How back reaction and hydrogen transport control the performance of hydrogen release from liquid organic carriers

TL;DR

LOHC-based hydrogen storage faces challenges from back-reaction and transport limitations that hinder dehydrogenation when bubbling is suppressed. The authors develop a reaction-diffusion model for a spherical catalyst pellet with an outer active shell, coupling dissolved and bound hydrogen via reversible kinetics and analyzing the system with non-dimensional DoH-based variables and Damköhler numbers. They identify two kinetic regimes (active vs inhibited) governed by external transport and back reaction, and provide an analytical expression for the inhibited flux in the $m=1$ limit, revealing a transition controlled by the non-dimensional length $\\lambda$ relative to the catalytic-layer thickness $h$. The findings explain disparate batch vs flow-through observations and offer design guidance for pellet microstructure and transport optimization, with applicability to other reversible reactions involving volatile products.

Abstract

Hydrogen, as a clean energy carrier, is a promising option for sustainable energy storage and utilization, yet its storage and transportation remain challenging. Liquid Organic Hydrogen Carriers (LOHCs) provide a potential solution by enabling the reversible chemical binding and release of hydrogen. However, recent experimental studies have revealed a puzzling inhibition of catalytic activity during LOHC dehydrogenation, associated with the absence of hydrogen bubble formation, reduced hydrogen production rates and significant variability across experiments. In this work, we derive a model to elucidate the mechanisms underlying this inhibition, taking into account both the reversible nature of the hydrogenation-dehydrogenation reaction and the role of transport phenomena. Our results demonstrate that efficient transport of hydrogen away from the catalytic pellet is essential to suppress back-reactions and thereby maximize the performance of porous catalysts. In particular, we demonstrate that two distinct kinetic regimes - with high or strongly inhibited hydrogen production - can arise depending on whether bubble nucleation is enabled or suppressed. Beyond LOHC systems, our findings are applicable to a broader class of reversible reactions, particularly those involving volatile products that can leave the liquid reaction medium in form of bubbles.

Figures (11)

• Figure 1: (a) Sketch of a catalytic pellet with the active sites, e.g. suitable surface atoms of the supported metallic nanoparticles, being schematically shown in red. These are homogeneously distributed in the active layer of thickness H of an egg-shell catalyst pellet. Dissolved hydrogen is indicated as shades of blue. (b) Simplified scheme of reversible dehydrogenation reaction. (c) Simplified model of a batch dehydrogenation experiment (distribution of dissolved hydrogen shown in blue). (d) Simplified model of the inlet region of a flow-through reactor.
• Figure 2: (a) Hydrogen flux density at the pellet surface for a given local degree of hydrogenation $c_{+}^{\mathrm{ex}}$ (see legend) and varying hydrogen oversaturation at the surface of the pellet $c_{H_2}^{\mathrm{ex}}$. (b) Hydrogen flux density at the pellet surface for $c_{+}^{\mathrm{ex}}\in [0.05;0.9]$, $c_{H_2}^{\mathrm{ex}}=1,2,5,12$ (black, blue, red, yellow triangles) and for $c_{H_2}^{\mathrm{ex}}\in [1;20]$$c_{H_2}^{\mathrm{ex}}=0.25,0.5,0.8,0.9$ (black, blue, red, yellow circles), collapsing upon a single curve. In both cases $\mathrm{Da}_+=10$. The other parameters are defined in Eq. \ref{['eq:default_pars']}.
• Figure 3: Ratio of hydrogen fluxes in the inhibited and active state, depending on the concentration of hydrogen outside of the pellet (a) for a fixed $\gamma=0.087$ and different values of the effective reaction order $m$ and (b) for a fixed $m=1.6$ and different values of $\gamma$. Dashed curves correspond to parameters defined by Eq.\ref{['eq:default_pars']} (H18-DBT at 573K). DoH outside of the pellet is $c_{+}^{\mathrm{ex}}=0.8$, $\mathrm{Da}_+=10$, $\epsilon$ and $h$ are defined in Eq. \ref{['eq:Da_def']}.
• Figure 4: Batch setup: (a) Hydrogen oversaturation $c_{H_2}^{\mathrm{ex}}$ and (b) local degree of hydrogenation $c_{+}^{\mathrm{ex}}$ in the pellet layer and (c) hydrogen flux in the inhibited state versus external transport parameter $\kappa$ for different $c_{+}^{\mathrm{out}}$ at $\mathrm{Da}_+=10$. Other parameters are defined in Eq. \ref{['eq:default_pars']}.
• Figure 5: Batch setup: (a) Ratio of the fluxes in the active and inhibited states versus $\mathrm{Da}_+$ in a batch setup with $c_+^{\mathrm{out}}=0.8$ and different values of the external transport parameter $\kappa$. (b) Hydrogen flux in the active (dashed) and the inhibited (solid) states as a function of $\mathrm{Da}_{+}$ for $c_+^{\mathrm{out}}=0.8$ and different $\kappa$. (c) Hydrogen flux in the active (dashed) and the inhibited (solid) states as a function of catalytic layer thickness $h$ for $c_{+}^{\mathrm{out}}=0.8$, $\kappa=1$, and varying $\mathrm{Da}_+$. Other parameters are defined in Eq. \ref{['eq:default_pars']}.