Efficiency of non-optimized direct carbon fuel cell with molten alkaline electrolyte fueled by carbonized biomass

Journal of Power Sources 321 (2016) 233e240

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Efficiency of non-optimized direct carbon fuel cell with molten alkaline electrolyte fueled by carbonized biomass A. Kacprzak*, R. Kobyłecki**, R. Włodarczyk, Z. Bis Department of Energy Engineering, Faculty of Environmental Engineering and Biotechnology, Czestochowa University of Technology, ul. Brzeznicka 60a, 42200 Cze˛ stochowa, Poland

h i g h l i g h t s
The direct carbon fuel cell (DCFC) with molten hydroxide electrolyte was investigated.
The energy, voltage and fuel utilization efficiencies of DCFC were investigated.
Binary alkali hydroxide mixture (NaOH-LiOH, 90e10 mol%) was used as electrolyte.
Biochar of apple tree origin carbonized at 873 K was used as fuel.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 November 2015 Received in revised form 26 April 2016 Accepted 29 April 2016 Available online 7 May 2016

The direct carbon fuel cells (DCFCs) belong to new generation of energy conversion devices that are characterized by much higher efficiencies and lower emission of pollutants than conventional coal-fired power plants. In this paper the DCFC with molten hydroxide electrolyte is considered as the most promising type of the direct carbon fuel cells. Binary alkali hydroxide mixture (NaOH-LiOH, 90e10 mol%) is used as electrolyte and the biochar of apple tree origin carbonized at 873 K is applied as fuel. The performance of a lab-scale DCFC with molten alkaline electrolyte is investigated and theoretical, practical, voltage, and fuel utilization efficiencies of the cell are calculated and discussed. The practical efficiency is assessed on the basis of fuel HHV and LHV and the values are estimated at 40% and 41%, respectively. The average voltage efficiency is calculated as roughly 59% (at 0.65 V) and it is in a relatively good agreement with the values obtained by other researchers. The calculated efficiency of fuel utilization exceeds 95% thus indicating a high degree of carbon conversion into the electric power. © 2016 Elsevier B.V. All rights reserved.

Keywords: Direct carbon fuel cell DCFC efficiency Molten hydroxide electrolyte Biochar Carbon anode

1. Introduction The direct carbon fuel cell (DCFC) is a power generation device converting the chemical energy of carbon directly into electricity by electrochemical oxidation of the fuel [1]. The basic structure of a direct carbon fuel cell is identical to any of the other fuel cells. The only difference is that the anode chamber is supplied with a solid carbonaceous fuel (e.g. hard coals, biomass-derived biochars, active carbons, carbon black, graphite, coke, etc.) that is oxidized directly at the electrode surface. There are four basic families of direct carbon fuel cells under

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (A. Kacprzak), [email protected] (R. Kobyłecki). http://dx.doi.org/10.1016/j.jpowsour.2016.04.132 0378-7753/© 2016 Elsevier B.V. All rights reserved.

development which generally differ with electrolyte types that can be either molten carbonates [2e7], solid oxygen ion conducting ceramics [8e12] aqueous [13] or molten hydroxides [14e20]. Also a composite electrolytes (so-called hybrid electrolytes) are widely used in DCFC prototypes [21e25]. The DCFC technology is relatively simple compared to other fuel cell technologies and requires no expensive preparation of any gaseous fuel, as well as accepts all carbonaceous substances as potential fuels. Most carbon fuel materials used in DCFCs are granular activated carbon, graphite, carbon black, hard and brown coal, charred biomass, or organic wastes. Over the past few years, more attention has been focused upon the use of biomass as fuel in the direct carbon fuel cells [4,7,13,17,26,27]. Biomass in its ‘raw’ state does not possess suitable chemical and physical properties for DCFC and thermal treatment (pyrolysis, hydrothermal carbonization, or torrefaction) is required to convert biomass into a

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carbonaceous product (biochar or charcoal) being a suitable fuel for DCFC anode. Many of previous works investigated the effect of char chemistry and carbon structure on the electrochemical performance but no papers have been published so far where the efficiency of the DCFC with molten alkaline electrolyte and fueled with granulated carbonized biomass (biochar) have been reported. The presentation and discussion of the efficiency of that type of nonoptimized fuel cell is the main goal of this paper. In this paper the direct carbon fuel cell with molten binary eutectic NaOH/LiOH electrolyte at temperature 723 K is considered due to its advantages [14], such as high ionic conductivity, higher electrochemical activity of carbon (higher anodic oxidation rate and lower overpotentials) and higher efficiency of carbon oxidation due to the lower operating temperature (the dominant product of carbon oxidation is CO2 vs. CO). Accordingly, the DCFC may be operated at lower temperatures (roughly 673e873 K) and thus cheaper materials may be used to manufacture the cell. Moreover, the theoretical maximum efficiency of carbon conversion in the DCFC is 100% as described in Section 2.1, but practical efficiencies have been demonstrated at roughly 40e60% (cf. Section 4). 2. Thermodynamics and efficiency of DCFCs 2.1. Theoretical efficiency Conventionally, chemical energy of carbonaceous fuels is first converted to heat, which is then converted to mechanical energy and then can be converted to electrical energy. For the thermal to mechanical conversion, a heat engine is conventionally used. Maximum efficiency of a heat engines is limited by the Carnot cycle efficiency expressed as:

TL TH

hC ¼ 1e

(1)

where TL and TH are the heat rejection and heat addition reservoir temperatures, respectively. Equation (1) showed that the efficiency of the heat engine depends on the temperatures of the reservoirs as shown in Fig. 1. For a steam engine operating with superheated steam of TH ¼ 700 K and release of the exhausted steam into a medium having an ambient temperature TL ¼ 298 K, the maximum efficiency according to Equation (1) is about 57.4%, so nearby half of the thermal energy is irretrievably lost. In a direct carbon fuel cell the electrochemical reaction between carbonaceous fuel and

0.8 0.7 0.6 0.5 0.3

Theoretical efficiency: Carbon fuel cell 5 Hydrogen fuel cell (pH2=10 Pa)

0.2

Carnot heat engine (T1 = 298K)

0.4

500

700

900

1100

1300

(2)

Consequently, DCFCs convert chemical energy directly into electrical energy so the theoretical efficiency (hth) for electrochemical conversion of fuel, operating reversibly, is then:

hth ¼

DG TDS ¼1 DH DH

(3)

where:

DG is the Gibbs free energy change of reaction (2) which represents the maximum available work potential (under constant temperature and pressure conditions), DG700K ¼ 395.37 kJ mol1 [28], DH is the enthalpy change of reaction (2) which represents the total chemical energy available in the fuel, DH700K ¼ 393.95 kJ mol1 [28], TDS is the inevitable entropy changes associated with the overall reaction (2) (this term represents the amount of heat that is produced by a fuel cell operating reversibly), T is the temperature of isothermal electrochemical conversion of fuel in DCFC, DS is the entropy change. The Gibbs free energy change can be expressed by the relation (4) which also represents the maximum electrical work (Wel) obtainable in a fuel cell operating at constant temperature and pressure.

DG ¼ EnF ¼ Wel

(4)

where E is ideal fuel cell potential (equal to the open circuit voltage (OCV) of the cell), n is the number of electrons involved in the charge transfer reaction (n ¼ 4 for reaction (2)) and F is Faraday’s constant (96485.3 C mol1). Equation (4) can be easily transformed to the formula for OCV:

(5)

Taking the above into account the theoretical efficiency of fuel cells is free of Carnot cycle limitations and may approach 100% (cf. Fig. 1). Thermodynamic efficiency of the DCFC calculated by Equation (3) may theoretically exceed 100% (hth ¼ 100.4% at 700 K) since the oxidation of elemental carbon into gaseous CO2 is accompanied by almost no entropy change (DS ¼ 2.25 J K1 mol1 at 700 K) but practical operational efficiencies of the cells are lower. Moreover, the efficiency of DCFC show almost no relationship to temperature compared with, for example, hydrogen fuel cell.

0.9

Efficiency [-]

C(s) þ O2(g) / CO2(g)

E ¼ DG=nF ¼ 1:024V

1.0

0.1 300

oxidizing agent (pure oxygen or air), that produce electricity, take place directly at the electrodes excluding the combustion or the moving machinery associated with conventional heat engines. The reaction of carbon fuel on the anode side of the DCFCs is complete oxidation of carbon by oxygen ions with the release of four electrons and CO2. Therefore for the DCFC to operate at its maximum efficiency the overall reaction must be:

2.2. Practical efficiency

1500

Temperature [K] Fig. 1. Example efficiency calculations of the carbon fuel cell, hydrogen fuel cell and Carnot heat engine for various temperatures.

The theoretical efficiency of the fuel cell (cf. Equation (3)) can be obtained only in case of perfect reversibility of processes occurring in it. This is related to infinitely small current flowing in the electric circuit of the cell. For practical purposes so small current drawn from the cell is insufficient. On the other hand, increasing the current, and thus the power, decreases the efficiency of the cell via a

A. Kacprzak et al. / Journal of Power Sources 321 (2016) 233e240

losses such as polarization of electrodes, internal resistance etc. Therefore, the cell designing process should adopted a compromise between the power and efficiency of the cell. Most often cells are designed for such constant load for which power of the cell is less than the maximum but performance is still acceptable for the user. The presence of losses causes that not all Gibbs free energy (DG) is converted into electrical energy (Wel). Therefore, it is very important to choose the right method of calculating the operational ef-

Z

hfc ¼

(LHV or HHV)fuel in, (LHV or HHV)fuel out e lower (LHV) or higher (HHV) heating value of a fuel before and after experiment, respectively, kJ kg1, wtfuel in, wtfuel out e weight of fuel before and after the cell operation, respectively, kg. Taking into account the Equations (6)e(8) the following relation was obtained:

t

UIt dt ðLHV or HHVÞfuel

0

in $wtfuel in

 ðLHV or HHVÞfuel

Pel Q fuel

(6)

The electrical work can be easily calculated from the relationship:

Zt Pel ¼

UIt dt

(7)

Equation (9) describes the practical efficiency of DCFC as the ratio of electricity (energy in joules) produced divided by the energy value of fuel (joules) consumed for electricity production. 2.3. Voltage (electric or load) efficiency For convenience, the efficiency of an actual fuel cell is often expressed in terms of the ratio of the electric power (product of stack voltage and stack load, Pel) to the consumed fuel power (Pfuel, consumed) what is known as the voltage or electric efficiency (hv) and is given by equation:

hv ¼

hv ¼

U e the average operating cell voltage, V, I e the electric current in electric circuit with fuel cell, A, t e the time of cell operation, h, The chemical energy of the fuel is either referred to the HHV (higher-heating value, also known as the gross calorific value) or the LHV (lower-heating value, also known as the net calorific value). The HHV is the heating value directly determined by calorimetric measurement, while the LHV is calculated with certain formula taking into consideration moisture and hydrogen content in the fuel. Since in practical applications the moisture and water products are usually released to the atmosphere in the gas phase the LHV is commonly used to calculate the process efficiency. The calculation of the efficiency based on the HHV is usually carried out for some theoretical or detailed calculations. For the convenience of the reader in this paper the calculations of the efficiency were related to both LHV and HHV. Finally the chemical energy of the reacted fuel can be estimated from the equation: in $wtfuel in

 ðLHV or HHVÞfuel where:

out $wtfuel out

U E

(11)

1.2 1.0

ηv = 99%

0.8 ηv = 49%

0.6 0.4 0.2 0.0

(8)

(10)

consumed

The voltage efficiency is a consequence of the chosen of DCFC operating point (cf. Fig. 2). For example with no current flowing, the cell voltage is about 1 V; this value is referred to open circuit voltage (E ¼ 1.024 V) so the voltage efficiency value is about 99%. If, however, the load draws a current the cell voltage will be lower (e.g.

Cell voltage [V]

where:

Pel Pfuel;

The electric efficiency can also be easily expressed as ratio of average operating cell voltage (U) to the ideal cell voltage (E):

0

Q fuel ¼ ðLHV or HHVÞfuel

(9)

out $wtfuel out

ficiency of the cell which, as is known, is not limited by Carnot cycle efficiency. Tested DCFC is supplied by carbon fuel, which is most commonly burned in power boilers to convert the chemical energy into heat, and then into electrical energy. Accordingly, it is advisable to reference electric energy generated by the DCFC to the heat obtained by the process of carbon combustion. Therefore, actual DCFC energy efficiency (hfc) can be defined as the ratio of measured electrical work (Pel) and the chemical energy of fuel consumed during operation of the cell (Qfuel):

hfc ¼

235

Current [I]

Fig. 2. Typical polarization curve for a direct carbon fuel cell.

236

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0.5 V) and voltage efficiency value will be about 49%. Fig. 2 illustrates, if current is increased the voltage and voltage efficiency will drop. Thus the chosen operating point of the cell determines voltage efficiency. To achieve an efficiency of e.g. 80%, the operating voltage must be no lower than about 0.8 V. It is also worth mentioning that the actual cell voltage is often less than the ideal cell voltage. In real conditions the theoretical voltage of the DCFC with molten alkaline electrolyte is determined by the Nernst Equation (12) which provides a relationship between the ideal standard potential (E ) for the cell reaction and the ideal equilibrium potential (EN) at other partial pressures of reactants and products.

EN ¼ E þ

    pO2 RT ln nF pCO2

(12)

where: R e universal gas constant, R ¼ 8.3145 J mol1 K1, pO2, pCO2 e partial pressures of oxygen and carbon dioxide. Based on the Equations (10) and (11) we can calculate a degree of conversion of chemical energy content in reacted elemental carbon directly to electricity. This assumption is correct for the case where Pfuel, consumed determines the amount of energy contained in reacted elemental C and when all of carbon is consumed in its entirety to produce electrons. This part of the carbon energy that was used for electricity production can be expressed by the equation:

Pfuel; consumed ¼

  jDH700 j $1000$ wtfuel in Cdin  wtfuel out Cdout M

where: jDH700 j M $1000

e the chemical energy of elemental carbon, z32800 kJ kg1, Cdin , Cdout e the carbon content in the fuel (in the dry state) before and after the test, g g1. Thus, by using Equations (7), (10), (11) and (13) can be written an equation for electric efficiency (hv.fc):

hv:fc ¼

Pel Pfuel; consumed

¼

Z M n$F

t

It dt expected carbon consumption 0 ¼ hf ¼ actual carbon consumption wtC in  wtC out

(15)

where: M e the molecular weight of carbon, M ¼ 12.01 kg kmol1, wtC in, wtC out e weight of carbon before and after the cell operation, respectively, kg. 3. Experimental

(13)

Z

has introduced the fuel utilization efficiency (hf), often called coulombic efficiency or faradaic efficiency, which is a measure of how much fuel that is entering the fuel cell is actually consumed by the electrochemical reaction. With hydrogen or other gaseous fuels such as CO, there is increasing fuel dilution with product gases forming on the surface of the anode and leading to kinetic and diffusion limitations for cell reactions and also have an effect on the actual cell voltage. Other factors that may lead to lower fuel utilization is parasitic leakage of fuel through the solid electrolyte (e.g. membrane) without current generation. In a DCFC, all the carbon fuel entering the cell may convert to electricity at a fixed voltage, because the reaction substrate and product (CO2) are in a separate phases (gas and solid), so their separation is easy and the fuel utilization can be almost 100%. In practical terms, the fuel utilization will not necessarily have a value of 100% because at high temperatures (especially above 923 K) some of the carbon may be chemically converted to CO via the Boudouard reaction (C þ CO2 ¼ CO). Generally, fuel utilization efficiency for a DCFC operated in batch mode can be calculated using the following formula [29]:

t

UIt dt 0   32800 wtfuel in $Cdin  wtfuel out $Cdout (14)

3.1. Electrolyte and fuel The binary eutectic mixture (90e10 mol%) of alkaline earth metal hydroxides NaOH and LiOH (supplied by POCH corp.) was selected for the investigations. The fuel used for the investigation was biochar derived from the carbonization of apple tree chips. In order to produce the biochar from the ‘raw’ fuel the biomass sample was crushed, then sieved (particle size <0.5 mm), and finally charred in laboratory electrical furnace at 873 K for 30 min. Biochar was analyzed according to Polish standards with respect to their ultimate and proximate analysis. The ultimate analysis was conducted with the use of Leco TruSpec CHNS analyzer, while automatic isoperibolic bomb calorimeter (model C2000 Basic, IKA WERKE, Germany) with automatic temperature control was used to determine the HHV of the samples according to European Standard UNI EN 14918:2010. The results of the analyses are summarized in Table 1. 3.2. DCFC test setup

2.4. Fuel utilization efficiency (coulombic efficiency or faradaic efficiency) Usually, not all of the mass of the fuel supplied to a fuel cell is used for the electric charges (coulombs) producing. Therefore, it

The experiments were conducted in a laboratory-scale DCFC test cell shown schematically in Fig. 3. The cell was manufactured from nickel and nickel alloys. The anode and cathode chambers were separated in order to prevent

Table 1 Main parameters of the biochar chosen for DCFC efficiency investigation (all values are given for a “dry” state). Ultimate analysis (wt%)

Biochar *

Proximate analysis

C

H

N

S

O*

Ash (wt%)

Volatile matter (wt%)

HHV (MJ kg1)

80.33 ± 0.16

2.80 ± 0.02

1.91 ± 0.13

0.00

4.31 ± 0.50

10.65 ± 0.19

16.81 ± 0.69

29.55 ± 0.14

Oxygen calculated by difference.

A. Kacprzak et al. / Journal of Power Sources 321 (2016) 233e240

237

Fig. 3. The outline of the experimental DCFC setup.

any mixing at the gases (CO2 above the anode and excess air above the cathode). The main cell was manufactured from Nickel® 201. The anode was also made from Nickel® 201, while the cathode was Ni-based Inconel® alloy 600. The details of configuration and the operating mechanism of DCFC cell was described elsewhere [15e18]. In our DCFC, as well as in all fuel cells that use a molten hydroxide electrolyte, general cell reactions are: Anode reaction: C(s) þ 4OH(electrolyte) / CO2(g) þ 2H2O(g) þ 4e(16) Cathode reaction: 4e þ O2(g) þ 2H2O(g) / 4OH(electrolyte)

(17)

Overall reaction: see reaction (2) The hydroxyl ions (OH) produced by reaction (17) at the cathode surface are transferred through the molten electrolyte to the anode, where they can electrochemically oxidize the carbon fuel (16). In this reaction, a carbon dioxide and water byproducts are given off as well as four electrons. High ionic conductivity and low melting temperature of hydroxide eutectics allows that cell to operate at intermediate temperatures in the range 673e923 K, where full oxidation of carbon to CO2 is thermodynamically favorable as opposed to the partial oxidation product CO.

Fig. 5. Voltage (black colored) and power (red colored) changes plotted versus time during the DCFC efficiency test. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

3.3. Fuel cell efficiency test methodology The experiments described in the present paper were conducted in a laboratory-scale facility shown in Fig. 4. The efficiency investigation of DCFC was conducted for biochar

Fig. 4. The picture of the laboratory-scale testing facility for DCFC.

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A. Kacprzak et al. / Journal of Power Sources 321 (2016) 233e240

Table 2 Biochar main properties before and after the DCFC experiment (all values are given for a “dry” state). Weight [g]

Biochar before test Biochar after test

4.1089 3.4314

Elemental carbon content [g g1]

[g]

0.803 0.826

3.2994 2.8343

Table 3 The efficiency of electricity generation from biomass for different energy technologies [32]. Technology

Efficiency, LHV [%]

Typical size [MWe]

Co-firing Dedicated steam cycles IGCC Gasification þ engine CHP Stirling engine CHP

35e40 30e35 30e40 25e30 11e20

10e50 5e25 10e30 0.2e1 <0.1

of the particle size of 0.18e0.25 mm. The tests were carried out for the binary eutectic NaOH/LiOH electrolyte at a temperature of 723 K. The air flow rate supplied to the cathode was 8.3  106 m3n s1 controlled by a thermal mass flow controller (Brooks 4850) witch local operator Interface (LOI) to view, control and configure the control device. The overall testing time was 12 h. During the experiment, the external load was adjusted to maintain the measured voltage in the range of 0.6e0.7 V. After the test the anode with fuel was slowly cooled to ambient temperature, then it was placed in glass container filled with de-ionized water and kept there for 4 h in order to get the solidified electrolyte removed. After this time the mixture was filtered through a filter paper and then repeatedly washed with de-ionized water and HCl solution to remove and neutralize any residual hydroxide. Biochar was then dried in a laboratory convection oven for 6 h. Finally, the recovered fuel sample was analyzed to determine the HHV and for carbon and hydrogen content. The lower heating value (LHV) was calculated from HHV using the equation:

ðw þ 8:94HÞ LHV ¼ HHVe2442$ 100

(18)

where: 2442 e the heat of evaporation of water in J g1 at 298 K, w e percentage concentration of water in fuel, H e percentage concentration of hydrogen in fuel. Biochar both before and after the DCFC test did not contain moisture so that the Equation (18) can be written as:

LHV ¼ HHV  218:31$Hd

(19)

H [%]

HHV [kJ kg1]

LHV [kJ kg1]

2.80 2.65

29,550 28,820

28,939 28,241

4. Results and discussion The voltage and power values determined during the 12-h experiment are plotted in Fig. 5. Moreover, Table 2 provides a summary of the biochar analysis results before and after the test. Data contained in the Table 2 show that after the test the carbon content in the biochar was higher than before the test. The increase was probably related to the decrease of ash content during the experiment since molten hydroxide electrolyte may not only react with carbon to release electrons but also with mineral matter in the fuel. Examples of various chemical process of the de-ashing of carbon fuels with the use of molten hydroxides are given e.g. in Refs. [30,31]. Furthermore, some H and/or O containing compounds could also be evolved during fuel oxidation bringing about the increase of carbon content in the residue. Another probable reason could also be the presence of sodium and lithium carbonates (formed by the reaction of hydroxides and CO2) in the pores of the remaining biochar recovered from the anode after the experiment. Those carbonates could remain inside of the biochar pores even after repeated washing with de-ionized water and thus could also be responsible for the increase of the total elemental carbon in the sample. The results indicated that the estimated DCFC efficiency (cf. Equation (9)) was roughly 41% and 40% based on a LHV and HHV, respectively. Efficiency of DCFC estimated for LHV can be compared with the efficiencies of traditional carbonaceous fuels processing technologies. Compared to the data contained in Table 3 obtained DCFC efficiency (which is an alternative to these technologies to convert biomass) is very promising, especially compared to systems with a capacity of less than 0.2 MWe. Furthermore, the DCFCs has the advantage over the other energy technologies that its efficiency practically does not depend on the size of the device. If power generated by a fuel cell stack depends on the number and size of the individual fuel cells, the efficiency does not depend on the size of that kind of device. Contrary to e.g. steam or gas turbines that suffer from scale effects the efficiency of the fuel cell does not drop for small systems (stacks or single cell) since the fuel cells produce electricity directly in one single step via electrochemical reactions and thus small cells (watt- or kilowatt-scale) are as efficient as larger ones (megawatt-scale). Assuming that the elemental carbon contained in biochar only react with the hydroxyl ions to generate electric charge, the voltage efficiency of the DCFC calculated from the Equation (11) should be about 64%. The average voltage at the terminals of working cell was calculated with Equation (20) for a period of ‘stable’ cell operation i.e. after the initial 2.5 h.

Table 4 Main developers of direct carbon fuel cells and prototypes efficiencies. Developer

Temperature [K]

Fuel

Efficiency [%]

Source

University of St-Andrews Scientific Applications & Research Associates (SARA) Inc. CellTech Contained Energy LLC Direct Carbon Technologies LLC, Stanford University

973 903 1273 1123 1178

Activated carbon Graphite rod Biochar Crushed graphite Activated carbon

30e40% at 0.7 V 60% at 0.6 V 67% at z0.77 V 24.4% at 0.6 V 62% at 0.68 V

[25] [14,20] [34] [29] [35]

A. Kacprzak et al. / Journal of Power Sources 321 (2016) 233e240

Z

References

t2

UðtÞdt U¼

239

t1

t2  t1

(20)

where: t1 ¼ 2.5 h, t2 ¼ 12 h (cf. Fig. 5). The calculated average voltage was 0.658 V. In turn, the degree of carbon conversion to electricity, estimated from Equation (14), was 59%. The difference of roughly 5% between theoretical and actual voltage efficiency may be associated with numerous possibilities, such as e.g. the consumption of carbon via Boudouard reaction, carbon reactions with the molten hydroxides (described below), or uncontrolled carbon loss during the washing of the biochar after the test. When CO is excluded, all the elemental carbon should be used in the preferred anodic reaction (16), and none is wasted in the Boudouard reaction. Using the relation (15) it was decided to calculate the fuel utilization efficiency to determine the degree of carbon consumption in reaction (16). A definite integral’s value for the current changes over time was z14256 As and the difference between the carbon content before and after experiment was 0.4651 g (cf. Table 2). Accordingly, fuel utilization efficiency value was above 95%. The remaining 5% was most likely reacted with oxygen situated in the spaces among the biochar particles (also inside the pores of biochar) while the anode with fuel was slowly immersed into the electrolyte at 723 K. Other hypothesis was that the carbon was consumed in the activation process of biochar with molten hydroxides in undesired reactions such as [33]: 4NaOH þ C / 4Na þ CO2 þ 2H2O

(21)

6NaOH þ 2C / 2Na þ 2Na2CO3 þ 3H2

(22)

Nonetheless, hf > 95% indicates a high degree of carbon conversion into electric power. In Table 4 summarizes a comparison of voltage efficiencies of different direct carbon fuel cells which are developing in the world. The calculated efficiency (59% at a voltage of 0.658 V) is comparable with the efficiencies of other DCFCs developers. It is also worth mentioning that the other DCFCs are working at much higher temperatures. Further optimization of the design and operating parameters of the cell prototype may allow to improve the performance and efficiency. 5. Conclusions On the basis of the analysis of the information discussed in the present paper the following major conclusions may be formulated: 1. The estimated energy efficiency of the DCFC, in a similar manner as for heat engines, was 41% (based on LHV of biochar), which is a very good and promising value especially in comparison with other energetic technologies for biomass chemical energy conversion into electrical power. 2. The designated voltage efficiency of non-optimized cell prototype was 59% (at 0.658 V) and was only 4% lower than theoretically possible to obtain in the assumed experimental conditions. It should also be noted that the voltage efficiency the tested fuel cell are comparable with the values obtained by other DCFC developers in the world. 3. Fuel utilization efficiency value was above 95% and indicates a high degree of carbon conversion into electric power

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