International Journal of

Molecular Sciences

Article
Recovery of Spent Sulphuric Acid by Diffusion Dialysis Using
a Spiral Wound Module
Arthur Merkel 1, * , Ladislav Čopák 1, *, Lukáš Dvořák 2 , Daniil Golubenko 3 and Libor Šeda 1

1 MemBrain s. r. o. (Membrane Innovation Centre), Pod Vinicí 87, 471 27 Stráž pod Ralskem, Czech Republic;
libor.seda@membrain.cz
2 Institute for Nanomaterials, Advanced Technologies and Innovation, Technical University of Liberec,
Studentská 2, 461 17 Liberec, Czech Republic; lukas.dvorak@tul.cz
3 Kurnakov Institute of General and Inorganic Chemistry of the Russian Academy of Sciences,
31 Leninsky Avenue, 119991 Moscow, Russia; golubenkodaniel@yandex.ru
* Correspondence: arthur.merkels@gmail.com (A.M.); ladislav.copak@membrain.cz (L.Č.);
Tel.: +420-777-539-924 (A.M.); +420-720-051-738 (L.Č.)

Abstract: In this study, we assess the effects of volumetric flow and feed temperature on the perfor-
mance of a spiral-wound module for the recovery of free acid using diffusion dialysis. Performance
was evaluated using a set of equations based on mass balance under steady-state conditions that
describe the free acid yield, rejection factors of metal ions and stream purity, along with chemical
analysis of the outlet streams. The results indicated that an increase in the volumetric flow rate of
water increased free acid yield from 88% to 93%, but decreased Cu2+ and Fe2+ ion rejection from 95%
to 90% and 91% to 86%, respectively. Increasing feed temperature up to 40 ◦ C resulted in an increase



in acid flux of 9%, and a reduction in Cu2+ and Fe2+ ion rejection by 2–3%. Following diffusion


dialysis, the only evidence of membrane degradation was a slight drop in permselectivity and an
Citation: Merkel, A.; Čopák, L.;
increase in diffusion acid and salt permeability. Results obtained from the laboratory tests used in
Dvořák, L.; Golubenko, D.; Šeda, L.
a basic economic study showed that the payback time of the membrane-based regeneration unit is
Recovery of Spent Sulphuric Acid by
approximately one year.
Diffusion Dialysis Using a Spiral
Wound Module. Int. J. Mol. Sci. 2021,
22, 11819. https://doi.org/10.3390/
Keywords: anion-exchange homogeneous membrane; membrane degradation; mass balance; case
ijms222111819 study; payback time

Academic Editor: Victor

V. Nikonenko
1. Introduction
Received: 4 October 2021 Industrial processes often generate wastewaters characterized by high acidity or high
Accepted: 28 October 2021
alkalinity with pH lower than 1 and above 14 respectively in some cases and/or a high
Published: 30 October 2021
metal content [1,2]. Membrane technologies facilitate the recovery of valuable dissolved
components such as metals and allow the reuse of acids or alkalis. Among the various
Publisher’s Note: MDPI stays neutral
membrane technologies presently available, diffusion dialysis (DD), nanofiltration (NF),
with regard to jurisdictional claims in
electrodialysis (ED), membrane distillation (MD) and forward osmosis (FO) are the most
published maps and institutional affil-
promising as regards the circular economy paradigm [3,4]. It is widely believed that DD
iations.
represents the optimal process for recovery of acids at high concentrations (i.e., >0.5 M) [3].
Compared to other technologies, DD has a number of advantages [5,6], including low
energy consumption (due to spontaneous processes driven by activity gradients), low
installation costs, simple operation and maintenance, and high product quality (due to the
Copyright: © 2021 by the authors.
high selectivity of anion-exchange membranes (AEMs) for acids). In addition, the process
Licensee MDPI, Basel, Switzerland.
is considered environmentally friendly due to the lack of post-processing and chemical
This article is an open access article
agents used [3,4,7].
distributed under the terms and
DD is a membrane separation process driven by a concentration gradient and, in
conditions of the Creative Commons
environmental engineering, it is mainly used for the recovery of spent acids or alkalis [5,8].
Attribution (CC BY) license (https://
The basic principle of separation utilises the high membrane permeability of acids and
creativecommons.org/licenses/by/
4.0/).
alkalis relative to metal salts, in association with proton-transport via the hydrogen bond

Int. J. Mol. Sci. 2021, 22, 11819. https://doi.org/10.3390/ijms222111819 https://www.mdpi.com/journal/ijms

Int. J. Mol. Sci. 2021, 22, 11819 2 of 16

network of water molecules, a process known as the ‘Grotthuss mechanism’ [9–11]. This
latter process explains why DD is most often used specifically to recover acids [3]. AEMs
are the most frequently used materials for processing of acids via DD. Owing to the
positively charged polymer matrix surrounding the pores, diffusion of cations, such as
Fe2+ , Fe3+ , Cu2+ or Pb2+ slows down in the AEM-matrix, making it possible to achieve
higher selectivity coefficients [6]. In recent years, development of DD has focused on the
synthesis of new membranes and modifications to known materials [12–15], optimization
of module structure [16,17], expanding known applications and researching potential new
applications [17–22].
While laboratory-scale acid recovery experiments using DD are mainly conducted
in batch configurations, plant-scale operations benefit from the use of a continuous dial-
yser, which provides a number of advantages, including higher productivity, lower costs,
convenient assemblage and transportation and a continuous process more appropriate
for practical production-level use [6,18]. As such, the next step towards advanced DD is
usually seen as optimization of the module configuration. At present, ‘plate-and-frame’ is
the most commonly used membrane module type; however, the space-saving characteris-
tics and modular nature of spiral-wound DD membrane modules has recently attracted
much attention [6,17,23]. Zhang et al. [23], for example, while studying the process of
hydrochloric acid separation from aluminium salts using a DD spiral-wound membrane
module, showed that acid yield, recovered acid concentration and metal salts rejection were
all affected by diffusate and dialysate flow rates. According to these authors, the optimized
ratio of feed over water flow rate is around 1. A relative increase in the feed (dialysate)
flow led to a decrease in acid yield due to the reduction in solution contact time in the
module, while the concentration of recovered acid and leaked aluminium salts increased.
Membrane stability is a key factor for their use in DD, which characterizes the steadi-
ness of the membrane’s physicochemical properties such as permeability and separation
factor under operation conditions [6]. In characterizing such membranes, researchers tend
to concentrate on the alkaline-stability of AEMs [24], primarily due to their frequent use in
alkaline fuel cells. In comparison, there is relatively little data available on the acid-stability
of AEMs. Commercial AEMs for DD tend to be more stable than nanofiltration membranes
in acid solutions when used for acid recovery based on polyamides [3]. Indeed, it has
been reported that commercial and tailor-made AEMs for DD based on bromomethylated
poly(phenylene oxide) (BPPO) degrade noticeably in acid solutions within 72 h [25,26], with
both loss of mass and reduced ion-exchange capacity reported. Other studies, however,
have reported high stability of BPPO-based membranes in acid solutions [27].
In the present study, we assess the capacity of a spiral-wound module designed for
continuous recovery of free acid using DD to separate sulphuric acid and Cu2+ and Fe2+
salts. During this experimental campaign, we also investigate impact of volumetric flow
and feed temperature on module performance and assess membrane degradation through
characterization of ion-exchange capacity and mechanical and transport properties before
and after DD operation.

2. Results
2.1. Effect of Volumetric-Flow Ratio
Electrical conductivity of the outlet streams increases over time for Test 1.1. This
behaviour is caused by the fact that diluted acidic solutions have higher conductivity than
demineralized water which was present in the module before its run-up. Steady state of
the system is visible from the 90th minute of the process on (Figure 1a). In case of Test 2.1,
when module was filled with liquid from the previous test, electrical conductivity of both
outlet streams decreases over time. From this observation results that acid is recovered
with higher efficiency. The electrical conductivity of the regenerated acid is on average 6 to
8 times higher than the electrical conductivity of the processed salty acid stream leaving
the module. The stationary electrical conductivity of the diffusate is higher in the case
of Test 1.1 (Figure 1a, 191 mS·cm−1 ) than in the case of Test 2.1 (Figure 2a, 160 mS·cm−1 ).
 Int.J.J.Mol.
Int. Mol.Sci.
Sci.2021,
2021,22,
22,11819
11819 33 of
of 17
17

Int. J. Mol. Sci. 2021, 22, 11819 withhigher

with higherefficiency.
efficiency.The Theelectrical
electricalconductivity
conductivityof ofthe
theregenerated
regeneratedacid acidisisononaverage
average 6
3 of616
to88times
to timeshigher
higherthanthanthetheelectrical
electricalconductivity
conductivityof ofthe
theprocessed
processedsalty saltyacidacidstream
streamleaving
leaving
themodule.
the module.The Thestationary
stationaryelectrical
electricalconductivity
conductivityof ofthe
thediffusate
diffusateisishigher
higherin inthe
thecase
caseof of
Test 1.1 (Figure 1a, 191 mS⋅cm −1) than in the case of Test 2.1 (Figure 2a, 160 mS⋅cm−1
Test 1.1 (Figure 1a, 191 mS⋅cm ) than in the case of Test 2.1 (Figure 2a, 160 mS⋅cm ). This
−1 −1). This

This comparison
comparison
comparison implies
implies implies
that that a volumetric-flow
thataavolumetric-flow
volumetric-flow ratiohas
ratio ratio
has has
animpact
an an on
impact impact
onthe on the concentration
theconcentration
concentration offree
of free
of free
acid in
acid acid
in the in the
the diffusate. diffusate.
diffusate. AA higher A
higher flux higher
flux of flux
of acid
acid inof
in theacid
the casein the
case of case
of Test
Test 2.1of Test 2.1 isby
2.1 isis caused
caused caused
by by a
aa higher
higher
higher logarithmic
logarithmic
logarithmic meanof
mean ofmean of concentration
concentration
concentration differencedifference
difference (adriving
(a (a driving
driving forcefor
force force
for for transfer).
mass
mass mass transfer).
transfer). Forthis
For For
this
this reason,
reason,the
reason, themass the
massflowmass
flowof flow
offree of
freeacid free
acidper acid per exchange-area
perexchange-area
exchange-areaunit unit
unitisishigher is
higherand higher
andresults and
resultsin resultsbiggera
inaabigger in
bigger yield
yield(Table
(Table1). (Table
1).Last 1).
Lasttwo Last
twopoints two
pointsof points of
ofdialysate dialysate
dialysateflowflowrate flow
ratefor rate
forTest for
Test1.1 Test 1.1
1.1exhibit exhibit a
exhibitaarelatively relatively
relativelybig big
yield
big deviation
deviation from from previously
from previously
previously measured measured
measured values values (Figure
values (Figure
(Figure 1b). 1b). Small
1b). Small perturbation
Small perturbation
perturbation could could
could be be
be
deviation
caused
causedby by inaccuracy
byinaccuracy
inaccuracyof of
ofthethe flow
theflow valves
flowvalves used
valvesused
usedfor for regulation
forregulation
regulationof of
ofthethe inlet
theinlet
inletfeedfeed flowrate.
feedflowrate.
flowrate.No No
No
caused
difficultieswere
difficulties wereobserved
observedwith withmaintaining
maintainingthe thesetsetvalue
valueof offlowrate
flowrateof ofthe
the inlet
inlet streams
streams
difficulties were observed with maintaining the set value of flowrate of the inlet streams
for Test 2.1 (Figure 2b).
for
for Test2.1
Test 2.1(Figure
(Figure2b).2b).

(a)
(a) (b)
(b)
Figure
Figure1.1.
Figure Conductivity
1.Conductivity (a)
Conductivity(a) and
(a)and flow
andflow rate
flowrate (b)
rate(b) as
(b)asasaaafunction
function of
functionof time
oftime for
timefor Test
forTest 1.1.
Test1.1. (1)
1.1.(1) diffusate;
(1)diffusate; (2)
diffusate;(2) dialysate.
(2)dialysate. Initial
dialysate.Initial fill:
Initialfill: water.
fill:water.
water.
Note
Note that
that the
the lines
lines connecting
connecting experimental
experimental points
points are
are not
not true
true
Note that the lines connecting experimental points are not true trendlines. trendlines.
trendlines.

(a)
(a) (b)
(b)
Figure
Figure2.2.
Figure Conductivity
2.Conductivity (a)
Conductivity(a) and
(a)and flow
andflow rate
flowrate (b)
rate(b) as
asaaafunction
(b)as function of
functionof time
oftime for
timefor Test
forTest 2.1.(1)
Test2.1.
2.1. (1) diffusate;
(1)diffusate; (2)
diffusate;(2) dialysate.
(2)dialysate. Initial
dialysate.Initial fill:
Initialfill: DD
fill:DD
DD
profilefrom
profile fromthe
theprevious
previoustesting.
testing.Note
Notethat
thatthe
thelines
linesconnecting
connectingexperimental
experimentalpoints
pointsare
arenot
nottrue
truetrendlines.
trendlines.
profile from the previous testing. Note that the lines connecting experimental points are not true trendlines.
Evidence that the mass transfer occurs in the dialyser can be concluded from the
change in the measured flow rates of the inlet stripping medium and the diffusate (Table 2).
Preferential transfer of acid is visible from the composition of the streams. In diffusate
is present mainly sulphuric acid beside solvent and small amount of iron and copper
sulphates. On the contrary, most salts are in dialysate, whereas sulphuric acid is almost
not present. Change in composition is also visible in densities of the solutions. Dialysate
leaving the module is less dense than feed because of the missing acid (Table 3).
Int. J. Mol. Sci. 2021, 22, 11819 4 of 16

Table 1. Summarized values for performance parameters used for Tests 1.1 and 2.1. Sym-
bols: Y—yield of acid, RCu 2+ —rejection of Cu2+ , RFe 2+ —rejection of Fe2+ , JH2 SO4 —flux of acid,
wH2 SO4 , FEED ( DIF/DI A) —weight fraction of acid in feed (diffusate/dialysate) solution, PFEED (DIF) —
ionic purity of feed (diffusate).

Parameter Unit Test 1.1 Test 2.1

Y % 88 ± 5 93 ± 6
RCu 2+ % 95 ± 5 90 ± 10
RFe 2+ % 91 ± 9 86 ± 10
JH2 SO4 g ·m−2 ·h−1 81 ± 3 87 ± 3
wH2 SO4 , FEED % 5.18 ± 0.10 4.84 ± 0.10
wH2 SO4 , DIF % 4.39 ± 0.09 3.48 ± 0.07
wH2 SO4 , DI A % 0.66 ± 0.01 0.41 ± 0.01
PFEED % 76.8 ± 1.3 76.0 ± 1.3
PDIF % 97.5 ± 0.2 95.6 ± 0.3
PDIF /PDIA - 3.2 4.4

Table 2. Flows of inlet and outlet streams (volumetric flows in L·h−1 and mass flows in kg·h−1 ).
.
Symbols: V FEED ( ROW/DIF/DI A) —volumetric flow rate of feed (RO permeate/diffusate/dialysate),
.
m FEED ( ROW/DIF/DI A) —mass flow rate of feed (RO permeate/diffusate/dialysate).

Parameter Test 1.1 Test 2.1

.
V FEED 8.55 ± 0.05 9.42 ± 0.05
.
V ROW 8.64 ± 0.05 11.45 ± 0.05
.
V DIF 8.98 ± 0.09 12.28 ± 0.12
.
V DI A 8.21 ± 0.08 8.58 ± 0.09
.
m FEED 8.83 ± 0.05 9.70 ± 0.05
.
m ROW 8.63 ± 0.05 11.42 ± 0.05
.
m DIF 9.22 ± 0.18 12.53 ± 0.25
.
m DI A 8.24 ± 0.16 8.59 ± 0.17

Table 3. Analytical measurements for Tests 1.1 and 2.1.

Composition Unit Feed Diffusate Dialysate Feed Diffusate Dialysate

Test 1.1 Test 2.1
H2 SO4 g ·L−1 53.5 ± 1.1 45.0 ± 0.9 6.6 ± 0.1 50.0 ± 1.0 35.5 ± 0.7 4.1 ± 0.1
Fe2+ ppm 284 ± 14 21 ± 1 263 ± 13 282 ± 14 30 ± 2 263 ± 13
Cu2+ ppm 50 ± 3 3.2 ± 0.2 50 ± 3 43 ± 2 3.4 ± 0.2 42 ± 2
Density kg·L−1 1.033± 0.001 1.026 ± 0.001 1.004 ± 0.001 1.030 ± 0.001 1.020 ± 0.001 1.001 ± 0.001

2.2. Effect of Feed Temperature

The temperature of the feed for Test 1.2 under laboratory conditions gradually in-
creased (from 22.1 ◦ C at the beginning to 24.4 ◦ C at the end of the test lasting 135 min).
This is caused by the dissipation of mechanical energy delivered by the pump. Since part
of the pumped feed solution is warmer and recycled back to the feed vessel, it mixes with
colder liquid which increases the feed temperature. In the remaining tests (Test 2.2 and
3.2), the set value of temperature was maintained without any issues.
Sulphuric-acid yield does not change much and remains constant over studied temper-
ature range, 76%. The value is low, which is caused by the low flow ratio of input streams
(Table 4). Furthermore, this is proof that different volumetric flows of input streams can
significantly influence system performance. The measured flow rates again prove that
mass transfer occurs in the dialyser and is visible in the increase of the mass flow rate
between the inlet RO permeate and the diffusate (Table 5).
Int. J. Mol. Sci. 2021, 22, 11819 5 of 16

Table 4. Summarized values of performance parameters used for Tests 1.2, 2.2, and 3.2. Symbols:
TFEED —temperature of feed, Y—yield of acid, RCu 2+ —rejection of Cu2+ , RFe 2+ —rejection of Fe2+ ,
JH2 SO4 —flux of acid, wH2 SO4 , FEED ( DIF/DI A) —weight fraction of acid in feed (diffusate/dialysate)
solution, PFEED (DIF) —ionic purity of feed (diffusate).

Parameter Unit Test 1.2 Test 2.2 Test 3.2

TFEED ◦C 20–25 30 40
Y % 75 ± 4 76 ± 4 76 ± 4
RCu 2+ % 96 ± 4 95 ± 5 94 ± 6
RFe 2+ % 96 ± 4 95 ± 5 93 ± 7
JH2 SO4 g ·m−2 ·h−1 66 ± 3 71 ± 3 72 ± 3
wH2 SO4 , FEED % 4.8 ± 0.1 4.9 ± 0.1 4.9 ± 0.1
wH2 SO4 , DIF % 4.4 ± 0.1 4.4 ± 0.1 4.6 ± 0.1
wH2 SO4 , DI A % 1.30 ± 0.02 1.19 ± 0.02 1.25 ± 0.03
PFEED % 75.7 ± 1.6 76.0 ± 1.3 75.8 ± 1.3
PDIFF % 98.2 ± 0.1 97.6 ± 0.2 97.2 ± 0.2
PDIF /PDIA - 2.2 2.3 2.2

Table 5. Inlet and outlet stream flows (volumetric flows in L·h−1 and mass flows in kg·h−1 )
.
for Tests 1.2, 2.2 and 3.2. Symbols: V FEED ( ROW/DIF/DI A) —volumetric flow rate of feed
.
(RO permeate/diffusate/dialysate), m FEED ( ROW/DIF/DI A) —mass flow rate of feed (RO perme-
ate/diffusate/dialysate).

Parameter Test 1.2 Test 2.2 Test 3.2

.
V FEED 9.04 ± 0.05 9.18 ± 0.05 9.36 ± 0.05
.
V ROW 6.93 ± 0.05 7.23 ± 0.05 6.95 ± 0.05
.
V DIF 7.36 ± 0.07 7.59 ± 0.08 7.51 ± 0.08
.
V DI A 8.59 ± 0.09 8.82 ± 0.09 8.81 ± 0.09
.
m FEED 9.32 ± 0.05 9.46 ± 0.05 9.65 ± 0.05
.
m ROW 6.91 ± 0.05 7.22 ± 0.05 6.94 ± 0.05
.
m DIF 7.57 ± 0.15 7.80 ± 0.16 7.72 ± 0.15
.
m DI A 8.66 ± 0.17 8.88 ± 0.18 8.87 ± 0.18

If the RV parameter is higher than 1, then acid yield decreases. On the other hand,
the weight fraction of acid in the diffusate increases and approaches the concentration of
acid in the feed stream (Table 6). With a higher feed flow rate, the residence time of the
dialysate in the module is shorter for acid transfer, so a smaller portion of the fed acid will
be recovered. Since stripping medium flows at lower velocity, it will leave the module
enriched with an acid (and metal ions as well) with a higher components’ concentration.

Table 6. Analytical measurements for Test 3.2.

Composition Unit Feed Diffusate Dialysate

H2 SO4 g ·L−1 50.4 ± 1.0 47.5 ± 0.9 12.6 ± 0.3
Fe2+ ppm 286 ± 14 25 ± 1 282 ± 14
Cu2+ ppm 45 ± 2 3.7 ± 0.2 45 ± 2
Density kg·L−1 1.031 ± 0.001 1.028 ± 0.001 1.008 ± 0.001

2.3. Membrane Properties

According to the manufacturer, the module includes a commercial anion exchange
membrane Fumasep® FAD-PET-75 (Fumatech BWT GmbH, Bietigheim-Bissingen, Ger-
many). Fumasep® FAD-PET-75 is a PET-reinforced anion exchange membrane with low
resistance, high acid transfer rate, high mechanical stability, and high stability in an acidic
environment. After exposition of the membrane to the acidic environment no significant
differences in the IR spectra are observed (Figure 3b). Figure 3b shows typical stress-strain
 2.3. Membrane Properties
According to the manufacturer, the module includes a commercial anion exchange
membrane Fumasep® FAD-PET-75 (Fumatech BWT GmbH, Bietigheim-Bissingen, Ger-
Int. J. Mol. Sci. 2021, 22, 11819 many). Fumasep® FAD-PET-75 is a PET-reinforced anion exchange membrane with6 low of 16
resistance, high acid transfer rate, high mechanical stability, and high stability in an acidic
environment. After exposition of the membrane to the acidic environment no significant
differences in the IR spectra are observed (Figure 3b). Figure 3b shows typical stress-strain
curves of membranes before and after use. The curves show the elastic region, yield and
curves of membranes before and after use. The curves show the elastic region, yield and
strain hardening.
strain hardening.

(a) (b)
Figure
Figure 3.
3. (a)
(a) Fourier
Fourier transform
transform infrared
infrared spectroscopy
spectroscopy (FT-IR)
(FT-IR) spectra
spectra and
and (b)
(b) stress-strain
stress-strain curves
curves for
for membranes
membranes (1)
(1) before
before
use (initial state) and (2) after use (in a dry state, Cl−− form).
use (initial state) and (2) after use (in a dry state, Cl form).

After
After the
the operation
operation Young’s
Young’s modulus, Yield strength and Elongation at break do not
change,
change, and the Tensile strength even
and the Tensile strength even increases
increases (Table
(Table 7).
7). Visually,
Visually, there are no cracks or
traces
traces of
of degradation
degradation of of the
the polyethylene
polyethylene terephthalate
terephthalate (PET)
(PET) mesh on both SEM images
(Figure
(Figure 4).
4). Most
Most of
of the
the physicochemical
physicochemical properties
properties of
of membranes
membranes do do not
not change
change signifi-
signifi-
cantly,
cantly, but diffusion permeability increases by 22% and permselectivity
permselectivity decrease
decrease by
by 1.4%
1.4%
(Table
(Table 7).

Table 7.
Table Physical and
7. Physical and chemical
chemical parameters
parameters of Fumasep®®FAD-75.
of Fumasep FAD-75.

Parameter Unit Value (Initial) Value

Value (after (after
Use)
Parameter Unit Value (Initial)
Thickness (dry) µ 76 ± 1 78 ± 1Use)
Ion exchange capacity (Cl− form) Thickness (dry)meq·g−1 1.51μ± 0.03 76 ± 1 1.53 ± 0.03 78 ± 1
− form −1 22 ± −1
Specific conductivity in SO4Ion exchange capacity (Cl mS−·cm
form) meq·g 2 1.51 ± 0.03 15 ± 1 ± 0.03
1.53
·kg−1 NaCl)
Permselectivity (at 0.1/0.5 molSpecific conductivity in SO4% − form 92.2 ± 0.4
mS·cm −1 22 ± 2 90.8 ± 0.4 15 ± 1
Water uptake wt.%−1 28 ± 1 26 ± 1
Permselectivity
Young’s modulus (at 0.1/0.5 mol·kg
MPa NaCl) %
750 ± 30 92.2 ± 0.4 740 ± 30 ± 0.4
90.8
Yield strength Water uptake MPa wt.%
8.5 ± 0.5 28 ± 1 26 ± 1
9.4 ± 0.5
Tensile strength Young’s modulus MPa 42 ± 1
MPa 750 ± 30 55 ±740
1 ± 30
Elongation at break Yield strength 2% −1 19 ± 2
MPa 8.5 ± 0.5 22 ±9.4
2 ± 0.5
CuSO4 diffusion permeability coefficient at 0.1M CuSO4 cm ·s (3.0 ± 0.2)·10−7 (3.7 ± 0.2)·10−7
Tensile strength 2 −1 MPa 42 ± 1 55 ± 1
H2 SO4 diffusion permeability coefficient at 0.1M H2 SO4 cm ·s (3.8 ± 0.2)·10−6 (4.6 ± 0.2)·10−6
Elongation at break % 19 ± 2 22 ± 2
CuSO4 diffusion permeability coefficient at
2.4. Economic Study cm2·s−1 (3.0 ± 0.2)·10−7 (3.7 ± 0.2)·10−7
0.1M CuSO4
The4 diffusion
H2SO followingpermeability
study deals with expenses
coefficient at and savings before and after implementation
of the spiral-wound diffusion dialyzers into a cm2·s−1plant
generic (3.8consuming
± 0.2)·10−6 15%
(4.6H
± 0.2)·10 −6
0.1M H2SO4 2 SO4 and
generating acidic waste. The study considers two cases of processing 90 kg·h−1 acidic
wastewater at various degrees of dilution (5% and 10%) by dialysis. Re-concentration to
15% H2 SO4 is also considered. The treatment section consists of neutralization by 20%
suspension of slaked lime (technical-grade purity, 90%) according to a scheme shown in
Figure 5A,B.
Int. J. Mol. Sci. 2021, 22, 11819 7 of 16
Int. J. Mol. Sci. 2021, 22, 11819 7 of 17

Int. J. Mol. Sci. 2021, 22, 11819 Figure 4. Scanning electron microscopy images detailing membrane state before use ((a) surface,8(c)of 17
Figure 4. Scanning electron microscopy images detailing membrane state before use ((a) surface,
cross-section)) and after use ((b) surface, (d) cross-section).
(c) cross-section)) and after use ((b) surface, (d) cross-section).
2.4. Economic Study
The following study deals with expenses and savings before and after implementa-
tion of the spiral-wound diffusion dialyzers into a generic plant consuming 15% H2SO4
and generating acidic waste. The study considers two cases of processing 90 kg·h−1 acidic
wastewater at various degrees of dilution (5% and 10%) by dialysis. Re-concentration to
15% H2SO4 is also considered. The treatment section consists of neutralization by 20% sus-
pension of slaked lime (technical-grade purity, 90%) according to a scheme shown in Fig-
ure 5A,B.
Solid-liquid suspension after neutralization is then processed in a filter press. The
moisture of the solid phase was considered 65%. Economic rentability is based on the us-
age of 10 modules processing 90 kg/h of acidic feed and on the consumption of 90 kg/h of
demineralized water. The yield of acid was considered 88% in the whole range of studied
concentrations of H2SO4 in waste from 5% to 10%. No other salts than CaSO4 were consid-
ered (treated wastewater did not contain any dissolved salt for the sake of simplicity). In
real applications, the metal ions (Fe2+, Zn2+, Ni2+, Cu2+, etc.) are precipitated in the hydrox-
ide form out of the solution together with gypsum. Therefore, the mass of solid waste
increases proportionally to the concentration of metal ions. To evaluate operating ex-
penses, consumption of electricity of the pumps for the dialyzers, demineralized water for
sulphuric acid stripping, 96% sulphuric acid for make-up, slaked lime and disposal of
solid waste were taken into consideration. Unit prices of the abovementioned inputs can
be found in Table 8. The values can vary from case to case and are only rough numbers.
The total power consumption of the pumps of the unit is considered 1 kW. The capital
cost of the unit containing 10 modules is around 52,400 USD. In practical applications pre-
filtration unit to prevent insoluble particles from penetration into modules is required and
its costs need to be considered. The time allowance for the calculation is 330 working days
per year and 24 h per day.

Figure 5. Process flow

flow diagram
diagramfor
forthe
theproposed
proposedtreatment
treatmenttechnology.
technology. (A)
(A) treatment
treatment of of acidic
acidic wastewater
wastewater without
without diffu-
diffusion
sion dialysis;
dialysis; (B) implementation
(B) implementation of dialysis
of dialysis into production-level
into production-level wastewater
wastewater management.
management.

Table 8. Unit costs of the considered sources. The price of electricity reflects the situation in the
Czech Republic.

Item Unit Unit Cost

Int. J. Mol. Sci. 2021, 22, 11819 8 of 16

Solid-liquid suspension after neutralization is then processed in a filter press. The

moisture of the solid phase was considered 65%. Economic rentability is based on the
usage of 10 modules processing 90 kg/h of acidic feed and on the consumption of 90 kg/h
of demineralized water. The yield of acid was considered 88% in the whole range of
studied concentrations of H2 SO4 in waste from 5% to 10%. No other salts than CaSO4 were
considered (treated wastewater did not contain any dissolved salt for the sake of simplicity).
In real applications, the metal ions (Fe2+ , Zn2+ , Ni2+ , Cu2+ , etc.) are precipitated in the
hydroxide form out of the solution together with gypsum. Therefore, the mass of solid
waste increases proportionally to the concentration of metal ions. To evaluate operating
expenses, consumption of electricity of the pumps for the dialyzers, demineralized water
for sulphuric acid stripping, 96% sulphuric acid for make-up, slaked lime and disposal of
solid waste were taken into consideration. Unit prices of the abovementioned inputs can
be found in Table 8. The values can vary from case to case and are only rough numbers.
The total power consumption of the pumps of the unit is considered 1 kW. The capital
cost of the unit containing 10 modules is around 52,400 USD. In practical applications
pre-filtration unit to prevent insoluble particles from penetration into modules is required
and its costs need to be considered. The time allowance for the calculation is 330 working
days per year and 24 h per day.

Table 8. Unit costs of the considered sources. The price of electricity reflects the situation in the
Czech Republic.

Item Unit Unit Cost

Electricity USD/kWh 0.1
Demineralized water USD/m3 10
96% H2 SO4 USD/t 400
90% Ca(OH)2 USD/t 120
Solid waste disposal USD/t 300

Regardless of the studied case, implementation of the recovery unit will lead to
significant savings of neutralization agent, concentrated sulphuric acid and money for
sludge disposal. Savings of sources, both material (sulphuric acid) and financial, are visible
in a summary of operational expenditures (Table 9). Despite 88% of acid recovery, saving of
neutralization agent needed to treat not only dialysate but also blowdown stream is 74%.

Table 9. Annual expenses for each case of the economic study. (A1) processing 5% H2 SO4 wastewater
without DD; (B1) processing 5% H2 SO4 wastewater with DD; (A2) processing 10% H2 SO4 wastewater
without DD; (B2) processing 10% H2 SO4 wastewater with DD.

Case Unit A1 B1 A2 B2
Slaked lime 90% USD 4230 1083 8444 2151
Sludge disposal USD 50,153 12,846 100,121 25,508
Electricity USD n/a 792 n/a 792
Sulphuric acid 96% USD 52,703 39,635 52,606 26,470
Water USD 8530 7490 9927 7848
Total USD 115,616 61,846 171,098 62,769

From the graphs, it is evident that a significant part of costs is represented by sludge
disposal (Figure 6). It is therefore important to pay attention to the maximal possible
removal of moisture. Economic calculations have shown that simple payback time can be
less than one year and is a strong function of the acid concentration in the treated feed
entering the recovery unit. The more dilute acid is processed, the longer is the payback
period (Table 10).
 From the graphs, it is evident that a significant part of costs is represented by sludge
disposal (Figure 6). It is therefore important to pay attention to the maximal possible re-
moval of moisture. Economic calculations have shown that simple payback time can be
less than one year and is a strong function of the acid concentration in the treated feed
Int. J. Mol. Sci. 2021, 22, 11819 9 of 16
entering the recovery unit. The more dilute acid is processed, the longer is the payback
period (Table 10).

Figure6.
Figure 6. Percentage
Percentagedistribution
distributionofofoperating expenses:
operating (A1)
expenses: processing
(A1) 5% 5%
processing H2SO
H42wastewater with-
SO4 wastewater
out DD;DD;
without (B1) processing
(B1) 5%
processing 5%HH2SO
2
4 wastewater
SO 4
with
wastewater withDD;
DD; (A2)
(A2) processing
processing 10%
10% HH2
2SO4wastewater
SO 4
wastewater
withoutDD;
without DD;(B2)
(B2)processing
processing10%
10%HH2SO SO4 wastewater
wastewater with
with DD.
DD.
2 4

Table10.
Table 10.Annual
Annualcash
cashflow
flowfor
foreach
eachcase
caseand
andexpected
expectedpayback
paybackperiod
periodfor
forDD
DDinvestment.
investment.

Item
Item Unit
Unit A1A1 B1B1 A2
A2 B2
B2
Expenses USD 115,616 61,846 171,098 62,769
Expenses USD 115,616 61,846 171,098 62,769
Savings
Savings USD
USD 0 0 53,770
53,770 00 108,329
108,329
Payback
Paybackperiod
period year
year - - 0.97
0.97 -- 0.48
0.48

3. Discussion
3. Discussion
The higher
The higher the
the flow
flow rate
rate of
of the
the stripping
stripping medium,
medium, the
the higher
higher acid
acid yield
yield will
will be
be
achieved, and the more diluted diffusate will be obtained (cf. Table 1).
achieved, and the more diluted diffusate will be obtained (cf. Table 1). This inherently This inherently
leads to
leads to aa higher consumption of of deionized
deionized water.
water.Electrical
Electricalconductivity
conductivityisisa afunction
function of
concentration
of concentration andandcomposition.
composition. In the casecase
In the of pure, diluted
of pure, sulphuric
diluted acid acid
sulphuric solution, elec-
solution,
electrical conductivity
trical conductivity is linearly
is linearly dependent
dependent on on an acid
an acid concentration.
concentration. Moreover,
Moreover, protons
protons ex-
exhibit highmobility,
hibit high mobility,therefore,
therefore,acidic
acidicsolutions
solutions have
have high electrical conductivity.
conductivity.Based
Basedon on
this
thisphysicochemical
physicochemicalknowledge
knowledgewe wecan
canassume
assumehow howmuch
muchisisthe
thediffusate
diffusaterich
richininacid.
acid.
The
The yield
yield of
of sulphuric
sulphuric acidacid can
can bebeapproximately
approximately 90%,
90%, which
which also
alsomeans
meanssaving
saving
roughly
roughly90% 90%ofofsources
sourcesin inthe
theneutralization
neutralizationstep.
step.Also,
Also,by
byimplementing
implementingDD DDthe
theamount
amount
of neutralized salt will be decreased by ~90%. The advantage of employing a counter-
current configuration of stream flows can be deduced from the obtained results. The
concentration of the recovered acid is close to the initial feed value (cf. Table 1). Therefore,
an extensive reconcentration step after DD will not be necessary for many applications.
Metal cations are retained mainly in the dialysate due to repulsion of cationic species by
AEMs with a small concentration of free acid, less than 1 wt. %.
After evaluation of data obtained from analytical analyses, it was found out that
the temperature of the feed has an effect on the module performance (cf. Table 4) up to
30 ◦ C. However, this effect is not as significant as the effect of a volumetric-flow ratio. The
yield of the acid increased, which is following increased sulphuric acid mass flux through
the membranes. Although, at the expense of lower rejection factors of metal ions. This
observation can be explained by the relaxation of the membranes. Higher temperatures
could modify the internal structure [28,29] of the AEM in a way that the membranes
became more permeable for each solute present in the solution. Also, increasing flows
can be attributed to the fact that diffusion is the activation process that is accelerated with
increasing temperature. Moreover, at temperatures higher than 30 ◦ C, temperature plays a
minor role in a mass transfer.
Concentrations of free acid and salts in the wastewater can vary from case to case. In
this experimental study, highly acidic conditions (acidity ~1 M) and somewhat moderate
Int. J. Mol. Sci. 2021, 22, 11819 10 of 16

conditions in terms of metal ion concentration (<1 g·L−1 ) were considered. Obtained
results showed that the yield of sulphuric acid was in the case of unit flowrate ratio 88%.
However, it was reported [18] that salts can enhance a mass transfer of a free acid what
consequently results in its higher yield.
The physicochemical properties change indicates the high chemical and mechanical
stability of membranes. The only evidence of degradation is a slight drop in membrane
selectivity and an increase in diffusion permeability. This is a good result relative to other
types of membranes, for membranes based on bromomethylated poly (phenylene oxide)
(BPPO) degradation manifested in a drop of ion-exchange capacity [25,26].
The payback period can be influenced by several phenomena. Expenses of the cleaning-
in-place procedure were excluded from the study since modules unlike RO modules and
at good feed quality (no oil, suspended solids, surfactants, or detergents), do not require
cleaning. Costs for replacements of the safety AC filters were also excluded from the
calculations because pre-filtering will be dependent on the individual cases. Another
parameter that is normally measured before release into surface water is dissolved solids.
The limit value varies with location and is not the same for each company. In the case of
neutralization of wastewater containing sulphuric acid, low soluble calcium sulphate is
generated. Its solubility at 25 ◦ C is 2.6 g·L−1 . From this point of view, emission of such
water usually should not lead to fees due to high total dissolved solids. However, the
situation is more complicated with wastewater containing HCl, since neutralization of this
acid generates very soluble CaCl2 . For this reason, recovery of HCl should have its place in
wastewater management instead of simple neutralization. However, the rejection factor
for some metal ions like Zn2+ in dialysis of HCl wastewater is lower due to the formation
of negatively charged chloro complexes [18], which are not repulsed by the fixed groups
and therefore diffuse through the AEM easily. Nevertheless, each case should be assessed
separately with a thorough economical study. Actual unit costs should be used to clarify
outcomes and benefits after the DD implementation.

4. Material and Methods

4.1. Feed Solution
A 25 L model solution consisting of sulphuric acid with impurities of iron and copper
sulphate was used for each experiment, with a fresh model solution being prepared for each
continuous test. The model solution comprised 0.732 L of 96% sulphuric acid (Penta s.r.o.,
p.a.), 37.3 g of iron(II) sulphate heptahydrate (Penta s.r.o., pure), 4.9 g of copper (II) sulphate
pentahydrate (Penta s.r.o., p.a.) and reverse osmosis (RO) permeate (қ< 10 µS·cm−1 ). When
made up to 25 L with demineralized water, the resulting solution comprised ca. 5 wt. % of
sulphuric acid, 300 ppm of Fe2+ and 50 ppm of Cu2+ (Table 11). The electrical conductivity
of the feed solution ranged from 215 to 231 mS·cm−1 at 25 ◦ C.

Table 11. Average composition of feed solution.

Composition Unit Feed Stream

H2 SO4 g ·L−1 51 ± 1
Fe2+ ppm 283 ± 14
Cu2+ ppm 45 ± 2
Electrical conductivity mS·cm−1 221.5 ± 1.1
Density kg·L−1 1.031 ± 0.001

4.2. Analytical Methods

Determination of composition was undertaken via potentiometric alkalimetry for
measuring free acid content and inductively coupled plasma (ICP-OES) coupled with
optical emission spectroscopy (both Thermo Fischer Scientific GmbH, Bremen, Germany)
for measuring metallic ion concentration by a method of a calibration curve. Standard
samples had concentrations of 0.1; 0.5; 1; 5; 10 and 100 ppm.
Int. J. Mol. Sci. 2021, 22, 11819 11 of 16

The main parameters which were measured during acid-recovery experiments were
electrical conductivity, temperature, density, volumetric flow, and mass flow. Electrical
conductivity and temperature were determined using a TetraCon 925/LV-P probe (Xylem
Analytics WTW, Germany) connected to a WTW 3430 Multimeter (Xylem Analytics WTW,
Germany). Density was measured with a portable hand-held Densito 30PX density meter
(Mettler Toledo, Japan). A KERN 572 balance (KERN & SOHN GmbH, Balingen), cylinder
and a timer were used for determination of mass flow.

4.3. Equipment
A WD-AR10-2001 spiral-wound module (Spiraltec GmbH, Germany) with an effec-
tive anion exchange area of ca. 5 m2 was used to test the effects of flow rate ratio and
temperature on recovery of spent sulphuric acid by DD (Table 12).

Table 12. Spiral-wound module characteristics. Parameters were downloaded from the online
module datasheet [30].

Parameter Value
Flow 5–15 L ·h−1 each channel
Pressure loss 80 mbar (at 5 L·h−1 )–400 mbar (at 15 L·h−1 )
Operating pressure 0.1–1.5 bar (g)
Differential pressure <200 mbar (between the channels)
Operating temperature 5 ◦ C–40 ◦ C
Empty weight ca. 8 kg
Fill volumes ca. 4.5 L each channel

4.4. Membrane Characterization

CuSO4 diffusion permeability was determined from the CuSO4 flow with the mem-
brane placed between the 0.1 and 0.001 M CuSO4 solutions. Measurements were con-
ducted at room temperature (24 ◦ C) in a two-section plexiglass cell with a 5 cm2 active
membrane area, the solutions being constantly stirred at ca. 400 rpm by a tailor-made two-
position magnetic stirrer. CuSO4 flow was determined using an Expert-002 conductometer
(Econix-Expert, Russia). Using a similar method, sulphuric acid diffusion permeability was
determined from the H2 SO4 flow with the membrane placed between the 0.1 M Na2 SO4
and 0.1 M H2 SO4 solutions. H2 SO4 flow was calculated from pH change in salt solution
determined using an Expert-pH pH-meter (Econix-Expert, Russia).
AC-membrane ionic resistance was determined via the four-electrode method, using
a thermostatic 25 ◦ C cell filled with a 0.5 M NaCl solution and a P-40X potentiostat-
galvanostat with an FRA-24M impedance measurement module (Elins, Russia). A detailed
description of the experiment can be found elsewhere [31].
Permselectivity was characterized by the potentiostat technique, the membrane being
placed between 0.1 M and 0.5 M NaCl solutions in a two-compartment cell. A detailed
description of the experiment and calculations can be found elsewhere [32].
Stress-strain experiments were performed using a Tinius Olsen H5KT universal testing
machine and a force sensor set at 100 N under ambient conditions (24 ◦ C/25% relative
humidity). The gauge length of the samples was adjusted to 50 mm for the machine and the
strain rate was set at 5 mm/min for all tests. A more detailed description of the experiment
can be found elsewhere [33].
Water uptake was determined from weight loss after drying the film at 80 ◦ C for several
hours. Dimensional swelling was determined by the change in geometric dimensions of
the membrane sample before and after dehydration.
Scanning electron microscope (SEM) images were obtained using a Quanta FEG
450 SEM (FEI, Hillsboro, OR, USA) at 10kV accelerating voltage and 80 Pa residual pressure.
A detailed description of ion exchange capacity measurement and calculation can be found
elsewhere [32]. The thickness of each sample was taken as the average value of five points
measured before the experiment using a Mitutoyo 293–805 micrometer (Mitutoyo, Japan).
Int. J. Mol. Sci. 2021, 22, 11819 12 of 16

FTIR spectra of the samples were measured using a Nicolet iS5 spectrometer (Thermo
Fisher Scientific, USA) in attenuated total reflection mode using a Quest Specac accessory
(400–4000 cm−1 spectral range, 32 scans, 2 cm−1 resolution).

4.5. Experimental Setup of Diffusion Dialysis Tests

Two series of tests were conducted in a continuous regime to study process parameter
impacts on system performance in terms of free-acid yield, metal-ion rejection, and output
stream composition. The first series consisted of tests performed at different ratios (RV ) of
acidic feed:demineralized water-inlet-volumetric flow in L.h−1 at laboratory temperature
(20–25 ◦ C). The second series consisted of tests performed at different feed temperatures
(TF ; from 20 ◦ C to 40 ◦ C) at fixed RV (conditions summarized in Table 13).

Table 13. Conditions for Series 1 and Series 2 tests. Symbols: RV —volumetric flow rate ratio (feed/RO
permeate), TF —temperature of the inlet feed.

Parameter Unit Test 1.1 Test 2.1 Test 1.2 Test 2.2 Test 3.2
RV - 9/9 9/11 9/7 9/7 9/7
TF ◦C 20–25 20–25 20–25 30 40

Samples were collected from the outlet streams once the process had reached a steady-
state. To check the state of the process, diffusate and the dialysate conductivity and flowrate
were measured over time, with flowrate measured using the cylinder method (i.e., time
needed to fill a cylinder with 100 mL of liquid).
The experimental process consists of two parts, a hydraulic feed and diffusate and
dialysate outlet streams (Figure 7). The hydraulic part consists of two Flojet pumps (Xylem
Int. J. Mol. Sci. 2021, 22, 11819 Inc., USA), two filters (a 5 µm filter for the RO permeate and an activated carbon13(AC) of 17
filter for the acidic feed stream) and a series of rotameters, pressure indicators and MARIC
flow control valves (Maric Flow Control, Australia). Manual needle valves were located
in the recirculation pipes to allow fine regulation of pressure and volumetric flow. High
The diffusate and dialysate were collected in separate tanks. Samples from the outlet
temperature levels (30 ◦ C and 40 ◦ C) were maintained in the feed solution by indirectly
streams were collected directly from the sampling cock valves (i.e., not from the tanks) at
heating the salty acid barrel with a heating belt.
pre-determined time intervals.

Figure7.7.Simplified
Figure Simplifiedprocess
processflow
flow diagram
diagram of of
thethe acid-recovery
acid-recovery system.
system. Instrumentation
Instrumentation key:key: (1) pump;
(1) pump; (2) needle
(2) needle valve;
valve; (3)
(3) rotameter;
rotameter; (4) pressure
(4) pressure sensor;
sensor; (5) manual
(5) manual valve;valve; (6) flow
(6) flow control
control valve;
valve; (7) manual
(7) manual valve.
valve.

4.6. Calculations
Water uptake (W) was calculated by the following Equation (1):
𝑚 −𝑚
𝑊= × 100% (1)
𝑚
Int. J. Mol. Sci. 2021, 22, 11819 13 of 16

The diffusate and dialysate were collected in separate tanks. Samples from the outlet
streams were collected directly from the sampling cock valves (i.e., not from the tanks) at
pre-determined time intervals.

4.6. Calculations
Water uptake (W) was calculated by the following Equation (1):

mwet − mdry
W= × 100% (1)
mdry

where, mwet and mdry represent the membrane weight before and after dehydration.
The diffusion permeability coefficients (Ps) was calculated using the following Equation (2):

Js dm
Ps = (2)
∆Cs

where, Js is solute flow, dm is membrane thickness and ∆Cs is the solute concentration
difference.
The area resistance (Rarea ) and specific conductivity (σ) were calculated using the
following Equations (3) and (4):

R area = ( Rcell +mem − Rcell ) × S (3)

dm
σ= (4)
R area
where, Rcell +mem and Rcell represent cell resistance with and without the membrane and S
is the membrane active area.
According to [34], Young’s modulus is calculated from the slope of the initial section
of the stress-strain curve. The yield strength (transition from elasticity to plasticity) corre-
sponded to the first local maximum of the 1-st order derivative of the stress-strain curve.
In this case, tensile strength corresponds to maximum stress.
Volumetric ratio (RV ) was defined according to the following Equation (5):
.
V FEED L.h−1


RV = . (5)
V ROW ( L.h−1 )
. .
where, V FEED represents volumetric flow of the acid fed into the module and V ROW
represents volumetric flow of demineralized water.
Data evaluation was based on mass balance under steady-state conditions, as de-
scribed in the following Equation (6):
. .
∑ minput − ∑ moutput = 0 (6)
. .

where, minput moutput represents the mass flow of streams entering or leaving the system.
For the purpose of this study, Equation (6) has the form:
. . . .
m FEED + m ROW = m DI A + m DIF (7)

Free-acid yield (Y) can then be calculated from either of the two following Equations (8) and (9):
.
m H + ,DIF
Y= . × 100% (8)
m H + ,FEED
. !
m H + ,DI A
Y= 1− . × 100% (9)
m H + ,FEED
Int. J. Mol. Sci. 2021, 22, 11819 14 of 16

In a steady-state, both Equations (8) and (9) are equivalent and can be derived from
the mass balance of free acid in a steady state. The reported values represent average
values of free-acid yield obtained from Equations (8) and (9).
Metal-ion rejection (Ri ) can also be calculated from the following two equivalent
Equations (10) and (11):
.
mi,DI A
Ri = . × 100% (10)
mi,FEED
 . 
mi,DIF
Ri = 1 − . × 100% (11)
mi,FEED
where, i = Cu or Fe.
Reported values of metal-ion rejection for each test were calculated as average values
from Equations (10) and (11).
Stream composition was used to evaluate stream ionic purity. The ionic purity (Pj ) of
stream j was defined as follows (12):
c H + ,j
Pj = × 100% (12)
c H + ,j + ∑i ci,j

where, j is FEED, DIF and DIA and i is Fe or Cu. ci,j is the concentration of the i-th
compound in the j-th stream in ppm.
.
The total flux of acid JH2 SO4 was defined as the mass flow of acid m H2 SO4 per effective
membrane area (S): .
m H2 SO4
JH2 SO4 = (13)
S
Equations (8)–(13) are especially useful for evaluating the module’s separation perfor-
mance, for comparing the degree of purification of recovered acid with inlet acidic feed or
for scaling-up the industrial technology if a required flow of recoverable acid is provided.

4.7. Statistical Analysis

Measurement uncertainties for electrical conductivity and temperature were obtained
from the manufacturer’s own documentation, while measurement uncertainties for heavy
metal ion concentration and acidity were obtained by applying the Student’s t-distribution
with a significance level of p < 0.05. Mass flow was characterized by a measurement
uncertainty of 2%, obtained from the propagation-of-error formula.

5. Conclusions
A membrane-based separation process driven by a chemical-potential gradient was
successfully used for the treatment of acidic wastewater and recovery of sulphuric acid,
with different combinations of acidic feed and demineralized water volumetric-flow ratios
influencing system performance in terms of sulphuric acid yield, metal ion rejection and
component concentration in recovered-acid and reject streams. The temperature of the
acidic feed stream increased mass transfer of both sulphuric acid and dissolved sulphate
salts, with a significant effect observed at temperatures up to 30 ◦ C.
A techno-economic study indicated that inclusion of DD into recovery of sulphuric
acid from wastewater was viable and feasible, even for dilute solutions (5 wt.% sulphuric
acid), with a simple payback period of ca 1 year. The payback period would be even shorter
where more concentrated spent streams were generated.
A comparison of basic membrane (Fumasep® FAD-PET-75) physicochemical properties
(i.e., ion exchange capacity, water uptake, thickness, permselectivity, acid and salt diffusion
permeability, ionic conductivity, and stress-strain curves) before and after dialysis indicated
only a slight drop in membrane selectivity and an increase in diffusion permeability.
Furthermore, there were no significant changes in membrane IR spectra. Taken together,
this indicates a relatively high chemical and mechanical membrane stability.
Int. J. Mol. Sci. 2021, 22, 11819 15 of 16

Author Contributions: Conceptualisation, L.Č., A.M., L.Š. and L.D.; Formal analysis, D.G., L.Č. and
L.Š.; Methodology, A.M., L.D. and L.Š.; Project administration, L.Č., L.Š. and A.M.; Visualization,
A.M., L.Č., and D.G.; Writing of original draft, A.M., L.Č., L.D., D.G. and L.Š.; Writing—review and
editing, A.M., L.Č., D.G. and L.D. All authors have read and agreed to the published version of the
manuscript.
Funding: Work performed by MemBrain s.r.o. (Membrane Innovation Centre) was performed under
an Institutional support project (Decision No. 6/2018) of the Ministry of Industry and Trade of the
Czech Republic.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The data presented in this study are available on request from the
corresponding author.
Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations

AC Activated carbon
AEMs Anion-exchange membranes
BPPO Bromomethylated poly (phenylene oxide)
DD Diffusion dialysis
DIA Dialysate
DIF Diffusate
FEED Salty acid fed to a module
PET Polyethylene terephthalate
R.H. Relative humidity
RO Reverse osmosis
ROW Permeate of reverse osmosis
SEM Scanning electron microscope
USD United States dollar

References
1. Watzlaf, G.R.; Schroeder, K.T.; Kleinmann, R.L.P.; Kairies, C.L.; Nairn, R.W. The Passive Treatment of Coal Mine Drainage; United
States Department of Energy National Energy Technology Laboratory Internal Publication: Pittsburgh, PA, USA, 2004; pp. 1–72.
2. Hughes, T.A.; Gray, N.F. Removal of metals and acidity from acid mine drainage using municipal wastewater and activated
sludge. Mine Water Environ. 2013, 32, 170–184. [CrossRef]
3. López, J.; Gibert, O.; Cortina, J. Integration of membrane technologies to enhance the sustainability in the treatment of metal-
containing acidic liquid wastes. An overview. Sep. Purif. Technol. 2021, 265, 118485. [CrossRef]
4. Merkel, A.; Ashrafi, A.M.; Ondrušek, M. The use of electrodialysis for recovery of sodium hydroxide from the high alkaline
solution as a model of mercerization wastewater. J. Water Process. Eng. 2017, 20, 123–129. [CrossRef]
5. Luo, J.; Wu, C.; Xu, T.; Wu, Y. Diffusion dialysis-concept, principle and applications. J. Membr. Sci. 2011, 366, 1–16. [CrossRef]
6. Zhang, C.; Zhang, W.; Wang, Y. Diffusion dialysis for acid recovery from acidic waste solutions: Anion exchange membranes and
technology integration. Membranes 2020, 10, 169. [CrossRef] [PubMed]
7. Jiang, S.; Sun, H.; Wang, H.; Ladewig, B.P.; Yao, Z. A comprehensive review on the synthesis and applications of ion exchange
membranes. Chemosphere 2021, 282, 130817. [CrossRef]
8. Wang, G.; Xu, J.; Sun, P.; Zhao, X.; Zhang, W.; Lv, L.; Pan, B.; Guo, Q.; Bin, Y.; Wang, J. Principle of diffusion dialysis method and
its application in treatment of wastewater of electroplating industry. Ion Exch. Adsorpt. 2015, 31, 569–576. [CrossRef]
9. Kreuer, K.-D. Proton conductivity: Materials and applications. Chem. Mater. 1996, 8, 610–641. [CrossRef]
10. Stenina, I.; Yaroslavtsev, A. Ionic mobility in ion-exchange membranes. Membranes 2021, 11, 198. [CrossRef]
11. Cukierman, S. Et tu, Grotthuss! and other unfinished stories. Biochim. Biophys. Acta (BBA)-Bioenerg. 2006, 1757, 876–885.
[CrossRef]
12. Zhang, P.; Wu, Y.; Liu, W.; Cui, P.; Huang, Q.; Ran, J. Construction of two dimensional anion exchange membranes to boost acid
recovery performances. J. Membr. Sci. 2021, 618, 118692. [CrossRef]
13. Wu, Y.; Luo, J.; Zhao, L.; Zhang, G.; Wu, C.; Xu, T. QPPO/PVA anion exchange hybrid membranes from double crosslinking
agents for acid recovery. J. Membr. Sci. 2013, 428, 95–103. [CrossRef]
14. Sharma, J.; Misra, S.; Kulshrestha, V. Internally cross-linked poly (2,6-dimethyl-1,4-phenylene ether) based anion exchange
membrane for recovery of different acids by diffusion dialysis. Chem. Eng. J. 2021, 414, 128776. [CrossRef]
Int. J. Mol. Sci. 2021, 22, 11819 16 of 16

15. Lin, J.; Huang, J.; Wang, J.; Yu, J.; You, X.; Lin, X.; Van Der Bruggen, B.; Zhao, S. High-performance porous anion exchange
membranes for efficient acid recovery from acidic wastewater by diffusion dialysis. J. Membr. Sci. 2021, 624, 119116. [CrossRef]
16. Ye, H.; Zou, L.; Wu, C.; Wu, Y. Tubular membrane used in continuous and semi-continuous diffusion dialysis. Sep. Purif. Technol.
2020, 235, 116147. [CrossRef]
17. Luo, F.; Zhang, X.; Pan, J.; Mondal, A.N.; Feng, H.; Xu, T. Diffusion dialysis of sulfuric acid in spiral wound membrane modules:
Effect of module number and connection mode. Sep. Purif. Technol. 2015, 148, 25–31. [CrossRef]
18. Gueccia, R.; Aguirre, A.R.; Randazzo, S.; Cipollina, A.; Micale, G. Diffusion dialysis for separation of hydrochloric acid, iron and
zinc ions from highly concentrated pickling solutions. Membranes 2020, 10, 129. [CrossRef]
19. Ruiz-Aguirre, A.; Lopez, J.; Gueccia, R.; Randazzo, S.; Cipollina, A.; Cortina, J.; Micale, G. Diffusion dialysis for the treatment of
H2SO4-CuSO4 solutions from electroplating plants: Ions membrane transport characterization and modelling. Sep. Purif. Technol.
2021, 266, 118215. [CrossRef]
20. Gueccia, R.; Winter, D.; Randazzo, S.; Cipollina, A.; Koschikowski, J.; Micale, G.D. An integrated approach for the HCl and metals
recovery from waste pickling solutions: Pilot plant and design operations. Chem. Eng. Res. Des. 2021, 168, 383–396. [CrossRef]
21. Saif, H.; Huertas, R.; Pawlowski, S.; Crespo, J.; Velizarov, S. Development of highly selective composite polymeric membranes for
Li+/Mg2+ separation. J. Membr. Sci. 2021, 620, 118891. [CrossRef]
22. López, J.; de Oliveira, R.; Reig, M.; Vecino, X.; Gibert, O.; de Juan, A.; Cortina, J. Acid recovery from copper metallurgical process
streams polluted with arsenic by diffusion dialysis. J. Environ. Chem. Eng. 2021, 9, 104692. [CrossRef]
23. Zhang, X.; Li, C.; Wang, H.; Xu, T. Recovery of hydrochloric acid from simulated chemosynthesis aluminum foil wastewater by
spiral wound diffusion dialysis (SWDD) membrane module. J. Membr. Sci. 2011, 384, 219–225. [CrossRef]
24. Henkensmeier, D.; Najibah, M.; Harms, C.; Žitka, J.; Hnát, J.; Bouzek, K. Overview: State-of-the art commercial membranes for
anion exchange membrane water electrolysis. J. Electrochem. Energy Convers. Storage 2020, 18, 1–46. [CrossRef]
25. Khan, M.I.; Luque, R.; Prinsen, P.; Rehman, A.U.; Anjum, S.; Nawaz, M.; Shaheen, A.; Zafar, S.; Mustaqeem, M. BPPO-Based
Anion Exchange Membranes for Acid Recovery via Diffusion Dialysis. Materials 2017, 10, 266. [CrossRef]
26. Mao, F.; Zhang, G.; Tong, J.; Xu, T.; Wu, Y. Anion exchange membranes used in diffusion dialysis for acid recovery from erosive
and organic solutions. Sep. Purif. Technol. 2014, 122, 376–383. [CrossRef]
27. Lin, X.; Shamsaei, E.; Kong, B.; Liu, J.Z.; Hu, Y.; Xu, T.; Wang, H. Porous diffusion dialysis membranes for rapid acid recovery. J.
Membr. Sci. 2016, 502, 76–83. [CrossRef]
28. Merkel, A.; Voropaeva, D.; Fárová, H.; Yaroslavtsev, A. High effective electrodialytic whey desalination at high temperature. Int.
Dairy J. 2020, 108, 104737. [CrossRef]
29. Merkel, A.; Fárová, H.; Voropaeva, D.; Yaroslavtsev, A.; Ahrné, L.; Yazdi, S.R. The impact of high effective electrodialytic
desalination on acid whey stream at high temperature. Int. Dairy J. 2021, 114, 104921. [CrossRef]
30. Spiraltec GmbH, Sachsenheim, Germany. Available online: https://www.spiraltecgmbh.com/en/downloads-en.html (accessed
on 30 October 2021).
31. Golubenko, D.; Pourcelly, G.; Yaroslavtsev, A. Permselectivity and ion-conductivity of grafted cation-exchange membranes based
on UV-oxidized polymethylpenten and sulfonated polystyrene. Sep. Purif. Technol. 2018, 207, 329–335. [CrossRef]
32. Golubenko, D.; Van Der Bruggen, B.; Yaroslavtsev, A.B. Novel anion exchange membrane with low ionic resistance based on
chloromethylated/quaternized-grafted polystyrene for energy efficient electromembrane processes. J. Appl. Polym. Sci. 2019,
137, 48656. [CrossRef]
33. Safronova, E.; Golubenko, D.; Pourcelly, G.; Yaroslavtsev, A. Mechanical properties and influence of straining on ion conductivity
of perfluorosulfonic acid Nafion® -type membranes depending on water uptake. J. Membr. Sci. 2015, 473, 218–225. [CrossRef]
34. Deshmukh, K.; Kovářík, T.; Muzaffar, A.; Basheer, A.M.; Pasha, S.K. Chapter 4—Mechanical analysis of polymers. In Polymer
Science and Innovative Applications; Elsevier: Amsterdam, The Netherlands, 2020; pp. 117–152. [CrossRef]