Reduction of greenhouse gas emissions from steam power plants through optimal integration with algae and cogeneration systems

Abstract

This paper presents an optimization approach for mitigating CO₂ emissions in the electric power generation through integrated algae and cogeneration systems. A framework is proposed for the integration of biofixation of CO₂ through the cultivation of microalgae, conversion of microalgae to biodiesel, and a steam power plant with cogeneration that is thermally coupled with an industrial facility. A systematic multi-objective optimization approach is developed to integrate the considered units while simultaneously addressing technical, economic, and environmental objectives. The solution of the optimization problem is carried out via a hierarchical decomposition approach, a genetic algorithm, and the ε-constraint method for solving the multi-objective optimization problem. A case study is considered to integrate an existing thermoelectric power station in Mexico with an algae-and-cogeneration system. The results show that important environmental, economic, and energy benefits can be achieved as a result of the proposed integration approach.

Appendix 1: Algae-to-biodiesel production model

This appendix presents the model for the algae cultivation system, which produces biodiesel and glycerol. This model is described as follows.

The algal biomass (F _AC) produced in the cultivation stage is computed as follows:

$$F_{\text{AC}} = \frac{{\alpha_{\text{AC}}^{{{\text{CO}}_{ 2} }} \tau_{\text{DT}} F_{{{\text{CO}}_{ 2} }} }}{{\delta_{{{\text{CO}}_{ 2} }} }} = \frac{(0.7)(0.5)}{1.83}F_{{{\text{FCO}}_{ 2} }} ,$$

(14)

where $\alpha_{\text{AC}}^{{{\text{CO}}_{ 2} }}$ is the efficiency of CO₂ transfer into the algal growth medium, $\delta_{{{\text{CO}}_{ 2} }}$ is the CO₂ demand in kg-CO₂/kg-biomass, τ _DT is the fraction of the whole-day hours that CO₂ from the power plant (feed gas) is delivered to the cultivation stage, and $F_{{{\text{FCO}}_{ 2} }}$ is the flowrate of CO₂ generated by the power plant boiler.

Also, the feed gas delivery is carried out only during the day, so τ _DT = 0.5. Thus, the mass balance equations for algal biomass in both harvesting steps are expressed as follows:

$$F_{\text{AH}}^{\text{FLOC}} = \alpha_{\text{AH}}^{\text{FLOC}} \;F_{\text{AC}} = (0.97)F_{\text{AC}}$$

(15)

$$F_{\text{AH}}^{\text{CENT}} = \alpha_{\text{AH}}^{\text{CENT}} \;F_{\text{AH}}^{\text{FLOC}} = (0.85)F_{\text{AH}}^{\text{FLOC}} ,$$

(16)

where $\alpha_{\text{AH}}^{\text{FLOC}}$ and $\alpha_{\text{AH}}^{\text{CENT}}$ are the recovery fractions of algal biomass in primary and secondary harvesting, respectively; $F_{\text{AH}}^{\text{FLOC}}$ and $F_{\text{AH}}^{\text{CENT}}$ represent the algal biomass flowrates leaving the flocculation and centrifugation operations, respectively.

In the oil extraction stage, the amount of recovered triglycerides (F _OIL) from algal biomass is

$$F_{\text{OIL}} = \alpha_{\text{OIL}} w_{\text{OIL}} F_{\text{AH}}^{\text{CENT}} = (0.8)(0.3)F_{\text{AH}}^{\text{CENT}} ,$$

(17)

where α _OIL is the recovery fraction of oil using n-hexane as solvent and w _OIL is the lipid content in algal biomass (wt% of dry biomass).

The consumption of fresh hexane for oil extraction is calculated as follows:

$$F_{\text{HEX}} = (0.5)(0.02)F_{\text{AH}}^{\text{CENT}} = 0.0016F_{{{\text{CO}}_{ 2} }} .$$

(18)

The lipid-depleted algal biomass or residual biomass (F _LD) generated by the extraction operation is obtained by the following relationship:

$$F_{\text{LD}} = (1 - \alpha_{\text{OIL}} w_{\text{OIL}} )F_{\text{AH}}^{\text{CENT}} = \left[ {1 - (0.8)(0.3)} \right]F_{\text{AH}}^{\text{CENT}} .$$

(19)

Combining Eqs. (14), (15), (16), and (18), the following relationship is obtained:

$$F_{\text{LD}} = \sigma_{\text{Algae}} F_{{{\text{FCO}}_{ 2} }}$$

(20)

with

$$\sigma_{\text{Algae}} = \frac{{(\alpha_{\text{AC}}^{{{\text{CO}}_{ 2} }} )(\tau_{\text{DT}} )(\alpha_{\text{AH}}^{\text{FLOC}} )(\alpha_{\text{AH}}^{\text{CENT}} )(1 - \alpha_{\text{OIL}} w_{\text{OIL}} )}}{{\delta_{{{\text{CO}}_{2} }} }} = 0.1198.$$

(21)

The biodiesel (F _BD) and glycerol (F _GLY) produced in the final stage of the system are determined as follows:

$$F_{\text{BD}} = F_{\text{OIL}}$$

(22)

$$F_{\text{GLY}} = (0.11)F_{\text{OIL}} .$$

(23)

Equations (14), (15), (16), and (22) give a simple expression for biodiesel produced in terms of the variable $F_{{{\text{FCO}}_{ 2} }}$:

$$F_{\text{BD}} = \frac{{(\alpha_{\text{AC}}^{{{\text{CO}}_{ 2} }} )(\tau_{\text{DT}} )(\alpha_{\text{AH}}^{\text{FLOC}} )(\alpha_{\text{AH}}^{\text{CENT}} )(\alpha_{\text{OIL}} w_{\text{OIL}} )}}{{\delta_{{{\text{CO}}_{2} }} }}F_{{{\text{CO}}_{2} }} = 0.03785F_{{{\text{CO}}_{2} }} .$$

(24)

The nitrogen and phosphate requirements for microalgae cultivation can be computed from the following equations:

$$F_{{{\text{N}}_{ 2} }} = (0.182)F_{\text{BD}} = (0.00689)F_{{{\text{CO}}_{ 2} }}$$

(25)

$$F_{\text{PH}} = (0.039)F_{\text{BD}} = (0.001475)F_{{{\text{CO}}_{ 2} }} .$$

(26)

The water losses due to evaporation and leakages (F _WLOP in ton/year) can be expressed as

$$F_{\text{WLOP}} = 1 \times 10^{6} \frac{{(h_{\text{WEV}} + h_{\text{WL}} )}}{{\gamma_{\text{AB}} }}F_{\text{AC}} = = 31.8761F_{{{\text{CO}}_{ 2} }} ,$$

(27)

where h _WEV is the daily evaporation depth (m/day), h _WL is daily water loss due to leakages (m/day), and γ _AB is the algal culture productivity (g/m² day). In Eq. (27), 1 × 10⁶ is the conversion factor between g and ton.

After the secondary harvesting step, all the water presents in the outlet stream (F _WLC) that is directed to the dryer is also lost. This water loss is calculated as follows:

$$F_{\text{WLC}} = \left( {\frac{{\rho_{\text{SOL}}^{\text{CENT}} }}{{C_{\text{ABS}}^{\text{CENT}} }} - 1} \right)F_{\text{AH}}^{\text{CENT}} ,$$

(28)

where $\rho_{\text{SOL}}^{\text{CENT}}$ is the density of the biomass slurry leaving the secondary step and $C_{\text{ABS}}^{\text{CENT}}$ is the concentration of algal biomass in that stream. This equation can be rearranged to another useful form:

$$F_{\text{WLC}} = \left( {\frac{{\rho_{\text{SOL}}^{\text{CENT}} }}{{C_{\text{ABS}}^{\text{CENT}} }} - 1} \right)\frac{{(\alpha_{\text{AC}}^{{{\text{CO}}_{ 2} }} )(\tau_{\text{DT}} )(\alpha_{\text{AH}}^{\text{FLOC}} )(\alpha_{\text{AH}}^{\text{CENT}} )}}{{\delta_{{{\text{CO}}_{ 2} }} }}F_{{{\text{CO}}_{ 2} }} = 0.8936F_{{{\text{CO}}_{ 2} }} .$$

(29)

To obtain this equation, $C_{\text{ABS}}^{\text{CENT}}$ = 150 g/L⁵³ and $\rho_{\text{SOL}}^{\text{CENT}}$ = 1000 g/L.

Thus, the amount of make-up water that must be added to the algae-to-biodiesel process to compensate for the loss of water can be expressed as

$$F_{\text{MW}} = W_{\text{WLOP}} \rho_{\text{W}} + F_{\text{WLC}} = 0.9565\rho_{\text{W}} F_{{{\text{CO}}_{ 2} }} + 0.8936F_{{{\text{CO}}_{ 2} }} ,$$

(30)

where ρ _W is the density of liquid water.

The annual net electric power for the integrated energy system is given as the difference between the electric power generated by the power plant and that consumed by the algae-to-biodiesel subsystem:

$${\text{NEP}} = 400{\text{ MW}} - E_{\text{AC}} - E_{\text{AH}} - E_{\text{OE}} - E_{\text{BP}} - E_{\text{PP}} ,$$

(31)

where E _AC, E _AH, E _OE, E _BP, and E _PP are the annual electricity requirements for microalgae cultivation, algal biomass harvesting, oil extraction, biodiesel production, and pumping of feedwater in the power plant, respectively (see Fig. 2). The energy consumptions for the stages of the algae-to-biodiesel system were calculated using the data shown in Table 1.