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A Decision Support Tool for Optimal Design of Integrated Biorefineries under Strategic and Operational Level Uncertainties Aryan Geraili, Santiago Salas, and Jose A Romagnoli Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b04003 • Publication Date (Web): 22 Jan 2016 Downloaded from http://pubs.acs.org on January 30, 2016

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Industrial & Engineering Chemistry Research

A Decision Support Tool for Optimal Design of Integrated Biorefineries under Strategic and Operational Level Uncertainties A. Geraili, S. Salas, J.A. Romagnoli* Chemical Engineering Department, Louisiana State University, Baton Rouge, LA 70803, United States

* Corresponding author. E-mail address: [email protected] (J.A. Romagnoli), Postal address: 220 ChE Building, Louisiana State University, Baton Rouge, LA 70803, United States. Phone: 001-225-5781377

Abstract In this work a decision support tool is presented to carefully design and optimize the business value of a renewable energy endeavor considering all types of uncertainties including uncertainties at strategic and operational level. A stochastic linear model is first developed to optimize production capacity of the plant and then process simulation coupled with stochastic optimization algorithm is employed to optimize the operating conditions of the plant. Market uncertainties are taken into account at the strategic planning level, and uncertainties related to parameters characterizing the processing technologies are addressed in operational level optimization. Monte-Carlo based simulation and global sensitivity analysis are utilized to identify the most critical parameters and optimize the operating conditions of the plant accordingly. Additionally, risk measurement strategies are introduced to the framework for explicit treatment of strategic and operational risks. To demonstrate the effectiveness of the proposed methodology, a hypothetical case study of a multiproduct lignocellulosic biorefinery is utilized.

Keywords: Decision support tool; Strategic planning; operational level optimization; Stochastic programming; Uncertainty analysis; Risk management; Renewables; Integrated biorefineries

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1. INTRODUCTION Driven by the increase in industrialization and population, the global demand for energy is steadily growing. Since the world primary sources for energy production are fossil fuels, this growth raises important issues at environmental, economic, and social levels. In recent years, there has been a marked surge in the search for alternative sources of energy that wean the world off of dependence on fossil fuels and reduce the carbon foot-print. As the world has recognized the importance of diversifying its energy resource portfolio away from fossil resources and more towards renewable resources such as biomass, there is also a need for developing strategies which can design renewable sustainable value chains that can be scaled up efficiently and provide tangible net environmental benefits from energy utilization. The improvement of renewable energy technologies will assist sustainable development and provide a solution to several energy related environmental problems. The biorefinery concept embraces a wide range of technologies able to separate biomass resources (wood, grasses, corn, corn stover, etc.) into their building blocks which can be converted to value-added products 1. After a boom in U.S. corn-based ethanol in the early part of the 21st century, the interest has gradually shifted towards more viable sources for production of biofuels and biochemicals. Second generation biofuels are examples of such fuels that are extremely attractive owing to the fact that the raw materials can be composed completely of “left-over” wastes of food crops and forest harvests that don't interfere with the human food chain and the natural ecosystem. It also can provide new income and employment opportunities in rural areas 2. Several contributions have appeared over the last few years in order to manage the complexity of decision making process for designing profitable renewable energy production systems. Painuly

3

developed a multi-phase, stakeholder-based approach to identify the 2 ACS Paragon Plus Environment

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barriers to renewable energy penetration and suggested measures to overcome these limitations. Banos, et al.

4

presented a review of computational optimization strategies that

have been applied to renewable energy production systems. There are existing research works that are devoted to explore the techno-economic feasibility of future biomass conversion processes. The National Renewable Energy Laboratory (NREL) has provided detailed techno-economic evaluation of different process configurations for cellulosic ethanol production

5-7

. Furthermore, many multi-echelon and multi-period models for biorefinery

design and planning have been employed 8-11. For example, Ekşioğlu, Acharya, Leightley and Arora

9

proposed a mathematical optimization based framework that considers different

techno-economic metrics to select the optimal set of products and the best route for producing them in integrated biorefineries. Many of the proposed studies in the literature use deterministic modeling approaches which assume that all the parameters are known in advance

12-14

. However, common to early stages of process design is the lack of certain

information that will introduce variability and significant risk into the decision-making problem. It is important to provide the decision-maker with as much guidance as possible to support their difficult task of making critical decisions. Uncertainties are introduced in process design in many ways. Insufficient knowledge about reaction pathways and kinetics contributes to uncertainty just like limited thermodynamic data for chemical components does; lack of experience when performing a scale-up with novel process equipment presents another source of uncertainty; fluctuations in product demand; volatility in prices of feedstock and product, and potential economic risk are also critical and should be taken into account 15. Some of the decisions that need to be made in the face of uncertainty are related to strategic planning and the others are made during the process design and operation. Failure to consider these uncertainties may lead to nonoptimal designs and cause significant extra expenses to accommodate unexpected events. Literature 3 ACS Paragon Plus Environment


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reviews have highlighted some of the key uncertainties inherent in integrated biorefining processes 16, 17. The significance of uncertainty has prompted a number of researchers to address optimal design of biorefineries in the face of uncertainty. A very common measure to account for risk stemming from uncertainty is overdesign. It may be simple solution, but it is a costly one too. Stochastic programming formulations have received increasing attention for explicitly handling uncertainty in process synthesis and design optimization problems by introducing probability distribution functions 18. Most of the preliminary work on stochastic optimization of biorefineries only consider one type of uncertainty, such as uncertainty in market parameters (product demand or sale price of products) or uncertainty in operational level (technical parameters) 19-21. However, development of a comprehensive framework which can link decision-making processes with consideration of all the uncertainties is of critical importance, and interaction and integration between them is required for successful process implementation. In our previous work

22

, the development of a systematic optimization framework for

biorefining processes under uncertainty was introduced focusing on one type of uncertainty (market uncertainty). The present paper is an extension to the proposed framework by developing a multi-layered decision support tool that can be utilized by energy entrepreneurs and technology investors in the renewable energy industry to carefully design and optimize the business value of their energy endeavors considering all types of uncertainties including uncertainties at strategic and operational levels. A structural approach is utilized for planning the production capacity, simulation of the process in detail, and optimizing the operating condition of the plant. First, a stochastic model is developed to optimize production capacity for the desired planning horizon and then process simultion coupled with stochastic optimization algorithm is employed to optimize the operating condition of the plant. Monte4 ACS Paragon Plus Environment

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Carlo based simulation and global sensitivity analysis are utilized to identify the most critical parameters and optimize the operating conditions of the plant. Product demand and price uncertainties are taken into account at the strategic planning level, and uncertainties related to parameters characterizing the processing technologies are addressed in operational level optimization. To demonstrate the effectiveness of the proposed methodology, a hypothetical case study of a multiproduct lignocellulosic biorefinery based on sugar conversion platform is utilized. 2. DESIGN OF THE DECISION SUPPORT TOOL The proposed framework aims to develop a model-based decision support system in order to investigate the inherent collaborative relationships between different decision layers of a renewable energy enterprise by utilizing a distributed architecture. The layered structure of the framework does not necessary imply a hierarchy; each layer is functionally dependent on the others for information in the form of constraints or parameters. This strategy has the advantage of not only being able to integrate long term planning based on financial optimization with nonlinear process mechanisms, but also optimize the operating conditions of the plant within a single optimization model. Each component of the proposed multilayered decision support tool is briefly described in the following section: 2.1. Strategic planning: A Mixed-Integer Linear programming (MILP) model is suggested in our work for the purpose of strategic planning. The strategic model is used to provide support in making decisions that will affect the enterprise in the long run. Process models for each node in the value chain are blended in with financial cost and profit model to calculate the net present value (NPV) of the enterprise (objective function). To overcome the mismatch between nonlinear process mechanisms (due to complex kinetic and thermodynamic models in energy systems) and LP-based strategic optimization, a decomposition strategy is proposed that combines net present value (NPV) optimization for long term planning with rigorous 5 ACS Paragon Plus Environment


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non-linear process simulation and process-level optimization. The major equations that are approximated linearly in the strategic planning models and modelled nonlinearly during operational level optimization include unit operations’ yield and unit operation energy balances. The optimal production capacity plan obtained from strategic planning is then passed on to the process simulation (Aspen Plus) and the process optimizer (Matlab) in order to determine optimal operating conditions. The details for the formulation of the strategic planning model can be found in a previous paper by the authors 22. In the strategic layer, different scenarios are developed based on stochastic forecasts for uncertain market parameters including price and demand of bioproducts. The process is formulated as a stochastic mixed integer linear programming (MILP) model which incorporates stepwise capacity expansion by defining binary variables in the formulation of the model. Stochastic analysis method is based on the idea of assigning a probability distribution to each uncertain model parameter. Uncertain parameters are represented as random variables. The challenge is to choose good probabilistic distributions. A good knowledge of the process and availability of historical data helps the decision maker to define accurate distributions. 2.2. Operational level planning: The results are then fed to the second stage of the optimization algorithm. The second stage, which optimizes the operating conditions of the plant, consists of three main steps including simulation of the process in the simulation software (nonlinear modeling), identification of critical sources of uncertainties through global sensitivity analysis affecting selected performance criteria, and employing stochastic optimization methodologies to optimize the operating condition of the plant under uncertainty. Moreover, a procedure based on calculation of confidence interval is embedded in operational level optimization formulation to mitigate the risks due to uncertainties in technical parameters. 6 ACS Paragon Plus Environment

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Figure 1 shows a general schematic structure of the proposed iterative decision support strategy. The iterative process is used to obtain a piecewise linear approximation of the nonlinear reaction and thermo-dynamics; the nonlinear dynamics are simulated and their linear approximations are used during strategic planning and optimization. Each component of the proposed algorithm is described in more detail in section 3.

Figure 1: Structure of the proposed iterative optimization framework

3. FRAMEWORK DETAILS In this section each component of the proposed framework (Figure 1) is described in some detail. While the description of the framework is based on the design of the case study presented in Section 4, each component, and the framework, can readily be adapted to other energy value chains. 3.1. Strategic Planning under Uncertainty The mathematical formulation in strategic planning is broken into sub-models for ease of description which include a process model, financial model, uncertainty characterization and risk management model. 7 ACS Paragon Plus Environment


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Figure 2: Structure of the strategic planning model under uncertainty

All major process systems are represented as linear black boxes in the planning model for the technology set considered for the framework demonstration. Financial model describes the price and demand evolution of the products in the planning horizon and calculates the capital costs, operating expenses, revenues and net present value (objective function). It is assumed that market of products is impacted principally by oil prices since alternative transportation fuels compete mainly with oil derivatives. The price of crude oil is represented as a stochastic input following Geometric Brownian Motion (GBM), based upon which the market parameters are derived, yielding stochastic price-demand sets. Furthermore, a scenario-based stochastic programming approach is used to transform the stochastic problem into a number of realizations. The main idea is to address only a finite number of selected realizations of 8 ACS Paragon Plus Environment

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uncertainty in the optimization. Each realization is regarded as one scenario and is assigned with a probability, yielding a Markov chain based decision tree. Mathematical formulation and detailed explanation of each sub-model in strategic planning has been presented in the previous publications by the authors 22, 23. To control and manage the financial risk associated with uncertain market parameters at the optimal design of production capacity, downside risk management strategy proposed by Eppen, et al. 24 is introduced to the model. Downside risk approach is adopted because it is a consistent measure of risk with good mathematical properties which enable efficient optimization by means of linear programming techniques. The output of the model includes optimal design of production capacity of the plant for the planning horizon by maximizing the expected net present value (NPV) and minimizing the financial risk (DRISK) (Multiobjective optimization in strategic planning level). 3.2. Operational Level Optimization under Uncertainty After obtaining the capacity plan which is designed strategically, this optimal capacity is utilized in the operational level model for rigorous nonlinear process simulation and optimization. Process simulation and optimization will be performed iteratively until the convergence criteria are met. To check the convergence, the optimal yields for each section of the plant (calculated in process simulation) are compared with the ones used in strategic planning. If the difference between the values is greater than the threshold, the strategic optimization solves the LP model again, based on the new yield values calculated in the process simulation. The systematic operational layer optimization model consists of several sub-steps which guide the user in solving a stochastic optimization problem in the face of uncertainty. The framework includes a number of methods and tools such as process simulation in Aspen Plus, global sensitivity analysis and Monte-Carlo based stochastic

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optimization. Figure 3 represents the proposed strategy for the operational level optimization under uncertainty.

Figure 3: Structure of the operational level planning under uncertainty

3.2.1. Process simulation By simulating the entire model in Aspen Plus, the implicit correlations between upstream and downstream stages of the process are taken into consideration. Additionally, based on the architecture that was introduced in previous paper by Geraili, et al.

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, complex kinetics of

bio-reactions is also incorporated in the simulation model that imparts a greater degree of realism to the actual representation of the process. This is based on dynamic data exchange between Aspen Plus and kinetic models of biological reactions implemented in Matlab 25. 3.2.2. Sensitivity analysis In order to reduce computational effort in optimization under uncertainty and focus on certain relevant process parameters, a sensitivity analysis is required. Sensitivity analysis is a general concept which aims to quantify the variations of an output parameter of a system with respect 10 ACS Paragon Plus Environment

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to changes into some input parameters. The global sensitivity analysis focuses on the pattern of change in model output due to changes in model input parameters over a potential variation range of parameter values rather than a single parameter value. Global sensitivity analysis gives insight into the bottlenecks in the process and quantifies the uncertainty due to technological risks. In this study, Sobol global sensitivity method

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, a variance–based

Monte-Carlo technique, is used to reduce the complexity of the stochastic optimization problem in operational level by focusing only on the parameters which are most influential on the outpout of the process model. This

global

sensitivity

analysis

where Decomposing the function

model

can

be

represented

are input factors and

in

the

form

of

is the model output.

and assuming that the input parameters are independent, it is

obtained: (1)

For the case study considered in this work,

is the cash flow of the biorefinery, and

are the parameters listed in Table S2 in Supporting Information. Sobol’s method aims to break down the function

into terms of increasing dimensionality in order to make

all the summands mutually orthogonal.The total variance of

can be decomposed as follows: (2)



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Where

denote the variance of

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respectively. Decomposition of

Eq.(2) yields two types of sensitivity indices. The first-order sensitivity index for the parameter is given by: (3)

This index represents the main effect of parameter

on the output variable Y and measures

the variance reduction that would be achieved by fixing that parameter. The values calculated for first order sensitivity can be used to rank individual parameters importance on the basis of contribution to the variance of Y. The total sensitivity index for the parameter

is given by: (4)

is the total sensitivity index for the ith parameter and is the sum of all the effects involving parameter . The index

. The parameter

is the sum of all variance terms that do not include

takes into account the interactions between the ith parameter and the other

parameters. The Sobol indexes calculated in this paper follow the efficient computational method developed and tested by Wu, et al. 27. For calculating the sensitivity indexes the next steps were followed: The sensitivity indices are computed using a Monte-Carlo method by generating random samples of parameters within the defined range for each of them followed by estimation of ,

,

based on the following procedure:

1) Select the sample dimension (N). 2) Generate two random sample matrices

and

of dimension

matrix is known as the ‘sampling’ and the second one the ‘re-sampling matrix’. 12 ACS Paragon Plus Environment

. The first

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3) Define a matrix from

formed by all columns of

, and a matrix

complementary to

the column of the ith taken from

except the ith columnwhich is taken formed with all columns of

.

4) Compute the model outputs which will be colmun vectors ( matrices

,

,

and with

for the sample

; resulting column vectors are denoted as:

5) Then the sensitivity indices are calculated based on the scalar products of the above vectors: (5) (6) (7)

(8)

(9)

To apply the Sobol sensitivity analysis to the proposed case study, the complete set of kinetic parameters characterizing the biological reactions in hydrolysis and fermentation are selected 13 ACS Paragon Plus Environment


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in the list of potential sources of uncertainties. These uncertainties may come from experimental procedures used to estimate parameter values, measurement accuracy and changes in enzyme and microorganism activities. Table S2 represents the parameters analyzed in this study. 3.2.3. Monte-Carlo simulation and optimization Once sensitivity measures have identified the significant sources of uncertainties in the process, a stochastic optimization algorithm is used to find out the optimal operating conditions with the aim of maximizing the annual cash flow in the plant. The generic mathematical form of the optimization problem is represented in Equation (10): (10) Constraints: (11) (12) (13)

The objective function (Eq.10) is composed of a deterministic term a constant vector and

, where

represents

is the vector of decision variables, and an uncertain term

which is the expected value to represent the uncertainty as a function of the decision variables, and

, and uncertain parameters,

.

is the vector of equality constraint

is the set of inequality constraints.

The proper choice of optimization methodology depends on the complexity of the problem. Although deterministic methods are relatively fast, they might get trapped in local optima due to the nonconvex functions involved in optimization of complex chemical processes such as biorefineries. Monte-Carlo based optimization strategy has the advantage of reducing the tendency to be entrapped in local optima since the sampling is global rather than local. Also it 14 ACS Paragon Plus Environment

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avoids the dependency on an assumed set of initial conditions since the simulation is performed for all the generated samples

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. Furthermore, for solving large scale nonlinear

optimization problems deterministically, constraints should be incorporated into the objective function and analytical properties of the problem are required to generate a deterministic sequence of points in the search space. However, in many practical large-scale applications, models in simulation environments are used to mimic complex processes behavior

29

.

Therefore, modeling equations are embedded in the simulation software and cannot easily be extracted. Monte-Carlo based optimization strategy can overcome this problem as they do not require tedious manipulations of the mathematical structure of the objective function and constraints. In fact, the optimizer treats the process simulation as a black box. The decision variable values are sent to the simulation in Aspen Plus where the process is simulated for these values. The simulated results are then passed back to the optimizer to re-solve the objective function. A general schematic structure of the proposed operational level optimization strategy is represented in Figure 4. This optimization algorithm is written in MATLAB and directly linked with the Aspen Plus simulator to facilitate the automation of process simulation and optimization.



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Figure 4: Monte-Carlo based optimization in operational level

The first step in this optimization method is performed by generating samples of parameters and variables from a high-dimensional space. This is possible by applying a sampling technique (e.g. Latin hypercube method) which employs a matrix of operating variables.Then a Monte-Carlo simulation is performed using the generated samples. The described procedure permits to estimate the uncertainty of model outputs used in the objective function calculations. The results from Monte-Carlo simulation are evaluated based on statistical techniques (mean value, 97.5% confidence interval and 2.5th percentile) in order to identify the optimal operating scenarios. The optimal operation scenarios will correspond to high mean cash flow (high profitability) with narrow confidence interval (narrow uncertainty range) and high 2.5th percentile outcome (higher cash flow for the worst-case).


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The reason that confidence interval and percentile are considered as performance criteria in addition to mean value is that by ranking the scenarios based on only the mean value, the optimization model does not reflect the variability associated with the uncertainty of parameters in the process, and there will be no guarantee that the process will perform at a certain level over all the uncertain parameter space. Consequently, a quantitative risk assessment strategy is incorporated in operational level optimization to reduce the occurrence of undesirable consequences due to uncertainty in technical parameters and controls the level of uncertainty. Figure 5 illustrates a schematic representation of the proposed risk assessment approach in operational level.

Figure 5: Uncertainty and risk management strategy in operational level optimization

4. APPLICATION CASE STUDY: LIGNOCELLULOSIC BIOREFINERY Process Description To demonstrate the effectiveness of the proposed framework, the aforementioned decision support system is applied to a hypothetical multi-product biorefinery that utilizes lignocellulosic feedstock to produce biobased fuels and chemicals. The lignocellulosic biorefinery used in this study is based on a sugar-based fermentation platform, with 3 products: cellulosic ethanol, biosuccinic acid, and bioelectricity. Results from our previously published paper for product portfolio selection showed that there is a huge improvement in the profitability of the biorefining process by incorporating succinic acid as a co-product of 17 ACS Paragon Plus Environment


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the plant

25

. Switchgrass serves as the selected feedstock for the biorefining process.

Although, a number of possible feedstocks can be used to provide lignocellulosic material for conversion, our application assumes a sample feedstock whose chemical composition resembles that of switchgrass. It is also assumed that there is limited land available within a 100 mile radius of the plant which can be used for the production of switchgrass for feedstock to the plant. The production chain comprises of 6 major processing steps (Figure 6): feedstock pretreatment, sugar hydrolysis, sugar fermentation, product purification, heat and power generation, and wastewater treatment. In our previous work

25

, a procedure to analyse

flowsheet configuration of integrated biorefineries was developed and an optimal configuration was obtained by investigating several options in each processing step. In the current study this optimal configuration is fixed which is composed of: 1. Dilute acid pretreatment to solubilize hemicellulose and lignin and increase the digestibility of cellulose 2. Ammonia conditioning for detoxification of pretreated biomass 3. Simultaneous enzymatic hydrolysis and co-fermentation for ethanol production (SHCF) 4. Separate hydrolysis and fermentation for succinic acid production 5. Ethanol purification using a configuration with distillation columns followed by molecular sieve 6. Solid separation in purification to extract the residual solids 7. Succinic acid recovery using a configuration based on cell filtration followed by crystallization 8. A sequence of anaerobic and aerobic digesters to digest organic materials contained in the waste water from the biorefining process


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9. Combined system of combustor, boiler, and turbogenerator for steam and electricity production

Figure 6: Block diagram for the multiproduct biorefinery plant

As described before one of the characteristics of the proposed approach is the incorporation of the complex kinetics of bio-reactions in the simulation model. Developed mathematical formulations for the kinetics are based on the validated models from literature

30-32

.

Technological configurations along with capital and operational cost, yield, and energy data for bioethanol production section are obtained from Humbird, et al. 33 and Kazi, Fortman and Anex 7. For succinic acid production, operational and economic data are obtained from Vlysidis, et al.

34

; these are used as starting estimates to begin the iterative optimization

process. 5. Results and Discussion In this section, the results for optimal strategic and operational level decisions of the multiproduct biorefinery are discussed. The decision variables considered in the framework are composed of the capacity plan for long term production, temperature for enzymatic hydrolysis, enzyme amount utilized in hydrolysis reaction and allocation of pretreated biomass for production of final products. Additionally, uncertain parameters are introduced in 19 ACS Paragon Plus Environment


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each layer of the optimization framework and risk management strategies are incorporated to reduce the occurrence of unfavourable scenarios. Plant life time considered in this study is 14 years with an annual discount rate of 10%. 5.1. Strategic Planning Results of the stochastic MILP model for the strategic optimization which is implemented in the modeling system GAMS and solved with a CPLEX linear solver are shown in Table 1 and Figure 7. Two different stochastic cases are considered to illustrate the impact of the downside risk management procedure. In one case, the stochastic model is solved just by maximizing the expected NPV (single objective, risk-neutral) and for the other case the stochastic model is solved by introducing financial risk management strategy and considering the tradeoff between financial risk and profitability of the plant (Multi-objective). Results of a deterministic model by considering fixed values for all the economic parameters through the planning horizon are also shown in Table 1. The values of the economic parameters used for the deterministic case study are the same with those in Geraili, Sharma and Romagnoli 23. As expected, by considering the evolution of market parameters through the planning horizon(stochasrtic case), more sugar is allocated to succinic acid production in comarison to deterministic case and a higher expected net present value is obtained. Currently, the market volume of succinic acid is relatively small due to the nascent stage of its market. However, with its high-value applications and product acceptance, application market of bio-based succinic acid has the potential to improve fast over the planning horizon and this market growth is taken into account in the stochastic model. Results of the multi-objective optimization model in the stochastic case study reveal the conflict between the two objectives, economic performance and financial risk. Results in Table 1 illustrate that minimization of downside risk leads to allocation of more sugar to succinic acid production and reduction in expected biomass processing capacity. 20 ACS Paragon Plus Environment

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Furthermore, it can be seen from the results in Figure 7 that by indtroducing the risk management strategy, the profitability (net present value) of scenarios have much higher chances to be between the desired target which leads to a more robust behaviour of the framework in the face of uncertainty. Table 1: Comparison of optimal capacities before and after financial risk management Case Study Expected NPV Downside Feedstock Capacity Sugar allocation ($MM) risk (1000tons/yr) ratio (ethanol production) 50.0 -160 0.66 Deterministic case 62.0 11% 200 0.54 Stochastic case 58.0 3% 152 0.48 Stochastic case with risk management

Figure 7: Comparison of NPV distribution before and after financial risk management

5.2. Global Sensitivity Analysis Kinetic parameters in biological reactions are considered as potential uncertainty sources in operational level model (technological risks) which resulted in a total of 86 parameters. A complete list of all the kinetic parameters and their description is given in the Supporting Information, Table S2. The Sobol global sensitivity analysis was performed to assess the relative sensitivity of these model parameters. Through extensive Monte Carlo simulations, it was found that some parameters are rather insensitive. The values of these insensitive 21 ACS Paragon Plus Environment


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parameters are fixed to simplify the stochastic model and reduce the complexity of the search space. Calculated sensitivity indices for model input parameters are shown in Figure 8 and Figure 9. It is found that 18 of the kinetic parameters are significantly affecting the uncertainty on cash flow of the process and the other uncertain parameters can be fixed at a value in their variation ranges without resulting significant fluctuations in the calculation of the objective function. The results show that the highest uncertainty is introduced by the parameters involved in enzymatic hydrolysis and fermentation of sugars for succinic acid production. This is due to the higher value of succinic acid in market in comparison to ethanol and also the higher cost of separation technologies for succinic acid production. Hence, the stochastic optimization for operational level will consider uncertainty particularly coming from succinic acid section of the multiproduct biorefinery. Moreover, the model is slightly sensible for the parameters in simultaneous saccharification and co-fermentation of ethanol as is shown in Figure 8 & 9.


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SA-Hydrolysis

SA-Fermentation

Figure 8: First order sensitivity indices of annual cash flow


ETSSCF


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Figure 9: Total sensitivity indices of annual cash flow

Important information can be recognized from Figure 8 and Figure 9. Results show that in enzymatic hydrolysis of sugars for succinic acid production, the conversion rate of cellulose to cellobiose is an important step in the reaction mechanism and a possible bottleneck in the process; uncertainty in parameters of this reaction can make significant changes in the profitability (cash flow) of the plant. Also, idenetification of αsa, K1r sa, Ea sa and E1 max sa as critical sources of uncertainty in the fermentation for succinic acid production reveals the competition between formic acid and succinic acid production for glucose consumption. Therefore, proper condition selection for fermentation process will reduce glucose conversion to formic acid and increases the succinic acid production which translates in higher profitability of the biorefinery. Due to the lower value of ethanol in the market in the considered case study, three parameters in simultaneous saccharification and co-fermentation of ethanol were selected as significant sources of uncertainty.


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5.3. Operational Level Optimization Based on our previous studies, Hydrolysis temperature, sugar allocation, and enzyme loading are selected as important operating variables to be optimzed

23

. Therefore a sample of

selected variables and also a sample for the shortlist of significant uncertain parameters were created to perform a Monte Carlo stochastic optimization. The optimization was performed with 80 samples of operating variables and 100 parameter samples resulting in a 80 x 100 process model evaluations. Figure 10 represents the results for all the Monte-Carlo stochastic optimization. Table 2 represents the results of the best scenarios from Monte Carlo simulation; these optimal scenarios are ranked based on the mean values and 2.5th percentile. Confidence interval is another perfomance criteria that can be used for selection of optimal scenarios and has been reported in Table 2. 95% confidence interval is a range of values that with 95% certainty contains the true mean of the population. However, in this study the average value of cash flow and 2.5th percentile are considered for ranking the scenarios. The scenarios which have high mean value and also high 2.5th percentile (higher value for worstcase scenario) are selected as the most feasible designs which can increase the profitability of the plant. Different combination of performance metrics can be used to maximize the profitability and explicitly measure the risks arising from uncertain parameters which allow managing the risks according to decision maker’s preference. Also, results of the operational level optimization for a deterministic case study by assuming that all the kinetic parameters are fixed based on the values that are suggested in literature are shown in Table 2 and 3.



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Figure 10: Monte-Carlo simulation results with 95% confidence interval

Table 2: Monte Carlo simulation results for cash flow maximization Sample

2.5th Percentile

Mean

95% CI

Improvement in 2.5th Percentile

Improvement in Mean

Deterministic Case Base Case 80 65 21 63 13 44 11 56 22 37

-8784 9621 9433 9400 9377 9346 9288 9255 9255 9215 9205

8860 8821 9675 9480 9449 9423 9395 9333 9314 9301 9256 9264

-73 108 93 99 92 98 90 117 93 83 118

-9.25% 7.39% 7.01% 6.75% 6.40% 5.74% 5.36% 5.36% 4.90% 4.79%

-9.68% 7.48% 7.13% 6.83% 6.51% 5.81% 5.59% 5.45% 4.94% 5.03%

The optimal values of the decision variables obtained from Monte-Carlo stochastic optimization model are shown in Table 3. For future work, a hybrid metaheuristic and Monte


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Carlo optimization will be developed as a further refining step to obtain better conditions for operating conditions under uncertainty by employing the results from the Monte-Carlo optimization as initial guess for Metaheuritic optimization. Table 3: Base case and optimal operating conditions

Sample Deterministic Case Base 80 65 21 63 13 44 11 56 22 37

Hydrolysis Temperature (°C) 34.00 33.45 36.47 30.70 36.67 39.63 37.91 37.46 31.72 34.26 30.93 35.05

Enzyme loading ratio (g enzyme/Kg cellulose) 34.8 25.00 16.21 22.37 27.06 18.09 27.78 19.94 11.96 28.21 19.69 10.52

Sugar allocation (Ethanol production) 0.59 0.44 0.21 0.25 0.21 0.26 0.21 0.29 0.31 0.26 0.34 0.32

Final configuration of the proposed framework for the optimal biorefinery process is shown in Table 4 which represents the optimal variables calculated in strategic planning and operational level optimization. Table 4 :Optimal Framework results Variable Optimal Value Feedstock Capacity (1000 ton/yr) 200.0 Ethanol production Capacity (MM gal/yr) 9 Succinic acid production Capacity (1000 ton/ yr) 16 Hydrolysis Temperature (°C ) 36.47 Enzyme loading (g enzyme/ Kg Cellulose) 16.21 Sugar allocation ratio (sugar to ethanol ) 0.21 Net present value ($ MM) 61

Framework section Strategic planning Strategic planning Strategic planning Operational level optimization Operational level optimization Operational level optimization Objective function

5. CONCLUSIONS In this study a new hybrid optimization methodology to determine the optimal production capacity plan and operating conditions for an integrated multi-product biorefinery in the face of stochastic inputs and outputs was presented. The optimization problem was solved in a two-level approach, fisrt stochastic linear model was developed to optimze production capacity for the desired planning horizon and then process simultion coupled with stochastic 27 ACS Paragon Plus Environment


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optimization algorithm was employed to optimize the operating conditions of the plant. Monte-Carlo based simulation and global sensitivity analysis were utilized to identify the most critical parameters and optimize the operating conditions of the plant. Incorporating financila risk mitigation metric in the framework (strategic model) shows that production capacity planning and sugar allocation between ethanol and succinic acid production are the two important factors that influence the performance of the model in the face of market uncertainty. Global sensitivity analysis in operational level optimization identified that the most critical parameters involved in the process are in hydrolysis and fermentation of succinic acid. Also, the Monte-Carlo optimization results show that it is possible to find a better alternative operation of the plant in comparison to the base case. Hence, results of the proposed optimization framework indicate that taking uncertainties into consideration is a fundamental step in decision-making processes and there is a signifacant potential for improving the profitability of biorefineries and reducing the rsiks due to uncertainties. In the future study, a hybrid optimization strategy based on Monte-Carlo and metaheuristic algorithms will be developed as a further refining step in operational level optimization to obtain better operating conditions of the plant. Furthermore, the applicability of the proposed framework for optimization of thermo-chemical pathways for conversion of biomass to biobased fuels and chemicals based on heat-based technologies such as gasification and pyrolysis will be evaluated. Supporting Information: Nomenclature and input uncertainty of kinetic parameters. This information is available free of charge via the Internet at http://pubs.acs.org/.


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8. Sammons, N.; Eden, M.; Yuan, W.; Cullinan, H.; Aksoy, B., A flexible framework for optimal biorefinery product allocation. Environmental Progress 2007, 26, (4), 349-354. 9. Ekşioğlu, S. D.; Acharya, A.; Leightley, L. E.; Arora, S., Analyzing the design and management of biomass-to-biorefinery supply chain. Computers & Industrial Engineering 2009, 57, (4), 1342-1352. 10. Karuppiah, R.; Peschel, A.; Grossmann, I. E.; Martin, M.; Martinson, W.; Zullo, L., Energy optimization for the design of corn-based ethanol plants. Aiche Journal 2008, 54, (6), 1499-1525. 11. Elia, J. A.; Baliban, R. C.; Xiao, X.; Floudas, C. A., Optimal energy supply network determination and life cycle analysis for hybrid coal, biomass, and natural gas to liquid (CBGTL) plants using carbon-based hydrogen production. Computers & Chemical Engineering 2011, 35, (8), 1399-1430. 12. Zhang, J.; Osmani, A.; Awudu, I.; Gonela, V., An integrated optimization model for switchgrass-based bioethanol supply chain. Applied Energy 2013, 102, 1205-1217. 13. Leduc, S.; Starfelt, F.; Dotzauer, E.; Kindermann, G.; McCallum, I.; Obersteiner, M.; Lundgren, J., Optimal location of lignocellulosic ethanol refineries with polygeneration in Sweden. Energy 2010, 35, (6), 2709-2716.



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29. Robertson, G.; Geraili, A.; Kelley, M.; Romagnoli, J. A., An active specification switching strategy that aids in solving nonlinear sets and improves a VNS/TA hybrid optimization methodology. Computers & Chemical Engineering 2014, 60, 364-375. 30. Kadam, K. L.; Rydholm, E. C.; McMillan, J. D., Development and validation of a kinetic model for enzymatic saccharification of lignocellulosic biomass. Biotechnology Progress 2004, 20, (3), 698-705. 31. Morales-Rodriguez, R.; Gernaey, K. V.; Meyer, A. S.; Sin, G., A Mathematical Model for Simultaneous Saccharification and Co-fermentation (SSCF) of C6 and C5 Sugars. Chinese Journal of Chemical Engineering 2011, 19, (2), 185-191. 32. Song, H.; Jang, S. H.; Park, J. M.; Lee, S. Y., Modeling of batch fermentation kinetics for succinic acid production by Mannheimia succiniciproducens. Biochemical Engineering Journal 2008, 40, (1), 107-115. 33. Humbird, D.; Davis, R.; Tao, L.; Kinchin, C.; Hsu, D.; Aden, A., Process Design and Economics for Biochemical Conversion of Lignocellulosic Biomass to Ethanol. National Renewable Energy Laboratory 2011, Technical Report NREL/TP-5100-47764, Golden Colorado. 34. Vlysidis, A.; Binns, M.; Webb, C.; Theodoropoulos, C., A techno-economic analysis of biodiesel biorefineries: Assessment of integrated designs for the co-production of fuels and chemicals. Energy 2011, 36, (8), 4671-4683.

For Table of Contents Only



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List of Figures Figure 4: Structure of the proposed iterative optimization framework Figure 5: Structure of the strategic planning model under uncertainty Figure 6: Structure of the operational level planning under uncertainty Figure 4: Monte-Carlo based optimization in operational level Figure 5: Uncertainty and risk management strategy in operational level optimization Figure 6: Block diagram for the multiproduct biorefinery plant Figure 7: Comparison of NPV distribution before and after financial risk management Figure 8: First order sensitivity indices of annual cash flow Figure 9: Total sensitivity indices of annual cash flow Figure 10: Monte-Carlo simulation results with 95% confidence interval

List of Tables Table 4: Comparison of optimal capacities before and after financial risk management Table 5: Monte Carlo simulation results for cash flow maximization Table 6: Base case and optimal operating conditions

Table 4 : Optimal Framework results Table S1: Nomenclature Table S2: Input uncertainty of kinetic parameters


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Market Model • Prices • Demands

Process Model • • • •

Mass balances Energy balances Supply quantities Capacity constraints

Probability Distribution Generation •

Up & down probabilities for uncertain parameters

Decision Tree Generation • Scenario genration

Income & Cash Flow Statement Revenues, Costs, Taxes, Profits

Risk Management Model Downside Risk (DRISK)

Decision making under uncertainty Max E[NPV] & Min E[DRISK] Constraints: Production ≤ Capacity Sales ≤ Demand


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Output Simulation for selected process configuration

Process Simulation

Global sensitivity analysis (Sobol)

Identification of significant uncertainty sources

Sampling

Sample generation for parameters and decision variables

Optimization based on MonteCarlo simulations

Optimized operating conditions under uncertainty



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Figure 4: Monte-Carlo based optimization in operational level 134x104mm (300 x 300 DPI)


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Figure 5: Uncertainty and risk management strategy in operational level optimization 66x22mm (300 x 300 DPI)



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Steam

Lignocellulosic Feedstock

Electricity

Ethanol

Detoxification Pretreatment

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Ammonia conditioning

Ash Heat & power generation

Simultaneous Hydrolysis & Co-Fermentation

Enzymatic Hydrolysis

Succinic acid Fermentation

Ethanol Purification

Succinic acid Purification

Solid/liquid separation

Waste Water treatment

Succinic acid Treated Water


Landfill

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Figure 8: First order sensitivity indices of annual cash flow 113x75mm (300 x 300 DPI)


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Figure 9: Total sensitivity indices of annual cash flow 117x76mm (300 x 300 DPI)



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Figure 10: Monte-Carlo simulation results with 95% confidence interval 115x80mm (300 x 300 DPI)


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