• Acceptability Envelope Tool released for metal hydride materials.
  • 3D Metal Hydride Finite Element model released.
  • Other models will be released in the near future.

What is the Metal Hydride Acceptability Envelope (AE)?

The design and evaluation of media based hydrogen storage systems require the use of detailed numerical models and experimental studies, with significant amount of time and monetary investment. Therefore it is important to have a scooping tool to screen candidate coupled media and storage vessel systems capable of achieving selected performance targets.

Savannah River National Laboratory, as leader of the DOE HSECoE, has developed such a tool, called the Acceptability Envelope.

The Acceptability Envelope tool can be used by researchers and scientists to determine which properties the system needs to have to achieve determined targets and compare different materials to each other. The code has been developed for metal hydrides and it provides a preliminary but precise idea on which materials can attain desired objectives (such as DOE targets). The results obtained can be used as inputs to more sophisticated models to develop a prototype design and predict the full-scale storage system behavior.


AE Model

The Acceptability Envelope is a one-dimensional model based on a steady state energy balance of the storage system considering the hydrogen charging process in a selected time range. The heat released during the charging process causes a temperature increase inside the bed material, which is evaluated by the model considering the balance between the thermal diffusion process inside the bed and the heat produced during the hydrogen up-take.



The model (.xlsx files format) has been developed for rectangular and cylindrical geometries (as shown in the picture) and it evaluates the relationship between media and vessel characteristics and the storage system performance targets.

The model is also extremely flexible and the input and output parameters can easily be switched, depending on the objective of the analysis being carried out.


More information can be found in the papers and presentations shown in the Progress Section. Anyone interested in having more details can contact us.

What is the Metal Hydride Finite Elements (MHFE) Model?

A full understanding of the complex interplay of physical processes that occur during the charging and discharging of a solid-state hydrogen storage system requires models which integrate the main phenomena. Such detailed models provide essential information about flow and temperature distributions and the utilization of the vessel itself. However detailed system simulations require the coupling of different complex physical phenomena often working against one another. In the past the models that have been developed tended to be either too limited in scope addressing either a limited number of physical phenomena simplifying the process or simplifying the bed geometry. A survey of these models, previously developed, can be found in Hardy 1.

The Savannah River National Laboratory, as the leader of the HSECoE, developed a new detailed 3D model (MHFE) based on a Finite Element approach. The model is valid for general metal hydride vessels.

The approach followed in developing the model is summarized here:

  1. Three simplified scoping models (for kinetics, scaling (geometry) and heat removal) have been set up (not currently available in the download section) in order to assess preliminary system designs prior to invoking the detailed 3D finite element analysis. Such simplified models can be used, along with the Acceptability Envelope (AE) model analysis, to perform a quick assessment of storage systems and identify those capable of achieving determined performance targets. The kinetics scoping model can be used to evaluate the effect of temperature and pressure on the loading and discharge kinetics, determining the optimum conditions for loading and discharge rates for the specific metal hydride and the maximum achievable loading. The geometry scoping tool can be used to calculate the size of the system, the optimal placement of heat transfer equipment and the gravimetric and volumetric capacities for the geometric configuration and the specific hydride material. The heat removal scoping model is used to calculate flow rates, pressure drops and temperature increases over the length of the cooling channels. More details about the scoping models are available in Hardy 2, Hardy&Anton 1.
  2. The MHFE model has been set up including energy (with heat and pressure work exchange), momentum and mass balances, along with chemical kinetics. To do that, the data available from the scoping models can be used as inputs tothe detailed 3D model. In particular: (1) the output from the geometry scoping tool can be used as inputs for the model geometry, or, alternatively, available data about bed dimensions can be directly used as inputstothe model; (2) the output from heat removal system scoping tool can be used as inputs for the energy balance equation or, alternatively data available about the heat transfer system (fluids, flow rates, pressures, velocities etc) can be used as inputs to the 3D model. More details about the 3D model are available in Hardy 1, Hardy&Anton 2.

MHFE Model

The Savannah River National Laboratory developed a new model applicable to a general metal hydride vessel, which is governed by the physical processes occurring as hydrogen is loaded into, or discharged from, the hydride. The model incorporates energy (with heat and pressure work exchange), momentum and mass balance, along with chemical kinetics for uptake and release of hydrogen.

  1. Energy Balance
    The energy balance equation accounts for:
    • Heat released during the exothermic and endothermic reactions occurring during uptake and release of hydrogen respectively
    • Pressure work
    • Convective heat transfer within the bed
    • Conductive heat transfer within the bed

  2. Momentum Balance
    The momentum balance equation (Darcy’s law) accounts for:
    • Pressure gradient (or hydrogen concentration gradient) which is the driving force for the gas flow within the bed
    • Ergun permeability equation
    • The void fraction and effective particle diameter

  3. Mass Balance
    The mass balance equation accounts for:
    • Hydrogen species source term (reaction rate) SH2 depending on temperature, pressure and composition of the solid phase
    • Dependence of reaction equilibrium on the state of the system

More details can be found in Hardy 1, Hardy&Anton 2.

A Base Case Study: Sodium Aluminum Hydride (MHFE-SAH)

One of the most promising metal hydride materials, studied all around the world, is Sodium Aluminum Hydride (SAH). A detailed 3D model for SAH based on the Finite Element approach has been implemented in COMSOL Multiphysics® Version 4.2a platform. Kinetics data were collected from the experiments previously carried out by United Technologies Research Center™ (UTRC) for their SAH prototypes (see Mosher 1) and the COMSOL® model has been applied to one of the UTRC prototype designs.


The bed model, here available in the Download section, has 9 coolant tubes and 8 tubes used for the injection of the hydrogen to be absorbed and desorbed.


The geometry of the model, implemented in COMSOL, is composed of a layer of hydride material located at sufficient distance from the axial ends of the bed, so that the axial symmetry conditions are periodic from the midplane of one fin to the midplane of the next adjacent fin.


The model can be used by researchers and scientists to see the detailed behavior of the SAH based storage system under different conditions. The COMSOL platform allows the user to post-process the data with all the predefined quantities (such as pressure, temperature, velocities, etc) as well as all the user-defined properties (such as species concentration, moles of hydrogen absorbed, etc). More details are available at Hardy 1, Hardy&Anton 2.


Metal Hydride Acceptability Envelope (MHAE)The MHAE allows the user to evaluate the distance (in rectangular or cylindrical coordinates) between two surfaces or walls inside the bed, containing the metal hydride material, needed to attain determined targets, with selected material properties. The file MHAERC refers to the rectangular coordinate model, while MHAECC refers to the cylindrical coordinate model.

Metal Hydride Finite Element - Sodium Aluminum Hydride (MHFE-SAH)MHFE-SAH is a 3D model, developed under COMSOL 4.2a, which allows the user to see the thermo-chemical behavior of a storage system composed of sodium aluminum hydride material. The storage bed is based on a shell-and-tube, finned heat transfer system, with the structure and geometry of the UTRC prototype.

Download Model