Xinran Zhang ,Hua Shang ,Jiangfeng Yang,2,*,Libo Li,2 ,Jinping Li,2

1 Research Institute of Special Chemicals,College of Chemistry and Chemical Engineering,Taiyuan University of Technology,Taiyuan 030024,China

2 Shanxi Key Laboratory of Gas Energy Efficient and Clean Utilization,Taiyuan 030024,China

Keywords:Natural gas Silicalite-1 Simulation Dynamic adsorption Pressure swing adsorption process

ABSTRACT In order to remove N2 from low quality natural gas,a mathematical model has been established by Aspen adsorption,using the CH4-selective sorbent silicalite-1 pellets.The dynamic adsorption isotherm was first simulated by breakthrough simulation of a CH4/N2 mixture at different adsorption pressures and feed flow rates based on breakthrough experiments.The resulting simulated CH4 dynamic adsorption amounts were very close to the experimental data at three different adsorption pressures (100,200,and 300 kPa).Moreover,a single-bed,three-step pressure swing adsorption (PSA) experiment was performed,and the results were in good agreement with the simulated data,further corroborating the accuracy of the gas dynamic adsorption isotherm obtained by the simulation method.Finally,based on the simulated dynamic adsorption isotherm of CH4 and N2,a four-bed,eight-step PSA process has been designed,which enriched 75% (vol) CH4 and 80% (vol) CH4 to 95% (vol) and 99% (vol),and provided 99% (vol) recovery.

1.Introduction

Natural gas is one of the important fossil fuels,and it is cleaner than coal or oil,having the highest H/C ratio,and its burning produces the least CO2per unit of energy,moreover,its lower sulfur and nitrogen contents also lead to lower SOxand NOxemissions[1-3].Faced with increasing energy demand in today’s global market and increasingly severe environmental problems,the effective use of natural gas is even more critical [4,5].However,natural gas is a mixture of multiple gases,its main component is CH4,which usually accounts for 75%-90%(vol)of the total,but N2is a common inert component,sometimes even reaching 25% (vol),greatly reducing the calorific value and increasing the transportation cost of natural gas,and so needs to be pre-separated [6-11].The separation of N2and CH4presents a significant challenge due to their relatively similar physical properties;they are both nonpolar gases with similar kinetic diameters (0.38 nm for CH4and 0.364 nm for N2) [12-14].

Normally,cryogenic distillation is a useful method for rejecting nitrogen,and is widely used commercially,but due to its high energy consumption,it is only suitable for large-scale processing[15,16].In contrast,pressure swing adsorption(PSA)is an alternative technology with promising potential because of its low energy consumption,relatively simple operation,and low equipment investment [17-19].However,it should be noted that currently used adsorbents rarely achieve the desired separation effect,and need to be assisted by an efficient PSA separation process.Research on PSA usually requires a combination of experiments and mathematical modeling in order to design and optimize the process or to evaluate the effect of the adsorbent,because the mathematical model can provide a good window for observing and understanding dynamic adsorption and desorption,effectively reducing the experimental cost,shortening the process cycle,and serving to guide practice by theory [20].

For example,the model can be used to estimate product recovery and purity,to explore the thermodynamics and kinetics of the adsorbent,to observe the material and temperature distribution in the bed,to study the influence of process parameters (feed rate,adsorption pressure,etc.) on PSA,and so on [21-28].Thus,it is essential to establish an accurate mathematical model.Xiaoet al.[18] enriched the CH4in a mixed gas of 75% (vol) CH4/25% (vol)N2to 90% (vol) purity,and achieved 90% (vol) recovery,using a kinetically nitrogen-selective molecular sieve carbon,MSC-3K 172,in a dual-reflux (DR) PSA process.Erden and co-workers[29] compared the results of three different four-bed,four-step PSA cycles,namely the heavy-end HR (HEHR),HEHR plus recycle(HEHR-Rec),and light-end HR plus Rec(LEHR-Rec),and by adopting the HEHR-Rec PSA cycle and BPL activated carbon,they succeeded in enriching the CH4in a mixed gas of 88% (vol) CH4/12%(vol) N2to 99.4% (vol) purity with a recovery of 99.2% (vol).

According to our investigation,there is no PSA study on CH4-selective molecular sieve to enrich CH4from a high ratio of CH4/N2mixture so far,and from our previous research [30],as a CH4-selective sorbent,silicalite-1 pellets exhibit very good CH4/N2separation performance.Moreover,the shape of these pellets avoids a huge pressure drop in the adsorption column.Indeed,we have proven that silicalite-1 pellets have good application prospects in the enrichment of CH4in low concentration coalbed gas,and a two-bed,six-step PSA process was designed to enrich 20%(vol)and 30%(vol)CH4to 40%(vol)and 57%(vol)with recoveries above 80%(vol)through the experiment and simulation method.In this work,through comparing breakthrough experiments and simulations,a 75% (vol) CH4/25% (vol) N2gas dynamic adsorption isotherm of silicalite-1 pellets has been obtained and verified,considering the competitive adsorption of CH4and N2in the adsorption bed.Based on the dynamic adsorption isotherm,a four-bed,eight-step PSA has been designed to reject N2from low-quality natural gas.

2.Experimental

2.1.Examination of the adsorption performances of the pure gas components

CH4and N2pure component adsorption isotherm data on silicalite-1 were acquired in our previous work [31].They could be fitted by the Langmuir-Freundlich (Eq.(1)) isotherm model in the framework of Aspen adsorption.

Here,qiis the amount of componentiadsorbed,Piis the partial pressure of componenti,anda1,a2,a3,anda4are constants.

2.2.Breakthrough experiments

The experimental set-up for mixed-gas dynamic breakthrough is shown in Fig.1.The inlet gas was 75% (vol) CH4/25% (vol) N2and 99.999%(vol)He,and each adsorption column(35 cm× 2.2 cm)was filled with adsorbent pellets(98 g).The physical properties of the adsorption bed,adsorbent,and gas are listed in Table 1 and Table 2,respectively.A gas mass spectrometer (Hiden Analytical,HPR-20 R&D) was used to monitor the composition of the outlet gas in real time,and a PC controlled the pneumatic valve and flow meter to realize automated control of the experiment.The adsorbent was activated at 423 K for 4 h,and then helium was used to purge the bed and lower the temperature until N2was not detected at the outlet;the temperature had then decreased to ambient (298 K).

Table 1Physical characteristics of adsorption bed and adsorbent

Table 2Gas model parameters

Table 3The effect of different values of Peclet number

Fig.1.The experimental device for dynamic breakthrough of mixed gas.

2.3.The single-bed,three-step PSA experiment

In the PSA experiment,a Programmable Logic Controller controlled switching of the pneumatic valve to realize automated circulation of the PSA.A buffer tank was added at the outlets of the upper and lower ends of the adsorption column,and a CH4concentration tester was used to detect the average CH4concentration of the outlet gas.The PSA experiment comprised three steps:pressurization (PR),adsorption (AD),and vacuum (VU).Of these,PR and AD lasted for 130 s in total,VU lasted for 130 s,and the two adsorption beds alternately performed 40 cycles until the average CH4gas concentration was almost constant at the top and bottom of the adsorption bed.

3.Modeling

3.1.Binary component adsorption model

The binary component adsorption isotherm was predicted on the basis of the pure component adsorption isotherm,using ideal adsorbed solution theory(IAST)(Eqs.(2)-(6)),which is an effective method based on a reasonable thermodynamic framework[13,32-37].

Here,is the standard-state pressure of pure componenticorresponding to the spreading pressure of the mixture,qTis the total amount adsorbed,andAis the specific surface area of the adsorbent.

3.2.Material,momentum,and energy balance models

Using Aspen adsorption to simulate breakthrough and PSA experiments,the adsorption bed,feed gas,product gas,valve,and gas pipe are shown in Fig.2.

Material,momentum,and energy-balance models were established in the adsorption bed system,solved by the Upwind Difference.Because PSA is a relatively complex system,the following reasonable assumptions were made when establishing the mathematical model.

(1) All the gases were regarded as ideal.

(2) Only the temperature,pressure,and velocity gradient in the axial direction of the bed were considered,ignoring radial changes.

(3) Uniform bed void ratio and adsorbent particle porosity were included.

Material balance (Eq.(7)) included axial gas diffusion,convection,accumulation in the bed porosity,and mass transfer with the adsorbent [38].

Here,εbis the bed void ratio,Daxis the axial dispersion coefficient,ciis the gas-phase concentration of componenti,zis the axial distance of the adsorbent bed,vgis the gas velocity,εpis the adsorbent particle porosity,tis the adsorption time,andqiis the adsorbed concentration of componenti.

As shown in Table 3,the degree of axial gas diffusion was determined by the type of gas flow,which was evaluated by the Peclet number (Eqs.(8)-(10)) [27].

Table 4Comparison of step time between PSA experiment and simulation

Table 5PSA process step timing diagram

Table 6Comparison of the simulation results of two PSA processes

Fig.2.Aspen Adsorption internal configuration diagram of breakthrough simulation.

Fig.3.75% (vol) CH4/25% (vol) N2 breakthrough experiment (dotted line) and simulation(solid line)at 298 K,100 kPa,500 ml·min-1 feed rate,based on the static adsorption isotherm.

Here,Dmis the molecular diffusivity,MAandMBare the relative molecular masses of A and B,andDV,AandDV,Bare the molecular diffusion volumes.In the following,the Peclet number was greater than 100,so the gas flow within the bed was regarded as a plug flow,and axial diffusion was ignored.

Gas energy balance(Eq.(11))included energy convection,accumulation of heat,heat transfer from gas to solid,and heat transfer from gas to the wall [39].

Here,Tgis the gas-phase temperature,T0is the ambient temperature,Tsis the solid-phase temperature,cv,gis the gas molar constant-volume heat capacity,ρgis the molar gas-phase density,hfis the heat-transfer coefficient between the gas and solid,hwis the heat-transfer coefficient between the gas and the wall,andDbis the bed diameter.

Solid energy balance (Eq.(12)) included the accumulation of heat,the heat of adsorption,and gas-solid heat transfer from the gas to the solid [39].

Here,cpsis the specific heat capacity of the adsorbent,and ΔHiis the heat of adsorption of componenti.

The pressure drop in the bed was calculated according to the Ergun equation (Eq.(13)) [30].

Here,τ is the adsorbent tortuosity factor,Mis the molar mass,and μ is the dynamic gas viscosity.

3.3.Mass-transfer model

In the mass-transfer equation (Eq.(14)),it was assumed that the mass-transfer coefficient was constant,consisting of two parts:one was the mass-transfer resistance formed by the gas passing through the boundary layer between the gas phase and the solid phase,and the other was the diffusion resistance of the gas in the internal pores of the adsorbent particles [40].

Here,qmiis the equilibrium adsorption amount,kiis the masstransfer coefficient,kfiis the film-resistance coefficient,calculated according to Eq.(15),andDpiis the effective gas-phase pore diffusion coefficient,calculated according to Eq.(16).

Here,Shiis the Sherwood number,Sciis the Schmidt number,andReis the Reynolds number.

Fig.4.Langmuir-Freundlich fitting curves of pure component static adsorption isotherms (dashed line) and adjusted adsorption isotherms (solid line) of CH4 and N2 at different temperatures.

Fig.5.75%(vol)CH4/25%(vol)N2 breakthrough experiment(dotted line)and simulation(solid line)at 298 K(a)100 kPa,300 ml·min-1(b)100 kPa,500 ml·min-1(c)100 kPa,700 ml·min-1 (d) 200 kPa,500 ml·min-1 (e) 300 kPa,500 ml·min-1,based on the adjusted adsorption isotherm (dynamic adsorption isotherm).

Here,Dkiis the Knudsen diffusion coefficient,andDmiis the multi-component molecular diffusion coefficient.

4.Results and Discussion

4.1.Breakthrough experiment and simulation

First,the breakthrough experiment was simulated at 100 kPa,298 K,and 500 ml·min-1feed (Fig.3),based on Langmuir-Freundlich fitting curves of pure component static adsorption isotherms(Fig.4,dashed line).The breakthrough times of N2and CH4were thereby evaluated as 150 s and 200 s,respectively.In the simulation,the breakthrough times of N2and CH4were both longer than those in the experiment,at 162 s and 228 s,respectively,because the dynamic adsorption capacity of the adsorbent was indeed smaller than its static adsorption capacity.Moreover,the inhomogeneity of the radial adsorption amount inside the adsorption column could be regarded as negligible during the experiment,due to the small diameter of the column and the high adsorption rate of the adsorbent.Hence,the decrease in adsorption capacity was only due to the dynamic adsorption process.This result showed that the simulation may incur great errors if the static adsorption isotherm was used for the dynamic adsorption process.

Fig.6.CH4 (a) and N2 (b) dynamic adsorption isotherm of 75% (vol) CH4/25% (vol) N2 gas at 298 K on silicalite-1 pellets.

Fig.7.Comparison of PSA experiment (black) and simulation (red and blue) results,red and blue line respectively represent the simulation using dynamic and static adsorption isotherm.CH4 recovery (a) and CH4 purity (b).

We attempted to simulate the dynamic adsorption isotherm from the relatively simple dynamic adsorption process of gas breakthrough.IP1is known to be the factor showing the least correlation with adsorption pressure and temperature in the Langmuir-Freundlich isotherm model.Therefore,IP1was adjusted to decrease the gas adsorption capacity of the adsorbent (Fig.4,solid line),and simulated breakthrough curves consistent with the experiment at different adsorption pressures and feed flow rates were thereby obtained.In Fig.5,taking the CH4breakthrough times as an example,the feed flow rates were 300,500,and 700 ml·min-1at 100 kPa,the CH4breakthrough times of the experiment were 330,200,and 155 s,respectively,and,surprisingly,the simulated CH4breakthrough times were close to the experiment data(332,199,and 152 s)(Fig.5(a)-(c)).Keeping the feed flow rate fixed at 500 ml·min-1,for adsorption pressures of 100,200,and 300 kPa (Fig.5(b),(d),(e)),the simulated CH4breakthrough times were 199,365,and 475 s,respectively,again very similar to the experimental data (200,360,and 470 s).Moreover,the same phenomenon was observed for N2at various adsorption pressures and feed rates,which showed the accuracy of the simulation.

Fig.8.First 120 s of the operation schedule of the four-bed eight-step PSA.

Based on the adjusted adsorption isotherms of CH4and N2(Fig.4,solid line),the competitive adsorption isotherms of 75%(vol)CH4/25%(vol)N2were predicted by IAST,which could be considered as the dynamic adsorption isotherms of the mixture.From the breakthrough curves of 75%(vol)CH4/25%(vol)N2at three different pressures of 100,200,and 300 kPa,the dynamic adsorption capacity of CH4in the mixture was also measured.In Fig.6a,the dynamic adsorption isotherm obtained by simulating breakthrough curves(solid line)was very close to the data directly measured in the breakthrough experiment (dotted line).On the contrary,the adsorption capacity of the mixed gas calculated from the pure component static adsorption isotherm (dashed line) was obviously higher than the dynamic adsorption capacity,which showed the feasibility of this method.As shown in Fig.S2 and Fig.S3 (in Supplementary Material),we applied this method to 55% (vol) CH4/45% (vol) N2mixture and found that it is still suitable.In addition,the gas dynamic adsorption data obtained by this method yielded a line,rather than a single point at a certain pressure.

4.2.Single-bed,three-step PSA experiment and simulation

Fig.9.CH4 adsorption amount on absorbent (a) and gas phase volume fraction (b) in a single cycle (480 s) of the adsorption bed (75% (vol) CH4/25% (vol) N2).

Based on the static and dynamic adsorption isotherms,a singlebed,three-step PSA was simulated.In Fig.7,the CH4product purity and recovery of PSA in the simulation were compared with the experimental results.When the feed rate was fixed at 2 L·min-1and the adsorption pressure increased from 100 to 200 kPa (Fig.7(a)),recoveries were 79% (vol) (115 kPa),93% (vol) (150 kPa),and 99% (vol) (200 kPa).The simulation results using the dynamic adsorption isotherm(81%(vol),94%(vol),and 99%(vol))were very close,whereas simulation results using the static adsorption isotherm showed significant error,amounting to 88% (vol),97%(vol),and 100% (vol),respectively.In Fig.7(b),the purities of the CH4product showed the same trend:the PSA simulation using dynamic adsorption isotherms was closer to the experiment.

Next,we compared the times required for each step in the PSA simulation and experimental process,especially the time required for PR,as shown in Table 4,and again found the PSA simulation using the dynamic adsorption isotherm to be almost the same as the experiment.For example,the PR time was 100 s(experiment),100 s (dynamic simulation),and 109 s (static simulation),respectively,at 115 kPa and 1.50 L·min-1.These results confirmed that the dynamic adsorption isotherm obtained by the above method was relatively reliable.

4.3.Four-bed,eight-step PSA simulation

Based on the dynamic adsorption isotherm,a more complicated four-bed,eight-step PSA process was designed to improve the purity and recovery of the CH4product.The adsorption bed performed the following eight steps in sequence.

(1) Pressurization with feed (PF).

(2) Adsorption (AD).

(3) Secondary adsorption (SA).

(4) Pressure equalization with depressurization (ED).

(5) Reflux with heavy component (RH).

(6) Vacuum (VU).

(7) Pressurization with light component (PL).

(8) Pressure equalization with pressurization (EP).

A schematic diagram of each step is shown in Fig.8,and the step sequence of each adsorption bed is shown in Table 5.Taking Bed 1 as an example,the feed gas first entered the bed for pressurization (PF),and the pressure remained constant during the adsorption process (AD).A part of the heavy component gas(CH4)in Bed 4 was then passed into Bed 1 from the bottom for secondary adsorption (SA).In this way,the bed was further utilized,and the adsorbed N2at the bottom of Bed 1 was partially replaced.The top of Bed 1 and the bottom of Bed 2 were then connected for pressure equalization (ED),because the CH4content at the top of Bed 1 was relatively high at this time,which prevented CH4from being wasted.Through the above steps,the inside of Bed 1 became filled with high purity CH4.Part of it was refluxed to Bed 3 for adsorption and replacement (RH),and the other part was used as product gas (VU).Finally,Bed 1 was pressurized by the light components flowing out from the top of Bed 2(PL)and pressure equalization by the pressurization step (EP).For the above complete cycle,the change in bed pressure with time is shown in Fig.S4.With 75%(vol)CH4/25%(vol)N2feed gas(1.6 L·min-1),an adsorption pressure of 280 kPa,and a desorption pressure of 10 kPa,a CH4product with 95%(vol)purity and 99%(vol)recovery was obtained.Moreover,under the same conditions,80% (vol) CH4/20% (vol) N2feed gas was enriched to 99% (vol) purity with 99% (vol) recovery,as shown in Table 6.

In order to analyze CH4concentration distribution in the adsorption bed,we simulated CH4adsorption amount on the absorbent and the corresponding gas volume fraction at different bed heights.As shown in Fig.9(a),at the end of the adsorption step at 120 s,the amount of CH4adsorbed was very low at the top of the bed,showing inefficient use of the adsorbent.After the second adsorption step from 120 s to 200 s,the bed utilization rate increased significantly.At 240 s,after the pressure equalization with depressurization step,the amount of CH4adsorbed at the top of the bed was very close to that at the bottom,indicating that the entire bed was almost fully utilized.Therefore,high purity CH4product gas could be obtained after vacuuming.In Fig.9(b),the CH4gas-phase volume fraction was seen to be almost zero at the top of the bed during the adsorption step (80-120 s),indicating that CH4would not flow out as waste gas,ensuring its high recovery

5.Conclusions

Applying the static adsorption isotherm of silicalite-1 pellets to simulate the breakthrough and PSA of a 75%(vol)CH4/25%(vol)N2mixture,the results were greatly divergent from the experiment.This was because breakthrough and PSA were both dynamic adsorption processes.The dynamic adsorption isotherm was obtained through mixed gas breakthrough simulations,and through experimental verification of two different concentrations CH4/N2we found that this method was accurate and believed that it could be applied to different concentrations of CH4/N2.Based on the dynamic adsorption isotherm,a four-bed,eight-step PSA process was designed,wherein silicalite-1 pellets still performed well in the rejection of N2from low quality natural gas.Indeed,the simulated CH4concentration distribution in the adsorption bed indicated why this process produced high purity and excellent recovery of CH4from low quality natural gas.

In the summer of 1937 there was a quiet wedding in France. The couple looked a bit nervous, especially the groom9, but only a year before he d been a king. Now he and his wife would be called the Duke and Duchess of Windsor.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2021.06.028.

Nomenclature

Aspecific surface area of the adsorbent,m-1

cigas-phase concentration of componenti,mol·m-3

cpsspecific heat capacity of the adsorbent,J·mol-1·K-1

cv,ggas molar constant-volume heat capacity,J·mol-1·K-1

Daxaxial dispersion coefficient,m2·s-1

Dbbed diameter,m

DkiKnudsen diffusion coefficient,m2·s-1

Dmmolecular diffusivity,m2·s-1

Dpieffective gas-phase pore diffusion coefficient,m2·s-1

DVMolecular diffusion volume,cm3·mol-1

dadsorption bed diameter,m

H0adsorption bed height,m

ΔHadsorption heat,kJ·mol-1

hfheat-transfer coefficient between the gas and solid,W·m-2·K-1

hwheat-transfer coefficient between the gas and the wall,W·m-2·K-1

kfifilm-resistance coefficient,W·m-1·K-1

kimass-transfer coefficient,W·m-1·K-1

Mirelative molecular masses of componenti,g·mol-1

PePeclet number

qmiequilibrium adsorption amount,mol·g-1

qTtotal amount adsorbed,mol·g-1

qiadsorbed concentration of componenti,mol·kg-1

ReReynolds number

rpparticle radius,m

rporeaverage pore size,m

ScSchmidt number

ShSherwood number

Tggas-phase temperature,K

Tssolid-phase temperature,K

T0ambient temperature,K

vggas velocity,m·s-1

μ dynamic viscosity,N·s·m-2

ρgmolar gas-phase density,kg·m-3

ρsbulk density,kg·m-3

εbbed void ratio

εpparticle porosity

τ adsorbent tortuosity factor