Stability analysis of an industrial salinity gradient solar pond

Stability analysis of an industrial salinity gradient solar pond 1 M. Montalà 1,2, J. L. Cortina 1,2,3, A. Akbarzadeh 4, C. Valderrama 1,2 2 1Chemical Engineering Department, UPC-BarcelonaTECH, C/ Eduard Maristany, 10-14 (Campus 3 Diagonal-Besòs), 08930 Barcelona, Spain 4 2 Barcelona Research Center for Multiscale Science and Engineering, C/ Eduard Maristany, 10-14 5 (Campus Diagonal-Besòs), 08930 Barcelona, Spain 6 3 Water Technology Center CETaqua, Barcelona, Spain 7 4 School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Australia 8 9 *Correspondence should be addressed to: César Valderrama 10 Departament d’Enginyeria Química, Universitat Politècnica de Catalunya-Barcelona TECH 11 C/ Eduard Maristany, 10-14 (Campus Diagonal-Besòs), 08930 Barcelona, Spain 12 Tel.: 93 4011818, Fax.: 93 401 58 14 13 Email: [email protected] 14 15 Abstract 16 In this study, an assessment of salinity gradient stability of an industrial solar pond during two operation 17 seasons (2014 and 2105) is presented. An industrial solar pond was constructed to supply a low-18 temperature heat (up to 60 ºC) to achieve the temperature requirements of the flotation stage in a mineral 19 processing plant (Solvay Minerales in Granada (Spain)). Along the first season, the salinity gradient was 20 considered technically destroyed in April 2015 as the height to the upper convective zone increases from 21 0.3 m in July 2014 to 0.8 m. Two different methodologies based on the stratification principle were 22 adapted and used in order to evaluate the salinity gradient stability. The boundaries of the salinity 23 gradient appeared as the main source of instability. In the upper zone it is associated with the 24 environmental parameters (e.g., rain and wind) that affect the upper convective zone and the upper 25 *Unmarked Revised Manuscript For Publication Click here to view linked References layers of the non-convective zone that subsequently transmit the instability to the lower layers. In the 26 bottom zone it is caused by operation parameters, such as the heat extraction or the addition of salt. Both 27 methodologies provided similar predictive capability of stability results. However, the results provided by 28 the stability analysis using the thermal and salinity expansion coefficients are a more useful tool in the 29 control of the salinity gradient for solar pond technology. 30 31 Keywords: solar energy; industrial solar pond; salinity gradient; stability analysis; mineral flotation 32 33 1. Introduction 34 The stability of salinity gradient is crucial to ensure the proper operation of solar pond technology. 35 Experimental studies in industrial or prototype solar ponds are difficult to be found, and most of the 36 studies reported in the literature are theoretical models (Husain et al., 2012; El Mansouri et al., 2018). 37 Only in the solar pond of El Paso, Texas, a stability analysis was reported (Lu et al., 2004). The concept 38 of stability is generally related with salinity/temperature stratification. Stratification in water is produced 39 when masses of water at different properties, such as salinity, density or temperature, form different 40 layers without mixing. 41 A solar pond is a system composed by three main zones: the upper convective zone (UCZ), the non-42 convective zone (NCZ) and the lower convective zone (LCZ). The upper and lower zones of the system 43 are characterized to transfer heat by convection. Convective heat transfer implies water movements; as a 44 consequence, stratification is not possible. On the other hand, the NCZ is the only part of the system 45 where no convective movements are found (Valderrama et al., 2016). When the solar pond is filled, the 46 NCZ is created overlapping layers with different salt concentrations. As a result, the NCZ of a solar pond 47 should be initially stratified, a stability analysis in this region provides information about the initial stability 48 and the evolution of the different layers (Zangrando,1980). The heat stored in the LCZ can be used as a 49 heat source for the heating of buildings, power production and industrial processing and more recently 50 the addition of heat from external sources (Alcaraz et al., 2018c; Ganguly et al., 2018a) has been 51 explored. Also in recent year a great effort has been made in optimizing the overall performance of solar 52 pond technology (Kumar et al., 2018; Ganguly et al., 2018b). 53 The solar pond of El Paso, Texas, has become a worldwide reference facility for solar pond technology. 54 From its construction and operation in 1985 different publications with a large amount of data have been 55 published. Leblanc et al. (2011) and Lu et al. (2004) also reported a stability analysis. The study was 56 based in the NCZ and the boundary regions, NCZ-UCZ and NCZ-LCZ. The internal stability was 57 quantified through the Stability Margin Number (SMN), which may be defined as the ratio of the 58 measured stability coefficient to the calculated stability coefficient required to satisfy the dynamic stability 59 criterion for the temperature profile of the solar pond at height within the NCZ. The solar pond of El 60 Paso was the first system that included the stability analysis of the NCZ as a routine procedure in its 61 operation and control. The difficulty to find in literature some reliable models resulted in the development 62 of a specific methodology for this system (Xu et al., 1987). The SMN is defined as described by Eq. 1: 63 (1) where, is the actual salinity gradient, in percentage, and is the theoretical salinity gradient, also in 64 percentage, necessary to satisfy the stability criterion for the temperature profile of the solar pond at 65 height within the NCZ. In principle, the SMN should be higher that 1 to ensure the stability of the 66 system. However, it is also reported that when the SMN is lower than 1.6 the gradient may be degraded. 67 The main problem with the model suggested in the El Paso solar pond is that the methodology to 68 determine is not specified. 69 Alenezi (2012) described in detail a theoretical model to analyze the stability of a solar pond. The work 70 was based on the idea that the minimum requirement to keep the stability in the solar pond is that the 71 density in the gradient zone should increase downward to prevent the different layers of the NCZ from 72 mixing and consequently to prevent the salinity gradient to be degraded. 73 The author pointed out the significant relevance of the solar pond filling process, if the salinity gradient is 74 not perfectly implemented during this process, the stability of the NCZ will be rapidly affected and, 75 consequently, it is highly probable to identify the degradation of the gradient after a short period of 76 operation. 77 Two different stabilities are identified and described in Alenezi (2012), static and dynamic stability. 78 Basically, static stability only considers the internal situation of the system (stratification), since it 79 identifies the vertical convection movements. Notwithstanding a solar pond can also be affected by 80 external disturbance factors, especially by environmental factors such as rain or wind; this may result in 81 an oscillatory movement of the surface of the system, if these waves arrive to the NCZ, the different 82 layers would be mixed. Dynamic stability provides information about all these effects. 83 As for the static stability, the salt concentration should increase downward; in this case, the lower layers 84 have a higher salt concentration than the upper ones. This situation is called as positive gradient. The 85 opposite situation, salt concentration decreasing downward, would be called negative gradient. If a 86 negative gradient dominates the system, the salinity gradient will be destroyed or at least the operation of 87 the solar pond reduced, which will result in a significant reduction in efficiency (Alenezi, 2012). 88 These effects are studied to predict the static stability of a solar pond. With all said, it is known that the 89 salt concentration value at some point of the NCZ should be higher than the point immediately above to 90 avoid vertical convection in the zone. Thus, the stability condition suggested is defined as follows by Eq. 91 2. (Alenezi, 2012): 92 (2) where, is the temperature gradient with depth (x), is the salinity gradient with depth (x), is the 93 thermal expansion coefficient and is the salinity expansion coefficient. 94 The density change with depth needs to satisfy Eq. 3, if the system is stable: 95 (3) Alenezi (2012) establishes also a relation between the saline, ( ), and thermal, ( ), Rayleigh 96 numbers, thermal, ( ), and saline, ( ), gradients and coefficients of thermal, ( ), and saline, ( ), 97 expansion. Thus, equation 4 provides information of the stability behavior. 98 (4) Liu et al. (2015) and Ouni et al. (2003) used the previous methodology to numerically simulate a 99 trapezoidal solar pond of prototype dimensions (2.4m x 2.4m at surface and 1m x 1m at the bottom) and 100 to model a salinity gradient solar pond (SGSP) in the south of Tunisia, respectively. 101 Talley et al. (2011) defined the static stability for seawater as a formal measure of the tendency of water 102 column to overturn. The authors related the static stability with the stratification, the higher is the 103 stratification the higher the stability. A layer of water is stable if a parcel of water that is moved 104 adiabatically is capable to return to its original position. This capacity depends on the density difference 105 between the layer and the immediately above and below layers. Thus, the static stability, ( ), of a layer is 106 defined in Eq. 5: 107 108 109 where is in situ density, the density variation with depth . If is positive, the system would be 110 stable, if 0, the system would be neutral and if negative, the system would be unstable. 111 (5) Except for the case of El Paso solar pond (USA), which developed a specific methodology to study the 112 stability of the system, the other studies focused on theoretical analyzes of the stability of a solar pond, 113 some of them tested with numerical simulation approaches, but none of them were validated with 114 operation data from an industrial solar pond. Two different methodologies based on the stratification 115 principle were adapted and used in order to evaluate the stability of an industrial solar pond (500 m2) 116 during two operation seasons (2014 and 2105). The analysis of construction, operation and efficiency of 117 this 500-m2 industrial solar pond has been previously reported (Alcaraz et al., 2018a,b) and stability has 118 been identified as the main issue from the point of view of the operation. The rationality of the analysis is 119 the need to develop a methodology for assessing the stability of the salinity gradient using the operation 120 data of the Granada solar pond. 121 122 2. Methodology 123 Although the stability of a solar pond is a key parameter to ensure proper functioning, most studies on 124 salinity gradient solar ponds have not reported the stability analysis due to the complexity in determining 125 this parameter. The stability cannot be directly measured from the sensors data installed for solar pond 126 performance monitoring and the procedure to be determined is, in general, quite complex. In that context, 127 in most of the solar pond the temperature and density gradients, which can be directly and easily 128 measured, are used to control the different zones of the system. 129 130 2.1 Evolution of the salinity gradient in the Granada Solar Pond 131 The solar pond in Granada started its operation in July 2014 as was described by Alcaraz et al. (2018a). 132 The degradation of the salinity gradient was detected by the density profile monitoring as the height to the 133 UCZ increases from 0.3 m in July 2014 to 0.8 m in April 2015. Although the same trend was observed in 134 the evolution of the temperature profile, the average monthly temperature of the LCZ not decreased 135 below 40 ºC. For the second, season, in April 2015, the salinity gradient was considered to be technically 136 destroyed. It was concluded by the solar pond monitoring and operation team that the weather 137 conditions, especially the influence of winds on surface waves, were the main mechanism affecting the 138 stability of the salinity gradient. Additionally, some operation and maintenance patterns would have 139 contributed to the deterioration of the gradient. In September 2015, the solar pond was refilled using the 140 water injection method (Zangrando,1980) and its operation was restarted. In this note, the solar pond 141 performance is evaluated in two seasons (2014 and 2015) in terms of the stability analysis. 142 2.2 Thermal and Salinity Expansion coefficients 143 The coefficients of thermal ( ), and salinity ( ), expansion were used in determining the stability as was 144 mentioned in the introduction section. However, none of the previous methodologies describes how these 145 parameters can be calculated. In that context the methodology suggested by (Lillibridge, 1989) based on 146 the 1980 Equation of State (EOS) is used to determine these parameters. 147 The model is based on the polynomial structure of the 1980EOS to determine the expansion coefficients. 148 The approach reviewed the differential equations published in 1980 EOS and developed a model based 149 on proved coefficients that notably simplifies the calculation process. The detailed description of the 150 calculation of these coefficients is summarized in Appendix 1. 151 152 2.3 Stability analysis methodology 153 This work combines and integrates some of previous methods used in order to evaluate the Granada 154 solar pond operation during two operation seasons (2014 and 2015). 155 On one hand, the methodology described by Talley et al. (2011), which analyzes how a body of water is 156 stratified and it is based on the Eq. 6: 157 (6) If the parameter E is positive, the system would be stable, if zero, neutral and if negative, unstable. 158 In addition, the methodology suggested by Alenezi (2012) is also considered in this analysis. The stability 159 condition is expressed through the Eq. 7: 160 (7) Which can be also expressed as: 161 (8) Once the coefficients of thermal and salinity expansion are calculated (see Appendix 1), the equation 7 is 162 plotted for each depth over time to elucidate the evolution of each parameter and identify where and 163 when the instabilities occur. 164 165 Both methodologies are based on the same principle, stratification as a synonym of stability. However, 166 the use of different methods provides a broader picture of the stability of the system and helps to 167 understand where and when the gradient starts the degradation process. 168 169 3. Results and discussion 170 In this section the initial stability of the solar pond at the beginning of each operation season in the 171 Granada solar pond and its evolution along each season are reported. As stability analyses of industrial 172 solar ponds in operation are not found in literature, the stability analysis of the Martorell pilot plant solar 173 pond (50 m2) was also performed (data not shown). Although the solar pond installed in Martorell was of 174 a pilot scale (Valderrama et al., 2011; Bernard et al., 2013), the salinity gradient never degraded during 175 its useful life (Alcaraz et al., 2016; 2018c), therefore it was considered a good example of successful 176 operation and a reference to test the proposed methodology. 177 3.1. First operation season 178 In this subsection the stability of the first operation season is deeply analyzed. Figure 1 and 2 contained 179 the analysis of stability suggested by Talley et al. (2011). In Figure 1, the stability (E) is plotted as a 180 function of the depth of the salinity gradient (NCZ), the different lines represent the stability profile for 181 each depth. 182 183 184 Figure 1. Variation of the Stability profile (E) as a function of solar pond depth (m) (from the 185 bottom) along first operation season in Granada solar pond using the methodology described by 186 Talley et al. (2011). 187 As can be seen in Figure 1, no significant instabilities has been identified. However, there are some 188 points that tend to be neutral (E = 0) especially from depths greater than 1.3 m from the bottom. It is 189 possible to identify periods of small instabilities in some points, 0.7, 1.3, 1.6, 1.7 and 1.9 m from the 190 bottom. Along these periods the parameter become negative. However, it is not possible to identify 191 when these instabilities occurred and if the system was able to recover stability in the next measurement 192 or not. In this way, Figure 2 plots the same data but represented in a completely different way. In this 193 case, the evolution of stability, , at each depth can be easily identified along the operation season. This 194 figure is useful to understand when the points (depths) mentioned above began to be unstable. 195 278 279 Figure 6. Stability analysis in terms of temperature ( and salinity for a) 0.7, b) 1.4, c) 280 1.5, d) 1.6, e) 1.7, f) 1.8, g) 1.9, h) 2.0 m from the bottom along second operation season in 281 Granada Solar Pond using the methodology described by Alenezi (2012). 282 283 4. Conclusions 284 The salinity gradient stability can be affected by the environmental and operational parameters. This note 285 evaluates the stability of the Granada solar pond during two seasons of operation that reported a 286 degradation of the salinity gradient. Two methodologies based on the principle of stratification were used 287 to assess the data collected during two seasons of operation. Results indicate that boundaries of the 288 gradient UCZ-NCZ and NCZ-LCZ are the main source of instability. This irregular profile may be caused 289 by the environmental conditions affecting the UCZ and then transmitted to the NCZ, while the cause of 290 degradation in bottom is more complex and can be connected with operational processes of the pond. 291 For first operation period, the neutral situation began at 2 m from the bottom and needed about a month 292 to be detected in the layer immediately below and five months at 1.4 m from the bottom. Otherwise, 293 according to the expansions coefficients, the salinity gradient was higher than temperature gradient for 294 most of the operation period at 0.7 m from the bottom confirming the stability condition. For second 295 period, the same trend was observed, the layer located at 2 m from the bottom is clearly unstable since 296 the beginning of the operation season, however, in this case, the instability only reached a depth of 1.6 m 297 from the bottom and no degradation was observed from the bottom of the NCZ. 298 The methodology employed in this study can be successfully used in the control of the salinity gradient in 299 the Granada solar pond since it provides information on how the degradation evolves once it has 300 occurred, as has been seen in both seasons of operation that followed the same trends. It is worth 301 mentioning that both methodologies showed the same results, however, the methodology based on the 302 coefficients of thermal and salinity expansion provides more detailed information that is of the greatest 303 interests in terms of operation of solar pond technology. 304 305 306 307 308 309 19 Appendix 1. Expansion coefficients 1 Both thermal (T) and salinity (S) gradients depend on density, pressure and temperature or salinity, 2 respectively. Hence, these parameters are not constant neither along the system nor along the time, in 3 other words, each point of the system at each time has a different value of these coefficients. 4 Thus, the coefficients of thermal ( ) and salinity ( ) expansion are determined through Eqs. A1 and A2 5 (Lillibridge, 1989): 6 (A1) (A2) where, and are the surface and subsurface density, respectively; K is compressibility; is the 7 pressure of the water layer; is temperature and is salinity. Figure A1 provides a global and 8 schematic overview of the procedure used to determine the expansion coefficients. 9 10 11 Figure A1. Schema of the methodology used to determine the expansion coefficients 12 20 Accordingly, seven terms needed to be calculated: , , , , , and . The pressure, , of 1 each layer is considered an input parameter. The pressure on solar pond surface can be assumed 2 equal to the atmospheric pressure and the pressure in each layer is the sum of the atmospheric 3 pressure and the pressure caused by the upper layers. 4 The equations needed to calculate the derivations ( , , and ) and parameters are presented 5 below. When a coefficient appears in the equations, marked in red, it means that it will be tabulated 6 specifically at the end of this section. To estimate the density, first, the surface density ( ) needs to be 7 determined: 8 (A3) may be obtained using the polynomial expressions A4 and 5, respectively: 9 (A4) (A5) Thus, the surface density ( may be expressed in only one equation as describes Eq. A6: 10 (A6) The subsurface densities are calculated using the surface densities values, , the pressure of the 11 water layer, , and the compressibility, as describes Eq. A7: 12 21 (A7) The bulk modulus of compressibility, , depends on , , and . Its dependence on is reported in 1 the Eq. A8: 2 (A8) The terms , and , may be expressed in polynomial equations as as described by Eqs. A9-3 A11: 4 (A9) (A10) (A11) The general equations of and include some derivatives, , , and , the main advantage 5 of this method is that equation A11 can be relatively easy derived. 6 Thus, utilizing the notation , the following set of equations (A12-A16) contains 7 derivatives of the previous parameters depending on temperature. 8 (A12) 22 (A13) Where, 1 (A14) (A15) (A16) Finally, the same parameters need to be derivative depending on salinity, ( and . These 2 parameters may be determined using the equations A17 and A18: 3 (A17) (A18) The parameters required to determine can be obtained using the equations (A19-A21), which are 4 the derivatives of the initials but, in this case, depending on salinity. 5 (A19) (A20) 23 (A21) All coefficients included in equations A12-A21, marked in red color, are reported in Table A1: 1 Table A1. 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