Prediction of nanofiltration rejection performance in brackish water reverse osmosis brine treatment processes

Journal of Water Process Engineering 32 (2019) 100900

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Prediction of nanofiltration rejection performance in brackish water reverse osmosis brine treatment processes

T

Ricky Bonner , Charné Germishuizen, Sebastian Franzsen ⁎

Miwatek, P/Bag X29, Gallo Manor, 2052, Johannesburg, South Africa

ARTICLE INFO

ABSTRACT

Keywords: Brine treatment Mine water treatment Nanofiltration modelling

A predictive nanofiltration model was built in Python to be used in reverse osmosis brine treatment processes. The model was fitted to rejection data obtained from NF trains functioning as a brine concentrator upstream of a gypsum precipitation reactor at a full-scale mine water treatment plant in Ahafo, Ghana. Over the six month operational period considered (September 2017 – March 2018) the rejection capability of the installed elements deteriorated considerably. This was reflected by a 13% increase in membrane pore radius, 40% decrease in effective active layer thickness and an 18% decrease in absolute value of the feed-membrane Donnan potential. Performance of elements from other manufacturers was simulated by loading their respective properties into the model. Cases modelled included a tightly wound Dow NF 90, a loosely wound Desal DS-5 DL and a Koch TFC SR2 element. Rejections obtained from the installed MDS elements most closely approximated the performance of a loose NF element. These modelling studies have shown that the NF model built is capable of modelling nanofiltration in brackish water treatment processes. The current disadvantage of the model is the number of membrane—specific input parameters which need to be verified with independent experimentation. As a start, it is recommended that electro-kinetic data be obtained for similar solutions to enable a membrane charge density sub-module to be incorporated into the model.

1. Introduction Reverse osmosis (RO) is one of few technologies used for the treatment of mine impacted water. Exposure of water and oxygen to pyrite inside mine voids generates sulphate and acidity, which enables the dissolution of carbonate and silicate based minerals with subsequent liberation of metals including Ba2+, Ca2+ and Sr2+ [1]. The volumetric recovery achievable in an RO plant is thus very much limited by the sulphate-based mineral saturation indices (Gypsum – CaSO4.2H2O, Celestite – SrSO4 and Barite – BaSO4) in the feed. Typical RO volumetric recoveries in mine water desalination plants are in the range 70–80%, with the remaining brine stream having a high sulphate scaling potential. The brine is typically sent to the tailings storage facility (TSF) and can be re-used as makeup water in the mine’s mineral recovery process. Treatment processes are designed for volume reduction, sulphate removal and ionic strength reduction of the primary RO brine before being fed into the mine’s water reticulation circuit. Membrane-based brine treatment processes typically employ a nanofiltration (NF) step downstream of the primary RO unit, which functions as a concentrator upstream of the gypsum precipitation reactor. The NF also produces a permeate stream rich in monovalent ⁎

species, which depending on the NO3− and NH4+ content, can be blended directly with the primary RO permeate to boost the overall volumetric recovery of the facility. In specific cases where zero liquid discharge (ZLD) is targeted the NF may be incorporated into a recycle loop with intermediate chemical demineralization. Salts which contain monovalent cations such as NaCl, KCl and Na2SO4 are highly soluble in water. Hence precipitation reactors are not capable of removing monovalent cations. In cases where ZLD is required, the NF permeate stream serves as the purge of monovalent species inside the treatment loop. Its ability to allow passage of monovalent cations as well as its SO42− rejection capability dictate if a brine bleed requires implementation and hence the possibility of achieving ZLD. Modelling of the NF and subsequent element selection thus forms an essential part of the design phase of such projects. Element suppliers are typically provided with a feed basis from the process consultant and a performance projection is provided based on the element and vessel configuration selected. Suppliers model the feed water as a combination of single salts (NaCl, Na2SO4, CaSO4 etc) for which they have salt permeability coefficients (B-values) calibrated with single salt rejection data. Salt flux obeys a simplified form of the solution-diffusion model, with flux directly proportional to the chemical potential gradient across the

Corresponding author. E-mail address: [email protected] (R. Bonner).

https://doi.org/10.1016/j.jwpe.2019.100900 Received 14 January 2019; Received in revised form 20 June 2019; Accepted 16 July 2019 2214-7144/ © 2019 Published by Elsevier Ltd.

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Nomenclature

Amembrane ci CX Di e0 F Ji Jv k k c,i k *c,i Ki,c

Ki,d K sp Pfeed Pperm Q feed R SA rp rs,i T zi

Pure water permeability constant (m/s.kPa) Concentration (mol/m3) Membrane charge density (mol/m3) Diffusivity (m2/s) Electronic charge (1.602 × 10−19 C) Faradayconstant (96,500 C/eq) Solute flux (m/s) Water flux (m/s) Boltzmannconstant (1.38066 × 10−23 J/K) Conventional mass transfer coefficient (m/s) Modified mass transfer coefficient (m/s) Convective hindrance factor

membrane [2]. There are multiple properties of NF membranes which enable them to reject dissolved ionic species, including:

sets of data are then provided to enable characterization of the element as the operational campaign developed. Finally, elements from other manufacturers were loaded into the model characterized by their pore size and active layer thickness determined elsewhere by other researchers and the individual species rejection compared with the current installed elements.

• The presence of pores on the membrane surface which enable steric (size) exclusion; • The development of a fixed charge on the surface of the membrane •

Diffusion hindrance factor Equilibrium constant Feed pressure (kPa) Permeate pressure (kPa) Feed volumetric flow rate (m3/s) Gasconstant (8.314 J/mol.K) Membranesurface area (m2) Membrane pore radius (m) Ion stokes radius (m) Temperature (K) Chargenumber

which excludes ions of the same charge sign from entering the membrane, commonly referred to as Donnan partitioning or the Gibbs-Donnan effect; and Confined spaces within the membrane pores restrict the movement of solvent (water molecules). This leads to a reduction in membrane pore dielectric constant compared to the feed bulk and hence an additional energy barrier for passage through the membrane is created, commonly referred to as the Born solvation energy barrier.

2. Methods A conceptual diagram of the NF membrane to be modelled is presented in Fig. 1. The diagram describes two distinct regions in which mass transfer of solutes occurs – (1) through the concentration polarization layer to the feed-membrane interface and (2) through the active layer inside the membrane to the membrane-permeate interface. Partitioning of solutes occurs at the feed-membrane and membranepermeate interfaces which are dependent on steric, Donnan partitioning and Born solvation effects. The concentration polarization layer develops on the feed side due to exclusion of solutes at the feed-membrane interface which then diffuse back down a concentration gradient into the bulk solution.

The said membrane properties are grouped together with the effect of operating conditions such as solution temperature and pH into a single regression parameter in the simplified solution-diffusion model, which is problematic for process designers particularly when more rigorous modelling of the system is required. The intent of this paper is to present the development of an alternative NF model – referred to in literature as the Donnan Steric Pore Partitioning and Dielectric Exclusion (DSPM&DE) model for use in brine treatment processes. The model includes solving the extended Nernst-Planck (ENP) equation for each species inside the active layer of the NF membrane with the mechanisms of diffusion, convection and electro-migration being considered. Boundary conditions used for solving the differential equations include partitioning at the feed-membrane and membrane-permeate interfaces with Steric, Born solvation and Donnan partitioning factors included. The technique used for solving the equations was based on the paper by Geraldes & Brites Alves [3]. This involved discretizing the membrane active layer into successive nodes and linearizing the system of equations to get the system to be described in the matrix form AX= B , with X being the solution vector comprising molar concentrations of each species at each node within the membrane. The system of equations was then solved iteratively using LU decomposition theory and Gauss elimination, with the code being built in the programming language Python. Species included in the system were Na+, Ca2+, Mg2+, SO42−, NO3and HCO3- all of which are considered to be the dominant ions found in mine impacted water sources. Feed solutions for the model were built using analytical data from six months of operation of a 4.3 Ml/day mine water treatment plant for a gold mine in Ahafo, Ghana. The initial set of analytical data from September 2017 was used to determine the installed NF elements’ physical properties – this included pore size and active layer thickness. A sensitivity analysis was performed to illustrate the effects of Donnan partitioning and Born solvation on the rejection capability of the membrane for a given set of hydraulic conditions and solution chemistry – this enabled an appropriate Donnan potential and membrane pore dielectric constant to be determined. Three additional

2.1. Solute mass transfer in boundary layer The net flux of a dissolved ionic species through the concentration polarization layer thus comprises a convective term to account for draw of solute with water in the direction of the hydraulic gradient, a diffusive term to account for diffusion towards the feed-bulk and an electro-migration term which enables an electrical potential to develop to ensure charge balance is maintained at the feed-membrane interface [4]. Computation of the flux is performed using Eq. 1 and electroneutrality within the boundary layer ensured using Eq. 2.

Fig. 1. Conceptual diagram indicating mass transport of dissolved species through an NF membrane and surrounding regions of fluid.

2

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k *c,i (c i,M

Ji = Jv c i,M

c i,b)

zi c i,M Di,

F RT

D,p , the Donnan potential at the membrane-permeate interface. Activity coefficients of each species inside the concentration polarization layer i,M, inside the permeate i,p and inside the active layer of the membrane i,1 N are determined using the Davies equation for brackish water sources [8] as shown in Appendix B.

(1)

Where Ji is the solute flux of species i, Jv is the water flux, c i,M is the membrane concentration of species i, c i,b is the bulk feed concentration of species i, zi is the charge of species i, Di, is the diffusivity in water of species i, F is the Faraday constant, R is the gas constant, T is the fluid temperature and is the electrical potential gradient in the concentration polarization layer.

2.3. Solute mass transfer in active layer Solute flux through the active layer of the membrane is determined using the ENP equation as shown in Eq. 9 below [9].

n

zi c i,M = 0

(2)

i= 1

Ji =

is the modified mass transfer coefficient of species i taking into account the suction effect which the water flux induces on each species as it passes through the concentration polarization layer. A correction factor is applied to the conventional mass transfer coefficient k c,i for its determination [5], with the method outlined in Appendix A.

k *c,i

k *c,i = k c,i

(3)

B exp

zi F RT

D,M

(4)

=

i,p c i,p

i

B exp

zi F RT

D,p

(5)

• •

i refers to Steric partitioning which occurs at both membrane interfaces and is a function of the solute and membrane pore radii. i is determined using Eq. 6, with the assumption that there exists well-defined cylindrical pores within the membrane [6]. Confined spaces within the pores of the membrane results in a reduction in dielectric constant and hence solvation capacity of the fluid, which presents a further barrier for ionic species to enter the active layer and is referred to as the Born solvation energy barrier Wi [7]. The dielectric exclusion factor B is related to Wi through Eq. 8.

i

Wi =

B

rs,i rp

= 1

8

z2i e20 0 rs,i

= exp

i)

1

1

p

b

Wi kT

groups. Polyamide membranes, which constitute the majority of NF membranes in industry, have carboxylic acid functional groups (−COOH). Under neutral to alkaline conditions the functional group dissociates into the COO- ion which contributes to a negative charge density; Counter-ion adsorption onto charged hydrophilic sites. This decreases the magnitude of charge developed due to acid/base ionization mentioned above; and Competitive ion adsorption onto the hydrophobic alkyl or aromatic functional groups (−CH–). Factors influencing adsorption include ion size and charge. Monovalent anions such as Cl− and NO3− and divalent anions such as SO42- are more easily adsorbed than their positively charged counterparts due to their smaller stokes radii. This enhances the negative surface charge density of NF membranes and has found to be the case for many types of brackish water as well as for sea water.

The mechanism for ion exclusion due to development of surface charge is introduced in this model by imposing a charge offset at each node inside the active layer of the membrane, equal in magnitude to the surface charge density CX as shown in Eq. 11 below. Donnan potentials at the feed-membrane and membrane-permeate interfaces ( D,M and D,p ) are thus iterated through to ensure the charge offset is met on the inside of the membrane.

2

= (1

(10)

• pH-dependent association/dissociation of the hydrophilic functional

Atx= x e i,N c i,N

(9)

In addition to Steric and Dielectric exclusion phenomena, the development of a surface charge density within the active layer of the membrane also plays a prominent role in species rejection. Mechanisms for surface charge development include [12]:

Atx= 0 i

z i c i Di,p d F RT dx

Di,p = Ki,dDi,

The molar concentration of species i at the first node inside the active layer of the membrane c i,1 is related to its molar concentration at the membrane surface c i,M according to Eq. 4. Eq. 5 relates the molar concentration of species i at the last node inside the active layer of the membrane c i,N with the molar concentration of species i in the permeate c i,p .

i,M c i,M

dc i +K c i Jv dx i,c

Due to the confined spaces inside the pores of the active layer a hindrance factor is applied to the diffusion coefficient in the bulk solution Di, to provide the hindered diffusion coefficient Di,p as shown in Eq. 10. Another hindrance factor is applied to the convective transport term in Eq. 9, referred to as Ki,c . Both hindrance factors are a function of the solute to pore radius and appropriate correlations for each are provided in Appendix C [10,11].

2.2. Partitioning at feed-membrane and membrane-permeate interfaces

i,1c i,1 =

Di,p

2

(6)

(7) (8)

n

zi c i =

Where rs,i is the stokes radius of solute i, rp is the membrane pore radius, e 0 is the electronic charge constant, 0 is the vacuum permittivity constant, p is the membrane pore dielectric constant, b is the feed-bulk solution dielectric constant and k is the Boltzmann constant. Since the ionic species in solution possess different physical (stokes radius) and electrical (charge) properties, their Steric and Born partitioning factors vary and hence have differing capabilities to pass into and out of the membrane at the feed-membrane and permeate-membrane interfaces respectively. To maintain charge balance within each region a potential difference is developed at both membrane interfaces – D,M , the Donnan potential at the feed-membrane interface and

CX

i= 1

(11)

2.4. Solute transfer into the permeate Transport through the permeate spacers of the membrane is assumed to be carried out without any hindrance and solute flux is described using the relation provided in Eq. 12. Electroneutrality on the permeate side is ensured by introducing Eq. 13.

Ji = Jv c i,p 3

(12)

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pressure drop, Pperm is the permeate backpressure, feed is the feed osmotic pressure and perm is the permeate osmotic pressure.

n

zi c i,p = 0

(13)

i= 1

Where c i,p is the permeate concentration of species i. Finally, flux continuity through the element for each species is ensured by equating the flux equations describing transport within each region of the membrane:

2.7. Solution algorithm for NF model The ENP differential equation for flux of each species (Eq. 9) was discretized by dividing the membrane active layer depicted in Fig. 1 into successive grid nodes, with equal spacing xj. A forward differences scheme was used to approximate the solute concentration and electrical potential gradients within the active layer, as shown in Eq. 17.

(14)

Ji,boundary layer = Ji,active layer = Ji,permeate = Jv c i,p 2.5. Permeate pH prediction

Ji =

pH change as the solution passes through the element is assumed to be dependent on carbonic equilibrium and the extent of rejection of the bicarbonate (HCO3−) ion. Carbonic equilibrium is enforced at the feedmembrane interface, active layer and at the membrane-permeate interface as shown in Eq. 15 below.

K sp =

(

+ c H+ )(

H

(

HCO3

(15)

2.6. Membrane hydraulics Water flux through the NF element is related to the applied feed pressure via the use of Eq. 16 below. The membrane A-value is commonly referred to as the pure water permeability constant and is provided by membrane manufacturers.

0.5 P

Pperm

feed

+

perm)

c i,j xj

+

1 K (c i,j+1 + c i,j)Jv 2 i,c j+1

j

xj

(17)

The solute flux equations within each region of the membrane as well as the membrane interface partitioning equations were then linearized according to the method developed by Geraldes & Brites Alves [3]. The method involves rewritng the equations as linear combinations of c i,M, c i,j, c i,j+1, and c i,p as well as , j, j+1 and p . The coefficients of the linear combinations comprise system properties such as i , B and Di,p as well as the values obtained from the previous iteration for the variables listed above – denoted as c i,M* , c i,j* , c i,j+1* , c i,p *, * , j* , j+1* and * p . Geraldes & Brites Alves [3] wrote their programming code in Fortran. The authors of this paper, however, preferred to develop the code in Python due to the availability of built-in functions for handling of matrices and arrays which allowed for a shorter and more efficient script. Refer to Fig. 2 for a logic diagram of the code used in this study. The code includes building the coefficient matrix (A matrix) and solution vector (B vector) which then solves for the solution vector (X vector) using LU decomposition and Gauss elimination. The coeffcient matrix is then updated and solved again. The process is repeated until

Where K sp is the solubility product constant for the dissociation reaction of carbonic acid into the bicarbonate ion and hydrogen ion.

Jv = Amembrane (Pfeed

c i,j+l

F 1 zi (c i,j+l + c i,j)Di,p 2 RT

cHCO3 )

H2CO3 cH2CO3 )

Di,p

(16)

Where Amembrane is the membrane pure water permeability constant, Pfeed is the membrane feed pressure, P is the membrane feed channel

Fig. 2. Logic diagram of NF simulation code developed in Python. 4

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the convergence criteria are met, provided in Eq. 18 below.

max

c i,j

c i,j

provide relatively high rejection of multivalent ions. In this case, the dominant cation in solution on a molar basis is Ca2+ and the dominant anion on a molar basis is SO42−. The degree of separation is greatly enhanced for these species as the rate of water transport across the membrane is increased. The behaviour is replicated for HCO3- and NO3-, although to a lesser extent compared to SO42− due to their smaller ion stokes radii. Hence there is still a relatively high HCO3- and NO3- content in the permeate stream. To compensate for the lack of Ca2+ in the permeate stream to maintain charge balance with HCO3and NO3-, there is a higher flux of Na+ across the membrane. The effect of membrane charge density on rejection for the six-ion system under study is presented in Fig. 3. Enhancing the negative membrane charge density – or feed-membrane Donnan potential D,M improves SO42− rejection due to electrostatic repulsion. The rejection 2+ 2+ of Ca and Mg reduces with increasing negative charge density due to electrostatic attraction. The rejection of monovalent anions NO3- and HCO3- are accordingly reduced to maintain charge balance with the increased passage of divalent cations. The rejection of the monovalent cation Na+, on the other hand, is improved to maintain charge balance with the reduced passage of divalent anions. The effect of varying the pore dielectric constant on species rejection for the six-ion system under study is presented in Fig. 4. Reducing pore enhances the Born solvation energy barrier Wi for all species at the feed-membrane interface and hence the rejection of all species is subsequently improved. Oatley et al. [13] conducted single salt rejection experiments using Dow Filmtec NF99HF and NF270 elements and fitted the data to the DSPM&DE model to determine an appropriate pore , which was determined to be in the range 37.8 – 42.2. Argelaguet [14] followed the same procedure using Desal DS-5 DK elements on sea water and found pore to be ˜35. For all further modelling work presented in this paper pore was set to 37. Table 3 below presents estimates of membrane pore size, effective active layer thickness and feed-membrane Donnan potential for the installed NF elements in Ahafo, Ghana as the campaign developed over the first six months of operation. A general trend of a decrease in all species rejection is observed with time, supported by an increase in rpore and a decrease in Δxe. SO42− rejection also deteriorates appreciably with time – from 99.6% to 96.2%, indicating a change in membrane surface chemistry and the element’s inherent ability to adsorb anions to develop a negative charge density. These results are supported by an 18% reduction in magnitude of the fitted ΔϕD,M over six months of operation. The NF trains in Ahafo are subjected to a high fouling and scaling potential feed water and frequent chemical cleans are required to restore the element flux. It is thought that the combination of foulant, scale and frequent exposure to high and low pH cleans have caused irreversible damage to the membrane active layer and reduced its rejection capability. These observations have been made before by other researchers [15]. The initial performance of the installed MDS elements (rpore

*

c i,j


(18)

In addition to discretization of the membrane active layer, the membrane was also discretized along the feed channel as well. Feed channel velocity decreases along the element string due to flux of water through to the permeate. This reduces each ionic species’ mass transfer coefficient (see Appendix A) and hence provides for a larger concentration polarization factor when compared to the lead section of the element (see Eq. 1). Discretizing the membrane along the feed channel thus allows for more accurate estimation of species concentration at the membrane surface and hence a more accurate overall prediction of rejection. Species bulk concentration at each successive node within the feed channel was then determined using a mass balance as shown in Eq. 19. The membrane hydraulics equation (Eq. 16) was then also applied to each node along the element string with the overall permeate flux related to individual node permeate fluxes through the use of Eq. 20.

Cb,i,k+1 =

Jv,tot =

1 k

Cb,i,k 1 k i= 1

(

Jv,k SAk Q feed,k

)

( 1

Jv,k SAk Q feed,k

(

)C

p,i,k

Jv,k SAk Q feed,k

Jv,i

)

(19) (20)

Where Q feed,k is the volumetric feed flow rate to element k in an element string and SAk is the surface area of membrane k in an element string. 2.8. NF model simulation specifications Table 1 below provides key design parameters of the installed NF trains at the brine treatment plant in Ahafo, Ghana. For all subsequent modelling presented in this paper the array design was kept the same as the installed trains. Operational data processed by SGS laboratories in Tema, Ghana during the first six months of operation are provided in Appendix D. Data from the initial stages of operation (Table D1) were used as modelling inputs for determination of the initial pore size and effective active layer thickness of the installed elements. The same feed basis was also used to model the performance of membranes from other manufacturers to compare with the installed MDS membranes. Data provided in Tables D2, D3 and D4 were used to determine how the installed elements’ pore size, effective active layer thickness and membrane charge density varied as the operational campaign developed. Appendix E provides physical properties of the ions used in the simulation. Table 2 lists additional simulation parameters which were kept constant throughout the modelling work. 3. Results and discussion The intent of Fig. 3 and Fig. 4 is to illustrate the effect of membrane charge density and membrane pore dielectric constant, both of which are input parameters in the model, on individual species rejection in a full-scale nanofiltration system. Species rejection was computed at multiple permeate fluxes, via manipulation of the overall train volumetric recovery target for each set of simulations. Permeate production rate is directly proportional to the applied net driving pressure across the membrane, while the rate of dissolved species transport across the membrane is independent of net driving pressure. Increasing net driving pressure thus increases the difference in transport rate across the membrane between clean water and dissolved solutes, providing the impression that dissolved solute rejection increases as permeate flux increases as is clear in both sets of figures. The exception in this case is Na+, whose rejection appears to decrease as permeate flux is increased. This phenomenon is related to the relative composition of species in the feed solution being studied. Nanofiltration membranes generally

Table 1 Installed NF train specifications at mine water treatment plant in Ahafo Ghana.

5

Key design criteria

Unit

Value

Design flow rate Design volumetric recovery Operating temperature Element description

m3/hr % °C –

18 40-50 30 –

Membrane surface area Feed spacer thickness Array design Average permeate flux Membrane type Active layer material Support layer material

m2 mil – lmh – – –

33.06 31 – 17.6 – – –

Comment/Description

MDS 8040 NF (modified Desal DS5 DK) 3 vessels/5 elements each Average flux over element string Thin film membrane (TFM) Polyamide (PA) Polysulfone (PS)

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HCO3- loading into the reactor using the NF 90 elements and the fact that the NF 90 is a much tighter membrane with lower pure water permeability, the TFC SR-2 in this case would be the optimal element for selection.

Table 2 Key NF model simulation parameters. Key model simulation criteria

Unit

Value

Comment / Description

No. of elements per string

–

5

No. of nodes per element in string Total no. of nodes in string No. of membrane active layer nodes Numerical solver under-relaxation factor Solver convergence tolerance

– – –

2 10 10

Same as design in Ahafo Ghana

–

0.5

–

1.00E-05

4. Conclusions Sensitivity analyses showed Donnan exclusion and Born solvation effects played the most prominent role in determining the high SO42− rejection (> 99%) commonly observed using NF membranes for brackish water sources. The model was fitted to data obtained from six months of operation of a full-scale mine water treatment plant for a gold mine in Ahafo, Ghana to determine how the membrane pore radius, effective active layer thickness and membrane charge density varied as the operational campaign developed. Results showed that all three properties of the membrane deteriorated with time, most likely due to a combination of fouling, scaling and frequent exposure to high and low pH chemical cleans. Performance of elements from different manufacturers was then simulated and compared to the installed elements at the plant. Results showed that the elements most closely resemble a loosely wound NF membrane. Concern was expressed for the low Ca2+ rejection obtained with the elements, bearing in mind that the NF functions as a concentrator upstream of a gypsum precipitation reactor. The projected NF brine streams from each element were then run in PHREEQC to determine the element which provided the highest gypsum SR. The tightly wound NF 90 and intermediate TFC SR-2 elements provided the same gypsum SR, suggesting that the high rejection of monovalent species using the tightly wound element increases the ionic strength of the brine sufficiently to impact the Ca2+ and SO42− activity coefficients. The tightly wound NF 90 provided a significantly higher HCO3- rejection thus increasing the lime addition requirement into the reactor and also has a lower pure water permeability constant compared to the intermediate TFC SR-2 element, which was thus considered to be the optimal element for this specific case. It must be noted, however, that if the brine treatment process is modified and the NF placed into a recycle loop with ZLD targeted then this would not be the case. A loosely wound element would be preferred as it would allow passage of monovalent species – for which there is no geochemical control inside a precipitation reactor – into the permeate stream and thus preventing the requirement for a brine bleed. Through this study it has been demonstrated that the model is powerful enough to simulate performance of a full-scale nanofiltration system with multiple ionic species being considered. The model contains enough membrane-specific input parameters to describe the behaviour of these complex systems. These parameters are (1) membrane pore radius, (2) membrane active layer thickness, (3) membrane charge density and (4) membrane pore dielectric constant. Parameters (1) and (2) largely account for the difference in transport behaviour between the larger multivalent ions, such as Ca2+ and Mg2+, and the smaller univalent ions such as Na+ and NO3−.

= 0.46 nm, Δxe = 0.25 μm) is compared with the simulated performance of elements from other manufacturers in Fig. 5 below. Three other membranes were used in the comparison – a Dow Filtec NF90 which is considered to be a relatively tight membrane with rpore = 0.34 nm and Δxe = 1.46 μm [16], a Desal DS-5 DL which is considered to be a relatively loose membrane with rpore = 0.5 nm and Δxe = 0.37 μm [17] and a Koch TFC SR-2 which is considered to be an intermediate between the two abovementioned membranes with rpore = 0.46 nm and Δxe = 1.09 μm [16]. All four membranes used in the simulation contain a polyamide active layer and thus the same value for 2− rejecD,M was used in each case. No significant difference in SO4 tion is observed for the membranes, with a rejection ratio > 99% for all cases at a typical volumetric recovery of 40%. From this it can be deduced that the Donnan exclusion and Born solvation effects are dominant with respect to SO42− rejection. For all other species the physical properties of the membrane active layer play a significant role in rejection. Of consequence is the reduced Ca2+ rejection for the installed elements compared to the NF90 and TFC SR-2 elements. This reduces the gypsum saturation ratio of the NF brine entering the gypsum precipitation reactor, which needs to be compensated for by an increase in lime addition. On the other hand, the combined rejection of monovalent species is enhanced using NF 90 and TFC SR-2 elements with the NF90 in particular more closely resembling an RO membrane. This enhances the ionic strength of the NF brine which suppresses the Ca2+ and SO42− activity coefficients and hence the gypsum saturation ratio (SR). Another consequence is the increased carbonic species loading entering the reactor – the HCO3- rejection at 40% recovery is projected to be 73.5% for the NF 90, as opposed to 12.6% for the installed MDS elements – which ultimately drives up the lime consumption rate. The results were used to determine the projected NF brine stream entering the gypsum precipitation reactor for the different elements at 40% recovery. PHREEQC, an open-source geochemical modelling software developed by the US Geological Survey [18], was then used in conjunction with its minteq database for thermodynamic properties of the relevant aqueous species to determine the ionic strength and gypsum SR of each NF brine stream to determine the “optimal” element. The results are presented in Table 4 below. The NF 90 and TFC SR-2 provide the highest gypsum SR (279%). Taking into account the increased

Fig. 3. Effect of membrane charge density on species rejection. SGS data from 2017/09/19 used as feed input for model. Feed flow rate to each element string taken as 6 m3/hr, providing a total train feed flow rate of 18 m3/hr. Membrane pore radius taken to be 0.46 nm and effective active layer thickness of 0.25 μm. pore = 39. 6

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Fig. 4. Effect of membrane pore dielectric constant on species rejection. SGS data from 2017/09/19 used as feed input for model. Feed flow rate to each element string taken as 6 m3/hr providing a total train feed flow rate of 18 m3/hr. Membrane pore radius taken to be 0.46 nm and effective active layer thickness of 0.25 μm. 7 mV . D, M =

Table 3 Results from fitting operational data from brine treatment plant in Ahafo, Ghana to the NF model to determine installed element pore size, effective active layer thickness and feed-membrane Donnan potential. Date

Data

2017/09/19

Modelled SGS Modelled SGS Modelled SGS Modelled SGS

2017/11/23 2017/12/21 2018/03/09

rpore

Δxe

ΔϕD,M

Na

SO4

Ca

Mg

HCO3

NO3

pH

nm 0.46

μm 0.25

mV −21.06

0.50

0.21

−20.65

0.50

0.21

−19.54

0.53

0.15

−17.32

rej% 9.1% 21.0% 30.5% 46.9% 27.0% 41.5% 34.8% 31.7%

rej% 99.3% 99.6% 98.3% 97.9% 98.4% 98.2% 96.4% 96.2%

rej% 88.3% 86.7% 82.8% 85.2% 82.1% 83.0% 80.4% 79.6%

rej% 94.1% 94.4% 87.5% 87.3% 87.2% 83.6% 83.5% 85.2%

rej% 15.7% 42.3% −33.1% 22.5% −23.1% 15.1% −32.1% 15.4%

rej% 12.4% −3.7% −38.2% −14.6% −26.8% −23.8% −35.3% −23.0%

– 7.8 7.7 7.9 7.8 8.1 7.8 7.8 7.7

Fig. 5. Comparison of modelled species rejection using NF elements from different manufacturers. SGS data from 2017/09/19 used as feed input for model. Feed flow 21 mV . rate to each element string taken as 5.5 m3/hr, providing a total train feed flow rate of 16 m3/hr. pore = 37 and D, M =

rejection of all species, but has the greatest effect on SO42- due to its ionic charge and small stokes radius when compared to the multivalent cations. The challenge with this model is the ability to verify these input parameters with independent laboratory experiments. Attempts have been made to verify parameters (1) and (2) using multiple methods. These range from indirect methods, such as the performance of gas bubble permeation tests, to direct methods such as capturing high resolution images of the membrane active layer surface. Parameters (3) and (4) are more difficult to verify independently. One common method for studying membrane charge density on the surfaces of polyamide membranes is through the use of an electro-kinetic analyser. Membrane charge effects are feed chemistry dependent. Once electro-kinetic data becomes available for calcium sulphate-dominated solutions similar to the those studied in this paper, it should be possible to incorporate a membrane-charge density sub-module into the model presented.

Table 4 Projected NF brine stream entering gypsum precipitation reactor in Ahafo, Ghana. SGS data from 2017/09/19 used as feed input for model. Ionic species

Na

SO4

Ca

Mg

HCO3

NO3

Ionic strength

Gypsum SR

Elements MDS install NF 90 TFC SR-2 DS-5 DL

mg/l 174 191 169 180

mg/l 4087 4100 4097 4086

mg/l 1459 1538 1513 1445

mg/l 276 283 281 272

mg/l 595 818 701 565

mg/l 342 425 398 324

mol/l 0.118 0.123 0.121 0.117

% 274% 279% 279% 273%

Parameters (1) and (2) alone cannot describe the high SO42- rejection (> 99%) and the slightly lower rejection for the multivalent cations (85–95%) which is observed in nanofiltration systems across a variety of feed water types. Parameter (3) i.e. the effect of Donnan partitioning greatly enhances the rejection of SO42- due to electrostatic repulsion, whilst also reducing the rejections of Ca2+ and Mg2+ due to electrostatic attraction. Parameter (4) i.e. Born solvation effects enhance the

7

Journal of Water Process Engineering 32 (2019) 100900

R. Bonner, et al.

Appendix A The mass transfer coefficient correction factor is computed for each species using Eq.s A1 and A2 below.

= i

=

i

(A1)

1.4 1.7 i )

+ (1 + 0.26

Jv k c,i

(A2)

The conventional mass transfer coefficient k c,i is determined using the Sherwood number computed for each species in the boundary layer according to Eq. A3:

Shi =

k c,iL Di,

(A3)

Where L is the characteristic length. In the case of modelling the performance of a spiral wound 8-inch NF element the characteristic length is assumed to be equal to the hydraulic diameter of the feed channel within each of the membrane leaves and is a function of the geometry of the installed feed spacer [19]:

L= dh =

4

( )+ 2 h

4

(1

)

(A4)

The Sherwood number for each species is typically determined using a dimensionless number correlation as a function of the Reynolds and Schmidt numbers, as shown in Eq. 8 below. The constants a1, a2 and a3 are regression parameters depending on the element geometry [20].

Shi = a1Rea2 Sc ai 3

(A5)

Appendix B The Davies equation for activity coefficients in brackish water sources is shown in Eq. B1.

ln( i) =

Az2i

I 1+

I

0.3I

(B1)

The parameter A is a function of the operating temperature and dielectric constant of the fluid as determined according to Eq. B2.

A= 1.82 × 106 ( T)

3

(B2)

2

Appendix C Correlations for the diffusive and convective hindrance factors for each species inside the active layer of the membrane are provided in Eq.s C1 and C2 respectively.

9 1.56034 i ln ( i) 8 2.81903 i 4 + 0.270788 i5

1+ Ki,d =

Ki,c =

+ 0.528155

i

1.10115

i

6

i

2

+ 1.91521 0.435933

i

i

3

7

(C1)

i

1 + 3.867 i 1.907 i2 0.834 1 + 1.867 i 0.741 i2

i

3

(C2)

Appendix D See Tables D2–D4 Table D1 SGS data from NF trains in brine treatment plant in Ahafo, Ghana. Sample date: 2017/09/19.

Stream RO brine NF perm

Na

SO4

Ca

Mg

Alk CaCO3

NO3

TDS

EC

pH

mg/l 162 128

mg/l 2460 11

mg/l 923 123

mg/l 170 9.6

mg/l 549 317

mg/l 322 334

mg/l 5144 910

μS/cm 4700 1150

– 7.9 7.7

8

Journal of Water Process Engineering 32 (2019) 100900

R. Bonner, et al.

Table D2 SGS data from NF trains in brine treatment plant in Ahafo, Ghana. Sample date: 2017/11/23.

Stream RO brine NF perm

Na

SO4

Ca

Mg

Alk CaCO3

NO3

TDS

EC

pH

mg/l 192 102

mg/l 3570 75

mg/l 1430 211

mg/l 208 26.5

mg/l 498 386

mg/l 370 424

mg/l 6038 1346

μS/cm 5600 1600

– 7.8 7.8

Table D3 SGS data from NF trains in brine treatment plant in Ahafo, Ghana. Sample date: 2017/12/21.

Stream RO brine NF perm

Na

SO4

Ca

Mg

Alk CaCO3

NO3

TDS

EC

pH

mg/l 162 94.8

mg/l 3410 63

mg/l 1170 199

mg/l 176 28.9

mg/l 522 443

mg/l 328 406

mg/l 4950 1320

μS/cm 5100 1600

– 8 7.8

Table D4 SGS data from NF trains in brine treatment plant in Ahafo, Ghana. Sample date: 2018/03/09.

Stream RO brine NF perm

Na

SO4

Ca

Mg

Alk CaCO3

NO3

TDS

EC

pH

mg/l 164 112

mg/l 3270 124

mg/l 1310 267

mg/l 240 35.5

mg/l 482 408

mg/l 356 438

mg/l 6079 1433

μS/cm 5350 1700

– 7.7 7.7

Appendix E Table E1 Table E1 Ion physical property data. Di, Species Na+ SO42− Ca2+ Mg2+ HCO3− NO3−

at 30 °C

m2/s 1.50E-09 1.20E-09 8.97E-10 8.00E-10 1.34E-09 2.15E-09

Ion stokes radius m 1.84E-10 2.29E-10 3.06E-10 3.44E-10 2.05E-10 1.30E-10

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