Thermochemical water splitting is considered as an energy-efficient, low-cost process for hydrogen production. Among the large-scale, cost-effective and environmentally-attractive hydrogen production processes, the Sulfur-Iodine (SI) thermochemical cycle appears to be one of the most promising. In this cycle, iodine and sulfur dioxide are combined with water, forming hydrogen iodide and sulfuric acid, which are immiscible and can be readily separated. Then, the sulfuric acid is decomposed at about 850°C releasing the oxygen and recycling the sulfur-dioxide. Finally, the hydrogen iodide is decomposed at about 400°C, releasing the hydrogen and recycling the iodine. According to the flowsheet proposed by General Atomics [1] this cycle can be split into the following sections:
• Recycle Acids Generation (Section I):
[xI₂]_l + [SO₂]_g + [2H₂O]_l ↔ [2HI_x]_aq + [H₂SO₄]_aq
This reaction, named the Bunsen reaction, proceeds exothermically in liquid phase and produces two immiscible aqueous acid phases, with the dense phase containing HI_x and the light phase containing H₂SO₄. This phase split is the key to the cycle’s success, but the resulting liquid-liquid equlibrium (LLE) is difficult to model.
• Sulfuric Acid Concentration and Decomposition (Section II):
[H₂SO₄]_aq ↔ [H₂SO₄]_l
[H₂SO₄]_l ↔ [H₂SO₄]_g
[H₂SO₄]_g ↔ [H₂O]_g + [SO₃]_g
[SO₃]_g ↔ [SO₂]_g + [½O₂]_g
Experience from the sulfuric acid industry can be applied for the simulation of this section. Modeling uncertainty arises from the high temperatures of this section and the complex formation of H₂SO₄ and H₂O at high temperatures and/or concentrations.
• HI Concentration and Decomposition (Section III):
[2HI_x]_aq ↔ [2HI]_g + [(x-1)I₂]_l + [H₂O]_l
[2HI]_g ↔ [H₂]_g + [I₂]_g
[I₂]_g ↔ [I₂]_l
The main difficulties that have to be overcome in this section include the extraction of HI from the HI_x mixture because of the presence of an azeotrope in the mixture, the possibility of iodine precipitating as a solid (T_m = 113.6°C) and the strong immiscibility of the H₂O-HI-I₂ mixture.

It is evident from the above that the greatest challenge in simulating the SI process is modeling of the chemical equilibria in the major unit operations. In particular, special attention has to be paid to predicting the equilibria of the electrolytes’ partial dissociation and the stable phase split. A significant bottleneck in the modeling of this process is the empirical nature of the existing models for multi-electrolyte solutions and their restricted validity (low temperatures and pressures). The model applied for the calculation of the chemical equilibria has to be valid for temperatures up to 800°C. Furthermore, the prediction of speciation in the process sections, which is not among the traditional virtues of electrolyte thermodynamic models, is important for the simulation of thermochemical cycles. Finally, hydration and ions-water complex formation add further complexity to the thermodynamic modeling of the system.   

Among the existing electrolyte thermodynamic models, two are most likely to succeed in this modeling challenge: the electrolyte NRTL model [2] and the Pitzer model [3]. These two models have the ability to predict reaction and phase (vapor-liquid and liquid-liquid) equilibria, they include the effect of temperature and they can handle multiple-electrolyte solutions. As the ability of these models to extrapolate is of high importance for the SI process, in this work their thermodynamic consistency is extensively examined. Although the thermodynamic consistency of any excess Gibbs free energy model is a priori guaranteed, under its specific assumptions, the effect of these assumptions on the derivation of the excess Gibbs free energy that is used to calculate the activity coefficients can be crucial. A new model has been developed [4] based on the full analytical derivation of the electrolyte NRTL excess Gibbs free energy and without the simplifying assumptions that were used in the original electrolyte NRTL model [2]. The new model reduces to the original electrolyte NRTL for binary mixtures, whereas it retains its thermodynamic consistency and generality for any extension to mixed-solvent, multi-electrolyte solutions. Because of its generality and consistency, the new model possesses better extrapolation abilities and predicts accurately the speciation.

In all the chemical equilibrium models developed in this work, the Gibbs free energy minimization approach is used for finding the point of equilibrium. Because of the nonlinearity of the electrolyte thermodynamic models, the equilibrium constant method (i.e., the calculation of equilibrium using the equality of chemical potentials between products and reactants) may lead to multiple solutions and only those that minimize the total Gibbs free energy are correct. The minimization of Gibbs free energy is formulated as a nonlinear program (NLP), that is, the minimization of the nonlinear Gibbs free energy function that constitutes the electrolyte thermodynamic model subject to mass balance and electroneutrality constraints. The Gibbs free energy minimization approach is also followed for the simulation of the liquid-liquid splits in the process. Phase equilibria of multicomponent mixtures are modeled using a reinterpretation of the Gibbs tangent plane stability criterion via Lagrangian duality [5]. The starting point for this formulation is the natural primal problem of minimizing the Gibbs free energy subject to material balance. The stable phase split is the solution of the corresponding Lagrangian dual problem, providing a necessary and sufficient dual extremum principle.

One of the difficulties with modeling the SI cycle is the absence of parameters for the electrolyte thermodynamic models at the conditions of interest. Recently [6-13], experimental data have become available for some of the process stages, whereas much more are expected in the near future [1]. The fitting of model parameters (P_i) to experimental data using the Gibbs energy minimization approach (with respect to the components moles N_j) , results in a bilevel optimization problem [14]. That is, the models are fitted to the experimental data, by solving the following bilevel program:

min [discrepancy between predicted and observed system properties]
  P_i
s.t. min G
       N_j
      s.t. elemental balance + electroneutrality

In conclusion, a comprehensive framework has been developed that deals with all aspects of the thermodynamics of the SI cycle. Using this framework, accurate steady-state and dynamic models of this promising process can be developed, which will increase the understanding of the process and provide the ability to set design and operational targets.

References

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2.         Chen, C. C. & Evans, L. B. (1986) A Local Composition Model for the Excess Gibbs Energy of Aqueous-Electrolyte Systems. AIChE Journal, 32, 444-454.
3.         Clegg, S. L., Pitzer, K. S. & Brimblecombe, P. (1992) Thermodynamics of Multicomponent, Miscible, Ionic-Solutions. 2. Mixtures Including Unsymmetrical Electrolytes. Journal of Physical Chemistry, 96, 9470-9479.
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11.       Belaissaoui, B., Thery, R., Meyer, X. M., Meyer, M., Gerbaud, V. & Joulia, X. (2007) Vapour reactive distillation process for hydrogen production by HI decomposition from HI-I2-H2O solutions. Chemical Engineering and Processing, doi:10.1016/j.cep.2007.01.018.
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