A neural network-based optimizing control system for a seawater-desalination solar-powered membrane distillation unit

Computers and Chemical Engineering 54 (2013) 79–96

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A neural network-based optimizing control system for a seawater-desalination solar-powered membrane distillation unit R. Porrazzo, A. Cipollina, M. Galluzzo ∗ , G. Micale Dipartimento di Ingegneria Chimica, Gestionale, Informatica, Meccanica, Università degli Studi di Palermo, Viale delle Scienze Ed.6, 90128 Palermo, Italy

a r t i c l e

i n f o

Article history: Received 19 October 2012 Received in revised form 14 March 2013 Accepted 18 March 2013 Available online 26 March 2013 Keywords: Membrane distillation Solar energy Neural network Control Optimization

a b s t r a c t Several schemes have been proposed so far for coupling desalination processes with the use of renewable energy. One of their main drawbacks, however, is the nature of the energy source that requires a discontinuous and non-stationary operation, with some control and optimization problems. In the present work, a solar powered membrane distillation system has been used for developing an optimizing control strategy. A neural network (NN) model of the system has been trained and tested using experimental data purposely collected. Afterwards, the NN model has been used for the analysis of the process performance under various operating conditions, namely distillate production versus feed flow rate, solar radiation and cold feed temperature. On this basis, a control system that optimizes the distillate production under variable operating conditions has been developed, implemented and tested. © 2013 Elsevier Ltd. All rights reserved.

1. Introduction and literature review Seawater desalination processes require substantial amounts of energy for the production of fresh water. Energy requirements may largely vary depending on the selected technology; however, in all cases the resultant cost of the produced water depends essentially on the cost of energy. Thus the efficient use of energy to power desalination processes is a key issue for their economical sustainability and consequential successful implementation. In recent years growing concern toward environmental and energy sustainability prompted toward the coupling between renewable energies and desalination processes. As a result, a number of alternative solutions have been proposed, e.g. solar powered thermal desalination, wind powered reverse osmosis, photovoltaic reverse osmosis, solar powered membrane distillation (Cipollina, Micale, & Rizzuti, 2009). When a renewable energy desalination process is chosen, the issue of optimal energy use becomes absolutely critical in determining the technical and economical sustainability of such choice. In all cases, the main problem to tackle is the unsteady nature of the renewable energy source, which requires the development of a specific design for such installations with special focus on the control system and energy buffering devices. The control of solar plants, to be used or not for desalination, has been studied by several authors. Predictive control has been in

∗ Corresponding author. Tel.: +39 091 23863740; fax: +39 091 6571655. E-mail address: [email protected] (M. Galluzzo). 0098-1354/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compchemeng.2013.03.015

particular suggested and tested in conjunction with some identification techniques or other control techniques. Arahal, Berenguel, and Camacho (1998) proposed and experimentally tested neural predictors for use in a nonlinear predictive control scheme. Ayala et al. (2011) presented a new predictive control strategy for the distributed collector field of a solar plant. The objective of the controller is to maintain constant the outlet-inlet temperature gradient. A nonlinear model predictive controller, extended with a dead-time compensator, was proposed by Galvez-Carrillo, De Keyser, and Ionescu (2009) for the control of a distributed solar collector field. Silva, Rato, and Lemos (2003) developed a model based predictive controller using time-scaling for obtaining a linear discrete state space model. Pickhardt (2000) presented the application of an indirect adaptive predictive controller to a solar test-plant using nonlinear models. Henriques, Gil, Cardoso, Carvalho, and Dourado (2010) proposed and experimentally tested a real-time indirect adaptive nonlinear control scheme of a solar power plant, combining a recurrent neural network and the output regulation theory. A genetic algorithm based fuzzy logic control system was developed by Luk, Low, and Sayiah (1999) also for the control of a solar power plant. Roca, Berenguel, Yebra, and Alarcon-Padilla (2008) presented the development and application of a feedback linearization control strategy for a solar collector field that supplies heat to a multi-effect seawater distillation plant. To the best of our knowledge, the control of a solar powered membrane distillation system has been only recently addressed by Lin, Chang, and Wang (2011). They developed a model of the MD unit and tested by simulation a control system with two feedback temperature control loops.

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Nomenclature ARX D Ffeed Fopt ss G1∗ G1 G1d G2∗ G2 G2d G3 G3d IR IT KR

auto regressive exogenous distillate flow rate (L/h) feed flow rate to the MD module (L/h) optimal steady state feed flow rate maximizing the distillate production (L/h) transfer function linking Radcol to Tav transfer function linking Radcol to D dynamic part of the transfer function G1 transfer function linking Tcond in to Tav transfer function linking Tcond in to D dynamic part of the transfer function G2 transfer function linking Ffeed to D dynamic part of the transfer function G3  constant of Eq. (2), relating Fopt ss and Radcol , function of Tcond in (L/h)  constant of Eq. (5), relating Fopt ss and Tcond in , function of Radcol (L/h)  linear coefficient relating Fopt ss and Radcol , function

of Tcond in (L m2 /h W)  linear coefficient relating Fopt ss and Tcond in , function ◦ of Radcol (L/h C) MD membrane distillation MSE mean square error NN neural network corrected solar radiation incident on collector tubes Radcol surface (W/m2 ) Radmeas solar radiation (W/m2 ) s Laplace complex variable of the transfer functions Tcollector in inlet temperature to the collectors (◦ C) Tcond in inlet temperature to the cold channel of the MD module (◦ C) Tcond out outlet temperature from the cold channel of the MD module (◦ C) Tevap in inlet temperature to the evaporator channel of the MD module (◦ C) Tevap out outlet temperature from the evaporator channel of the MD module (◦ C) Theat source in inlet temperature to the hot side of the heat exchanger (i.e. outlet temperature from solar collectors) (◦ C) Theat source out outlet temperature from the hot side of the heat exchanger (◦ C) average vapor pressure difference driving force Pav within the MD module (mbar) Tav average temperature difference driving force within the MD module (◦ C) inlet–outlet temperature difference in the collectors Tcol (◦ C) KT

In the present work, an optimizing feedforward control system based on a neural network (NN) model is proposed for a solarpowered membrane distillation plant for seawater-desalination. The adoption of a purposely developed control system is in fact the key element for the optimization and operability of a membrane distillation system powered by solar energy. The difficulty of controlling such a system is originated by the coupling with solar energy, a frequently variable and unpredictable source of heat. The main objective of the control system can be defined as maximizing the desalination plant efficiency in terms of daily production of distillate. Additional objectives are the minimization of operating costs, the optimization of the use of solar energy and the possibility of using stand-alone systems in remote locations.

The use of a purposely implemented neural network model of the process allowed to identify a range for the feed flow rate, in which optimal operating conditions (i.e. maximum production of distillate) can be obtained. The controller has been preliminarily evaluated through performing numerical simulation tests and then implemented in the LabView environment and tested on the solar-powered Membrane Distillation unit.

2. The solar-powered membrane distillation unit 2.1. The solar membrane distillation technology The membrane distillation (MD) technology is a hybrid thermal/membrane desalination process that can be used to perform the separation of water vapor from brine by means of a hydrophobic membrane. The membrane allows only the passage of vapor driven by a temperature difference, which generates a difference in the vapor pressure of water between the two sides of the membrane. The vapor that passes through the membrane can then be condensed within the same module or extracted and sent to an external condenser, depending on the configuration of the process. In particular, the most commonly adopted configurations are: air gap membrane distillation (AGMD), direct contact membrane distillation (DCMD), and permeate gap membrane distillation (PGMD), where the condensation takes place within the MD module itself; sweeping gas membrane distillation (SGMD) and vacuum membrane distillation (VMD), where the condensation takes place in an external auxiliary unit. Among the several advantages that characterize the use of MD with respect to conventional separation technologies, the very easy modularity of the system and the possibility of using discontinuous and low temperature heat sources make MD particularly suitable for coupling with solar energy, especially for the development of stand-alone systems to be used in remote areas. In this regard, a number of examples of pilot units have been installed and presented in the literature (Koschikowski, Wieghaus, & Rommel, 2009; Saffarini, Summers, Arafat, & Leinhard, 2012). Most of them are small scale systems (less than 1000 L/day capacity), although some larger plants have been recently installed and operated (Cipollina, Koschikowski, et al. 2011). Two different coupling schemes can be adopted in solarpowered MD systems: (1) single-loop; (2) two-loop. In a single-loop unit (often referred to as “compact system”) the solar energy captured in solar collectors is directly used to heat seawater before entering the evaporation channel of the MD unit. The advantage of such coupling scheme is related to the absence of an intermediate heat exchanger transferring heat from the collector to the MD unit and, therefore, to the higher temperature achievable in the hot feed entering the MD unit. However, the materials used in solar collectors must be corrosion-resistant (CuNi alloys are often adopted), with a higher cost of the system. In a two-loop unit the solar energy is collected and then transferred to the feed stream by means of a corrosion-resistant heat exchanger (typically CuNi or titanium plate and frame HXs) that connects the “solar energy loop” to the “seawater MD loop”. The advantage of this scheme is that cheap and commercially available solar collectors can be adopted and a better control of corrosion and scaling problems can be achieved, confining the flow of salty streams inside an easy-to-clean heat exchanger. On the other side, the need to transfer heat from one loop to the other generates a drop in the maximum temperature achievable by the seawater feed, thus reducing the maximum potential driving force in the MD process. Finally, the two-loop system also allows an easy integration of the “solar energy loop” with a heat storage facility, which can guarantee a more stationary operation of the

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system under variable weather conditions and extended operation also during night hours. 2.2. Plant description The pilot unit adopted in the present study consists of: (1) a membrane distillation unit; (2) a solar field with evacuated tubes collectors; (3) a heat storage tank; (4) all relevant hydraulic circuits. A sketch of the plant is shown in Fig. 1 (Cipollina, Di Sparti, Tamburini, & Micale, 2012). The MD desalination unit, purchased from Solar Spring GmbH, is based on a spiral wound module with nominal water production capacity of 150 L/day. The MD module is characterized by a PGMD configuration, with internal heat recovery, which allows the pre-heating of the cold feed water at the expense of the heat subtracted to the vapor condensing on a polymeric film in contact with it (Fig. 2) (Koschikowski et al., 2009). For a full description of the heat and mass transfer phenomena in the spacer-filled channels of membrane modules (in particular for MD) the reader can refer to a number of literature papers (Al-Sharif, Albeirutty, Cipollina, & Micale, 2013; Cipollina, Di Miceli, Koschikowski, Micale, & Rizzuti, 2009; Cipollina, Micale, & Rizzuti, 2011a; Schofield, Fane, & Fell, 1987; Tamburini, La Barbera, Cipollina, Ciofalo, & Micale, 2012). The unit is also equipped with a feed storage tank (1000 L), two circulation pumps (for the feed circulation and the feed tank refilling with cold salt water from a “refill tank” of 500 L), a CuNi shell and tubes heat exchanger for connecting the “solar loop” to the “MD loop” and a simple automation system, which allows to switch on and off the plant according to the operating temperatures reached by the process streams. The thermal energy for the desalination unit is provided by a solar collectors field (12 m2 ) with evacuated tubes (heat-pipe type). A thermal buffer of 300 L is used to store a small amount of heat coming from the solar collectors, when the collected energy exceeds the instantaneous consumption of the MD unit. The presence of a heat storage system may allow in principle the operation of the system under different plant configurations, according to the instantaneous radiation and the stored energy, e.g. for operations during night-time or with cloudy days (Cipollina et al., 2012). However, only the direct coupling between the solar collectors and the MD unit has been investigated in the present work. A water–glycol mixture is circulated inside the solar collectors loop, including also the heat storage buffer, by means of a circulation pump automatically switched on and off by a dedicated control unit. This latter, which makes use of three thermocouples placed, respectively, at the exit of the solar panels, at the top and bottom of the boiler, activates the pump only when the exit temperature from the collectors is higher than the temperature at the bottom of the boiler of a predetermined difference (usually 5 ◦ C). 2.3. Process description and nominal operating ranges The feed water is pumped from the feeding tank into the “cold channel” of the MD module, passing through a cartridge filter, a control valve and a rotameter. The pre-heated feed stream exits from the “cold channel” and reaches the CuNi heat exchanger where it is heated by the hot water–glycol mixture coming from the solar collectors. The hot feed is then fed to the evaporator channel, where it produces vapor that passes through the hydrophobic membrane. This then condenses in contact with the polymeric foil, which eventually transfers the condensation heat to the cold feed that is pre-heated in the “cold channel”. Finally, the permeate is extracted from the top of the module and stored in a 100 L tank. The brine exiting from the evaporator channel is sent back to the feed tank for a continuous closed-loop daily operation.

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During the day, the temperature and salinity of the feed water increase due to the recirculation of the exiting brine. This causes a driving force decrease, which leads to a reduction of the process performance. To tackle this problem, a refill tank, containing cold feed water, is used to refill the feed tank by a refill pump automatically activated when the cold feed temperature exceeds a set point (usually fixed between 40 and 45 ◦ C). The feed tank is also connected to the refill tank through a weir that allows the return of the warm water in excess to the refill tank. The main switch of the desalination unit is controlled by a relay that activates the feed pump only when the temperature of the water–glycol mixture arriving to the HX from the collectors reaches a set value (usually set at 60 ◦ C). Conversely, a safety shutdown switch stops the feed pump when the inlet feed temperature exceeds 85 ◦ C, in order to avoid damage to the module. Finally, the feed flow rate is adjusted by a valve positioned on a recycle loop and operated by a feedback controller (Fig. 29). Further indications on the operating ranges of the system are taken from the Orix150 operating manual (Wieghaus & Wolf, 2010): • for safety reasons, the feed flow rate must be chosen so that the temperature in the evaporator inlet to the channel does not exceed 85 ◦ C; • the module is designed to operate with a flow rate between 50 and 600 L/h, even if the recommended range of operation is between 350 L/h and 550 L/h. 2.4. Data acquisition system The use of an advanced data acquisition system (National Instruments Compact Rio) made it possible to analyze in detail the trend of all main variables of the system during several days of operation. All variables were monitored with a sampling frequency of 1 Hz; samples were then averaged to record only one value per minute, considering the relatively large time constants of the observed phenomena. A list of the monitored variables is reported in Table 1. 2.5. Experimental investigation of the uncontrolled system A preliminary experimental investigation of the behavior of the unit was performed before developing the advanced control system. Three different testing procedures were adopted in order to collect information on the unit operation necessary for the subsequent development of the control system. In particular the unit was tested: (1) under almost “steady-state” operation (i.e. setting all operating variables at constant values except the radiation, which is naturally almost stationary only during the hours around noon); (2) varying the feed flow rate every 30 min and analyzing the dynamic response of the system; (3) keeping constant all operating conditions, but covering the solar collectors in order to introduce a sudden disturbance in the solar radiation input. 2.5.1. Behavior of the system on a typical sunny day As regards the first tests, performed under almost steady-state operation, some indicative trends are reported in the following graphs, showing the variation of all main operating variables of the plant. In particular, it is worth noting how the solar radiation, directly measured by the Pyranometer SR11 (Radmes ) is corrected (Radcol ) in order to take account of the cylindrical surface of the collector tubes on which the radiation is perpendicular for a longer time than on a planar surface. In particular, a simple geometrical relationship, which for brevity is not reported here,

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Fig. 1. Schematic representation of the operating configuration 1 (cold hours of a sunny day): Solar energy is directly used to power the MD plant (Cipollina et al., 2012).

Fig. 2. Scheme representing the heat recovery layout of the PGMD module (Koschikowski et al., 2009). Table 1 List of the variables monitored by the NI Compact Rio data acquisition system. Nomenclature (units)

Description

Sensor type

Tevap in (◦ C) Tevap out (◦ C) Tcond in (◦ C) Tcond out (◦ C) Theat source in (◦ C) Theat source out (◦ C) Tcollector in (◦ C) Radmeas (W/m2 ) Ffeed (L/h) D (L/h)

Inlet temperature to the evaporator channel of the MD module Outlet temperature from the evaporator channel of the MD module Inlet temperature to the cold channel of the MD module Outlet temperature from the cold channel of the MD module Inlet temperature to the hot side of the heat exchanger (i.e. outlet temperature from solar collectors) Outlet temperature from the hot side of the heat exchanger Inlet temperature to the collectors Solar radiation Feed flow rate to the MD module Distillate flow rate

Pt100 Pt100 Pt100 Pt100 Pt100 Pt100 Pt100 Pyranometer Hukseflux SR11 Rotative flow meter Rotative flow meter

1100 8

900 800 700

6

600 500 2

400

Radcol [W/m ]

300

Radmeas [W/m ]

200 100 10

Tcol [°C]

2

Radcol ; Radmeas [W/m ]

1000

4 2

T

col

11

[°C] 12

13

14

15

16

17

18

2 19

Time [h] Fig. 3. Daily trend of the measured and corrected radiation (Radmeas and Radcol ) and inlet–outlet temperature difference in the collectors (Tcol ).

R. Porrazzo et al. / Computers and Chemical Engineering 54 (2013) 79–96

83

1100

82

1000

78

600 66

500

62

Radcol

400 300

58

Theat source in Tevap in

200

54 10

11

12

13

14 15 Time [h]

16

17

[W/m2]

700

70

col

800

Rad

Temperature [°C]

900 74

100 19

18

Fig. 4. Daily trend of the corrected radiation (Radcol ), inlet temperature of the fluid arriving to the HX from collectors (Theat source in ) and temperature of the hot feed entering the MD module (Tevap in ).

between the instantaneous inclination of the solar radiation and the angle of inclination on the cylindrical surface has been considered. The trend of the solar radiation and the difference between the inlet–outlet temperatures of solar collectors, measured in a typical sunny day, are reported in Fig. 3, while Fig. 4 reports the trend of the corrected radiation, the heat source temperature (arriving to the heat exchanger from the solar collectors) and the temperature of the seawater entering the evaporator channel. As expected, the difference between the inlet and outlet temperatures of solar collectors follows a pattern very similar to that of the corrected solar radiation, although at higher temperatures a slightly flatter profile is held, probably due to an increase of the heat losses to the environment. A larger difference can be noted between the hot stream temperatures and Radcol . In fact, while the solar radiation reaches a maximum between 1 p.m. and 2 p.m., both temperatures reach a maximum value much later, between 3 p.m. and 4 p.m. Such singularity is related to the continuous increase of the temperature of the cold feed, Tcond in , which leads to a general increase of all temperatures of the system (see Fig. 5). This, coupled with a fairly stationary Radcol until 3 p.m., generates a continuous increase of the hot temperatures until about 4 p.m., when the fast reduction of solar radiation leads again to a rapid decrease until the minimum value of 55 ◦ C is reached by Tevap in , leading to the automatic shutdown of the plant. As regards the other monitored temperatures of the MD module, Fig. 5 shows the daily trend of the temperatures entering (Tevap in and Tcond in) and exiting (Tevap out and Tcond out) the MD module channels. The increasing sun radiation in the first part of the day, coupled

with the hot brine recirculation within the system, leads to a general increase of all temperatures until about 4 p.m. and a continuous daily increase of the energy content of both the feed tank and the refill tank. In fact, in order to avoid sudden variations of Tcond in , due to a sudden start-up or shut-down of the refill pump, this latter has been kept always active during the tests, thus resulting in increasingly higher values of Tcond in . Only at the end of the day, the decrease of radiation and, consequently, of all temperatures causes a reduction of the rate of increase of Tcond in . Finally, the trend of the produced distillate along with the average temperature difference and the vapor pressure difference between the hot and cold channels of the module are shown in Fig. 6. These latter are normally referred as the main driving forces for the vapor passage in the MD process. In particular, the vapor pressure difference across the membrane is the real driving force for the vapor flux through the membrane itself, but the total actual driving force (considering both the hot and cold channels) in DCMD, AGMD and PGMD modules can vary depending on the main transport mechanisms characterizing the three configurations. The partial pressure difference across the membrane is the effective driving force in DCMD modules, where condensation takes place when the vapor is directly in contact with the cold flowing stream. In AGMD modules the vapor, exiting from the membrane, has to pass a (normally stagnant) air gap before condensing on a surface cooled by the cold flowing stream. In this case the driving force for the vapor passing through the air gap is still a partial pressure difference, while the transfer resistance through the condensing film is usually negligible. Thus also in this case the total vapor

78

T

evap in

74

T

Temperature [°C]

70

evap out

66

T

62

Tcond in

cond out

58 54 50 46 42 38 34 30 10

11

12

13

14

15

16

17

18

19

Time [h] Fig. 5. Daily trend of the temperatures entering (Tevap in and Tcond in) and exiting (Tevap out and Tcond out) the MD module channels.

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10

T

av

6

9

5.5

8

5

7

4.5

6

4 5

3.5

4

3

D T

2.5

3

av

2 1.5 10

D [L/h]

[°C] ; P

av

[10*mbar]

6.5

2

Pav 11

12

13

14 15 Time [h]

16

17

18

1 19

Fig. 6. Daily trend of the distillate flow rate and average driving force in terms of temperature (Tav ) and vapor pressure (Pav ) differences between the hot and cold channels of the MD module.

pressure difference can be addressed as the main driving force of the separation process. In PGMD modules the vapor, exiting from the membrane, encounters the permeate filled gap thus condensing by direct mixing with it, leading to the need of transferring the condensation heat to the cold flowing stream by simple heat transfer through the permeate gap first and, eventually, through the condensation foil and the cold stream polarization layer. Indeed, experimental data from literature show that in systems characterized by a PGMD configuration, the higher resistance to heat transfer is found in the permeate channel (Cipollina et al., 2012). This is in accordance with the experimental evidence of Fig. 6, where the distillate flow rate tends to follow more the trend of the average T rather than the average P. 2.5.2. Effect of the feed flow rate variation The uncontrolled system was operated under different operating conditions in terms of feed flow rate for four days. In particular, the feed flow rate was kept constant throughout the day, with the following four different feed flow rates: 350, 390, 450 and 520 L/h. In all cases, the refill pump was kept always on in order to avoid sudden temperature variations of the cold feed entering the unit, which would affect the daily trend of all other variables. In Figs. 7–9 a comparison between the four cases is shown for the most significant operating variables. It is worth noting that all experiments were performed with a very similar daily radiation

measured within the considered time range (i.e. from 11:30 a.m. to 4:00 p.m.). Indeed, the analysis of the system behavior at different feed flow rates provided information on the interdependence of the system variables, very useful for the development of the control system. Fig. 7, in particular, shows the trend of the average temperature driving force within the module. A feed flow rate decrease normally leads to an increase of the average T: fixing the same radiation, i.e. the same amount of energy supplied, at larger feed flow rates, the inlet temperature Tevap in of the evaporator channel will be lower (as shown in Fig. 8) and the driving force will be smaller. On the other hand, the variation of Tcond in is much less sensitive to the variation of the feed flow rate, thus highlighting the dependence of the above described T trend mainly on the Tevap in variation. Nevertheless, in general, different initial values of Tcond in (due to different cooling phenomena during the night or to the use of an external cooler, which may be adopted for improving the process efficiency (Cipollina, Micale, & Rizzuti, 2011c)) can somehow affect the average values of T during the day. Finally, Fig. 9 shows the trend of the distillate flow rate for the same cases considered above. It can be seen that the increase of the driving force Tav is not the only variable affecting the production of distillate. In fact, while the decrease of the feed flow rate causes an increase of the theoretical T driving force, on the other hand the decrease of the fluid flow velocity in the feed channels may reduce the

80 6.5

75

[°C]

6

evap in

5

T

Tav [°C]

5.5

70

65 F

4.5 Ffeed 520 [L/h] Ffeed 450 [L/h]

4

Ffeed 390 [L/h]

13

14

15

feed feed

520 [L/h] 450 [L/h]

F feed 390 [L/h] F feed 350 [L/h]

Ffeed 350 [L/h]

3.5 12

F

60

16

Time [h] Fig. 7. Variation of the average temperature difference driving force (Tav ) at four different feed flow rates.

55 12

13

14 Time [h]

15

16

Fig. 8. Variation of the evaporator channel inlet temperature, Tevap in , at four different feed flow rates.

R. Porrazzo et al. / Computers and Chemical Engineering 54 (2013) 79–96

85

10 9.5

D [L/h]

9 8.5 8 F

520 [L/h]

F

450 [L/h]

F

390 [L/h]

F

350 [L/h]

feed

7.5

feed

7

feed feed

6.5 12

13

14 Time [h]

15

16

Fig. 9. Variation of the instantaneous distillate production at four different feed flow rates.

heat transfer coefficients thus increasing the effect of polarization phenomena, negatively affecting the effective driving force of the separation process. This explains why, passing from a feed flow rate of 390–350 L/h, despite the increase in the theoretical T driving force, there is a reduction in the distillate production. Thus, the objective of the optimizing control strategy developed in the present work, i.e. an optimal flow rate, which maximizes the actual driving force and the distillate production, is clearly highlighted by the previous experimental results. Table 2 summarizes the main process data for the four test cases discussed above. It is worth noting that slight variations in the operating time of the system in the different days depend on small differences in the actual radiation in the first part of each day.

2.5.3. Effect of a sudden variation in the feed flow rate In order to assess the dynamic response of the plant to a sudden variation of the feed flow rate, some further tests were carried out, by imposing 50 L/h step-changes to the flow rate every 30 min. Also in this case, for the sake of brevity, only results of tests carried out in one day will be presented, being the most representative of all similar tests performed during the campaign. Fig. 10 shows the trend of distillate and feed flow rate, the latter being varied every 30 min, in a time interval in which the radiation can be considered almost constant (values between 900 and 1000 W/m2 ), as already shown in Fig. 3. Fig. 10 shows how sudden reductions in the feed flow rate lead to a sudden transient reduction in the distillate production, followed by a slower increase. The sudden reduction in flow rate may be related to several factors: (1) a sudden reduction of the flow velocity leads to a reduction in the heat transfer coefficients in the channels, which in turn reduces the actual driving force across the membrane (temperature polarization (Cipollina, Di Miceli, et al., 2009; Cipollina et al., 2011a; Schofield et al., 1987)); (2) a slight sudden reduction of the T driving force due to the fast phenomena of feed pre-heating and brine cooling within the MD module, which anticipate the heating process in the external heat exchanger; (3) a reduction of the hydraulic pressure in the feed channels, which

leads to the expansion of the distillate channel (compressed among the two feed channels) causing a sudden decrease in the measured instantaneous distillate flow rate exiting from the module. After such sudden initial decrease, however, the distillate production increases, due to the increase of the temperature driving force (as already discussed in the previous paragraph). This increase typically occurs when the feed flow rate is decreased with step changes from 520 to 275 L/h, although a lower “steady-state” value is reached with flow rates below 350 L/h (as will be shown in the following paragraphs). A completely reversed behavior was observed for positive step-variations of the feed flow rate, corresponding to a sudden increase of the distillate flow rate, followed by a slow asymptotical reduction of the distillate production. To confirm what stated above, Fig. 11 reports the variation of the distillate production and Tav driving force, both related to the described step-variation of the feed flow rate. As already mentioned, the step-reductions of the feed flow rate generate first a step-reduction of the T driving force followed by a slower and asymptotical increase of Tav . It is also worth noting that the sudden reduction of the distillate flow rate (shown in Fig. 10) cannot be justified only by the slighter reduction of T, as well as the continuous increase of Tav does not lead to an increase of the distillate production with feed flow rates below 350 L/h. This indicates that there are other phenomena that cause the variation of the distillate production, as already discussed.

2.5.4. Effect of a sudden variation in solar radiation In order to characterize the dynamic response to a sudden variation in solar radiation, some tests were performed covering the collectors for 30 min and then quickly uncovering them, while keeping constant all process operating conditions. Since the distillate flow rate measured by the flow meter is affected by noise and given the strong relation already analyzed between the distillate rate and the Tav driving force in the MD module, the response of the latter was considered, as shown in Fig. 12. In fact, this shows the trend of solar radiation and temperature driving force measured during sun peak hours, after suddenly uncovering the solar

Table 2 Synthesis of the main process data of four test cases. Ffeed [L/h]

Theat source in max [◦ C]

Tevap in max [◦ C]

Initial Tcond in [◦ C]

Produced distillate [L]

Operating time [hh:mm]

520 450 390 350

69.7 73.4 80.7 83.0

64.5 68.7 76.2 79.0

25.3 31.0 31.0 28.7

55 52 64 60

8:40 7:30 8:40 8:20

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550

11

500

10

7

[L/h] F

feed

8 400 350

D [L/h]

9

450

6

300

F

feed

5

D 250 11

12

13

14

4 16

15

Time [h] Fig. 10. Trend of the distillate instantaneous production and feed flow rate registered imposing a step-change of the feed flow rate every 30 min.

6

11 10 9 8

5 7

D [L/h]

Tav [°C]

5.5

6

4.5 Tav

5

D 4 11

12

13

14

4 16

15

Time [h] Fig. 11. Trend of the distillate instantaneous production and average T driving force registered imposing a step-change of the feed flow rate every 30 min.

collectors. The graph shows that the sudden increase of the solar radiation does not lead to a sudden increase of the temperature driving force, but the system response is, on the contrary, quite slow, showing a delay of approximately 2 h before achieving again the steady state. 3. Development of an optimizing feedforward control scheme The objective of an efficient control system of the plant is to ensure that the maximum amount of distillate is produced

depending on the daily weather conditions. The analysis of the uncontrolled system shows that the choice of the feed flow rate operating range is critical for the achievement of a high amount of distillate since any flow rate change causes two different effects, the first on the average temperature difference between hot and cold channels, Tav (i.e. the T-driving force), and the second on the temperature polarization phenomena. The maximization of the distillate production relies on the determination of the best combination of an efficient fluid flow regime (in order to reduce polarization) and a total driving force of the process.

1200

6

1100 1000

5

4

700

av

600

[°C]

800

T

2

Rad col [W/m ]

900

500

3

400 300 200

Radcol

100

Tav

0 14

15 Time [h]

2

1 16

Fig. 12. Response of the system in terms of the average temperature driving force within the MD module (Tav ) following a sudden increase in the solar radiation on collectors (Radcol ).

R. Porrazzo et al. / Computers and Chemical Engineering 54 (2013) 79–96

For the previous considerations a feedback control with a constant production of distillate is obviously not able to achieve the desired objective. It is instead more appropriate to use an optimizing feedforward control scheme that, depending on disturbances, change the manipulation variable (e.g. the feed flow rate) in order to produce the maximum amount of distillate obtainable moment by moment. In order to design the feedforward controllers a dynamic model should be available. The lack of a reliable dynamic mathematical model of the process led to consider transfer functions experimentally obtained, which link the main disturbances and the manipulation variable to the controlled variable. Such links are characterized by constant dynamic parts and variable steady state gains, both functions of the disturbance variables as indicated by the analysis of the process. The dynamic part of the transfer functions was determined, as illustrated in the following paragraphs, by means of experimental identification tests, applying step changes to the inputs. The variable gains of transfer functions were obtained by a procedure adopting a neural network model of the process, and led then to the estimation of the ratios of the gains between disturbances and the output variable, and between the manipulation variable and the output variable. A simplified steady state model allows to state that the distillate flow rate (D), can be expressed as a function of the most significant input variables: the radiation (Radcol ), the feed flow rate (Ffeed ) and the inlet temperature of the cold channel of the MD module (Tcond in ). Experimental tests have shown that the variations of Tcond in due to changes of the ambient temperature and Tevap out are very slow and negligible in the short period, therefore Tcond in can be considered an independent input variable as far as the control action is concerned. The above considerations suggested the possibility of using a neural network based black box model with radiation (Radcol ), feed flow rate (Ffeed ) and the inlet temperature of the cold channel of the MD module (Tcond in ) as inputs, and the distillate flow rate (D) as output. 3.1. Development of a neural network model of the system 3.1.1. Artificial neural networks Artificial neural networks (NN) are calculation structures that mimic on the computer the information processing of biological nervous systems. A comprehensive introduction to NN can be found in (Haykin, 1999). A NN consists of a network of simple elements, called neurons, connected via communication links. Fig. 13 shows the structure of a neuron with R inputs and an output. Each link has an appropriate weight w, which represents the importance of

Fig. 13. Structure of a neuron. (Source: MATLAB Neural Network Toolbox).

87

the link. The sum of the weighted inputs, to which a constant (bias) is usually added, determines the input to the activation function f, by which an output is generated. Typical activation functions are linear, sigmoidal and hyperbolic tangent functions. In a NN, neurons are organized in layers: an input layer containing the neurons that receive and process the input data, an output layer that contains neurons responsible for the final calculation of outputs and one or more hidden processing layers. The information flow between neurons belonging to different neural layers can be directed from input to output (feedforward network), or from the output of a layer’s neuron to the input of a preceding layer’s neuron (recurrent or feedback network) or also between neurons of the same layer (these links are called lateral connections). Given this general classification there may be several other hybrid connections. In Fig. 14 a simple feedforward network with one hidden layer is shown. The development of a NN to model the relationships between the input and output variables of a real system essentially consists in adjusting the network weights by means of an appropriate training procedure, so that the network mimics the behavior of the real system. There are several methods of training, including the supervised training. The outputs calculated by the neural network are compared with the desired outputs (target) and the errors are used by an appropriate algorithm (usually the back-propagation and its variants such as the Levenberg–Marquardt algorithm) to update the weights of the network so as to minimize an objective function, which usually is the mean square error (MSE) between the outputs of the network and the desired outputs. However, the result obtained with the trained network is only valid for the training data while a model should instead be able to represent a system in each operating condition. The generalization of the model is obtained by a validation phase, in which a data set not used for the training phase is submitted to the network. A high degree of generalization is achieved for a neural network model when a low value of the performance function (e.g. MSE) is obtained for the validation set. One problem that may occur during the training of a neural network is the overfitting: this happens when, though the error with the training data set is very low, if a new set of data is submitted to the network, the error is very large. This means that the network has not learned to generalize. In Fig. 15 an example of overfitting is shown: after a certain number of epochs (an epoch corresponds to the entire training set going through the entire network once), the error for the training data continues to decrease while the error on the validation data changes slope and tends to increase. To solve this problem the method known as early stopping is often used. This consists in stopping the training phase at the number of epochs at

Fig. 14. Feedforward neural network with one hidden layer. (Source: MATLAB Neural Network Toolbox).

88

R. Porrazzo et al. / Computers and Chemical Engineering 54 (2013) 79–96

• Choice of the activation functions: typically sigmoidal nonlinear activation functions for the hidden layer and linear activation functions for the output layer are used. • Choice of the training algorithm: the algorithm of Levenberg–Marquardt is very often used (this algorithm is the fastest method for training feedforward neural networks of moderate size). • Training, validation and verification of the network.

Fig. 15. Comparison between MSE with training data and validation data. (Source: MATLAB Neural Network Toolbox).

which the error for the validation set starts to increase and using the weights and biases determined at that point. This method requires dividing the available data into three subsets: training, validation and verification sets. The verification set is then used to compare different networks. Neural networks can be divided into static and dynamic. Static neural networks reproduce static relationships between inputs and outputs, i.e. the output of the network at time t depends only on the input at the same time t. In dynamic neural networks the output at a given time t depends not only on current inputs, but also on the previous behavior of the system. Dynamic networks can be constructed starting from a static architecture through the use of memory elements (in this case they are called neural networks with external dynamics). For a nonrecurring network, the output y(t) depends exclusively on a certain number of past values of the input x(t): y(t) = f (x(t − 1), . . . , x(t − d))

(1)

Fig. 16 shows the architecture of a dynamic non-recurring neural network for a MISO (multi inputs single output) system, with delay elements (TDL) on the inputs. The development of a neural network ultimately consists of the following steps: • Choice of the type of network: recurring or non-recurring. • Choice of the sequences of input-output data to be submitted to the network. • Division of data into three subsets to be used for three separate operations: training, validation and verification (early stopping method). • Choice of the neural network architecture: a network with three layers (only one hidden layer) usually ensures a good performance. • Choice of the number of neurons in the hidden layer and the number of delays (TDL) for the inputs of a dynamic network while only one neuron is used for the output layer of a MISO system.

3.1.2. The neural network model of the solar-MD process A non-recurring feedforward dynamic neural network, in which the output y of the system at time t is a function only of a certain number of past values of input x, was chosen and the neural network toolbox of MATLAB® was used for the development of the NN model. In order to train the network, data collected during six days of operation with different values of Ffeed were selected. In the first four days, the system worked at different constant Ffeed (respectively 450, 390, 340 and 350 L/h), while in the following two days Ffeed was changed approximately every half hour in the range of 275–540 L/h. Of course Radcol and Tcond in varied during the operation. The slow dynamic response of the distillate flow rate to disturbances, especially to radiation variations, required a large number of “time delays” on the inputs. A sampling interval of 1 min was used, but data were compressed using the average values in 5 min. This operation has the advantage of reducing the calculation load and the complexity of the network, which works with fewer inputs, avoiding overfitting problems without losing information. Thus, using 12 time delays (5 min each) the output of the system at a certain instant t is in principle dependent on the values of the inputs of the last hour. Obviously the weight given to the different delayed inputs can be very low or even zero. In Fig. 17 the architecture of the dynamic non-recurring neural network is shown. Its main characteristics are: • one hidden layer consisting of 5 neurons with sigmoidal activation function; • the output layer consisting of 1 neuron with linear activation function; • 12 delays on the inputs; • learning algorithm: Levenberg–Marquardt supervised backpropagation; • iteration condition end: early stopping method. For the six chosen days, a sequence of 540 samples was considered for each input variable and for the output variable. The neural network was developed using a matrix of 3 × 540 inputs (3 variables and 540 samples concerning a sequence of six training days) and a desired output vector consisting of 540 samples. The set of input and output samples was randomly divided into three subsets: training, validation and verification subsets; in particular 80% of the data was used for training, 15% for validation and the remaining 5% for verification.

Fig. 16. Non-recurring neural network.

R. Porrazzo et al. / Computers and Chemical Engineering 54 (2013) 79–96

89

Fig. 17. The architecture of the adopted dynamic neural network. (Source: MATLAB Neural Network Toolbox).

day 2

day 1

10

day 5

day 4

day 3

day 6

D [L/h]

8 6 4 2 0

Target NN output 0

5

10

15

20 25 Time [h]

30

35

40

45

Fig. 18. Comparison between the NN model output after training and the experimentally measured target.

Table 3 Performance indexes of the neural network.

Training Validation Checking

MSE (L2 /h2 )

R

0.293 0.413 0.268

0.975 0.953 0.985

In Fig. 18 the output calculated by the NN model after training and the desired output (experimentally measured target) are compared. Table 3 reports the values of the mean square error (MSE) between the output calculated by the NN model and the target value, and the regression coefficient (R) obtained with the network (R equal to 1 indicates a perfect fitting between the calculated output and the target, while a value of 0 indicates a total absence of relation). A data set of another day of operation, never shown to the network, was used to test the reliability of the neural network model. Fig. 19 shows the comparison between the values of distillate flow rate calculated by the network and the measured ones, while Table 4 shows the corresponding performance parameters. For comparison purposes a different approach, based on the non-linear auto regressive exogenous (ARX) identification system (Lyung, 1987) was used. The corresponding non-linear structure is very similar to the neural network previously described, in particular for the number of delays on the inputs, the algorithm and the sigmoidal units. The set of data provided to the ARX model was the Table 4 Performance indexes of the NN tested with a set of new independent data.

Independent check

MSE (L2 /h2 )

R

0.170

0.981

same used to train the neural network. The comparison between the target output and the ARX model prediction led to a best fit of 91% that indicates a very good black box model. However the best fit obtained in the verification phase dropped to 53.8%. This result clearly demonstrates a much higher performance of the neural network compared with the ARX model, due to the significantly higher degree of generalization of the neural network. 3.1.3. Use of the neural network for the development of the control system The developed neural network was then used to obtain the steady-state relationships linking the distillate flow rate to Ffeed , Radcol and Tcond in . Three sequences of values of the input variables were used as inputs of the neural network: • Radcol was changed from 1000 to 300 W/m2 with steps of 100 W/m2 ; • for each value of radiation, Ffeed was changed from 300 L/h up to 500 L/h with steps of 20 L/h; • the above step variation analysis was carried out for four different values of Tcond in (32, 37, 42 and 47 ◦ C). Each couple of values of radiation and Ffeed needed to be kept constant for a period of time tF greater than 60 min, corresponding to 12 samples, in order to overcome the transitory response of the neural network and to allow the output of the neural network to reach a steady state value. To achieve this a tF equal to 110 min was chosen. In Fig. 20 the distillate flow rate calculated by the neural network at the above described conditions for Radcol and Ffeed and for Tcond in = 37 ◦ C is shown. From the trends shown in Fig. 20 it is possible to obtain Fig. 21, in which the steady state values of the distillate flow rate are

90

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9 Target NN output

8 7

D [L/h]

6 5 4 3 2 1 0

0

1

2

3

4

5

6

7

Time [h] Fig. 19. Comparison between the flow rate of distillate calculated by the neural network using the verification set and the real distillate flow rate of the process.

expressed as function of Ffeed for different values of radiation and Tcond in = 37 ◦ C. Similar graphs were obtained also for the other values of Tcond in , but are not reported here for the sake of brevity. At all radiations, Ffeed values above 400 L/h determine lower values of Tevap in , thus reducing the driving force of the process and the distillate production, while for Ffeed values below 360 L/h the opposite occurs. In fact, though lower Ffeed values lead to an increase of Tevap in , and more generally of the theoretical driving force of the process, there is no improvement in the production of distillate since the excessive Ffeed reduction determines a dramatic increase of the temperature polarization phenomena. The variations of Ffeed , in the range between 360 L/h and 400 L/h, at lower radiations, do not appreciably affect the maximum production of distillate, showing that different combinations of Tav and Ffeed allow to obtain similar results in terms of distillate. Selecting for each curve reported in Fig. 21 the maximum value of the distillate flow rate, it is possible to obtain the trend of the maximum achievable values of distillate flow rate as a function of the radiation for four different Tcond in , as shown in Fig. 22. As expected, the maximum of the distillate flow rate increases as the incident radiation increases at constant Tcond in and decreases as Tcond in increases at constant radiation. In order to obtain the Ffeed values to be used to maximize the amount of distillate, Fig. 23 was derived, where the Ffeed values corresponding to the maximum values of distillate flow rate are shown as a function of the radiation for different values of Tcond in . T

Interestingly, for higher Tcond in , higher values of Ffeed are expected to optimize the distillate production, while for lower Tcond in , lower values of Ffeed are required, with a significantly stronger dependence on the incident radiation. This highlights the importance of using a variable feed flow rate, especially with systems equipped with a brine-cooling device for the maximization of the process driving force. In the same way it is possible to plot the values of optimal Ffeed as a function of Tcond in for different values of radiation, as shown in Fig. 24. In conclusion, the use of the neural network model developed from experimental data allows to obtain steady-state relationships showing the optimal value of Ffeed to be used to maximize the distillate flow rate even with variable radiation and Tcond in . From the curves of Fig. 23 it is possible to derive an equation to calculate the optimal steady state feed flow rate to use with specific values of radiation and Tcond in .  Fopt

ss

= Radcol · KR (Tcond

in ) + IR (Tcond in )

(2)

where KR = −0.0032 · Tcond

in

IR = 3.4288 · Tcond

+ 232.57

in

+ 0.1596

(3) (4)

A similar equation can be derived from Fig. 24:  Fopt

cond in

ss

= Tcon

in

· KT (Radcol ) + IT (Radcol )

(5)

= 37 °C

2

1000 W/m

10

900 W/m

800 W/m

8 D [L/h]

2 2

2

700 W/m

6

600 W/m

4

2 2

500 W/m

400 W/m

2 0

0

50

100

150 Time [h]

200

2 2

300 W/m

250

300

Fig. 20. The distillate flow rate variation predicted by the NN model with Tcond in = 37 ◦ C and changing Radcol and Ffeed . Each set of data with fixed solar radiation is characterized by Ffeed varying from 300 to 500 L/h.

R. Porrazzo et al. / Computers and Chemical Engineering 54 (2013) 79–96

91

10

2

Rad 1000 W/m

9

2

Rad 900 W/m

8

Rad 800 W/m2

7

Rad 700 W/m2

D [L/h]

6

Rad 600 W/m2

5

2

Rad 500 W/m

4

Rad 400 W/m2

3

2

Rad 300 W/m

2 1 0 300

320

340

360

380

400

420

440

460

480

500

Ffeed [L/h] Fig. 21. Steady state distillate flow rate as function of Ffeed at different values of radiation and Tcond in = 37 ◦ C.

10

410

T

D max [L/h]

8

6

cond in cond in

= 32 °C 400

= 37 °C

Tcond

= 42 °C in

Tcond

in

Fopt ss [L/h]

T

= 47 °C

4

390 380 Tcond in = 32 °C

370

Tcond in = 37 °C Tcond in = 42 °C

360

2

Tcond in = 47 °C

0 200

350 300

400

600

800

400

500

600

700

800

900

1000

Radiation [W/m2]

1000

Radiation [W/m 2 ] Fig. 22. Maximum attainable values of distillate flow rate as a function of radiation for four different Tcond in .

Fig. 23. Values of optimal Ffeed as a function of the radiation for different values of Tcond in .

of the procedure, it is appropriate to use an average of the values calculated by them, i.e.:

where KT = −0.0035 · Radcol + 3.7452

(6)

IT = 0.171 · Radcol + 221.85

(7)

In principle, it would be possible to use any one of the two above sets of equations but to compensate for the inherent approximation

Fopt

ss

=

[Radcol · KR (Tcond

in )

+ IR (Tcond

in )]

+ [Tcond 2

in

· KT (Radcol ) + IT (Radcol )]

This expression corresponds to a steady-state feedforward control law, giving the optimal steady state Ffeed depending on the main disturbances within the system. It should be noted that both Radcol and Tcond in are expressed as deviation variables, though the reference values are fixed at

410

2

Rad 1000 W/m

405

2

Rad 900 W/m

400

Rad 800 W/m2

Fopt ss [L/h]

395

Rad 700 W/m2

390

Rad 600 W/m2

385

2

Rad 500 W/m

380

Rad 400 W/m2

375

Rad 300 W/m

2

370 365 360 355 32

34

36

38 T

40 [°C]

(8)

42

44

46

cond in

Fig. 24. Values of optimal Ffeed as a function of Tcond in for different values of the radiation.

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5

7.5

4.5

7 6.5 Tav [°C]

Tav [°C]

4 3.5

6 5.5

3 5

2.5 4.5

2 1.5

Calculated output Measured output 0

20

40

60 80 Time [min]

100

4

120

Radcol = 0 and Tcond in = 0, thus making them basically equal to the normal variables. 3.2. Determination of optimal dynamic feed flow rates To get a dynamic control law, it is necessary to know the dynamic response of the distillate production rate to changes of the manipulation variable, Ffeed , and to the independent disturbances in radiation and Tcond in . To this purpose, tests with step inputs were carried out. The effect of a step change in the radiation on the distillate flow rate, at constant Ffeed and Tcond in , was already shown in Fig. 12, obtained by covering the collectors and then suddenly uncovering them to determine the time to reach a steady state behavior. As explained above, the effect on the Tav was first analyzed, since its measurement is less affected by noise than flow measurement. This measurement was then related to the distillate flow rate, given the very good relationship observed between these two variables. Using the System Identification Toolbox of MATLAB the parameters of the transfer function linking the radiation to the average T (Tav ) were estimated. By inspection a transfer function of the first order plus dead time was chosen and the dynamic parameters were calculated. The resulting transfer function is the following: K ∗ e−5s Tav (s) = 1 23s + 1 Radcol (s)

(9)

with a time constant of 23 min, a dead time of 5 min and s being the Laplace complex variable. Furthermore, it is necessary to add the dead time between a change of Tav and a change of distillate flow rate, experimentally estimated in 3 min. The transfer function between radiation and distillate flow rate is thus: G1 =

K1 e−8s D(s) = = K1 G1d 23s + 1 Radcol (s)

(10)

Fig. 25 shows the comparison between the Tav calculated by the transfer function and that experimentally measured for a step disturbance in the radiation. The percentage of the response reproduced by the model (best fit) was calculated by the following expression:



Best fit =

1−

  y − y   |y − y∗ |

× 100

0

5

10 Time [min]

15

20

Fig. 26. Comparison between the measured and calculated Tav variation for a step change in Tcond in .

Fig. 25. Comparison between the measured and calculated Tav variation for a step change in the radiation.

G1∗ =

Calculated output Measured output

(11)

where y is the measured output, y is the simulated output and y* is the mean value of the measured output. The calculated best fit is 96.1%, which highlights the efficiency of the adopted transfer function. The transfer function linking the response of Tav to a step change in Tcond in , with constant radiation and Ffeed , was determined with a similar procedure. To apply a step change in Tcond in , it was necessary to work using only the feed tank. Then, the activation of the refill pump made it possible to introduce cold sea water in the feed tank, thus generating an abrupt change in Tcond in , which is shown in Fig. 26. The calculated transfer function is: G2∗ =

K ∗ (24.43s − 1) Tav (s) =− 2 9.538s + 1 Tcond in (s)

(12)

Its structure is a “lead-lag” with a pole equal to −1/9.538 and a zero equal to 1/24.43. A dead time of 3 min was added to obtain the transfer function between Tcond in and the distillate flow rate, as already explained for the radiation step change. G2 =

D(s) K2 (24.43s − 1) × e−3s =− = K2 G2d 9.538s + 1 Tcond in (s)

(13)

A comparison between the measured output and the output calculated with the transfer function derived with the model identification toolbox of MATLAB is shown in Fig. 26. In this case, the best fit of the linearized model is 81.37%. Finally, to characterize the dynamic response of the distillate flow rate to a change in Ffeed , some tests at constant values of radiation (1000 W/m2 ) and Tcond in (35 ◦ C) were performed. In this case, the distillate flow rate curves were obtained directly. Experimental data (already presented in Fig. 10) relative to the response of the distillate both to a negative (from 405 L/h to 365 L/h) and to a positive step change (from 355 L/h to 410 L/h) in Ffeed were used to obtain the following transfer function: G3 =

D(s) K3 (30.448s + 1) = K3 G3d = 17.253s + 1 Ffeed (s)

(14)

Its structure is a “lead-lag” with a pole equal to −1/17.253 and a zero equal to −1/30.448. In Figs. 27 and 28 a comparison between the measured and calculated distillate flow rate for a positive and a negative step change in Ffeed is shown. The best fit concerning Fig. 27 is 83.1% while that for Fig. 28 is 76.2%.

R. Porrazzo et al. / Computers and Chemical Engineering 54 (2013) 79–96

93

8.5

11 Calculated output Measured output

8

10.5

10

D [L/h]

D [L/h]

7.5

9.5

7 6.5 6

9 5.5

8.5 0

5

10

15 20 Time [min]

25

5 0

30

Calculated output Measured output 10

20 30 Time [min]

40

50

Fig. 27. Comparison between the measured and calculated distillate flow rate for a positive step change in Ffeed .

Fig. 28. Comparison between the measured and calculated distillate flow rate for a negative step change in Ffeed .

Gains K1 , K2 , K3 in Eqs. (10), (13) and (14) were not determined since the optimizing gains obtained by the neural network will be used in the feedforward control law. The dynamic parts of the transfer functions (G1d , G2d , G3d ) were introduced in equation 8 to make it a dynamic optimizing feedforward control law:

4. Evaluation of the control system performance

Fopt

d

=

[(G1d /G3d ) · Radcol · KR (Tcond

The use of the neural network model of the process led to the identification of a range of Ffeed for the optimal production of distillate throughout the day.

in ) + IR (Tcond in )] + [(G2d /G3d ) · Tcond in

· KT (Radcol ) + IT (Radcol )]

2

The control system obtained was imported into LabVIEW environment and interfaced to the system, inside a simulation loop, by means of a National Instruments Compact Rio device. The latter returns the optimal value of flow rate in L/h, which is converted into a 4–20 mA signal to be sent to the control valve. The first implementation of the feedforward control system was unsatisfactory for two reasons: • The valve exhibits hysteresis phenomena. • During the daily plant operation, the change of temperature in the module determines a change of the resistance offered to the feed flow, so that the same degree of valve opening corresponds to different flow rate values depending on the time of operation. These problems were solved using a cascade control scheme with a secondary PI controller. The error, as the difference between the optimal value of Ffeed , coming from the optimizing FF controller and the measured Ffeed , is used as input of the PI controller, whose output is sent to the control valve, as shown in Fig. 29. The direct synthesis method was used to design the PI controller, based on an experimental model of the system. Fine tuning of the controller was then carried out by a trial and error method, obtaining a controller gain equal to −0.8 and an integral constant time of 0.5 min.

(15)

It has been already highlighted that values of Ffeed above 420 L/h and below 360 L/h, normally, do not lead to the maximum production of distillate; on the contrary, in the range between 360 L/h and 420 L/h of Ffeed , the production of distillate generally reaches its maximum values. In this range, with constant radiation and Tcond in , variations of Ffeed do not determine a relevant change of the distillate flow rate because different combinations of Ffeed and Tav produce equivalent results. An optimizing feedforward control system was developed to operate in this range. The control system was first tested by simulation of the possible real operating scenarios and then implemented in the LabView environment and tested under real conditions on the experimental plant itself. 4.1. Simulation results Simulation tests were performed in the SIMULINK environment of MATLAB comparing first the distillate production obtained with the uncontrolled plant with a constant value of Ffeed , chosen within the optimal range, and that obtained with the plant controlled by the optimizing feedforward control system. In both cases the

Fig. 29. Sketch of the control developed scheme.

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R. Porrazzo et al. / Computers and Chemical Engineering 54 (2013) 79–96

10 9 8

D [L/h]

7 6 5 4 3 Non controlled system (F

2 1

feed

= 390 L/h)

Controlled system 0

50

100

150

200

250

300

350

400

450

500

Time [min] Fig. 30. Distillate productions obtained by simulation of the uncontrolled system, working with Ffeed = 390 L/h, and the controlled system.

12 10

D [L/h]

8 6 4 2

Non controlled system (F feed = 450 L/h) Controlled system

0

0

50

100

150

200 Time [min]

250

300

350

400

Fig. 31. Distillate productions obtained by simulation of the uncontrolled system, working with Ffeed = 450 L/h, and the controlled system.

neural network was used as process model and the same sequences of values of radiation and Tcond in , chosen among those experimentally recorded during the real plant operation, were used as inputs. A comparison between the productions of distillate obtained by simulating these conditions with data recorded in the plant working with Ffeed = 390 L/h, are reported in Fig. 30. In this case, the increase of the daily production obtained with the control system (62 L against 60.4 L, i.e. a 1.6 L increase) is very

negligible. This is due to the fact that the constant Ffeed value fixed for the uncontrolled plant is already within the optimal operating range (360–410 L/h) observed for the given operating conditions (in terms of radiation and Tcond in ). In Fig. 31 a similar comparison, with the uncontrolled plant working with Ffeed = 450 L/h (thus, out of the observed optimal range, but still within the operating range suggested by the supplier (Wieghaus & Wolf, 2010)), is shown. In this second case, the increase of the daily production obtained with the control system is much more significant (58.5 L against 48.5 L,

420

12

400

10 8

360 6 340

D [L/h]

Ffeed [L/h]

380

4

320

2

F

300

feed

D 280

0

1

2

3

4

5

6

7

8

9

0

Time [h] Fig. 32. Experimentally measured trend of the distillate flow rate and Ffeed in the controlled plant in a typical operating day.

R. Porrazzo et al. / Computers and Chemical Engineering 54 (2013) 79–96

corresponding to 17.2% more), thus highlighting the improvement achievable using the optimizing control system, especially when non-stationary operating conditions (as will be shown in Fig. 34) can lead the plant out of the optimal range.

95

420 400

Ffeed [L/h]

380

4.2. Experimental results The optimizing feedforward control system was tested on the real plant for 10 days. For the sake of brevity, the trend of the distillate flow rate and Ffeed of the controlled plant, for only one typical operating day, are reported in Fig. 32. In Fig. 33 the actual Ffeed and the output of the optimizing feedforward controller, used as set point of the secondary PI controller, are shown. The actual Ffeed is close to its set point; the use of the cascade PI controller ensures the optimal management of the opening and closing of the valve, which results in a good agreement between the value of Ffeed and its set point. In Fig. 34 the valve opening, expressed by the corresponding value of the command signal (in mA), and the real Ffeed are shown. Notice that in the final part of the day the degree of opening of the control valve increases. This is explained by the change, during the day, of the temperature profiles between the channels of the module, that results in lower pressure losses requiring an increase of the valve opening (in the recycle loop) to keep a constant value of the flow rate. This means that, without control, Ffeed might increase, exceeding the limit of 420 L/h and causing a significant decrease of the distillate production.

360 340 320 F

feed

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Ffeed set point 280

0

2

4 6 Time [h]

8

Fig. 33. Comparison between the Ffeed set point and the actual value on the same day of Fig. 32.

It must be highlighted that the automatic change of Ffeed and the correct opening position of the valve, in the recycle loop, can greatly enhance the productivity of the desalination plant. In Fig. 35 the change of the optimal Ffeed due to abrupt changes of the radiation, on a day characterized by strong cloudiness, is shown. In agreement with Fig. 23, lower values of radiation correspond to lower optimal values of Ffeed . This ensures a minor decrease in the values of the temperature driving force due to the decrease of the radiation. Fig. 36 shows the relevant variation of the distillate flow rate with the optimizing Ffeed .

440

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Ffeed [L/h]

400 8.5

380 360 340

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Valve position F

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feed

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2

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4

5

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Time [h] Fig. 34. Degree of valve opening (4-20 mA signal sent to the control valve) and real Ffeed measured the same day of Figs. 32 and 33.

1200

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col

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3

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Time [h] Fig. 35. Variation of the Ffeed set point due to abrupt changes of the radiation.

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R. Porrazzo et al. / Computers and Chemical Engineering 54 (2013) 79–96

440

10 Ffeed set point D

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300 280 0

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Time [h] Fig. 36. Distillate flow rate and optimizing Ffeed on the same day of Fig. 35.

5. Conclusions A membrane distillation system powered by solar energy has been set-up and tested under real weather conditions with the aim of developing an optimizing feed-forward control system based on a neural network model of the plant. The system has been tested with and without the control system. The experimental tests show that the distillate production increases using the proposed control system. The results obtained with the neural network model and the use of the optimizing feedforward control system allow to draw the following conclusions: • A greater understanding of the relationships between inputs variables, main disturbances, manipulated variable and distillate production was achieved. • There exists an optimal range of Ffeed (360–410 L/h). • The values of Ffeed that maximize the production of distillate, when the incident radiation and the temperature Tcond in vary, were obtained using the neural network model. • The optimizing feedforward control system allows to set the feed flow rate at the optimal value, which continuously maximizes the production of distillate, even when the external operating conditions (e.g. solar radiation and cold feed temperature) would not normally allow to operate the system within the standard nominal state. It was also possible to identify some process improvements that are only briefly reported here. The use of solar collectors with higher efficiency or larger area, in conjunction with the use of a cooling system (Cipollina et al., 2011b), that decreases the temperature of the input flow of the MD module cold channel, can lead to a substantial increase of the average difference of temperatures between the channels of the module. This condition would allow to operate with higher Ffeed with a net increase of the daily production of distillate. Acknowledgments The authors would like to thank Solar Spring GmbH for supplying the MD system and providing valuable suggestions for the experimental testing and Mr. Davide Capobianco, Mr. George Stafford and Dr. Bartolomeo Cosenza for their support in setting-up the system and performing some of the experiments. References Al-Sharif, S., Albeirutty, M., Cipollina, A., & Micale, G. (2013). Modelling flow and heat transfer in spacer-filled membrane distillation channels using open source CFD code. Desalination, 311, 103–112.

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