*2.4. Exergoeconomic Analysis*

The exergoeconomic analysis consists of the formulation of a cost balance and its auxiliary equations at a component level, for each component of the process. The general cost balance [17] is shown in Equation (20) where *cout* and *cin* represent the costs of the outflows and inflows respectively, *cw*,*k* represents the cost rate related with the work and . *Zk* represents the investment cost of each component. Table 2 shows the cost balance of each component present in the system.

$$
\sum\_{k} c\_{q,k} \dot{E}\_{q,k} + c\_{w,k} \dot{\mathcal{W}}\_{k} + \sum\_{\text{in}} c\_{\text{in}} \dot{E}\_{\text{in}} - \sum\_{\text{out}} c\_{\text{out}} \dot{E}\_{\text{out}} - c\_{D,k} \dot{E}\_{D,k} + \dot{Z}\_{k} = 0 \tag{20}
$$

The cost balance can be written in terms of the fuel and product formulation [28] as is shown in Equations (21) and (22).

$$
\dot{\mathcal{C}}\_{P,k} = \dot{\mathcal{C}}\_{F,k} + \dot{\mathcal{Z}}\_{k} - \dot{\mathcal{C}}\_{D,k} \tag{21}
$$

$$
\omega\_{P,k}\dot{E}\_{P,k} = \omega\_{F,k}\dot{E}\_{F,k} + \dot{Z}\_k - \dot{C}\_{D,k} \tag{22}
$$

.

where *CP*,*<sup>k</sup>* is the product cost rate, *CF*,*<sup>k</sup>* is the fuel cost rate, and *CD*,*<sup>k</sup>* is the cost rate associated with the destroyed exergy for each component.

.

The exergy destroyed in the *k*-th component has an associated cost rate . *CD*,*<sup>k</sup>* that can be calculated in terms of the cost of the additional fuel (*cF*,*<sup>k</sup>*) that needs to be supplied to this component to cover the exergy destruction and to generate the same exergy flow rate of the product, when . *EP*,*<sup>k</sup>* stay constant (Equation (23)) [17]. Table 4 shows the cost balance of each component present in the system.

$$
\dot{\mathcal{C}}\_{D,k} = c\_{F,k} \dot{E}\_{D,k} \tag{23}
$$


**Table 4.** Cost balance equations and auxiliary equations for exergy costs of the system.

.

There are some non-energetic costs used in the calculations of the cost balance of each component. In the boiler, the fuel used to generate vapor was fuel oil 6. The price of the liquid fuel (stream 49) was

\$1.07 per gallon [32]. The potable water (stream 48) had a cost of \$0.53 per cubic meter [33]. The price of carbon dioxide (stream 1) injected into the coffee extract was \$24.22 per kg.

The variable . *Zk* was calculated as the sum of capital investment ( . *Z CI k* ) and operation and maintenance costs ( . *Z OM k* ) for each component, as is shown in Equation (24) [17].

$$
\dot{Z}\_k = \dot{Z}\_k^{\text{OM}} + \dot{Z}\_k^{\text{CI}} \tag{24}
$$

The capital investment for each component can be calculated by using Equation (25) [17]:

$$\dot{Z}\_k^{CI} = \frac{\text{PEC}\_k \* \text{CRF}}{\tau} \tag{25}$$

where *PECk* is the purchase price of the kth component and τ is the number of annual operating hours (24 h per day, 365 days per year). It was assumed that the ordinary annuities transaction occurs at the end of each time interval, thus the *CRF* (capital recovery factor) could be obtained using Equation (26) [17], where *ieff* is the interest rate (10%), and n is the lifetime of the system (20 years).

$$\text{CRF} = \frac{i\_{eff} \* \left(1 + i\_{eff}\right)^n}{\left(1 + i\_{eff}\right)^n - 1} \tag{26}$$

The rate of operation and maintenance costs ( . *Z OM k* ) can be calculated by using Equation (27). The operation and maintenance cost (OMCk) of each component is determined by using Equation (28), which is a close approximation used by Bejan et al [17]. The constant-escalation levelization factor (CELF) was determined by using Equation (29), which depends on the factor *kOMC* defined by Equation (30) [17]. For the nominal escalation rate (*rOM*), it was assumed that all costs except fuel costs and the values of by-products change annually with the constant average inflation rate of 4% [17].

$$\dot{Z}\_k^{\text{OM}} = \frac{\text{OMC}\_k \* \text{CLEF}\_{\text{OM}}}{\tau} \tag{27}$$

$$\text{OMC}\_k = 0.2 \ast \text{PEC}\_k \tag{28}$$

$$\text{CELF}\_{\text{OM}} = \frac{k\_{\text{OMC}} \* (1 - k\_{\text{OMC}}^{\*}) \* \text{CRF}}{(1 - k\_{\text{OMC}})} \tag{29}$$

$$k\_{\rm OMC} = \frac{1 + r\_{\rm OM}}{1 + i\_{eff}} \tag{30}$$

For a better interpretation of the results, the exergoeconomic factor (*fk*) and relative cost difference (*rk*) were determined. The first factor represents the relationship between the investment cost and the total operating cost rate, while the *rk* represents the increase of the specific exergy cost in a component divided by the specific exergy cost of the fuel.

$$f\_k = \frac{\dot{Z}\_k}{\dot{Z}\_k + \dot{\mathcal{C}}\_{D,k}} \tag{31}$$

$$r\_k = \frac{c\_{P,k} - c\_{F,k}}{c\_{F,k}} \tag{32}$$

## *2.5. Advanced Exergoeconomic Analysis*

The unavoidable ( . *C UN D*,*k* ) and avoidable cost ( . *C AV <sup>D</sup>*,*<sup>k</sup>*) associated with exergy destruction were calculated using Equations (33) and (34). The unavoidable ( . *Z UN k* ) and avoidable investment cost rates ( . *Z AV k* ) were calculated by using Equations (35) and (36). The relation between the investment cost rate and the exergy product rate ( . *Zk*/ . *EP*)*UNk* was estimated by using the unavoidable cost conditions presented in Table 4. For the heat exchangers, a Pro/II ®simulator was used to estimate the new heat transfer area based on the minimum temperature difference.

$$
\dot{\mathbf{C}}\_{D,k}^{\rm LIN} = c\_{F,k} \dot{E}\_{D,k}^{\rm INN} \tag{33}
$$

$$
\dot{\bar{C}}\_{D,k}^{AV} = \dot{\bar{C}}\_{D,k} - \dot{\bar{C}}\_{D,k}^{AV} \tag{34}
$$

$$
\dot{Z}\_k^{\text{LIN}} = \dot{E}\_{P,k} \left(\frac{\dot{Z}\_k}{\dot{E}\_P}\right)\_k^{\text{LIN}} \tag{35}
$$

$$
\dot{Z}\_k^{AV} = \dot{Z}\_k - \dot{Z}\_k^{lIN} \tag{36}
$$

## **3. Results and Discussions**
