Colin A.Scholes ,Shufeng Shen

1 Department of Chemical Engineering,The University of Melbourne,VIC 3010,Australia

2 School of Chemical and Pharmaceutical Engineering,Hebei University of Science and Technology,Shijiazhuang 050018,China

Keywords:Membrane Contactor Carbon dioxide Desorption Two phases Mass transfer correlations

A B S T R A C T Membrane gas-solvent contactors are a hybrid technology combining solvent absorption with membrane gas separation,which demonstrates potential for CO2 capture through the ability of the membrane to rigidly control the mass transfer area.Membrane contactors have been successfully demonstrated for CO2 absorption,and there is strong research interest in using membrane contactors for the complimentary CO2 desorption process to regenerate the solvent.However,understanding and modelling the various stages of mass transfer in the desorption process is less well-known,given the existing mass transfer correlations had been developed from absorption experiments.Hence,mass transfer correlations for membrane contactors are reviewed here,and their appropriateness for desorption analysed.This is achieved through simulating CO2 desorption through a membrane contactor from loaded 30wt%monoethanolamine solvent to enable comparison of the correlations.It was found that the most cited correlations by Yang and Cussler were valid for shell side parallel flow,while that of Kreith and Black was viable for shell side cross flow.A limitation of all of these correlations is that they assume single phase flow on both sides of the membrane;however,the high temperature of CO2 desorption can lead to partial solvent vaporisation and hence two phases present on one side of the membrane contactor during desorption.A mass transfer correlation is established here for two phase parallel flow on the shell side of a membrane contactor,based on experimental results for three composite and one asymmetric hollow fibre membrane contactors stripping CO2 from loaded MEA at 105–108°C.This correlation is comparable to that reported in the literature for mass transfer in other two phase systems,but differs from the standard format for membrane contactors in terms of the exponent on the dimensionless Schmidt and Reynolds numbers.

1.Introduction

Membrane gas solvent contactors for CO2capture are able to combine the high selectivity for CO2of a solvent absorption process within the compact module of a membrane[1,2].This is achieved by a semipermeable membrane separating the solvent and gas phases,and hence the mass transfer area per unit volume is significantly higher than a traditional solvent column,while the phases'flows are strictly controlled within the membrane module to avoid flooding and entrainment[3].These advantages have made membrane contactors attractive alternatives to traditional solvent absorption processes,with a number of pilot plants trialled[4–6].The majority of membrane contactor research for CO2capture has focused on the absorption process using both porous and non-porous membranes with various solvents[7],with recent studies emphasising the benefits of non-porous membranes[8–11].Importantly,this research has demonstrated that membrane contactors'can reduce the required volume of equipment needed to undertake CO2absorption compared to traditional solvent columns,which is known as process intensification[12].This is important in many carbon capture situations where space is limited,such as offshore platforms.Regeneration of the CO2loaded solvent(i.e.,stripping)through a membrane contactor is less reported in the literature,though a number of recent studies have demonstrated the feasibility[13–17].The major advantage of membrane contactors in solvent regeneration is the ability to remove the CO2from the solvent(Fig.1),through either the permeate gas phase being under vacuum or applying a sweep gas of steam[16,18].Critically,for membrane contactors undertaking solvent regeneration the overall mass transfer is strongly dependent on the temperature and hence phase of the loaded solvent.At the boiling temperature of the solvent the overall mass transfer for CO2,removal is two orders of magnitude greater than that observed at lower temperatures[19].This is because the loaded solvent has partially vaporised,and there is two phase flow within the membrane contactor promoting mass transfer.This situation can be partially avoided by using non-volatile solvents,and hence,there is no vaporisation of the solvent during desorption,as demonstrated by Mulukutla et al.[17]Hence,for CO2desorption,it is possible to operate a membrane contactor with the solvent in the liquid or vapour phase,impacting separation performance and operating conditions.

Fig.1.Schematic of membrane gas-solvent contactors undergoing CO2 desorption and solvent regeneration and the stages of mass transfer resistance.

A number of mass transfer correlations have been developed for membrane contactors undertaking absorption,and there is the potential for them to be applicable in CO2desorption.However,modelling mass transfer in a gas-solvent membrane contactor where two phase flow is present has not been addressed in the literature,to the best of the authors knowledge;though such correlations are vital for simulating a large scale process for CO2solvent regeneration and for determining process optimisation and intensification.

This investigation aims to present a critical review of absorption mass transfer correlations developed for membrane contactors in terms of solvent desorption,and hence provide insight into their suitability for modelling membrane contactors performing CO2desorption from a loaded solvent.Importantly,the presented correlation models are applied to a theoretical CO2desorption process and the performanc e compared to evaluate which correlations are the most appropriate.This investigation will also address the lack of mass transfer correlations for two phase flow within a membrane module,through modelling of experimental data for three composite and one asymmetric membrane contactors stripping CO2from loaded 30 wt%monoethanolamine(MEA)where the solvent was partially vaporised.

2.Theory

For the desorption of CO2through a membrane contactor,the molar flux(N)is given by:

where KOLis the overall liquid phase mass transfer coefficient,and ΔCLMrepresents the log mean average of the concentration driving force between the solvent and gas phases.The overall mass transfer across a non-porous membrane consists of four mass transfer stages(Fig.1),the transfer of CO2across the solvent boundary layer,the transfer of CO2through the non-porous membrane,the transfer of CO2through the membrane's porous support and finally the transfer of CO2across the gas phase boundary layer(Fig.1).Each stage acts as a resistance to mass transfer and hence the overall mass transfer coefficient(KOL)can be expressed as a sum of the resistance of each stage[15,20]:

where kg,kps,kmand klare the gas,porous support,membrane and liquid side physical mass transfer coefficients respectively,H the dimensionless Henry's Law constant,E is the enhancement factor for the reaction producing CO2and d0,diand dInare the outer,inner and logarithmic mean diameters of the membrane fibre.The mass transfer in the gas boundary layer is orders of magnitude faster than that of the membrane,porous support and solvent boundary layer, and so it is often assumed negligible.

2.1.Mass transfer in the porous support

The transport of CO2through the pores of the membrane support layer is well-established,and the mass transfer coefficient corresponds to[21]:

where DCO2is the diffusivity of CO2in the pores;δpsis the thickness of the support layer;ε is the porosity of the support layer,and τ is the tortuosity of the pores.The diffusivity is dependent on the pore size;with CO2following Knudsen diffusion in smaller pores while in larger pores bulk diffusion is appropriate.This is dependent on the Knudsen number of CO2,which is a function of mean free path and pore size[22].For most porous supports,diffusion is based on bulk flow because of the relative size of the pore channels,but the porous structure does restrict diffusion by increasing the effective path length through the structure[23].The tortuosity of the support layer is often related to the porosity[24]:

These equations are valid for a membrane contactor undergoing solvent desorption at elevated temperature since they are based on standard diffusion through a constrained geometry.

2.2.Mass transfer in the non-porous membrane

Mass transfer through the non-porous membrane layer is by the solution-diffusion mechanism[25],which is dependent on both the diffusivity of CO2within the non-porous layer as well as CO2solubility within the membrane material.These two parameters are combined and reported as a membrane's permeability(P),which represents a pressure independent measurement of gas transport through a non-porous polymer film.Hence,the mass transfer coefficient for the non-porous membrane is related to the permeability[8]:

where δmis the thickness of the membrane layer,and vmis the molar volume of the gas(m3·mol-1).This mass transfer coefficient is valid for contactors based on non-porous membranes undergoing solvent desorption,given the solution-diffusion mechanism is valid over wide range of temperature and pressure conditions.

2.2.1.Mass transfer for solvent flow in the lumen

For solvent flow in the lumen side of the hollow fibre membrane,mass transfer through the solvent boundary layer is well-established through the Leveque correlations,which are analogous to heat transfer[26,27].The correlations are based on the Reynolds and Schmidt dimensionless numbers,with two options available dependent on the Graetz Number(a measurement of where laminar flow has been established in the fibre).The Reynolds number for solvent flow inside the lumen is:

where ρ is the density of the solvent;u is the solvent velocity,and μ is the solvent viscosity.The Leveque correlations determine the Sherwood number of the system,which is the dimensionless ratio describing the convective to diffusive mass transfer.The Leveque correlations are applied extensively in membrane contactor systems for both gas–solvent separation and solvent–solvent extraction,in part because of the well-defined flow regimes that are established within a tube geometry.Two alternative correlations have also been presented in the literature by Kreulen et al.[28]and Sieder et al.[29].These correlations were developed for membrane contactors and are alternatives to the Leveque correlation.The three correlations are summarised in Table 1,along with the conditions over which they are valid.

Table 1 Correlations for lumen-side mass transfer in membrane contactors

Comparison of the lumen side mass transfer correlations are provided in Fig.2,based on a PDMS contactor module(details in Table 2)for CO2desorption from loaded 30wt%MEA solvent at 90°C,as a function of Reynolds number.A comparison of the Leveque and Sieder correlations reveals that both have similar profiles of increasing mass transfer coefficient with Reynolds number,with the Sieder correlation consistently having a coefficient 0.0005 m·s-1higher than the Leveque correlation.The Kreulen correlation under laminar flow is substantially higher than either the Leveque or Sieder correlations,as flow transitions to turbulent the Kreulen correlation approaches the other two correlations results.Hence,the comparison of the different correlations presented indicate that for membrane contactors undertaking CO2desorption from solvents the Leveque correlation is likely to be the most consistent model.

Fig.2.Mass transfer coefficient(m·s-1)for CO2 desorption through the PDMS membrane module for lumen flow from 30wt%MEA at 90°C,based on literature correlations in Table 1.

Table 2 Contactor specifications for asymmetric PDMS membranes,based on commercial modules[19]

2.2.2.Mass transfer for solvent flow in the shell

For solvent on the shell side of the membrane contactor,the geometry and arrangement of the fibres impact the fluid flow pattern,and hence,mass transfer through the boundary layer is complex.The shell-side mass transfer coefficient can be predicted from the Sherwood number based on a general expression of the packing density(φ),contactor diameter relative to length and the dimensionless Reynolds and Schmidt numbers[22]:

where dhis the hydraulic diameter and l the length of the module,and A is a constant.The definition of the mass transfer correlation is dependent on the flow regime,parallel or cross flow(Fig.3).Parallel flow is along the fibres and corresponds to counter current arrangement,while cross flow is tangential flow across the fibres,which is often established inside a module through a baffle arrangement.The definition of Reynolds number is different for both flow regimes,taking into account solvent velocity and hydraulic diameter.For parallel flow,Reynolds number is defined as[30]:

Fig.3.Parallel flow and cross flow arrangements in hollow fibre membrane modules.

and for cross flow[31]:

where ρ is density,Q volumetric flowrate,n number of fibres in the module,doutthe outer diameter of the fibre,dcinthe inner diameter of the module,dcothe outer diameter of the central tube for cross flow,l the length of the fibre and η the viscosity.Generally,cross flow arrangement achieves greater mass transfer than parallel flow because of the difference in the boundary layer formed on the membrane fibre surface;and two sets of correlations have been reported in the literature for both flow regimes.

Correlations for mass transfer in the solvent boundary layer for parallel flow on the shell side of membrane modules reported in the literature are summarised in Table 3,along with the conditions over which they are valid.All correlations have the Schmidt number exponent of a third.In contrast,the exponent on the Reynolds number in the correlations are various numbers less than 1,but always greater than the Schmidt number.These exponent values indicate that while mass transfer increases with increasing Reynolds and Schmidt numbers,the rate of increase reduces with higher values.

Yang and Cussler have undertaken an extensive study of parallel flow in contactor shell side over a large range of Reynolds number and determined three correlation equations for flows from laminar to turbulent[26].In contrast,other authors have put forward specific correlations that are well within the laminar region, except the Kartohardjono correlation which is stated by the authors to be for turbulent conditions[35].Included in the table is a measure of the impact of each correlation based on the number of citations in the literature(Scopus,November 2017).This indicates the relevance of each correlation to the membrane contactor field and can be used as a guide for validity.The number of citations for the Yang and Cussler correlation clearly indicates that they have been widely applied to membrane modules,but this may be in part be due to the three correlations presented cover a wide range of flow conditions,and the study was one of the earliest published.The Prasad correlation also has been cited extensively in the literature,which is also attributed to it being one the first papers in this field being published only 2 years after Yang and Cussler.

A comparison of the shell side correlations for mass transfer under parallel flow conditions is provided in Fig.4,for the PDMS module desorbing CO2from loaded 30wt%MEA solvent at 90°C.The comparison clearly demonstrates a similar mass transfer coefficient for the Al-Saffar,Li as well as Yang and Cussler correlations over the Reynolds number range studied.Hence,the good agreement strongly supports their suitability for modelling mass transfer on the shell side when studying CO2desorption from a loaded solvent at high temperature.The Prasad correlation calculates a significantly lower mass transfer coefficient than the other correlations;this is attributed to inclusion of fibre packing density in the equation.The PDMS model system has a very high packing density compared to the experimental system reported by Prasad[33].This result highlights the importance of matching module packing density with the appropriate correlation.In contrast,the Fang correlation calculates a substantially higher mass transfer coefficient,which is approaching the performance of a cross flow module.There is no readily available explanation for this behaviour,but it is likely that a mixture of parallel and cross flow regimes exist within the experimental Fang membrane system,giving rise to greater mass transfer and hence the substantially different correlation performance.

Fig.4.Mass transfer coefficient(m·s-1)for CO2 desorption through the PDMS membrane for 30wt%MEA at 90°C under parallel flow in the shell,based on literature correlations in Table 3.

Table 3 Correlations for shell side mass transfer in parallel flow membrane contactors

For cross flow in membrane modules,the mass transfer correlations are summarised in Table 4,along with the conditions over which they are valid.Similar to parallel flow,the Schmidt number exponent is a third,which is common for most mass transfer correlations.However,the Reynolds number exponent is reduced compared to the parallel flow correlations,indicating the stronger contribution momentum transport has in mass transfer in the boundary layer through tangential flow.Again,the literature citations are included with each correlation to provide a measure of impact and validity.The Yang correlation was published by Yang and Cussler,but is shortened to the one author here to avoid confusion with the correlations already presented for parallel flow.Importantly,the difficulty of establishing viable cross flow in a membrane contactor,through baffles,means that the Reynolds numbers range studied are small compared to other flow systems.The number of citations indicates the Yang correlation has been used extensively in the literature,but again this may be attributed to it being one of the first published studies of cross flow behaviour.The Mauvoudi correlation is also reasonably well-cited,given that it was published 11 years ago and 20 years later than Yang;similarly the Wickramasinghe correlations published in 1992 have been widely cited in the literature,given that it was published 6 years after Yang.

Table 4 Correlations for shell side mass transfer in cross flow membrane contactors

A comparison of the correlations is provided in Fig.5,for the PDMS membrane module desorbing CO2from 30wt%MEA at 90°C.The resulting mass transfer is an order of magnitude greater than that observed for parallel flow(Fig.4),because of the reduced thickness of the solvent boundary layer in tangential flow.The Kreith and Black,Mauvoudi and Wickramasinghe correlations have similar mass transfer coefficients over the Reynolds number range in which they are valid.In contrast,the Yang correlation produces a higher mass transfer at low Reynolds numbers,but approaches the Kreith and Black correlation at Reynolds numbers greater than 100.The Zheng correlation result leads to a significant higher mass transfer coefficient compared to the other correlations over its Reynolds No.range.The reason for this discrepancy is unknown.The comparison indicates that the Kreith and Black correlation is a reasonable model to apply to CO2desorption from a loaded solvent at elevated temperature for cross flow behaviour,given it is valid over a wide range of Reynolds numbers and is comparable with other models.

2.3.Mass transfer for two-phase flow in the lumen

Fig.5.Mass transfer coefficient(m·s-1)for CO2 desorption through the PDMS membrane for 30wt%MEA at 90°C under cross flow in the shell,based on literature correlations in Table 4.

The desorption of CO2from a solvent is generally undertaken at elevated temperatures to reverse the CO2-solvent reaction.Previous mass transfer correlations for the solvent side are based on liquid phase behaviour,when the temperature is high enough to enable CO2stripping but not great enough to vaporise the solvent.However,it is most likely that membrane contactors for CO2desorption will be operated at temperature conditions that correspond to partial vaporisation of the solvent.This will result in two phases being present within the module's lumen or shell side.The presence of two phases will significantly impact the mass transfer,because the boundary layer present will be unstable and consist of a mixture of liquid and gas phases[43,44].As such the previously presented correlations for mass transfer are not valid under these conditions.

Pecherkin and Chekhovich have derived a correlation for mass transfer in tube(or lumen)flow when two phases are present[45]:

where the Reynolds,Schmidt and Sherwood number parameters are based on the solvent phase.This correlation was derived from the corresponding heat transfer model,similar to the Leveque correlations presented for solvent phase lumen flow(Table 1).The Pecherkin and Chekhovich correlation assumes a liquid boundary layer on the membrane through which mass transfer occurs.As a consequence this assumes that there is no gas phase boundary layer under these conditions.This assumption is needed given two phases are present in the lumen and the actual boundary layer may consist of both phases,but the proportion of membrane surface coverage and thickness of each phase's boundary layer is unknown.The correlation has the standard format based on the Reynolds and Schmidt numbers;however the exponent of the Schmidt number is a quarter,lower than that reported for correlations for a single phase.This Schmidt number exponent is also seen for other two phase mass transfer correlations in channels with complex configurations[45,46].In contrast,the Reynolds number has an exponent of unity,with the higher exponent in part to account for the increase mass transfer through the gas phase proportion as well as the dominance inertia forces have on the process.This correlation is the only available model for predicting mass transfer in two phases within the lumen side of the membrane contactor,which can be used for CO2desorption from a partially vaporised solvent.

3.Results and Discussion

A corresponding two phase mass transfer correlation on the shell side of a membrane module can be determined from experimental data;as to the authors'best knowledge,no such correlation has previously been reported in the literature.Three membrane contactors based on composite PTMSP,PIM-1 and Teflon AF1600 on a porous PP support as well as an asymmetric PDMS membrane contactor have been trialled for CO2desorption from loaded 30wt%MEA on the shell side.Details of these experiments have been previously published[18,19].Here,CO2desorption results are presented for the four membrane contactors operating at temperatures between 105 and 108°C,corresponding to two phases present on the shell side in parallel flow.Experimental details can be found elsewhere[18,19],and details of the contactors are provided in Table 5,which have also previously been reported in the literature.These modules were constructed in-house and have low packing density.

Table 5 Membrane contactors specifications for shell side two phase flow

Fig.6.Overall mass transfer coefficient(m·s-1)for CO2 desorption from 30wt%MEA between 105 and 108°C,for PDMS,PTMSP,PIM-1 and Teflon AF1600 membrane modules.

The overall mass transfer coefficients of the four membrane contactor are provided in Fig.6,where the data are presented as Reynolds numbers based on solvent parameters.The data set for the PDMS membrane was previously reported as the solvent being vaporised[19],but has been recognised by the authors to consist of a two phase flow;while the composite membrane results have not previously been published.The three composite membranes have very similar performance given the same porous support,membrane area and contactor length;with the only difference being the active layer.The PTMSP and PIM-1 membranes have a slightly higher overall mass transfer coefficient than Teflon AF1600,because these two polymers have ultra-high porosity with much greater CO2permeability than Teflon AF1600[47,48].The asymmetric PDMS contactor has a higher overall mass transfer compared to the other three modules because of a thinner active layer and difference in membrane configuration.For all four membranes,the overall mass transfer increases with Reynolds number,because of the corresponding reduction to the shell side boundary layer.Importantly,these reported overall mass transfer coefficients are greater than those observed when the contactors were operated below the boiling temperature of the solvent[18,19],and hence,the presence of two phases in the shell side results in greater mass transfer performance.

Assuming the mass transfer through the gas boundary layer is negligible and mass transfer through the non-porous and porous membrane layers can be modelled as gas transport by the correlations reported above;then the mass transfer coefficient through the two phase boundary layer can be calculated,and is provided in Fig.7 as the corresponding Sherwood number.For all four modules there is a clear trend between the Reynolds and Sherwood numbers,and all four contactor data points associate with each other implying that the behaviour within the shell side is comparable for all four systems.This is partly due to the similar modular nature of the four membranes,given that they were constructed in-house,which enables a correlation to be formulated.Assuming the Schmidt number exponent is a quarter,as reported for two phases in the lumen side,then the correlation for two phase parallel flow on the shell side of the module was determined to be:

Fig.7.Wilsons plot of the mass transfer coefficient in two phase flow on the shell side,with the Reynolds number based on solvent parameters.

This correlation is valid for Reynolds number 400 to 2200,and module packing density of 0.25 to 0.42.The Reynolds number exponent is high compared to that observed for single phase correlations(Table 3),representing the importance of inertia forces on mass transfer in two phase systems.The correlation's small pre-exponential factor is partially attributed to the low packing density of the membrane modules,and it would be expected that a larger value will be observed for a more densely packed module.Importantly,this correlation can assist in modelling membrane contactors for CO2desorption where there is partial vaporisation of the solvent on the shell side of the module.

4.Conclusions

Membrane contactors are a viable technology for undertaking CO2desorption from loaded solvents and achieving solvent regeneration.To maximise CO2flux the mass transfer through the various stages of the process must be known,with the greatest unknown attributed to the solvent boundary layer.When the solvent is in the lumen side of the membrane,the mass transfer can be modelled through wellestablished Leveque correlations for tube flow.However,when the solvent is on the shell side of the module,the corresponding correlation is not clear and dependent on the flow regime.A comparison of the reported correlations in the literature has been presented and a few key correlations have been highlighted for their suitability,based on relative performance.Importantly,two phase flow is possible in CO2desorption processes because of the elevated temperature.A two phase mass transfer correlation has been established for flow on the shell side of a membrane module,based on a general expression format established from experimental data for four membrane modules stripping CO2from 30wt%MEA.