**3. Method of Evaluation**

#### *3.1. Energy and Exergy Efficiency*

The total energy required to re-liquefy BOH is calculated using Equation (1).

$$
\dot{W}\_{\text{net}} = \dot{W}\_{\text{Comp}\,1} + \dot{W}\_{\text{Comp}\,2} - \dot{W}\_{\text{Exp}\,1} - \dot{W}\_{\text{Exp}\,2} \tag{1}
$$

. Wnet: Total work required to re-liquefy BOH .

WComp 1: Work input for Comp 1 .

WComp 2: Work input for Comp 2 .
