A generic adsorption heat pump model for system simulations in TRNSYS

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1 A generic adsorption heat pump model for system simulations in TRNSYS Christian Glück and Ferdinand P. Schmidt Karlsruhe Institute of Technology, Kaiserstraße 12, Karlsruhe, Germany Phone: , Fax: christian.glueck@kit.edu Internet: 1. Introduction In new hybrid applications of solar-driven heating, cooling and supply with domestic hot water, the statistical distribution of operating conditions for adsorption heat pumps and chillers is not yet well known, but is required for the design of a new generation of efficient sorption devices. From this situation arises a need for a simple and flexible generic adsorption heat pump model that requires only basic heat exchanger parameters and the adsorption equilibrium data of the working pair (adsorbate / adsorbent) under investigation. With such a model, it would be easier to find the best suitable working pair for the operating conditions of the application that is being modelled and to properly size the heat exchangers of heat pump / chiller. In this paper, we present a new TRNSYS model based on the approach of T. Núñez [1, 2]. The model evaluates machine-internal heat and mass transfer during the adsorption and desorption process with respect to thermodynamic sorbent properties. Modelling the heat exchangers of the sorption heat pump (or chiller) as NTU models allows for simulating the part load behaviour based on the supply and inside temperatures at the heat exchangers. 2. Modelling of adsorption equilibrium data Any working pair of an adsorption heat pump is characterized primarily by the adsorption equilibrium data, given by the loading field X(p,T) with loading X in grams adsorbate per gram of dry adsorbent at adsorbate pressure p (considering only a pure atmosphere of the working fluid without any inert gases) and adsorbent temperature T. The basic adsorption cycle operates between two isosteres (lines of minimum and maximum loading) and two isobars (corresponding to evaporator and condenser pressure, respectively). There are different methods of parameterization

2 of the loading field X(p,T). A still popular one is based on the use of Dubinin s characteristic curve [3] which gives the adsorbed volume W = X/ ads as a function of the adsorption potential A = RT ln(p s (T)/p), where p s (T) is the saturation pressure of the pure working fluid at the adsorbent temperature T and P is the equilibrium pressure at the same temperature (see [1,2,4] for more details). Under the assumption that W(A) is temperature invariant (i.e. the temperature dependence of W is fully described by that of A) and by approximating ads (T) with the bulk liquid density, the whole loading field X(p,T) can be obtained from a fit of measured adsorption equilibrium data to a single W(A) curve. In the example presented below, we have used the data for Grace silica gel 127B and water from [1] and [4]. The isosteric heat of adsorption q st (p,t) can either be obtained by numerical differentiation from the Clapeyron equation [5] or from an expression directly derived from Dubinin s theory, cf. [2]. The integral heat of adsorption Q ads or desorption Q des is obtained through integration of q st along the adsorption or desorption path (between the minimal and maximal loading). Additionally, the sensible heats of the adsorber heat exchanger(s) Q sens, consisting of the thermal masses of heat exchangers and tubing, adsorbent, adsorbate (loading dependent), and heat exchange fluid, need to be considered, both for the adsorption/desorption and for the isosteric steps of the cycle. Depending on the temperature and pressure conditions, there may be a temperature overlap between the heat released during the adsorption phase and the heat taken up during the desorption phase. Such overlap enables a (sorptive) heat recovery that reduces the demand on the external heat source Q gen and therefore increases the COP of the cycle. Even without a temperature overlap between adsorption and desorption, a sensible heat recovery between the two isosteric steps is possible. There have been various advanced sorption cycles proposed to realize an improved heat recovery [6,7] compared to the standard configuration of two-adsorber chillers that enable only sensible heat exchange between the two adsorbers during the isosteric cycle phases. Therefore, our generic adsorption heat pump model considers a variable degree of heat recovery to be able to analyse the sensitivity of the system performance in the application of interest to this parameter. 3. Heat transfer modelling and implementation The model described above has been used by T. Núñez and co-workers [1] for a (stationary) thermodynamic analysis of the achievable performance of various

3 adsorption cycles for heating, cooling or heat storage. Although the same paper already advocated the idea of extending the model by coupling it to heat transfer resistances (cf. fig. 1) and thus making it a suitable model for transient system analysis, to our knowledge such an extension has not been realized to date. Most models of sorption chillers or heat pumps that are in use with the TRNSYS simulation environment are parameterizations of models originally developed for absorption systems such as [8]. When adsorption models with the level of detail on the materials side as described above have been used in transient simulations involving adsorption processes, the level of detail on the process side has usually been such that the true periodic process of adsorption/desorption with its characteristic fluctuations in power and temperature has been resolved (e.g. in chapter 6 of [2] and in [4]). However, this level of detail on the process side makes it very inconvenient to use such models in typical TRNSYS applications like the annual energy balance analysis of complete energy systems for buildings comprising various energy sources and sinks. Especially the characteristic timescales of the adsorption / desorption process model and those of the building model do not fit together well. For the generic adsorption heat pump model for TRNSYS, we therefore follow up on the idea from [1] to encapsulate the adsorption cycle model in a simple heat transfer model, and in effect, we obtain a stationary model of adsorption cycles that is well suited for system simulations in TRNSYS and still retains the essential aspects of the sorption materials and heat recovery. Fig. 1: Illustration of the modelling approach of coupling an adsorption equilibrium model (as described in section 2) to its environment through heat transfer resistances at each of the four heat exchangers. Taken from [1]. As proof-of-concept and for evaluation of sorption pairs in annual system simulations, the model has been implemented as a subroutine in Fortran 90 (a so-called type ) usable in TRNSYS 17. Modelling the heat exchangers of the outer supply loops is required to account for part load behaviour, which has been done based on the effectiveness, which is calculated using the NTU-method [9] with the given properties and mass flows. As a simplification, the heat exchangers are modelled as maintaining a constant temperature at the inside surface area due to evaporation or

4 condensation taking place. For a condensing heat exchanger i (i = adsorber, condenser..), the effectiveness ε is, (8) where k [W/m 2 K] is the heat transfer coefficient, A [m 2 ] the effective area of the heat exchanger, [kg/s] is the mass flow at the heat exchanger and c [J/kgK] the specific heat capacity of the fluid in the outer heating or cooling loop, which is usually water. The temperature at the inside of the i th condensing heat exchanger is then, (9) where [W] is the heat transfer at the heat exchanger, for example the heating power during a simulation time step. [K] is the inlet temperature at the heat exchanger and is the mass flow [kg/s]. In this manner, the inside temperatures of the four heat exchangers can be calculated. A heat balance over the four heat exchangers is required to obtain all the heat transfers and the required inside temperatures. For that, an assumption regarding the COP has to be made before a COP can be calculated directly from heat ratios as stated in the previous section. For example, the ratio of heat intake from the generator and the adsorber in the cooling case is, (10) which has to be guessed at the beginning of the routine, so that all heat transfers and temperatures can be calculated. Subsequently, the heat transfers at the corresponding heat exchangers are calculated using the characteristic curve and the true COP is obtained in an iterative process once the heat balance converges. That means, at the end of each iterative loop, the COP is be calculated from the integrated differential heats, e.g. (here : for cooling, without any heat recovery), (11)

5 COP [-] where is the amount of heat taken up per time by the condensate in the evaporator, is the heat per time gained from evaporation of the condensate in the evaporator. [J] is the total heat per time required for desorption, as from equation (7). are the sensible heats per time and the amount of heat required for heating up utilities such as heat exchangers and hydraulic water, for both the isobaric and isosteric phases of the desorption cycle. With the COP known, the entire system of equations can be solved and the heat transfers at all four heat exchangers can be obtained, enabling calculations at any time step of a simulation. When calculating the differential adsorption and desorption heats from the characteristic curve, the evaporation pressure of water is required, which is obtained from a fit to the vapour pressure curve of water. Alternatively, data from Xsteam [3] can be used. Also, the specific heat capacities of the sorbent, the sorbate, the heat exchangers and of other utilities have to be known or estimated. Heat recovery can be taken into account by reducing the heat demand for desorption by the recoverable amount of heat, e.g. to model new cycle concepts like a stratisorp-cycle [4] that uses a stratified storage for inter-cycle heat storage /25/18, 80% heat recovery /30/18, 80% heat recovery /35/18, 80% heat recovery /35/18, 30% heat recovery 75/30/18, 30% heat recovery 75/25/18, 30% heat recovery Average Cooling Power [kw] Fig. 2: Power characteristics of a sorption chiller with the sorbent 127B at different inlet temperatures (generator inlet / heat rejection inlet / chilled water inlet) and at different heat recovery shares. The dashed lines are for 30% heat recovery, the solid lines for 80% heat recovery. The chilled water outlet temperature is 15 C. Average cooling power corresponds to different chilled water mass flows.

6 mass flow of hot water / generator circuit 1000 kg/hr mass flow of cold water / evaporator circuit variable, rated 1250 kg/hr mass flow of cooling water / adsorber + condenser circuit 1150 kg/hr (each) heat transfer coefficient (k A) of evaporator heat exchanger 1500 W/K heat transfer coefficient (k A) of adsorber, condenser, generator heat ex W/K (each) Tab. 1: Assumptions made regarding the heat transfer coefficients and mass flows of the heat exchangers, for the results shown in fig Conclusion and outlook We have presented a method to evaluate the capacity of new adsorption chillers and heat pumps based on very few assumptions in a simple method, taking only thermodynamic principles and a characteristic curve of the sorption pair into account. In applications where no manufacturer- or machine data is available for simulation and evaluation, this method can be used to investigate sorption pairs in the given application and e.g. to rank available options. With no additional modification of the model, the power output (cf. fig. 2) might be underestimated due to using the maximum desorption temperature instead of the average desorption temperature over the cycle. 5. References [1] Núñez, T., Henning, H.-M., and Mittelbach, W., (1999), Adsorption cycle modeling: characterization and comparison of materials, Proc. Int. Sorption Heat Pump Conf. 1999, pp [2] Núñez, T. (2001): Charakterisierung und Bewertung von Adsorbentien für Wärmetransformationsanwendungen. Dissertation Univ. Freiburg, faculty of physics. [3] Dubinin, M. M. (1975): Physical adsorption of gases and vapors in micropores. In: Progress in Surface and Membrane Science, vol. 9. Academic Press, pp [4] Schicktanz, M. and Núñez, T. (2009): Modelling of an adsorption chiller for dynamic system simulation. Int. J. Refrig. 32, pp [5] Cacciola, G. and Restuccia, G. (1995): Reversible adsorption heat pump: A thermodynamic model. Int. J. Refrig. 18, pp [6] Meunier, F.: Adsorption heat powered heat pumps (2013). Applied Thermal Engineering. In press, DOI: /j.applthermaleng [7] Schwamberger, V., Joshi, C., and Schmidt, F. P., (2011), Second law analysis of a novel cycle concept for adsorption heat pumps, Proc. Int. Sorption Heat Pump Conf. (ISHPC11), pp [8] Albers, J., Besana, F., Krause, M., Safarik, M., Sparber, W., Witte, K. T. (2008): Absorption chiller modelling with TRNSYS - requirements and adaptation to the machine EAW Wegracal SE 15. In: Proc. Eurosun 2008, Oct. 2008, Lisbon, Portugal. [9] Incropera, F.P. et. al., Fundamentals of heat and mass transfer, (2006), John Wiley & Sons, 6 th edition. [10] IAPWS (1997): International Association for the Properties of Water and Steam. Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam. (See also XSteam, steamtables

Basic Principles of an Adsorption Heat Storage System

Basic Principles of an Adsorption Heat Storage System Development of a High Energy Density Sorption Storage System Günter Gartler, Dagmar Jähnig, Gottfried Purkarthofer, Waldemar Wagner AEE-INTEC, A-82 Gleisdorf, Feldgasse 19, Austria Phone: +43/3112/5886/64,