As a feedstock, microalgae have great potential to produce a wide range of products under the broad market penetration of biorefinery, including biofuels and a set of value-added chemicals. Such products contribute to environmental sustainability by producing less amounts of CO
2 than traditional fossil fuels [
1]. However, microalgae-based biorefinery requires complex processing pathway compared with earlier generations of biorefinery [
2], and its economic feasibility has not yet been evaluated fully [
3]; therefore, it is crucial to develop a systematic methodological framework to determine the optimal biorefinery processing pathway.
In the recent literature, a number of methodologies have been proposed for the generation of promising biorefinery configurations. These methodologies range pure mathematical programming-based methods [
4,
5,
6,
7] to heuristic-based methods [
8,
9], where the superstructure-based mathematical programming model has been recognized as a useful tool to generate an optimal technology pathway for the production of bio-based products from biomass derived feedstock [
10]. This optimization provides a detailed consideration of the equipment and each potential interconnection, such as various processing steps, feedstocks, and products [
11]. Several studies have developed the superstructure-based mixed-integer nonlinear programming (MINLP) models to generate the optimal biorefinery configuration [
12]. Martin and Grossman [
13] proposed a conceptual design method for the production of biodiesel from cooking oil and algae oil by proposing a superstructure of alternative technologies for the transesterification of the oil. The production cost and energy consumption of algae oil was found to be 0.42 USD/gal and 1.94 MJ/gal, respectively. From the economic and environmental point of view, Gebreslassie et al. [
14] proposed a multiobjective MINLP model for determining the optimal algae-based hydrocarbon biorefinery configuration. The proposed potential processing pathway included carbon capture, algae growth, harvesting, lipid extraction, anaerobic digestion, power generation, and algal oil biorefinery. In the following study, Gong and You [
15] proposed a new superstructure model to design the optimal algal biorefinery configuration. The proposed potential processing pathway included biological carbon sequestration and utilization, encompassing off-gas purification, algae cultivation, harvesting and dewatering, lipid extraction, remnant treatment, biogas utilization, and algal oil upgrading stages. Galanopoulos et al. [
16] proposed a superstructure-based MINLP model with the objective of minimizing the total biodiesel production costs for the techno-economic optimization of an integrated algae biorefinery. Their work was developed and implemented in the advanced interactive multidimensional modeling (AIMMS) software. Taking the preliminary and uncertain nature of technologies into consideration, Rizwan et al. [
17] proposed an optimal design method for determining the most promising biorefinery configuration. They represented that such an issue was one of the major biorefinery challenges, and it should be addressed systematically. Haghpanah et al. [
18] proposed a superstructure to develop the MINLP model to minimize the total annualized cost (TAC) and environmental impacts simultaneously. The multiobjective optimization model was reduced into a single objective model using the augmented ε-constraint method. Considering lipid extraction and pyrolysis of defatted microalgae residues, Huang et al. [
19] proposed a method to determine the processing pathway for the biofuel from microalgae biomass. Moreover, the environment impact assessment on the resulted biorefinery processes is generally provided in the recent literature to confirm the sustainability for the proposed approach. Using life cycle assessment (LCA), Li et al. [
20] proposed a new method of wastewater adjustment for enhancing microalgal biofuel production and then the environmental impacts of the whole process were measured. From their recent research [
21], the utilization of microalgae to produce high-quality biodiesel was investigated and the LCA analysis was provided to evaluate the proposed method from an environmentally sustainable point of view.
From the above analysis it is concluded that a characteristic shared by most of these methodologies is the processing pathways/networks for producing biofuels and various platform chemicals from microalgae with an emphasis on the development of the systematic modeling framework using superstructure optimization. However, the main limitation for the abovementioned approaches is that a result of tight processing integration, which makes the production of microalgal biofuels, is not economically viable. Although these limited works have been improved using a heuristic-based approach, compared with mathematical programming the processing design for the most promising alternatives is being completed simultaneously with the fixed mass balance constraints. Moreover, most of the hierarchical decomposition-based works were mainly developed for the thermochemical conversion pathway rather than bio-chemical or biological conversion pathways [
8]. Therefore, it is important to decompose the complex tasks of the superstructure-based optimization into the hierarchical sub-problems, and in the meantime the active correlation between these sub-problems is ensured to relax the variables in the middle stages and then an appropriate level of redundancy for designing the processing is provided.
To address the above-mentioned problem, we propose a two-tier superstructure optimization framework for the production of biodiesel from the lipid contents of microalgal biomass and the processing of microalgae residue into useful products. The key idea is to investigate the active correlation between two hierarchical sub-problems by relaxing the flow in the middle stages with a set of inequality constraints. Thus, this complex task is reduced to two small-scale optimization problems, in which the overall economics and yield of the biofuels production from microalgae are considered. In the outer-tier superstructure optimization problem, the cultivation of microalgae, the harvesting of microalgal biomass, and the conversion of the residue are involved, except feed and product steps, whose products are regarded as the intermediates. In the inner-tier, according to a set of inequality constraints with respect to the flow of intermediates, a large number of potential technological alternatives exist for producing a variety of end-products from intermediates and their residues. Finally, the optimization results obtained show the ability of this framework to provide the promising configurations and cost-effectiveness of microalgae-based biorefinery.