Solubility of Nitrogen into Jet Fuel - American Chemical Society

Article Cite This: Ind. Eng. Chem. Res. 2018, 57, 2441−2448

pubs.acs.org/IECR

Solubility of Nitrogen into Jet Fuel Nicolas Gascoin,* Brady Manescau,* Safaa Akridiss, and Khaled Chetehouna INSA Centre Val de Loire, Université Orléans, PRISME EA 4229, 88 Boulevard Lahitolle, F-18022 Bourges, France ABSTRACT: Gas absorption and desorption into liquids are dynamic phenomena that can occur in process engineering. Consequences could be dramatic if these changes are sudden and uncontrolled. Thus, prediction is expected to keep them under control, but it requires some preliminary work to know more about the diffusion coefficient and Henry’s law coefficient for accurate modeling. Transient behavior is even trickier and shall be studied. In this work, a pure jet fuel fluid is used as a solvent with pure nitrogen (N2) to study its solubility. As N2 is the main component of atmospheric air, this work is also related to the natural absorption of N2 by the jet fuel, which is related to the aging and alteration of fuel when stored at ambient conditions. An experimental test bench has been developed specifically to physically and chemically quantify the gas absorption. Pressures up to 50 bar are considered over long pressurization time (up to 24 h) to study saturation conditions. Sudden pressurization and depressurization steps are achieved for unsteady investigations. The effects of the contact surface between liquid and gas, the penetration depth of gas into fluid, the pressure level, and the time of pressurization were observed. The contact surface is demonstrated to play a multiplier role on gas absorption, while the pressure and the depth of fluid strictly transmit their own evolution in a proportional way on the solubility phenomenon. An analytical model is developed, and values of Henry’s law coefficient (510 atm) and of diffusion coefficient (3.10−8 m2 s−1) are determined experimentally for making this analytical model to be predictable for larger and realistic configuration. An example of application is provided.

1. INTRODUCTION First, in looking at operational configurations in some industrial processes, flows can undergo compression or decompression phases. Particularly when the flows are multicomponent, different physical phases can appear and complex transfers from one phase to another are observed.1,2 Some pressurization strategies of liquids in process even do use gas as the pressurization device instead of piston-like compression or pumps for example. This increases the risk of unexpected interaction between liquid and gas.3,4 In addition, naturally, when liquids get in contact with ambient gaseous atmosphere (during storage for example), dissolution of gas into the liquid phase does start.5 If the reasons for having dissolved gas into liquids are numerous, when gas is dissolved, the depressurization can then lead to bubble formation, which has a direct negative impact on processes.6 Gas existence in the liquid flow piping might reduce the accuracy of the flow meters and therefore makes the tests quality less reliable.7 This is particularly true with fuel flow within industrial motorist mockups because of the possible high fuel volatility, the need for safety, and the high need for accuracy of operating systems. Second, by looking at phenomena behind the operational issues, different sources of bubbles can be listed: (1) cavitation, (2) thermodynamic phase change, and (3) gas desorption. (1) Cavitation is related to vapor formation in the liquid flow due to its very high speed.8 (2) The thermodynamic phase change is related to pressure and temperature changes and now well documented.9 (3) However, the interaction of two species (or © 2018 American Chemical Society

more) coexisting at different phases under the same operating conditions is still to be understood. This phenomenon can be related to the general topic of absorption and desorption of gas into liquid. Absorption and desorption are reverse phenomena that imply material exchanges between a gas phase and a liquid one having different chemical natures.10 When absorption is occurring, one or several compounds of the gas phase are dissolved in the liquid one; the gas is therefore called solute while the liquid is solvent. Absorption consists of putting in contact gas and liquid mixture so as to make one compound solvable. This process requires mass transfer from the gas phase into the liquid one. Solubility is the concentration of one compound in liquid phase when this one is in a thermodynamic equilibrium state with the same compound in gas phase.1 The gas solubility is hence the key parameter to evaluate the total amount of gas into liquid, and it depends on the nature of the specie.2 Pressure and temperature play major roles in this case. A gas mixture may lead to observe various absorption phenomena of compounds in the same liquid phase, each specie absorption having its own dynamic.9 In this above framework, the present work intends particularly to investigate the relationship between gaseous nitrogen and liquid jet fuel. Nitrogen and jet fuel together form Received: Revised: Accepted: Published: 2441

October 26, 2017 January 14, 2018 January 29, 2018 January 29, 2018 DOI: 10.1021/acs.iecr.7b04455 Ind. Eng. Chem. Res. 2018, 57, 2441−2448

Article

Industrial & Engineering Chemistry Research

few percent at maximum), while Raoult’s assumes species with similar concentrations.

a virgin couple in literature which still needs to be investigated. Jet fuel is seen as a high potential fuel, while nitrogen is not only the major air component but it is also used for pressurization system in some high-end strategic applications. On the one hand, experimentally, only a few studies on nitrogen absorption can be found in the literature. Most of them rather focus on CO2 absorption into fuels11−14 because of its large use, for example, in enhanced oil recovery techniques for oil drilling.14 Fornari et al.15 also studied the CO2 absorption into water. Technically, a large number of studies investigate the gas solubility into liquid;14 some also using chemical analysis for quantification of gas into liquid.14 For an order of magnitude, gases above liquid generally dissolve in a range of 100 to 10000 ppm at equilibrium state.3 On the other hand, the analytical approach is possible for enhancing not only the understanding of phenomena but also their prediction. On the basis of kinetics, one consideration may explain the gas absorption as follows. In the liquid phase, the molecules are permanently in an agitation state. Among dissolved gas molecules near the interface, due to random collisions, a constant portion of molecules acquires sufficient energy to favorably pass into gas state, escaping from the liquid. The evasion rate is proportional to the volumetric concentration of the dissolved gas.37 The liquid surface is constantly struck by a statistically same amount of gas molecules. The majority of them bounce, but a small fraction sticks constantly into the interface, entering the liquid. Thus, the quantity of molecules that undergoes this phenomenon per surface unity and per time unity is proportional to the molecules spatial density in the gas phase, which is associated with the partial pressure of the gas.22−24 This explanation deals with the macroscopic equilibrium notion due to permanent flux between absorption and desorption. This general consideration drives the analytical approach and laws that follow and enables to draw the test matrix for experiments. Because the industrial processes are dynamically evolving, transient prediction of multiphase phenomena are essential to evaluate as a function of time what could happen in the system. In the literature, to the authors’ knowledge, no analytical equation or even empirical law exists explicitly in a transitory state in order to carry out numerical simulations of substance absorption or desorption in a solvent. Mostly they are designed under steady-state regime (saturation conditions). Several laws, such as Raoult’s,5 Henry’s,7,8 Sieverts’,4 and Lewis and Randall’s,10 related to strong or weak solubility properties, have been referred. Ideal solution (i.e., solution is composed of various species with no chemical interaction, therefore no volume change nor internal energy one) does apply for Raoult’s law.4 The work of Hildebrand5 can be used for detailed analysis of the validity domain of Raoult’s law. Henry’s law (eq 1 according to molar fraction or eq 2 regarding the concentration1) also deals with ideal solution but in the case of highly diluted mixture. This law determines the maximal concentration (i.e., saturation point at equilibrium state) of a gassy compound in a liquid with different chemical nature. It assumes that the gassy compound does not change chemically into liquid when mixing with the solvent. When temperature is constant, the compound solubility is proportional to its partial pressure. This is valid if the concentration at steady-state of the gas in the liquid phase is very weak.6 Henry’s coefficient shall be a function of temperature and of each of the considered chemical phases(gas and liquid).6 Note that Henry’s law considers a highly diluted body compared to another one (i.e., a

pi = HiXi*

(1)

pi = H′i Ci

(2)

where pi is the partial pressure of the “i” gas in the gas phase, X*i is the molar fraction of the “i” gas at saturation point in the liquid phase, Hi is the Henry’s coefficient of the “i” gas, Ci is the concentration of the “i” gas at saturation point; , and Hi′ is also called the Henry’s coefficient of the “i’ gas, using different unit. Considering Henry’s law, it is now interesting to look at solubility phenomenon. The gas solubility is decreasing when temperature is increasing, and it is increasing when the pressure increases.7 However, the gas pressure increases proportionally with temperature (i.e., law of perfect gas) and hence impacts the solubility. So there is an opposite effect of pressure and temperature on solubility. Henry’s coefficient shall represent this complex interaction. However, the equilibrium coefficient (called Henry’s coefficient) decreases much more strongly when the temperature increases due to slightly exothermic characteristics of dissolution phenomenon. Henry’s law does not explicitly mention the solvent effect, either of pressure or of temperature, even though those parameters have a strong influence on Henry’s coefficient. For these reasons, Battino and Clever advised limiting the use of Henry’s law as a simplified approach.8 Apart from the well-known Henry’s law, the Lewis−Randall’s law is more accurate in the case of strong concentration, while Henry’s is more adapted for low concentration solution.10 Specifically to predict the system in steady-state conditions, Clapeyron and Antoine’s laws can also be considered.10 Referring to Wilhelm,3 Henry’s law or the use of fugacity may be applied with a reasonable error, although, for better results, Krichevsky−Ilinskaya approaches using the Poynting corrector formula and Tait equation shall be implemented.6 An additional source of complexity in the mass transfer between gas and liquid phase depends on the state of the gas phase when conditions are in fact those of supercritical conditions.25 Hildebrand5 explains by his approach that after the critical point passage, considering the imperfections of the fluid characteristics, Raoult’s and Henry’s laws have to at least be extrapolated because the notion of saturating vapor does not have any more signification, even if this notion is used in those equations. This is confirmed by Fornari et al.15 Furthermore, Battino and Clever have shown that if the gap of critical characteristics between gas and liquid is too weak (less than 100 °C on critical temperature, for instance), then it is not possible to consider the system as a gas dissolution into a liquid.8 Chrastil’s law26 can be used when studying liquid solubility into supercritical concentrated gas. The benefit of using this law allows relating the liquid solubility (which is difficult to measure) to the system density. This law has been used mainly by Fornari et al.15 in order to predict the solubility of some gases and liquids, especially CO2 into hydrocarbons. The approach proposed by Riazi and Roomi27 appears to be preferable in the case of supercritical gas like N2 into a hydrocarbon because, as stated by Hildebrand,5 it is adapted to real fluids (contrary to the Raoult’s or Henry’s laws, for example, showing some limitations in the case of high-pressure or supercritical states). This was confirmed by Fornari et al.15 and by Battino and Clever.9 Using the work of Riazi and Roomi27 shall enable improving the accuracy of the present 2442

DOI: 10.1021/acs.iecr.7b04455 Ind. Eng. Chem. Res. 2018, 57, 2441−2448

Article


Figure 1. Instrumented experimental setup for unsteadily (de)pressurizing fuel with gas.

approach. The molar fraction of the gas at saturation point X*i can be written as per eq 3 (where the total pressure mentioned ptot is indeed the partial pressure of the gas). The pure liquid fugacity at standard conditions f Li,0 depends on temperature and pressure (eq 4). Equation 4 is valid for a reduced temperature below 2.5 °C. Equations 4−7 provide the expressions necessary to determine all the parameters of eq 3. The solubility parameter is calculated according to Hildebrand’s law5 through eq 8, which considers the vaporization enthalpy. This enthalpy is equal to 50000 J/mol for jet fuel and 5560 J/mol for nitrogen. Xi* =

δ=

(3)

⎞ ⎛ 8.19643 fiL,0 = exp⎜7.902 − − 3.08 × ln(Tr)⎟ × PC Tr ⎠ ⎝ L ⎡ V (P − 1.013) ⎤ ⎥ × exp⎢ i RT ⎣ ⎦

2. EXPERIMENTS AND ANALYTICAL DEVELOPMENT 2.1. Investigation of Gas Absorption and Desorption. 2.1.1. Material. Autoclave equipment made of Hastelloy C276 was used for this study in order to pressurize and depressurize the liquid with or without contact with the gas phase (Figure 1). Nitrogen is supplied by a bottle (1) and enters (2) the autoclave (3). This autoclave is a volume filled by nitrogen and shall ensure the mechanical resistance and tightness seal to avoid leakage. An open recipient (beaker, 4) is placed inside this autoclave and filled with jet fuel (different volume and height of recipient are possible). A membrane could be added onto the recipient to avoid contact between the gas and liquid phases for some tests. A heating device ensures the stable and uniform temperature of the entire system. Sensors allow measuring temperature and pressure in the system (5, 6). All signals are acquired and postprocessed by computer (7, 8). A plunging tube can be used for draining the liquid phase out of the autoclave through a vent controlled manually or by a vacuum pump to study the depressurization phase and for sampling. Verification was done using 200 mL of jet fuel in an open beaker in order to observe the pressure decrease as a function of time (i.e., absorption of N2 into jet fuel). Then, the same experiment with 200 mL of jet fuel inside a Tedlar balloon avoiding contact between gas and liquid was done. This proves that the pressure decrease is achieved by gas absorption. Chemical analysis of the jet fuel sample from the Tedlar balloon showed the same signature as the initial jet fuel (no gas absorption). This was compared to chemical analysis of jet fuel undergoing gas pressurization that demonstrated clear gas absorption as it will be detailed in section 3.

(4)

⎧ Pr, i φi = exp⎨ × [(0.083 − 0.422 × Tr,−i1.6) T ⎩ r ,i ⎪

⎪

⎫ + ωi(0.139 − 0.122 × Tr,−i4.2)]⎬ ⎭ ⎪

⎪

⎛ (vapor pressure Pσ ) ⎞ ωi = −1 − log 10⎜ ⎟ ⎝ (critical pressure Pc) ⎠

(5)

(6)

where φi represents the fugacity coefficient, γi is the activity coefficient of dissolved gas, VLi is the partial volume of specie i, Tr,i is reduced temperature of i, Pc is critical pressure, Pr,i is reduced pressure of i, R is the perfect gas constant, T is the nitrogen temperature in the vessel, and ωi is the acentric factor of the species i (in the the case of N2, this parameter is equal to 0.037 under normal conditions25). ⎛ V L × ((δ − δ ) × (1 − Φ ))2 ⎞ i i j i ⎟ γi = exp⎜⎜ ⎟ RT ⎝ ⎠

Φi =

(7)

Xi* × ViL Xi* × ViL + (1 − Xi*) × V jL

(9)

where υ is the molar volume (m3/mol) and Hv is the vaporization enthalpy (J/mol). In this paper, the physical phenomenon of nitrogen dissolution into a specific fuel showing industrial interest (jet fuel) is investigated through an experimental approach. An additional analytical approach is proposed to simulate and predict the transient behavior of a realistic system to evaluate the dynamic of the two phases’ system. An example of industrial application is provided for pressurization phase followed by a depressurization one with time variation under different operating conditions.

φi × Ptot γi × fiL,0

H v − RT υ

(8) 2443


Article

Industrial & Engineering Chemistry Research 2.1.2. Method. First, for each test, after setting up the bench, the tightness seal is carefully monitored by having the bench pressurized once, initially, and observing the possible decay of the autoclave pressure as a function of time (for 2 h). As seen in Figure 2, the pressure history is used as the blank for the system

As seen above, the dissolved gas quantity was determined based on the gap between initial pressure and the one observed when reaching steady-state during the test (in compliance with the procedure described in refs 19 and 28, pp 38/102). This is related to the physical quantification method of gas absorption into liquid. Another chemical one was used thanks to GC-MS analysis (model Thermo Scientific DSQTM II series single quadrupole) by quantifying directly the nitrogen content into pure jet fuel (samples were analyzed immediately after sampling to avoid aging or sample alteration). Regarding depressurization tests, the vent (plunging pipe) is opened under controlled dynamic to investigate the depressurization behavior. The test matrix is established to investigate the effects of (i) contact surface between liquid and gas (28.3 cm2, 38.5 cm2, 50.3 cm2), (ii) depth of liquid (1.3 cm, 2.6 cm, 3.9 cm), (iii) pressure level, (iv) dynamic of phenomena, and (v) time of pressurization (10 min, 60 min, 120 min, 300 min, 600 min). The experiments will lead to calculate Henry’s coefficient in the different planned operating conditions.19 2.2. Analytical Laws. Because of the number of possible equations or laws found in the literature (each having its own advantages or not), the authors chose Henry’s law for providing a “universal” approach to be used by the scientific and engineering community. When dealing with Henry’s law, the work of Battino et al.29 can be seen as a good reference for nitrogen solubility in hydrocarbons, despite the fact that the one for jet fuel does not exist. Other research works also provide some values for different liquids.16−18 In terms of phenomenology, Battino et al. showed the effects of pressure, temperature, and liquid solvent (through its family, alkane/ aromatic/cyclic, and the carbon quantity contained by the solvent). The thermal effect appeared weaker than the pressure one. The carbon quantity into the alkanes plays an important role on the N2 solubility, and isomers may represent quite different solubility values (around 25%) as per examples of cisand trans-1.2-dimethylcyclohexane. In the case of dissolved gas such as N2 or O2 into jet fuel, at strong pressure (several bars), it is necessary to determine whether interactions between species act or not on the solubility. In this work, let us assume that the interactions are not chemical (meaning that there is no hydrogen link between the gas and jet fuel) and that the molar fraction at saturation point remains very weak compared to unity. By considering the critical temperature of jet fuel of 698 K, a critical pressure of 3.733 MPa, a critical density of 2.16 mol/dm3, and the planned absorption in this work at ambient temperature, it is therefore acceptable1 to consider V0i as close to the molar volume at normal boiling temperature (for instance, estimation through incrementing method of Le Bas). By applying the Henry’s law approach to study N 2 dissolution into jet fuel, the coefficients from refs 6 and 28 are used. Considering the Rakymkul’s works,28 Henry’s coefficient can be obtained under different operating conditions (see Table 1) and written: He = −20.397 × T + 2667. Henry’s coefficient for N2 in kerosene is equal to 5500 atm.6 This work used the following numerical data: δ = 9.082 (J/cm3)0.5 and VL = 34.6723 cm3/mol for nitrogen.20,21 For jet fuel, δ = 19.89 (J/cm3)0.5 (referring to21 values of 1-methylnapthalene having molar volume closest to jet fuel for a rough formula of C11H10) and VL = 139.4 cm3/mol at 25 °C.30 Note that some semiempirical works propose calculating methods for Henry’s coefficient based on the solute and the solvent.31,32

Figure 2. Pressure drops in the autoclave with/without absorption in liquid.

because the compression of nitrogen when filling the autoclave could generate temperature variations that impact the pressure stability during thermal stabilization. Second, this step is then redone after filling the relevant beaker with the required volume of jet fuel in order to complete the test matrix. When pressurized over the liquid surface, nitrogen will dissolve in it and the autoclave pressure will thus decrease accordingly. Removing the blank signal from the one obtained with fuel enables identification of the quantity of nitrogen dissolved in the liquid phase. The mole number of the present jet fuel is given by the following expression: n jet fuel =

ρjet fuel Vjet fuel Wjet fuel

(10)

and the quantification of nitrogen lost by absorption into jet fuel is expressed as Δn = n2 − n1 = (P2 − P1)*

V RT

(11)

where P1 is the initial pressure inside the pressurization vessel, P2 is the final pressure inside the vessel, n1 is the mole number of the initial nitrogen, n2 is the mole number of the final nitrogen, njetfuel is the mole number of jet fuel, R is the perfect gas coefficient, i.e., R = 8.314 J·mol−1·K−1, and T is the nitrogen temperature in the vessel and Wjet fuel is the molar mass (kg/ mol). The molar fraction of the dissolved nitrogen into jet fuel, noted XN2, can be written as follows: X N2 = =

nabsorbed n jet fuel + nabsorbed Δn jet fuel − Δnblank

(ρ

V /Wjet fuel jet fuel jet fuel

) + Δnjet fuel − Δnblank

(12)

Each test was repeated three times in order to ensure the reliability of the obtained values. The dynamic of pressurization can also be investigated for transient studies and waiting for a long time enables observing steady-state behavior (for getting the Henry’s law constant for example). 2444


Article

Industrial & Engineering Chemistry Research Table 1. Data of N2 Solubility in a Paraffinic Mixture at 30 bar (Adapted from ref 28) temperature (K)

concentration of N2 at saturation point in a paraffinic mixture (mol/m3)

Henry coefficient (Pa·m3/mol)

300 400 463

145 165 172

20690 18182 17442

To introduce the time evolution in the system, the gas desorption is modeled using the second law of Fick33−36 as follows: CG = (CG0 − CGi ) e−k·t − CGi

Figure 3. Effect of time and gas pressure on the absorbed N2 quantity.

(13)

3. RESULTS AND DISCUSSION The chemical composition of the initial fuel (jet fuel) was identified and quantified by GC-MS. Preliminary work showed that pressurizing jet fuel with mechanical device up to 50 bar does not modify the chemical composition itself and the contact with N2 also does not alter the chemical composition. The contact between the fuel and materials like stainless steel were found not to conduct to catalysis. The composition of the jet fuel is mostly 94.7 wt % of the endoisomer and 4.7 wt % the exoisomer (ion 136 m/z is predominant). Trace compounds were found (CO2, H2O, and O2) under an unquantifiable amount but still much higher than the noise signal. Additional analyses of chemiluminescence were achieved for validation, and similar results were found. 3.1. Experimental Absorption of Nitrogen in Jet Fuel. A significant number of tests (i.e., more than 200) were done in order to characterize finely the pressurization system and to ensure reliable results in triplicate. In this paper, the results corresponding to Table 2 are presented.

Figure 4. Apparent variation of Henry’s coefficient versus saturation time.

Table 2. Table of Experiments Quantitatively Post-Processed

Figure 5. Preweighing effect of exchange surface gas−liquid in relation to gas pressure on the dissolved gas quantity.

surface will generate a factor of 7 on the dissolved gas quantity. Thus, the contact surface between liquid and gas is of high importance on the gas absorption process. It was found also that the more the liquid volume for a given volume of gas, the less the dissolved quantity in mole fraction in the liquid. At 50 bar, for the same gas quantity, increasing the volume with the same contact surface of liquid from 50 to 150 mL reduces the molar fraction of nitrogen into jet fuel from about 4 mol % down to about 2 mol %, which is not directly linear because of the complex diffusion process of gas along the liquid deepness. Furthermore, the study has shown that the applied force of gas on the liquid surface (Figure 6) is directly linked to the gas dissolution which is a synergic effect of pressure and contact surface (force equals pressure by surface), while the parameters alone like pressure, surface, or layer thickness have less impact if not combined. Hence the proportionally available gas quantity

Figure 3 shows the evolution of the molar fraction of nitrogen as a function of pressure for different duration of pressurization. It is found that the molar fraction of nitrogen increases with the duration of pressurization. Using the experimental data and plotting Henry’s coefficient as a function of the experimental time (Figure 4) is a good way to evaluate the time needed to reach saturated steady-state conditions. The impact of the liquid−gas contact surface showed a multiplier effect on the dissolution. Figure 5 shows that a factor of 5 on the pressure will generate as well a factor of 5 on the dissolved gas quantity. On the other hand, a factor of 2 on the 2445


Article


Figure 6. Illustration of mechanical effect of pressurization on the gas dissolution.

and its capacity to mechanically integrate the liquid phase are the key parameters in the process. 3.2. Comparison between Experimentation and Analyses. Experiments using a 70 mm diameter beaker (100 mL) were chosen as the reference at 30 bar (during 1, 11, and 24 h). Based on this, the Henry’s coefficients have been reassessed at 510 atm. The diffusion coefficient was estimated at 3.10−8 m2/s. These values are those enabling obtaining the best agreement between analytical and experimental results at 30 bar (Figure 7; error bars given for a relative uncertainty of 15% on the mole fraction). Using these values, the results obtained at 10 and 50 bar are considered as satisfactory (Figure 8a,b).

Figure 8. (a) Analytical capacity to predict gas dissolution into liquids at 10 bar (a) and 50 bar (b) based on data evaluated at 30 bar experimentally.

Figure 9. Gas volume (m3) related to pressure relief of compressed jet fuel at 298 K.

Figure 7. Validation of computed gas dissolution into liquids at 30 bar by comparison with experiments.

Using these, Henry’s coefficient and diffusion coefficient enable evaluation that a one bar pressurization of nitrogen leads to a saturated molar fraction of 0.19 mol % gas in the jet fuel liquid phase. The saturation time was found around 15 h. 3.3. Operational Consequences on Industrial Process. Further computations were achieved on the basis of this work. To put these first results in perspective with regard to the industrial application, the depressurized volumes have been assessed according to their dissolved gas quantities based on the conditioning pressure undergone by the fuel inside the tank, and dissolved gas quantity changes at different volumes according to the final pressure after depressurization (Figure 9). The computation of gas volumetric fraction in biphasic fuel shows significant gas quantity that varies according to the relief pressure (Figure 10). It is also pointed out that the ratio of the relief pressure on the compression is strongly correlated to the gas volumetric fraction in the biphasic fuel at relief (Figure 11).

Figure 10. Gas volumetric fraction related to pressure relief of compressed jet fuel at 298 K.

2446


Article


factors increasing gas dissolution into the liquid are found as follows (in decreasing priority order): increase of the exchange surface between liquid and gas, decrease of the ratio between the liquid and the gas volume, and increase of processing time and increase of gas pressure level. Aside from the transient study, it was found experimentally that about 24 h are needed to reach a quasisaturated state. The “residual” quantity of N2 dissolved in jet fuel by contact with air is lower than 0.2 mol %. This negligible quantity represents up to 10% of the total volume when the liquid is expanded to 0.4 bar, which highlights the need for such a study to avoid any negative and unexpected bubble formation that would impact the process control. The Henry’s coefficient has been evaluated at 510 atm. The diffusion coefficient was estimated at 3.10−8 m2/s.

■

Figure 11. Effect of the ratio of relief pressure/compression on the gas volumetric fraction in biphasic fuel.

AUTHOR INFORMATION

Corresponding Authors

*B.M.: phone, 00 33 762 31 96 71; E-mail, brady.manescau@ insa-cvl.fr. *N.G.: phone 00 33 762 31 96 71; E-mail, nicolas.gascoin@ insa-cvl.fr.

This has been obtained by using the integrality of results generated in various geometrical operating conditions and for different values of Henry’s coefficients. Hence it is possible to define an admissible maximal level of gas in the liquid phase (to avoid any disturbance on flow meters) in order to recommend an acceptable maximal level of pressurization for each pressure level looked for at injection. It is also interesting to represent Figure 10 versus the molar fraction of initially dissolved N2 in the fuel in order to identify how pressure relief generates visible increase of N2 volumetric fraction in the liquid (Figure 12).

ORCID

Brady Manescau: 0000-0003-0537-1305 Funding

Funds used in order to support the research of this manuscript have been given by the laboratory’s own budget (annual allocation of the Ministry, by the MESRI (Ministère de l’Enseignement supérieur de la Recherche et de l’Innovation)). Notes

The authors declare no competing financial interest.

■

NOMENCLATURE Ci = concentration of “i” gas at saturation [mol·m−3] f Li,0 = pure liquid fugacity at standard conditions Hi = Henry’s coefficient of “i” gas [Pa·m3·mol−1] Hv = vaporization enthalpy [J·mol−1] Pr = reduced pressure, i.e. P [−] Pc

Ptot = total pressure [Pa] R = perfect gas constant [i.e., 8.314 J·mol−1·K−1] Tc = critical temperature [K] Tr = reduced temperature, i.e. T [−] Tc

υ = molar volume [m3·mol−1] VLi = partial molar volume of specie i [cm3·mol−1] Wjetfuel = the molar mass [kg/mol] X*i = molar fraction of “i” gas [−]

Figure 12. Gas volumetric fraction with regard to the fuel vs its initial content at 298 K.

Greek Letters

4. CONCLUSIONS Phase change in industrial processes may lead to sudden bubbles formation and two-phase flow that impact negatively the operating conditions and that makes the sensors less accurate. Apart from cavitation, thermodynamic phase change, and chemical reactions, gas absorption and desorption into liquids is another phenomenon which has not yet been studied when considering nitrogen and jet fuel. A specific test bench was designed and used for generating experimental data and for further developing adapted laws for calculations. It was found by chemical analysis that the pressurization under N2 does not modify chemically the fuel but it provokes a strong dissolution of N2 (more than 4 mol %). The experimental tests of pressurization and depressurization were carried out. The

■

δi = specific value of i defined by eq 9 [J0.5·cm−1.5] γi = activity coefficient of dissolved gas [−] φi = fugacity coefficient [−] ωi = acentric factor of i [−] Φi = fraction of i in a mixture defined by eq 8 [−]

REFERENCES

(1) Wild, G.; Charpentier, J. C. Solubilité des gaz dans les liquides. Techniques de l’Ingénieur April 10, 1987, article p605. (2) Association des Chimistes de l’ULg; Association des Chimistes de L’Université de Liège: Liège, Belgium, 2015; https://www.aclg.ulg.ac. be/Create/Modules_Evaluation1_CG/page_29.htm (accessed April 15, 2015). (3) Wilhelm, E. Solubility of gases in liquids: a critical review. Pure Appl. Chem. 1985, 57 (2), 303−322. 2447


Article


and oxygen from 60 to 2000 K at Pressures up to 2000 MPa. J. Phys. Chem. Ref. Data 2000, 29, 331. (26) Chrastil, J. Solubility of Solids and Liquids in Supercritical Gases. J. Phys. Chem. 1982, 86, 3016−3021. (27) Riazi, M. R.; Roomi, Y. A. A method to predict solubility of hydrogen in hydrocarbons and their mixtures. Chem. Eng. Sci. 2007, 62, 6649−6658. (28) Rakymkul, Y. Solubilities and Mass Transfer Coefficients of Gases in Heavy Synthetic Hydrocarbon Liquids. Master Thesis. University Of Pittsburgh, Swanson School Of Engineering, November 30, 2011. (29) Battino, R.; Rettich, T. R.; Tominaga, T. The solubility of Nitrogen and Air in Liquids. J. Phys. Chem. Ref. Data 1984, 13, 563. (30) LookChem; LookChem: Hangzhou, China, 2008; http://www. lookchem.com (accessed April 14, 2015). (31) Majer, V.; Sedlbauer, J.; Bergin, G. Henry’s law constant and related coefficients for aqueous hydrocarbons, CO2 and H2S over a wide range of temperature and pressure. Fluid Phase Equilib. 2008, 272, 65−74. (32) Ortiz-Corrales, J. A.; Carrero-Mantilla, J. I. Calculation of Henry’s law constants for some volatile organic compounds dissolved in aqueous Na2SO4 and NaCl solutions using the LIFAC activity coefficient model. Fluid Phase Equilib. 2014, 376, 96−104. (33) Yu, W.; Sepehrnoori, K. Simulation of gas desorption and geomechanics effects for unconventional gas reservoirs. Fuel 2014, 116, 455−464. (34) Wang, Z.; Sun, R.; Qi, L.; Liu, J. Theoretical equation of gas desorption of particle coal under the non-uniform pressure condition and its analytical solution. Safety Sci. 2012, 50, 861−864. (35) Sheng, M.; Li, G.; Huang, Z.; Tian, S.; Shah, S.; Geng, L. Porescale modeling and analysis of surface diffusion effects on shale-gas flow in Kerogen pores. J. Nat. Gas Sci. Eng. 2015, 27, 979−985. (36) Moulin, J. P.; Pareau, D.; Rakib, M.; Stambouli, M. Spectrométrie de massePrincipe et appareillage. Techniques de l’Ingénieur, February 2, 2010, article J1074. (37) Jacobs, M. H. Diffusion Processes; Springer-Verlag: New York, 1967.

(4) Rist, A.; Ancey-Moret, M. F., Gatellier, C.; Riboud, P. V. Équilibres thermodynamiques en sidérurgie. Techniques de l’Ingénieur, Dec. 10, 1974, article m1730. (5) Hildebrand, J. H. Solubility; The Chemical Laboratory of the University of California, May 18, 1916. (6) Green, D. W.; Perry, R. H. Perry’s Chemical Engineers’ Handbook; McGraw-Hill: New York, 1962; Vol. 2, pp 125−133. (7) Solubility and factors affecting solubility. UC Davis ChemWiki; UC Davis: Davis, CA, 2015, https://chem.libretexts.org/Core/ Physical_and_Theoretical_Chemistry/Equilibria/Solubilty/ Solubility_and_Factors_Affecting_Solubility (accessed May 5, 2015). (8) Rey, R.; Bakir, F.; Sarraf, C. Tenue en cavitation des pompes rotodynamiques. Techniques de l’Ingénieur, January, 2011, article bm4314. (9) Battino, R.; Clever, H. L. The solubility of Gases and Liquids. Chem. Rev. 1966, 66, 395−463. (10) Corriou, J. P. Thermodynamique chimique: diagrammes thermodynamiques. Techniques de l’Ingénieur, March 10, 1985, article j1026. (11) Kariznovi, M.; Nourozieh, H.; Abedi, J. Experimental results and thermodynamic investigation of carbon dioxide solubility in heavy liquid hydrocarbons and corresponding phase properties. Fluid Phase Equilib. 2013, 339, 105−111. (12) Sebastian, H. M.; Lin, H.; Chao, K. C. Correlation of the Solubility of Carbon Dioxide in Hydrocarbon Solvents. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 508−511. (13) Im, U. K.; Kurata, F. Solubility of Carbon Dioxide in Mixed Paraffinic Hydrocarbon Solvents at Cryogenic Temperatures. J. Chem. Eng. Data 1972, 17 (1), 68−71. (14) Avlonitis, G.; Mourikas, G.; Stamataki, S.; Tassios, D. A generalized correlation for the interaction coefficients of nitrogenhydrocarbon binary mixtures. Fluid Phase Equilib. 1994, 101, 53−68. (15) Fornari, T.; Hernández, E. J.; Reglero, G. Solubility of supercritical gases in organic liquids. J. Supercrit. Fluids 2009, 51, 115−122. (16) Tsuji, T.; Shinya, Y.; Hiaki, T.; Itoh, N. Hydrogen solubility in a chemical hydrogen storage medium, aromatic hydrocarbon, cyclic hydrocarbon, and their mixture for fuel cell systems. Fluid Phase Equilib. 2005, 228-229, 499−503. (17) Vins, V.; Hruby, J. Solubility of nitrogen in one-component refrigerants: Prediction by PC-SAFT EoS and a correlation of Henry’s law Constants. Int. J. Refrig. 2011, 34, 2109−2117. (18) Cheung, H.; Wang, D. I. Solubility Of Volatile Gases In Hydrocarbon Solvents At Cryogenic Temperatures. Ind. Eng. Chem. Fundam. 1964, 3 (4), 355−361. (19) Blath, J.; Christ, M.; Deubler, N.; Hirth, T.; Schiestel, T. Gas solubilities in room temperature ionic liquids − Correlation between RTiL-molar mass and Henry’s law constant. Chem. Eng. J. 2011, 172, 167−176. (20) Courtial, X. Détermination de coefficients de partage et de limites de solubilité du méthanol dans des mélanges liquides comportant azote et hydrocarbure(s) aux conditions opératoires des unités de fractionnement du gaz naturel. In Chemical Sciences; Ecole Nationale Supérieure des Mines de Paris: Paris, 2008. (21) Riazi, M. R. Characterization and Properties of Petroleum Fractions, 1st ed.; ASTM: West Conshohocken, PA, 2005. (22) Marche, C.; Delepine, H.; Ferronato, C.; Jose, J. Apparatus for the On-line GC Determination of Hydrocarbon Solubility in Water: Benzene and Cyclohexane from 70 to 150 °C. J. Chem. Eng. Data 2003, 48, 398−401. (23) Spigolon, A. L. D.; Lewan, M. D.; de Barros Penteado, H. L.; Coutinho, L. F. C.; Mendonça Filho, J. G. Evaluation of the petroleum composition and quality with increasing thermal maturity as simulated by hydrous pyrolysis: A case study using a Brazilian source rock with Type I kerogen. Org. Geochem. 2015, 83−84, 27−53. (24) Barton, A. F. M. Solubility Parameters. Chem. Rev. 1975, 75 (6), 731−753. (25) Lemmon, E. W.; Jacobsen, R. T.; Penoncello, S. G.; Friend, D. G. Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon 2448


Solubility of Nitrogen into Jet Fuel - American Chemical Society

Recommend Documents