*4.1. Energy Analysis of the Integrated Systems*

The objective functions that are used in the energy analysis for system performance evaluation are electrical efficiency (ηen,sys,electrical) and cogeneration efficiency (ηcogen). The electrical efficiency of the systems is defined as the ratio of the net electrical power output of the system to the lower heating value of the feed and fuel entering the system, as expressed in Equation (9) for the steam methane reforming-based system and in Equation (10) for the steam methanol reforming-based system [27,54].

$$
\ln \eta\_{\text{en,CH4,electrical}} = \frac{\text{P}\_{\text{net, electrical}}}{\left(\dot{\text{n}}\_{\text{feed,CH4}\_4} + \dot{\text{n}}\_{\text{fuel,CH4}\_4}\right) \text{L.H} \text{V}\_{\text{CH4}\_4}} \tag{9}
$$

where LHVCH4 is the lower heating value of CH4. The net electrical power (Pnet,electrical) is calculated by subtracting the power consumed in the system (Ppump−<sup>1</sup> + Ppump−<sup>2</sup> + Ppump−<sup>3</sup> + Pcomp−<sup>1</sup> + Pcomp−<sup>2</sup> + Pcomp−3) from the power generated in the HT-PEMFC (PHT-PEMFC,AC).

$$\ln\_{\text{en,CHylOH,electrical}} = \frac{\text{P\_{net, electrical}}}{\dot{\text{m}\_{\text{feed,CHylOH,}}} \cdot \text{LHV}\_{\text{CHylOH}}} \tag{10}$$

where LHVCH3OH is the lower heating value of CH3OH. The net electrical power (Pnet,electrical) is calculated by subtracting the power consumed in the system (Ppump−<sup>1</sup> + Ppump−<sup>2</sup> + Ppump−<sup>3</sup> + Pcomp−<sup>1</sup> + Pcomp−<sup>2</sup> + Pcomp−<sup>3</sup> + Pcomp−<sup>4</sup> + Pcomp−5) from the power generated in the HT-PEMFC (PHT-PEMFC, AC). The electrical power generated by HT-PEMFC (PHT-PEMFC, AC) can be calculated as follows [65]:

$$\mathbf{P\_{HT-PEMFC,AC}} = \eta\_{\text{IFT}-PEMFC} \cdot \dot{\mathbf{n}}\_{\text{H}\_2} \cdot \text{L.H} \mathbf{V}\_{\text{H}\_2} \cdot \eta\_{\text{Corvertex}} \tag{11}$$

where . nH2 is the molar flow rate of hydrogen that reacts in the HT-PEMFC, LHVH2 is the lower heating value of hydrogen, ηHT-PEMFC is the electrical efficiency of the HT-PEMFC, and ηConverter is the efficiency of the converter.

The efficiency of HT-PEMFC (ηHT-PEMFC) can be found from [65]

$$
\eta\_{\rm HIT-PEMFC} = \mu\_{\rm f} \frac{V\_{\rm c}}{\rm EMF\_{\rm max}} \cdot 100 \tag{12}
$$

where μ<sup>f</sup> is the fuel utilization factor, Vc is the produced voltage of the cell, and EMFmax is the electromotive force when all the energy from the hydrogen fuel cell, the heating value or enthalpy of formation, was converted to electrical energy. Fuel utilization factor, μ<sup>f</sup> and EMFmax can be determined as follows:

$$
\mu\_{\rm f} = \frac{\text{H}\_{\rm 2, consumed}}{\text{H}\_{\rm 2, supplied}} \tag{13}
$$

$$\text{EMF}\_{\text{max}} = -\frac{\Delta \text{h}\_{\text{f}}}{2\text{F}}\tag{14}$$

The heat produced in the fuel cell stack can be determined from [66]

$$\dot{\mathbf{Q}}\_{\text{hat},\text{eff}\text{-}\text{PEMF}} = \sum (\mathbf{h}\_{\text{in},\text{c}} \cdot \dot{\mathbf{n}}\_{\text{in},\text{c}}) - \sum (\mathbf{h}\_{\text{out},\text{c}} \cdot \dot{\mathbf{n}}\_{\text{out},\text{c}}) + \sum (\mathbf{h}\_{\text{in},\text{a}} \cdot \dot{\mathbf{n}}\_{\text{in},\text{a}}) - \sum (\mathbf{h}\_{\text{out},\text{a}} \cdot \dot{\mathbf{n}}\_{\text{out},\text{a}}) \\ - \mathbf{P}\_{\text{HT}-\text{PEMF},\text{DC}} \tag{15}$$

The cogeneration efficiency of the system (ηen,sys,cogen) is defined as the ratio between the summation of the rate of available heat output and the net electrical power to the lower heating value of the fuel and feed entering the system, as expressed in Equation (16) for the steam methane reforming-based system and in Equation (17) for the steam methanol reforming-based system [54].

$$\eta\_{\text{en,CH}\_4,\text{cogen}} = \frac{\text{P}\_{\text{net, electrical}} + \text{Q}\_{\text{net}}}{\left(\dot{\text{n}}\_{\text{CH}\_4,\text{feed}} + \dot{\text{n}}\_{\text{CH}\_4,\text{fuel}}\right) \cdot \text{LHV}\_{\text{CH}\_4}} \tag{16}$$

$$\text{In}\_{\text{len, CH}\_3\text{OH, oxygen}} = \frac{\text{P}\_{\text{net, electrical}} + \text{Q}\_{\text{net}}}{\left(\dot{\text{n}}\_{\text{CH}\_3\text{OH, feed}}\right)\text{LHV}\_{\text{CH}\_3\text{OH}}} \tag{17}$$

where

$$\mathbf{Q\_{net}} = \mathbf{Q\_{hot\ water(W13)}} - \mathbf{Q\_{water(W3)}} \tag{18}$$
