Elsevier

Computers & Chemical Engineering

Volume 68, 4 September 2014, Pages 128-139
Computers & Chemical Engineering

Robust design and operations of hydrocarbon biofuel supply chain integrating with existing petroleum refineries considering unit cost objective

https://doi.org/10.1016/j.compchemeng.2014.05.003Get rights and content

Highlights

  • An MILFP model for biofuel supply chain integrating with petroleum refineries.

  • A robust optimization formulation to consider uncertainty.

  • Application of two tailored solution algorithms for MILFP.

  • A comparison between unit cost objective and the total cost optimization.

  • County-level case study for the state of Illinois.

Abstract

This paper addresses the optimal design and planning of the advanced hydrocarbon biofuel supply chain with the unit cost objective. Benefited from the drop-in properties of advanced hydrocarbon biofuels, the supply chain takes advantage of the existing petroleum infrastructure, which may lead to significant capital and transportation savings. A mixed-integer linear programming model is proposed to simultaneously consider the supply chain design, integration strategy selection, and production planning. A robust optimization approach which tradeoffs the performance and conservatism is adopted to deal with the demand and supply uncertainty. Moreover, the unit cost objective makes the final products more cost-competitive. The resulting mixed-integer linear fractional programming model is solved by tailored optimization algorithm. County level cases in Illinois are analyzed and compared to show the advantage of the proposed optimization framework. The results show that the preconversion to petroleum-upgrading pathway is more economical when applying the unit cost objective.

Introduction

Biofuels have been shown to be a promising fuel source of the future. They can be produced domestically from a wide variety of biomass sources and reduce the dependence on fossil fuels (DOE, 2012). Moreover, greenhouse-gas emissions from biofuels are lower than those from their petroleum counterparts (Tong et al., 2014a). Consequently, many countries have set national biofuels targets and provided incentives to accelerate the growth of bioenergy industry. In the U.S., the Renewable Fuels Standard (RFS), part of the Energy Independence and Security Act (EISA) of 2007, establishes an annual production target of 36 billion gallons of biofuels by 2022, of which 16 billion gallons should be advanced biofuels made from non-starch feedstocks to avoid adverse impacts on the food market (EISA, 2007). With the development of the third generation biofuel technologies, advanced biofuels can now be produced from cellulosic biomass such as crop residues, wood residues or dedicated energy crops (Yue et al., 2014b). Moreover, advanced hydrocarbon biofuel products (e.g. cellulosic-biomass-derived gasoline, diesel and aviation fuel) are functionally equivalent to the petroleum derivatives. Considering all these promising properties, the expansion of the hydrocarbon biofuel industry is foreseeable in the next few decades, thus requiring the design and development of cost-effective biomass-to-biofuel supply chains (DOE, 2012).

Many studies have been conducted on the design and planning of biofuel supply chains from economic and environmental aspects (Akgul et al., 2012, Bowling et al., 2011, Dunnett et al., 2008, Elia et al., 2011, Giarola et al., 2011, Sokhansanj et al., 2006, You et al., 2012, Yue and You, 2014, Yue et al., 2014a, Zamboni et al., 2009). However, the drop-in property of advanced hydrocarbon biofuel is not well explored. The U.S. Department of Energy, DOE (2012) has pointed out the opportunities for the integration of emerging hydrocarbon biofuel supply chains with existing petroleum production and distribution infrastructures. Although minimum retrofitting costs would be required in petroleum refinery for compatibility reasons, the integration indicates considerable capital savings on the construction of biofuel production facilities, which would help the biofuel products to be cost-competitive and bring in extra environmental benefits to the petroleum refineries (DOE, 2012). Researchers are investigating the possibility of converting biomass into biofuel in the traditional refinery. Huber and Corma (2007) summarized that catalytic cracking, hydrotreating, and hydrocracking are the three main techniques for converting biomass into biofuel in existing petroleum refineries. DOE (2012) is investigating three possible insertion points into the petroleum refinery. They note that after converting the biomass into liquid bio-intermediates, they can be mixed with crude oil that feeds the Crude Distillation Units (CDU), or sent directly to upgrading units to produce gasoline and diesel. However, the studies on explicit economic evaluation of the integration possibility from the supply chain point of view are limited (Elia et al., 2012, Tong et al., 2014a, Tong et al., 2014b). In this work, we propose and analyze a biofuel supply chain model integrating with existing petroleum refineries, combined with unit cost objective and the robust optimization framework.

Most of the existing works consider the absolute economic performance, such as maximizing the total profit or minimizing the total cost. However, the economic objective along with per functional unit of the final product provides further opportunities for improving the economic performance, as the cost or profit would be reflected in the functioning outputs of the system: functional unit (Yue et al., 2013b). For instance, in the traditional supply chain models with cost minimization objective, the product demands are usually given with lower bounds. The optimal solution tends to produce and sell biofuels as less as possible to reduce the overall cost. This is obviously not an economical solution, as the unit cost might be high. By using the unit objective, the optimal solution can guarantee the lowest cost per unit, hence making the final products more cost-competitive. The unit objective can be defined as the total cost or profit divided by the total amount of functional unit. The problem can then be formulated as a mixed-integer linear fractional program (MILFP), which is a special type of non-convex mixed-integer nonlinear programs (MINLPs). Although the general MINLP solvers can be used, there might not be so efficient as some tailored solution algorithms. The parametric algorithm (Zhong and You, 2014) and reformulation-linearization approach (Yue et al., 2013a) are two efficient tailored solution algorithms for MILFP problems as they take advantage of the efficient mixed-integer linear programming (MILP) methods to globally optimize the MILFP problems. Although unit objective has been chosen in many studies (You et al., 2009, Yue et al., 2013a, Yue et al., 2013b), the advantage of unit objective is rarely discussed. In this work, we present a detailed comparison between total cost minimization objective and unit cost minimization objective, and try to find out advantages of using the unit cost objective.

The uncertainties in biofuel supply chain are critical and should be carefully considered. These uncertainties include seasonal and geographical fluctuation of biomass supply (Gebreslassie et al., 2012, Tong et al., 2014a, Tong et al., 2014b), variability of biofuel demand due to unstable economic situations (Giarola et al., 2013, Kim et al., 2011, Marvin et al., 2012), fluctuating market price (Dal-Mas et al., 2011, Kim et al., 2011), and imprecise processing of data due to the process fluctuation and immature technologies (Tong et al., 2014a). The inability to handle these uncertainties may lead to either an infeasible supply chain design or suboptimal performance. The widely used approaches for optimization under uncertainty (Sahinidis, 2004) include stochastic programming (Birge and Louveaux, 1997, Tong et al., 2011), chance constraint programming (Charnes and Cooper, 1959, Yang et al., 2009), and robust optimization (Ben-Tal and Nemirovski, 2002, Li et al., 2011, Li and Floudas, 2012). The goal of stochastic programming is to find the decision that is feasible for all the instances and maximizes the expectation of objective function over the random variables (Birge and Louveaux, 1997, McLean and Li, 2013). However it relies on the probability distributions of uncertain parameters. In the chance-constrained approach, uncertainties are represented through random variables with known probability distribution and included in the constraints (Charnes and Cooper, 1959). In robust optimization, only bounds of uncertain parameters are considered. Robust optimization aims to find the solution that is feasible under all the uncertainties (Ben-Tal et al., 2009). Generally speaking, a solution that is feasible for all the uncertainties usually does not leads to the best objective value, so the tradeoff between robustness and performance is the main issue in the robust optimization.

In this work, we address the optimal design and planning of advanced hydrocarbon biofuel supply chain under demand and supply uncertainties. Bertsimas and Sim's robust counterpart optimization (Bertsimas and Sim, 2003, Li and Ierapetritou, 2008) is used to tradeoff the robustness and performance. Although uncertainties in biofuel supply chain optimization have been studied in many works, robust optimization is rarely used. A spatially explicit MILFP model with the unit cost objective is proposed to account for the drop-in properties of advance hydrocarbon biofuel supply chain, i.e. integrating with existing petroleum refinery infrastructures. Moreover, two efficient algorithms, parametric method (Zhong and You, 2014) and reformulation-linearization (Yue et al., 2013a), are adopted in this model, and their computational performance are compared with general purpose MINLP solvers. Additionally, the difference between total cost minimization and unit cost minimization are carefully analyzed and discussed based on the Illinois cases. The results show that the unit cost objective prefers the preconversion to petroleum-upgrading pathway to produce biofuels. And the budget parameter Γ, which is defined as the maximal number of uncertain parameters that can reach their worst cases, provides a mechanism to tradeoff between conservatism and economic performance.

The rest of this article is organized as follows. The background of biofuel supply chain and its major drop-in feature are highlighted in the next section. This is followed by a formal problem statement. A brief introduction of the mathematical formulation of MILFP model is presented in Section 4. Detailed model formulation and nomenclature can be found in the supporting materials. The specified solution approaches are given in Section 5. A comprehensive comparison and analysis is presented in the case study section, and the concluding remarks are given at the end of the paper.

Section snippets

Background

The superstructure of the advanced hydrocarbon biofuel supply chain is illustrated in Fig. 1. A typical advanced hydrocarbon biofuel supply chain consists of harvesting sites, biorefineries, preconversion facilities, upgrading facilities, and demand zones. The biomass is cultivated and harvested in harvesting sites. The harvested biomass feedstocks can either be sent to integrated biorefineries for direct production, or undergo a two-stage conversion process (Wright et al., 2008, You and Wang,

Problem statement

The problem we addressed in this work is stated as below.

The superstructure of biofuel supply chain integrating with petroleum refineries are shown in Fig. 1. We are given a set of biomass harvesting sites, potential preconversion facility locations, possible upgrading facility locations, potential biorefinery locations, existing petroleum refineries, and the demand zones. A set of biomass feedstocks (namely crop residues, wood residues, and energy crops) with their major properties, including

Mathematical model formulation

We develop an MILFP model addressing the optimal design and planning of advanced hydrocarbon biofuel supply chain integrating with existing petroleum refineries with the unit cost objective. This model is a modification and simplification of the previous work by Tong et al. (2014a). The overall cost minimization objective is replaced by the unit cost minimization objective. The multiperiod model is replaced by the single period spatially explicit design model. Considering the length of the

Robust optimization

Robust optimization usually outperforms other methods to handle uncertainties due to its independence on the probability distribution of uncertain parameters. The objective of the robust counterpart optimization is to choose a solution that is able to cope best with the various realizations of the uncertainty data (Li and Ierapetritou, 2008). There are several well-known robust counterpart optimization formulations, namely Soyster's formulation (Soyster, 1973), Ben-Tal and Nemirovski's

Input data

To illustrate the application of the proposed framework, we solved a series of county level cases for the state of Illinois. Except the data related to time periods, all the other data are the same as the one in the previous work (Tong et al., 2014a), which are obtained from technical reports (DOE, 2011, DOE, 2012) and existing literatures (You and Wang, 2011).

The state of Illinois is comprised of 102 counties, each of which is recognized as a node in our model that represents a harvesting

Conclusions

This paper addresses the robust design and planning of the advanced hydrocarbon biofuel supply chain integrating with existing petroleum infrastructure considering the unit cost objective. Two tailored algorithms are adopted in solving the resulting MILFP problems. Demand and supply uncertainties are incorporated in the robust optimization framework. Comprehensive comparisons between overall cost minimization objective and unit cost objective, and between deterministic model and robust

Acknowledgements

The authors gratefully acknowledge Dajun Yue for his helpful discussion on the tailored MILFP algorithms. The authors would like to acknowledge the financial support from the Institute for Sustainability and Energy at Northwestern University (ISEN), and the National Basic Research Program of China (2012CB720500).

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