Thermodynamic analysis of hydrogen tank filling. Effects of heat losses and filling rate optimization

https://doi.org/10.1016/j.ijhydene.2014.06.069Get rights and content

Highlights

  • Van der Waals and Redlich Kwong gases are in good agreement with NIST database.

  • The behavior of hydrogen and nitrogen differ significantly during the filling.

  • The gas temperature is sensitive to the heat transfer modeling in tank walls.

  • Heat losses should be maximized to increase the final mass of gas in the tank.

Abstract

A thermodynamic analysis of the refueling of a gaseous fuel tank and a thermal analysis of heat losses through tank walls is presented. The objective of the thermodynamic analysis is to compare the temperature and pressure evolutions coming from different equations of state and from thermodynamic tables. This comparison is performed with nitrogen and hydrogen and the compression is assumed adiabatic. It is shown that the ideal-gas assumption results in under-prediction of the tank temperature and pressure for hydrogen but in over-prediction for nitrogen. An approximate analytical expression of the Redlich–Kwong equation of state is given which is in very good agreement with thermodynamic tables. To handle heat losses, different approaches are used and compared. First, a global thermal conductance is introduced which allows deriving analytical expressions. Then, a thermal nodal modeling of tank walls is proposed to take into account thermal capacity effects. Finally a 1D semi-infinite modeling of the tank walls is presented. Finally, this model is used to optimize mass flow rate in order to limit the temperature rise during the filling process.

Introduction

Hydrogen is a promising energy carrier that may help human society to deal with energy issues thanks to its high specific energy density of about 39 kWh/kg. However its volumetric energy density of 3.5 kWh/m3 is such that it cannot be used under standard conditions. Various technologies have emerged for storing hydrogen [1] like compressed hydrogen, liquefied hydrogen, hydrides … Energy efficiency of these technologies is not constant but varies significantly [2], [3], [4]. One of them consists in storing hydrogen in a high-pressure tank. Under a pressure of 300 bar, the volumetric energy density becomes 800 kWh/m3 and reaches 1500 kWh/m3 at 700 bar. The benefit is significant but it is still far from common gasoline which provides a volumetric energy density equal to about 9000 kWh/m3 under standard conditions.

High pressure hydrogen storage requires tank designed for such pressure which involves some constraints of cost and safety. These tanks are classified from Type I to Type IV [5]. They differ in the structure and the materials used in the tank walls (Type 1: Metal tank, type 2: Metal tank with reinforcement by fiber wrapping, type 3: Metal tank with full reinforcement by fiber wrapping, type 4: Polymer tank with full reinforcement by fiber wrapping). In this work, only Type IV tank is considered. It is made of a plastic liner which ensures gas tightness and a composite layer which ensures mechanical stresses. In order to achieve comparable filling process time of today's gasoline vehicles, a complete filling with hydrogen should be performed in few minutes. This constraint involves the use of significant mass flow which induces critical temperature rise. To meet safety requirement, the current maximum temperature allowed in the hydrogen tank is currently 85 °C [6].

Concerning filling stations, different technologies are currently under development. Maus et al. [5] present four different types of filling station based on compressed or liquefied hydrogen reservoir and introduced some parameters of interest related to filling processes. Petitpas et al. [7] proposed a filling station based on a liquid hydrogen reservoir which avoids the use of mechanical compressors. The pressure rise is performed by heating cryogenic hydrogen. Common filling stations are based on a single or multiple stacks that are connected sequentially to the hydrogen tank that has to be filled. Compared to the single stack system, multiple stack system is more energy efficient since it does not require storing the whole mass of hydrogen at maximum pressure. It results that the compression work is lower. To keep the system simple, three stacks are often used, but in theory, increasing the number of hydrogen stack should decrease the temperature rise in the hydrogen tank, while minimizing the required compression work. Farzaneh-Gord et al. [8] shows that three stack systems achieve better state of charge, lower entropy generation but increased the filling time. Zheng et al. [9] proposed an algorithm to optimize the use of a three stack systems depending on the number of hydrogen tank to fill.

Simulating the hydrogen filling process is complex since it requires computing the velocity, temperature and pressure fields associated to a 3D turbulent unsteady compressible flow. Attempts have been made to predict the temperature of the gas using computational fluid dynamics (CFD) but generally some assumptions are made to simplify computations. For example, Zhao et al. [10] assumes a constant inlet flow mass, neglects buoyancy effects, and uses a 2D-axisymmetric geometry. Results are compared to experimental data provided by an experiment carried out in Ref. [11]. By interpolating multiple results, Zhao derives a simple analytical expression to evaluate the temperature rise with respect to some ambient condition and process related parameters. However, this expression may only be valid with the same hydrogen tank considered (length over diameter ratio of 3.5).

Similar assumptions are made by Dicken et al. [12]. Results are compared to temperature fields interpolated from a set of 63 thermocouples distributed throughout the hydrogen tank. An other 2D axisymmetric modeling is proposed by Li et al. [13]. Two hydrogen tanks, which differ in their length of diameter ratio (3.6 and 2.0), are considered. The influence of different constant mass flows is evaluated as well as some time-varying mass flows. A 3D modeling is achieved by Heitsch [14]. Results are compared to the experimental data given in Ref. [15]. Galassi et al. [6] performs 3D simulations up to 700 bar by using different pressure-rise rate and shows the effect of cold filling, which is one technology used to ensure the gas temperature does not exceed the limit temperature of 85 °C. An other comparison between 3D simulation and an experiment are given by Kim et al. [16]. The experimental setup consists in a type IV hydrogen tank and 6 thermocouples are used to evaluate the mean gas temperature. The influence of the initial pressure is investigated. Most studies mentioned previously involve a turbulence model. A comparison of 4 models is proposed by Suryan et al. [17].

CFD simulations allow computing the full field of fluid velocity and temperature which are not always necessary. Indeed, the temperature rise, with respect to external parameters, can be evaluated using simpler model such as 0D-models which derive from the energy conservation principle. 0D-Models assume that gas properties, i.e. temperature, pressure, density …, are homogeneous. The validity of these assumptions relies on many conditions, especially on the geometrical aspects of the hydrogen tank. Indeed, with low length over diameter ratio and from a thermal point of view, it appears acceptable to assume that temperature and pressure fields are homogenous, at least during the filling stage, i.e. before buoyancy effects become significant. This assumption become less relevant as the length over diameter ratio increases since it tends to increase temperature variations as shown by CFD analysis [10], [13].

0D-Models are generally dedicated to hydrogen tank only and neglects the filling station. Moreover, models developed by Hosseini et al. [18] and by Yang [19] assume that the input mass flow is constant. As mentioned by Farzaneh-Gord et al. [20], if the pressure differential between tank and reservoir is high enough (about twice the tank pressure), the gas flow is choked somewhere in the pipes of the filling station. Therefore, the mass flow depends only on the thermophysical state of the gas in the reservoir which is constant as long as the volume of the reservoir can be assumed infinity compared to the tank. In Refs. [18], Hosseini et al. evaluates the exergy destruction with respect to initials conditions by neglecting heat transfer through tank walls. Yang derives closed-form expressions for the temperature rise in a hydrogen tank for an adiabatic filling and for an ideal gas. To take into account heat losses through tank walls, a 2-temperature process is proposed and in order to handle non ideal behavior of hydrogen, a recent equation of state [21] is presented. Monde et al. developed a model based to simulate hydrogen tank filling with a multiple-stack filling station. Model outputs are in quite good agreement with experimental data. However, it appears clearly that model outputs are very sensitive to the internal heat exchange coefficient which is not well-unknown. Woodfield et al. [22] performed the same kind of study.

Whatever is the model, real gas behavior is modeled by using an equation of state. Nasrifar [23] compares eleven equations from Redlich–Kwong and Peng–Robinson families. This study shows that all these equations of state success in predicting compressibility factor, enthalpy and heat capacity in the temperature and pressure range encountered with compressed hydrogen storage system.

The first part of this study is devoted to the simulation of adiabatic filling using hydrogen or nitrogen. Results found with different equations of state, i.e. ideal gas, Van der Waals and Redlich–Kwong, are compared to thermophysical data obtained from the NIST Chemistry Webbook [24]. Even with a variable mass flow, these equations of state allow us to derive analytical expressions of the temperature and pressure rises. In the second part, different approaches to handle heat losses through tank walls are compared. In some cases, analytical expressions of the temperature rise are given. Finally, the optimization of the input mass flow is investigated. It consists in finding the mass flow that maximizes the mass of gas at the end of the filling process without exceeding the limit temperature of 85 °C.

Section snippets

Filling apparatus modeling

The filling apparatus is made of a reservoir assumed to be large enough so that the state of the gas is constant and defined by Pr, Tr (Fig. 1).

Let Et be the total energy of the gas inside the tank, it is the sum of the internal energy, the kinetic energy and the potential energy [25]:Et(t)=m(u+ec+ep)with{ec=1mc(m)22mep=1mgh(m)mWith m the mass of gas inside the tank, u the specific internal energy, ec the specific mean kinetic energy due to non-random motions of the particles of the gas,

Comparison of equations of state (EoS)

In the adiabatic case, heat losses from the inner gas to the tank walls are null (ϕ=0):ut+m˙mu=m˙mhrwithm(t)=m0+t=0tm˙(z)zandu(0)=u0

The solution is:u(t)u0hru0=1exp(0tm˙mt)=1m0m(t)

Heat loss modeling

Three different approaches to handle heat losses are now presented and compared. They differ in the way of taking into account the heat conduction in fuel tank walls. Concerning the inner boundary condition, i.e. between the gas and the liner, a heat transfer coefficient is introduced. Furthermore, in this section, only the ideal gas assumption is used since it is assumed main conclusions would still hold with other equations of state.

Comparison of heat losses modeling

In this section, two examples are presented to compare the three heat loss models presented above. For the first one, the mass flow m˙ is constant and equal to m˙0 (Fig. 5a) with m˙0=m˙0H2=3.57gs1 for hydrogen and m˙0=m˙0N2=50gs1 for nitrogen. For the second example, the mass flow is variable. Thick and continuous lines refer to gas temperatures and dash lines correspond to the inner surface temperature.

The semi-infinite model is used as the reference solution here, since it is based on an

Mass flow optimization

In the case of adiabatic H2-filling, the simple Eq. (7) shows that the specific internal energy depends only on m(t). It means that the optimization of the filling process is not possible with systems based on a single reservoir. The only way to minimize the temperature rise is to maximize heat losses through the tank walls. It is seen in Fig. 6 that a constant mass flow (thick dashed lines) is preferable to a three steps mass flow (thick continuous lines) introduced in Fig. 4. Indeed, the

Conclusion

A thermodynamic and a thermal analysis of the filling process of a gaseous hydrogen fuel tank have been presented. Some analytical expressions for adiabatic gas filling with time varying mass flow were derived for the ideal-gas, Van der Waals and Redlich Kwong gases. They are compared to a fourth model based on NIST database. It is shown that results found with Redlich Kwong and NIST database are in good agreement. It suggests that with the filling conditions involved in this work, specific

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