Modeling Efforts

As part of the H2SEs modeling effort, it was found useful to develop simplified models that can quickly estimate optimal loading and discharge kinetics, effective hydrogen capacities, system dimensions, and heat removal requirements of various materials based hydrogen storage system designs. Parameters obtained from these models were then used as inputs into the detailed models to obtain an accurate assessment of system performance that includes more complete integration of the physical processes. In addition, to meet the objectives of the Center, there was a need to quickly and efficiently evaluate various materials based storage systems and to compare their performance against DOE light duty vehicle targets. To accomplish this task, a modeling approach was created that enabled the exchange of one hydrogen storage system for another while keeping the vehicle and fuel cell systems constant. As such a modeling “framework” that was used for system evaluation and comparison by the Center was developed. The framework was used to implement the integrated vehicle, the power plant, and the storage system models. This framework tool was used across the engineering center to evaluate candidate storage system designs on a common vehicle platform with consistent set of assumptions.

It was felt, by DOE, that these models and the modeling framework could provide benefit to research efforts outside of the HSECoE and therefore should be made available to university and laboratory researchers working in this area. Below are select models, including the center modeling framework, that are available for download and use by the broad research community. Model descriptions, a user’s manual and presentations detailing the models validation are also available for download below. These models are open for use by material developers and storage system designers, but caution should be used when applying these models to materials and operating conditions that have not been validated. Please send any questions or comments to the technical assistance e-mail provided.

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The H2 Vehicle Simulation Framework is a MATLAB/Simulink tool for simulating a light-duty vehicle powered by a PEM fuel cell, which in turn is fueled by a hydrogen storage system. The framework is designed so that the performance of different storage systems may be compared on a single vehicle, maintaining the vehicle and fuel cell system assumptions.

The Framework is composed of a vehicle module, a fuel cell module, and a hydrogen storage module. The figure below shows these components and the main responsibilities and interfaces.

The vehicle module computes demand for a given drive cycle. Power demand is based on acceleration, aerodynamic drag, rolling resistance and component efficiencies. The drive cycles are repeated until some failure condition is encountered. This could be that the hydrogen has been depleted, the flow rate is insufficient, or some components are undersized for the vehicle's demand.

The fuel cell block's responsibility is to translate power demand from the vehicle into hydrogen demant to the storage system. It also manages thermal balance and makes waste heat stream available for harvesting by the storage system. Note that this is not a fuel cell sizing tool: The performance curve is chosen to match DOE targets for efficiency (50% at rated power, 60% at 20% of rated power).

The hydrogen storage system responds to hydrogen flow demands from the fuel cell system. It may also request auxilliary electrical powr from the vehicle if needed, such as for heating and powering balance-of-plant components.

More details may be found in the user manual as well as in Pasini et al. (2012) and Thornton et al. (2012).

Click here to view "Vehicle Simulation Framework User Manual"J.M. Pasini, B.A. van Hassel, D.A. Mosher, and M.J. Veenstra (2012), "System modeling methodology and analyses for materials-based hydrogen storage." Int. J. Hydrogen Energy 37, pp. 2874-3884.

M. Thornton, J. Cosgrove. M.J. Veenstra, and J.M. Pasini (2012), "Development of a vehicle-level simulation model for evaluating the trade-off between various advanced on-board hydrogen storage technologies for fuel cell vehicles", 2012 SAE World Congress, Detroit.

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.

The Acceptability Envelope tool was developed by Savannah River National Laboratory (SRNL), as leader of the DOE Hydrogen Storage Engineering Center of Excellence (HSECoE).

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.

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 select 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 file format) has been developed for rectangular and cylindrical geometries (as show in the figure) 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.

Find more information by reviewing our past presentations.

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.
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.

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.

PNNL Tank Mass Estimator ("Tankinator")

PNNL has developed a simple computational tool for estimating the mass and material composition of cylindrical Type 1, Type 3, and Type 4 vehicular hydrogen storage tanks. This tool is useful for cross-comparison of various pressure vessel types, to estimate gravimetric, volumetric, and cost performance of hypothetical tanks in the conceptual phases of design. The HSECoE has considered a broad range of storage conditions for on-board hydrogen storage, from cryo-compressed to the high temperature ranges. The Tankinator tool provides an estimate of basic tank geometry and composition from a limited number of geometric and temperature inputs. This estimate covers the tank shell material only; all other component masses needed to be added to determine full system mass.

It is important to emphasize that Tankinator is only an estimation tool. This is achieved by estimating the necessary vessel wall thickness in the cylindrical portion of the tank based largely on the classic thin-walled pressure vessel hoop stress formula. End cap geometry is assumed to be perfectly hemispherical, with wall thicknesses equal to the cylindrical section.

It has been verified through finite element analysis (FEA) that the wall thicknesses predicted by the estimation tool result in an acceptable stress state. The 3D FEA models assume the same simplified tank geometry as the spreadsheet, and merely confirm that stress in the pressure vessel wall remains below material allowable limits. For Type 1 tanks an eighth symmetry model of the tank was used. For Type 3 and Type 4 tanks, a 3D ring model was used, which represents the cylindrical portion of the tank while not specifically modeling the end geometry.

Additional comments on each tank estimate type are included in the model.

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. This model requires Microsoft Excel.

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.

H2 Tank Mass and Cost Estimator ("Tankinator"): This tool is useful for cross-comparison of various pressure vessel types, to estimate gravimetric, volumetric, and cost performance of hypothetical tanks in the conceptual phases of design. The "Tankinator" tool provides an estimate of basic tank geometry and composition from a limited number of geometric and temperature inputs. This model requires Microsoft Excel.

H2 Vehicle Simulation Framework: The H2 Vehicle Simulation Framework is a MATLAB/Simulink tool for simulating a light-duty vehicle powered by a PEM fuel cell, which in turn is fueled by a hydrogen storage system. The framework is designed so that the performance of different storage systems may be compared on a single vehicle, maintaining the vehicle and fuel cell system assumptions. This model requires Matlab and Simulink.

Note: 64 bit Matlab users, a compiler is required. Please direct software configuration questions to Mathworks support. As an alternative, 32 bit Matlab packages are distributed with an appropriate compiler.

Download the Vehicle Simulation Framework User Manual

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