Long term filtration modelling and scaling up of mixed matrix ultrafiltration hollow fiber membrane: a case study of chromium(VI) removal

Author’s Accepted Manuscript Long term filtration modelling and scaling up of mixed matrix ultrafiltration hollow fiber membrane: a case study of chromium(VI) removal Raka Mukherjee, Prasenjit Bhunia, Sirshendu De www.elsevier.com/locate/memsci

PII: DOI: Reference:

S0376-7388(18)31443-1 https://doi.org/10.1016/j.memsci.2018.10.026 MEMSCI16542

To appear in: Journal of Membrane Science Received date: 25 May 2018 Revised date: 7 October 2018 Accepted date: 8 October 2018 Cite this article as: Raka Mukherjee, Prasenjit Bhunia and Sirshendu De, Long term filtration modelling and scaling up of mixed matrix ultrafiltration hollow fiber membrane: a case study of chromium(VI) removal, Journal of Membrane Science, https://doi.org/10.1016/j.memsci.2018.10.026 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Long term filtration modelling and scaling up of mixed matrix ultrafiltration hollow fiber membrane: a case study of chromium(VI) removal

Raka Mukherjee, Prasenjit Bhunia, Sirshendu De* Department of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur – 721302, India *

Corresponding author: Tel: +91-3222-283926; fax: +91-3222-255303, [email protected]

Abstract Mixed matrix membrane (MMM) belongs to the special class of filter where adsorptive removal of smaller sized solutes is realized by more open pore sized ultrafiltration grade membrane operated at higher throughput. Incorporation of nanoparticles having adsorption tendency towards a specific smaller sized solute in the polymer matrix is responsible for such a behavior. Since solute adsorption is the dominant mechanism of removal, the breakthrough behavior of the membrane dictates its life indicating its regeneration or eventual replacement. Thus, quantification of long time fouling behavior of a scaled up MMM filter is of utmost importance. A detailed two-dimensional transient model is formulated in this work starting from first principles using equations of continuity, motion and convective-diffusiveadsorption based solute transport for filtration through hollow fiber MMM module. The set of governing equations is solved using finite element method by COMSOL v5.3® software package. A case study was considered for adsorptive removal of chromium(VI) using graphene oxide incorporated MMM hollow fibers. The model parameters were evaluated using the experimental long term filtration data of synthetic chromium(VI) solution. The same set of model parameters was used in predictive mode to quantify the long-term performance behavior of a real life chrome tanning effluent that showed remarkable predictive capability of the model in terms of throughput and rejection characteristics of chromium(VI). The validated model is further extended for simulation of large scale filter with high breakthrough volume interrelating number and length of fibers (nf and L) with the operating conditions (trans-membrane pressure drop, TMP and cross flow rates, CFR) so that 1

the filter can sustain its performance over long period of time (i.e., long filter life). Based on the simulation, at a fixed TMP and CFR, a performance curve was generated linking nf, L and breakthrough volume of the filter that can be used as a guideline for designing of large scale filtration units with hollow fiber MMM for industrial applications. In general, the theoretical framework formulated in this work can be used as a foundation for design and scale up of any hollow fiber MMM based filtration system. Keywords: Mixed matrix hollow fiber; transport-adsorption model; scale-up; graphene oxide; Cr(VI).

1.

Introduction Toxic and carcinogenic heavy metals, like chromium (Cr), cadmium, copper and

lead are some of the most dangerous pollutants identified by US Environmental Protection Agency [1-2]. Several methods have been investigated for their removal, including chemical precipitation, ion exchange, adsorption and electrochemical precipitation [3-6]. Limitations, like toxic by-product, low throughput, high energy requirement, need of pre and post processing [7-9] demand a continuous, high throughput and low energy intensive process for commercial application.

2

Membrane technology, being a physical separation process, can be an attractive solution to this challenge. However, removal of small sized cations requires dense membranes, like reverse osmosis/nanofiltration where low throughput and high transmembrane pressure drop are the limiting factors [10]. Such issues can be circumvented by designing a suitable mixed matrix open pore ultrafiltration (UF) membrane combining adsorption ability of the dopant, specific towards the target pollutant and general filtration capability of the membrane to sieve large sized pollutants, simultaneously [11, 12]. Preparation and application of hollow fiber mixed matrix membranes are the state of the art technology in such applications due to their immense potential for direct scaling up requiring low transmembrane pressure drop realizing high throughput. Similar to any adsorption-based process, mixed matrix membrane (MMM) has a certain lifetime, beyond which the concentration of contaminant exceeds the safe limit, known as breakthrough time. Total volume of water processed before reaching breakthrough time is the breakthrough volume. Implementation of such mixed matrix hollow fiber based system in large scale needs methodical upscale strategy, so that sufficient volume of contaminated stream can be processed before reaching breakthrough for commercial and technical viability. This objective can be achieved by considering a detailed modelling of the filtration system from first principles capturing the physics of fluid flow and mass transport. Modelling in MMM is available by considering one dimensional transient mass transport inside the membrane phase in case of a flat sheet membrane and hollow fiber [13, 14]. However, details like effect of fluid flow in the flow channel, transmembrane pressure drop, coupling of velocity and concentration field, effect of osmotic pressure and most importantly effect of (flow) channel length were not considered in those analysis. Additionally, in the analysis presented in above works, permeate flux was considered as invariant. It is needless to mention that forecasting long-term behavior of the filtration system is necessary with sustainable operation. On the other hand, there are reported studies where sufficient detailed models are available to predict the short-term behavior of MMM which have little significance in terms of sustainable applicability [15-17]. In order to fill this gap, the present work is undertaken to develop a comprehensive three-dimensional (two dimensions in space and one dimension in time) model from first principles considering transport in flow channel as well as the porous membrane phase for hollow fiber MMM. The model is exploited to achieve the appropriate scaling up in large scale sustainable filtration. Finally, performance curves are generated inter-relating the number of fibers, their length and breakthrough 3

volume for long-term operation. The model was validated by conducting experiments for Cr(VI) removal from synthetic solution as well as real life tannery effluent using graphene oxide (GO) incorporated MMM hollow fiber system. 2.

Theoretical development The mathematical model is segregated into two parts which are coupled at the

membrane solution interface (see Fig. 1). In Domain 1 (

;

), two-

dimensional time dependent velocity and concentration profiles are solved. However, in the porous medium, domain 2 (

, only the convective-diffusive-adsorptive solute

balance equation is solved considering the Darcy velocity (which is a function of

and not )

through the membrane. An axis-symmetric cylindrical ( , ) system is selected to model the mass transport in the hollow fiber membrane geometry. The dimensional equations with the relevant boundary conditions are presented first, followed by the non-dimensionalized system which are solved numerically. = 0

=

= 0

Line of symmetry Domain 1

Feed inlet

Retentate outlet

= Domain 2 =

+ Permeation

Permeation

Fig. 1: Schematic of the membrane filtration system for symmetric and cylindrical hollow fiber. 2.1 Governing equations Domain 1 (fluid channel): The incompressible Navier-Stokes equation in -direction is given as (ignoring the since the aspect ratio of the channel (

)

[

term

is too small), (

)

]

4

(1)

Similarly, the equation of motion in the -direction (

(

)

[

(

) is,

)]

(2)

The equation of continuity is, (3) From above three equations, the three unknown variables

,

and

are to be solved subject to the following boundary and initial conditions. (i) Symmetry condition: at (ii) At

for all

.

for all (membrane surface):

(no-slip) and

(which is coupled

with domain 2 by the Darcy velocity). (iii) At the entrance of the channel (iv) To solve for

for all

and

we need one boundary condition in

. which is given at

. (v) At

,

.

The average flow velocity,

is obtained by dividing the cross-flow velocity by internal

cross-sectional area of the membrane membrane module and

, where

is the number of fibers in the

is the inner radius of the fiber.

The solute transport equation (once again ignoring the second order term in ) is, [

(

)]

(4)

The above equation is subjected to the following initial and boundary conditions: (i) at (ii) at r = 0;

, , 5

(iii) at

|

;

|

(from the mass balance at the membrane

surface), (iv) at

for all .

Domain 2 (membrane): In this porous medium domain, we make an assumption that the membrane wall thickness ( ) is smaller compared to the core radius (

) and flow is uni-directional in

direction.

Therefore, the Darcy velocity is presented as [

]

Where,

(5)

(trans-membrane pressure); [15]. Here,

[|

is expressed as

of the cation and anion of the salt;

|

|

and

|]

, where,

and

are the valence

denote ideal gas constant, operating

temperature and molecular weight of the salt. Values of in Table 1.

and

and other parameters are presented

in adsorption resistance is presented as

∫

. The species

convective-diffusive-adsorptive equation within membrane phase is [ Here,

(

)]

(6)

is the porosity of the membrane, and

is the diffusivity of the contaminant through

the membrane matrix. Considering the flow is unidirectional in the r-direction, the above equation is reduced to ( where,

)

(7)

is the amount of solute adsorbed given by the adsorption kinetics [18, 19], (8)

At equilibrium (

), the above equation is simplified to the Langmuir isotherm

equation, expressed as: 6

(9) where,

(l/mg) and

and (i) at

(mg/g) are the maximum adsorption capacity. Values of

are presented in Table 1. Eq. (7) is solved with the boundary conditions: |

;

|

(mass balance at the membrane-solution

interface), (ii) at

;

0,

(iii) at

.

It should be mentioned here that Eq. (7) is one dimensional in space. However, because of the interface boundary condition at function of adsorption

, which is dependent on , solute concentration

is a

. Since, the adsorption kinetics ( ) is dependent on c, the solute is a function of

.

2.2 Non-dimensionalization In this section, the non-dimensional forms of the key equations are presented, using the following scaled variables, ̅

̅

̅

̅

̅

7

and ̅

.

Domain 1 The continuity equation, Eq. (3) is modified as,

̅

̅

̅ ̅ ̅

(10)

̅

The momentum balance equations, Eqs. (1) and (2) in the and ̅

(

̅

̅

(

̅

̅

̅

̅

̅

̅

̅ ̅

̅

̅

̅

̅

) ̅

̅

̅

( ̅

̅

) ̅

̅

̅

̅ ̅

directions become,

)

(11)

̅

( ̅

̅

)

̅ ̅

(12)

The unknowns, ̅ ̅ ̅ are solved subject to the boundary and initial conditions: ̅

(i)

at ̅

;

(ii)

at ̅

;̅

(iii) at ̅

̅

,

̅

and

̅

, ̅ ̅

̅

(iv)

̅

̅

̅

̅ ̅

, where ̅

,

̅

In reality,

so the transient terms in Eqs. (11) and (12) can be ignored. However, the

boundary condition at ̅

, is a function of , making ̅ and ̅ as function of

including ̅

and ̅. Non-dimensionalization of advection-diffusion equation, Eq. (4) is written as: ̅

(̅

̅

̅

̅

̅

̅

) ̅

̅

̅

( ̅ ̅

)

(13)

The relevant boundary and initial conditions are: (i)

at

(ii)

at ̅

̅ ̅

,

(iii) at ̅ (iv) at ̅

.

̅

̅

|̅ ̅

̅

|̅

̅ ̅ ̅

̅

8

.

Domain 2 After non-dimensionalizing Eq. (5), it is transformed to ̅

̅

̅

(14)

̅

( ̅|

̅

where, and ̅

and

̅

̅| ̅

) ̅

̅ ̅

̅

̅. Non-dimensionalizing Eq. (7), with the dimensionless parameters

∫

̅

̅

, the following equation is resulted, ̅ ̅

̅

̅

̅

( ̅ ̅

)

(15) ̅

It may be noted here that

. In order to solve for , we need to incorporate

the non-dimensionalized form of Eq. (8), as ̅

(16)

where,

(i) at ̅

and

, ̅

̅

̅

̅| ̅

̅

̅

(ii) at ̅ (iii)

̅|

. The non-dimensional boundary and initial conditions are,

and

̅ ̅ ̅

(coupled interface with domain 1),

, (no diffusive flux), .

2.3 Summary In summary, Eqs. (9 to 13) are solved for the variables ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅

and ̅ ̅ ̅

̅ ̅ ̅

in domain 1 and Eqs. (15 and 16) for the variables ̅ ̅ ̅

in domain 2 with the coupled boundary interface at ̅

. Since

, and

, Eqs. (11)

and (13) are solved in pseudo steady state using a time dependent boundary condition, and Eqs. (15) and (16) are solved for the transience.

9

The quantities of interest are length averaged permeate flux and permeate concentrations, ̅

∫

̅

∫ ̅|

̅ and

̅

̅

̅, respectively, for different

transmembrane pressure drop (TMP) and cross flow rates (CFR). The unknown variables are ̅ ,

and

which are estimated by minimizing the sum of the relative error of the

experimental and theoretical prediction, using an optimization technique of interior point algorithm following a trust region method [20]. The model parameters, ̅ ,

and

,

physically signify non-dimensional adsorption resistance in Eq. (14), power-law coefficient for change of adsorption resistance with adsorption capacity and forward adsorption rate constant. Enhancement in the values of ̅ and Higher value of

results in higher total adsorption resistance.

signifies faster rate of adsorption. It may be noted that these three

parameters represent interactions between the solute and membrane matrix. The objective function

∑

where,

for error minimization is given as,

(

)

∑

(

)

(17)

are the number of experimental data points in the filtration of Cr(VI)-rich

synthetic solution. The absolute tolerance for the objective function was considered as 0.01. The number of optimization iterations required was more than 12, depending on the experimental conditions. The sequence of calculation is presented in Fig. 2. All the experimental conditions, membrane properties, isotherm parameters, solution and solute properties, model parameters are presented in Table 1.

10

Fig. 2: Algorithm for estimation of model parameters, permeate concentration and permeate flux.

11

3. Experimental details 3.1 Materials and membranes Polysulfone (PSF) of average molecular weight 22,400 Da, was supplied by Solvay Chemicals, Mumbai, India. N, N-dimethyl formamide and polyethylene glycol (molecular weight 6, 10, 20, 35 100 and 200 kDa), were purchased from Merck (India) Ltd., Mumbai, India. Dextran (70 kDa) was procured from Sigma-Aldrich, USA. Di-potassium hydrogen phosphate, potassium di-hydrogen phosphate, hydrochloric acid, sodium hydroxide, analytical grade sodium chloride, sodium sulfate, chromium tri-oxide, lead nitrate, cadmium nitrate and copper sulfate were purchased from Merck (India) Ltd., Mumbai, India. Real life effluent from the chrome tanning was collected from the Common Effluent Treatment Plant, Leather Complex, Kolkata, India. 3.2 Preparation of graphene oxide (GO) Modified Hummers method, using graphite as raw material and sulfuric acid, potassium permanganate and hydrogen peroxide, were used for GO preparation. Production was carried out in different stages: pretreatment of the graphite, oxidation and the purification through dialysis. Detailed description of the process is available [22]. 3.3 Spinning of hollow fiber mixed matrix membrane 3.3.1 Preparation of spinning solution The spinning solution was a homogeneous dispersion of GO in PSF solution consisting of 20 wt% PSF, GO (0, 0.2, 0.5, 1.0 and 1.5 wt%) and solvent DMF. Initially, GO was added to DMF and the mixture was sonicated for six hours using a probe type sonicator (supplied by Optic Invymen System, model CY-500, Las Rozas de Madrid, Spain). Subsequently, PSF was added to the solution with continuous stirring for six hours followed by sonication for one hour. The concentration of PSF (20 wt%) was selected to obtain uniform membrane matrix exhibiting good mechanical strength [23].

3.3.2 Spinning of the membrane and module preparation The hollow fibers were spun by the wet-spinning method, through extrusion of the polymer solution using a two-needle assembly. Details of the spinning conditions and module preparation are available [24]. The hollow fiber membranes with 0, 0.2, 0.5, 1 and 1.5 wt% 12

GO were named as hGO0.0, hGO0.2, hGO0.5, hGO1.0 and hGO1.5, respectively. The available filtration area in each module was 0.031 m2. 3.4 Membrane properties 3.4.1 Estimation of permeate flux and observed rejection Permeate flux was measured using distilled water for different TMP (69, 54, 35 and 21 kPa) at fixed cross flow rate. At a fixed TMP and CFR, the permeate flux was calculated using the following relation experimentally measured permeate flux, time

(s) and

, where

(m3/m2 s) is the

(m3) is the volume of permeate collected in

(m2) is the membrane area [25].

The membrane was compacted with distilled water at a TMP of 100 kPa for 3 h. Membrane permeability was measured by plotting the pure water flux at different TMP and fitting a straight line through origin. The slope of the line was the hydraulic permeability of the membrane. The rejection of the solutes is estimated using the following relation: ( where,

and

)

(18)

are the Cr(VI) concentration (mg/l) in the permeate and feed solutions,

respectively.

3.4.2 Zeta Potential Measurement of zeta potential of hollow fibers was carried out using zeta potential analyzer (model: ZetaCad-DC, manufacturer: CAD Instruments, Les Essarts-le-Roi, France) using the streaming potential analysis. The salt (NaCl) concentration was maintained at 1mM and zeta potential of hGO1.0 was measured at pH7.0.

3.4.3 Adsorption isotherm To construct the adsorption isotherm, six batches of synthetic solution of same volume (200 ml) but different concentrations of Cr(VI) (10, 25, 50, 100, 250, 500 mg/l) were prepared. The solution batches, with membrane samples of fixed weight (0.2 g) were kept in a shaker at 150 rpm at 25oC for one day to attain equilibrium. The pH of all solutions was adjusted using the phosphate buffer. The amount of Cr(VI) adsorbed by the adsorbent, (mg/g) was calculated by following mass balance equation 13

(19) where

(mg/l) and

(mg/l) are the initial and final concentration of Cr(VI) in the liquid

phase,

(g) is the mass of the adsorbent used and

(l) is the volume of the solution used

for the equilibrium isotherm experiments. The details of the estimation of the adsorption isotherm constants are described in section S.1 of the supporting document. 3.5 Experimental setup and operating conditions The membrane module was fixed in a hollow fiber filtration unit with continuous cross-flow arrangement with valves to control the transmembrane pressure drop and crossflow rate [25]. The details of the experimental set-up are available [26]. To compare the performance of different membranes, TMP and CFR were fixed at 35 kPa and 8 l/h, respectively using synthetic Cr(VI) solution. To study the effects of different operating conditions, first the CFR was fixed at 8 l/h and TMP was varied from 35 to 69 kPa for synthetic solution. Subsequently, TMP was fixed at 35 kPa and CFR was varied from 5 to 10 l/h. The concentration of Cr(VI) in synthetic solution was 20 mg/l. Each experiment was repeated three times and the average of the data recorded is reported. Range of variation of these data is expressed as error bar in figures of this manuscript. 3.6 Membrane regeneration After prolonged use with synthetic solution, the membrane was regenerated following in-situ chemical regeneration. It has various advantages like lower energy, simplicity and faster operation. The adsorbed heavy metal molecules can be desorbed from GO in acidic solution [27]. The membrane module was thoroughly washed with distilled water for 10 minutes followed by an acidic solution of pH 5.5 (prepared by addition of 0.1N HCl solution) for 30 minutes at high cross flow rate and low pressure in the total recirculation mode. Subsequent rinsing with distilled water was continued till the pH of permeate was neutral. 3.7 Experiment with tannery effluent The tannery effluent was filtered through the hollow fiber MMM having selected GO concentration at optimum operating conditions (TMP and CFR) in two stages, for removal of Cr(VI) along with other contaminants. The raw effluent was used as feed in the first cycle. Permeate from the first stage was utilized as the feed stream to the second stage.

14

3.8 Analysis The concentration of Cr(VI) in aqueous solution was measured using atomic absorption spectrophotometer (model: Analyst 700 coupled with MHS-15 Perkin Elmer Instruments, USA). The samples were stored after adding a few drops of concentrated nitric acid in the solution to reduce the solution pH below pH 2. All the measurements were done in triplicate and the average values are reported. Conductivity, total dissolved solid (TDS) and pH of different streams were measured using a multivariable meter (model: PCSTestr 35, Eutech 220 Instruments, Germany). The chemical oxygen demand (COD) of the tannery effluent was measured using digester assisted closed reflux instrument, supplied by Merck (India) Ltd. Mumbai, India (Model spectroquant TR 320). Prior to the analysis, 3-ml kit-reference solution was added to the sample, followed by digestion at 120°C, for 2 h. Subsequently, the absorbance was noted for the blank and sample. The total solid (TS) content of each sample was determined gravimetrically. The average of three measurements was considered. The total suspended solids (TSS) were calculated by subtracting the TDS from the TS. The characteristics of the tanning effluent is presented in Table S2, in supporting document. 4. Results & discussion 4.1 Purity and other properties of the obtained graphene oxide Detailed characterization of GO is reported in Mukherjee et al. [28]. The characterizations are described in brief. Fourier transform infra red spectroscopy indicated presence of oxygen functionalities in form of -OH, >C=O and C-O. Transmission electron microscope image confirmed presence of a few layers of GO showing a morphology similar to the crumpled silk veils. Atomic force microscopy analysis showed that the thickness of synthesized GO sheet was 1.6 nm, indicating bi-layer formation. The particle-size distribution of GO in the solution, after sonication, was measured using dynamic light scattering, showing an average particle size of 191 nm. Energy-dispersive X-ray spectrum indicated elemental composition of GO and it was: C 77.5 wt%, O 13.6 wt%, S 1.7 wt%, Ca 1.22 wt%, Mn 0.0 wt% and trace amount of sodium. This above data showed that impurities in GO was minimum. 15

4.2 Chromium(VI) removal using MMM hollow fiber 4.2.1 Experimental observations using synthetic solution The effects of operating conditions and membrane composition on Cr(VI) rejection, and permeate flux were investigated. The detailed results are presented in the section S.2 and S.3 of supporting document, respectively. From the experimental results, described in section S.2, 54 kPa TMP and 8 l/h CFR were found to be the optimum operating conditions, for 20 mg/l Cr(VI) concentration in feed solution. From the results presented in section S.3, it was observed that hGO1.0 (membrane containing 1 wt% GO) was most suitable membrane with reasonable permeate flux of 20 l/m2h and high rejection (84%) of Cr(VI), at optimized operating conditions of 54 kPa TMP and 8 l/h CFR. The permeability of the hGO1.0 membrane was found to be 1.2 × 10−10 m/Pa.s and the zeta potential was -32.6 mV at pH 7. Since, adsorptive removal of Cr(VI) by the membrane is the main mechanism in this work, the breakthrough behavior of the laboratory scale hollow fiber (0.031 m2 filtration area) was investigated by conducting long duration experiments, using synthetic solution, at optimum operating conditions (54 kPa TMP and 8 l/h CFR) using the desirable membrane (hGO1.0). The results are presented in detail in the section S.4. It is observed that the laboratory scale hollow fiber cartridge starts to show lower rejection with filtration time after 13.5 hours for 20 mg/l synthetic Cr(VI) solution. Regeneration of used hollow fibers was also studied by circulating acidic solution of pH 5.5. The detailed experimental observation of regeneration study in presented in Fig. S5 in the section S.5 of supporting document. Filtration experiments after 1 hour clearly shows that the membrane has yielded insignificant loss of permeate flux and selectivity over three consecutive regeneration cycles. For example, after one hour of filtration, permeate flux was decreased from 20 l/m2h to 17 l/m2h and Cr(VI) rejection was reduced from 88% to 81% under the optimum operating conditions using hG01.0 membrane. As discussed in section S.5, flux recovery ratio of the membrane was quite high (~90%) indicating good reusability of the membrane.

16

4.2.2 Comparing the model result with experimental observation in long term filtration experiments Synthetic solution The model results were also validated by comparing them with the experimental data for ultrafiltration of synthetic Cr(VI) solution, using graphene oxide doped mixed matrix membrane. Experimental conditions and model parameters considered for the theoretical simulation are presented in Table 1. Comparison of permeate concentration and permeate flux between experimental and simulated results is presented in Figs. 3(a) and (b). Calculations were performed at the experimental conditions - module length 0.2 m, crossflow rate 8 l/h, TMP 54 kPa with feed concentration as 20 mg/l and 80 hollow fibers in a single module. The values of the parameters ̅ ,

and

are found to be 3.6, 5.5 and 910 l

/mg.s by optimizing the results of the theoretical calculations with the experimental data (minimizing the difference between the actual observations and the theoretical predictions as explained in section 2.3). It may be noted that earlier works dealing with adsorption in MMM are for short term filtration experiments where the long term breakthrough was never attempted [15-17]. In fact, the long term filtration characteristics are of utmost importance to have an idea of membrane life and its implementation. In the long run, when the breakthrough behavior appears, the filtrate concentration as well as permeate flux undergo a sharp change in its variation. This can only be captured when the adsorption resistance is proportional to adsorbed amount by a large exponent

. In this case, for Cr(VI)

filtration n is found to be 5.5. This is in sharp contrast to the case of modelling short term dynamics where

. It can be observed from the figures, Figs. 3(a) and 3(b), that the

simulated results match very well with the experimental data, corroborating the correctness of the model. The profile of permeate concentration, with respect to the cumulative filtration volume is shown in Fig. 3(c).

17

Table 1: Experimental conditions and model parameters for long term performance study of the membrane and its theoretical simulation. System parameters

Value

Membrane

Membrane tag

hGO1.0

properties

Contact angle (o) (experimentally measured)

61

Zeta potential (mV) (experimentally measured)

-32.6

Membrane permeability (m/Pa.s) (experimentally

1.2×10-10

measured) Molecular weight cut off (kDa) (experimentally

83

measured) Total length of fiber (m) Total number of fibers (

0.2 80

)

Fiber internal diameter (mm) (measured from

0.61

scanning electron microscope, SEM, imaging) (m2)

Effective filtration area Membrane aspect ratio (

) (measured from

0.031 0.003

SEM imaging) Average wall thickness,

(mm) (measured from

0.19

SEM imaging) (l/mg) (experimentally measured)

Isotherm parameters

(mg/g) (experimentally measured)

9.5×10-3 175.6

Operating

TMP (kPa)

54

conditions

CFR (l/h)

8

Cross flow velocity,

(m/s)

Cr(VI) concentration in feed effluent (mg/l)

340±20

Cr(VI) concentration in synthetic solution (mg/l)

20

Solute and

Viscosity (Pa.s)

9×10-4

solution

Diffusivity of Cr(VI) in aqueous solution (m2/s) 1.6×10-9

properties

[21] 99.1

Osmotic pressure coefficient, (

[|

|

|

|]

)

18

̅

Model parameters

(estimated from model simulation) (estimated from model simulation) (l/mg.s) (estimated from model simulation)

Quantities to

∫ ̅

̅

̅

be estimated ∫ ̅|

cp / c0

̅

̅

Experimental result Simulated result

1.0 (a) 0.8

̅

Membrane: hGO1.0 L: 0.2 m nf : 80 TMP: 54 kPa CFR: 8 l/h c0 : 20 mg/l

0.6 0.4 0.2 0.0

0

5

10

15

20

Time (h)

Fig. 3: Comparison of experimental and simulated results for synthetic solution with module length, the number of hollow fibers, volumetric flow-rate and TMP fixed at 0.2 m, 80, 8 l/h and 54 kPa, respectively, for profiles of (a) permeate concentration flux

and (c) permeate concentration

volume.

19

, (b) permeate

with respect to cumulative filtered

Tannery effluent The experimental performance of the membrane during two stage filtration of an actual chrome tanning effluent, in terms of permeate flux and Cr(VI) rejection and the simulation results are reported in Fig. 4. It may be noted that simulation is carried out in predictive mode considering the same parameter values of ̅ ,

and

as obtained from

parameter optimization using the experimental data of synthetic solution (as described in section 2.3). The raw effluent was used as feed in the first stage, while the permeate of the first stage was used as feed to the second stage using the same membrane. Apart from high amount of Cr(VI) (340 mg/l), the untreated effluent contains some bigger sized solutes retained by the membrane. Consequently, the rejection of these material leads to flux decline. The two stage filtration results in 92% overall rejection of the Cr(VI) (Table S2, in supporting document). Since, some of the adsorption sites are already occupied in the second stage, lower rejection of Cr(VI) is obtained in this stage compared to first one.

1.0

cp/c0

0.8 0.6 0.4

Experimental result Simulated result

(b)

Membrane: hGO1.0 L: 0.2 m; nf : 80 TMP: 54 kPa CFR: 8 l/h c0 : 340 mg/l

0.2 0.0

0

5

10

15

20

Time (h)

1.1

(c)

1.0

Experimental result Simulated result

0.9 vw / v 0 w

0.8 0.7 0.6

cp/c0

Membrane: hGO1.0 L: 0.2 m; nf : 80 TMP: 54 kPa CFR: 8 l/h c0 : 340 mg/l

(d)

0.8

Membrane: hGO1.0 L: 0.2 m; nf : 80 TMP: 54 kPa CFR: 8 l/h c0 : 340 mg/l

0.6 0.4

Experimental result Simulated result

0.2

0.5 0.4 0.3

1.0

0.0 0

5

10

15

20

0

5

10 Time (h)

Time (h)

20

15

20

Fig. 4: Comparison of experimental and simulated results for real tannery effluent with length of the module, the number of hollow fibers, volumetric flow-rate and TMP fixed at 0.2 m, 80, 8 l/h and 54 kPa, respectively, for profiles of (a) permeate flux concentration concentration

at first stage and (c) permeate flux

, (b) permeate , (d) permeate

at second stage.

It may be noted that for an effluent treatment, there are few other species present in the solution which can also contribute to adsorption, leading to additional fouling resistance. The total suspended solid content in actual effluent was low indicating insignificant cake resistance. In case of synthetic solution, the total resistance is due to adsorption only (because size of Cr(VI) molecule is much smaller than the pore size of MMM). Looking into permeate concentration (Fig. 4c and Fig. 4d), it can be seen that the model results compare well with the experiments for second stage filtration of effluent (Fig. 4d). This is corroborating to the fact that the second stage (where TSS content is negligible, as shown in Table S2 of supporting document), the fouling resistance is solely due to adsorption. There were three parameters in the model. These are: ̅

and

with adsorption resistance of the membrane and

. Out of these, ̅ and

are associated

is a parameter relevant to adsorption of

Cr(VI) on the active sites of MMM. Therefore, these three parameters represent the interaction between solute, Cr(VI) and the MMM and they are inherent characteristics between solute and membrane. Thus, these parameters do not depend on the concentration of solute in the feed. For this reason, same set of parameters were used for simulation of experiments conducted by synthetic solution and actual industrial effluent. The filtrate after the treatment of chrome-tanning effluent with this membrane does not reach the safe discharge limit criteria (2 mg/l of Cr(VI)). The rejection efficiency can be improved further with pre-treatment of the effluent. However, that study is out of the scope of this work. The main objective of this work is to validate the model for performance prediction of MMM. For that purpose, an industrial effluent was considered to test the model. 4.3 Scale up and breakthrough time Scaling up of heavy metal purification system using MMM, is the most essential aspect in successful implementation of this technology for large scale application. It must be emphasized that the membrane filtration is not a constant throughput system, unlike an adsorption column. With bigger system dimensions (larger membrane area), the total number 21

of adsorption sites increase resulting in higher filtration capacity [28]. The effect of different operating conditions, on long term system performance can be predicted using the theoretical model, presented in this work. During scale up, the rate of permeation can be altered by changing the length of the module, total number of hollow fibers, input volumetric flow-rate and applied trans-membrane pressure. Effect of each of this individual aspect is analyzed by simulating long term system performance, using the same parameter values obtained from optimizing the experimental results already mentioned in Table 1. Breakthrough is generally defined when the adsorption medium starts to be exhausted with the adsorbent species and solute concentration at the filter outlet approaches feed concentration. However, regarding filtration of toxic chemicals, like Cr(VI), filtration should be conducted till the safe limit of Cr(VI) is maintained (safe discharge limit of Cr(VI) is 2 mg/l, for discharge of industrial effluent in general outlet [29] corresponding to

=

0.1 for synthetic solution). For fixed bed adsorption column, the rate of output is unaltered throughout the entire period of filtration. However, in MMM, the rate of output or permeate flux constantly decreases with time owing to the increasing adsorption resistance. Therefore, the breakthrough behavior of the system in this work, is presented with respect to cumulative volume of filtered stream ( reaches

Once the solute concentration of the filter at the outlet

= 0.1 (for feed concentration of Cr(VI),

as 20 mg/l), the filter needs to be

regenerated. 4.3.1 Length of the module A system of MMM hollow fiber can be upscaled by increasing the length of the module, while the flow rate, number of hollow fibers and trans-membrane pressure remain unaltered. The effect of changing the module length on long-term system behavior is presented in Fig. 5(a). It can be observed from the figure that increasing the module length leads to higher cumulative volume of filtrate, before breakthrough is attained. The membrane module with length 0.2, 1, 5 and 10 m, offers constant

of 65, 110, 232 and 341 l, respectively, for

of 8 l/h with 80 fibers in a module and TMP of 54 kPa. Increasing the length of

the module signifies more membrane area, leading to higher mass of the adsorbent available and consequently higher processing capacity. Therefore, breakthrough volume increases with fiber length.

22

(a)

(b)

Fig. 5: Long term system behavior of MMM for (a) increasing , length of the module from 0.5 m to 1, 5 and 10 m, for a fixed number of hollow fibers ( (

= 8 l/h) and TMP (45 kPa) , and (b) with increasing

= 80), volumetric flow-rate

, number of fibers from 20 to 80,

1000 and 2000, for a fixed module length ( = 1 m), volumetric feed flow-rate ( = 8 l/h) and TMP (45 kPa). 4.3.2 Number of hollow fibers Scaling up of the process capacity can be achieved by increasing the number of hollow fibers in the module. This situation can be achieved by two alternate routes. All the hollow fibers can be packed in one single cartridge where the inner diameter of the cartridge should be suitably increased, otherwise multiple number of cartridges can be used in parallel while maintaining the number of hollow fibers same in each cartridge. Positioning of the cartridges has significant effect on the long-term filtration performance. Arranging those in series will have same effect as that of increasing the length of the cartridge (this effect is discussed earlier in Section 4.3). In this case, the outlet of the preceding cartridge will be the inlet stream of the next cartridge. If the multiple cartridges are arranged in parallel, it will have same effect of increasing number of hollow fibers in a single cartridge. In this case, all the fibers will have same input stream. Depending solely on the manufacturing complexity and requirement of individual application, the orientation of the modules can be selected. Effect of increasing number of hollow fibers in a single module or parallel arrangement of different cartridges on long term filtration behavior of the system, is presented in Fig. 5(b). It can be observed from the figure, that increasing number of hollow fibers delays the breakthrough. Increasing number of hollow fibers has two major effects on 23

the process: (i) increasing the adsorbent amount and (ii) decreasing cross-flow velocity. Thus, increase in hollow fibers results in enhanced filtration capacity of the membrane. On the other hand, increasing the number of hollow fibers increases filtration area, lowers cross-flow velocity assisting the adsorption process thereby increasing the filtration capacity. Therefore, increasing the number of hollow fibers by aligning the modules in parallel is an excellent route to enhance the breakthrough volume. 4.3.3 Throughput Throughput from the membrane module in scaled up configurations are presented in Fig. 6. Throughput can be defined as the volume of filtered water obtained from the module per unit time. It can be expressed as permeate flux multiplied by the cross-sectional area. Following cases are selected for investigation:

;

and

. For all these

cases, the TMP and CFR are maintained at 54 kPa and 8 l/h. Effect of adsorption resistance can be observed in each case. After an initial period, the throughput decreases due to adsorption resistance, offered by the adsorbed species. After certain time duration, the throughput reaches a steady value and remains constant. Higher throughput is resulted due to availability of larger filtration area. From this analysis, the range of throughput in the whole operating duration of different scaled up systems can be easily determined.

10000 1: L=3000 m; nf = 10000 3: L=10 m; nf = 10000

Throughput (l

/ s)

1000

2: L=3000 m; nf = 100 4: L=10 m; nf =100

100 1

10 1

2 3

0.1 0.01

4

1E-3 0

100

200

300

Time (days)

24

400

Fig. 6: Variation of throughput in different hollow fiber membrane modules of various dimensions. 4.4 Performance curve Guideline for optimum design of the filtration module based on requirement criteria of breakthrough volume is presented in Fig. 7. The required

values for different sets of

(100, 500, 1000, 1500, 3000 m) are plotted with respect to the breakthrough volume. For fixed , increasing requirement of

needs higher

the preceding section. With known requirement of

to increase surface area, as explained in , different set of

and

values can be

selected from this graph. The most important advantage of this study is that the design parameters, like, number of fibers and their length can be suitably selected to achieve a desired breakthrough volume.

Fig. 7: Performance curves for the scaled up membrane modules with respect to breakthrough volume (TMP 54 kPa and CFR 8 l/h).

5.

Conclusion A generalized three-dimensional model was developed for performance prediction of

hollow fiber MMM. Three model parameters ̅ adsorption resistance parameter and

and

̅ and

are membrane

is related to solute adsorption by the membrane) were

estimated using long term filtration performance data of synthetic Cr(VI) solution in grapheme oxide incorporated MMM. The values ̅̅̅

25

and

are found to be 5.6 0.1,

5.5 0.3 and 910 17 l/mg.s. The same set of parameters were used in the model to predict the filtration behavior in long term for a real life chrome tanning effluent treated in two stages in series. Hollow fiber incorporating 1% GO was found to be the most suitable one among other fibers spun with GO concentration in the range of 0.2 to 1.5 wt%. The experimental observations showed that 54 kPa TMP and 8 l/h CFR were optimum operating conditions for filtration of Cr(VI) solution. The developed model was further used to scale up the hollow fiber MMM modules having large breakthrough volume for a scaled up filter. From the simulation results following conclusions have emerged: (i) breakthrough volume or membrane life can be extended by increasing the fiber length and number of fibers. Long fiber length at fixed number of fibers can be realized by sequencing number of modules in series. On the other hand, large number of fibers of fixed length can be obtained by placing a number of modules in parallel; (ii) Increase in TMP and lowering in CFR also lead to overall increase in higher breakthrough volume. A general performance curve was developed to select number of fibers with corresponding length to attain a specific breakthrough volume. It is envisaged that the developed modelling and simulation scheme would be of immense help to design and scale up of hollow fiber MMM based filters. Acknowledgements The authors would like to acknowledge the support from the Department of Science & Technology (SERB) and INAE through the Abdul Kalam Technology Innovation National Fellowship vide letter INAE/121/AKF dated 21.12.2017. The authors are thankful to University of Oxford for the provision to use numerical packages of COMSOL version 5.3, having the license number 1010551. Any opinions, findings and conclusions expressed in this paper are those of the authors and do not necessarily reflect the views of funding agencies.

Nomenclature Total internal cross flow area in the module , m2

Membrane filtration area

Temkin isotherm equilibrium binding constant, l/mg Temkin isotherm constant, J/mol

26

, m2

Concentration of the species to be separated, kg/m3 ̅

Non-dimensional solute concentration as defined in section 2.2 Feed concentration, kg/m3 Equilibrium concentration of the adsorbate species, kg/m3 Experimental permeate concentration, kg/m3 Solute concentration in permeate, kg/m3 Solute diffusivity in the bulk, m2/s Solute diffusivity in the membrane matrix (Domain 2), m2/s Wall thickness of the hollow fiber membrane, m Desorption rate constant of the adsorption kinetics in Eq. (8), 1/s Forward rate constant of the adsorption kinetics in Eq. (8), m3/kg.s , m3/kg

Langmuir adsorption isotherm constant Freundlich isotherm constant, mg(1-1/n) l(1/n)/g

Length of the hollow fiber membrane, m Mass of the adsorbent used for the batch equilibrium isotherm experiment, g Molecular weight of the solute, kg/kmol Adsorption intensity (Freundlich isotherm) Number of fibers in hollow fiber cartridge Number of experimental data points

̅

Absolute pressure in Domain 1, Pa Non-dimensional absolute pressure as defined in section 2.2

̅

Atmospheric pressure, Pa Non-dimensional atmospheric pressure Peclet number Amount of solute adsorbed by the adsorbent, kg/kg Width averaged solute adsorption

27

∫

, kg/kg

̅

Spatially averaged non-dimensional adsorption capacity (Domain 2), Equilibrium solute concentration in adsorbent, kg/kg Maximum solute adsorption capacity, kg/kg Cross flow rate in the module, m3/s Volume of permeate collected during measurement of flux, m3 Radial co-ordinate, m

̅

Non-dimensional radial co-ordinate Internal radius of the hollow fiber, m Membrane adsorption resistance, m-1

̅

Non-dimensional membrane adsorption resistance Reynolds number Universal gas constant, J/mol.K Membrane hydraulic resistance, m-1 Objective function for error minimization as defined in Eq. (17) Time, s Temperature of the system, K Fluid velocity in the z-direction in Domain 1, m/s

̅

Non-dimensional fluid velocity in z-direction as defined in section 2.2 Inlet velocity (z-direction) at

, m/s

̅

Fluid velocity in the r-direction in Domain 1, m/s Non-dimensional fluid velocity in r-direction as defined in section 2.2 Volume of the solution used for the batch equilibrium isotherm experiment, l Permeate flux obtained from the experiments, m3/m2 s r-direction fluid velocity at the membrane surface, m3/m2 s Pure water permeate flux, m3/m2 s Experimentally measured permeate flux, (m3/m2 s)

28

̅

Non-dimensional r-direction fluid velocity at the membrane surface Axial co-ordinate in the cylindrical system, m

̅

Non-dimensional axial co-ordinate as defined in section 2.2

Abbreviations CFR

Cross-flow rate (l/h)

Cr(VI)

Chromium with valency VI

COD

Chemical oxygen demand (mg/l)

GO

Graphene oxide

hGO0.0 Hollow fiber mixed matrix membrane with 0.0 wt% graphene oxide in spinning solution hGO0.2 Hollow fiber mixed matrix membrane with 0.2 wt% graphene oxide in spinning solution hGO0.5 Hollow fiber mixed matrix membrane with 0.5 wt% graphene oxide in spinning solution hGO1.0 Hollow fiber mixed matrix membrane with 1.0 wt% graphene oxide in spinning solution hGO1.5 Hollow fiber mixed matrix membrane with 1.5 wt% graphene oxide in spinning solution MMM

Mixed matrix membrane

PSF

Polysulfone

SEM

Scanning electron microscope

TDS

Total dissolved solid (mg/l)

TMP

Transmembrane pressure drop (Pa)

TS

Total solid (mg/l)

TSS

Total suspended solid (mg/l)

UF

Ultrafiltration

29

Greek symbols Dimensionless parameter in Eq. (15) Coefficient in calculation of the ̅

, m-1

Non-dimensional form of Power exponent in the estimation of the Non-dimensional form of the adsorption and desorption rate constants as defined in Eq. (16) Vant-Hoff coefficient for estimating the osmotic pressure of dilute solution expressed as

[|

|

|

|]

Non-dimensional of the adsorption capacity ̅

Non-dimensional osmotic pressure difference across the membrane wall Transmembrane pressure (TMP) drop across the membrane wall, Pa Time interval between two successive readings for measurement of permeate flux, s Osmotic pressure difference across the membrane wall, Pa Aspect ratio of the hollow fiber Viscosity of the solution, Pa.s Valence of the cation and anion of the salt Non-dimensional parameter in Eq. (14) Osmotic pressure, Pa Density of the solution, kg/m3 Membrane density, kg/m3 Non-dimensional time as defined in section 2.2 Membrane porosity

30

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33

Highlights 

First principle model of mixed matrix hollow fiber filtration is developed.



Long term dynamics of the mixed matrix membrane system is modelled successfully.



The model result is useful for scaling-up and design of larger scale filtration units.



Case study of chromium(VI) removal using graphene oxide hollow fiber is done.

34