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Pit-TES Tank-TES Modeling Large-Scale Seasonal Thermal Energy Stores F. Ochs 1*, W. Heidemann 1, H. Müller-Steinhagen 1, 2 1 Institute of Thermodynamics and Thermal Engineering, Pfaffenwaldring 6, 7569

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Pit-TES Tank-TES Modeling Large-Scale Seasonal Thermal Energy Stores F. Ochs 1*, W. Heidemann 1, H. Müller-Steinhagen 1, 2 1 Institute of Thermodynamics and Thermal Engineering, Pfaffenwaldring 6, 7569 Stuttgart, Germany 2 DLR Stuttgart, Institute of Technical Thermodynamics * Corresponding Author, Abstract More than 3 international research and pilot seasonal thermal energy stores (TES) have been realized within the past 3 years. Experience with operation of these systems shows that TES are technically feasible and work well. However, thermal losses have to be reduced and lifetime has to be enhanced, while construction costs are reduced. Performance of TES is influenced by location, construction type, size, geometry, storage medium and used materials. Furthermore, TES are integrated in a heating (and cooling) system. with a great variety of system configurations and control strategies. Furthermore, boundary conditions influence the energetic and exergetic efficiency of TES. Hence, for a realistic comparison system simulations are required, which include all sensitive parameters. In the present paper aspects of TES modeling will be discussed. Based on modeled and measured data the influence of construction type, system configuration and boundary conditions on thermal losses of large-scale TES will be identified. 1 TYPES OF SEASONAL THERMAL ENERGY STORES During the past 12 years four different storage concepts have been developed and monitored in Germany in a solar assisted district heating systems [1]. Four storage concepts include tank TES with and without liners, pit thermal energy stores (PTES), borehole thermal energy stores (BTES) and aquifer thermal energy stores (ATES). In contrast to BTES and ATES, for which special geological conditions are required, tank and pit TES can be built at nearly every location. The volumetric thermal capacity of hot water tanks is with 6 kwh/m³ to 8 kwh/m³ 5 % higher than that of gravel-water TES and 1 % higher than that of ATES. BTES show the lowest volumetric thermal capacity ranging from 15 kwh/m³ to 3 kwh/m³ depending on the soil properties. However, tank and pit TES feature the highest specific construction costs. Seasonal TES are distinguished according to the type of construction and the storage medium in gravel-water TES (GW), soil/sand-water TES (SW) and hot water TES (HW). Tank TES consist of a structure made of concrete, (stainless) steel or fibre reinforced plastic (sandwich elements). Concrete tanks are built utilizing in-situ concrete or prefabricated concrete elements. An additional liner (polymer, stainless steel) may be mounted on the inside of the tank. The insulation is installed outside the tank. Pit TES are constructed without further static means by mounting insulation and a liner in a pit, see Fig. 1. The design of the lid depends on the storage medium Fig. 1: Tank and pit thermal energy store and the geometry of the TES. Whereas in the case of a gravel- or soil/sand-water TES the lid may be constructed analogue to the envelope, the construction of the lid of a hot water TES requires major effort and is the most expensive part of the TES. Hot water pit TES can be built with floating cover (e.g. in Marstal) or with self-supporting cover (e.g. barel or dome type shell cover, e.g. in Stuttgart). The wall of a buried TES is an assembly of several layers, see Fig. 2. The complexity of the design of such a composite wall arises due to the fact that on the one hand the envelope has to guarantee protection of the thermal insulation from moisture penetration from the inside and the outside but on the other hand desiccation has to be enabled in case the thermal insulation is already wet. soil protective fleece (optional) drainage (labyrinth-like polymer core, filter) diffusive layer, welded or adhesive bonded (lost) form work (or geocontainer/geobag) thermal insulation (bulk or sheets) vapour barrier (optional) concrete, reinforced liner: stainless steel, compound or polymer soil steel, concrete (special geotechnical works) drainage (labyrinth-like polymer core, filter) diffusive liner, welded or bonded protective fleece (optional) thermal insulation (bulk or sheets) (lost) form work (or geocontainer/geobag) protective fleece (12 g) liner: stainless steel, compound or polymer Fig. 2: Multilayered (composite) side wall of a seasonal thermal energy store, left: insulation outside with respect to the concrete/steel structure and right: insulation inside with respect to the concrete/steel structure 2 GENERAL ASPECTS OF TES MODELLING The comparison of different (seasonal) TES is difficult. Comparing different types of TES (tank, pit, ATES, BTES) without consideration of the entire energy system (including production, distribution and load) may lead to wrong conclusions. Several parameters have to be considered. The volume and geometry of the TES, the design of the composite wall (concrete, insulation, liner), the distribution of insulation (cover, side wall and bottom), the insulation thickness and type may differ. The geometry (e.g. cuboid, cylinder, cone) influences both, the surface-to-volume-ratio which determines the thermal losses and the height-todiameter-ratio which influences the quality of thermal stratification. The location may affect performance: thermal losses depend on the ambient and soil temperature and on soil properties, in particular the thermal conductivity and the volumetric heat capacity; at locations with ground water, with or without ground water flow, thermal losses are higher. The operational conditions such as the (average and maximum/minimum) operation temperatures, the return flow temperature of the heating net or the number of charging cycles may differ with each system. All these constructional and operational characteristics as well as the boundary conditions influence the energetic and exergetic efficiency of (seasonal) TES. Hence, system simulations, which include all sensitive parameters, are required for a realistic comparison of different TES. Obviously, quality of system simulations depends on the quality of applied models for the individual components such as solar collector, heat pump or TES. Basically, TES models can be distinguished into detailed models (CFD) and coarse models. Detailed or CFD models enable the exact representation of the real geometry in a discretized fashion (FDM, FEM, FVM). All transport phenomena occurring in reality can be considered. CFD models require the solution of partial differential equations (PDE) for all the physical values such as temperature, pressure and velocity. It is possible to integrate CFD models, which predict the thermo-hydraulic behaviour in a detailed way, into system simulation tools. However, the computational effort is enormous. (Multi-) annual system simulations with CFD models are not feasible. A further disadvantage of CFD models is that every change of the geometry requires a time-consuming new mesh generation. Coarse models apply simplifying assumptions with respect to geometry, material properties and boundary conditions. Depending on the problem, the computational effort can be significantly reduced compared to CFD simulations. Generally, in coarse structure models flow is considered as one-dimensional (plug) flow. The decision for detailed or coarse models depends on the objective of the investigation. In system simulations it may be sufficient that the energy balance is fulfilled in the majority of cases. The programme TRNSYS is most broadly applied for transient system simulations. It applies a comprehensive collection of coarse models to describe e.g. solar collectors, thermal energy stores, pipes, boiler, and heat pump. Several models are available for the calculation of thermal energy stores within the TRNSYS environment. A very flexible model is the multiport-store-model (MST, type 34, [7]). Like most TES models in TRNSYS, the multiport-store-model can only be applied for free-standing cylindrical thermal energy stores. For modelling of buried thermal energy stores only two so-called non-standard types are available in TRNSYS: The XST-model (type 342, [9]) and the ICEPIT-model (type 343, [4]). The XST-model is based on the SST/MST-model [8], and was later modified by [9]. A detailed description is given in [3], [5]. In contrast to the XST-model, the ICEPIT model (type 343, [4]) was developed for gravel-water pit TES. However, it is possible to consider water as storage medium. The ICEPIT-model allows to simulate cylindrical geometries and truncated cones, which is one of the advantages compared to the XST-model. Assumptions and simplifications are similar in both models. They consider one-dimensional plug flow in the store and two-dimensional heat conduction in the surrounding soil. However, some features, such as the geometry and the modelling of the cover insulation or the generation of the numerical grid are different. 3 COMPARISON OF MST-, XST- AND ICEPIT-MODEL The comparison of the TES-models was conducted for a TES with a volume of V = 1 m³, with a heat transfer coefficient of the insulation of.133 W/(m² K) and 1 m of soil cover. Depending on the selected geometry deviations of up to 13 % with respect to annual thermal losses have been found for the predictions of the three models, as shown in Fig. 3. Thermal losses from the top to the ambient are rather equal; however, differences between calculated thermal losses at bottom and side walls are significant. The multiport storage model was developed for free-standing TES. Hence, it is obvious that calculated thermal losses deviate from the results yielded with the other two models. The difference between the ICEPIT- and the XST-model is less obvious: the comparison of annual thermal loss rates q=q/a calculated with the XST and the ICEPIT-model for TES with various volumes (but equal height-to-diameter-(h/d)-ratios) is shown in Fig. 3 (right). Charging conditions were kept comparable by keeping the ratio of charging mass flow to storage volume at constant values (V/V store = const.). Deviations between the total thermal losses predicted by both the models were.7 %, 3.8 %, 5. % and 5.3 %, respectively. A Q / [MWh] Q/A / [MWh/m 2 ] thermal conductivity of ins =.6 W/(m K) for the XST and a corresponding U-value of.2 W/(m² K) for the ICEPIT- model were assumed for this comparison. One reason for the differences between the two types is that different numerical grids with respect to cell size and grid dimensions are used. A further reason is the different consideration of the top insulation with (ICEPIT) and without (XST) thermal mass. 18 left: MST center: XST 16 right: ICEPIT 14 bottom wall top bottom wall top left: ICEPIT; right: XST d / [m] V / [m³] Fig. 3: (left) Comparison of annual thermal losses Q calculated with MST-, XST and ICEPIT-model for a 1 m³ store with diameters of 2 m, 3 m and 4 m corresponding to A/V-ratios of.65 m -1,.83 m -1 and 1.21 m -1 ; (right) Comparison of annual thermal loss rates q=q/a calculated with XST and ICEPIT-model for several volumes V / [m³] COMPARISON OF PREDICTED AND MEASURED DATA The XST-models is validated by comparing predicted and measured data. Measured charging and discharging temperatures and flow rates (1 minute averaged values) of 26 of the TES in Friedrichshafen and of 22 of the TES in Hanover are used. For the application of the XST-model the real TES geometry has to be modelled as a cylinder. For the TES in Friedrichshafen satisfying agreement between simulation results and measured data was obtained for a model cylinder with a height of 18 m. Good agreement is obtained by using a thermal conductivity of 3 W/(m K) for the soil and of.6 W/(m K) for the thermal insulation. With.6 W/(m K) the thermal conductivity of the insulation is 5 % higher than the reference value according to manufacturer information. In terms of storage temperatures good agreement is obtained, however, in terms of the soil temperatures deviations of up to 2 K below the TES and 3 K laterally can be observed. The annual thermal losses sum up to 277 MWh compared to measured 16 MWh (heat flux sensors) or 42 MWh (heat flow meter), see [1]. For the tank TES in Hanover, Raab [3] determined values of the thermal conductivity of the insulation of.1 W/(m K) and for the soil of 2.78 W/(m K) for the validation of the XSTmodel based on measured heat quantities (charging and discharging enthalpies measured in 22). The insulation material of the TES in Hannover is expanded glass granules with a reference thermal conductivity of R =.8 W/(m K). The agreement between measured and calculated quantities was found to be good for storage temperatures, however, deviations of 2 Kto 3 K in the case of the soil temperatures were obtained. Thermal losses of 7 MWh are yielded using measured data from 22 as input for the simulation according to own calculations for these material properties and set of parameters. The measured thermal losses in 22 are 87 MWh determined by balancing and 56 MWh measured with heat flux sensors. Hence, non-satisfying deviations between modelled and measured losses of 24 % or 2 %, respectively, are obtained. / [ C] / [ C] Simulation Measurement T top T bottom Simulation Measurement T store, top T soil,wall h c = 18. m s = 3. W/(m K) =.6 W/(m K) ins T soil,bottom T soil, below 2 = 3. W/(m K) s 1 T soil, 2.5 m ( lateral) T soil, 4.5 m (lateral) =.1 W/(m K) ins t / [h] t / [h] Fig. 4: Simulated and measured temperatures of the TES in (left) Friedrichshafen (26), water temperature at top and bottom of the TES as well as soil temperatures positioned 3.3 m below envelope and 2.5 m laterally; (right) Hanover (22); positions central 2.5 m and 4.5 m below as well as.6 m and 2.5 m lateral of the envelope of the TES (in the centre with respect to the height of the TES); 5 4 T soil, bottom 5 LIMITS OF AVAILABLE TES MODELS In order to demonstrated which assumptions and simplifications of available TES models are acceptable and which ones will lead to non tolerable errors, geometrical considerations and aspects of modelling boundary conditions will be discussed in the following section. 5.1 BOUNDARY CONDITIONS Heat and moisture transfer mechanisms occuring at the boundary of TES are illustrated in Fig. 5. Coarse structure TES-models assume heat conduction in the surrounding soil. Boundary conditions on the top (ambient) as well as at the bottom and in radial direction have to be specified and are considered similarly in the XST- and the ICEPIT-model: The soil at the bottom boundary of the calculation domain is assumed to have constant temperature (Dirichlet boundary condition) of e.g. 1 C. At the outermost boundary of the soil domain in lateral direction a negligible heat flux is applied (Neumann boundary condition). For an accurate simulation it is neccessary that the radial and axial extension of the calculation domain is sufficiently large such that the boundary is not influenced by the storage temperature within a simulation period that is relevant for seasonal storage (2 to 4 years). In reality, ground or surface water may influence the soil temperature at any distance from the envelope of the TES. Hence, the surrounding soil may not or only partially serve as additional storage medium. Increased thermal losses would be expected. The influence of ground water may be modelled by decreasing the distance of qconv,b q conv,b. q rad, B g v,b gv,b T w T,S w,b g v,b g l, B q cond,b g v,b Fig. 5: Boundary conditions for a covered and for an exposed wall of a buried seasonal thermal energy store, convective (conv.) conductive (cond.) or radiative (rad) heat transfer (q), mass transfer consisting of vapour (g v ) or liquid water (g l ) transfer via boundary (B). g l,b T amb, amb top ground surface T soil, soil ground water level Q / [MWh] h/d / [-] & A/V / [m - 1] Q / [MWh] h/d / [-] & A/V / [m - 1] the outermost boundary, where a fixed temperature (Dirichlet boundary condition) may be assumed. Depending on the location a value in the range of 8 C to 12 C may be realistic. The influence of ground water is demonstrated using the ICEPIT-model with two different numerical grids. In the case of the original modell the numerical grid has an extension of 3 m x 3 m. A modified version is established such that the bottom boundary is.5 m below the bottom of the store (with a grid spacing of.1 m). Thus, two cases are compared: (i) undisturbed soil and (ii) ground water.5 m below bottom. Furthermore, two variations of the thermal insulation are examined: a) ins =.6 W/(m K), d ins =.5 m and b) ins =.6 W/(m K), d ins,cover/wall =.5 m, d ins,bottom =. Five different variations of the geometry of a TES with a volume of V = 1 m³ are examined, two cylinders (h=11.4 m and h=7.7 m) and three cones (h=11.4 m, h=7.7 m and h=4.1 m). The following results are obtained for sinusoidal charging with a period of 876 h in a temperature range from 3 C to 9 C and with a mass flow of 14 kg/h. Calculations were performed for five years simulation period starting with an initial temperature of = 1 C for the entire calculation domain. Storage temperatures increase at the beginning of the simulation and approach quasi-steady-state in year two. Data of year five are taken for the following analysis. Annual thermal losses for the five different geometries with bottom insulation with (GW) and without ground water (no GW) are compared in Fig. 6 for the case with and without bottom insulation. The difference between the cases GW and no GW on the one hand and bottom insulation or not on the other hand is more pronounced for larger bottom areas. In case of bottom insulation ground water does not have significant influence. However, it is important to note that in this example a relatively high U-value of.12 W/(m² K) was chosen. The total thermal losses are highest for cone 3 due to the highest A/V-ratio. The specific thermal losses, however, are the lowest. This can be explained by the lower level of the annual mean storage temperature. For the case of equal storage temperature the effect of ground water on the thermal losses would be even more pronounced. In presence of ground water the correlation between the thermal losses and the A/V-ratio is less distinct. The influence of the bottom area dominates. Depending on the bottom area thermal losses increase by 29 % to 45 % for the case without ground water and from 73 % to 89 % for the case with ground water for the given set of parameters and operation conditions. Without ground water thermal losses decrease after they reach a maximum value in year two bottom wall top left: GW right: no GW bottom wall top left: GW right: no GW cylinder 1 cylinder 2 cone 1 cone 2 cone 3 Fig. 6: Total thermal losses (Q) and specific (area weighted) thermal losses (q=q/a); influence of ground water (GW), for the case with bottom insulation (left) and without bottom insulation (right), year five cylinder 1 cylinder 2 cone 1 cone 2 cone 3 u / [kg/m³] eff / [W(m K)] u / [kg/m³] / [ C] / [ C] q / [KWh/(m 2 a)] The effect is more pronounced without bottom insulation. In presence of ground water total thermal losses approach the maximum value only after three years and remain at the maximum value. The effect can be explained by the fact that without ground water the surrounding soil heats up and thus serves as additional storage medium with reduced thermal losses as a result. This conclusion applies for all geometries. The investigated example shows that significant errors may result if a parameter identification with the objective to determine the thermal conductivity of insulation and soil is conducted based on unrealistic boundary conditions, i.e. assuming undisturbed soil in spite of ground water. 5.2 MATERIAL PROPERTIES Thermal losses of realized TES are often significantly higher than expected values. As one reason moist thermal insulation was identified. The thermal conductivity of porous materials increases wi

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