LONG-TERM SOLAR THERMAL ENERGY STORAGE USING AQUEOUS CALCIUM CHLORIDE

LONG-TERM SOLAR THERMAL ENERGY STORAGE USING AQUEOUS CALCIUM CHLORIDE Josh A. Quinnell Jane H. Davidson University of Minnesota 111 Church Street Minneapolis, MN 55455 quinnell@me.umn.edu jhd@me.umn.edu ABSTRACT The development of a thermal storage tank that supplies both long-term thermochemical and short-term sensible storage for solar hot water and space heating is reported. The thermochemical storage is based on the absorption of water by aqueous calcium chloride, a non-toxic and inexpensive liquid desiccant. Compared to water storage, the dual purpose tank provides 2.35 times the amount of energy storage per volume. Water, diluted, and concentrated calcium chloride solutions are stored in a single tank. In this paper we summarize numerical modeling and experimental work on a lab prototype that demonstrate the performance during transient charging operation. Reported data include concentration distributions, streamlines, and mass transfer rates over a relevant range of the governing dimensionless parameters. Analysis of the measured results demonstrate that the absorption storage time constant is on the order of 160 days or longer, suggesting that this concept is a promising development for solar thermal space heating systems in need of seasonal storage. 1. INTRODUCTION The potential of using highly efficient solar thermal systems to meet space conditioning and hot water loads is enormous, yet at present only 1.5% of the energy consumed in buildings is provided by solar [1]. Currently, the major applications of solar thermal systems are domestic hot water (DHW) and swimming pool heating. These applications are the most economical options because only diurnal storage is required, and in the case of DHW, the load is nearly constant year round. The major impediment facing the extension of solar thermal systems to space heating is the mismatch of the space heating load and the availability of solar energy. Solar thermal collector arrays sized to meet winter heating loads are grossly oversized during the remainder of the year. On the other hand, with long-term, compact storage, it is theoretically possible to use a smaller collector array to collect ample summertime solar energy and store it for winter space heating. The desirable attributes of a long-term storage system for solar space heating are high energy density, charge temperatures achievable with flat-plate or evacuated tube collectors, discharge temperatures suitable for the load, adequate charge/discharge power, and materials that are stable over many cycles, non-toxic, environmentally safe, and inexpensive. Today, sensibly heated water is by far the most common storage medium for solar thermal systems because it satisfies many of these requirements. However it has relatively low energy density and high thermal losses for use as a long-term storage. Energy density, which is defined as the energy stored per volume, is a critical metric for compact, long-term storage. The sensible energy density of water is (1) where, ρ H,H2O is the density at temperature T H, c p,h2o is the specific heat and T H and T L are the temperature limits of the storage. T H is limited by the boiling point (i.e. ~95 C), and T L is limited by the temperature required of the load (e.g. 55 C for space heating). With these temperature limits, the energy density is ~45 kwh/m 3. Furthermore, sensible water storage suffers thermal losses to the ambient that deplete the storage over time. Consequently, it is generally limited to daily or weekly storage time scales. The required storage volumes are prohibitory large for seasonal storage. To overcome these limitations, researchers worldwide are 1

studying thermochemical storage [2-5]. Thermochemical reactions are most simply understood using the charge/discharge reactions (2,3) [6]: To store energy (2), heat is applied to thermally dissociate AB into materials A and B. A and B are then stored separately. To use the stored energy (3), materials A and B are recombined, their reaction is exothermic, and the stored energy is converted to thermal energy and delivered to the load. The energy is stored in chemical bonds and thus thermal losses are small. In practice, thermochemical materials are restricted by the temperatures attainable with non-concentrating solar thermal collectors (i.e. < 150 C). One promising match to evacuated tube collectors is sorption storage, which refers to the potential of a sorbent material to adsorb/absorb water vapor and release heat. The energy storage is due to the enthalpy of sorption, h s, which is the energy released when water vapor is sorbed onto a solid surface or into the volume of a liquid. It is the sum of the binding energy of the water and sorbent molecules in the condensed state, h b, and the enthalpy of vaporization of the water, h fg. The sorption energy storage density depends on the operating limits of mass fraction, S H2O, (concentration) of water in the host material: (2) (3) (4) ( ) ( ) (5) where S H2O is the mass fraction of water, and S H - S L represents the total water uptake useful for energy storage. M H2O is the total mass of sorbed vapor and V is the volume necessary to store the materials. The mass of water that can be added and removed from the sorbent is a function of temperature and pressure. Reported material energy densities are double to over ten times that of water (106 to 780 kwh/m 3 [4,7]). In practice, storage is limited to the binding energy (h b ) while the heat of vaporization (h fg ) is typically used by an absorption heat pump to transform a low-quality energy source into a useful form. In other words, the energy to vaporize water must come from within the system or be supplied by an external source (e.g. the ground or a solar thermal collector) [5]. Hence, unlike sensible storage, the system energy density depends on the availability of thermal energy sources. Our work focuses on aqueous calcium chloride. Calcium chloride is selected because it is inexpensive, non-toxic, has high material energy storage density, and the liquid solution can be directly pumped through the system and directly boiled in an evacuated tube solar collector. The solar charge (desorption) and discharge (absorption) processes are described by the pair of reactions (6,7): In reaction (6), solar energy is stored in a concentrated calcium chloride solution by desorbing water vapor in the solar collector. In reaction (7), the stored energy is released by rehydrating the concentrated solution in a absorption heat pump. The enthalpy of absorption is released as sensible energy when required. Thermal losses are small because the enthalpy of absorption is a weak function of temperature. Furthermore, the water and CaCl 2 (aq) can be used to store and use sensible energy on shorter timescales. Systems with sorption storage require more components than sensible storage systems to facilitate the sorption reactions. Consider the closed-cycle calcium chloride absorption storage system shown in Fig. 1. In the summer diluted CaCl 2 (aq) boils in the solar collector, producing concentrated CaCl 2 (aq) and water. Boiling requires temperatures up to 137 C. In the winter water is reabsorbed into the concentrated CaCl 2 (aq) solution via an absorption heat pump. This process produces diluted CaCl 2 (aq) solution and releases the binding energy. The heat pump also transfers latent energy from the water to the CaCl 2 (aq) solution enabling an additional temperature lift. When there is insufficient solar resource for boiling, the solar collector heats the solution. If the solution in the tank is hot enough it can bypass the heat pump and meet the load directly. Although the sorption storage is limited to binding energy, the addition of sensible heat storage allows energy storage densities that greatly exceed the energy storage density available from water as shown in Fig. 2, where energy density is plotted as a function of change in CaCl 2 mass fraction ( S). For a solar space heating system with unity solar fraction, T L = 55 C. For sensible water storage, T H is limited by the boiling point (~95 C). The sensible energy storage density of water is practically limited to 45 kwh/m 3. For CaCl 2 -H 2 O, the boiling point is elevated and T H can be increased to 105 C. The minimum useful temperature is reduced due to the presence of the heat pump. Assuming a minimum temperature lift of 8 C, T L is reduced to 47 C, yielding a sensible energy density of 54-67 kwh/m 3. It varies with S because heat capacity depends on CaCl 2 mass fraction. The binding energy (absorption storage) adds additional energy. The absorption storage density is based on a maximum solubility of the CaCl 2, S H = 0.59 kg-cacl 2 /kg-soln. The absorption storage density initially (6) (7) 2

cost because the total volume of the tanks must exceed the solution volume. For example, in the system of Fig. 1, separate tanks for water, diluted, concentrated solution requires ~2 times the storage volume compared to material volume and results in a decrease in energy density from 106 to 53 kwh/m 3, about the same as water. Fig. 1: Closed-cycle absorption heating system. Fig. 2: Energy storage density of calcium chloride as a function of ΔS is compared to the energy density of sensibly heated water. increases with increasing S due to the larger binding energy at high CaCl 2 mass fraction. It decreases for S > 0.3 kg-cacl 2 /kg-soln. because the binding energy decreases for S L < 0.3. The maximum total energy density is 106 kwh/m 3, which is over 2.35 times the sensible energy density of water. If one assumes the availability of an external heat source to evaporate water (e.g., ground with T > 10 C), the material energy storage density increases from 106 to 381 kwh/m 3. Design and operation of the storage vessel is crucial to the efficient operation and economics of the system and is the focus of our work. In the closed-cycle water, diluted, and concentrated solution must all be stored without mixing. Premature mixing of water and concentrated solution results in the conversion of binding energy into sensible energy and the loss of long-term storage. In the past, systems that use liquid desiccants for air conditioning have avoided mixing of diluted and concentrated solution through the use of two or three tanks where each of the solutions is stored separately [8]. This approach decreases the system energy density substantially and increases the Here we consider a unique system that requires only a single tank. In our design, mixing of stored solutions is minimized by using internal devices to control temperature and fluid motion and taking advantage of natural density gradients between different solutions. The proposed storage system is shown in Fig. 3. In the tank the storage fluid is stratified in regions according to density, which is proportional to CaCl 2 mass fraction. Density gradients form at the interfaces between regions of water, diluted and concentrated CaCl 2. In a quiescent tank, diffusion of CaCl 2 between these regions is up to 10000 times slower than thermal conduction in water (D = 10-9 to 10-11 m 2 /s). Hence, mixing by diffusion is not a problem over the timescale of seasonal storage. However, as in a sensible water storage tank, mixing is intensified when fluid motion is present during charge and discharge of the stored energy. Mass transfer of CaCl 2 across the density interfaces depends on the relative strength of the fluid motion and the thermal buoyancy to the gravitationally stable density gradient between the fluid regions. Low mass transfer rates are desired to preserve the long-term absorption storage. During charge or discharge operation, an immersed paralleltube heat exchanger and a stratification manifold minimize mixing between regions of different CaCl 2 mass fraction, while allowing heat and mass to be added or removed from the tank. The heat exchanger thermally stratifies the tank and increases the performance of the sensible energy storage. The stratification manifold returns fluid to the region in the tank where the fluid in the tank has the same CaCl 2 mass fraction as the fluid flowing through the manifold. In this manner, the manifold stratifies the tank by CaCl 2 mass fraction. For instance, during charging, heated fluid from a solar collector enters through the top of the heat exchanger. As the heated solution descends through the tubes, the tank is heated top-tobottom via natural convection. The fluid then enters the stratification manifold where it rises until reaching a point of neutral buoyancy (equal CaCl 2 mass fraction) and enters the tank. In the tank natural convection develops via heating from the heat exchanger. This fluid motion is restricted to regions of uniform mass fraction because the thermal buoyancy force is less than the solute buoyancy force at the density interfaces. The parameters governing the natural convection dynamics are the Rayleigh number, Ra = gβ T ΔT 0 h 3 /να, the buoyancy ratio, N = β S ΔS/β T ΔT, and the dimensionless fluid properties, Pr and Le. The dimensionless geometry is specified by the aspect ratio of a region a = h/l. 3

method is briefly described and the main results are presented. Further details are provided in a prior publication [7]. The two-dimensional computational domain is shown in Fig. 4. The modeling domain is restricted to half of the width because the tank is symmetric about the heat exchanger. The tank volume is initially split into two regions; a water region on top of a CaCl 2 (aq) region separated by a sharp density gradient. The FLUENT software is used to solve the transient two-dimensional laminar, incompressible momentum, energy, and species equations. Density, viscosity, specific heat, and thermal conductivity are specified as a function of temperature and CaCl 2 mass fraction from Conde s aggregated property data [9]. The binary diffusion coefficient was fixed at D=10-9 m 2 /s. (a) (b) Fig. 3: Schematic of absorption/sensible storage tank: (a) illustration of immersed heat exchanger and stratification manifold in an unmixed storage with water, diluted and concentrated aqueous calcium chloride; (b) anticipated convective flow patterns during sensible charging. Ra is the ratio of the thermal buoyancy force to the viscous force and it denotes the strength of natural convection. Low Ra (i.e. Ra < 10 4 ) represents conduction dominated heat transfer with little fluid motion. High Ra (i.e. Ra > 10 4 ) represents convection dominated heat transfer, where heated fluid near the heat exchanger is continually away by the boundary layer. N is the ratio of the solute buoyancy force to the thermal buoyancy force. For N << 1, such as occurs in regions of uniform mass fraction, the fluid dynamics are dominated by the thermal buoyancy force. For N >> 1, the fluid dynamics are dominated by the solute buoyancy force. At the density interface, a large N resists fluid motion and the density interface remains stably stratified. Mass transfer is quantified by the dimensionless Sherwood number, Sh = kh/ D. Sh represents the increase of mass transfer across the density interface relative to diffusion. The purpose of this paper is to summarize our progress on the development of the new storage tank and present an analysis of the storage timescales associated with both the sensible and absorption storage mechanisms. 2. NUMERICAL PREDICTIONS An initial computational fluid dynamic model was developed to investigate the ability of density interfaces to resist mixing during natural convection. The numerical The boundary conditions of the enclosure are no slip and zero mass flux. All walls are adiabatic except for x = 0, where T w varies linearly from 30 C at y = 0 m to 50 C at y = h 1 +h 2 m to simulate the immersed heat exchanger. In all cases T 1,0 = T 2,0 = 30 C and S 2,0 = 0 kg-cacl 2 /kg-soln. A range of N and laminar Ra were investigated: 13 < N < 131 and 3 10 5 < Ra < 3 10 8. Pr and Le were fixed at 3.3 and 158, respectively. At t = 0, T w was applied at x = 0. The simulations show in all cases that the water and CaCl 2 (aq) regions are independently heated by a rotational natural convection flow, as shown by the streamline pattern in Fig. 4b for Ra = 3 10 8 and N = 131. Tightly spaced streamlines near the heat exchanger surface, x = 0, show the accelerating boundary layer. The boundary layers discharge into each of the regions and the flow is diverted by the density interface to form a rotational pattern. The flow does not cross the density interface. For 3 10 5 < Ra < 3 10 8, velocities parallel to the interface are on the order of 1 mm/s. Velocities within the density interface are essentially zero. Subsequently, the density interface is stable and mass transfer is diffusive in nature and relatively insensitive to Ra. Initially, Sh are approximately 80 with only slight variations for different Ra. In all cases Sh converge and decrease to approximately 35 over the course of each transient simulation. The fluid dynamics are the same for variations of buoyancy ratio, 13 < N < 131. During the initial heating, Sh fluctuates for N < 38, but these fluctuations diminish and Sh converges and decreases to yield the same mass transfer rates, Sh ~35. 3. EXPERIMENTAL RESULTS Based on the promising numerical results, we designed and constructed a prototype tank to investigate the concept under operating conditions more likely to lead to mixing, namely larger Ra and lower N. A schematic of the apparatus and a photo of the facility and are shown in Fig. 5. The glass prototype is rectangular (1.62 x 1.01 x 1.01 m) and insulated 4

(a) (b) Fig. 4: (a) Computational domain for 2-D numerical simulations and (b) Streamlines and CaCl 2 distribution after during natural convection for Ra = 3 10 8 and N = 131. (a) with 5.1 cm thick rigid polystyrene insulation. The insulation is removable to permit optical measurements of velocity and CaCl 2 mass fraction. The immersed heat exchanger consists of 128 thin-walled polypropylene tubes plumbed in parallel. It is 0.99 m wide by 1.52 m tall with a total external heat transfer area of 3.57 m 2. The tubes are each 6.35 mm O.D. and 0.45 mm thick and the tube-to-tube spacing is 1.27 mm. A detailed description of the experimental apparatus is provided in a prior publication [10]. Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF) are optical measurement techniques used to measure velocities and CaCl 2 mass fractions over a 2-D imaging plane in the tank, as shown in Fig. 5. This equipment is used to measure velocity and CaCl 2 mass fraction near the density interface in order to validate the predictions of the numerical work. The PIV system measures velocity by tracking the displacement of particles immersed in the tank fluid and the PLIF system measures CaCl 2 mass fraction by measuring the fluorescence of a dye that is proportional to CaCl 2 mass fraction. A series of ten transient experiments were conducted to simulate sensible charging for 8.4 10 8 < Ra < 5.5 10 10, 0.8 < N < 18.2, and 0.2 < a < 1.08. Each experiment begins with a water (S 2,0 ) region of height h 2 on top of a denser CaCl 2 (aq) (S 1,0 ) with height h 1. Initially there is a 1 3 cm thick density interface between the two regions and each region is a uniform temperature (T 0 ). Transient sensible charging is initiated by flowing heated water (b) Fig. 5: (a) Side view of the tank including dimensions and the location of the imaging plane for PIV and PLIF measurements. (b) Photo of the prototype tank including laser sheet and PIV/PLIF imaging cameras. through the heat exchanger. Fluid at the exit of the heat exchanger does not enter the tank. The experiments are terminated when the temperature of the fluid at the top of the tank reaches the inlet temperature (~ 5 8 hr). All transient experiments confirmed the predicted numerical results. The density interfaces remain stable and the natural convection flows are confined to regions of uniform CaCl 2 mass fraction. The density interface stability is demonstrated in Fig. 6 for Ra = 5.2 10 10 and N = 2.2 after 6.55 hr. The 5

density interface is unchanged compared to the initial conditions and is about 1.5 cm thick. It isolates the water from the CaCl 2 (aq) region. Mass transfer rates, as presented using the dimensionless Sherwood number (Sh), are 11 < Sh < 62, suggesting that mass transfer is on the order of 100 1000 times slower than conduction. The results so far do not include the use of a stratification manifold and fluid entry into the tank. A preliminary design of a functioning rigid manifold has been tested with excellent performance at fixed operating conditions (i.e. mass flow rate, CaCl 2 mass fraction), but because the performance of the rigid manifold ins known to depend on operating conditions, we are investigating alternative designs, including a flexible porous manifold. A properly designed manifold will discharge fluid far from the density interfaces to minimize momentum induced mixing and enhance heat transfer by disturbing the boundary layer. The results with the prototype are promising and we expect the results to apply to a real storage tank despite a few differences in design. A cylindrical tank will require a coiled tube or circular parallel vertical tube heat exchanger. 4. STORAGE TIMESCALES A useful metric for long-term storage performance is the time constant associated with losses due to mass transfer. In this section we present a storage timescale analysis to evaluate the long-term storage ability of the absorption mechanism and compare it to the storage timescale of the sensible energy mechanism. The timescale of sensible energy storage can be thought of as the time constant of a 1-D energy balance on the tank assuming only thermal loss to the ambient: The time constant can be expressed as: where τ ΔT, the time constant of sensible storage, is equivalent to the time it takes to deplete 63% of the sensible energy by thermal losses. Similarly, a 1-D species balance on a region of water separated from a CaCl 2 (aq) solution by a density interface, (10) (8) (9) Fig. 6: The CaCl 2 distribution at the density interface for Ra = 5.2 10 10 and N = 2.2 after 6.55 hr of heating by natural convection. yields the following mixing time constant, (11) where τ ΔS, the mixing time constant, is equivalent to the time it takes the water region to reach 63% of the final mixed CaCl 2 mass fraction. The time constant for absorption storage is not equivalent to the mixing time constant because the binding energy is a nonlinear function of CaCl 2 mass fraction and temperature. Therefore we solve the analytical solutions to equations (8) and (10) as functions of time and explicitly calculate the sensible energy and binding energy at every time step. The time constant is the time at which 63% of the sensible or binding energy is depleted by thermal losses or mixing, respectively. This approach allows us to include property variations due to changing S and T as well as compare the relative rates of energy loss as a function of time. We assume a fixed tank volume of 4 m 3. The tank is charged with binding energy and split between water and CaCl 2 (aq) with S max = 0.59 kg-cacl 2 /kg-soln. both with height h = 0.75 m. The tank is fully charged with sensible energy at T H = 95 C. We assume the sensible storage is discharged at T L = 47 C and absorption storage is discharged at S 2 = 0.35 kg- CaCl 2 /kg-soln. The ambient temperature is fixed at T amb = 20 C. The thermal loss coefficients are varied to study the effect of this parameter sensible storage. Sh is varied to determine time constants based on the measured rates of mass transfer. In Fig. 7 the sensible energy of the storage tank is plotted versus time for several R-values of insulation. These results 6

display the loss of stored energy due to thermal losses. For R-10, the insulation on the lab prototype, 63% of the energy is lost in 14 days. For R-20 and R-50 insulated storages, τ ΔT = 28 and 75 days, respectively. In other words, for < R-50 sensible energy can only be stored for a few weeks. Even at R-50 insulation, approximately half the stored sensible energy is gone after 42 days. This result points out why very large tanks are required if sensible heat is the only mechanism for long-term storage. In Fig. 8 the binding energy in the storage tank is plotted versus time. In this case the only mechanism for loss is mass transfer. Data are plotted for 0 < Sh < 210. Sh = 35 100 are representative of the mass transfer rates in our experiments. The case Sh = 0 represents multiple storage tanks that preclude any mixing and Sh = 210 is a very high value chosen to serve as an extreme case. The time constant for Sh = 0 is undefined because an unmixed storage never loses more than 18% of its binding energy. For Sh = 35, 62, 100, the τ ΔS = 286, 160, and 88 days, respectively. These time constants obtained from experimental Sh are comparable to the maximum 140 day storage period need for space heating in a cold climate. Thus, even allowing for continuous mass transfer in a single-vessel, absorption storage is suitable for long-term storage. Even the extreme case, Sh = 210, yields τ ΔS = 30 days, which is still comparable to τ ΔT. One interesting feature of this analysis is clearly seen for Sh = 0 when there are no losses due to mass transfer. For 60 < t < 140 days, the loss of binding energy is entirely due to thermal losses because the binding energy is a function of temperature. The absorption heat pump operates between 47 < T < 75 C [11], and as the temperature decreases, the binding energy decreases. In fact, for all Sh about 18% of the binding energy is lost by thermal loss. This effect is less noticeable with increasing Sh because binding energy is lost by mixing. Thermal loses are the same order as mass transfer losses. Thus, the single vessel is even more attractive compared to multivessel storage because thermal losses are increased with the use of multiple tanks due to increased surface area. A constant Sh is assumed as a worse case to represent mixing timescales associated with continuous natural convection. In practice, we would expect periods of natural convection to be interspersed with periods of no fluid motion and only diffusion mass transfer, hence a lower average Sh. On the other hand, this analysis does not take into account discharge from a manifold which is likely to increase Sh. Nonetheless mixing timescales associated with the operating the immersed heat exchanger are deemed sufficient to proceed with further tank development. Fig. 7: Sensible energy depletion by thermal losses for different R-values (ft² F h/btu) of insulation. Fig. 8: Binding energy depletion by thermal and mass transfer losses for different Sh with R-50 insulation. 5. CONCLUSIONS We have presented the concept of a single-vessel storage tank that stores energy using both sensible and absorption mechanisms. The storage tank operates in a solar thermal system in which sensible energy is used on short timescales while the binding energy of the absorption process is stored seasonally. The simple design uses the natural density difference between solutions to prevent them from mixing and an immersed vertical tube heat exchanger and stratification manifold to add energy and fluid, respectively. Our progress to date has focused on the mass transfer loss that occurs between the stored solutions during the operation of the immersed heat exchanger. An initial numerical model predicts that the density interface prevents mixing and mass transfer rates are low. Experiments with a laboratory prototype confirm the numerical results. No large scale mixing is observed. Measured mass transfer rates are 11 < Sh < 62 for 8.4 10 8 < Ra < 85.5 10 10 and 2.2 < N < 18.2. We have demonstrated under a wide range of operating conditions that 7

the density interfaces are robust and prevent mixing during natural convection. Based on the estimated mass transfer rates, we presented the time constants of absorption storage and compared them to the time constants of sensible storage. For 35 < Sh < 62, the absorption time constants are 160 < τ ΔS < 286 days, which are longer than the maximum seasonal storage timescale in a cold climate (140 days). On the other hand, sensible energy storage time constants are 14 < τ ΔT < 75, suggesting that the sensible energy storage is better suited for daily or weekly storage. Furthermore, the loss of binding energy due to thermal losses is not insignificant (18%), but makes the single-vessel look more attractive compared to multi-vessel storages that have higher thermal losses due to larger surface area. 5. NOMENCLATURE a Fluid region aspect ratio, h/l c p Specific heat, kj/kg-k D Mass diffusivity, m 2 /s g Acceleration by gravity, m/s 2 h Fluid region height, m h b Binding energy, kj/kg-h 2 O h fg Heat of vaporization, kj/kg-h 2 O h s Heat of sorption kj/kg-h 2 O k Mass transfer coefficient, m/s L Fluid region length, m Le Lewis number, α/ D Mass flow rate, kg/s N Buoyancy ratio, β S ΔS/ β T ΔT Pr Prandtl number, ν/ α Ra Rayleigh number, gβ T ΔTh 3 /να S Salt fraction, kg-cacl 2 /kg-soln. Sh Sherwood number, kh/ D t Time, s T Temperature, C T amb Ambient temperature, C UA Conductance, W/K V Tank volume, m 3 Greek α Thermal diffusivity, m 2 /s βs Expansion coefficient, kg-soln./kg-cacl 2 β T Thermal expansion coefficient, 1/K λ ΔT Sensible energy storage density, kwh/m 3 λ ΔS Absorption energy storage density, kwh/m 3 ρ Density kg/m 3 τ ΔT Sensible storage time constant, days τ ΔS Absorption storage time constant, days ν Kinematic viscosity, m 2 /s Subscripts 0 Initial value 1 Bottom region 2 Top region H High limit H 2 O Water L Low limit 6. ACKNOWLEDGMENTS This study was supported by the National Renewable Energy Laboratory, the US Department of Energy, and the University of Minnesota Initiative for Renewable Energy and the Environment. We would like to thank FAFCO for supplying the parallel-tube heat exchanger. 7. REFERENCES [1] U.S. Department of Energy, DOE Buildings Energy Data Book, http://buildingsdatabook.eren.doe.gov/, accessed 3/1/12. [2] International Energy Agency, Task 42: Compact Thermal Energy Storage: Material Development and System Integration, http://www.iea-shc.org/task42/, accessed 3/1/12. [3] Bakker, M., van Helden, W.G.J., Hauer, A., 2008, Advanced materials for compact thermal energy storage: a new Joint IEA SHC/ECES Task, Proceedings of Eurosun 2008, Lisbon, Portugal, pp. 1-3. [4] Hadorn, J. C., 2008, Thermal energy storage: overview of technologies and status for solar heat, Proceedings Eurosun 2008, Lisbon, Portugal, pp. 1-8. [5] Bales, C. Gantenbein, P., Jaehnig, D., Kerskes, H., van Essen, M., Weber, R., and Zondag, H., 2008, Chemical and sorption storage results from IEA-SHC task 32, Proceedings of Eurosun 2008, Lisbon, Portugal, pp 1-8. [6] Hauer, A., 2008, Sorption storages for solar thermal energy possibilities and limits, Proceedings of Eurosun 2008, Lisbon, Portugal, pp. 1-8. [7] Quinnell, J. A., Davidson, J. H., and Burch, J., 2011. Liquid calcium chloride solar storage: concept and analysis, J. Solar Energy Engineering, 133, doi:10.1115/1.4003292. [8] Bales, C., 2008, IEA Task 32 Subtask B Report 4: Laboratory tests of chemical reactions and prototype sorption storage units, http://www.iea-shc.org. [9] Conde, M. R., 2004, Properties of Aqueous Solutions of Lithium and Calcium Chlorides: Formulations for use in Air Conditioning Equipment Design, International Journal of Thermal Sciences, 43, pp. 367-382. [10] Quinnell, J. A., and Davidson, J. H., 2012, Buoyancy driven mass transfer in a liquid desiccant storage tank, Proc. Energy & Sustainability, San Diego, CA., pp. 1-7. [11] Woods, J., Burch, J., and Kozubal, E., 2011, High-solarfraction heating and cooling systems based on liquid desiccants, Proceedings of the American Solar Energy Society, Rayleigh, N.C. U 8