Applied Thermal Engineering 179 (2020) 115646

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Applied Thermal Engineering

journal homepage: www.elsevier.com/locate/apthermeng

Design and evaluation of a parallel-connected double-effect mechanical T

vapor recompression evaporation crystallization system
⁎
Hua Jianga, , Ziyao Zhanga, Wuqi Gongb
a
School of Energy, Xi’an University of Science and Technology, Xi’an 710054, China
b
School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

H I GH L IG H T S

• ATheparallel-connected double-effect MVR evaporation crystallization system is proposed.

• Highlycombination of two types of evaporators in wastewater treatment is explored.
• The effectconcentrated real solution is taken as the working medium in exergy analysis.
• of key parameters on system performance is investigated.

A R T I C LE I N FO A B S T R A C T

Keywords: This paper proposes a parallel-connected double-effect mechanical vapor recompression (MVR) evaporation
High salinity wastewater treatment crystallization system, which combines the falling film evaporator with the forced circulation evaporator. With
Mechanical vapor recompression (MVR) the purpose of treating high salinity wastewater, the circulation process of the system was designed and
Double-effect evaporation mathematical models were established according to the mass and energy balance as well as thermodynamic
Crystallization
properties in the heat transfer process. Model calculation was conducted using 5% sodium sulfate solution, based
Exergy analysis
on which the effects of evaporation temperature, feed concentration, and temperature difference between sa-
turated boiling solution and condensate on the system performance were analyzed by a parametric study. The
results showed that the optimal values of evaporation temperature and saturation temperature difference could
be determined based on a trade-off between power consumption and heat transfer area. After that, the perfor-
mance of the proposed system was compared with that of a traditional multi-effect evaporation crystallization
system, and it was revealed that the coefficient of performance (COP) and exergy efficiency of the proposed
system were 21.4 and 49.1%, respectively, 82.2% and 51.5% higher than those of the traditional system under
the same working condition. Meanwhile, the exergy destruction of the proposed system was 24.7% lower than
that of the traditional system, indicating that the new system performs better regarding energy saving and
thermodynamic perfection.

1. Introduction stage flash (MSF), multi-effect evaporation (MEE), thermal vapor re-
compression (TVR) and mechanical vapor recompression (MVR).
According to official estimates [1], the global market of industrial Among these techniques, MVR is recognized as one of the most pro-
wastewater treatment is expanding at an average annual rate of 5%. mising. MVR is characterized by recycling the energy of secondary
Wastewater with a high concentration of inorganic salt is difficult to vapor generated in the evaporator or flasher to the utmost, with a small
treat, which may cause great pollution when discharged directly. In amount of electricity consumption. The advantages of the technique
addition, direct discharge is also a waste of salts dissolved in the water, include high thermodynamic efficiency, compact structure, easy in-
which should be recycled. Hence, developing efficient wastewater tegration with traditional systems, convenience in installation and op-
treatment technology is of great social and economic significance [2–4]. eration, and low cost, among others [5–7].
At present, inorganic salt wastewater is generally treated with eva- A considerable number of experimental studies have been con-
poration techniques, such as single effect evaporation (SEE), multi- ducted on the MVR technique. Aly and Figi [8] examined the

⁎
Corresponding author.
E-mail address: Jianghua10@xust.edu.cn (H. Jiang).

https://doi.org/10.1016/j.applthermaleng.2020.115646
Received 12 November 2019; Received in revised form 16 May 2020; Accepted 21 June 2020
Available online 29 June 2020
1359-4311/ © 2020 Elsevier Ltd. All rights reserved.
H. Jiang, et al. Applied Thermal Engineering 179 (2020) 115646

Nomenclature W Evaporation rate, kg/h

w Feed concentration, %
A Heat transfer area, m2 ρ Density, kg/m2
C Specific heat capacity of solution, kJ/(kg·°C)
C* Specific heat capacity of water, kJ/(kg·°C) Subscripts
D Vapor flow rate, kg/h
F Mass flow rate of feed, kg/h cr Crystal
H Enthalpy, kJ/kg g Gas
N Power consumption, kW j Solvent
P Pressure, MPa l Liquor
Q Heat transfer rate, kW m Molar quantity
q Mass flow rate of condensate, kg/h ov Superheated vapor
r Latent heat of the saturated vapor, kJ/kg p Spray water
T Temperature of vapor, °C x Circulating solution
t Temperature of liquor, °C z Solute
V Volume flow rate of vapor, m2/h

performance of a single-effect MVR desalination system with 5 m3/d MSF-MVR system was designed for the crystallization of high con-
evaporation capacity and the experimental results are in agreement centrated ammonia sulfate solution, and the effects of operating vari-
with the theoretical results. Bahar et al. [9] studied a double-effect MVR ables on the system performance were analyzed by mathematical
system with a rated capacity of 1 m3/d. Yulong Li et al. [10] reported modeling.
experimental data of a single-effect MVR system for condensing di- While energy analysis is the primary method to evaluate system
methylacetamide wastewater, and the system demonstrates a high performance, exergy analysis, a method developed based on the second
coefficient of performance (COP). Songhui Ai et al. [11] examined a law of thermodynamics, is a more powerful tool to assessing a thermal
MVR system for recovering strong sodium chloride solution and ana- system. Through quantifying the magnitude of irreversible losses of a
lyzed the effects of different operating variables on the system perfor- system or the devices in the system, the energy-saving performance and
mance. thermodynamic perfection of the system can be obtained. The reported
Mathematical modeling and subsequent simulations as well as data studies pertaining to exergy analysis of MVR systems largely used ideal
analysis pertaining to the MVR system have been developed over the solutions such as seawater [22–24]. For example, Nafey et al. [23]
past few decades. Aybar [12] established a mathematical model based proposed a MEE-MVR desalination system and established the corre-
on mass and energy balance using the logarithmic mean temperature sponding exergy analysis model, and the model was improved by Jamil
difference (LMTD) method to analyze the heat transfer in a single-effect et al. [24] through incorporation of more details during calculation.
MVR desalination system. Ettouney [13] presented a more compre- Comparatively, only very limited studies took highly concentrated real
hensive model that takes into account more details in heat transfer solutions as the working medium [25]. In addition, even fewer studies
assessment. Jiubing Shen et al. [14] built a model of single-effect MVR took crystal energy into account in exergy analysis.
using water injected twin screw compressors and analyzed the effects of The above mentioned studies on the integration of MVR technique
main operating variables on the system performance. Dong Han et al. in traditional multi-effect systems involves only one type of evaporator.
[15] designed both a single-effect and a double-effect MVR systems to Among many types of evaporators, the falling film evaporator is the
condense ammonium sulfate solution using the self-heat recuperation most popular due to the large temperature difference, low vapor con-
technology (SHRT). Through mathematical modeling for parameter sumption, and applicability of high concentration solution, but it is not
analysis, they found that in addition to the operating variables, the form suitable for crystallization. In contrast, the forced circulation eva-
of system also had a great impact on system performance. porator is suitable for crystallization of inorganic salts or other sub-
The MVR technique can also operate in combination with tradi- stances, whereas it is driven by external power [26–28]. In this regard,
tional systems. For example, Mabrouk et al. [16] depicted the simula- the forced circulation evaporator may remedy the inapplicability of the
tion results of a desalination system integrating MSF and MVR techni- falling film evaporator if the two are applied together. To our knowl-
ques. Lei Gao et al. [17] proposed a lye recovery system combining the edge, there are not yet studies exploring the combination of these two
multi-effect and MVR techniques; their analyses of the thermal per- evaporators in wastewater treatment. In addition, in published studies
formance of the system under varying effects detected that the theo- on MVR systems with multiple evaporators, the evaporators were
retical COP values under all the effects were above 20. Furthermore, usually connected in series and the scales of the MVR systems were
MVR technique also has great potential in its utilization of renewable often small.
energy. Aly [18] designed a wind-driven MVR desalination system Based on the above understanding, we propose in this paper a
taking use of the consistent annual wind speed in the Red Sea region. parallel-connected double-effect MVR evaporation crystallization
Helal et al. [19] designed a diesel-solar-assisted MVR desalination system for recovering sodium sulfate wastewater, which combines the
system for the remote areas of the UAE, where solar energy is abundant. falling film evaporator with the forced circulation evaporator. The
Given the extensive research on MVR technology, studies on its mathematical modeling is conducted first, followed by a parametric
application in wastewater treatment are fairly limited. Reports of the study to assess the effects of operating variables on the system perfor-
design of MVR system in wastewater treatment are particularly sparse. mance. A traditional multi-effect evaporation crystallization system is
One example is that of Yasu Zhou et al. [20], which presented the de- employed as reference. The proposed system and the reference system
sign, simulation and experimentation of a MVR system in treating so- are compared through energy analysis and exergy analysis.
dium sulfate solution, and pointed out a direction for system optimi-
zation. Moreover, most published studies focused merely on the
2. System process and thermodynamic principle
evaporation concentration; only very few regarded the subsequent
crystallization together with the evaporation concentration as a whole
Fig. 1 shows the schematic diagram of the proposed parallel-con-
system. A representative study of this is Lin Liang et al. [21], in which a
nected double-effect MVR evaporation crystallization system, in which

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H. Jiang, et al. Applied Thermal Engineering 179 (2020) 115646

compression process. The saturation treatment of superheated vapor by

condensate is represented by line c-d. The saturated heating vapor
condenses after heat exchange in the evaporator. In this process, the
vapor is converted from saturated gas to saturated liquid, as re-
presented by line d-e.

3. Mathematical modeling

The main equipment for energy conversion in the proposed system

includes a falling film evaporator, a forced circulation evaporator, a
preheater and a vapor compressor. The mathematical modeling of the
system is based on the following assumptions: (1) the system operates
in a stable condition; (2) the evaporation temperature, feed tempera-
ture and concentration remain constant; (3) the discharged condensate
does not contain salt and the effect of non-condensable gas on heat
exchange is ignored; (4) energy losses of the devices, heat leakage, and
pressure drop along the pipes can be ignored; (5) condensate in the
system is saturated.

3.1. Falling film evaporator

The evaporation capacity of the falling film evaporator (W1) can be

calculated according to the mass balance relationship.

w
W1 = F0 ⎛1 − 0 ⎞
⎜ ⎟

⎝ w1 ⎠ (1)
Fig. 1. Schematic diagram of the parallel-connected double-effect MVR eva-
poration crystallization system. ①-Solution pump; ②-Preheater; ③-Water pump; The heat used during evaporation is latent heat that changes little
④-Condensate tank; ⑤-Falling film evaporator; ⑥-Heating chamber of forced with pressure, so the vapor consumption (D1) is approximately the same
circulation evaporator; ⑦-Evaporation chamber of forced circulation eva- as evaporation capacity. A certain extra coefficient of 1.1, the ratio of
porator; ⑧-Gas-liquid separator; ⑨-Vapor compressor; ⑩-Circulation pump; vapor consumption to evaporation capacity, is taken into account
⑪-Crystal-liquid separator; ⑫-Crystal tank. The numbers 1 to 19 represent the during the modeling.
operating processes in the proposed system.
D1 = 1.1W1 (2)
the circulating medium consists of sodium sulfate solution, vapor, and The heat transfer area (A1) of falling film evaporator is given by
condensate water. In the preheater, sodium sulfate solution absorbs formula (3). The empirical data range of the heat transfer coefficient of
sensible heat from high-temperature condensate water discharged from the evaporator is 1200 to 3500 W/(m2·°C) [29]. In the process of
the two evaporators to reach the pre-set evaporation temperature. modeling, the coefficient is set as 1200 W/(m2·°C) by considering the
Then, the heated feed enters the falling film evaporator at the set worst scenario.
evaporation temperature and evaporates through absorbing latent heat
Q1 D × r0
of the compressed vapor there. After the first evaporation, the feed A1 = = 1
K1 Δt1 K1 Δt1 (3)
flows out of the falling film evaporator and enters the forced circulation
evaporator for further evaporation at saturation concentration. Finally, Both the saturated vapor and boiling liquid in the evaporator have
the slurry, which is formed by the mixture of crystal precipitated in the phase change, so the heat transfer between the two is at a constant
forced circulation evaporator and saturated liquor, enters the crystal- temperature. However, as evaporation develops, the feed concentration
lization separator for solid–liquid separation. Crystal is stored in the increases, leading to an elevation of the boiling point of feed. As a re-
tank and saturated liquor returns to the forced circulation evaporator sult, the effective heat transfer temperature difference (Δt1) is con-
for recirculation by the pump. The secondary vapor generated by the sidered to be the temperature difference between compressed vapor
evaporator is first introduced into the gas–liquid separator to remove
the trapped droplets, and then enters the compressor. The superheated
vapor at the compressor outlet is treated by the condensate discharged
from the preheater to get saturated. The compressed vapor, as the heat
source, is then introduced into the evaporators to form high-tempera-
ture condensate by releasing latent heat. In the preheater, high-tem-
perature condensate releases sensible heat to form low-temperature
condensate, which is then pumped into the condensate tank. The re-
plenishing vapor is only used during the start-up stage or where there is
too much heat loss during operation.
The H-S diagram shown in Fig. 2 illustrates the thermodynamic
principle of MVR technology, the core of the proposed system. Line a-b
represents the state change of solvent water in the evaporators, where
the water is converted from saturated liquid to saturated gas at eva-
poration temperature. The dotted line b-c’ represents the adiabatic
compression process. Point c stands for the outlet vapor of the com-
pressor, which has a higher degree of superheat due to the irreversi-
bility of actual compression. Therefore, line b-c is the actual Fig. 2. Enthalpy entropy chart of water and vapor.

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H. Jiang, et al. Applied Thermal Engineering 179 (2020) 115646

and feed’s boiling point at the outlet of evaporator. It is given by: by diffusion and is eventually absorbed by the solution. However, the
evaporation of solution requires a large quantity of heat; the crystalline
Δt1 = T1 − (t1 + Δ) (4)
heat only accounts for 3.4% and is thus ignored during calculation.
The boiling point elevation (Δ) of solutions at any pressure can be
D3 H0 + F1 C2 t2 = D4 H2 + F2 C2 t2 + D3 C ∗T2 (14)
calculated approximately by formula (5), where Δ0 is the boiling point
elevation at atmospheric pressure and f is the correction factor [29].
3.3. Preheater
Δ = f × Δ0 (5)
The boiling point elevation of sodium sulfate solution obtained from Depending on the basic equation of heat transfer, the preheater is
the engineering manual is fitted as follows [30]: modeled as follows:
Δ0 = 69.8w 3 − 8.15w 2 + 5.19w (6) Q0 = F0 C1 (t1 − t0) (15)

where w is the solution concentration. The correction factor is given by: Q0 = C ∗q (t1 − tp) (16)
T2 Q0 = K 0 A0 Δt 0 (17)
f = 0.0162
r (7)
where
where T is the temperature of saturated water vapor under specified
operating conditions and r is the latent heat of vaporization of water q = D1 + D3 (18)
under corresponding operating conditions. Adding the calculated (T1 − t1) − (tp − t0)
boiling point elevation and evaporation temperature up, the boiling Δt0 = T −t
ln t 1 − t1
point of feed at the outlet of evaporator is obtained. Consequently, the p 0 (19)
effective heat transfer temperature difference (Δt1) can be calculated.
In theory, the production of condensate can be equal to the con-
The secondary vapor product (D2) is calculated based on energy
sumption of vapor. All the heat contained in the condensate is used to
balance, as shown in (8) below. Theoretically, the secondary vapor
heat the feed in the preheater. Counterflow plate heat exchanger is
temperature (T2) is the same as the solution temperature at the eva-
selected as the preheater due to its high heat transfer capacity. The
porator outlet (t2), and the condensate temperature is the same as the
empirical data range of the heat transfer coefficient of the preheater is
saturated compressed vapor (T1). For calculating the specific volume of
3000 to 5000 W/(m2·°C) [29]. In the modeling, the coefficient is set as
solution, the properties of sodium sulfate and water should be com-
3000 W/(m2·°C). The heat transfer area is calculated using the LMTD
bined as shown in formula (9). The calculation of C2 is the same as that
method shown as (17) and (19). Heat transfer quantity (Q0), heat
of C1, except for the difference in the concentration of solution.
transfer area (A0), and the temperature of condensate discharged from
D1 H0 + F0 C1 t1 = D2 H1 + F1 C2 t2 + D1 C ∗T1 (8) preheater (tp) are obtained according to the above calculation.

C1 = Crz × w0 + C ∗ (1 − w0 ) (9)
3.4. Vapor compressor

3.2. Forced circulation evaporator In the modelling, the actual compression of vapor is supposed to be
polytropic, and the polytropic efficiency (ηn) involved is a performance
The inlet flow rate of the forced circulation evaporator (F2) contains index of the compressor itself. The general range of the efficiency is
the flow rate of solution separated from the crystal separator (Fx) in 0.70 to 0.84 [31], and it is set as 0.7 during the modeling. When the
addition to that of the saturated solution discharged from the falling compressor saturation temperature rise and inlet vapor temperature are
film evaporator (F1). The slurry flow rate (Fm) and crystal mass (Fcr) given, the saturated pressure of outlet vapor (Pout) can be determined
involved in formula (10) will be given in detail in the calculation of and in turn the compressor consumption (N1) can be calculated. The
crystal separator. compressor suction (V) is the sum of the secondary vapor generated by
both evaporators. Based on the state parameters of inlet vapor, the state
F0 w0
F2 = F1 + Fx = - (Fm − Fcr ) parameters of outlet superheated vapor are available. Finally, according
F1 (10)
to energy balance shown in formula (23), the quantity of condensate
The vapor consumption of the forced circulation evaporator (D3) is (qp) required for saturation treatment is obtained.
calculated in the same way as that of the falling film evaporator (D1). n k
= ηn
D3 = 1.1W2 = 1.1(W − W1) (11) n−1 k−1 (20)
n−1
The heat transfer area (A2) of forced circulation evaporator is cal-
n Pin V ⎡ ⎛ Pout ⎞ n ⎤
culated by formula (12). The empirical data range of the heat transfer N1 = ⎢ ⎜ ⎟ - 1⎥
n−1 η Pin ⎠
coefficient of this evaporator is 1200 to 7000 W/(m2·°C) [29]. The value ⎣⎝ ⎦ (21)
is set as 1200 W/(m2·°C) in the process of modeling when the worst
D D + D4
scenario is under consideration. Due to the short stay of the solution in V= = 2
ρ ρ (22)
the evaporator, the change of boiling point can be ignored, and the heat
transfer process is at a constant temperature, i.e., the feed temperature qp h p + DHov = (qp + D) H1 (23)
at the evaporator outlet. Consequently, Δt2 = Δt1.
Q2 D × r0
A2 = = 3 3.5. Separators
K2 Δt2 K2 Δt2 (12)
The empirical value of power consumption per unit heating area is A gas–liquid separator is an important equipment to prevent the
0.4 to 0.8 kW [28], and 0.6 kW is selected for calculation. compressor from being damaged by droplets mixed in secondary vapor.
In this system, a centrifugal gas–liquid separator working on the basis of
N2 = 0.6A2 (13)
density difference in gas and liquid is selected. In formula (24), volu-
The secondary vapor product (D4) is obtained based on energy metric separation intensity (U) is the quantity of secondary vapor that
balance. The heat released during crystallization passes to the solution can be separated per cubic meter per second. It is set to be 1.1 m3/

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H. Jiang, et al. Applied Thermal Engineering 179 (2020) 115646

(m3·s) here. α = γm (34)

D = ρVU × 3600 (24) where m is the mass of crystal and γ is the mean activity coefficient of
ions, which can be solved by Pitzer general equation:
A spiral sieve centrifugal separator with high production capacity
and low energy consumption is selected. Ideally, most solutes are ex- 2νm νx γ 2(νm νx )3/2 ν
lnγ = |Zm Z x | f γ + m Bmx + m2 Cmx
tracted in the form of crystal except for a small part dissolved in the ν ν (35)
circulating solution. Crystal mass (Fcr) and slurry flow rate (Fm) are
In the above equation, Zm and Zx are the charge number of cation
important parameters for the selection of the spiral sieve centrifugal
and anion, respectively; νm and νx are the numbers of cation and anion
separator.
released from electrolyte during ionization. The remaining parameters
Fcr = F0 w0 (1 − w1) − Fm w1 (25) are shown as follows:

Fm = F0 − W (26) I 1/2 2
f γ = −Aφ [ + ln(1 + bI 1/2)]
1 + bI 1/2 b (36)

3.6. Energy analysis (1)

2βmx 1/2
γ
Bmx (0)
= 2βmx +
α 2I
[1 − (1 + αI 1/2 − 0.5α2I ) e−αI ] (37)
COP and specific energy consumption are employed for an intuitive
γ φ
evaluation of the system performance. COP, as shown in (27), is defined Cmx = 3/2Cmx (38)
as the ratio of heat quantity (Q) absorbed by feed to the energy con-
More details of the parameters are available in Lili Chen [33].
sumption (N) of the whole system during the process of evaporation
crystallization.
3.8. Exergy balance and efficiency
Q
COP =
N (27) Fig. 3 shows the exergy balance of the system.
The specific energy consumption, as shown in (28), is the energy The inlet exergy of the whole system is divided into two parts. One
consumption of the whole system when the evaporation capacity is is the directly available exergy, including the power consumption of
1 kg. vapor compressor, forced circulation evaporator, and other power-
draining devices in the system. This part is also called pay exergy. The
N
c= other part is the exergy of feed steam. The outlet exergy, also known as
W (28)
earn exergy, consists of that of condensate and slurry. The exergy de-
struction (L) is caused by the irreversibility of thermodynamic process.
3.7. Exergy analysis Thus, the exergy balance of the system can be expressed as:
E0 + E1 + E2 + E3 + E4 = E5 + E6 + L (39)
The total energy of steady flow in an opening system includes en-
thalpy, kinetic energy, and potential energy. The latter two are me- The exergy efficiency of the system is depicted as the ratio of earn
chanical energy, and the value of their exergy equals to their energy. exergy to pay exergy:
Therefore, only enthalpy is considered in the calculation. ηget E5 + E6
For gas stream, all the gas in this system is regarded as ideal gas. The ηe = =
ηpay E1 + E2 + E3 + E4 (40)
specific exergy is given by the formula below:
eg = h − h′ − T ′ (s − s′) (29)
4. Results and discussion
where h' and s' are enthalpy and entropy of the gas, respectively, and T'
is the temperature under the standard state. 4.1. Model validation
For feed stream, sodium sulfate wastewater is regarded as the actual
solution. The property of inorganic salt, therefore, must be taken into The numerical model is validated by comparing the calculation re-
account together with that of water [23,32]. The physical exergy of sults with those of a reported MVR system model [20]. As shown in
feed stream is calculated as: Table 1, the deviation between the two systems is in a reasonable range,
indicating that our modeling results are consistent with that in the
T P − P′ ⎤
elph = Cp,m (T − T ′) − T ′ ⎡Cp,m ⎛ln ⎞ −
⎜ ⎟[23] literature and the proposed model can be used to predict the behavior
⎢ ⎝ T0 ⎠ T ′ρm ⎥ (30)
⎣ ⎦ of the target system.
The chemical exergy is calculated as:

elch = −Fm RT ′ (x z ln x z + x j ln x j)[23] (31)

By adding up the physical exergy and chemical exergy, the exergy of
the actual solution is obtained:

el = elph + elch (32)

The slurry stream, due to the additivity of exergy, can be expressed
as the sum of solution exergy and crystal exergy. According to the
principle of phase equilibrium, crystal exergy is calculated as:
α
ecr = νT ′R ln
α′ (33)
where ν is the total number of ions, α is the activity of saturated solu-
tion, and α' is the activity under standard condition. The activity is Fig. 3. Exergy balance of the parallel-connected double-effect MVR evaporation
determined by the following formula: crystallization system.

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H. Jiang, et al. Applied Thermal Engineering 179 (2020) 115646

Table 1 consumption have a similar variation trend since the compressor is the
Model validation. dominating power-consuming device in the system. At an evaporation
Process parameters Unit Literature [20] Model % Error temperature of 100 °C, the specific energy consumption of the system
increases by 28.6% when the saturation temperature difference rises
Feed temperature, t0 °C 25 25 – from 10 °C to 14 °C. Whereas, when the evaporation temperature is
Feed flow rate, F0 kg·h−1 20 20 –
increased from 85 °C to 130 °C and the saturation temperature differ-
Feed concentration, w0 % 2 2 –
Emission concentration, w1 % 10 10 –
ence is 12 °C, the specific energy consumption decreases by 15.2%. It is
Evaporation temperature, t1 °C 70 70 – indicated that the system power consumption is more impacted by sa-
Evaporation capacity, W kg·h−1 20 20 – turation temperature difference than evaporation temperature. The
Heat transfer temperature °C 5 5 – declining trend shown in Fig. 6 is similar to the result that obtained by
difference, Δt
Ettouney [13].
Equipment parameters
Heat transfer area of evaporator, S1 m2 1.64 1.70 −3.7 Fig. 6 presents the effects of evaporation temperature and saturation
Heat transfer area of preheater, S3 m2 0.17 0.19 −11.8 temperature difference on the COP of the system. It is obvious that COP
Heat transfer quantity of kW 13.07 14.16 −8.3 increases as the evaporation temperature gets higher and decreases as
evaporator, Q1
the saturation temperature difference becomes larger. As mentioned
Heat transfer quantity of preheater, kW 1.16 1.02 12.1
Q0
above, higher evaporation temperature leads to lower system power
Compressor power consumption, N1 kW 0.30 0.34 −13.3 consumption. Owing to this, higher evaporation temperature will lead
to higher COP of the system in the condition of constant quantity of
heat absorption. Similarly, as the saturation temperature difference
4.2. Calculation instance increases, the total power consumption of the system increases, and the
COP thus decreases.
The established mathematical model of the proposed system is The effects of evaporation temperature and saturation temperature
executed using MATLAB. The properties of condensate and vapor are difference on the total heat transfer area is demonstrated in Fig. 7. It
from REFPROP 9.1 database. The design parameters required to solve seems that the higher the evaporation temperature is, the bigger the
the mathematical models under normal atmosphere are listed in heat transfer area will be, and with the increase of saturation tem-
Table 2, and the results are listed in Table 3. perature difference, the heat transfer area increases. In addition, the
The exergy balances of main devices are established in the same sensitivity of total heat transfer area to evaporation temperature is
way as of the system. The performance parameters, including exergy lower than that of saturation temperature difference [20,25]. Taking
efficiency and destruction of each device, are listed in Table 4. the saturation temperature difference of 10 °C as an example, the total
heat transfer area increases by merely 7% with the evaporation tem-
4.3. Parametric study perature varying from 85 °C to 130 °C. At evaporation temperature of
100 °C, the total heat transfer area decreases about 410.9 m2 with a
Parametric study is conducted on the basis of calculation instance. declining amplitude of 34.2% owing to the increase of saturation
The temperature difference between saturated boiling solution and temperature difference from 10 °C to 14 °C.
condensate (ΔTs-w = T1-t2) has an important effect on a MVR system, Based on the above analysis and the previous study [21], the total
especially on the compressor. Fig. 4 shows the effects of evaporation power consumption and the total heat transfer area of the system have
temperature and saturation temperature difference on compressor opposite trends with the variation of saturation temperature difference.
power consumption. It can be concluded that the compressor power At a certain evaporation temperature, there must be an optimal sa-
consumption decreases with the increase of evaporation temperature turation temperature difference bringing about lower total power
and a larger saturation temperature difference leads to more com- consumption and smaller heat transfer area. As shown in Fig. 8, 11.8 °C
pressor power consumption. is approximately the optimal saturation temperature difference at the
Higher evaporation temperature will result in higher secondary evaporation temperature of 100 °C.
vapor temperature, which means higher inlet temperature of com- Likewise, the total power consumption and the total heat transfer
pressor. Compression ratio decreases in the condition of constant area of the system also present contrary trends along with varying
compression temperature rise, and the compressor power consumption evaporation temperature. Once the saturation temperature difference is
decreases consequently. On the other hand, raising the saturation given, the optimal evaporation temperature, which brings about lower
temperature difference at a specific evaporation temperature increases total power consumption and smaller heat transfer area, can be ob-
the condensate temperature as the temperature of saturated solution is tained. Fig. 9 exemplifies the optimal evaporation temperature of
constant, which raises the enthalpy of superheated vapor and the 106 °C at a saturation temperature difference of 12 °C.
compressor power consumption correspondingly. Depicted in Fig. 10 is the effect of feed concentration on the area of
It can also be drawn from Fig. 4 that the compressor power con- each heat exchanger in the system. As the feed concentration rises from
sumption is more sensitive to saturation temperature difference than to 2% to 10%, the total heat transfer area of the system reduces slightly.
evaporation temperature. When the saturation temperature difference For the falling film evaporator applied to condense the feed to satura-
is 12 °C and the evaporation temperature rises from 85 °C to 130 °C, the tion, there is a significant decrease in heat transfer area. This decrease
compressor power consumption is reduced by 87.1 kW, with a declining results from a lower workload of the evaporator, which is caused by
amplitude of 17.6%. However, when the evaporation temperature is
100 °C and the saturation temperature difference rises from 10 °C to Table 2
14 °C, the compressor power consumption increases 162.9 kW, with an Design variables for the proposed system.
amplitude of 42.5%. The results are approximately consistent with that
Variable Unit Value
reported by Ahmadi et al. [25].
The effects of evaporation temperature and saturation temperature Feed concentration, w0 % 5
difference on the specific energy consumption of the system are de- Emission concentration, w1 % 29
monstrated in Fig. 5. It shows that higher evaporation temperature Feed flow rate, F0 kg·h−1 15,900
Evaporation capacity, W kg·h−1 15,000
results in higher specific energy consumption and higher saturation
Evaporation temperature, t1 °C 100
temperature difference leads to higher specific energy consumption. Compressor saturation temperature difference °C 12
The specific power consumption and the compressor power

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Table 3
Thermal properties of operating processes in the proposed system.
No. Temperature Concentration Flow rate Enthalph Exergy Specific exergy Medium type
°C % kg·h−1 kJ·kg−1 kW kJ·kg−1

1 20 5 15,900 – 484.5 109.7 Solution

2 100 5 15,900 – 495.5 112.2
3 102.5 29.8 2741.4 – 35.4 46.5
4 102.5 29.8 2877.7 – 38.9 48.7
5 102.5 29.8 136.3 – 1.8 46.5
6 102.5 – 900 – 15 53.6 Slurry
7 – – 763.7 – 13.2 62.2 Crystal
8 114.5 – 16,617 2697.9 2581.6 559.3 Vapor
9 114.5 – 14474.5 2697.9 2248.8 559.3
10 114.5 – 2025.5 2697.9 314.7 559.3
11 102.5 – 14,577 2679.5 2025.8 500.3
12 102.5 – 2040 2679.5 283.5 500.3
13 102.5 – 16,617 2679.5 2309.3 500.3
14 140.6 – 16,617 2752.4 2646 573.2
15 102.5 – 14474.5 429.8 210.5 52.4 Condensate
16 102.5 – 2025.5 429.8 29.5 52.4
17 102.5 – 16,500 429.8 240 52.4
18 26.1 – 16,500 109.4 8.3 1.8
19 26.1 – 349.9 109.4 0.2 1.8

increased feed concentration and constant discharge concentration. The

forced circulation evaporator works to further concentrate the satu-
rated solution to precipitating crystal. At a constant flow rate, higher
feed concentration tends to increase the mass fraction of sodium sulfate
and the quantity of crystal. Consequently, the workload of the eva-
porator rises and its heat transfer area increases. For the preheater, the
heat transfer area decreases slightly when the feed concentration gets
higher. A reason for this is that only the specific heat of solution is
weakly affected by the feed concentration during the calculation of heat
transfer area.
Fig. 11 illustrates the influence of feed concentration on the power
consumption of the total system, the forced circulation evaporator, and
the compressor, as well as on COP under the condition of an evapora-
tion temperature of 100 °C and a saturation temperature difference of
12 °C. The total power consumption increases by almost 33.5% as the
feed concentration goes from 2% to 10%. As the analysis above, higher
feed concentration leads to larger heat transfer area of the forced cir-
culation evaporator and, in turn, higher power consumption of it. This
is actually the cause of the increase in the power consumption of the
entire system, as the compressor power consumption does not change Fig. 4. Effects of evaporation temperature and saturation temperature differ-
with the change of feed concentration. Meanwhile, COP of the system ence on compressor power consumption.
decreases by nearly 25.7%. This is caused by, besides a higher total
power consumption, the lower quantity of heat absorbed by feed in the
According to the technological requirements of multi-effect eva-
progress of crystallization.
poration crystallization, the first effect demands a constant input of
fresh heating vapor and only the first effect consumes fresh vapor.
4.4. Comparison with a traditional multi-effect evaporation crystallization Ideally, the consumption of fresh heating vapor is 5000 kg/h when the
system distribution ratio of evaporation capacity among each effect is set as
1.0:1.1:1.2. The quantity of available latent energy contained in the
A traditional three-effect evaporation crystallization system is in- vapor is 3080 kW.
troduced as a contrast [34]. The schematic diagram of the reference The last effect of multi-effect evaporation crystallization demands
system is shown in Fig. 12. Except for the parameters same to those in an additional condenser to cool the secondary vapor. Obtained by
Table 2, other parameters required by the system are listed in Table 5.

Table 4
Performance parameters of devices.
Device Exergy destruction Exergy efficiency Heat transfer quantity Evaporation capacity Power consumption Remarks
kW % kW kg/h kW

Preheater 220.7 77.5 1422.9 – – heat transfer area: 54.5 m2

Falling film evaporator 472.6 75.1 8958 13158.6 – heat transfer area: 787 m2
Forced circulation evaporator 91.7 73.2 1253.6 1841.4 66.1 heat transfer area: 110.2 m2
vapor compressor 126.8 72 – – 463.5 compressor ratio: 1.5
gas–liquid separator – – – – 3.0 Volume: 6.4 m3
crystal-liquid separator – – – – 3.0 Mass flow rate: 900 kg/h

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H. Jiang, et al. Applied Thermal Engineering 179 (2020) 115646

Fig. 8. Effect of saturation temperature difference on total power consumption

and heat transfer area.
Fig. 5. Effects of evaporation temperature and saturation temperature differ-
ence on total energy consumption.

Fig. 9. Effect of evaporation temperature on total power consumption and heat

transfer area.

Fig. 6. Effect of evaporation temperature and saturation temperature difference

on the system COP.

Fig. 10. Effect of feed concentration on heat transfer area.

Fig. 7. Effects of evaporation temperature and saturation temperature differ-

ence on the total heat transfer area.

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H. Jiang, et al. Applied Thermal Engineering 179 (2020) 115646

Table 5
Some operating parameters for the three-effect evaporation crystallization
system.
Flow media Temperature Pressure Adding
°C MPa

Heating vapor 114.5 0.167 Discharging as condensate

Cooling water 20 – Cooling secondary vapor of last
effect
Operating unit
The first effect 100 0.101 Adiabatic evaporation
The second effect 80 0.047 Adiabatic evaporation
The third effect 60 0.020 Adiabatic evaporation

Table 6
Thermal performance of the proposed system and the reference system.
Performance index MVR system Three-effect Unit
system

Fig. 11. Effect of feed concentration on power consumption and COP. Evaporation capacity 15,000 15,000 kg·h−1
Consumption of heating vapor – 4545.5 kg·h−1
Power consumption of heating – 3080 kW
energy balance of the last effect, the quantity of secondary vapor is vapor
6000 kg/h. The heat transfer quantity required to cool the vapor to Quantity of cooling water – 57.9 kg·h−1
60 °C condensate water, as stipulated by the emission standard, is 3929 Power consumption of system 543.1 – kW
kW. Reclaimed water with an initial temperature of 20 °C is selected as Coefficient of performance 21.4 3.8 –
Specific energy consumption 130.3 739.2 kJ·kg−1
the cooling medium of condenser, whose outlet temperature is 50 °C. Exergy efficiency 49.1 32.4 %
After calculation, the required flow rate of reclaimed water is 112 t/h. Exergy destruction 772.6 1025.4 kW
With reference to the establishment of exergy balance of the pro-
posed parallel-connected double-effect evaporation crystallization
system, the exergy balance of the three-effect evaporation crystal- due to which evaporation of solution at high concentration and high
lization system is also established, through which the exergy efficiency boiling point is avoided. In contrast to this, the final effect of the tra-
and exergy destruction can be obtained. In practice, the three-effect ditional system is where the majority of evaporation happens, and it
evaporation crystallization system will consume some electricity due to also has the highest concentration and boiling point among all the ef-
the delivery of feed from a preceding effect to the next. However, this fects. As a consequence, the specific energy consumption of the pro-
energy consumption is less than 1% as compared with the quantity of posed MVR system is only 17.6% of that of the traditional system.
heat contained in fresh heating vapor, and is thus ignored in calcula- Furthermore, the energy analysis demonstrates a significantly better
tion. Table 6 presents the performance parameters of the two systems. performance of the MVR system over the traditional system.
With the same evaporation capacity, the proposed system based on When it comes to exergy efficiency and destruction, the core impact
MVR is able to recycle the latent heat of secondary vapor and merely factors are pay exergy and earn exergy. The pay exergy of the proposed
consumes a small quantity of electricity to obtain the heating vapor that system is derived from electricity. Since electricity is high quality en-
meets the evaporation requirements. In contrast, the traditional multi- ergy, the quantity of exergy is exactly that of electric energy in theory.
effect evaporation system obtains vapor by heating water from vapor- The pay exergy of the traditional system is mostly from the heat of
generating equipment such as boilers, which may consume a huge vapor. Unlike electricity, vapor energy is not of high quality, and the
quantity of energy. The COP of the MVR system is 82.2% higher than quantity of vapor exergy is far smaller than that of vapor energy. Due to
that of the traditional system. the same evaporation capacity and crystal production, the two systems
In the proposed system, most of the evaporation occurs in the falling have nearly equal quantity of earn exergy. As a result, the exergy effi-
film evaporator where the boiling point is relatively lower. The eva- ciency and the exergy destruction of the MVR system is 51.5% higher
poration capacity of the forced circulation evaporator is quite small, and 24.7% lower, respectively, than that of the traditional system. In

Fig. 12. Schematic diagram of the three-effect falling film evaporation crystallization system.

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H. Jiang, et al. Applied Thermal Engineering 179 (2020) 115646

brief, the exergy analysis demonstrates a higher degree of thermo- recompression system, Fluid Mach. 45 (06) (2017) 16-20+60 (in Chinese).
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