Exergy expression

Stream

$B=B_k+B_p+B_{ph}+B_{ch}$

B_k is Kinetic Exergy, B_p is Potential Exergy, B_ph is Physical Exergy, Bch is the Chemical Exergy [25] .

Process

$B_{\text{product}}=B_{\text{input}}–B_{\text{losses}}–B_{\text{waste}}$

B_product is the Useful energy, B_loss is mainly due to inner friction, B_waste is the energy of solid and liquid waste from product and air emissions. B_input is the sum of B_fuel, B_elasticity and B_others that are applied to the production process [25] .

Work

$B=W-W_{surr}$

Where $W_{surr}=P_o\left(V_2–V_1\right)$ [25] .

Heat transfer

$B_{\text{heat}}=Q\left[1-\frac{T_o}{T}\right]$

T_o is the temperature of the environment, T is the temperature at which the heat transfer takes places, Q is heat transfer rate.

Chemical

$B_{ch}=\phi HHV$

φ, the fuel chemical exergy factor = For diesel [26] , φ is 1.07 and for natural gas, it can be approximated as 0.94 [27] quoted in [28] . HHV = higher heating value.

Control mass

$B_2-B_1={{\displaystyle \sum }}^{\text{}}\left[1-\frac{T_o}{T_k}\right]Q_k-\left[W-P_o\left(V_2-V_1\right)\right]T_o{S}_{gen}$

T_o―reference temperature, S―entropy.

Control volume

$B_2-B_1={{\displaystyle \sum }}^{\text{}}\left[1-\frac{T_o}{T_k}\right]Q_k-\left[W-P_o\left(V_2-V_1\right)\right]T_o{S}_{gen}+M_i{\Psi }_i-M_e{\Psi }_e$