Steady-state Model for Closed-Sorption Thermochemical Heat Storage Systems

ISHPC2024 International Sorption Heat Pump Conference Steady-state Model for Closed-Sorption Thermochemical Heat Storage Systems Dorian Höffner (a), Elisabeth Thiele(a), Robert Knorre(a), Thomas Meyer(a) (a) Technical University Berlin, Institute for Energy Engineering Marchstraße 18, 10587 Berlin, Germany doria[email protected] ABSTRACT In the field of energy storage, the classification and evaluation of thermochemical storage systems pose significant challenges. Unlike for traditional thermal storage systems, capacity, power, and other key performance indicators (KPIs) cannot be described easily, because they strongly depend on diverse and interdependent boundary conditions. The lack of a straightforward methodology for assessing these systems hinders the understanding of their application potentials and hence its deployment. This paper introduces a modeling approach aimed at simplifying the assessment of absorption based thermo-chemical storage systems, particularly assessing the thermodynamic steadystate conditions. Methodically, the proposed model applies the NTU-effectiveness method for the description of the coupled heat and mass transfer and works as a modeling framework. While no specific heat or mass transfer correlations are implemented, the model allows for the incorporation of such, making it a versatile modeling tool. The practical utility of the proposed model is demonstrated through its application to a specific sorption storage system using sodium hydroxide (NaOH) that could fit into a basement of a single-family dwelling. With a complete system setup consuming approximately 8.5m3, simulations predicted an overall capacity of 473.3 kWh. The system storage density results in 55.7 kWh/m3. The energy density based on the storage material alone was estimated to 126.2 kWh/m3. Although the current state of the model does not include dynamic system behavior, its value as a control planning tool and design heuristic could be shown. Furthermore, the model's applicability at an energy system level offers potential through which the application of thermochemical storage systems can be evaluated, and hence contributes to the broader understanding and optimization of energy storage solutions. Keywords: absorption, thermal storage, thermochemical storage, thermodynamics, heat and mass transfer, model, simulation 1. INTRODUCTION Thermo-chemical energy storage (TCES) systems are gaining significant attention due to their potentially high energy storage density and their long-term storage capacity. This document introduces a simple numerical model designed to predict thermodynamic steady-state working conditions in a TCES system utilizing the physisorption mechanism. The developed model aims to fill a gap in existing literature, where a comprehensive system-level model to estimate key performance indicators (KPIs) has been lacking. While system-based models for absorption thermal storage are scarce in the literature, falling film reactors have been analyzed and modeled by numerous scientists, focusing on fitting experimental data to heat and mass transfer correlations. For example, [1] conducted experiments for a vertical falling film reactor for LiBr and Water by formulating Nuand Sh-correlations for heat and mass transfer. [2] conducted an experimental study on vertical falling film reactors focusing on fluid flow and heat transfer. Specific mass flow correlations for pure water were described by [3] and [4], who determined evaporation and condensation coefficients. Falling film heat transfer was investigated and ISHPC2024 International Sorption Heat Pump Conference modeled by [5] and [6] for water. [7] developed a general approach aiming to describe heat transfer for falling films for diverse fluids and pipe diameters. In summary, although absorption chillers and sorption heat pumps have been previously integrated into system simulations using TRNSYS or similar programs [8] [9] [10], specific simulations for absorption-based TCES systems have been more limited. For instance, [11] conducted simulations to compare different working fluids, while [12] modeled the dynamic integration of solar thermal energy with the LiBr-water working pair, evaluating TCES as a seasonal energy storage solution. However, [12] addresses the potential crystallization of the salt solution, presenting operational challenges, and [11] omits a solution heat exchanger, crucial for system efficiency. Additionally, both studies lack detailed information on temperature conditions in the heating and cooling circuits, which is essential for system integration. 2. SYSTEM DESCRIPTION The system under consideration is a thermochemical storage based on a closed absorption cycle, where water is absorbed by a highly concentrated sodium hydroxide (NaOH) brine. This approach leverages the hygroscopy of NaOH - and the resulting vapor pressure depression effect - to store and release thermal energy. Figure 1: Simplified illustration of the thermochemical storage system modeled in this study. During the charging (desorption) phase, external heat, typically sourced from solar thermal energy, is applied to the system's high-temperature side. This process involves transporting diluted NaOH to the Absorber-Desorber (AD) unit, where it is dispersed over a horizontally oriented falling film reactor. The applied heat induces the evaporation of water, effectively concentrating the NaOH solution, which is subsequently directed to a storage tank. Concurrently, the water vapor generated is condensed in the Evaporator-Condenser (EC) unit, transferring heat to a low-temperature sink, such as the ambient air. This process continues until the diluted solution tank is completely emptied, signifying the system's fully charged state. Conversely, the discharging (absorption) phase is initiated when there is a demand for heat. In this phase, water is evaporated at low pressures and temperatures within the EC unit, utilizing heat sources like ambient air or low temperature geothermal energy. The vapor is then absorbed by the highconcentrated NaOH solution as it flows over the falling film reactor in the AD unit. This exothermal ISHPC2024 International Sorption Heat Pump Conference absorption process releases the heat of condensation and mixing, making it available for heating applications at the high temperature heat sink. The system continues to discharge until the concentrated NaOH solution tank is completely emptied. 3. MODEL The primary objective of this model is to predict the steady-state conditions between the Evaporator/Condenser (EC) unit and the Absorber/Desorber (AD) unit, focusing on their coupled thermodynamic states considering the low and high temperature heat sink and source, respectively. The scope of this model includes providing a structured approach for steady-state modeling of closedtransported sorption thermal energy storage systems as described by [13] and illustrated in Figure 2. While the model does not aim to detail specific heat or mass transfer phenomena, its structure is designed to accommodate the future incorporation of such details. The model uses all input parameters and general system parameters from the inflowing streams to calculate steady-state conditions. This is illustrated in Figure 2, where input variables are depicted in black and the output variables in gray. This figure is applicable to both the charging and discharging processes, providing a comprehensive overview of the model's capabilities. Figure 2: Input and output parameters for the proposed model. Legend: p - pressure, A - area, U - heat transfer coefficient, d - thickness, 𝝀 - heat conductivity, x - brine mass fraction, T/t - temperature, 𝒎 󰇗 - mass flow, 𝜻 - friction coefficient for pipe flow The model is built on the foundation of heat and mass balances, utilizing NTU-effectiveness (ε-NTU) methods to describe heat and mass transfer processes within the EC and AD units. A distinctive feature of our approach is the coupling of ε-NTU for heat and ε-NTU for mass transfer through substance properties, as illustrated exemplary in Figure 3. This coupling method was inspired by [14] and allows for the prediction of the film surface temperature. Additionally, the model incorporates one-dimensional, steady-state, and linear modeling of heat conduction through the film and tubes in the AD unit, where the film bulk temperature is assumed to be the arithmetic mean between the liquid surface and the tube wall. As mentioned above, the model inherently entails the possibility for incorporating more detailed heat and mass transfer coefficients in future versions. ISHPC2024 International Sorption Heat Pump Conference Figure 3: Illustration of the process condition ε-NTU model for the heat and mass exchangers. 𝑻𝑨𝑫,𝒔𝒂𝒕 and 𝒙𝑨𝑫,𝒔𝒂𝒕 represent the solution film surface conditions. The depicted graphs show the discharging process. 4. RESULTS With the proposed model, a calculation of the mean film surface temperature and concentration in relation to certain boundary conditions and design features of a specific system is achieved. This mean surface condition, in turn, can then be used to calculate the mean heat and mass transfer rates and help predicting the system behavior. Figure 4 illustrates the working conditions of an exemplary system for typical conditions. As visible, the substance saturation conditions are different from the film surface conditions as heat and mass transfer limitations are imposed. This is shown in Figure 4 (left). Figure 4: Illustration of the film surface conditions calculated by the model. On the left side, a single operation point is shown. On the right side, the solution mass flow was varied. Using the model, we can theoretically analyze how the performance (KPIs) of the storage system varies with a single input variable, while keeping other parameters constant, such as heat and mass transfer coefficients and film thickness. For instance, by adjusting the solution mass flow, we identified a temperature maximum (Figure 4, right) and power maximum (Figure 5, left). The positions of these maxima depend on the operational boundary conditions, for example the size of the solution heat exchanger (SHX) as illustrated in Figure 5. Specifically, when the solution enters the ISHPC2024 International Sorption Heat Pump Conference absorber at a lower temperature, the necessary preheating reduces the power output and shifts the power maximum downward and to the left. Figure 5: Effect of the variation of solution mass flow and solution heat exchanger (SHX) heat transfer area. 5. CASE STUDY This chapter demonstrates the practical application of the thermochemical absorption storage model introduced earlier. By utilizing the model, key performance indicators (KPIs) for the storage system are calculated and analyzed, highlighting the system's potential effectiveness and areas for improvement. KPIs such as efficiency, energy density, and operational times are crucial for evaluating the performance and viability of thermal storage systems. The simulated case study was built around a seasonal storage system designed to fit into a basement of a single-family dwelling. Specifically, the storage tank for the high concentrated solution is 3.0 m3, resulting in a solution mass of 4584 kg. Assuming a concentration change of 10%, the low concentrated solution tank would need to be 3.7 m3. In a combined tank setup using movable membranes, we assume a total space consumption of 5.0 m3. The separate water tank would require an additional 1.5 m3 of space. The evaporator/condenser (EC) and the absorber/desorber (AD) units are designed as horizontally staggered tube falling film reactors. The heat transfer area for the ECunit is 1.0 m², while the AD-unit area is 3.0 m². The solution heat exchanger area is configured as a plate heat exchanger with a heat transfer area of 2.0 m². Heat and mass transfer assumptions were collected from the literature. The U-value for the evaporator/condenser (E/C) unit was assumed to be 1600 W/m²K, based on literature values ranging from 700 to 4000 W/m²K for falling film water evaporators [15] [16]. The U-value for the A/D-unit was assumed to be 700 W/m²K during absorption, derived from research on horizontal falling film absorbers with values between 300 and 3000 W/m²K [17] [18] [19]. These studies focused on copper tubes, which have significantly better heat conductivity than the stainless-steel tubes used in our case study. During desorption, an increased heat transfer coefficient of 1000 W/m²K was assumed, due to steam formation and the resulting heat transfer improvement reported by [16]. The mass transfer coefficient 𝛽 was estimated to be 0.005 kg/m²s. This assumption was backed by theoretically calculating 𝛽 = 𝐷 𝛿𝜌 based on the diffusion coefficients 𝐷 for water in aqueous sodium hydroxide [20] and an estimated mean boundary layer thickness 𝛿 of 0.01 mm. The film thickness for the fixed solution mass flow was set to 0.2 mm. The heat transfer coefficient of the solution heat exchanger was assumed to be 1600 W/m²K. Boundary conditions for the model include a tank temperature of 12°C, a geothermal source temperature of 10°C, and a solar thermal temperature of 75°C during charging times. To reach a ISHPC2024 International Sorption Heat Pump Conference satisfactory mass fraction change during absorption, the solution needs to be recirculated. The building return temperature was set at 36, 35, 34 °C for the first, second, and third pass, respectively. The external mass flows were set to reaching a temperature lift of 2 K. The solution mass flow was fixed at 0.02 kg/s, ensuring good wetting and functionality as proven by experimental work. Under the specified boundary conditions, the model produces several key performance indicators (KPIs), which are displayed in Table 2. Table 2: Simulation results and basic storage KPIs. The charging and discharging power and the charged or discharged energy indicate the power/energy transferred between the A/D unit and the hot temperature sink/source. Cycle efficiency is determined as the ratio of discharged energy to charged energy. Charging (Single Pass) Discharging (Three Passes) Charging Power 7.538 kW Discharging Power 2.478 kW Charged Energy 478.9 kWh Discharging Energy 473.3 kWh Charging Time 63.7 h Discharging Time 191.0 h Cycle Efficiency* 0.986 System Energy Density 55.7 kWh/m3 *no heat losses during sorption or preheating modeled Material Energy Density 126.2 kWh/m3 6. CONCLUSION AND FURTHER RESEARCH The presented model serves as a coherent framework that can be integrated with various heat and mass transfer correlations. It offers a robust approach to modeling absorption-based storage systems, accommodating all relevant boundary conditions. This comprehensive model enables overall performance assessments and supports the development of optimized storage solutions containing all key design parameters. Future iterations of the model should incorporate additional features to enhance its accuracy and applicability. These features include accounting for thermal losses during the process to better reflect real-world conditions and dynamizing the model to depict transient behaviors, potentially through time constants derived from further experimental work. Additionally, conducting in-depth comparisons with other storage systems using a broader set of KPIs will provide a more comprehensive analysis. Detailed experimental validation will also be crucial to confirm the model's reliability and accuracy. These enhancements will contribute to a more thorough understanding and optimization of thermochemical absorption storage systems, paving the way for their practical implementation and integration into energy systems. 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