In this contribution, we perform computer simulations to expedite the develop- ment of hydrogen storages based on metal hydride. These simulations enable in-depth analysis of the processes within the systems which otherwise could not be achieved. That is, because the determination of crucial process properties require measurement instruments in the setup which are currently not available. Therefore, we investigate the reliability of reaction values that are determined by a design of experiments. Speci cally, we rst explain our model setup in detail. We de ne the math- ematical terms to obtain insights into the thermal processes and reaction kinet- ics. We then compare the simulated results to measurements of a 5-gram sample consisting of iron-titanium-manganese (FeTiMn) to obtain the values with the highest agreement with the experimental data. In addition, we improve the model by replacing the commonly used Van't-Ho equation by a mathematical expression of the pressure-composition-isotherms (PCI) to calculate the equilib- rium pressure. Finally, the parameters' accuracy is checked in yet another with an exist- 1Institute of Technology, Resource and Energy-Ecient Engineering, Bonn-Rhein-Sieg Uni- versity of Applied Sciences, Grantham-Allee 20, 53757 Sankt Augustin, Germany 2GKN Sinter Metals Engineering GmbH, Krebsoege 10, 42477 Radevormwald, Germany 3Fraunhofer-Institute for Algorithms and Scienti c Computing (SCAI), Schloss Bir- linghoven, 53757 Sankt Augustin, Germany Preprint submitted to Journal of Elsevier January 18, 2021 ing metal hydride system. The simulated results demonstrate high concordance with experimental data, which advocate the usage of approximated kinetic re- action properties by a design of experiments for further design studies. Fur- thermore, we are able to determine process parameters like the entropy and enthalpy. Keywords: Metal hydride storage, simulations 2010 MSC: 00-01, 99-00 1. Introduction Water is not only indispensable for every form of life, its elements hydrogen and oxygen will shape the future, when energy supply becomes more and more critical due to the global population growth [1]. 5 Therefore, the challenge is to store this huge amount of hydrogen, whereas oxygen is already available in the air. The state of the art mainly provides three di erent technical solutions: Pressure tanks store the hydrogen at a great pressure level, hence they require high safety standards; liquid storages require extremely low temperatures, which makes it inecient; last, solid-state storages 10 contain the hydrogen in chemical form. Latter have a high storage density of hydrogen at a low pressure compared to pressure tanks, at the price of large weights. Due to the properties of the systems, the storage systems have di erent eld of applications. Depending on their operating conditions, the storages are selected. 15 Despite the relevance of all technical solutions, this study focuses on solid- state storages and investigates the reaction behavior of hydrogen and a solid- state alloy. Recent studies [2][3][4] already dealt with solid-state hydrogen stor- ages based on metal hydride and their simulations. The purpose of these stud- 20 ies was to achieve in-depth understanding of the processes inside metal hydride solids. These studies provide thermodynamic and kinetic reaction coecients 2 for several metal hydride materials. For example, conventional values are avail- able for a basic iron-titanium alloy [5] [6]. However, the kinetic reaction prop- erties of iron-titanium-manganese (FeTiMn) utilized by this research have not 25 yet been suciently studied in the literature. There is no precedent literature available for our alloy or similar additives. Although these coecients are es- sential to simulate the reaction behavior between metal hydride based on this iron-titanium-manganese alloy and hydrogen. This is why the conventional val- ues have to be checked. 30 This study provides mathematical principles of the reaction processes be- tween metal hydride and hydrogen and describes the physical processes inside a characteristic storage system. Hence, the development of the charge level can be calculated considering the movement of gaseous hydrogen, thermal conduc- 35 tion inside the metal hydride solid as well as the system's pressure level. This leads to a simulation model which allows to analyze several design concepts of solid-state storages regarding various metal hydrides. The model requires to be veri ed to assess the accuracy of the simulation. Therefore, data collected in the laboratory is compared to simulation results. However, the crucial kinetic 40 reaction parameters cannot be determined due to not available measurement instruments. This is why a design of experiments is used: Kinetic reaction coecients are approximated by comparing them to experimental data and ref- erences of a basic FeTi alloy. The reliability of this process is investigated. 3 2. Mathematical model 45 This paragraph provides a description of the mathematical model. Previous projects [2][3][4] dealt with the reproduction of the reaction behavior of metal hydrides with a mathematical model. Conservation laws describe the mass distribution (i.e. hydrogen density; metal hydride density) and energy (i.e. temperature) distribution inside the tank system. An equation considers these 50 state variables and calculates the reaction rate between hydrogen and metal hydride. This contribution assumes the fundamental model and re nes it. Figure 1: Illustration of the model structure. The simulation model consists of three di erent areas: metal hydride solid (porous media); volume bu er (empty area) and the heat exchanger (lined area). Model structure. The model considers 3 areas: The metal hydride solid; the volume bu er and the heat exchanger lled with water. Figure 1 illustrates the model's structure. The metal hydride area is presented by a homogeneous 55 solid. A volume bu er has to be taken into consideration for design concepts because of the volume expansion during the absorption. The tank's cylindrical geometry favors a simpli cation: Instead of observing a 3 dimensional volume, 4 the tank is represented by a two-dimensional numerical grid in radial r and axial z direction (i.e. metal hydride solid; volume bu er). However, the annular 60 gap is represented by a one-dimensional numerical grid in axial direction. It is assumed that variation of state variables in radial direction are negligible within the annular gap. Depending on the areas the model considers the following state variables: Metal hydride solid: 65 •h2- Hydrogen density •mh- Metal hydride solid density •Tmh- Metal hydride solid temperature Volume bu er: •h2- Hydrogen density 70 •Th2- Hydrogen temperature Heat exchanger (gap): •Th2o- Water temperature 5 Conservation of energy. The model considers the solid's temperature Tmh, the temperature within the volume bu er Th2and the water's temperature Th2o. 75 Conservation equations of energy calculate the temperature changes of these mediums. Regarding the cylindrical geometry of the pressure tank the equations may be written as follows [2][3][7]: (cp)eff@Tmh @t=eff 1 r@Tmh @r+@2Tmh @r2+@2Tmh @z2 _mrH+_Qmh-h 2o(1) (cp)h2@Th2 @t=h2 1 r@Th2 @r+@2Th2 @r2+@2Th2 @z2 +_Qh2-h2o (2) (cp)h2o@Th2o @t=h2o@2Th2o @z2uh2o(cp)h2o@Th2o @z_Qmh-h 2o (3) The rst terms on the right side describe the heat conduction inside the medium, whereby is the thermal conductivity of each medium. Using cylinder 80 coordinates rde nes the radial direction and zthe axial direction. The amount of heat which is produced or absorbed inside the solid is related to the amount of hydrogen, which is charged _ mr absand/ or _mr desdischarged per unit time, and is represented by the middle term on the right side of Equation 1, whereby  H describes the enthalpy of the reaction; is the density; and cpthe heat capacity. 85 The middle term on the right side of Equation 3 takes the water ux inside the heat exchangers into account. For the calculation of the temperature change inside the solid, both factors de ne e ective values, considering the behavior of hydrogen and metal hydride [3][8]: (cp)eff= (cp)mh+(cp)h2(4) eff=mh+h2 (5) _Qde nes the heat ux between the heat exchanger's medium and the solid or 90 hydrogen inside the storage. The heat ux depends on the temperature gradient Tbetween the mediums, the exchange area A, in this case the tank surface, and the heat transition coecient U[9]: 6 _Q=UATz}|{ Th2oTmh / h2 (6) Conservation of mass. A conservation equation of mass calculates the hydrogen distribution considering processes such as the reaction and the gas transfer. This 95 equation may be written in general as follows[2][3][8]: @h2 @t=r(h2uh2)_m (7) whereby _mrepresents sources and/ or consumption of hydrogen (i.e. reaction rate _mrbetween the solid and hydrogen or the ow through the valve of the pressure tank) and the porosity of the metal hydride. The rst term on the right side of the Equation 7 describes the gas transfer through the porous 100 solid. The equation is transformed by regarding the cylindrical geometry of the pressure tank: @h2 @t=1 r@ @r rh2ur h2 @ @z h2uz h2 _m (8) The gas velocity uis mainly in uenced by a pressure di erence and is ob- tained from the Darcy equation. The Darcy theorem represents the ow through a porous medium and is written as follows [7][10][11][12]: 105 uh2= rp (9) Assuming that hydrogen is an ideal gas with p=TRm1 mol.Rde nes the universal gas constant and mmolthe molar mass of hydrogen, gives: @h2 @t= R mmol1 r@ @r rh2@h2Th2 @r +@ @z h2@h2Th2 @z _m (10) with the dynamic viscosity . The Konzeny-Carman equation is used to determine the permeability as follows with the diameter of the used powder dp[13]. 110 7 =2dp 150 (1)2(11) The conservation of mass also describes the development of metal hydride densitymh. This development is only in uenced by the reaction rate _ mrbe- tween the metal hydride solid and the hydrogen [2]: @mh @t= _mr (12) Reaction rate. The core of the metal hydride simulation is based on the calcu- lation of the reaction kinetics for absorption ( abs) and desorption ( des). The 115 mathematical term takes process variables like the temperature, the pressure as well as the mass concentration into account to calculate the reaction rate _ mr [2]: _mr abs=kexpE RTmh peqp peq(max mhmh) (13) _mr des=kexpE RTmh peqp peq|{z} f2(mhmin mh)|{z} f3(14) The rst term describes the reaction behavior of the metal hydride alloy used and takes into consideration that the activation energy Ehas to be over- 120 come by the reaction. The reaction coecient kde nes the ability of the metal to absorb the hydrogen. The relation between the pressure level pinside the pressure tank and the equilibrium pressure peqis described by the second term. The greater the di erence between these values, the more hydrogen is charged or discharged. M.Ron [14] describes di erent ways to describe this relation- 125 ship. The last term calculates the di erence between the loading status and the equilibrium state of stored hydrogen [15]. maxandminare constant values or de ned by an approximated function. Figure 2 illustrates the relation of the involved variables. For example, two operation points are marked. Depending 8 on the current state of charge and pressure the relation of the discussed terms 130 are illustrated according to the PCI. State of chargeEquilibrium pressureDesAbsf3 f2 ρminρmax peq peq Figure 2: Illustration of the involved variables of the reaction equation by means of a pressure- composition-isotherm. Red area: Desorption; blue area: Absorption. The partial di erential equations must be completed by initial and boundary conditions: At the beginning of the simulation, the metal hydride's temperature and density, the pressure of the gas and the temperature of the water assumed to be homogeneous [3]. Therefore, the initial conditions are chosen as follows.: 135 Temperatures: Tmh(r;z;t = 0) =T0 mh Th2(r;z;t = 0) =T0 h2 Th2o(z;t= 0) =T0 h2o Densities: mh(r;z;t = 0) =0 mh h2(r;z;t = 0) =0 h2 The ow temperature of the water at the inlet to give values for Tin(t) is set. At the edge of the metal hydride bed it is assumed that there is no temperature change. Therefore, the boundary conditions are as follows, where 9 z= 0 describes the bottom of the pressure Tank, z=Zthe top,r= 0 the axis of the cylindrical pressure tank and r=Rthe surface of the pressure tank [3]: 140 Temperatures: Th2o(z;t) =Tin(t) atz= 0 @Tmh @z= 0 atz= 0 @Th2 @z= 0 atz=Z @Tmh @r= 0 atr= 0;r=R @Th2 @r= 0 atr= 0;r=R Densities:@h2 @z= 0 at z= 0;z=Z @h2 @r= 0 at r= 0;r=R Numerical methods. The de ned mathematical models are partial di erential equations (PDE). Matlab provides well-engineered tools to solve ordinary dif- ferential equations (ODE). These equation solvers require a conversion of the PDEs into ODEs by the method of lines. After a discretization in space the lo- cal derivatives are approximated by nite di erences [16]. This leads to a large 145 system of ODEs. The di erential equations system is then solved by taking the solver ode15s from Matlab [17]. 10 3. Iron-titanium-manganese alloy The material used for the model validation consists of an iron-titanium- manganese alloy (FeTi xMnyjx=4447 y=47). The material is made by GKN. The 150 advantage of this alloy is its usability at low pressure and temperature levels. The alloy composition based on iron (Fe) and titanium (Ti). In addition, Man- ganese (Mn) is added to avoid a dual pressure plateau, but instead to obtain one sloping pressure plateau. The additive also enables better activation properties compared to pure FeTi [18]. 155 Pressure-composition-isotherms - data. Figure 3 illustrates pressure-composition- isotherms (PCIs) of FeTiMn used (gray dashed lines). The data was given by the company GKN. The maximal level of stored hydrogen is achieved at 1.8wt-% at 30°C and is decreased to 1.5wt-% at 90 °C. The PCI describes the correlation between the pressure level and the hydrogen capacity achieved in equilibrium 160 for a temperature. In other words, the amount of hydrogen stored in metal hy- dride for a given pressure and temperature after a long term. This characteristic pressure is known as equilibrium pressure and in uences the formation of metal hydride and therefore the reaction behavior. 165 00.3 0.6 0.9 1.2 1.5 1.8 Mass concentration [wt-%]0.1110100Equilibrium pressure [bar] 30◦C 90◦CReference Experiment Figure 3: Measured PCIs of FeTiMn based on courtesy of GKN. Reference is taken from H. Buchner [19] that is given for 25 °C and 90 °C 11 A hysteresis is shown between the absorption and desorption. The hystere- sis can be explained through the conducted work during the absorption, since the lattice expansion requires more energy, whereas during the desorption the lattice is already expanded and the hydrogen atoms escape freely. Therefore, the pressure plateau is always higher during absorption than desorption. With 170 increasing temperature, the lattice expansion grows. The required energy de- creases and therefore the hysteresis does too. H. Buchner [19] provides PCI data for 25 °C and 90 °C. The characteristic of the measured PCI curves correlate with the reference data in the literature. The small gap in the comparison of the lower temperature can be explained due to the temperature di erence of 175 the reference data used. Pressure-composition-isotherms - mathematical model. The equilibrium pres- surepeqis essential to calculate the reaction rate of metal hydrides (Equation 13 14). Previous studies [13][11][2] used the Van't-Ho equation to determine the equilibrium pressure at any given state assuming an ideal PCI: The pres- 180 sure plateaus have no gradient. However, this idealized assumption results in a calculation error, which is shown in [20]. Hence, Herbrig et al. [20] have developed a mathematical model to represent PCIs in an accurate way. This model is based on exponential functions, which 185 include a series expansion. The respective terms are weighted by adjusted coef- cients and to express the PCI characteristic of an individual material alloy. The advantage of this model is that the equilibrium pressure can be determined at any given temperature Tin kelvin and concentration win weight-percentage. It has to be said, that this equation has not any physical explanation but shows 190 high accordance with the measured data. peq=10w 1 + 10w(exp 0T1+ 1T+ 2T2+ 3w+ 4w2+ 5w3 (15) + exp 0T+ 1T2+ 2Tw+ 3w+ 4w2 + exp (50 ( w 5))) 12 The coecients and are obtained by means of a Matlab curving t- ting tool (cftool). This tool provides capabilities to approximate measured data points by polynomials, interpolation or custom equations. The adjusted coef- cients are shown in Table 1. Compared to Herbrig et al. [20] this study uses 195 a slightly modi ed series expansion, which ts better the material's PCI mea- sured. The PCI-model is more accurate than using the Van't-Ho equation, which is already shown in [20]. The Van't-Ho equation disregards the state of charge. Hence, only one equilibrium pressure is calculated for a given temper- ature. This approach is acceptable for an ideal PCI with a constant pressure 200 plateau, but not for the material used in this study. Figure 3 shows the de- scribed curve model for FeTiMn using adjusted coecients and compares the model to experimental data. Table 1: Adjusted coecients of the mathematical PCI curve model for FeTiMn Coecient Absorption Desorption Coecient Absorption Desorption 0 -2793 / -2506 0 -0.08377 / -0.1186 1 0.05211 / 0.0329 1 8.617e-5 / 3.193e-4 2-7.184e-5 / -3.011e-5 2 0.04009 / 0.01629 3 2.3760 / 4.124 3 5.804 / -20.42 4 -0.3568 / -2.964 4 -3.313 / 11.89 5 -0.2035 / 0.961 5 1.735 / 1.74 13 Van't-Ho isochores - enthalpy and entropy. Van't-Ho isochores describe the state of equilibrium of any chemical reaction. In case of metal hydrides this state 205 of equilibrium is expressed by the correlation between the equilibrium pressure and the temperature. Therefore, these isochores can be determined due to the measured PCI. The Van't-Ho equation demonstrates the relationship between these parameters and requires further variables such as the enthalpy and entropy. logpeq p0 =H RT+S R; (16) Hde nes the enthalpy; Rthe universal gas constant;  Sthe entropy; peqthe 210 equilibrium pressure; p0the atmospheric pressure and Tthe temperature. With the aid of value pairs ( T,peq) given from the measured PCI, the isochores can be approximated for both absorption and desorption. The Van't-Ho isochroes are approximated using the PCIs to investigate the entropy  Sand enthalpy Hof FeTiMn. The entropy can be de ned as  S=109:88 J K1whereas 215 the enthalpy changes due to the sloping PCI. The determined enthalpy for both absorption and desorption can be expressed by Equation 17 and Equation 18 in the range between 0.2wt-% and 1.3wt-% depending on the state of charge. Otherwise, the limit value of the boundaries (0.2wt-%; 1.3wt-%) is used. Habs=2327w2+ 8424w35230 (17) Hdes=2668w2+ 8500w36510 (18) 4. Model validation 220 The calculated results are validated by a comparison with measurements: First, the simulation of a heating-cooling process veri es the thermal di usion inside the metal hydride's solid; then, a design of experiments approximates kinetic reaction coecients to reproduce the reaction kinetics; nally, a com- parison with data of an existing system checks the validity of the calibrated 225 values. 14 Figure 4: Tankdesign used for the thermal validation that is lled with metal hydride (porous media) and provides a volume bu er. An annular gap surrounds the pressure tank as a heat exchanger (lined). The temperature can be measured due to a sensor within the solid (red dot) Temperature validation. A pressure tank used for the validation is illustrated in Figure 4. The pressure tank is lled with FeTiMn described and is evacuated to avoid endothermic or exothermic reaction e ects. An annular gap surrounds the pressure tank as a heat exchangers. Then, water inside this gap in uences the 230 thermal activity of the solid and allows a control of system. One temperature sensor is placed inside the metal hydride storage to measure the temperature process which is compared to the simulation results. The used properties are shown in Table 2. The thermal parameters mhandcmh pare measured by GKN. 235 The comparative data describes a heating-cooling process. It is assumed that the initial bed temperature is homogeneous. The measured water temper- 15 Table 2: Summary of the material properties used for FeTiMn which are the input parameters of the simulation. Properties Symbol Value Unit Thermal conductivity mh 6.2 { 5 W m1K1 25°C { 100 °C h2 0.1805 W m1K1 h2o 0.6 W m1K1 Enthalpy  Habs -33638 { -28211 J Hdes -34917 { -29969 J Entropy  S -109.88 J K1 Heat capacity cmh p 682.4 J kg1K1 ch2p 14304 J kg1K1 ch2o p 4182 J kg1K1 ature of the inlet is approximated and is set as the data input for the simulation. Figure 5 illustrates the simulation results compared to the measured temper- atures. It can be demonstrated that the characteristic form of the simulated 240 temperature process resembles the measured temperature. Thus the validation of the temperature conductivity is proven. 16 0 50 100 150 200 Time [min]203040506070Temperature [◦C] sim|exp H2Oin H2Oout TMHFigure 5: Validation of a thermal conduction process inside a metal hydride storage. The thermal activity is in uenced by the input temperature of the water inside the heat exchangers. The validation of the thermal conduction is consisting of a heating-up and a cooling-down process. exp descripes the measured data and calc the simulated results. Reaction validation. A high-pressure weighting station 'STA HP1' from the company Linseis is utilized to measure the storage capacity. The set-up is illus- trated in Figure 6. This measurement aperture bases upon an electromagnetic 245 beam scale with a measurement precision of 0 :1µg and is designed for hydrogen experiments. The measured weight gain of metal hydride results in the mass concentration and therefore the hydrogen capacity achieved. The pressure tank has a total volume of 2L. This allows an accurate dosage of pressure. A 5 g sample of metal hydride is in a case, which is located on the temperature sensor. 250 The heating element in form of a spiral surrounds the case. The cooling occurs due to convection. The determination of crucial process properties require further measurement instruments in the setup which are currently not available. This is why we uti- 255 lize a design of experiments to approximate the reaction coecient kfor both desorption and absorption. The values of the activation energy are taken from the basic alloy FeTi: [5] Eabs= 23800J mol1andEdes= 19870J mol1. 17 Figure 6: Illustration of the high-pressure weighting station used to measure the hydrogen capacity of FeTiMn. The measurement aperture bases upon an electromagnetic beam scale and is designed for hydrogen experiments from the company Linseis. A metal hydride sample is xed in a case. A heating element surrounds the case and controls the sample's temperature. Then, the weight gain is measured. The aim of this approach is the reproduction of the stored hydrogen of 260 several experiments (i.e. 15 bar and 30 °C; 40 bar and 30 °C; 40 bar and 40 °C). The reaction coecient is varied in the range of 1 to 100. A comparison operator R2rates the accordance with the measurements. This operator is calculated as follows [21]: R2=Pnr i=1( ^yiy)2 Pnr i=1(yiy)2(19) The factorR2indicates the extent of variability of the dependent parameter, 265 wherebynrde nes the quantity of data; yide nes the experimental data; ^ yi 18 de nes the simulation data and yis the average of the simulated results. The operatorR2takes a value of one if the simulated results correspondent to the experiment; or deviates from one if the simulated results di er from the exper- iment. Figure 7 shows the averaged values of the comparison operator for the 270 reaction coecients of both absorption and desorption. 0 10 20 30 40 50 Reaction coeﬃcient k0.950.960.970.980.991.00Coeﬃcient of determination R2 Desorption Absorption Reference Approximated value Figure 7: Illustration of the values of comparison operator of the DoE in order to calibrate the reaction coecient. The value that demonstrate the highest accordance to the experimental data are marked with 'x'. The simulated results with the best comparison operator, demonstrate high concordance with the experiments, which can be shown in Figure 8. [6] Mat- sushita et al. give values of reaction coecients for a conventional FeTi alloy. 275 These values are marked in Figure 7. As shown, the approximated values are similar to those of Matsushita et al., which also result in high accuracy. Thus, the striven values of the reaction coecients ( kabs= 25kdes= 17) are su- ciently approximated. The reaction kinetics is reproduced accurately for each experiment. However, a di erence in hydrogen capacity is achieved, for the case 280 of 40bar and 30 °C which results from an insucient modeling of the PCI at the boundary. Transfer validation. Data from GKN's pilot project of a residential home is given (Knappenhaus in south Tirol - www.hy2green.de). A metal hydride stor- 285 19 0 1 2 3 4 5 6 Time [min]0.501.001.50Mass concentration [wt.%] 0 5 10 15 20 25 30 Time [s] exp|sim 15Bar, 30◦C 40Bar, 30◦C 40Bar, 40◦CFigure 8: Illustration of the computed results (calculation) compared to the measured data (exp) using the values of kinetic reaction properties with the best comparison operator R2. The measured data is shown by an average with its standard deviation. Left: Absorption; Right: Desorption; A:exp. 15bar and 30 °C;B:exp. 40bar and 30 °C;C:exp. 40bar and 40 °C 0 10 20 30 Time [h]0102030405060Temperature [◦C] Pressure [bar] exp|sim Pressure Temp. mh Temp. H 2Oin 0 2 4 6 8 10 Time [h] Figure 9: Illustration of the comparison of the simulated and the measured results of the GKN's Knappenhaus. Left: Absorption process, where the supplied mass ow of hydro- gen is 6 :6L min1.Right: Desorption process, where the released mass ow of hydrogen is 36:5L min1for the rst 4h and is then decreased. The mass ows as well as the water temperature are smoothed by mathematical terms. 20 Figure 10: Tankdesign of Knappenhaus used for the transfer validation that is lled with metal hydride (porous media) and provides a volume bu er. An annular gap surrounds the pressure tank as a heat exchanger (lined). The temperature can be measured due to a sensor within the solid (red dot). 21 age system is already implemented, where the pressure tank is lled with 79 :8 kg of FeTiMn. Instead of measuring the mass of the metal hydride to draw con- clusions about the mass concentration, the current hydrogen capacity can only be estimated using the pressure level. The temperature of the metal hydride is measured in one location. The 290 position of the sensor can be shown in Figure 10. For the simulation, the water temperature of the heat exchanger is utilized as input data. The supplied or extracted hydrogen mass ow is de ned as a constant value (Absorption: 6:6L min1; Desorption:36:5L min1). This mass ow is set as long as possible till the decreasing kinetic reaction process limits the mass ow through the valve. 295 As can be shown in case of desorption, the extracted hydrogen mass ow is decreased after 4 h due to the low loading status. The amount of hydrogen reacted decreases and this is why the e ect of an endothermic process does. The in uence of the heat exchange becomes stronger. This leads rapidly to an increased temperature inside the solid, which can be shown in Figure 9. 300 The comparisons of both simulated and measured data show an accordance of the process. The temperature process as well as the pressure evolution in- side the tank are reproduced with the simulation model and the approximated kinetic reaction coecients. Therefore, this study advocates the approach of a DoE for calibration crucial properties when there is no access to kinetic measure- 305 ment equipment. In particular, the approach is an appropriated opportunity to calibrate an existing tank design for further improvements 5. Conclusion The present study investigates solid-state hydrogen storage systems based on 310 metal hydrides such as an iron-titanium-manganese alloy (FeTiMn). A mathe- matical model is utilized to analysis the reaction behavior of this material. The aim is to obtain insights and an understanding of the processes inside the system components such as the pressure tank or the heat exchanger. 22 315 This study provides an equation which ts the measured pressure-composition- isotherms (PCIs) of FeTiMn. Therefore, the equilibrium pressure can be calcu- lated for any working temperature and state of charge. The simulation model requires thermodynamic properties of FeTiMn which have not been studied in available publications and therefore require to be determined. In this contri- 320 bution Van't-Ho isochores are deduced by using measured PCIs of FeTiMn to maintain the entropy and enthalpy of formation. These isochores repre- sent the equilibrium pressures which in uence the formation of metal hydride. The Van't-Ho equation de nes these isochores and involves the entropy  S as well as the enthalpy  H. With the aid of a tting tool the unknown 325 properties are calibrated ( S=109:88J K1, Havg. abs =29748J mol1; Havg. des=31212J mol1). Further reaction parameters are approximated by a design of experiments because there was no access to measurement equipment. The reaction coe- 330 cients are altered for several simulation cycles and then assessed by comparing to experimental data. The simulations show high concordance with the mea- surements given by an real metal hydride storage system ( kabs= 25kdes= 17). This supports the reliability of approximated parameters by a DoE for tank modeling and to achieve an understanding of the occurred processes. 335 The next steps are to investigate the usage of metal hydride storages in real applications. Question arises if it is possible to use metal hydride storages to supply enough energy in form of hydrogen. These questions are discussed in our following paper, which is actual in preparation [22]. 340 Acknowledgement This research was supported by GKN Sinter Metals GmbH. We thank our colleagues Bettina Neumann, Thomas Schupp, Dr. Markus Schneider and 23 Markus Laux for helpful discussions and Dominik Wilde for comments that greatly improved the manuscript. 345