Abstract

Based on the pinch theory and energy cascade utilization principle, the performance of a multi-effect shipboard vertical tube climbing film desalination system combined thermal vapor compression with different preheating configuration has been analyzed. The mathematical model is established for thermodynamic simulation, in which various thermodynamic losses caused by boiling point elevation and pressure drop are considered, and the effective heat transfer temperature difference and the hot side temperature difference are used to analyze the influences of heating steam temperature, final effect evaporation temperature, and concentration ratio on thermal performance including gained output ratio (GOR)—specific heat transfer area for different preheating configuration. The results show that the internal average effective heat transfer temperature difference determines characteristics of multi-effect distillation (MED) system. While for system with similar average effective heat transfer temperature, the temperature difference of hot side is the controlling parameter. And the energy cascade utilization principle shows the controlling attribute in MED thermodynamic system, as GOR is improved mainly due to utilization of the secondary energy and residual energy of the heating steam for preheating process.

1 INTRODUCTION

Energy crisis, which is combined with the environmental problems such as climate change and global warming issues caused by greenhouse gas emission [1], and freshwater crisis, which means more than 1.2 billion people (or about one-fifth of the world’s population) live in areas of physical scarcity and another 1.6 billion people (or almost one quarter of the world’s population) will face economic water shortage by the year 2030 [2], are two important and critical issues all over the globe in the 21st century and beyond. And seawater desalination, as an energy-consuming process, should combine with renewable energy, nuclear energy and waste heat energy extensively for sustainable development in the future, to help the water-scarce countries and regions surviving freshwater crisis in the history of ‘Carbon Peak’ and ‘Carbon Neutrality’ [3–6].

The two main types of modern desalination techniques adopted around the world are thermal and membrane technologies. Many early desalination projects developed in the 1940s used thermal desalination, mainly including multi-stage flash (MSF) and multi-effect distillation (MED), and are still the dominant desalination technology in the Middle East. Membrane technologies were developed in the 1960s, among which reverse osmosis (RO) is by far the most dominant process and at present constitute 84% of total number of operational desalination plants, producing 69% of total global desalinated water [7]. Among various seawater desalination technologies, MED operating at low temperature, especially large capacity unit combined with thermal vapor compressor (TVC), shows strong competitiveness and has sharp increase in the market in terms of contracted capacities in Gulf countries and South East Asia, occupied about 35.9% of total capacity by 9.4% portion of plant number in china [8].

Schematic diagram of climbing film desalination system with TVC and two-stage preheating configuration.
Figure 1

Schematic diagram of climbing film desalination system with TVC and two-stage preheating configuration.

For MED, among three common forms of evaporators, which are vertical tube climbing film evaporator, vertical tube falling film evaporator and horizontal tube falling film evaporator, the vertical tube climbing film evaporator is widely used as shipboard desalination plants [9] because it is suitable for utilization of small and medium capacity low-grade waste heat. Swing and rocking on the shipboard have little effect on formation of liquid film and heat transfer characteristics in climbing film evaporator. It has remarkable stability and reliability because of no need for liquid distributor, low requirements for manufacturing and installation, high convenience for operation and control, which are suitable for complex marine environment. The local heat transfer coefficient between feed seawater and evaporator surface can reach more than 6000 W/(m2·°C) [10]. The scaling phenomenon can be effectively controlled because the scouring of high speed inside two-phase flow, especially under low evaporation temperature condition. Generally, climbing film evaporator is the lowest cost desalination plant in unit volume so far. It shows wide application prospect on shipboard desalination field with advantages of distillate product quality matching well with the boiler feed water requirement with no effect by seawater quality, especially when waste heat is available on shipboard.

In the paper, based on the pinch theory and energy cascade utilization principle, a multi-effect shipboard climbing film desalination system in vertical tube with thermal vapor compression is proposed. The mathematical model is established for thermal characteristics analysis, in which various thermodynamic losses caused by boiling point elevation (BPE) and vapor pressure drop are considered. Based on temperature difference analysis method, the influence of heating steam temperature, evaporation temperature and concentration ratio (R, Ratio of seawater salinity of concentrate bine of last effect to the feed seawater) on thermal performance of system including GOR and specific heat transfer areas are analyzed. And the influences of different preheating configuration are compared.

2 MATHEMATICAL MODELING FOR CLIMBING FILM EVAPORATION DESALINATION SYSTEM WITH THERMAL VAPOR COMPRESSION

2.1 Analysis model of the system

Figure 1 shows the schematic diagram of vertical tube climbing film desalination system with thermal vapor compression and two-stage preheating process. As shown in the figure, the system is mainly composed of evaporator, condenser, thermal vapor compressor, desuperheater and preheater. Three climbing film evaporators are arranged in forward feed configuration. After fresh seawater is preheated and partially degassed in condenser, a part enters two-stage preheaters as feed seawater, which is preheated by the condensate and secondary steam of first effect evaporator to the near boiling temperature point, and then enters the first effect evaporator. The excess cooling seawater is discharged from the device. The preheated feed seawater is further heated by the discharging steam form TVC in the vertical tube bundles to generate secondary steam for next effect evaporator. The concentrated seawater enters next effect evaporator under pressure difference between effects for continuous evaporation until discharged from the last effect evaporator. The high-pressure primary steam enters TVC, recycling part of secondary steam of the last effect evaporator as heat source of the system. Part of condensate in first effect evaporator is sent to the desuperheater and the rest enters first preheater for residual heat utilization. The other effect evaporators are propelled by secondary steam generated by the former effect, which contains part of flashing steam of bine.

Mathematical model of the i-th effect evaporator.
Figure 2

Mathematical model of the i-th effect evaporator.

As shown in Figure 2, each effect climbing film evaporator is composed of a group of vertical tubes. The feed seawater enters from the bottom of the evaporator, heated by the condensing steam outside. The secondary steam generates high-speed updraft inside vertical tube, which drives the evaporated seawater to climb up along the tube wall associating with pressure difference of adjacent effects, and a film of brine is established combined with bubbly, plug, churn and annular flow patterns. There is a non-boiling zone and a sub-cooled boiling region at the bottom section. And the overall heat transfer coefficient can achieve 4000 W/(m2·°C) without non-condensable gases in some boiling region and the temperature difference should to be controlled above 5 °C to propel the updraft, below which the local heat transfer coefficient drops obviously and the height ratio (the ratio of height of feed seawater to the height of tube) deviates from the optimal value [10–13]. The secondary steam and concentrated seawater are separated by gravity and the demister on the top of the evaporator after which the concentrated brine is converged through the central down tube, which is led to the next effect evaporator. So the evaporator is names as climbing film or rising film evaporator in new configuration [14].

2.2 Mathematical model of the system

The mass balance model and energy balance model of the evaporator are as follows:
(1)
(2)
(3)
where subscript i or i-1 is the number of evaporator effect, b denotes brine, v denotes vapor and d denotes distillate. So mb,iin, mb,iout, mv,iin and mv,iout are the mass flow rate of feed seawater, concentrate brine, heating steam, secondary steam of i-th effect evaporator, respectively; sb,iin and sb,iout are seawater salinity of feed seawater and concentrate brine; hv,iin, hv,iout, hb,iin, hb,iout and hd,iout are enthalpy of heating steam, secondary steam, feed seawater, concentrate brine and distillate product of i-th effect evaporator, respectively.
In the heat transfer model, the effective heat transfer temperature different Δteff,i is employed to calculate the heat transfer area of evaporator. As the first effect evaporator contains both preheating and evaporating portion, so the heat transfer in it should be calculated as follows:
(4)
where tv,iin and tb,iout are temperature of heating steam and concentrate brine, respectively; Ky,i and Kz,iare heat transfer coefficient of preheating section and evaporating section, respectively; and Fy,i and Fz,i are heat transfer area of preheating section and evaporating section, respectively.
To calculate the effective heat transfer temperature different Δteff,i, thermodynamic losses caused by BPE, pressure drops within the tube bundle, demister and tubes, and losses associated with condensation in the tube in addition to non-equilibrium allowance should be considered carefully, and temperature can be calculated as follows:
(5)
(6)
where BPEi is the boiling point elevation of seawater; Δth,i is thermal loss caused by hydrostatic head in tube; and Δtt,i, Δtb,i and Δtd,iare thermal losses caused by transmission tube, tube bundles and demister, respectively. To make the model simple, the thermal losses caused by pressure drops were set constant value.
The heat transfer model includes convective heat transfer model for preheating portion in single phase by Hausen and evaporating portion in two-phase by Coulson and Mcnelly [15], as shown in equations (7) and (8).
(7)
where Nuy, Reb,y and Prb,y are for preheating portion in tube, din is inside diameter of heat transfer tube, Ly is the length of the preheating portion in first effect evaporator, μb,y and μw are dynamic viscosity of brine or at temperature of wall.
(8)
where Nuz,i, Reb,z,i and Prb,z,i are for evaporating portion, Rev,iis for secondary steam in evaporating region, ρb,z,i and ρv,i are density of brine and secondary steam for i-th effect evaporator and μv,i and μb,z,iare dynamic viscosity of secondary steam and brine.
The convective heat transfer model for condensation outside of tube is as shown in equation (9) by Nusselt. As the preheating portion is at the bottom of the first effect evaporator, so condensation heat transfer model should combine with equation (10).
(9)
where αout,i is condensation heat transfer coefficient of outside of tube; γc,i is latent heat of condensation; μl,i, λl,i and ρl,i are dynamic viscosity, thermal conductivity and density of distillate liquid; tv,iin and tw,iare temperature of vapor and wall.
(10)

In which αout,y is condensation heat transfer coefficient of outside of tube for preheating portion, αout,L andαout,z are condensation heat transfer coefficient for length of total tube or evaporating portion, L and Lz are total tube length or length of the evaporating portion.

To calculate the performance of climbing film desalination system with TVC and two-stage preheating process, the performance of the two-stage preheaters and TVC should calculated at the same time. The heat transfer model for preheater and condenser follows recommendation by EI-Dessouky [16] and the TVC model is based on aerodynamic theory of Sokolov [17].

2.3 Calculation method for variable condition characteristics of climbing film desalination system

Based on the mathematical model built in Sections of 2.1 and2.2, the performance of climbing film desalination system can be calculated based on equal area design principle, in which different evaporators have same heat transfer area [18]. Figure 3 shows the calculation flow chart of variable condition characteristics of the system, such as different operating temperatures of the first effect evaporator or last effect evaporator and different concentration ratio. To calculate the performance of system, total fresh water product Mz, number of effect of evaporator N, seawater salinity of feed seawater sb,1in, temperature of heating steam of the first effect evaporator tv,1in, evaporation temperature of last effect tv,nout, temperature of feed seawater of the first effect evaporator tb,1in, which determines the capacity of the two-stage preheaters, concentration ratio R should be set firstly. Based on the given parameters, mass flow rate of feed seawater can be calculated. And then the initial value of effective heat transfer temperature different Δteff,i can be determined. Based on the assumed GOR which is associate with the entrainment ratio of TVC, mass flow rate of secondary steam of every effect evaporator can be calculated based on the internal parameters for secondary steam, concentrate brine, thermal losses of every effect evaporator, and based on the iterative loop of total product of the secondary steam Mzf, the accurate value of GOR can be matched. To keep every effect evaporator has in same heat transfer areas, each effective heat transfer temperature difference Δteff,i should be matched with mass flow rate of secondary steam and heat transfer area of each effect evaporator. At last, condenser parameters and thermal characters of the system can be calculated.

Calculation flow chart of multi-effect climbing film desalination system.
Figure 3

Calculation flow chart of multi-effect climbing film desalination system.

3 PERFORMANCE OPTIMIZATION ANALYSIS OF CLIMBING FILM DESALINATION SYSTEM WITH PREHEATING PROCESS

3.1 Optimization analysis of preheating process base on pinch theory and energy cascade utilization principle

Based on the thermodynamic analysis model proposed above, the climbing film desalination system with TVC is analyzed. The performance of system without preheating process, with one-stage preheating configuration by secondary steam of first effect evaporator, with two-stage preheating configuration by secondary steam of first effect evaporator and distillate product of first effect evaporator are compared respectively. The basic operating condition of the system is as shown in Table 1.

Basic operating condition of the desalination system

Table 1
Basic operating condition of the desalination system
Total fresh water production, Mz60 t/d
Effect number of evaporator, N3
Concentrate ratio, R1.5
Pressure of primary flow for TVC, Pm0.3 MPa
Temperature of primary flow for TVC, Tm150 °C
Temperature of heating steam for first effect evaporator, tv,1in76 °C
Last effect evaporation temperature, tv,3out44 °C
Temperature of feed seawater, tsw20 °C
Salinity of feed seawater, sb,1in35 g/kg
Total fresh water production, Mz60 t/d
Effect number of evaporator, N3
Concentrate ratio, R1.5
Pressure of primary flow for TVC, Pm0.3 MPa
Temperature of primary flow for TVC, Tm150 °C
Temperature of heating steam for first effect evaporator, tv,1in76 °C
Last effect evaporation temperature, tv,3out44 °C
Temperature of feed seawater, tsw20 °C
Salinity of feed seawater, sb,1in35 g/kg
Table 1
Basic operating condition of the desalination system
Total fresh water production, Mz60 t/d
Effect number of evaporator, N3
Concentrate ratio, R1.5
Pressure of primary flow for TVC, Pm0.3 MPa
Temperature of primary flow for TVC, Tm150 °C
Temperature of heating steam for first effect evaporator, tv,1in76 °C
Last effect evaporation temperature, tv,3out44 °C
Temperature of feed seawater, tsw20 °C
Salinity of feed seawater, sb,1in35 g/kg
Total fresh water production, Mz60 t/d
Effect number of evaporator, N3
Concentrate ratio, R1.5
Pressure of primary flow for TVC, Pm0.3 MPa
Temperature of primary flow for TVC, Tm150 °C
Temperature of heating steam for first effect evaporator, tv,1in76 °C
Last effect evaporation temperature, tv,3out44 °C
Temperature of feed seawater, tsw20 °C
Salinity of feed seawater, sb,1in35 g/kg

Figures 4 and 5 show the effect of preheating process on GOR under different temperature of heat steam for first effect evaporator and last effect evaporation temperature. As shown in Figure 4 and Figure 5, preheating process can improve GOR significantly. The system with two-stage preheating configuration has the highest GOR under different operating temperature, and the system without preheating process has the lowest GOR. As the preheater can increase the temperature of the inlet seawater of first effect evaporator, the amount of steam for preheating seawater in first effect evaporator will decrease, which reduces the steam consumption of first effect evaporator, so GOR of the system increases.

Effect of temperature of the heating steam of first effect evaporator on GOR.
Figure 4

Effect of temperature of the heating steam of first effect evaporator on GOR.

Effect of evaporation temperature of final effect evaporator on GOR.
Figure 5

Effect of evaporation temperature of final effect evaporator on GOR.

Based on the energy cascade utilization principle [19] and pinch theory [20], when secondary steam is used for preheating, the energy grade of preheated steam is lower than the heating steam of first effect evaporator, reducing the heat transfer temperature difference within the thermodynamic system, so performance ratio of system is improved. When the second preheater is introduced, distillate product of first effect evaporator is used to preheat the feed seawater, which means the residual heat of condensate is further utilized to reduce the invalid discharge of thermodynamic system, at the same time the temperature difference of cold side is reduced, so the utility consumption of the system drops obviously. Therefore, the performance ratio of system is improved further and GOR is highest when two-stage preheating configuration is used.

As shown in Figure 4, whether there is preheating process or not, GOR decreases with the increasing of temperature of the heating steam of first effect evaporator. As with increase of temperature of the heating steam, the latent heat of condensation decreases, and the temperature of secondary steam increases which means the preheating load of first effect increases, so the amount of heating steam required for first effect increase. At the same time, as shown in Figure 6(a), the heat transfer temperature difference of evaporation system increases, so the performance or GOR of system decreases based on pinch theory. As show in Figure 6(a), with the heat temperature of first effect evaporator increases from 64 °C to 80 °C, the total heat transfer temperature difference of evaporators increase from 20 °C to 36 °C, and the average effective heat transfer temperature differenceΔteff,a(whereΔteff,a=Δteff,i/N) increases correspondingly, so GOR for system without preheating, with secondary steam preheating and with secondary steam and condensate two-stage preheating reduce by 32.9%, 30.3% and 29% respectively.

Effect of preheating configuration on temperature difference.
Figure 6

Effect of preheating configuration on temperature difference.

As shown in Figure 5, with increase of the final effect evaporation temperature, GOR of system for three different procedure all increase. As with the heating capacity of condenser increase, preheating load of seawater decreases in first effect evaporator which means the steam consumption decreases. At the same time, based on pinch theory, the heat transfer temperature difference within evaporation system decreases, so performance ratio of system is improved. Meanwhile, with final effect evaporation temperature increasing, the suction pressure of TVC rises and the entrainment ratio increases, so GOR of system increases. However, the temperature of cooling sweater discharged from the system increases, which means the invalid discharge of system increases, so the increasing trend of GOR slows down compared with the influence of heating steam temperature. As shown in Figure 6(b), with final effect evaporation temperature increase from 40 °C to 50 °C, the total heat transfer temperature difference of evaporators reduce from 36 °C to 26 °C, and the average effective heat transfer temperature difference Δteff,a decreases commensurably, so GOR for system without preheating, with secondary steam preheating and with secondary steam and condensate two-stage preheating increase by 29.2%, 20.7% and 19.3% respectively.

Figure 6 (a) and (b) also show the effect of the temperature difference of hot side Δths(where Δths=tv,1intb,1in,tb,1inis the mean temperature of feed seawater of first effect evaporator) on performance of system. As is shown in Figure 7, in the forward feed configuration of desalination system, as concentrate ratio of system for different preheating presses are all 1.5, the total heat transfer temperature difference of evaporating system Δttotalis same and the total thermal losses caused by BPE et al is near equal, so the average effective heat transfer temperature difference Δteff,afor different preheating presses in nearly same. In this condition, based on pinch theory, the temperature difference of hot side Δths of the evaporating system plays key role to determine the performance ratio of desalination system. As shown in Figure 6 (a) and (b), the temperature difference of hot side Δths of configuration without preheating process is highest for different heat steam temperature and last effect evaporation temperature, so GOR is the lowest. And the temperature difference of hot side Δthsof configuration with two-stage preheating configuration is the lowest under different operating temperature, so GOR of system is always the highest. The conclusion certificates that for MED system in forward feed configuration, where the minimum internal temperature difference of the cold and hot fluids is nearly zero (the temperature difference with the secondary steam of the cold fluid brine, is regenerated by the flashing process in evaporator), the temperature difference of hot side Δthsof the internal MED system is the determinant parameter. And the energy cascade utilization principle controls the whole thermodynamic system, configuration with two-stage preheating process with utilization of the secondary energy of the internal system and the residual heat of the primary energy is the best system, owns the highest GOR all the time.

Temperature difference distribution of MED system with forward feed configuration.
Figure 7

Temperature difference distribution of MED system with forward feed configuration.

4 UNIVERSALITY OF PINCH THEORY AND ENERGY CASCADE UTILIZATION PRINCIPLE IN MULTI-EFFECT DISTILLATION SYSTEM

Figure 8 shows the effect of concentration ratio on GOR with different preheating configuration. As shown in the figure, with increasing of concentration ratio, the feed seawater flow rate gradually reduces which means the preheating load of system decreases correspondingly, so GOR increases commensurably with different preheating configurations. When concentration ratio raises from 1.2 to 2, GOR for system without preheating, secondary steam preheating and two-stage preheating increase by 22.8%, 15.1% and 15.3% respectively, meanwhile, as shown in Figure 9 and Figure 10, the total effective heat transfer temperature differenceΔteffand the average effective heat transfer temperature difference Δteff,a decrease. The results show the universality and decisiveness of pinch theory, which means the internal temperature difference determine the performance ratio of thermodynamic system, based on which an inference might be obtained that the internal average effective heat transfer temperature difference Δteff,a determines the characteristics of MED system. While for MED system with same Δteff,a, the temperature difference of hot side Δthsis the controlling parameter. As shown in Figure 8 and Figure 9, GOR for system with two-stage preheating configuration is always the highest correspond to the minimum temperature difference of hot side Δthswith the similar average effective heat transfer temperature difference Δteff,a.

Effect of concentration ratio on GOR.
Figure 8

Effect of concentration ratio on GOR.

Effect of concentration ratio on temperature difference.
Figure 9

Effect of concentration ratio on temperature difference.

Effect of concentration ratio on total effective heat transfer temperature difference.
Figure 10

Effect of concentration ratio on total effective heat transfer temperature difference.

Figure 11 shows effect of concentration ratio on the specific heat transfer area (SHTA, ratio of total heat transfer area including evaporator, preheater and condenser to total fresh water product). As shown in the figure, for system without preheating configuration, the specific heat transfer area decreases firstly and then increases gradually with increase of concentration ratio. As with increasing of concentration ratio, the need for feed seawater reduces and the preheating load decrease correspondingly, so heat exchange area for preheating portion reduces, meanwhile the amount of flashing steam decreases with feed seawater reducing which lead to the reduction of load and condensing heat transfer area of condenser. However, as shown in Figure 10, with increase of concentration ratio, the salinity of brine in evaporators increase, temperature difference losses caused by BPE increases which means the effective heat transfer temperature difference decreases, so specific heat transfer area increases commensurably. Under the superposition of two effects, specific heat transfer area has a local optimal value with concentration ratio. The design optimal value of GOR for climbing film distillation system with TVC is 1.4, while for system without TVC is 1.5.

Effect of concentration ratio on specific heat transfer area.
Figure 11

Effect of concentration ratio on specific heat transfer area.

Under preheating configuration, the influence trend of concentration ratio on specific heat transfer area changes. As shown in Figure 11, specific heat transfer area increases with concentration ratio for one-stage and two-stage preheating. As preheater increases the feed seawater temperature, reducing the influence of heat transfer area for preheating portion in the first effect evaporator and the evaporating load increases which neutralizes the effect of flashing process on specific heat transfer area, so specific heat transfer area increases with concentration ratio meanwhile the effective heat transfer temperature difference decreases. But when concentration ratio is reduced to 1.3, the benefit of reducing concentration ratio is attenuated and specific heat transfer area nearly keeps a constant value.

Generally, the energy cascade utilization principle shows the controlling attribute in MED thermodynamic system. GOR is improved mainly due to utilization of the secondary energy and residual energy of the heating steam for preheating process. When the residual energy of the heating steam is not used, the specific heat transfer area can keep the minimum value, as heat transfer coefficient of concentrate preheater is lower than steam preheater.

5 CONCLUSIONS

Based on the pinch theory and energy cascade utilization principle, performance of a multi-effect shipboard vertical tube climbing film desalination system combined TVC with different preheating configuration has been analyzed. The mathematical model is established for thermodynamic simulation, in which various thermodynamic losses caused by BPE and pressure drop are considered, and the effective heat transfer temperature difference and temperature difference of hot side are used to analyze the influences of heating steam temperature, final effect evaporation temperature, and concentration ratio on the thermal performance including GOR, specific heat transfer area for different preheating process. And main conclusions are obtained as follows:

(1) GOR of MED system can be improved by preheating process, the system with two-stage preheating configuration owns the best performance, as the secondary energy and residual energy of the heating steam is utilized for preheating process.

(2) The internal average effective heat transfer temperature difference Δteff,adetermines the characteristics of the MED system, GOR increases with the decreasing of Δteff,a.

(3) For MED system with similar Δteff,a, the temperature difference of hot side Δthsis the controlling parameter. GOR increases with the decreasing of Δths.

(4) For influence of concentration ratio on specific heat transfer is different for MED system with different preheating process. The specific heat transfer area decreases firstly and then increases gradually with increase of concentration ratio for system without preheater. While for system with preheating configuration by secondary steam of first effect evaporator or two-stage preheating combined with the distillate product of first effect evaporator, the specific heat transfer area increases with concentration ratio.

Acknowledgements

This research is supported by the Key Project of National Natural Science Foundation of China (no. 51936002) and the Science and Technology Innovation Foundation of Dalian (no. 2020JJ26SN063).

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