Hydrogen Storage Systems Modeling

The modeling framework was developed by the Hydrogen Storage Engineering Center of Excellence (HSECoE) to quickly and efficiently evaluate various materials-based hydrogen storage systems and compare their performance against DOE light-duty vehicle targets. The modeling approach enables the exchange of one hydrogen storage system for another while keeping the vehicle and fuel cell systems constant.

This framework was used to implement the integrated vehicle, the power plant, and the storage system models. The tool was used across the HSECoE to evaluate candidate storage system designs on a common vehicle platform with a consistent set of assumptions. An additional simplified version of the framework model was also developed that can quickly estimate optimal discharge kinetics, effective hydrogen capacities, system mass and volume, and heat removal requirements of various materials-based hydrogen storage system designs. Parameters obtained from these models can then be used as inputs into the detailed framework models to obtain an accurate assessment of hydrogen storage system performance.

The models are being updated and maintained beyond the life of the HSECoE to benefit research efforts outside of the HSECoE and allow university and laboratory researchers to assess the performance of their materials and compare the results to the DOE technical targets.

The Hydrogen 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 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 demand to the storage system. It also manages thermal balance and makes waste heat streams 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 auxiliary electrical power from the vehicle if needed, such as for heating and powering balance-of-plant components.

Hydrogen Vehicle Simulation Framework References

Vehicle Simulation Framework User Manual (2017)

System modeling methodology and analyses for materials-based hydrogen storage, International Journal of Hydrogen Energy (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, SAE World Congress (2012).

The design and evaluation of media-based hydrogen storage systems require the use of detailed numerical models and experimental studies, with a 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 as leader of the DOE Hydrogen Storage Engineering Center of Excellence.

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 uptake.

The model has been developed for rectangular and cylindrical geometries 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.

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 that 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.

Savannah River National Laboratory, as the leader of the HSECoE, developed a new detailed 3D model—the Metal Hydride Finite Element (MHFE) model—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) were set up (not currently available for download) 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 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.
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 to the 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 inputs to the model; (2) the output from the 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.

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 was 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, and the COMSOL model was applied to one of the UTRC prototype designs.

The bed model, available for download, has nine coolant tubes and eight 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 (e.g., pressure, temperature, velocity) as well as all the user-defined properties (e.g., species concentration, moles of hydrogen absorbed).

Metal Hydride Finite Element Model References

Integrated Hydrogen Storage System Model, SRNL Technical Report (2007)

Geometry, Heat Removal and Kinetics Scoping Models for Hydrogen Storage Systems, SRNL Technical Report (2007)

Hierarchical methodology for modeling hydrogen storage systems. Part I: Scoping models, International Journal of Hydrogen Energy (2009)

Hierarchical methodology for modeling hydrogen storage systems. Part II: Detailed models, International Journal of Hydrogen Energy (2009)

High Density Hydrogen Storage System Demonstration Using NaAlH4 Based Complex Compound Hydrides, United Technologies Research Center Technical Report (2007)

Pacific Northwest National Laboratory 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 need 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 that the wall thicknesses predicted by the estimation tool result in an acceptable stress state. The 3D finite element analysis 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.