literature.In addition, supporting information presents a statistical comparison between the results for water content in pure CO 2 in equilibrium with hydrates measured by Adeniyi et al. [2] using a TDLAS sensor and the results presented in this work and measured using DSH methodology (Appendix B).Additional details about set-up comparison, methods validation and uncertainty calculation are discussed by Cavalcanti Filho [7] and Burgass et al. [6].

Experimental procedure
The experimental procedure includes the cell charging with the fluid of interest, followed by several steps to establish the thermodynamic equilibrium, and then, the opening of the top valve to allow the fluid inside to flow through the heated line and the hygrometer, to frost temperature or water content measurements, see Figure 1.

Equilibrium Cell
At the start of a test, around 2 mL of deionised water are placed in a cup shaped depression in the top of the piston.The cell is then closed and evacuated using a vacuum pump before injecting the fluid.Pressure cell adjustment is reached through gas injection at the top and the bottom of the system, see Figure 1, while temperature is adjusted by setting the cooling circulating medium temperature.To promote hydrate formation, the following temperature cycle is carried out: the cell is initially charged with CO 2 or the CO 2 -rich mixture up to pressures around 4 MPa and maintained at temperatures above the hydrate dissociation.After that, temperature is reduced below 273.15 K, to initially lead to ice formation inside the equilibrium cell.The third step comprises of returning cell temperatures above 273.15K, and cycled at conditions which guarantee at least 3 K of sub-cooling in the L  -V-H region.This procedure has been confirmed as being sufficient for hydrate formation.After that, T and P cell conditions are adjusted to the desired values.

Humidity measurements
When the equilibrium conditions in the cell are reached, the valve at the top is opened and the flowrate is adjusted (Figure 1).The sample gas flows through the cooling section, at a constant rate, and a Labview ® data acquisition interface is used to monitor and control the temperature in the loop, which is initially kept at few degrees above the expected frost temperature until a constant hygrometer is obtained.At this point, the temperature is reduced below the expected saturation point, which is followed by a reduction in the hygrometer output, see Figure 3 (a).Cooling section temperature is maintained at this conditions for enough time to guarantee ice formation.After this period, temperature is slowly increased at constant rate until the initial conditions are reached and the cycle is completed.For each reported measurement, between 8 and 20 cycles have been carried out.These results have been used to evaluate repeatability.Measurements using TDLAS: Alternatively, two tunable diode laser hygrometers (Yogokawa model 5200 and Endress+Haussen UK) have been used for checking standard stated concentrations and initial DSH results.In this case, once equilibrium conditions had been achieved the valve at the top of the cell was opened in order to fill the section of heated line up to the valve prior to the hygrometer at the same time gas is introduced into the base of the cell in order to maintain the pressure constant.Following this, the valve prior (inlet) to the TDLAS is opened sufficiently to achieve a flow rate of between 100 -300 mL per minute through the spectrometer.The water content reading from the hygrometer is then monitored until it was stable for at least 10 minutes.This is then taken as the moisture content of the equilibrated fluid in the cell (i.e., flowing out of the cell).During sampling the heated line was maintained at a temperature of 463.15K.

Thermodynamic Modelling
The present work included the fitting and evaluating of a representative range of equations of state to industrial applications.It comprised three modified versions of SRK CEoS: 1) Huron-Vidal-modified SRK combined with the predictive approach developed by Jaubert and co-workers [14,16,28,29,15,27,26] named predictive SRK+HV model (p-SRK+HV+NRTL); 2) Edmonds-Moorwood-Szcepanski (EMS) mixing rule combined with the same predictive approach by Jaubert and co-workers (p-SRK-EMS); 3) the simplified version of the cubic plus association (sCPA) developed by Chapoy and co-workers.
For comparative purposes, the multi-fluid Helmholtz energy approximation (MFHEA) recently presented by Burgass and Chapoy [3] has also been included.Further description are given in the supplementary material.

Water Content and Frost Point Interconversion
The DSH methods measures directly the dew/frost temperature or the hydrate dissociation temperature for undersaturated conditions.These temperatures are related to the water content in the fluid phase.A crucial part of the investigation carried out in this work required the interconversion of frost temperatures into water concentration.
Since the fluid composition, in a dry basis, is known, one can calculate the amount of water in the sample using the fundamental phase equilibrium criteria and an appropriate equation of state.At the measured frost temperature   and where fluid phase fugacity is calculated using the equation of state and the ice fugacity is calculated using expression presented in the Supporting Information.Secant method is used to solve Equation 1 and an initial estimation for   is obtained from the semi-empirical correlation developed by Mohammadi et al. [23] and Chapoy et al. [8].The upper limit for the numerical method is obtained from the Raoult's law:

Results
The DSH method was employed to measure frost temperatures of carbon dioxide, CH 4 + CO 2 , and CO 2 -rich mixtures in equilibrium with water or hydrates.Unless explicitly stated, these saturation points correspond to the barometric pressures measured during the tests.The measurements reported in this work covered a wide range of equilibrium conditions: temperatures from 229.05 to 285.65 K and pressures up to 50 MPa.Since most of publications in the subject report water content in terms of mole fraction (or ppm), a thermodynamic procedure has been used to convert all the experimental dew/frost temperatures into water mole fractions.For a more detailed discussion about this procedure, see Cavalcanti Filho [7].In the same way, uncertainties for these experimental saturation temperatures (at the given pressures) and the calculated correspondent water concentration - (  ,  = 2) and  (  ,  = 2), respectively -have been calculated according to the procedure described in Appendix A.

Standard Mixtures
Table 5 presents results for the atmospheric frost temperatures (  ) and the corresponding calculated water concentrations obtained in the initial tests using certificated mixtures.Given the stated uncertainties, nominal water concentrations in these gases demonstrated good agreement with results from TDLAS hygrometers.

Water Content in Carbon Dioxide
Initially, tests measuring frost temperatures for carbon dioxide were carried out at 0.894 MPa and temperatures between 268.15 and 285.65 K.It corresponds to equilibrium conditions with ice, water, or hydrates.Moreover, under these circumstances, most EoS could yield reliable results.Table 6 reproduces the measured frost temperatures (  ) at barometric conditions (P  ) and the corresponding water content (  ).In this case, the DSH method exhibited uncertainties for   ,  (  ,  = 2), of approximately 0.23 K, which represents  (  ,  = 2) below 3%.For all the model, good agreement is observed with deviations well below 1%, except for the MFHEA equation.
Figure 4 compares the experimental water content measurements obtained at temperatures between 229.05 and 263.15K with data published by other authors [2, 4, 3, 13, 30, 5] and calculations from the four adjusted models Table 6 Experimental frost temperatures (T  ) at barometric pressures (P  ) and the correspondent calculated water content (  in ppm or 10 6 mole fraction) measured with the DSH method for CO 2 in equilibrium with water or ice.P = 0.894 MPa and T represent the conditions in the equilibrium cell and standard uncertainties are given by u(P) = 0.003 MPa and u(T) = 0.05 K, respectively.Also,  (  ,  = 2) and  (  ,  = 2) are the correspondent expanded uncertainties for   and   .Phases refer to the type of equilibrium in the cell: VI = vapour -ice; VL  = vapour -liquid water.

T (K)
considered in this work.These results are also presented in tabular form in the Supplementary Material, which includes the measured frost temperatures.Likewise, Figure 5 (a) compares the results published by Burgass et al. [4] and Burgass and Chapoy [3] for the water content in the vapor phase at low temperatures, while Figure 5 (b) depicts measurements at 50 MPa.Frost temperatures measured at 50 MPa and their respective water content can also be found in tabular form in the supplementary material.Overall, good agreement has been observed among the measurements carried out with the DSH methodology and the data recently published by Adeniyi et al. [2] and Burgass and Chapoy [3], using the TDLAS method, Jasperson et al. [13], using the gravimetric and electrolytic methods, and Burgass et al. [4], using a chilled mirror.Wells et al. [30] has introduced a in situ Raman Spectrocopy sensor for measuring the carbon dioxide water content and ,as showed in Figure 4, results are much higher than those presented by the other authors.Wells et al. [30] have attributed these discrepancies to the presence of metastable phases in the equilibrium cells.In addition, the data presented by Burgass et al. [5] for hydrate equilibrium (melting) temperature (HET) of hydrates formed from low water content CO 2 .These authors have discussed the equivalence between HET and water content.Despite their HET results suggesting slightly higher water concentrations than those presented in this work, these measurements were carried out in a similar setup to the one shown in Figure 2(b).
Regarding thermodynamic modelling, the outcomes from the three modified versions of SRK agree with the literature data [4,3], see Figure 5 (a).On the other hand, MFHEA yields slightly higher water concentrations, particularly in the vicinity of vapour-liquid transition for CO 2 .For the liquid carbon dioxide equilibrium with hydrates, according to Figure 4 and 5 (b), the models exhibit distinct pressure dependencies for the water content.While results from MFHEA suggest an almost flat profile in the liquid region, sCPA yields a steeper dependence.Conversely, HV and EMS give similar curves, with higher water concentrations for the latter mixing rule.At 50 MPa, MFHEA calculations yielded lower water concentration, while the upper limit is observed for cubic plus-association modification of SRK.The poorer performance of MFHEA is believed to stem from the fundamental nature of Helmholtz-explicit equations of state.Since  and T are the independent variables, parameters for methane/water and CO 2 /water have been adjusted in a density range different from those observed, in many circumstances, for CH 4 /CO 2 binary systems.However, this observation requires additional investigations, which are beyond the scope of this study.

Water Content in CO 2 +CH 4 Mixture
Measurements carried out at 0.915 MPa for the equimolar methane/carbon dioxide mixture (composition is given in Table 2) are presented in Table 7.Additionally, Figure 6 shows results for water content measured for the mixture with 75%CO 2 + 25%CH 4 , composition is given in Table 2, in equilibrium with hydrates at 4.2 and 14.9 MPa, respectively.This figure also depicts outcomes from the different models considered in this work.The correspondent results in tabular, including the respective frost points, are given in the Supplementary Material.In addition, Figure 6(b) includes the data published by de Oliveira Cavalcanti Filho et al. [25], showing good agreement between those results obtained with TDLAS and those measured with the DSH method.One observes that the three modified versions of SRK showed good agreement with absolute average deviations below 5%, while MFHEA yielded values close to 13%.

Table 7
Experimental frost temperatures (T  ) at barometric pressures (P  ) and the correspondent calculated water content (  in ppm or 10 6 mole fraction) measured with the DSH method for the CO 2 /CH 4 equimolar mixture (composition is given in Table 2) in equilibrium with water or ice.P = 0.915 MPa and T represent the conditions in the equilibrium cell and standard uncertainties are given by u(P) = 0.003 MPa and u(T) = 0.05 K, respectively.Additionally,  (  ,  = 2) and  (  ,  = 2) are the correspondent expanded uncertainties for   and   .Phases refer to the type of equilibrium in the cell: VI = vapour -ice; VL  = vapour -liquid water.

Multicomponent Mixture
Most thermodynamic models rely solely on binary parameters, creating a framework of paired expressions for mixtures.In many circumstances, equations of state that perform satisfactorily to binary systems are unable to extend their performance to multicomponent mixtures.Because of that, the evaluation of thermodynamic models for predicting water content should include calculations for multicomponent.Table 8 reproduces results for frost temperatures measured at equilibrium conditions ranging between 253.22 to 283.15 K for a multicomponent gas mixture (composition given in Table 3).Furthermore, Figure 7 compares those results at 15 MPa with those obtained by de Oliveira Cavalcanti Filho et al. [25] for the same gas mixture using a TDLAS.This plot also includes the results calculated with p-SRK+HV, p-SRK+EMS, sCPA, and MFHEA.
Considering the given uncertainties, Figure 7 demonstrates a good agreement between the DSH and TDLAS.These findings corroborate previous observations about the application of DSH for measuring water content in multicomponent mixtures such as natural gas [6].Concerning the thermodynamic modelling of water content in such a multicomponent system, the outcomes from the modified versions of SRK show better agreement with experiments than the MFHEA approach.Average absolute deviations for SRK + HV, EMS, and cubic-plus-association are 11.8, 6.0, and 3.9%, respectively.The semi-predictive approach proposed in this work yields excellent results for HV and EMS mixing rules.Overall, one can obtain similar results with either the sCPA or the SRK+EMS.Nevertheless, the latter is more straightforward and faster to compute.In contrast, as observed for pure CO 2 and CO 2 /CH 4 mixtures, MFHEA underestimates water concentration in the fluid phase with an average deviation of 24.0%.These modelling findings illustrate that some equations of state fall short in extending the good performance observed for binary systems to multicomponent mixtures.It demonstrates the complexity of extending models based solely on parameters fitted from binary systems to complex multicomponent mixtures.

Table 9
Experimental direct high-pressure equilibrium temperatures (  ℎ , frost or hydrate dissociation temperature) and the correspondent calculated water content ( ℎ  in ppm or 10 6 mole fraction) measured with the DSH method for the certificated CO 2 -water mixtures (composition as given in Table 4, water concentration   in ppm or 10 6 mole fraction) at pressure P in the cooling section (Figure 2(b)).For situations involving hydrates, the cooled section has been closed for 24 h under pressurized conditions.Standard uncertainty for pressure is given by u(P) = 0.003 MPa, while  (  ℎ ,  = 2) and  (  ,  = 2) represent the corresponding expanded uncertainties for   ℎ and   .

Direct High-Pressure(HP) Equilibrium Temperature Measurements
The original set-up was slightly modified to evaluate the potential of the DSH methodology in measuring frost/hydrate temperatures at pressurized conditions, as described in Figure 2(b).A back pressure valve regulator has been used to maintain the cooling sections at pressures up to 2 MPa.Tests were performed with CO 2 /water certificated standard mixtures at two distinct concentrations (27 and 97 ppm), using the same procedure and temperature profiles described for the atmospheric readings (Figure 3 (a)).In this case, one assumes that the process leads exclusively to ice formation, and the measured temperatures represent the frost point.In some cases, however, to promote hydrate formation inside the loop, two valves were placed in the U-tube and used to close the cooled section for 24 hours at subcooled pressurized lower plateau (depicted as Valves 1 and 2 in Figure 2(b) ).After this period, the flow is re-established, and one performs the heating step steadily.Table 9 shows results for two certificated CO 2 2 mixtures with 27 and 97 ppm of water.
Frost and hydrate dissociation temperatures (T  ℎ ) from Tables 9 are used to estimate water content (y ℎ ).A comparison with the reference values demonstrates a satisfactory correlation between the pressurized measurements and water content in both cases.Thus, the DSH method emerges as an alternative for measuring not only hydrate dissociation temperatures at undersaturated conditions but also frost points.By performing pressurized tests, one can minimize problems with condensation in sampling lines.
Additionally, Figures 8 and 9 compare results obtained for frost and hydrate dissociation temperatures for the undersaturated mixtures given in Table 9 with calculations from SRK+HV, EMS, sCPA, and MFHEA.Overall, these models yielded better results for the 97 ppm mixture.Also, cubic equations and sCPA showed a slightly better performance than the MFHEA.While those models displayed average absolute deviations around 11.0% with a maximum deviation of 17.1%, the multi-fluid approach yielded an average value of 14.1%, and a maximum around 30.7%.

Discussion
Accurate water content measurements in fluids are an important source of information for validating thermodynamic models, enabling safe design and operation, and preventing problems such as corrosion and the formation of ice or hydrates.The available technologies have several pros and cons.Most of them are limited to operations at low pressure, which results in pressure drop requirements for sampling systems.Apart from that, many others require continuous calibration and maintenance procedures.TDLAS also is composition-dependent, and outputs are flowdependent.
On the other hand, the primary standard chilled mirror employs complex schemes and temperature programs to detect frost/dew formation over the mirror surface or rely on skilled operators.As a contribution to overcoming some of these limitations, this work proposes a new alternative approach based upon a simple principle, which may have significant benefits over other methods.One could highlight as DSH methodology advantages: • Low sampling flow rates; • Wide range of operational pressures, which allows direct high-pressure(HP) equilibrium temperature measurements, minimizing pressure drop requirements in sampling systems; • No calibration is required; • Applicable to a wide range of water concentrations; • It is fluid-composition independent; • Results regarding dew/frost point are more intuitive from an operational point of view than water ppm.
In addition, it is well known that in natural gas pipelines, for systems where the gas has specific water contents, gas hydrates are predicted to form at temperatures higher than the dew/frost point of water; hence, the system changes from vapour to vapour/hydrate.If the amount of hydrate increases significantly over time, this will lead to pipeline restriction and blockage in the worst-case scenario.This transition can be measured using the proposed method because the formation of hydrates will reduce the water content of the gas as it passes through the flow tube at temperatures inside the hydrate stability zone.Heating the flow tube to melt the hydrates will also give an accurate hydrate dissociation point that, being a point of thermodynamic equilibrium, can be used to validate predictions from a thermodynamic model.
For the range of conditions considered in this work, one can conclude that the DSH method has measured dew/frost temperatures with an average uncertainty below 0.4 K.In terms of water content, this value corresponds to circa 4%.Taking into account most of the commercially available hygrometers, these results are reassuring.
The results from pressurized measurements show the potential of the DSH method for determining the hydrate dissociation and frost temperatures for under-saturated NG and CCSU fluids at pipeline conditions.A sensor based on such a simple principle as the one applied for DSH can be used for water content monitoring without significant pressure drops in sampling lines.By doing so, one could avoid problems in depressurization during inline sampling, which usually leads to condensation and humidity misreadings.Moreover, such an approach provides a better representation of pipeline transportation.
From a field operation perspective, these   ℎ results are more intuitive than water concentration.However, if necessary, frost temperatures and hydrate dissociation conditions can be easily converted to water concentrations, as demonstrated in this work, using modified versions of cubic equations of state.

Conclusion
New measurements for water content in CO 2 and CO 2 -rich mixtures have been carried out using the differential scanning methodology introduced by Burgass et al. [6].Thermoelectric cooling and QCM detection have been used to improve the original set-up that has also been applied for performing pressurized measurements.The DSH method intends to emulate what occurs in fluid transport pipelines where an undersaturated gas stream continuously flows as it experiences temperature variations and the possibility of water condensation.The DSH method submits gas samples to a controlled temperature reduction in a tube section while tracking the shift in water content in the fluid phase, avoiding the complexity of detecting frost/dew/hydrates in the cooled surface.In this way, it is possible to determine the temperature at which such phases are formed.From an operational point of view, this temperature is more helpful information than a water concentration.It refers directly to the lower operational limit.
Experimental results showed satisfactory agreement with literature data carried out using other analytical techniques.These observations demonstrate the auspicious potential of the DSH methodology.
Thermodynamic modelling focused on industrial applications for estimating water content in natural gas and CCSU-compatible mixtures has been carried out using three modified versions of SRK CEoS: Huron-Vidal, Edmonds-Moorwood-Szczepanski, and sCPA.For comparative purposes, the MFHEA approach has also been included.A thorough fitting process was carried out, including tuning saturation pressure for single components, VLE data, hydrate dissociation, and mutual solubility in binary systems involving water.Once adjusted, one has assessed the capabilities of these adjusted models in describing water content in multicomponent mixtures.Overall, comparisons with the experimental data showed that SRK+EMS yielded results as satisfactory as sCPA.On the other hand, MFHEA usually underpredicts water concentrations for the studied fluids.

Acknowledgment
Research presented in this paper was conducted in support of projects funded by Galp Energia, Linde AG, Petrobras, Petronas, Equinor and Total which is gratefully acknowledged.Valderio de Oliveira Cavalcanti Filho acknowledges the financial support from Petrobras through his PhD Grant.The authors would like also to thank Endress+Hausser for the loan of the TDLAS setup.

A. Uncertainties in Humidity Measurements
A considerable number of publications have discussed in details several aspects of assessing uncertainties in measuring humidity [1,10,19,31,12,9].These works are mainly focused on the calibration and humidity generation for dynamic systems and frequently expressed for relative humidity (% RH).Using error propagation approach, two types of distribution are considered as follow: • Type A: estimations are provided by statistics from repeated readings; • Type B: uncertainty estimation from other information source such as calibration certificates or manufacturers.
For type A, the standard error of the mean ( x) is given by: where   represents the standard deviation: For a type B, a rectangular distributed uncertainty can be used.In this case, a Type B evaluation is obtained by dividing the full-width by the square root of 3 [12]: where b is defined as the half-width between the upper and lower error limits.To estimate the combined uncertainty u  in the measurement of a variable  =  ( 1 ,  2 , ⋯ ,   ), a combination of the standard errors is used: where the sensitivity coefficient c  can be obtained by partial derivatives, i. e., using: where F is the variable for which uncertainty is calculated.The final expanded uncertainty (U) is calculated as: where k = 2 is used for a level of confidence of 95%.
In the present work, the sources of uncertainty were divided into two groups, those ones related to the equilibrium cell and humidity generation (  ) and those associated with the measuring device (  ): where  (  ℎ , ) stands for the expanded uncertainty of the frost or hydrate dissociation temperatures (  ℎ ) reported in this work.Consider firstly those measurements carried out for the certificated standard mixtures for which water content (  ) and expanded uncertainty  (  ,  = 2) are known.In this case, an uncertainty for the water content was informed by the manufacturer and this was converted to saturation temperatures (  ℎ ) so that: where the sensitivity coefficients (   ℎ   ) was estimated by numerical derivation using the equations of state to estimate the variations in dew/frost temperatures due to the uncertainty in the certificated water content   .In contrast, for measurements using the quasi-static variable volume cell, the uncertainty of generation was calculated by: where   and   refers to the equilibrium conditions in the cell.In this case, a Labview interface was used to log the   and   during the measurement.

)
were estimated by numerical derivation using the equations of state to estimate the variations in water content due to variations and   and   and how they affected the dew/frost temperatures.
In addition, uncertainty for the calibration of the T and P probes is accounted as ( , ) and ( , ), assuming a rectangular statistic distribution.Table 10 presents a typical uncertainty budget used to estimate the uncertainty in dew/frost temperature and hydrate dissociation conditions using the DSH method proposed in this work.It was based on the work of Meyer et al. [20], Heinonen [12], Abd El-Galil and Ahmed [1],Wettstein and Mutter [31], Fitzgerald [10], and Meyer and Solano [21] and considers the contributions deemed as more important.
On the other hand,   takes into account the standard deviation of the temperature measured (repeatability of measurement), (  ℎ ); the resolution of temperature measurement, (  ℎ, ); T-probe calibration, ( , ); and temperature probe tolerance, (  ).Thus:

B. Method Validation
In the preview sections, results from the DSH methodology obtained from several experimental setups were compared with measurements available in the literature.Unfortunately, it is rare to find published data under the same experimental conditions.This fact considerably limits the possibility of further comparing methods.Some standard certificated mixtures were also tested, reinforcing the DSH results and water content concentration correlation.Carefully considering that this work performed a comparative statistical analysis between the TDLAS results recently published by Adeniyi et al. [2] and those obtained in this work with DSH methodology for water content in pure carbon dioxide in equilibrium with hydrates.Table 11 recapitulates the data considered and helps to highlight the differences in temperature and pressure equilibrium conditions.These differences do not exceed 5% in terms of absolute deviation.In addition, Figure 10  The main picture demonstrated in Figure 10 (a) is that there is a meaningful correlation between the DSH and TDLAS results, also highlighted by the coefficients summarized in Tables 12 and 13.A strong fit is highlighted by an excellent multiple R and a significance F less than the p-value = 0.05, i.e., the correlation is statistically significant.
In addition, Figure 10 (b) depicts the termed Bland and Altman (B&A) plot, a methodology to investigate the agreement between two quantitative sets of measurements.Since the true values are unknown, the average content is the best estimation, and differences are plotted as a function of these average values.Table 12 shows that the d is only -3ppm, within the uncertainty levels estimated for both methods.Table 14 details the bias analysis and range of agreement: with a probability of 95%, the shaded area in Figure 10 (b) emphasises that the observed correlation is not biased, as the reference zero is within the confidence interval.

Figure 1 :
Figure 1: Schematic illustration of the equilibrium rig and measurement set up.TDLAS hygrometer has employed for comparative purposes.The different setups for measurements based on the DSH methodology are detailed in Figure 2.

Figure 2 :
Figure 2: Application of DSH methodology included testing different devices for providing flowing sample cooling and water monitoring: (a) Configuration 1, original setup as discussed by Burgass et al. [6]; (b) A modified version of configuration 1 includes a back-pressure valve to perform dew/frost point measurements above atmospheric conditions; (c) Configuration 2, a thermoelectric cooler is used for attaining fast cooling.Configuration 3 differs from (c) exclusively by replacing the capacitive sensor for a QCM.

Figure 3 :
Figure 3: Typical outputs obtained using different configurations: (a) a typical cooling/heating cycle used for determine dew/frost temperature with configuration 1; (b) obtained with setup configuration 2, a procedure consist of repeating cooling/heating cycles for better results; (c) QCM gives upward and downward baselines, but results for Configuration 3 are very consistent (d) using a faster heating rate (1 K/min), configuration 3 can still provide good results.

Figure 4 :Figure 5 :
Figure 4: Calculations for water content in carbon dioxide.

Figure 6 :
Figure 6: Calculations for water content in a certificated 75%CO 2 + 25%CH 4 mixtures at equilibrium cell conditions T and P = (a) 4.2 MPa and (b) 14.9 MPa.The experimental results are provided in the supplementary material in tabular format.Mixture composition is presented in Table 2.

Figure 8 :Figure 9 :
Figure 8: Prediction for frost temperature and hydrate dissociation in low water content in equilibrium with the 30 ppm CO 2 standard (certificated as 27ppm ± 5%).
depicts (a) a scatter diagram for paired values; (b) a Bland-Altman (B&A) plot, representing the difference between TDLAS and DSH versus the mean of the two measurements.

Figure 10 :
Figure 10: A comparison between the water content measurements for pure carbon dioxide in equilibrium with hydrates obtained from the DSH method and those published by Adeniyi et al. [2], as summarized in Table 11.(a) Scatter diagram for paired values.Statistical analysis for the regression is given in Table 12 (b) Bland-Altman (B&A) plot compares the difference between methods with the average water content values.Dashed lines outline the average difference and the confidence interval with p = 95%.Shaded areas present confidence interval limits for mean and agreement limits.

Table 2
Composition and expanded uncertainty ( ) of the certificated methane/carbon dioxide mixtures supplied by Air Liquid products and used in this work.

Table 3
Composition and expanded uncertainty ( ) of the certificated multicomponent mixture supplied by BOC and used in this work.

Table 4
List of Spectra-Seal® certified humidity standard mixtures supplied by BOC Ltd., used in this work, with respective water content and expanded uncertainty (U).Concentrations are expressed as   × 10 6 mole fraction or ppm.

Table 5
Results for frost temperatures (T  ) at barometric pressures (  ) and correspondent water content (   × 10 6 mole fraction or ppm) measured for the certified humidity Spectra-Seal ® water standard mixtures supplied by BOC Ltd (Table4) using the DSH method.The certificated water concentration and its correspondent expanded uncertainty are given by  and  (   ,  = 2).Additionally, U(T  ,k=2) and  (   ,  = 2) are the expanded uncertainties for   and    , respectively.  ), the water fugacity in the fluid, f    (  ,   ,   ), and ice,    (  ,   ), phases must be equal, i.e.: V. de O. Cavalcanti Filho et.al.: Preprint submitted to Elsevier

Table 8
Experimental frost temperatures (T  ) at barometric pressures (P  ) and the correspondent calculated water content (  in ppm or 10 6 mole fraction) measured with the DSH method for a multicomponent gas mixture (composition given in Table3) in equilibrium with hydrate.P = 15 MPa and T represent the conditions in the equilibrium cell and standard uncertainties are given by u(P) = 0.003 MPa and u(T) = 0.05 K, respectively.Additionally,  (  ,  = 2) and  (  ,  = 2) are the correspondent expanded uncertainties for   and   .
V. de O. Cavalcanti Filho et.al.: Preprint submitted to Elsevier V. de O. Cavalcanti Filho et.al.: Preprint submitted to Elsevier The acquired data was used to estimate (  ) and (  ) based on the

Table 10
Uncertainty budget for the dew/frost point measurements using the DSH method proposed in this work.
V. de O. Cavalcanti Filho et.al.: Preprint submitted to Elsevier

Table 11 A
[2]parison of the water content measurements in liquid carbon dioxide in equilibrium with hydrates using DSH method and TDLAS from Adeniyi et al.[2].

Table 13
ANOVA analysis for the two methods represented in Figure10(a) using p = 0.05 (probability of 95%).
V. de O. Cavalcanti Filho et.al.: Preprint submitted to Elsevier

Table 14
Bland and Altman plot statistics from the data of Table11, including confidence intervals (c.i.) for mean difference and upper and lower limits.F = degree of freedom.
V. de O. Cavalcanti Filho et.al.: Preprint submitted to Elsevier