Solubility of Nitrogen into Jet Fuel - Industrial & Engineering Chemistry

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Solubility of Nitrogen into jet fuel Nicolas Gascoin, Brady Manescau, Safaa AKRIDISS, and Khaled Chetehouna Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b04455 • Publication Date (Web): 29 Jan 2018 Downloaded from http://pubs.acs.org on January 31, 2018

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Industrial & Engineering Chemistry Research

Solubility of Nitrogen into jet fuel Nicolas GASCOIN, Brady MANESCAU, Safaa AKRIDISS, Khaled CHETEHOUNA INSA Centre Val de Loire, Univ. Orléans, PRISME EA 4229, F-18022 Bourges, France

Corresponding author: Nicolas GASCOIN Address: INSA Centre Val de Loire, Univ. Orléans, PRISME EA 4229, 88 Boulevard Lahitolle, 18022 Bourges Email address: [email protected] Tel: 00 33 762 31 96 71

Keywords: gas absorption and desorption, pressurized liquid, bubble formation, jet fuel, cavitation

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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 diffusion coefficient and Henry’s law coefficient for accurate modelling. 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 bars are considered over long pressurization time (up to 24 hours) 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 deepness of gas into fluid, the pressure level and the time of pressurization were observed. The contact surface is demonstrated to play a multiplier role onto the gas absorption while the pressure and the deepness 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 (3.108 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.


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Highlights •

Pressure changes generate flow instability like bubble formation or cavitation

•

Solubility of N2 into jet fuel is studied up to 50 bars and 24 hours

•

Saturation conditions enabled to evaluate the Henry and diffusion coefficients

•

Contact surface area with liquid is the main parameter acting on gas solubility

•

An industrial configuration is simulated as a transient case of application

Nomenclature : concentration of “i” gas at saturation

: molar volume [m3.mol-1]

[mol.m-3]

: partial molar volume of specie i

, : pure liquid fugacity at standard

[cm3.mol-1]

conditions

Wjetfuel : the molar mass [kg/mol]

: Henry’s coefficient of “i” gas

∗ : molar fraction of “i" gas [-]

[Pa.m3.mol-1]

Greek letters : vaporization enthalpy [J.mol-1]

: specific value of i defined by Eq. 9

: reduced pressure, i.e. [-]

[J0.5.cm-1.5]

: total pressure [Pa]

: activity coefficient of dissolved gas [-]

: perfect gas constant [i.e. 8.314 J.mol-

: fugacity coefficient [-]

: acentric factor of i [-]

1

.K-1]

: critical temperature [K]

Φ : fraction of i in a mixture defined by

: reduced temperature, i.e. [-]

Eq. 8 [-]



1. Introduction Firstly, 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 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 mockup because of the possible high fuel volatility, the need for safety and the high need for accuracy of operating systems. Secondly, 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 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 4 Environment ACS Paragon Plus

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gas is therefore called solute while the liquid is solvent. Absorption consists in 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 thermodynamically 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 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 few studies on nitrogen absorption can be found in the literature. Most of them rather focus on CO2 absorption into fuels [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 ppm to 10 000 ppm, at equilibrium state [3]. On the other hand, analytical approach is possible for enhancing not only the understanding of phenomena but also their prediction. Based on kinetics consideration one may explain the gas absorption as follows. In the liquid phase, the molecules are permanently in 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 to the partial pressure of the gas [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 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], 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 the Raoult’s law [4]. The work of Hildebrand [5] can be used for detailed analysis of validity domain of the Raoult’s law. The Henry’s law (Equation 1 according to molar fraction or Equation 2 regarding the concentration [1]) is also dealing with ideal solution but in 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


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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]. The Henry’s coefficient shall be function of temperature and of each of the considered chemical (gas and liquid) [6]. Note that Henry’s law considers a highly diluted body compared to another one (i.e. few percent at maximum), while Raoult’s assumes species with similar concentration. = ∗

(1)

= ′

(2)

where is the partial pressure of the “i” gas in the gas phase; ∗ is the molar fraction of the

“i ” gas at saturation point in the liquid phase; is the Henry’s coefficient of the "i" gas; Ci is the concentration of the “i ” gas at saturation point; ′ is also called the Henry’s coefficient of the "i" gas, using different unit. Considering the 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. The 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 the Henry’s coefficient. For these reasons, Battino and Clever advised to limit the use of Henry’s law as a simplified approach [8].



Apart of the well-known Henry’s law, the Lewis-Randall’s law is more accurate in case of strong concentration, while Henry’s one 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, altough, for better results, Krichevsky-Ilinskaya approaches using 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]. Hildebrand [5] 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 since the notion of saturating vapor does not have any signification no more, 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), it is then not possible to consider the system as a gas dissolution into a liquid [8]. Chrastil’s law [26] can be used when studying liquid solubility into supercritical concentrated gas. The benefit of using this law allows to relate 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 Roomi [27] appears to be preferable in 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 state). This was confirmed by Fornari et al. [15] and by Battino and Clever [9]. Using the work of Riazi and Roomi [27] shall enable improving the accuracy of the present approach. The molar fraction of the gas at saturation


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point ∗ can be written as per equation 3 (where the total pressure mentioned is indeed the partial pressure of the gas). The pure liquid fugacity at standard conditions , depends on

temperature and pressure (Equation 4). Equation 4 is valid for a reduced temperature below 2.5°C. Equations 4 to 7 provide the expressions necessary to determine all the parameters of Equation 3. The solubility parameter is calculated according to Hildebrand‘s law [5] through Equation 8 which considers the vaporization enthalpy. This enthalpy is equal to 50 000 J/mole for jet fuel and 5560 J/mole for nitrogen. ∗ = , = () *7.902 −

1.23456 7

×"#"

(3)

$ ×% ',&

− 3.08 × :; × ? × () @

A ' <B2.26= C

D

(4)

B2.4 B5.L = () E 7, × FG0.083 − 0.422 × , I + G0.139 − 0.122 × , IMN

(5)

= −1 − :OP10

Solubility of Nitrogen into Jet Fuel - Industrial & Engineering Chemistry

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