Mohammad Yousefi,Shima Azizi*,S.M.Peyghambarzadeh*,Zoha Azizi

Department of Chemical Engineering,Mahshahr Branch,Islamic Azad University,Mahshahr,Iran

Keywords:Absorption Ethylene N-methyl-2-pyrrolidone(NMP)Nanoparticles Solubility

ABSTRACT The effect of presence of silver nanoparticles in pure N-methyl-2-pyrrolidone(NMP)solvent for ethylene gas absorption in an experimental pressure decaying setup has been investigated.All experiments were performed at temperatures of 278.15 K,298.15 K and 328.15 K and different pressures(up to ethylene dew point)as well as different concentrations of silver nanoparticles(0.05 g·L?1 and 0.1 g·L?1).The kinetic data of absorption,Henry's law constants,and heat of absorption were calculated.Comparison of the pure solvent and the nanofluids absorption results revealed that the presence of small amounts of nanoparticles could improve the absorption performance between 1.5%-18%.Finally,the effect of temperature,pressure,and nanoparticle concentration on the equilibrium results were investigated.

1.Introduction

Different additives were used to increase the solubility and absorption of gases in different pure solvents.These additives can be used either as ionic salts to facilitated transport[1,2]or as nanoparticles[3,4].The use of nanofluids to enhance different mechanisms of heat transfer(free convection,forced convection and even boiling),and on the other hand,the similarity between the heat transfer and mass transfer phenomena led the researchers to study the effect of nanoparticles on gas absorption by solvents.They expected the nanofluids decrease the mass transfer resistance compared to the pure solvents[3].

One of the pioneers of this research were Kars et al.[5]who studied the adsorption of propane gas in a slurry of active carbon in water in a stirred cell.In their research,they introduced the effect of“grazing”effect on adsorption enhancement and also found the values of mass transfer coefficient and mass transfer resistance by means of experiments and a conventional model.Similarly,other researchers have investigated the effect of nanoparticles and nanofluids on the mass transfer and gas separation:e.g.Zho et al.[6],Wen et al.[7],Prasher et al.[8],and Kim et al.[9–11].Here,other studies of nanoparticles roles on olefin separation and gas solubility are reviewed and the results of some of these investigations were presented.

Kang et al.[12]examined the effect of three types of ionic liquids on the formation of a partial positive charge on the surface of silver nanoparticles and its subsequent effect on the facilitated transport of olefins.They found that the higher the positive charge density of the silver nanoparticles,the better the separation performance of paraffin/olefin mixtures because the ionic liquids directly enhanced the facilitated olefin transport by surface positive charge of nanoparticles.

Pozun et al.[13]investigated the effect of silver nanoparticles or silver ions on olefin/paraffin separation and found that silver had less chemical absorption to ethylene than other metals.They have found that the smaller the particle size of the nanoparticles,the greater the tendency to bind to ethylene.

Merkel et al.[14]investigated the effect of light,hydrogen,hydrogen sulfide,and acetylene on a facilitated olefin transport membrane containing silver salt.All of these factors significantly reduced the selectivity of ethylene/ethane gas mixtures.Light,for example,reduced the selectivity from 40 to 1.1 after 34 days due to photo-reduction of the silver carrier ions.They used a regeneration method using a peroxide/acid liquid or vapor phase treatment to stabilize membrane performance,to oxidize reduced silver carrier inside the membrane.

Azizi et al.[3]studied the solubility of propane and propylene pure gases separately at different temperatures and pressures and nanoparticle concentrations by adding a small amount of TiO2nanoparticles in pure NMP solvent.The nanofluid increased the absorption rate and the maximum amount of absorbed gas,thereby reducing the time required to reach equilibrium.

Najari et al.[15]investigated the effect of the presence of inorganic nanoparticles on polymeric membranes for olefin/paraffin separation and adjusted the separation performance,mechanical integrity,thermal and mechanical stability as well as the economical process ability of the resulting nanocomposite.

Rezende et al.[16]showed selective absorption of propylene/propane on the polyurethane(PU)membrane containing silver nanoparticles.Propylene solubility in the nanoparticle-containing membrane was 4 times better than that of the pure PU membrane,indicating a high affinity for silver and propylene.

Jeong et al.[17]studied the effect of the presence of Ag2O nanoparticles on the long-term stability of specific membrane complexes for olefin/paraffin separation.Adding nanoparticles improved the separation performance of the propane/propylene gas mixture.In fact,selectivity improved from 15 to 21.7 and performance of separation of gas mixture from 4.36×10-10to 1.44×10-9mol.m-2.s-1.Pa-1.They searched for the reason for this better performance by various analyses and finally attributed to the barrier effect of Ag2O nanoparticles for propane molecules and the enhanced activity of Ag ions as an olefin carrier.

Rahmatmand et al.[18] investigated CO2absorption at an initial pressure of 20 to 40 bars and a temperature of 308 K in the presence of 0.02%(mass)to 0.1%(mass)of nanoparticles of SiO2,Al2O3,Fe3O4and carbon nanotube dispersed in water in a custom designed high pressure experimental setup in which the CO2gas and nanofluid are in direct contact at static state in a closed vessel.The absorption performances of different nanofluids were compared with the base solutions and with other nanofluids at different conditions.They found that gas adsorption on the nanoparticles surface led to higher absorption capacity of nanofluids at equilibrium condition.

Sun et al.[19]used a novel copper(I)-based supported ionic liquid membrane (SILM) to separate the ethylene/ethane mixture,which was able to show high permeability.Pure and mixed gas permeation experiments were carried out to investigate the influences of ILs composition,transmembrane pressure,temperature,and time upon the separation performance.This SILM showed comparable C2H4selectivity but outstanding permeability with a long-term stability beyond the reported polymeric membrane upper bound.

Kirsch et al.[20]modeled the absorption of ethylene from the ethane/ethylene mixture in a hollow fiber membrane by a silver nitrate solution.The method of calculation of the mass transfer was the method of lines with a longitudinal laminar flow in an array of parallel fibers.By numerical solution of a set of convection-diffusion equations with chemical reaction,ethylene flux was obtained.

Dou et al.[21]studied synergy of high permeability,selectivity and good stability properties of silver-decorated deep eutectic solvent(DESs)based facilitated transport membranes(FTMs)for efficient ethylene/ethane separation.In this series of DESs,the anion wasand transport carrier was AgNO3(silver cation).They reported that if the hydrogen bond acceptors(HBAs),hydrogen bond donors(HBDs),and carrier concentration were well adjusted,the ethylene/ethane selectivity would increase to 125.By decreasing operating temperature and transmembrane pressure,they were able to increase selectivity.

Mi et al.[22]investigated the characteristics of ethylene absorption in aqueous AgNO3solutions for ethylene/ethane separation in microchannels.They indicated that a significant improvement in the absorption performance was observed at higher AgNO3concentrations.Also,Mi et al.[23]studied the performance of ultrasound assisted absorption of ethylene with aqueous AgNO3solutions in microchannels for ethylene/ethane separation.They concluded that even though the mass transfer was largely improved by ultrasound,the absorption process was still limited by mass transfer as the intensification effect also increased with the increase of AgNO3concentration.

In this study,the aim was to investigate the effect of the presence of nanoparticles on improving the absorption of gas in solvent.Adding nanoparticles increases Brownian motion and increases system irregularities,creating new pathways and channels in the solvent boundary layer.In fact,the mechanism of mass transfer is physical absorption.The above articles are all in the presence of silver ion or silver salt which is facilitated transport.The mechanism of mass transfer in these cases is chemical reaction and d-π bonding.In other words,this paper although related to ethylene absorption,it is fundamentally different from the articles mentioned.

As can be seen,several investigations proved that the presence of small amounts of nanoparticles enhances the gas separation performance of the solvent.It is vital in any separation process that the equilibrium and kinetics information be available for solute/solvent binary.Although these data would be available for pure solvent,rare studies can be found that report the equilibrium and kinetics data for gas/nanofluids combinations.

The current work presents an in-depth study into the equilibrium and kinetics of absorption of ethylene in N-methyl-2-pyrrolidone(NMP)solvent in the presence of silver nanoparticles at different temperatures and pressures.Furthermore,Henry's law constants and heat of absorption and enhancement of absorption were also reported.

2.Experimental

2.1.Materials

Ethylene(C2H4)and NMP(C5H9NO)were supplied from Amir Kabir Petrochemical Company(AKPC),Mahshahr,Iran.NMP is a colorless liquid with a slight amine odor and is miscible with water.Since NMP has a low vapor pressure at the operating temperatures (e.g.0.07 kPa at 298.15 K compared with 3.2 kPa for water),and this value is very small in comparison with the operating pressures,its loss and evaporation during the operation can be neglected.Indeed,high normal boiling point of NMP(475.15 K)in comparison with other customarily used solvents enhances its ability to use as solvent.The reason for choosing this solvent was its high solubility and polarity,which enables it to separate olefins from paraffines.One of the most important properties of this solvent is that it solubilizes unsaturated hydrocarbons more than saturated hydrocarbons[24].Result of chemical analysis of NMP used in this study showed that its water content was about 1%(mole).

Silver nanoparticles purchased from ASEPE were also used in these experiments.The nanoparticles properties include the average size of 20 nm,molecular mass of 196.97 g·mol?1,purity of 99.9%,and actual density of 19,300 g·L?1.

The specifications of the materials used in this study are shown in Table 1.Materials were purchased from Amir Kabir Petrochemical Company(AKPC),Mahshahr,Iran,and were used without any further purification.The Antoine equationwas used to calculate the vapor pressure of the compounds.The critical properties,the acentric factors,and the constants of Antoine equation for the components of interest in this study are also listed in Table 1.

Table1 The properties of the materials used in this study[25,26]

2.2.Apparatus

The solubility experiments are terminated when the solvent is saturated with the gas and the equilibrium attained.The experimental procedure used in this study is no exception.The experimental apparatus is a batch pressure decaying absorption device.The temperature setting of this set up is controlled manually by a water bath equipped with PT-100 Ω as a temperature sensor.Reasons for using water as heating media include its low cost and availability,lack of toxicity,high heat capacity,and appropriate boiling temperature in accordance with the temperature range of the experiments.

As shown in Fig.1,the gas absorption in the NMP solvent containing Ag nanoparticles has beed occurred in an absorption cell equipped with a magnetic stirrer.Gas storage tank,regulator,middle or intermediate cell,absorption or equilibrium cell,magnetic stirrer,vacuum pump,water bath,pressure and temperature transmitters,and some indicators are components of this set up.

For each test,the required amounts of nanofluid as solvent with different concentrations poured into the absorption cell and the lid was tightened.Then,using the vacuum pump (JB Industries DV-200N,USA),the air was completely discharged from this set up.After ensuringcomplete evacuation,the valve between the intermediate cell and equilibrium cell was closed.The ethylene feed gas can now be directed from the storage tank to the middle cell.This cell is 0.5 L in volume with 20,000 kPa pressure tolerance and made of stainless steel.The purpose of the intermediate cell is to regulate the temperature and pressure of the gas before it enters the absorption cell.Using the intermediate cell initial pressure,the total amount of the initial moles of the injected gas can be calculated.After making sure the temperature and pressure are adjusted in the middle cell,it is necessary to open the valve between the middle cell and the absorption cell to begin the absorption.Due to the sudden increase in volume,the pressure drops sharply and stabilizes instantly.Then,the pressure reduction continued slowly to reach the equilibrium.In all these experiments,pressure changes were recorded by time.

The equilibrium cell was equipped with a temperature RTD sensor(PT-100Ω)with the accuracy of±0.2°C,and absolute pressure transducer(model PSCH0025BCIJ of Sensys Co.)with the precision of±1 kPa.The volume of this cell and its connections,which were equipped with a magnetic stirrer,were 0.37 L.The equilibrium cell was able to withstand pressure up to 2500 kPa.The magnetic stirrer speed should be adjusted to increase heat and mass transfer rate as well as to reduce the time to reach the equilibrium.It should be noted that the vortex should not be created on the surface of the solvent inside the absorption cell,while thorough mixing should also be performed.The temperature and pressure measured in this appurtenance are displayed by digital indicators.

It was ensured that no leakage occurred during the absorption process.The accuracy and performance of the instruments (RTD and pressure transducer) were also ensured.The accurate volume of all media including the absorption cell,intermediate cell,and all connections and tubing was measured with a precision of ±0.003 L.The similar apparatus had previously been used[2,27–29],and the obtained results had been approved by different approaches.

Fig.1.Schematic representation of the experimental apparatus.

2.3.Preparation of nanofluid

To prepare the required nanofluids,the required amount of pure silver nanoparticles was added to 0.1 L of pure NMP solvent.Then,the balloon was shaken mechanically for initial mixing of the suspension.Now,the suspension was placed in an ultrasonic apparatus(model Elmasonic Easy 30H of Elma Schmidbauer GmbH)for 90 min to disperse the nanoparticles well.The experimental glass container should be covered with the aluminum foil because of the sensitivity of the silver nanoparticles to the light.

2.4.Assumptions and calculations

The followings are the main assumptions considered in calculating the equilibrium mole fractions:

(1) Due to the low volatility of NMP,the amount of solvent in the vapor phase was negligible,therefore,the vapor phase was considered to be pure.It is worth mentioning that if the molar fraction of NMP in the vapor phase is taken into account,the ethylene molar fraction in the vapor phase is changed to y1=0.9999 instead of y1=1.It results in maximum 5%variation in solubility values(in the fourth decimal place of solubility).That is,the assumption that the vapor phase is pure is a reasonable assumption.

(2) After the evacuation,the amount of air in the system was abandoned.

(3) No mass transfer resistance occurred at the gas phase since this phase was considered as a pure substance.

(4) No volume change in the liquid phase was considered.As the volume of the gas phase was nearly 8 times greater than that of the liquid phase,the volumetric expansion of liquid which was a portion of liquid volume did not change the volume of gas significantly.Furthermore,the solubility of ethylene in NMP was low enough (x <0.1) to change the volume of the solvent considerably.

The volume of gas in the absorption cell can be calculated from the difference between the total volume of the cell and the volume of the solvent as follows:

where Vsis the initial volume of the solvent,Vtis total volume of the cell,and Vg,fis the final volume of the gas.

At constant temperature and constant volume of the solvent,a mass balance from initial pressure to equilibrium pressure must be established for relating the initial moles of the gas with the final moles of the gas in the system to obtain the moles of gas absorbed in the solvent.

Where Vg,1is the initial volume of the gas(intermediate cell volume),R is gas constant,T/K is the operating temperature,P1/kPa is the initial pressure,Peq/kPa is the final or equilibrium pressure,Z1is compressibility factor at the initial condition,and Zeqis compressibility factor at the equilibrium condition.The compressibility factor was calculated using Peng Robinson EOS[30,31]as below:

The terms A and B and their associated parameters were calculated as follows:

where Tc/K is critical temperature,Pc/kPa is critical pressure,ω is acentric factor,Tris reduced temperature,and Z is compressibility factor.

The number of moles of solvent can be calculated as follows:

where ρs/g·L?1is density of the solvent,Vsis the solvent volume,and Ms/g·mol?1is the molecular weight of the solvent.

Finally,the solubility was calculated by dividing the moles of the absorbed gas by the sum of the moles of the absorbed gas and the moles of the solvent:

where x is mole fraction of the gas in the solvent(solubility),ngis moles of the absorbed gas and nsis moles of the solvent.

In addition,Henry's law constants were calculated from the solubility data using the slope of the equilibrium pressure versus solubility at each temperature.It should be noted that pressure variation versus solubility should be considered linear if the Henry's law established.

According to Eq.(12),the relation between equilibrium pressure and solubility of dilute solution is expressed as:

where KHis Henry's law constant.

In accordance with the van't Hoff model,the Henry's law constant can be correlated with temperature as Eq.(13):

A plot of lnKHin terms of the inverse of temperature gives a straight line whose slope and intercept provide values of ΔH(=R×slope)and ΔS(=?R×intercept)and the parameter of the van't Hoff equation H0(=exp(intercept)).

Finally,the Gibbs free energy value was calculated according to Eq.(14):

3.Resuls and Discussion

3.1.Determination of optimum concentration of nanoparticles

Different concentrations of silver nanoparticles(0.05 g·L?1,0.1 g·L?1,0.3 g·L?1,1 g·L?1,2 g·L?1,5 g·L?1and 10 g·L?1)were studied at 30 min,60 min,and 90 min ultrasonic times for stability testing.The 0.01 L samples were shaken well and placed in an ultrasonic bath.The samples were kept away from light and were photographed every hour to assess the stability and deposition of the nanoparticles.In general,30 min was not suitable for any sample,and 90 min had better stability and better particle distribution.Among the concentrations,the concentration of 10 g·L?1was not stable at all and was eliminated from the options.The rest of the concentrations were placed under absorption test(0.1 L of the solvent)and amount of solubility obtained and compared.The concentration of 5 g·L?1had no advantage over pure solvent.The lower the concentration of nanoparticles from 2 g·L?1to 0.1 g·L?1,the better the absorption conditions.From the concentration of 0.1 g·L?1to 0.05 g·L?1,the conditions were reversed and the absorption was weaker.That is,the optimum concentration of nanoparticles at all operating conditions was about 0.1 g·L?1.Fig.2 shows the ethylene solubility (x) versus different concentrations of nanoparticles.The maximum point indicated the optimum concentration for maximum absorption.

3.2.Kinetics of absorption

Fig.3 (a) and (b) shows the variation of pressure and absorbed moles with time at constant temperature of 278.15 K and constant initial pressure and 600 kPa,respectively.Different curves related to different concentrations of nanoparticles added to the pure NMP solvent(0.05 and 0.1 g·L?1).Other similar graphs were obtained at other operating conditions and not shown here.Theses curves also show a good comparison for pure solvent and nanofluid experiments at different concentrations under the same temperature and pressure conditions.The duration of all experiments,varied from 90 min to 194 min,was recorded at all pressures,temperatures and concentrations of silver nanoparticles.

Fig.3 (a) shows that the pressure gradient curves have steeper slope at early stages of absorption when the fluid is free of the gas phase.Then,the slope becomes lower over the time as more ethylene diffuses into the liquid phase.Hence,with faster diffusion of gas into the liquid at early times,the initial pressure drop is more than that at the late times.According to Fig.3(a)and(b),at constant temperature and pressure,the absorption rate and absorbed moles increase with increasing the concentration of nanoparticles in pure solvent.It is clearly shown that increasing the nanosilver concentration from 0.05 g·L?1to 0.1 g·L?1results in an increase in the slope of the curves,indicating an enhanced effect on absorption rate of ethylene in the solvent.

In fact,the presence of nanofluids reduced the absorption time,which was more pronounced at high pressure.The absorption rate of ethylene increased with the presence of silver nanoparticles.According to Kars et al.[5],the presence of nanoparticles can perform the absorption of nanofluids faster than pure solvent under similar temperature and pressure conditions.These nanoparticles in the liquid phase move to the concentration boundary film,absorbed the gas and finally,released the gas into the liquid bulk.The curves also show that when small amounts of silver nanoparticles are added to the NMP,the amount of pressure drop during absorption increases,which results in more absorption in nanofluids rather than the pure solvent.This mechanism became known as the grazing effect.As shown in Fig.4,the distribution of nanoparticles between adjacent molecules of the solvent as well as their higher activity creates some new pathways for solute to penetrate and be absorbed into the solvent.In fact,the nanoparticles by random Brownian motion channelize the solvent to the concentration boundary layer and provide pathways for gas species for rapid and intense diffusion.By creating a microconvection in the liquid phase,a velocity disturbance field obtained and thus an effective convective flow is achieved to improve the mass transfer.This mechanism is similar to the effect of increasing pressure on absorption and is named Brownian motion [3,32–34].Increasing concentration leads to extra Brownian motions by more nanoparticles which enhances the mass transfer of ethylene.

Fig.2.Determination of optimum concentration of silver nanoparticles added to pure solvent.

Fig.5 (a) and (b) show the variation of pressure and absorbed moles with time at constant temperature of 328.15 K and constant concentration of nanoparticles 0.1 g·L?1and different initial pressures.As can be seen,the higher the initial pressure,the grater the pressure drop.Eventually more moles will be absorbed under these conditions.When the initial pressure increases from 400 kPa to 600 kPa and then 800 kPa,the initial slope of the curves increases from 0.0054 to 0.0087 and 0.0094,respectively.It is clear that when the absorption conducted at higher pressures,more time was needed to reach the equilibrium and hence,more amount of ethylene gas was absorbed in the solvent.When the pressure is increased,the micro-convections caused by Brownian motion in the liquid phase increased.Hence,transportation of gas molecules from the interface to the bulk of liquid increased which resulted in solubility increment.Other similar graphs were obtained at other operating conditions which not shown here.

Fig.6 (a) and (b) show the variation of pressure and absorbed moles with time at constant pressure(about 600 kPa)and constant nano-silver concentration (0.05 g·L?1) and at different temperatures,respectively.It can be seen that at lower temperatures,more absorption observed and more time is needed to reach the equilibrium.

When the liquid temperature increases from 278.15 K to 328.15 K,the slope of the curve decreases.It should be noted that the higher the temperature,the faster the absorption rate.It means that increasing temperature shows contradicting effect of kinetics and thermodynamics of the absorption.It enhances the rate of absorption (kinetics view) and reduces the equilibrium concentration(thermodynamics view).

3.3.Absorption equilibrium

Fig.3.Ethylene absorption in nanofluid at initial pressure of 600 kPa and 278.15 K and various nanoparticle concentrations,(a)pressure decay data(b)absorbed moles.

Fig.4.Effect of nanoparticle addition on the absorption ability of the solvent(a)pure solvent(b)nanofluid solvent[3].

Fig.5.Ethylene absorption in nanofluid at 328.15 K and 0.1 g·L?1 Ag nanoparticle and various initial pressure,(a)pressure decay data(b)absorbed moles.

The equilibrium mole fraction of ethylene gas in NMP solvent was calculated using Eq.(11).Fig.7 presents the equilibrium data at constant concentrations of nanoparticles(0.05 g·L?1and 0.1 g·L?1)and at constant temperatures.This equilibrium data is presented in terms of equilibrium pressure against equilibrium solubility(mole fraction).According to Fig.7,decreasing the temperature and enhancing the concentration of the silver nanoparticles at constant pressure improves ethylene solubility in nano-solvent.At higher pressures,the effect of temperature on the gas solubility is more significant.Furthermore,it should be mentioned that linear regressions of the data considering(0,0)as intercept are also shown in Fig.7.The fitted equations and the relevant R2are also shown in the graph.As can be seen,the slope of the lines monotonically decreases with increasing the nanoparticle concentration and reducing the temperature.It is obvious that variation of temperature has greater effect on the solubility lines rather than the variation of nanoparticle concentration.

Fig.7.The equilibrium data (Peq ?x) for the absorption of ethylene in nanofluid at different temperatures and nanoparticle concentrations.

The slope of the equilibrium pressure versus solubility curve gives the Henry’law constant KHfor each temperature.The values of Henry's law constants of this study are presented and compared with previous works in Table 2.

By plotting lnKHversus inverse of temperature,the van't Hoff model constant is obtained using the experimental solubility data.Fig.8 shows these curves for different concentration of nanoparticles.In fact,the activation energy(ΔH=?E)indicates the temperature dependence of the absorption.Higher activation energy reveals that the solvent absorption capacity would be more sensitive to temperature variation.According to Svenssons et al.[35],the absorption enthalpy of less than 14–16 kJ·mol?1indicates physical absorption.Based on the heat of absorption presented in Table 2,the ethylene solubility in NMP+Ag nanoparticles is intrinsically physical and occurs during low energy exchange absorption.

Although in this work the water content of NMP is constant(xw=0.011),it is clear from the previous works[36,39]that the higher water content increases the Henry's law constant and therefore,decreases the solubility of ethylene in NMP/water mixture.

Fig.6.Pressure decay of ethylene in nanofluid at 600 kPa and 0.05 g·L?1 Ag nanoparticle and various temperatures,(a)pressure decay data(b)absorbed moles.

As can be seen from the results,the decrease in the concentration of nanoparticles increased the heat of absorption.At constant temperature,the concentration of 0.1 g·L?1nanoparticles showed a lower Henry's law constants than the concentration of 0.05 g·L?1.According to Table 2,due to the negative heat of absorption,the absorption process is exothermic.As can be seen from the results,at any experimental temperature the value of|TΔS|is higher than the|ΔH|value,i.e.,the absorption is more affected by the increased irregularity than the absorption energy.Also,as the temperature increases,increases.This case shows that at higher temperatures,the entropy is more effective than the enthalpy on the Gibbs free energy and absorption process.Increasing the temperature decreases the system's irregularity.The negative Gibbs free energy also indicates the spontaneous absorption process and the positive Gibbs free energy indicates the non-spontaneous process.As the temperature increases,the Gibbs free energy increases further(its value gets more positive).This is precisely because of the greater effect of entropy on Gibbs free energy with increasing temperature.In fact,in such systems,at high temperatures the process will be non-spontaneous and at low temperatures it will be spontaneous,i.e.,it can be considered reversible[40–42].

Table2 Henry's law constants and the constants of van't Hoff equation for ethylene absorption in nanofluid system

Fig.9 demonstrates the ethylene solubility in terms of silver nanoparticle concentrations at different temperatures and pressures.As shown in Fig.9,the solubility increases with silver concentration and pressure while decreases with temperature.

Fig.10 compares the solubility of ethylene gas absorption in nanofluids and in pure solvent,at 800 kPa pressure and different temperatures.It should be noted that for all the operating conditions attempted,the same graphs are resulted and not shown here.As can be inferred,the absorption enhancement range for ethylene and nanofluids containing 0.1 g·L?1of silver nanoparticles relative to pure solvent was from 1.5%to 18.5%.The nanofluid results with concentration of 0.05 g·L?1provide about 1.5% to 16% performance improvement.The results showed that at lower temperatures and higher pressures this solubility enhancement was more pronounced.

Although addition of nanoparticles to the solvent does not alter the nature of the solvent,it can provide suitable conditions for solute that are absorbed in the solvent.When the nanoparticles are added to the base solvent,the solvent viscosity is increased,which is unpleasant in the diffusive mass transfer.This effect was similar to the increase in pressure in the absorption phenomenon.With the addition of nanoparticles,Brownian motion causes the solvent to be channelized to the concentrated boundary layer and prepares paths for the gas to diffuse and disperse rapidly.These changes actually increase the absorption rate and the amounts of absorbed moles.Increasing the pressure and adding nanoparticles thus increases the specific surface area of the solvent molecules and as a result,influences the kinetics and equilibrium of gas absorption.

Another possible mechanism is similar to the bubble absorber phenomenon that has been interpreted by Kim et al.[43].After gas absorption on the nanofluid,the stable nanoparticles cause the gas bubbles to break into small bubbles and increase the mass transfer area so that solubility of the small gas bubbles intensifies and finally leads to enhancing total absorption in the nanofluid.The mechanism may be explainedthrough stability and motion of the nanoparticles in the nanofluid.Stirring of the nanofluid and motion of the nanoparticles results in a collision with gas bubbles that cause to cracking and distortion of gas bubbles which are dispersing in nanofluid.However,due to presence of a nozzle in the bubble absorber the mechanism of motion of the bubbles are different.Here utilize a stirrer in an equilibrium cell leads to reduction of the size of gas bubbles and as a result,the gas solubility inmproves.

Fig.8.The van't Hoff model to calculate Henry's law constant as a function of temperature.

Fig.9.Solubility of ethylene as a function of silver nanoparticles concentration.

4.Conclusions

Ethylene absorption has been performed in a batch stirred vessel using nanofluid(NMP+Ag)as solvent and the following important conclusions were obtained:

(1) Physical absorption has taken place in these experiments.

(2) Absorption was faster at higher temperatures.This conclusion was more obvious at higher pressures

Fig.10.Ethylene solubility enhancement using NMP/Ag nanofluids.

(3) Increasing pressure,decreasing temperature,and increasing the concentration of nanoparticles improved the absorption and solubility of ethylene in the solvents,and decreased the required time to reach the equilibrium.

(4) The van't Hoff model was compatible with the experimental data for Henry's law constant calculation to show its dependence on temperature.

(5) Increasing the temperature and decreasing the nanoparticles concentration increased Henry's law constant.

(6) The optimum ultrasonic time and optimum concentration of nanoparticles were 90 min and 0.1 g·L?1,respectively.

(7) Due to agglomeration and sedimentation,at lower concentrations of the nanoparticles,better stability was achieved.

(8) Increasing the nanoparticles concentration decreased the heat of absorption.

(9) The nanofluid reduced the equilibrium time and provided better solubility than pure solvent.

Declaration of Competing Interest

The authors have full access to all the data in the study and have final responsibility for the decision to submit for publication.The information provided here including data collection,analysis,interpretation;or any aspect pertinent to the study have been performed by us and there is no conflict of interest with other company or agency.

Acknowledgements

This paper was prepared from a Ph.D.thesis conducted in the Department of Chemical Engineering,Mahshahr branch,Islamic Azad University,Mahshahr,Iran.

Nomenclature

E activity energy,kJ·mol?1

G Gibbs free energy,kJ·mol?1

H enthalpy,kJ·mol?1

KHHenry's law constant,kPa

Mwmolecular weight,g·mol?1

n moles,dimensionless

P pressure,kPa

R gas constants,kJ·mol?1·K?1

S entropy,kJ·mol?1·K?1

T temperature,K

V volume,L

x solubility or mole fraction in liquid phase,dimensionless

Z compressibility factor,dimensionless

ω acentric factor,dimensionless

ρ density,g·L?1

Subscripts and superscript

1 initial

c critical

exp experimental

eq equilibrium

f final

g gas

i component i

j component j

r reduced

s solvent

sat saturation

t total