Optimal processing pathway selection for microalgae-based biorefinery under uncertainty

Accepted Manuscript Title: Optimal Processing Pathway Selection for Microalgae-based Biorefinery under Uncertainty Author: Muhammad Rizwan Muhammad Zaman Jay H. Lee Rafiqul Gani PII: DOI: Reference:

S0098-1354(15)00263-X http://dx.doi.org/doi:10.1016/j.compchemeng.2015.08.002 CACE 5253

To appear in:

Computers and Chemical Engineering

Received date: Revised date: Accepted date:

15-6-2015 3-8-2015 4-8-2015

Please cite this article as: Rizwan, M., Zaman, M., Lee, J. H., and Gani, R.,Optimal Processing Pathway Selection for Microalgae-based Biorefinery under Uncertainty, Computers and Chemical Engineering (2015), http://dx.doi.org/10.1016/j.compchemeng.2015.08.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Highlights Identification of optimal microalgae processing pathways under uncertainty.

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Techno-economic uncertainties in the dataset are considered.

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The optimization problem is formulated as a stochastic MINLP model.

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Optimal processing pathways are determined under different objective functions.

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Optimal structures are compared with respect to different objective functions used.

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Optimal Processing Pathway Selection for Microalgae-based Biorefinery under Uncertainty Muhammad Rizwana, Muhammad Zamana, Jay H. Leea,*, Rafiqul Ganib Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of

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Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea

CAPEC, Department of Chemical & Biochemical Engineering, Technical University of

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Denmark, DK-2800 Kgs Lyngby, Denmark

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Abstract

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*Corresponding Author: [email protected], +82-42-350-3926

We propose a systematic framework for the selection of optimal processing pathways for a

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microalgae-based biorefinery under techno-economic uncertainty. The proposed framework promotes robust decision making by taking into account the uncertainties that arise due to

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inconsistencies among and shortage in the available technical information. A stochastic

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mixed integer nonlinear programming (sMINLP) problem is formulated for determining the

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optimal biorefinery configurations based on a superstructure model where parameter uncertainties are modeled and included as sampled scenarios. The solution to the sMINLP problem determines the processing technologies, material flows, and product portfolio that are optimal with respect to all the sampled scenarios. The developed framework is implemented and tested on a specific case study. The optimal processing pathways selected with and without the accounting of uncertainty are compared with respect to different objectives. Keywords: Biofuels, Microalgal biorefinery, Uncertainty analysis, Stochastic mixed integer nonlinear programming (sMINLP), Decision-making under uncertainty.

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1. Introduction Under the broad concept of microalgal biorefinery, microalgae is to be cultivated and

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processed to produce a wide range of products such as biofuels, chemicals, animal feed, pigments, power/heat, etc. (Yen et al., 2013; Rawat et al., 2013). Despite the various claimed

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benefits associated with the development of microalgae based biorefinery (such as potentially significant improvements in the overall economics of biofuels), there are many challenges yet

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to be overcome. These challenges include (1) existence of a large number of potential

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processing pathways for the biorefinery development, and (2) inconsistency and shortage in the process information available in the literature because the involved processing

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technologies are still at a nascent stage. Potential development of additional technologies as well as the likely future improvements further increases the uncertainty one faces at the

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current preliminary assessment phase. Consequently, the optimal biorefinery configuration

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determined based on uncertain parameters can prove to be highly suboptimal later due to discrepancies among the assumed and actually realized parameter values. Therefore, it

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becomes necessary to identify the optimal biorefiney configurations with due considerations given to the effect of the existing uncertainties in order to ensure robust decision making. Process systems engineering’s tools and concepts can be applied to address these challenges of microalgal biorefinery by developing a systematic modeling framework to determine the optimal biorefiney configurations in a cost effective, robust, and environmentally sustainable manner (Liu et al., 2009; Yue et al., 2014). Under the domain of energy systems engineering, stochastic programming/optimization is a widely used tool to determine the optimal processing networks under stochastic uncertainty, and this approach has been presented in many studies (for example, Dua and Pistikopoulos, 1998; Grossmann, 2005). Karuppiah and 3

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Grossmann (2008) proposed a two stage stochastic model to determine the optimal design of an integrated water system under uncertainty. A superstructure was optimized under uncertainty that incorporates all feasible design alternatives for wastewater treatment, reuse,

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and recycle. Kim et al., (2011) addressed the challenge of stochastic uncertainty for the optimal design of biomass supply chain networks by formulating a two stage stochastic

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mixed integer program. The robustness and global sensitivity of stochastic design vs. nominal

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design was analyzed via Monte Carlo simulation. Quaglia et al., (2013) developed a systematic framework for enterprise-wide optimization in order to determine the optimal

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process networks under uncertainty. The developed framework was implemented on an industrial case study where a stochastic mixed-integer nonlinear programming (sMINLP)

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model was formulated and solved to identify optimal processing of soybean oil under uncertainty. Cheali et al., (2014) adapted this framework for the purpose of determining

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optimal processing networks under uncertainty for lignocellulosic biorefinery. The impact of

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market price uncertainties on the optimal solution was evaluated by integrating superstructure

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based process synthesis approach with uncertainty analysis. The effect of uncertainty on the optimal configurations of microalgae-based biorefinery has not been evaluated yet. However, many studies on microalgae-based biorefinery have been carried out recently but all these contributions focus only on identifying optimal processing networks for the production of biofuels from microalgae under a deterministic model (Rizwan et al., 2013a; 2013b; Gebreslassic et al., 2013; Gong and You, 2014a; 2014b, Rizwan et al., 2015). It is thus the objective of this paper to address and evaluate the effect of uncertainty on the optimal processing pathway for a microalgal biorefinery. In this paper, a framework to determine the optimal/promising processing pathways for the production of biofuels from microalgae by considering the effect of uncertainties present in 4

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microalgal biorefinery design is proposed. The proposed framework is based on biorefinery superstructure model developed in an earlier study (Rizwan et al., 2015), which has been extended to handle and address the uncertainties in the problem dataset so that the decisions

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made are robust with respect them. First, a sensitivity analysis is performed to select the influential key parameters for the uncertainty analysis so as to reduce the design problem to a

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manageable size. The problem of determining the optimal biorefinery configurations under

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given parameter uncertainties (modeled as sampled scenarios) is then formulated as a sMINLP problem and solved in the software package GAMS using a database built in Excel.

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The performance of the stochastic optimal solution (in terms of the average gross operating margin (GOM) over the whole set of sampled scenarios) are then computed and compared

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against those of the deterministic optimal solution and the “worst-case” optimal solution. The results from these optimizations and their comparison give useful technical insights about the

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optimal configurations of microalgal biorefinery from the perspective of both cost-

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effectiveness and robustness with respect to uncertainty.

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2. Modeling Framework

The problem of determining the optimal biorefinery configurations for the production of biofuels from microalgae by developing a superstructure based optimization model was addressed in a previous work (Rizwan et al., 2015). In this contribution, the major uncertainties have been incorporated into the biorefinery superstructure model, which leads to the formulation of a stochastic optimization model. The steps involved are described in details in this section.

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2.1 Problem definition In the first step, the problem scope is defined by identifying and selecting the objective

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function to be optimized with respect to various techno-economic constraints while considering the uncertainties in the important, sensitive model parameters. A general problem

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statement is given below.

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Given is a superstructure of microalgae-based biorefinery (Fig. 1) which encompasses all the available potential technological alternatives/options for the various processing steps

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involved in the microalgal biorefinery, such as the cultivation of microalgae, harvesting of microalgal biomass, pre-treatment step including drying and cell disruption of harvested

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biomass, lipid extraction, transesterification, post-transesterification purification, pretreatment of microalgae residue, and conversion of residue to useful products. The

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optimization problem is defined as to determine the optimal processing network(s) for the

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production of biofuels from microalgae. When the uncertainties are expressed as distributions

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in the parameter space or discrete scenarios sampled from it, it leads to the formulation of a sMINLP problem. The objective function chosen in this work is to maximize the expected value of GOM over the space all probable scenarios. Maximization of the average GOM over those scenarios leading to the lowest GOM values (the “worst-case” scenarios) is also examined.

2.2 Data collection and superstructure development A biorefinery superstructure has been developed for the production of biodiesel from the lipid contents of microalgae and the simultaneous conversion of microalgae residue into the useful products, e.g, biooil, bioethanol, biogas, etc. It includes all the major known processing 6

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steps/stages for the production of biofuels from Chlorella vulgaris, and at each processing step various potential technological alternatives/options are considered. As shown in Fig. 1, each option included in the superstructure is represented by two indices; the first index

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represents the option number and the second index represents the processing stage. The list of technological options included in the biorefinery superstructure model is given in Table 1.

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The empty boxes represent the bypassing of certain processing stages, e.g., to accommodate

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wet lipid extraction, in-situ transesterification, etc. The detailed description of the problem data, superstructure development and process description can be found in our previous study

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(Rizwan et al., 2015).

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2.3 Deterministic formulation

In this step, a deterministic optimization problem is formulated and solved to find the optimal

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processing network with nominal parameter values while disregarding the uncertainties in

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them. The deterministic problem results in the formulation of a MINLP model. The detailed

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information on formulating MINLP model can be found in Rizwan et al., 2015). The results obtained in this step locate the deterministic optimal processing pathway for the production of biofuels from microalgae.

2.4 Selection of influential parameters/uncertain parameters In this step, sensitivity analysis is performed based on the deterministic MINLP model (formulated in step 2.3) to investigate the effect of the 25 key model parameters (listed in Fig. 2) on the optimal solution as well as on GOM. The objective of this analysis is to identify a set of dominant parameters among the 25 parameters.

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This analysis is done by varying each parameter individually, and then examining its effect on GOM (Fig. 2). The value of GOM obtained under the deterministic formulation (step 2.3) is used as a reference. Out of the 25 parameters, 11 parameters affect GOM while the rest of

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the parameters have no effect. Furthermore, out of these 11 parameters, 7 parameters (fractional conversion of residue into biogas, fractional conversion of residue into bioethanol,

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fractional conversion of lipids into biodiesel via base catalyzed transesterification, fractional

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conversion of lipids into biodiesel via acidic in-situ transesterification, CO2 conversion for the open pond system, CO2 conversion for the photobioreactor, and lipid yield for the wet

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extraction method) affect both optimal design and its GOM value, whereas the other 4 parameters (lipid content, cost of CO2, cost of nitrogen, and cost of phosphorus) affect the

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GOM only in a minor way. This analysis, thus, reveals that uncertainties in these parameters can have significant impact on the optimal design of microalgal biorefinery, and therefore,

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they are taken into account in the further analysis.

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2.5 Uncertainty characterization

The uncertain parameters (identified in step 2.4) are generally characterized in terms of distributions in the multi-dimensional parameter space. Based on the approach described in Brun et al., 2002 and Sin et al., 2009, three classes of uncertainties are defined, such as low, medium and high which correspond to 5 %, 25 % and 50 % variations around the mean value, respectively. The uncertain parameters and their uncertainty categories are given in Table 2. In this study, these classes are defined on the basis of available information or data in the literature. For example, the fractional conversion of lipids into biodiesel via base catalyzed transesterification is known with good accuracy; hence, it is classified as a parameter of low uncertainty. The available information about the fractional conversion of 8

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lipids into biodiesel via in-situ transesterification, CO2 conversion, lipid yield for wet lipid extraction method, and cost of feed are not consistent in the literature; therefore, these are classified as having medium uncertainty. The same is true for the lipid contents but with a

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very large range of variations; therefore, it is put in the category of high uncertainty. Even less and highly inconsistent information is available for the conversion of microalgae residue

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(for bioethanol and biogas production), and therefore it is also placed in the class of high

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uncertainty.

In the uncertain parameter space, the realizations of the parameters are generated by using the

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Latin Hypercube Sampling (LHS) method (Mckay et al., 1979). LHS is a well-known deterministic sampling method that can ensure a good uniform coverage of the sampling

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space compared to probabilistic sampling techniques like the Monte-Carlo method (Mckay et

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al., 1979; Sin et al., 2009). Given the lack of better knowledge, uniform probability

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distribution (within the given bounds) in the uncertain parameter space is assumed for the scenarios generation. 200 samples are generated from the distribution to be used as discrete

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scenarios. Generally, the sample average approximation (of the expected value) becomes more accurate as the number of scenarios is increased but the size of the optimization problem can also grow with it (linearly as in Eq (1) for the evaluation of the expected GOM) and becomes computationally expensive to handle (Karuppiah and Grossmann, 2008). For a reasonable compromise, it has been decided to work with 200 samples, following the choice reported by others (Quaglia et al., 2013; Cheali et al., 2014).

2.6 Stochastic formulation In this step, a sMINLP model is formulated to find the optimal processing pathways under uncertainty, which is solved via sample average approximation (Birge and Louveaux, 1999). 9

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Objective function: The objective function is to maximize the expected value of GOM over the uncertain space, which is approximated by the average of the results from the 200

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sampled scenarios. GOM: GOM is defined as the difference between total sales and the operating cost, and its

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expected value over S (=200 in this case) scenarios is given by Eq (1): S

GOM   ( Prs  (Sales(s)  Operating Cost(s)))

(1)

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s 1

products for scenario s and is given by Eq (2): Sales ( s )   ( P1i  Fi ,10 ,s )

(2)

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i

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where Prs is the probability of realization of scenario s. Sales(s) represents the sales of

where P1i is the sale price of product i and Fi ,10 , s is the flow of products for scenario s out of

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the final stage. In Eq (2), the component index i covers over the set of products only, which

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includes biodiesel, glycerol, bio-oil, bioethanol and biogas.

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Operating Cost(s) represents the operating cost for scenario s. In this work, it is considered as the sum of raw material cost, chemicals/solvents cost and utilities cost for scenario s, which is given by Eq (3):

Operating Cost(s)   ( P2i ,s  Fi ,1, s )  ( P3i  Qi , j , s )   ( P4 l  U l , j , s ) i

i, j

(3)

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where P2 i ,s is the price of raw material (feed) for scenario s whereas P3i and P4l are the cost factors for the chemicals/solvents and utilities, respectively. Constraints: Constraints include the mass balances constraints and energy balance constraints which are adapted from our previous study (Rizwan et al., 2015) and re-modeled for scenario 10

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s. The formulation of all these constraints is given and explained through a process flow diagram in the Appendix.

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2.7 Worst-case formulation In this step, for a given pathway candidate solution, a chosen number of the worst scenarios

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among the 200 scenarios are to be selected where GOM will be the lowest. 10 worst-case scenarios are considered in this study. Then, the stochastic optimization problem is

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formulated to determine the optimal biorefinery configuration that results in the average

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highest GOM value for its corresponding 10 worst-case scenarios, thus ensuring further robustness against potentially bad outcomes. This is a “risk-averse” solution appropriate for

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those who are pessimistic and want to guard against worst possible outcomes. The objective function is to maximize the expected value of GOM over Sʹ, the set of the worst-case

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scenarios, which can be expressed as:

(4)

Sales ( s)   ( P1i  Fi ,10 , s  )

(5)

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sS 

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GOM  ( Prs  (Sales(s)  Operating Cost(s)))

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Operating Cost(s)   ( P2 i ,s  Fi ,1, s )  ( P3i  Qi , j , s )   ( P4l  U l , j , s ) i

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(6)

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All the constraints (as described in the Appendix) should be reformulated for scenario sʹ. It is extremely important to note that the worst-case scenario set Sʹ varies with each pathway and cannot be chosen a priori. Therefore, at each iteration of the optimization, the corresponding 10 worst-case scenarios among the 200 scenarios must be identified, making the optimization problem very challenging to solve.

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2.8 Optimization model solution The sMINLP model is formulated and solved in the software package of GAMS with the

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DICOPT solver (which is linked to CONOPT (NLP solver) and CPLEX (MIP solver)), using a database built in Excel. The dataset from Rizwan et al., 2015 is adapted for this study. The

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problem database contains the input values of all model parameters, and these values are

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taken from the published literature (see Table 1).

The optimization problem is non-convex due to the bilinear terms present in Eq (A.2) – Eq

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(A.6). To ensure/check the quality of the solution as well as the ease of the solution procedure, in our earlier work (Rizwan et al., 2013a) we also tested the approach of linearizing the

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MINLP model to an equivalent MILP form by using the technique by Glover (1975). The results showed that the same (optimal) solution is obtained from the both approaches.

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However by linearizing the model, the size of the optimization problem got significantly

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bigger and the solution time longer. Therefore in this study, the MINLP (or sMINLP) form is

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solved directly. A more detailed discussion can be found in our earlier study (Rizwan et al., 2013a).

3. Case Study

The developed modeling framework is implemented on a case study to determine the optimal processing pathways under uncertainty for the production of biofuels from microalgae.

3.1 Overview The biorefinery superstructure is developed for the production of biofuels from microalgae (Chlorella vulgaris) as shown in Fig. 1, and briefly described in section 2.2. For this case 12

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study, it is assumed that Chlorella vulgaris is composed of 31.5% lipids, 54.5% proteins and 14% carbohydrates (Mata et al., 2010; Becker, 2004). The optimization problem is defined as to determine the optimal processing pathway under uncertainty for the production of biofuels

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from microalgae. The objective function chosen for maximization is the expected value of GOM, possibly over the assumed set of uncertain parameters. Hence, the optimal pathway is

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computed first and then the resulting GOM for the nominal scenario only as well as for the

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entire 200 sampled scenarios and just the 10 worst-case scenarios among them, as elaborated

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earlier, are compared

3.2 Results and discussion

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Before a discussion on the optimal solutions under different assumptions (e.g., the nominal case, 200 sampled scenarios case, and 10 worst-case scenario case) and their significances,

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first the deterministic optimization problem has been formulated for each of 200 scenarios

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separately, and the optimal processing pathway for each scenario is determined. The purpose

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is to examine the impact of parameter variations on the optimal solution. As shown in Table 3, 8 different processing pathways exist among the optimal pathways for the 200 scenarios. Also, a large variance of GOM is observed over the 200 scenarios (ranging from $ -69.385 to $ -15.392). The frequency of these pathways appearing as the optimal solution and the cumulative distribution of GOM are shown in Fig. 3 (a) and (b), respectively. The results in Table 3 and Fig. 3 indicate that the uncertainty in the problem dataset indeed has a large impact on the selection of optimal processing pathways as well as the on their economic performances, and therefore the uncertainty needs to be considered for robust decision-making.

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The optimal processing pathway for the nominal scenario (Solution 1), one out of the 200 scenarios with the nominal values of the parameters, can be found in Table 4. The solution of the stochastic optimization problem, the processing pathway maximizing the average GOM

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value over the 200 scenarios (Solution 2), is also given in Table 4. Finally, the optimal pathway maximizing the average GOM value over just the 10 worst-case scenarios (Solution

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3) is also calculated and given in the same table. The economic performance indicators (such

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as the GOM value under the nominal parameter set, the average GOM value over the 200 scenarios, and the average GOM value over the respective 10 worst-case scenarios) of the

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three different optimal solutions are given in Table 5. A summary of model and solution statistics is provided in Table 6. The computational time reported in Table 6 is obtained by

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using a computer with an Intel® Core™ i3-2100 @ 3.10 GHz processor and 8 GB RAM.

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Appendix (see Table A.2).

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Other information associated with these pathways such as product yield is provided in the

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3.2.1 Solution 1: Deterministic optimal solution for the nominal scenario Fig. 4 represents the optimal processing pathway obtained by solving the deterministic optimization model for the maximization of GOM under the nominal scenario; it consists of the open pond cultivation, harvesting of microalgal biomass by flocculation using poly electrolyte as a flocculent, drying of harvested biomass, acidic in-situ transesterification, post-transesterification purification, and anaerobic digestion for conversion of microalgae residue into biogas. GOM for this pathway is found to be a loss of $46.493 which implies that the operating cost is higher than the revenue. For economic feasibility, there needs to be more technical breakthroughs in both the engineering and biological aspects of microalgae (Rizwan et al., 2015). 14

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The deterministic optimal solution describes the production of biodiesel from the lipid contents of microalgae via in-situ transesterification along with the production of biogas from the residue via anaerobic digestion. The expected value of GOM over the 200 scenarios is

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found to be $ -53.613. For the worst 10 scenarios, the value drops further to $ -73.374. It is possible that the deterministic optimal pathway only performs well under the nominal

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scenario and is not a robust solution when the uncertainties are present.

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However, considering the advantages of in-situ transesterification (e.g., direct conversion of microalgal lipids into biodiesel thus avoiding/bypassing the lipid extraction stage),

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researchers need to pay more attention and devote more experimental efforts to it with the

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aim of producing a more reliable dataset.

3.2.2 Solution 2: Average-optimal solution over the 200 sampled scenarios

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The stochastic optimal processing pathway found by maximizing the average GOM value for

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the 200 sampled scenarios is shown in Fig. 5, which is different from the one obtained by the

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previous deterministic optimization. The pathway under uncertainty consists of the open pond cultivation, harvesting of microalgal biomass by flocculation using poly electrolyte as a flocculent, wet lipid extraction, base catalyzed transesterification followed by the purification step, and anaerobic digestion for the conversion of microalgae residue into biogas. In contrast to the previous solution, here the biodiesel production is described by the wet lipid extraction method followed by base catalyzed transesterification while all the other technological alternatives remain the same. This implies that the production of biodiesel via base catalyzed transesterification is a more robust choice than the newly developed alternative, i.e., in-situ transesterification which performs well under the nominal scenario but may come with more downside risks. Wet lipid extraction also comes with the advantage that 15

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no drying operation is required prior to the extraction of lipids, thus eliminating one of the energy intensive processes (Rizwan et al., 2015). On the other hand, wet lipid extraction also

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has some drawbacks such as low lipid yield and the requirement of large volume of solvents. The expected value of GOM over the 200 scenarios is found to be $ -47.748, which is slightly

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lower than the value achieved based on the nominal scenario parameters ($ -47.054). However, this is a significant improvement over the deterministic-optimal solution, which

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gave much a lower average GOM of $ -53.613. In addition, GOM achieved under the nominal scenario was sacrificed very little ($ -47.054 vs. $ -46.493). In other words, by

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solving a more elaborate stochastic programming model considering the uncertainties, an alternative solution is found that increases the expected value of GOM by more than 10%.

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These findings highlight that the uncertainties in the problem dataset have significant effect on the optimal structure of microalgae-based biorefinery and should be considered in the

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decision-making process. The pathway also gives a higher average GOM value over its 10

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worst-case scenarios compared to the deterministic optimal solution (as presented in Table 5).

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However, a better solution may exist for this objective as the solution found is not optimal for

3.2.3 Solution 3: Average-optimal solution over the 10 “worst-case” scenarios (not preselected)

The pathway obtained by solving the stochastic programming model considering the 10 worst-case scenarios is given in Fig. 6, which is slightly different from the previous two solutions. It consists of open pond cultivation, harvesting of microalgal biomass by flocculation using poly electrolyte as a flocculent, wet lipid extraction, base catalyzed transesterification followed by the purification step, and enzymatic hydrolysis and 16

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fermentation for the conversion of microalgae residue into bioethanol. In contrast to the optimal pathway for the 200 scenarios, here bioethanol is produced from the processing of microalgae residue instead of biogas because the conversion of the residue into bioethanol is

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less sensitive compared to its conversion into biogas at the extreme lower side of the values

from the residue is more robust than the production of biogas.

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(worst values), as can be seen in Fig. 2. Thus, under worst scenarios, bioethanol production

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The average value of GOM over its 10 worst-case scenarios is found to be $-67.740, which is higher than those (i.e., the average GOM values over their respective 10 worst-case

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scenarios) of the other two pathways ($ -70.743 and $ -73.374). On the other hand, compared to Solution #2, it gives a lower average value of GOM if the whole uncertain space is

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considered ($ -51.585 vs. $ -47.748). Given the on-going research efforts by many

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researchers in this area, the uncertainty levels should decrease in the future, which should

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lead to more insights and predictable economic assessments.

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4. Conclusions and Future Recommendations In this paper, a stochastic optimization model has been developed to assess the impact of major uncertainties in the model parameters on the selection of optimal processing pathways for the production of biofuels from microalgae under uncertainty. The previously developed superstructure based modeling framework has been extended to formulate sMINLP problem by incorporating major uncertainties in the model parameters into the optimization. The developed framework has been implemented on a specific case study (based on microalgal biorefinery) that demonstrates and highlights the capability of the framework to address the major uncertainties present in the techno-economic assessment and optimal processing pathway selection for the microalgal biorefinery design. 17

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The optimization results show that the uncertainty in the problem dataset has a large impact on the optimal biorefinery configurations as well as on the achieved GOM. The optimal biorefinery design determined by considering the 200 sampled scenarios in the uncertain

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parameter space gives better performance compared to the deterministic design that considers the nominal values of the parameters only. As future work, the modeling framework will be

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extended to consider a more diverse set of objective functions that reflect different risk

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aversion strategies.

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Acknowledgement

This work was supported by the Advanced Biomass R&D Center (ABC) of Global Frontier

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Project funded by the Ministry of Education, Science and Technology (ABC-2011-0031354).

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Appendix

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In this appendix, the mass balance constrains and energy balance constraints (adapted from

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our previous study (Rizwan et al., 2015)) are reformulated for scenario s. The indices, input parameters, and the decision variable are defined and listed in Table A.1. Mass balance constraints

Mass balance constraints must be satisfied at each processing stage. The general flow diagram for a processing stage and that for each technological alternative/option within a stage are given by the illustrations in Fig. A.1 (a) and (b) respectively. The nomenclature is given in Table A.1. As illustrated in Fig. A.1 (a), there are three kinds of incoming streams to stage j for each component i (which is an index used to keep track of all the components involved including those in the feed, product, and additive streams); 1) 18

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process stream Fi( i ), j 1 continuing from stage j-1 onto stage j, 2) recycle stream Ri , j 1 coming from stage j+1 to stage j and 3) externally added/makeup stream Qi , j fed to stage j. Here to

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keep the model form simple, it is assumed that the recycling is considered from stage j+1 to stage j, as it is the case for the recycling of water from the harvesting stage to the preceding

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one, i.e., the cultivation stage, and it does hold true for the recovery and recycling of methanol as well. However, the index j+1 can be generalized to incorporate recycling from

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any later stage. In the similar fashion to incoming streams, there are also three kinds of

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outgoing streams; 1) process stream Fi , j leaving stage j and continuing onto stage j+1, 2) recycle stream leaving stage j and will be added in stage j-1 and 3) waste stream Wi , j leaving

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stage j for disposal.

Binary variable y k , j is used for the selection of option k from stage j (if the corresponding

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option is selected, y k , j equals to 1; otherwise y k , j equals to 0). These binary variables determine the optimal processing pathways and thus are the main decision variables. In the

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proposed biorefinery superstructure, it is assumed that only one option can be selected at each processing stage. Therefore, the following constraint is enforced:

y k

k, j

1

(A.1)

Given the constraint as in Eq (A.1), Fi , j , s , the flow of process stream for scenario s leaving stage j is given by:

Fi , j , s   ( yk , j  Fˆi , k , j , s ) k

19

Page 19 of 50

(A.2) where Fˆi , k , j , s is the flow of component i in process stream for scenario s, leaving option k of

ip t

stage j. The flow of component i in waste stream leaving the stage j without continuing on to the next

cr

stage Wˆi , k , the flow of stream Qi , j , the flow of recycle stream Ri , j , and the flow of utility

us

stream U l , j are modeled for scenario s in a similar fashion as given below:

an

Wi , j , s   ( yk , j  Wˆi , k , j , s ) k

M

(A.3)

Qi , j , s   ( yk , j  Qˆi , k , j , s )

(A.5)

Ac ce p

k

te

Ri , j , s   ( yk , j  Rˆi , k , j , s )

(A.4)

d

k

U , j , s   ( yk , j  Uˆ  , k , j , s ) k

(A.6)

As shown in Fig. A.1 (b), it is assumed that a sequence of tasks is occurring for each option/technological alternative box. These tasks include (1) mixing (2) reaction and (3) separation. Considering these tasks, mass balance around option k of processing stage j is modeled by equations (A.7) – (A.14) for scenario s. Mixing

20

Page 20 of 50

Fˆi ,ink , j , s   i , k , j  Fi , j 1, s  Ri , j 1, s  Qˆ i , k , j , s

(A.7)

ip t

where Fi , j 1, s is the flow of process stream of component i for scenario s going from stage j-1 to option k of stage j,  i ,k , j is a split factor of component i entering to option k of stage j and

cr

is used for the separation of microalgae residue from the lipid stream, Ri , j 1, s is the flow of

us

the recycle stream of component i for scenario s coming from stage j+1 to option k of stage j and Qˆ i , k , j , s is the flow of the externally added/makeup stream of component i for scenario s

Qˆ i , k , j , s    i , i, k , j  Fi, j 1, s 

M

i

an

fed to option k of stage j which is given by:

d

(A.8)

Ac ce p

incoming component iʹ.

te

where  i ,i,k , j is the fraction of chemicals/solvents (component i) added with respect to

Reaction

 Fˆmin,k, j,s  ˆ in   ( Fˆi,out F  )   MWi    k , j ,s i,k , j ,s i,r ,k , j m,r ,k , j ,s   MW r m , m  

(A.9)

where  i ,r ,k , j is the stoichiometric coefficient of product i in reaction r,  m , r , k , j , s is the fractional conversion of reactant m for reaction r for scenario s, Fˆmin, k , j , s is the flow of reactant m for scenario s at the inlet of option k of stage j, MWi is the molecular weight of components, The conversion of microalgae residue is modeled with the help of yield 21

Page 21 of 50

coefficient as: ˆ in ˆ in Fˆi ,out k , j ,s  Fi ,k , j ,s  (i ,i,k , j ,s  Fi,k , j ,s )

(A.10)

i

ip t

where i ,i , k , j , s is the yield coefficient of product (obtained from residue) i with respect to the

cr

incoming flow of component (components in the residue) iʹ for scenario s in option k of stage j, Fˆi in, k , j , s is the flow of component (components in the residue) iʹ for scenario s in option k of

us

stage j.

an

Separation

M

ˆ ˆ Fˆi , k , j , s  Fˆi ,out k , j , s  Ri , k , j , s  Wi , k , j , s (A.11)

d

where Fˆi , k , j , s is the flow of process stream of component i for scenario s leaving option k of

Ac ce p

given by:

te

stage j. Rˆi , k , j , s is the flow of recycle stream for scenario s leaving option k of stage j which is

ˆ out Rˆi , k , j , s  irecycle , k , j  Fi , k , j , s

(A.12)

is the split factor for the recycle stream. where irecycle ,k , j

Wˆi , k , j , s is the flow of waste stream for scenario s leaving option k of stage j which is given by: ˆ out Rˆi , k , j , s  iwaste , k , j  Fi , k , j , s (A.13) where iwaste , k , j is the split factor for the waste stream. 22

Page 22 of 50

Raw material/Feed assignment Option 1 of stage 1 describes the state of raw material (feed) which is represented by: Fˆi ,1,1, s  i , s

cr

where i,s is the composition of feed/raw material for scenario s.

ip t

(A.14)

us

Energy balance constraints

Energy balances involve the amount of energy required to operate all the technologies

an

included in the proposed biorefinery superstructure based on the mass flows. These energy requirements are met by the use of utilities such as steam, electricity, etc. The flow of utility

(A.15)



d

i

te



Uˆ , k , j , s   ,i , k , j  Fˆi in, k , j , s

M

stream Uˆ l , k , j , s for scenario s, fed to option k of stage j is given by:

Ac ce p

where  l ,i , k , j is the fraction of utilities added and is calculated with respect to each component i of the incoming process streams.

References

Amaro, H. M., Guedes, A. C., Malcata, & F. X. (2011). Advances and perspectives in using microalgae to produce biodiesel. Applied Energy, 88, 3402-3410. Araujo, G. S., Matos, L. J. B. L., Goncalves, L. R. B., Fernandes, F. A. N., & Farias, W. R. L. (2011). Bioprospecting for oil producing microalgal strains: Evaluation of oil and biomass production for ten microalgal strains. Bioresource Technology, 102, 5248-5250.

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Becker, E. W. (2004). Microalgae in human and animal nutrition, in: Richmond A. (Ed.), Handbook of Microalgal Culture. Blackwell Publishing: Oxford, pp. 312-351. Bilad, M. R., Vandamme, D., Foubert, I., Muylaert, K., & Vankelecom, I. F. J. (2012).

ip t

Harvesting microalgal biomass using submerged microfiltration membranes. Bioresource Technology, 111, 343-352.

cr

Birge, J. R., & Louveaux, F. (1999). Introduction to stochastic programming (Springer Series in Operation Research), Springer: New York, U. S.

us

Brentner, L. B., Eckelman, M. J., & Zimmerman, J. B. (2011). Combinatorial life cycle assessment to inform process design of industrial production of algal biodiesel.

an

Environmental Science and Technology, 45, 7060-7067.

Brun, R., Kuhni, M., Siegrist, H., Gujer, W., & Reichert, P. (2002). Practical identifiability of

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ASM2d parameters – systematic selection and tuning of parameter susets. Water Research, 36, 4113-4127.

d

Cheali, P., Quaglia, A., Gernaey, K. V., & Sin, G. (2014). Effect of market price uncertainties on the design of optimal biorefinery systems – A systematic approach. Industrial and

te

Engineering Chemistry Research, 53, 6021-6031.

Ac ce p

Chisti, Y. (2007). Biodiesel from microalgae. Biotechnology Advances, 25, 294-306. Choi, S., Oh, Y., Jeong, M., Kim, S. W., Lee, J., & Park, J. (2014). Effects of ionic liquid mixtures on lipid extraction from Chlorella vulgaris. Renewable Energy, 65, 169-174. Dassey, A. J., Hall, S. G., & Theegala C. S. (2014). An analysis of energy consumption for algal biodiesel production: Comparing the literature with current estimates. Algal Research, 4, 89-95.

Davis, R., Aden, A., & Pienkos, P. T. (2011). Techno-economic analysis of autotrophic microalgae for fuel production. Applied Energy, 88. 3524-3531. Demirbas, A. (2011). Competitive liquid biofuels from biomass. Applied Energy, 88, 17-28. Dhar, B. R., & Kirtania, K. (2009). Excess methanol recovery in biodiesel production process using a distillation column: A simulation study. Chemical Engineering Research Bulletin, 13, 24

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55-60. Dua, V., & Pistikopoulos, E. N. (1998). Optimization techniques for process syntesis and material design under design. Chemical Engineering Research and Design, 76, 408-416.

ip t

Ehimen, E. A., Connaughton, S., Sun, Z., & Carrington, G. C. (2009). Energy recovery from lipid extracted, transesterified and glycerol codigested microalgae biomass. GCB Biology, 1,

cr

371-381.

Gebreslassie, B. H., Waymire, R., & You, F. (2013). Sustainable design and synthesis of sequestration. AIChE Journal, 59 (5), 1599-1621.

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algae-based biorefinery for simultaneous hydrocarbon biofuels production and carbon

an

Glisic, S. B., & Skala, D. U. (2009). Design and optimization of purification procedure for biodiesel washing. Chemical Industry and Chemical Engineering Quarterly, 15, 159-168.

M

Glover, F. (1975). Improved linear integer programming formulations of nonlinear integer problems. Management Science, 22(4), 455-460.

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Gong, J., & You, F. (2014a). Optimal design and synthesis of algal biorefinery processes for

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biological carbon sequestration and utilization with zero direct greenhouse gas emissions: MINLP model and global optimization algorithm. Industrial and Engineering Chemistry

Ac ce p

Research, 53, 1563-1579.

Gong, J., & You, F. (2014b). Global optimization for sustainable design and synthesis of algae processing network for CO2 mitigation and biofuel production using life cycle optimization. AIChE Journal, 60, 3195-3210. Granados, M. R., Acien, F. G., Gomez, C., Fernandez-Sevilla, J. M., & Grima, E. M. (2012). Evaluation of flocculants for the recovery of freshwater microalgae. Bioresource Technology, 118, 102-110.

Grossmann, I. (2005). Enterprise-wide optimization: A new frontier in process systems engineering. AIChE Journal, 51, 1846-1857. Holm-Nielsen, J. B., Al Seadi, T., & Oleskowicz-Popiel, P. (2009). The future of anaerobic digestion and biogas utilization. Bioresource Technology , 100, 5478-5484. 25

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Jeon, J., Choi H., Yoo, G, Choi, Y., Choi, K., Park, H., Park, S., Kim, Y., Kim, H. J., Lee, S. H., Lee, Y. K., & Yang, Y. (2013). New mixture composition of organic solvents for efficient extraction of lipids from Chlorella vulgairs. Biomass and Bioenergy, 59, 279-284.

ip t

Karuppiah, R., & Grossmann, I. E. (2008). Global optimization of multiscenarios mixed integer nonlinear programming models arising in the synthesis of integrated water networks

cr

under uncertainty. Computers and Chemical Engineering, 32, 145-160.

Kim, J., Realff, M. J., & Lee, J. H. (2011). Optimal design and global sensitivity analysis of

us

biomass supply chain networks for biofuels under uncertainty. Computers and Chemical Engineering, 35, 1738-1751.

an

Kim, Y., Park, S., Kim, M. H., Choi, Y., Yang, Y., Kim, H. J., Kim, H., Kim, H., Song, K., & Lee, S. H. (2013). Ultrasound-assisted extraction of lipids from Chlorella vulgaris using

M

[Bmim][MeSO4]. Biomass and Bioenergy, 56, 99-103.

Lam, M. K., & Lee, K. T. (2013). Catalytic transesterification of high viscosity crude

d

microalgae lipid to biodiesel: Effect of co-solvent. Fuel Processing Technology, 110, 242-248. Lee, A. K., Lewis, D. M., & Ashman, P. J. (2012). Disruption of microalgal cells for the

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Bioenergy, 46, 89-101.

te

extraction of lipids for biofuels: Processes and specific energy requirements. Biomass and

Liu, P., Pistikopoulos, E. N., & Li, Z. (2009). An energy systems engineering approach to polygeneration and hydrogen infrastructure systems analysis and design. Chemical Engineering Transactions, 18, 373-378. Mata, T. M., Martins, A. A., & Caetano, N.S. (2010). Microalgae for biodiesel production and other applications: A review. Renewable and Sustainable Energy Reviews, 14, 217-232. Mckay, M. D., Beckam, R. J., & Conover, W. J. (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21, 239-245. Mendes, R. L., Coelho, J. P., Fernandes, H. L., Marrucho, I. J., Cabral, J. M. S., Novais, J. M., et al. (1995). Application of supercritical CO2 extraction to microalgae and plants. Journal of Chemical Technology and Biotechnology, 62, 53-59. 26

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Moncada, J., Jaramillo, J. J., Higuita, J. C., Younes, C., & Cardona, C. A. (2013). Production of bioethanol using Chlorella vulgaris Cake: A technoeconomic and environmental assessment in the Colombian context. Industrial and Engineering Chemistry Research, 52,

ip t

16786-16794. Moon, C., Ahn, J. H., Kim, S. W., Sang, B. I., & Um, Y. (2010). Effect of biodiesel-derived raw glycerol on 1,3-propanediol production by different microorganisms. Applied

cr

Biochemistry and Biotechnology, 161, 502-510.

us

Mu, Y., Teng, H., Zhang, D. J., Wang, W., & Xiu, Z. L. (2006). Microbial production of 1,3propanediol by Klebsiella pneumoniae using crude glycerol from biodiesel preparations.

an

Biotechnology Letters, 28, 1755-1759.

Orta, S. B. V., Lee, J. G. M., & Harvey, A. (2012). Alkaline in situ transesterification of Chlorella vulgaris. Fuel, 94, 544-550.

M

Park, J.Y., Oh, Y. K., Lee, J. S., Lee, K., Jeong, M. J., & Choi, S. A. (2014). Acid-catalyzed hot-water extraction of lipids from Chlorella vulgaris. Bioresource Technology, 153, 408-412.

d

Plata, V., Kafarov, V., & Moreno., N. (2010). Optimization of third generation biofuels

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production: Biodiesel from microalgae oil by homogenous transesterification. Chemical

Ac ce p

Engineering Transactions, 21, 1201-1206. Quaglia, A., Sarup, B., Sin, G., & Gani, R. (2013). A systematic framework for enterprisewide optimizaion: Synthesis and design of processing networks under uncertainty. Computers and Chemical Engineering, 59, 47-62. Rashid, N., Rehman, S. U., & Han, J. (2013). Rapid harvesting of freshwater microalgae using chitosan. Process Biochemistry, 48, 1107-1110. Rawat, I., Kumar, R. R., Mutanda, T., & Bux, F. (2013). Biodiesel from microalgae: A critical evaluation from laboratory to large scale production. Applied Energy, 103, 444-467. Rizwan, M., Lee, J. H., & Gani, R. (2013a). Optimal processing pathway for the production of biodiesel from microalgal biomass: A superstructure based approach. Computers and Chemical Engineering, 58, 305-314. 27

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Rizwan, M., Lee, J. H., & Gani, R. (2013b) Superstructure optimization of biodiesel production from microalgal biomass. Proceedings of the 10th IFAC International Symposium on Dynamics and Control of Process Systems (DYCOPS) 2013; Elsevier Science: Pages 111-

ip t

116. Rizwan, M., Lee, J. H., & Gani, R. (2015). Optimal design of microalgae-based biorefinery:

cr

Economics, opportunities and challenges. Applied Energy, 150, 69-79.

Safi, C., Zebib, B., Merah, O., Pontalier, P., & Vaca-Garcia, C. (2014). Morphology,

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composition, production, processing and applications of Chlorella vulgaris: A review. Renewable and Sustainable Energy Reviews, 35, 265-278.

an

Salim, S., Vermue, M. H., & Wijffels, R. H., (2012). Ratio between autoflocculating and target microalgae affects the energy-efficient harvesting by bio-flocculation. Bioresource Technology, 118, 49-55.

M

Sin, G., Gernaey, K. V., & Lantz, A. E. (2009). Good modeling practice for PAT Progress, 25 (4), 1043-1053.

d

applications: Propgataion of input uncertainty and sensitivty analysis. AIChE Biotechnology

te

Sostaric, M., Klinar, D., Bricelj, M., Golob, J., Berovic, M., & Likozar, B. (2012). Growth, lipid extraction and thermal degradation of the microalgal Chlorella vulgaris. New

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Biotechnology, 29, 325-331.

Tran, D. T., Yeh, K. L., Chen, C. L., & Chang, J. S. (2012). Enzymatic transesterification of microalgal oil from Chlorella vulgaris ESP-31 for biodiesel synthesis using immobilized Burkholderia lipase. Bioresource Technology, 108, 119-127. Vandamme, D., Foubert, I., Fraeye, I., Meesschaert, B., & Muylaert, K. (2012). Flocculation of Chlorella vulgaris induced by high pH: Role of magnesium and calcium and practical implications. Bioresource Technology, 105, 114-119. Wang, K., Brown, R. C., Homsy, S., Martinez, L., & Sidhu. S. S. (2013). Fast pyrolysis of microalgae remnants in a fluidized bed reactor for bio-oil and biochar production. Bioresource Technology, 127, 494-499. Yen, H. W., Hu, I. C., Chen, C. Y., Ho, S. H., Lee, D. J., & Chang, J. S. (2013). Microalgae28

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based biorefinery – From biofuels to natural products. Bioresource Technology, 135, 166-174. Yue, D., You, F., & Snyder, S. W. (2014). Biomass-to-bioenergy and biofuel supply chain optimization: Overview, key issues and challenges. Computers and Chemical Engineering,

ip t

66, 36-56. Zhang, Y., Dube, M. A., McLean, D. D., & Kates, M. (2003). Biodiesel production from

cr

waste cooking oil: 1. Process design and technological assessment. Bioresource Technology, 89, 1-16.

us

Zheng, H., Yin J., Gao, Z., Huang, H., Ji, X., & Dou, G. (2011). Disruption of chlorella vulgaris cells for the release of biodiesel-producing lipids: A comparison of grinding,

an

ultrasonication, bead milling, enzymatic lysis, and microwaves. Applied Biochemistry and Biotechnology, 164, 1215-1224.

M

Zheng, H., Gao, Z., Yin, J., Tang, X., Ji, X., & Huang, H. (2012). Harvesting of microalgae

Ac ce p

te

d

by flocculation with poly (γ-glutamic acid). Bioresource Technology, 112, 212-220.

29

Page 29 of 50

ip t cr us an

List of Figures

M

Fig. 1. Biorefinery superstructure for the production of biofuels from C. vulgaris (Rizwan et

d

al., 2015)

te

Fig. 2. Sensitivity analysis of the 25 key model parameters

Ac ce p

Fig. 3. (a) Probability of selection of pathways, (b) Cumulative distribution of GOM Fig. 4. Deterministic optimal processing pathway for the nominal case Fig. 5. Optimal processing pathway under uncertainty Fig. 6. Worst-case processing pathway Fig. A.1. Representation of (a) stage j and (b) option k in stage j (taken from Rizwan et al., 2015)

30

Page 30 of 50

ip t cr us an

M

List of Tables

Table 1. List of technological alternatives/options (Rizwan et al., 2015)

te

d

Table 2. Uncertain parameters and their assigned uncertainty class

Ac ce p

Table 3. Distribution of optimal process pathways obtained for 200 scenarios Table 4. Optimal process pathways under different assumed parameter sets Table 5. Economic performance of the three optimal solutions Table 6. Solution statistics Table A.1. Nomenclature

Table A.2. Product yield associated with optimal solutions

31

Page 31 of 50

ip t cr us an

Feed

Cultivation

Harvesting

Pretreatment

Lipid extraction

1,2

3,5

4,4

4,5

4,3

5,3

6,3

5,4

Conversion of residue

Products

1,8

1,9

Biodiesel

2,8

2,9

Glycerol

3,8

3,9

Bio-oil

4,8

4,9

Bioethanol

5,8

5,9

Biogas

1,6

2,6

1,7

3,6 5,5

Feed

2,2

Pretreatment of residue

d

3,4

Ac ce p

3,3

Post transesterification purification

2,5

te

2,3

2,4

Transesterification

1,5

1,4 1,3

M

Fig. 1

6,5 7,5 4,6

Main stream

8,5

7,3

9,5

Microalgae residue

5,6

Recycle stream

8,3

10,5

6,6 2,7

7,6

Fig. 1. Biorefinery superstructure for the production of biofuels from C. vulgaris (Rizwan et al., 2015)

32

Page 32 of 50

ip t cr us an

Ac ce p

te

d

M

Fig. 2

33

Page 33 of 50

ip t cr us an M d

Ac ce p

te

Fig. 2. Sensitivity analysis of the 25 key model parameters

Fig. 3 34

Page 34 of 50

us

cr

ip t te

d

M

an

(a)

Ac ce p

(b)

Fig. 3. (a) Probability of selection of pathways, (b) Cumulative distribution of GOM

35

Page 35 of 50

Fig. 4 Flocculation by poly electrolyte (1,3)

Biodiesel (8.814 GGEs)

Empty (1,9)

Empty (1,8)

Glycerol (0.468 GGEs)

Empty (2,9)

Empty (2,8)

Drying (5,4)

Acidic in-situ transesterification (5,6)

Empty (10,5)

Purification of biodiesel

Washing of biodiesel layer

Flash separation

Washing of glycerol layer

ip t

Open pond cultivation (1,2)

Gravity separation

Methanol recovery

cr

Chlorella vulgaris (Basis: 100 kg dry biomass)

Anaerobic digestion (5,9)

Empty (5,8)

Empty (2,7)

Main stream Microalgae residue

an

Biogas (4.912 GGEs)

us

(1,7)

Ac ce p

te

d

M

Fig. 4. Deterministic optimal processing pathway for the nominal case

36

Page 36 of 50

Fig. 5 Chlorella vulgaris (Basis: 100 kg dry biomass)

Open pond cultivation (1,2)

Flocculation by poly electrolyte (1,3)

Alkaline transesterification (1,6)

Wet lipid extraction (4,5)

Empty (4,4)

Empty (1,9)

Empty (1,8)

Purification of biodiesel

Washing of biodiesel layer

Glycerol (0.427) GGEs)

Empty (2,9)

Empty (2,8)

Flash separation

Washing of glycerol layer

Gravity separation

Methanol recovery

us

cr

Biodiesel (8.031 GGEs)

ip t

Empty (7,6)

(1,7)

Anaerobic digestion (5,9)

Empty (5,8)

an

Biogas (4.900 GGEs)

Empty (2,7)

Main stream Microalgae residue

Ac ce p

te

d

M

Fig. 5. Optimal processing pathway under uncertainty

37

Page 37 of 50

Fig. 6 Chlorella vulgaris (Basis: 100 kg dry biomass)

Open pond cultivation (1,2)

Flocculation by poly electrolyte (1,3)

Alkaline transesterification (1,6)

Wet lipid extraction (4,5)

Empty (4,4)

Empty (1,9)

Empty (1,8)

Purification of biodiesel

Washing of biodiesel layer

Glycerol (0.159 GGEs)

Empty (2,9)

Empty (2,8)

Flash separation

Washing of glycerol layer

Gravity separation

Methanol recovery

us

cr

Biodiesel (2.992 GGEs)

ip t

Empty (7,6)

(1,7)

Enzymatic hydrolysis (4,8)

Fermentation (4,9)

an

Bioethanol (2.381 GGEs)

Empty (2,7)

Main stream Microalgae residue

Ac ce p

te

d

M

Fig. 6. Worst-case processing pathway

38

Page 38 of 50

Fig. A.1 Qi , j

Fi , j

Ri , j

k,j

Fˆi ,k , j

Fˆi ,out k, j

Rˆi ,k , j

Ri , j 1

Wˆi ,k , j

us

Ri , j 1

Fˆi ,ink , j

Fi( i ), j 1

cr

Fi ( i ), j 1

ip t

Qˆ i ,k , j

Wi , j

(a)

(b)

Ac ce p

te

d

M

an

Fig. A.1. Representation of (a) stage j and (b) option k in stage j (taken from Rizwan et al., 2015)

39

Page 39 of 50

Table 1 Table 3. List of technological alternatives/options (Rizwan et al., 2015) Technological alternative/option

Reference

1,1

Feed

Safi et al., 2014

1,2

Open pond system

Davis et al., 2011; Dassey et al., 2014

2,2

Photobioreactor

Davis et al., 2011; Dassey et al., 2014

1,3

Flocculation with poly electrolyte

Granados et al., 2012

2,3

Flocculation with NaOH

Araujo et al., 2011

3,3

Flocculation with PGA

Zheng et al., 2012

4,3

Flocculation

chitosan

cr

us

with

ip t

Box No.

acid Rashid et al., 2013

an

solution 5,3

Bioflocculation + Centrifugation

Salim et al., 2012

6,3

Centrifugation

7,3

Auto flocculation (induced by high Vandamme et al., 2012

M

Salim et al., 2012

pH)

Microfiltration + Centrifugation

Bilad et al., 2012

1,4

Grinding in liquid nitrogen

Zheng et al., 2011

2,4

Drying + Ultrasound

3,4

Drying + Grinding + Microwave + Sostaric et al., 2012

te

d

8,3

Ac ce p

Kim et al., 2013

Ultrasound

4,4 5,4 1,5 2,5

Empty

Drying

Lee et al., 2012; Sostaric et al., 2012

Grinding-assisted lipid extraction

Zheng et al., 2011

Ultrasound assisted extraction by

Kim et al., 2013

[Bmim][MeSO4]

3,5

Ultrasound and microwave assisted

Sostaric et al., 2012

lipid extraction 4,5

Wet lipid extraction

Park et al., 2014

5,5

Solvent extraction (Bligh and Dyer’s Jeon et al., 2013 Method)

6,5

Solvent extraction (Modified Bligh Jeon et al., 2013 40

Page 40 of 50

and Dyer’s Method) Supercritical fluid extraction

Mendes et al., 1995; Brentner et al., 2012

8,5

Extraction by ionic liquids mixture

Choi et al., 2014

9,5

Extraction by [Bmim][MeSO4]

Kim et al., 2013

10,5

Empty

1,6

Base catalyzed transesterification

Plata et al., 2010

2,6

Acid catalyzed transesterification

Lam and Lee, 2013

3,6

Enzymatic transesterification

Tran et al., 2012

4,6

Alkaline in-situ transesterification

Orta et al., 2012

5,6

Acidic in-situ transesterification

Orta et al., 2012

6,6

Enzymatic in-situ transesterification

Tran et al., 2012

7,6

Empty

1,7

Methanol recovery + Gravity

an

us

cr

ip t

7,5

Dhar and Kirtani, 2009; Glisic and Skala, 2009; Zhang et al., 2003

M

separation + Washing of biodiesel

layer + Purification of biodiesel layer + Washing of glycerol layer + Flash

1,8

Empty

2,8

Empty

3,8 4,8 5,8 1,9 2,9 3,9

te

Empty

Ac ce p

2,7

d

separation

Empty

Enzymatic hydrolysis

Moncada et al., 2013

Empty Empty Empty

Fast pyrolysis

Wang et al., 2013

4,9

Fermentation

Moncada et al., 2013

5,9

Anaerobic digestion

Ehimen et al., 2009

1,10

Biodiesel

Chisti, 2007; Demirbas, 2011; Amaro et al., 2011

2,10

Glycerol

Moon et al., 2010; Mu et al., 2006 41

Page 41 of 50

3,10

Bio-oil

Wang et al., 2013

4,10

Bioethanol

Moncada et al., 2013

5,10

Biogas

Holm-Nielsen et al., 2009; Ehimen et al.,

Ac ce p

te

d

M

an

us

cr

ip t

2009

42

Page 42 of 50

Table 2 Table 4. Uncertain parameters and their assigned uncertainty class Uncertainty Class

Variations (%)

Low

5

Fractional conversion of lipids (for base catalyzed transesterification)

ip t

Parameters

cr

Fractional conversion of lipids (for acidic in-situ transesterification) Medium

Lipid yield (for wet lipid extraction) Cost of feed (CO2, nitrogen,

an

phosphorous) Lipid contents Fractional conversion of residue (for

M

High

25

50

Ac ce p

te

d

bioethanol and biogas production)

us

CO2 conversion/fixation

43

Page 43 of 50

Table 3 Table 3. Distribution of optimal process pathways obtained for 200 scenarios

(2,9) (5,9) (1,10) (2,10) (5,10)

(1,1) (2,2) (1,3) (4,4) (4,5) (1,6) (7,6) (1,7) (2,7) (1,8) (2,8) (5,8) (1,9)

cr

2

(2,9) (5,9) (1,10) (2,10) (5,10)

(1,1) (1,2) (1,3) (4,4) (4,5) (1,6) (7,6) (1,7) (2,7) (1,8) (2,8) (4,8) (1,9)

us

3

(2,9) (4,9) (1,10) (2,10) (4,10) 4

(1,1) (1,2) (1,3) (5,4) (10,5) (5,6) (1,7) (2,7) (1,8) (2,8) (5,8) (1,9) (2,9)

an

(5,9) (1,10) (2,10) (5,10) 5

(1,1) (2,2) (1,3) (5,4) (10,5) (5,6) (1,7) (2,7) (1,8) (2,8) (5,8) (1,9) (2,9) (1,1) (2,2) (1,3) (4,4) (4,5) (1,6) (7,6) (1,7) (2,7) (1,8) (2,8) (4,8) (1,9) (2,9) (4,9) (1,10) (2,10) (4,10)

(1,1) (1,2) (1,3) (5,4) (10,5) (5,6) (1,7) (2,7) (1,8) (2,8) (4,8) (1,9) (2,9)

d

7

M

(5,9) (1,10) (2,10) (5,10) 6

Frequency of selection 51

ip t

Pathway Processing pathways No. 1 (1,1) (2,2) (1,3) (4,4) (4,5) (1,6) (7,6) (1,7) (2,7) (1,8) (2,8) (5,8) (1,9)

32 25 24 22 19 17

(1,1) (2,2) (1,3) (5,4) (10,5) (5,6) (1,7) (2,7) (1,8) (2,8) (4,8) (1,9) (2,9)

10

(4,9) (1,10) (2,10) (4,10)

Ac ce p

8

te

(4,9) (1,10) (2,10) (4,10)

44

Page 44 of 50

Table 4 Table 4. Optimal process pathways under different assumed parameter sets Optimal processing pathways

ip t

Solution 1: Deterministic (1,1) (1,2) (1,3) (5,4) (10,5) (5,6) (1,7) (2,7) (1,8) (2,8) (5,8) (1,9) (2,9) (5,9) (1,10) (2,10) (5,10)

optimal under the

cr

nominal scenario

(1,1) (1,2) (1,3) (4,4) (4,5) (1,6) (7,6) (1,7) (2,7) (1,8) (2,8) (5,8)

optimal over the 200

(1,9) (2,9) (5,9) (1,10) (2,10) (5,10)

us

Solution 2: Average-

scenarios

(1,1) (1,2) (1,3) (4,4) (4,5) (1,6) (7,6) (1,7) (2,7) (1,8) (2,8) (4,8) (1,9) (2,9) (4,9) (1,10) (2,10) (4,10)

an

Solution 3: Averageoptimal over the respective 10 worst-case

Ac ce p

te

d

M

scenarios

45

Page 45 of 50

Table 5 Table 5. Economic performance of the three optimal solutions Avg. GOM over the

Avg. GOM over the

nominal scenario ($)

200 sampled

10 worst-case

-46.493

-53.613

Solution 2

-47.054

-47.748

Solution 3

-50.323

-51.585

-73.374 -70.743 -67.740

Ac ce p

te

d

M

an

us

Solution 1

scenarios ($)

cr

scenarios ($)

ip t

GOM under the

46

Page 46 of 50

Table 6 Table 6. Solution statistics

Number of binary

Maximization of

Maximization of

Maximization of

GOM over the single

GOM over the 200

GOM over the 10

nominal scenario

scenarios

worst-case scenarios

23,212

4,631,246

90

90

29,608

4,696,118

variables Number of

0 0.156

231,606 90

234,918

78,251

3,927

0

0

4,978

19.78

Ac ce p

te

d

CPU time (s)

266

M

Optimality gap

an

continuous variables Number of iterations

ip t

Solution 3

cr

Number of equations

Solution 2

us

Objective

Solution 1

47

Page 47 of 50

Table A.1 Table A.1. Nomenclature

Component (i = lipids, carbohydrate, CO2, water, etc.)

l

Utility

j

Processing stage

k

Option/technological alternative

r

Reaction

m

Key reactant, a subset of i

s

Scenario (s = 1,2,…,S where S=200)

sʹ

Worst scenario, a subset of s (sʹ=1,2,… Sʹ where Sʹ =10)

an

Parameters

Fraction of chemical i added with respect to the incoming flow of component iʹ in option k of processing stage j

l ,i , k , j

M

 i ,i  , k , j

us

cr

i, iʹ

ip t

Indices

Fraction of utility l added with respect to the incoming flow of component i in

d

option k of processing stage j

Split factor of component i in option k of processing stage j

 i,r ,k , j

Stoichiometric ratio coefficient of product component i during reaction r in option

te

 i,k , j

Ac ce p

k of processing stage j

 m,r ,k , j , s

Fractional conversion of reactant m during reaction r for scenario s in option k of

processing stage j

MWi

Molecular weight of component i

i ,i ', k , j , s

Yield coefficient of product i with respect to the incoming flow of component iʹ for

scenario s in option k of processing stage j

irecycle ,k, j

Recycle fraction of component i in option k of processing stage j

iwaste ,k , j

Waste fraction of component i in option k of processing stage j

i, s

Composition of raw material/feed for scenario s

P1i

Sale price of products

48

Page 48 of 50

P2i ,s

Cost of raw material (feed) for scenario s

P3 i

Cost of chemicals/solvents

P4l

Cost of utilities

yk,j

ip t

Binary variable

Binary variable; 1 if option k from stage j is selected and 0 if otherwise

cr

Continuous variables

flow of component i in the process stream for scenario s, coming from stage j-1

Fi , j , s

flow of component i in the process stream for scenario s, leaving stage j

Ri , j , s

flow of component i in the recycle stream for scenario s, leaving stage j

Qi , j , s

flow of component i in the chemical/solvent stream for scenario s, added to stage j

Wi , j , s

flow of component i in the waste stream for scenario s, leaving stage j

U l , j ,s

flow of utility l for scenario s, added to stage j

Fˆi , k , j , s

flow of component i in the process stream for scenario s, leaving option k of stage j

Rˆi , k , j , s

flow of component i in the recycle stream for scenario s, leaving option k of stage j

Qˆ i , k , j , s

flow of component i in the chemical/solvent stream for scenario s, added to option k of stage j

te

d

M

an

us

Fi , j 1, s

flow of component i in the waste stream for scenario s, leaving option k of stage j

Uˆ l , k , j , s

flow of utility l for scenario s, added to option k of stage j

Ac ce p

Wˆi , k , j , s

49

Page 49 of 50

Table A.2

Nominal value

Expected value under 200

Yield

Yield

Yield

biodiesel

glycerol

biogas/

biodiesel glycerol

biogas/

(GGEs)

(GGEs)

bioethanol

(GGEs)

bioethanol

8.814

0.468

4.912a

7.855

8.154

0.433

4.910a

8.031

8.154

0.433

3.650b

pathway

biodiesel

glycerol

biogas/

(GGEs)

(GGEs)

bioethanol

8.031

(GGEs)

3.292

0.175

2.783a

0.427

4.900a

2.992

0.159

2.783a

0.427

3.641b

2.992

0.159

2.381b

Ac ce p

a: biogas, b: bioethanol

Yield

te

Worst-case

d

uncertainty

Yield

4.899a

0.417

M

Pathway under

Yield

(GGEs)

an

Pathway

Yield

us

(GGEs)

(GGEs)

Deterministic

worst scenarios

Yield

Yield

Expected value under

cr

scenarios

ip t

Table A.2. Product yield associated with optimal solutions

50

Page 50 of 50