4.2.2. Energy Recovery

The amount of energy provided by the power source to the circuit (WE) is expressed as

$$\mathbf{W\_{E}} = \sum\_{\perp}^{n} \left( \mathbf{I} \mathbf{E\_{d^{x}}} \Delta \mathbf{t} - \mathbf{I}^{2} \mathbf{R\_{c^{x}}} \Delta \mathbf{t} \right) \text{ (adjusted for losses across the resistor)},\tag{10}$$

where Eap (V) denotes the voltage applied, Rex is the external resistor, and Δt (s) is the time increment for n data points measured during a batch cycle [61]. Energy balances based on combustion heats are usually used for electrolyzers and for predicting the amount of energy contained in organic matter. The amount of energy added by the substrate is expressed as

$$\mathsf{W}\_{\mathfrak{k}} = \Delta \mathsf{H}\_{\mathfrak{k}} \mathsf{n}\_{\mathfrak{k}} \tag{11}$$

where ΔHs= 870.28 kJ·mol−<sup>1</sup> is the heat of combustion of the substrate, and nS denotes the total number of consumed moles of the substrate during a batch cycle based on COD removal. The ratio of the total energy of the hydrogen produced to the input of required electrical energy is the energy efficiency relative to the electrical input (nE).

$$\mathbf{n}\_{\rm E} = \frac{\mathbf{n}\_{\rm H\_2} \Delta \mathbf{H}\_{\rm H\_2}}{\mathbf{W}\_{\rm E}},\tag{12}$$

where ΔHH2 = 285.83 kJ·mol−<sup>1</sup> is the energy content of hydrogen based on the heat of combustion (upper heating value), and WH2 = nH2<sup>Δ</sup>HH2 . The efficiency relative to the added substrate (nS) is calculated as

$$\mathfrak{m}\_{\rm S} = \frac{\mathcal{W}\_{\rm H\_2}}{\mathcal{W}\_{\rm S}}.\tag{13}$$

The overall energy recovery based on both the electricity and the substrate inputs (ηE+S) is expressed as

$$
\eta\_{\rm E+S} = \frac{\mathcal{W}\_{\rm H\_2}}{\mathcal{W}\_{\rm E} + \mathcal{W}\_{\rm S}}.\tag{14}
$$

The percentages of energy contributed by the power source (eE) and substrate (eS) are calculated as follows:

$$\mathbf{e}\_{\rm E} = \frac{\mathbf{W\_{E}}}{\mathbf{W\_{E}} + \mathbf{W\_{S}}'}, \mathbf{e\_{S}} = \frac{\mathbf{W\_{S}}}{\mathbf{W\_{E}} + \mathbf{W\_{S}}}.\tag{15}$$

#### **5. MEC Reactor Architecture**

Similar to MFC, an elementary MEC architecture has two chambers that are connected employing an ion-exchange membrane. Over time, many different combinations of MECs, which are described below, have been developed for hydrogen yield improvement. The previous layouts comprised a basic H-type cell containing gas collection parts connected to a cathode chamber [62]. Eventually, various refinements were made to develop dualchambered MECs for straightforward operation.

According to the findings of the research, based on a comparative analysis of various combinations, single-chambered MEC had higher hydrogen production rates and current densities than dual-chambered MEC. As a result, significant efforts have been made to further refine this combination for use in scale-up investigations. This surplus amount of MEC configurations indicates that the system setup for hydrogen generation in MEC is quite important. Substantial research was carried out to determine suitable MEC configurations. Several types of reactor modifications were assembled according to the results: cylindrical design, tubular reactor design, two-chamber MEC, up-flow single-chamber reactor, single-chamber membrane-less MEC, and many others. The hydrogen output and Coulombic efficiency of the MEC depend largely on the reactor configuration. Initially, researchers used dual-chambered MECs; the single-chambered MEC was introduced later for increasing the volumetric power density of the cathode and the hydrogen yield.
