Mechanistic Studies of Liquid Metal Anode SOFCs II: Development of a Coulometric Titration Technique to Aid Reactor Design
Introduction
Solid oxide fuel cells (SOFCs) with liquid metal anodes (LMAs) have substantial potential for power generation. The advantages over combustion systems and other types of fuel cell have been reviewed (Toleuova et al., 2013). The technology is able to provide high efficiency and low environmental impact with flexibility regarding fuels, including solid fuel such as coal (Jayakumar et al., 2011). Development of this promising technology, including scale up to pilot plant and industrial systems, requires an in-depth understanding of the mechanism of operation and solutions to a number of technological challenges.
In order to facilitate analysis and interpretation, initial studies have been carried out with a simple system in which hydrogen is used as the fuel and the liquid metal electrode is operated in a potential region where it effectively behaves as an ‘inert’ solvent for dissolved gases. The previous paper (Part I) described the fundamental electrochemistry of such a LMA SOFC system (Toleuova et al., 2015). It was demonstrated that the oxidation of hydrogen takes place via a Chemical-Electrochemical mechanism, (so-called CE mode), whereby hydrogen undergoes fast dissolution, then rate-determining homogeneous oxidation by oxygen dissolved in the liquid tin, followed by diffusion-controlled anodic oxygen injection to replace oxygen removed by the chemical reaction. In summary, the process involves:
- •
Fast dissolution of hydrogen via Sievert’s law (Lee, 1976, Wagner, 1952, Campbell, 2008, Hosford, 2005):
- •
Homogeneous (rate-determining) oxidation of dissolved hydrogen by dissolved oxygen:
- •
Anodic injection of oxygen to replace that consumed in (2):
The oxygen injected diffuses into the bulk of the tin from the interface.
The assumptions made in developing the model were as follows:
- i)
The electrochemical kinetics of the electrode reaction are fast, so that the concentration of dissolved oxygen at the YSZ-tin interface is fixed by the applied potential and is not disturbed by the current flow.
- ii)
The concentration of dissolved hydrogen in liquid tin is the saturated concentration appropriate to the partial pressure of the hydrogen supplied (bubbled) as a gas and obeys Sievert’s law.
- iii)
Homogeneous oxidation of hydrogen by dissolved oxygen is the rate-determining step and is governed by a rate equation which is first-order with respect to monatomic oxygen.
- iv)
Under potentiostatic control, diffusion of oxygen away from the YSZ-tin interface to replace that removed by reaction with hydrogen occurs through a diffusion layer of constant thickness, , as a result of convection induced by bubbling and thermal effects.
- v)
The system is in quasi-equilibrium.
Consider the following: hydrogen is bubbled through the liquid tin at partial pressure p1’, a potential, E, is applied to the Sn / YSZ interface and eventually a steady current, i1, is observed. The partial pressure of H2 is then increased to p2’ and the current, i, increases with time and eventually stabilises at i2 (Fig. 1). Oxygen concentrations within the liquid tin are described schematically in Fig. 2.
In the theoretical treatment, hydrogen concentration is denoted by a single prime and oxygen concentration is denoted by a bar.
The rate of removal of oxygen via Reaction (2) is , (i.e. per unit volume of tin) where k1 is the rate constant for the reaction and V is the volume of tin.
The rate of injection of oxygen via Reaction (3) is (n=2). Thus the net rate of removal of oxygen via the two reactions is . The concentration of hydrogen, c’, for given hydrogen partial pressure, p’ is given by (according to Sievert’s law):where k2 is a constant for a given temperature (Sievert’s constant).
Expressing the total amount (gram atoms) of [O] in tin as , it follows that
Applying Fick’s first law to the diffusion of [O] from the interface, the flux, , is given by:where is the diffusion coefficient, A is the area of the interface and is the concentration gradient within the diffusion layer. So Eq. (6) becomes (see Fig. 2):
Equating the flux with current via Faraday’s law:
Eliminating between (7) and (8):
This will be written as:where k3 is given by:
In the steady-state situation, we have p’=p2’,, i=i2 and .
So using Eq. (5):
And from (10)
Eliminating i2 between (12) and (13) and rearranging:
Writing
Then
Note that is a function of p’ and ≤ 1. Likewise:
We may write:
Eliminating i between (5) and (10) for p’=p’2
From (18) and (19):
Then using Eq. (15)
Followed by (16):
Integrating:
And from (12) and (16):
A new key parameter (), herewith termed the Dynamic Oxygen Utilisation Coefficient, has evolved during the model development, the value of which is important for LMA-SOFC design.
The coefficient () is defined by Eq. (15) above and contains the dimensionless group, with similarity to the Damköhler number, which relates the chemical reaction timescale to the transport phenomena rate occurring in a system (Fogler, 2006, Madou, 2011).
The general definition of Damköhler number, Da, is given by the following ratio (Madou, 2011):where τC is the characteristic time of the chemical reaction and τM is the mixing time that can be controlled by hydrodynamics. In systems that include interphase mass-transfer (via diffusion), a second Damköhler number, DaII, is defined by the following ratio (Marin and Yablosnky, 2011):Where kw is the rate coefficient in m3(kgcat)−1s−1, kf is the mass-transfer coefficient in m s-1 and as is the specific external surface area of the reacting substrate in m2(kgcat)−1.
The dimensionless group, , together with Eq. (11) can be represented by the expression . At a given temperature, this term is dependent upon geometric factors (V/A), mass transfer factors (via δ/D which decreases with increasing degree of convection), and a kinetic factor (k1), complementary to the factors as, kf and kw respectively in the definition of DaII (see above).
The value of determines the output current of the cell, as shown in Eq. (26). The larger the value of k3 (i.e. large A; small δ) then tends towards unity; conversely, the smaller the value of k3 (i.e. small A; large δ) then tends towards small values with a limiting value of zero.
In this paper, a new method is proposed, namely Anodic Injection Coulometry (AIC), similar in principle to the well-known technique of anodic stripping voltammetry (ASV) (Copeland and Skogerboe, 1974), to determine . To this end, two related regimes of operation are proposed. These regimes are run in a mixed mode (i.e. potentiostatic and open-circuit), whereby electrode potential is switched between a fixed value E and open-circuit. During the open-circuit periods, hydrogen reacts with oxygen dissolved in tin according to a Chemical-Electrochemical (CE) mechanism (Toleuova et al., 2015). In the first regime (Regime 1) the flow of H2 into the tin is constant, whereas in the second (Regime 2) it is intermittent. This method applies theory developed specifically for each regime. An example of the application of this method for measurement of is presented.
Section snippets
Experimental
The work employed a SOFC with liquid tin anode. A schematic of the apparatus employed in this work is shown in Fig. 3 and is described as follows. Dry argon was supplied to the oxygen sensor (Kent Industrial Measurements, UK) and then downstream was mixed with hydrogen (both gases were zero grade, BOC, UK) prior to being supplied to the cell (Fig. 4) held at operating temperature (780 oC) by an electric furnace (Carbolite, UK). Gases entered and exited the cell via alumina tubes, the lower end
Determination of the Dynamic Oxygen Utilisation Coefficient using Anodic Injection Coulometry
In this paper, a technique, namely Anodic Injection Coulometry (AIC) (with similarities to anodic stripping voltammetry), is proposed as a method for determination of the Dynamic Oxygen Utilisation Coefficient, , which evolved out of the model for hydrogen oxidation in LTA SOFC operating in the Chemical-Electrochemical mode as shown above. The method proposes AIC applied under two different modes of oxygen injection (termed Regimes 1 and 2). Subsequent analysis of the experimental data in
Conclusion
Operation of a liquid metal anode SOFC fuelled with hydrogen via a Chemical-Electrochemical mechanism was investigated using the newly-proposed Anodic Injection Coulometry technique applied in two regimes of operation. The technique allows determination of the Dynamic Oxygen Utilisation Coefficient, , which has important implications with regard to design and operation of liquid metal anode SOFCs. The parameter contains a new dimensionless number, which is similar to the Damköhler number.
Acknowledgements
The authors would like to thank Nazarbayev University and the Government of Republic of Kazakhstan for the BOLASHAK Scholarship for Dr. Aliya Toleuova and the EPSRC Supergen Fuel Cells programme (EP/G030995/1) and EPSRC projects (EP/J001007/1, EP/M014045/1 and EP/M014371/1), for supporting the research in the UCL Electrochemical Innovation Lab. Shearing recognises the Royal Academy of Engineering for support. We also acknowledge Prof. Ted Roberts (University of Alberta) for valuable technical
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2017, ECS Transactions