Article pubs.acs.org/IECR
Optimum Biorefinery Pathways Selection Using the Integer-Cuts Constraint Method Applied to a MILP Problem Stefano Maronese,*,† Adriano V. Ensinas,‡ Alberto Mian,§ Andrea Lazzaretto,† and François Maréchal§ †
Department of Industrial Engineering, University of Padova, via Venezia 1, 35131 Padova, Italy Universidade Federal do ABC (UFABC), CEP:09210-580, Santo André, Brazil § Industrial Energy Systems Laboratory (LENI), Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland ‡
ABSTRACT: Biorefineries are multi-product facilities that convert biomass into a broad variety of products (energy, biofuels, chemicals, feed, and food). In this paper, a new systematic approach to select and rank different biorefinery conversion pathways is proposed using the Integer-Cut Constraint (ICC) method applied to a MILP problem. In particular, two different statements of the constraints are analyzed. The first step is building a superstructure collecting several biomass conversion models. The ICC method allows different conversion pathways to be evaluated inside the superstructure and ordered according to the objective function values. The key value of a rank of pathways including suboptimal routes allows a fair comparison between alternative biorefinery options and may widen the choice to suboptimal ones. The method is applied to a case study in which various biomass-to-fuel technologies are analyzed to set up a rank of the most promising conversion processes in the current Swiss market.
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INTRODUCTION Biorefineries are not a brand new concept. The very first biorefineries were developed at the beginning of the Industrial Revolution, and they provided chemicals until the Second World War. From the 1950s on, the cheap crude oil price determined the decline of the biobased industrial supply chain.1 Nowadays, the increasing concerns about fossil fuel depletion and the need to diversify the resource supply together with raising environmental issues has caused a rebirth of the biorefinery concept. In one word, the call for sustainability is the future challenge, and biorefineries can be a possible answer to tackle the problem and steer from a fossil-based economy to a biobased one. Indeed, the keyword in the definition of biorefinery is sustainability. The International Energy Agency (IEA) proposed an organic definition of biorefinery2 as a concept (process, facility, or cluster of facilities) that converts biomassof any kindinto a spectrum of marketable products (food, feed, chemicals) and energy (fuels, power, heat) in a sustainable way.3 Biomass is a renewable source, though its availability is limited, so the raw material must be exploited in the best way, maximizing the conversion efficiency and minimizing the wastes. This goal can be achieved through multi-purpose multi-product facilities such as biorefineries. Much literature is dedicated to the analysis of the peculiar aspects of biorefineries.4 The works of Kamm and Kamm5−7 and Cherubini et al.8,9 deal with the classification and organization of different biorefinery concepts, focusing on the possible design of such facilities. The staggeringand still increasingvariety of materials that can be obtained from a biorefinery was analyzed both by the IEA10 and U.S. Department of Energy; in the works of Spath and Dayton11 and Werpy and Petersen,12 the most promising biobased products obtainable from syngas are evaluated, while in Holladay et al.13 and Cherubini and Stromman,14 special attention is given to the lignocellulosic-derived materials. For © 2015 American Chemical Society
concerns about the analysis of wooden biorefineries, the reader is referred to the most recent studies by Horhammer et al.,15 Danserau et al.,16 Cheali et al..17,18 and Mansoornejad et al.19 A huge number of processes and technologies can be applied to biorefineries,20 and numerous designs are possible.21 The literature available about biorefinery design is therefore insufficient in embracing such a wide field.22 An attempt at summarizing the most outstanding processes and technologies was carried out by Fernando et al.23 and Menon et al.;24 Swain et al.25 focused on biomass-to-liquid conversion pathways, while a more general approach was proposed by Martin et al.26 However, despite the great potential, several weaknesses slow the development of biorefineries. As pointed out in the SWOT analysis carried out by van Ree and Annevelink27 and de Jong et al.,2 the roll-out of biorefineries is mostly undermined by the great uncertainty in cost evaluation of conversion technologies and the lack of established know-how. Nevertheless, biorefineries will play a determinant role in the future economy, but only a strong cooperation between different players (government, chemical and energy industries, agriculture) can foster the development of a sustainable biobased economy centered on biorefineries.
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OBJECTIVES AND STRATEGIES The novelty of the present paper consists in developing a methodology to explore, analyze, and systematically generate a rank of different biomass conversion pathways for biorefineries according to the objective function and constraints (e.g., available technology, market prices). The method must detect the pathways inside a complex superstructure in the shortest Received: Revised: Accepted: Published: 7038
April 16, 2015 June 15, 2015 June 30, 2015 June 30, 2015 DOI: 10.1021/acs.iecr.5b01439 Ind. Eng. Chem. Res. 2015, 54, 7038−7046
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Industrial & Engineering Chemistry Research time without resorting to complex solving methods. 28 Numerous researches focused on the evaluation of the optimal conversion process,26,29 while the systematic evaluation of different alternatives with the creation of a rank of promising alternatives has begun to be treated in the literature in recent years: in particular, in the works of Santibanez-Aguilar et al.,30,31 a multi-objective optimization model is presented providing a set of optimal solution for both objectives. At this level of research, the aim is not to provide a full integrated analysis but to compare and evaluate in the shortest time a broad variety of different processes with multiple outputs. Such is a preanalysis of a wide number of alternatives. A more detailed process flow design and analysis is conducted in the following steps, and it is not the object of this work. The challenge is to elaborate a simple and light model with a robust problem statement: the call for robustness requires to go for MILP and the need to retrieve results in a brief time raises computational issues. The nonlinearity of the considered processes is accounted for in the modeling phase, which is not the object of this study. What is kept linear is the scaling of the thermal/material/electricity streams with respect to the reference mass flow of the process (inlet fuel, inlet biomass). Without this assumption, the corresponding MINLP, although more accurate,32 would be difficult to solve because of the number of involved variables (binary and continuous) as well as the number of nonlinear constraints of the problem. This clarifies why the MILP approach was followed, as it is considered the best problem statement in terms of robustness. The idea of developing a method to create a list of pathways is due to the fact that biomass conversion technologies are still young and the biobased product market is currently in a developing phase. Such is a crucial aspect of biorefineries; the uncertainty about the best application to convert raw biomass materials is due to the large, increasing, variety of products that can be obtained, which also results in the possibility of applying different criteria to evaluate pathways. The extension of the analysis to suboptimal configurations creates a set of possible alternative technologies, which can then be judged according to other criteria, therefore, making the decision process simpler and flexible at the same time. If several pathways are remarkably close in terms of objective function, other criteria can be applied in selecting the most suitable technology (market request or market forecast, available utilities).
Figure 1. General scheme of OSMOSE.
interaction with the simulation model is performed in a presolve phase in order to generate/calculate mass and energy balance for the reference size of each process or utility. After this phase, the optimization model is solved. OSMOSE sends the necessary data to the optimization software, and the results are sent back to OSMOSE. It is also possible to perform multiple iterations. In the proposed study, the problem is relaunched several times to obtain all the feasible pathways. Among other features, OSMOSE has a complete suite of computation and results analysis tools (such as optimization, sensitivity analysis, Pareto curve analysis).34 Three main uses of OSMOSE can be identified: 1. OSMOSE can manage models created with other software and use the results coming from those models to perform post-analysis such as Pinch Analysis. For instance, OSMOSE can extract values of temperature, pressure, and mass flow rate of each thermal stream to build the composite curves and study the internal heat integration of the system or perform thermo-economic analysis by using both the thermodynamic data of the streams and the associated costs. 2. OSMOSE can also directly deal with the flow-sheeting software and perform sensitivity analysis or optimizations (mono- and multi-objective), in which the decision variables are chosen by the user. In this mode, OSMOSE can collect models of components, utilities, or energy systems to create superstructures. 3. OSMOSE can split a complex energy system into several units and perform energy or economic analysis of each unit. A detailed presentation is reported in Bollinger.35 To create the desired superstructure, in this work, OSMOSE is used in the above-mentioned mode (2) by combining units (which represent components or subsystems of any kind modeled with different software), layers (nodes of mass and energy balances), streams (mass, energy or costs, connecting units, and layers), and tags (sets of data that can be declared by the users and then used as input data instead of similar data of the single model). Superstructure Formulation. The superstructure is built by organizing in a single structure all process models associated
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METHODOLOGY The first two steps of the suggested methodology consist in (1) analyzing the desired biomass conversion technologies and (2) building a superstructure that includes all pathways that derive by putting together the models of the various processes involved in each technology. Finally, the proper criterion to evaluate and sort the conversion trajectories is developed. The tool used in this work is the OSMOSE Wood2CHem Platform. The general structure and rationale of OSMOSE is presented in Figure 1. The goal of the OSMOSE Platform is to allow the integration of flow-sheeting tools, process integration (e.g., Pinch Analysis), and costing tools (e.g., thermoeconomics methods) to study integrated energy conversion systems. The Platform is built in MatLab environment, but it can also interact with other software and programming languages (like Belsim Vali, Aspen Plus, GLPK, AMPL).33 For instance, Model 1 in Figure 1 could be created in Aspen, and OSMOSE can send input value and retrieve the corresponding results. The 7039
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Industrial & Engineering Chemistry Research with the technologies for the conversion of the raw biomass sources into the considered products. A similar approach to superstructure formulation has been proposed by SantibanezAguilar et al.30 and Rizwan et al.36 In the work of Kim et al.,37 the superstructure is obtained gathering conversion processes decomposed into intermediate subprocesses; Garcia et al.38 developed a special MINLP branch-and-refine optimization model applied to an integrated process network. In the proposed superstructure, each model is composed of a simple black box, and it is created by analyzing the conversion process features and then building its flow-sheet model. This step may also require a detailed literature review of the process being considered.17 Then, the boundary of the process model has to be set and the cross-boundary flows evaluated, extracting the values of the relevant input/output mass, energy, and cost streams. Finally, the collected data are organized in the black box model to be plugged into the platform. In conclusion, each black box model describes a complex process/utility system, which is simulated using flow sheeting software (e.g., Aspen) and then linearized (by considering linear variations of mass and energy input/output) with respect to a reference size (e.g., reference input biomass). The hypothesis underlying the black box model is constant efficiencyregardless of the sizeand linear operating and investment costs. Such simple methodology allows the integration of several processes of different kind in a quick, straightforward way. Figure 2 presents the superstructure created in OSMOSE. In such a scheme, the above-mentioned black box models (which account for the simulated processes) are highlighted together with the other elements of the superstructure: layers (mass/ energy balance nodes), resource units (input nodes), and service units (output nodes). The developed superstructure models the conversion of wooden biomass into electricity and fuels: synthetic natural gas (SNG), methanol (MeOH), dimethyl ether (DME), and Fischer−Tropsch crude (FT). It consists of four sets of technologies, each one with a different configuration. Refer to the Case Study section for more details about the models. MILP Problem Statement. The MILP problem can be stated as minimization of the objective function, which is the total cost (TC) of the selected configuration, i.e., the sum of operating cost (OC) and linearized investment cost (IC) of each subsystem s:
Figure 2. Scheme of the superstructure used in the case study.
multiplication factor, which represents the size of the unit in MW. The constraints are • Energy conversion technology selection: fmin, s ·ys ≤ fs ≤ fmax, s ·ys
∑ (OCs + ICs)
Ns , l s=1
where Ns is the number of subsystems (also called units) in the superstructure, OCs is the operating cost and ICs is the investment cost of subsystem s. Operating and linearized investment costs are calculated according to OCs = Cost1, s·ys + Cost 2, s·fs
ICs = Cinv1, s·ys + Cinv2, s·fs
∀s∈S
∀s∈S
Ns , l
∑ fs es+ + ∑ fs es− = 0
(1)
s=1
(4)
where f min,s and f max,s are the minimum and maximum allowed size for subsystem s. • Mass/energy balance for each layer (see Methodology section):
Ns
min TC =
∀s∈S
s=1
∀l∈L (5)
A layer is a node in which mass/energy balance calculations are performed. e+s and e−s are dimensionless quantities associated representing the power/mass flow rate associated with an entering/exiting mass or energy stream referred to the unit size N (kW/MW or kg/s/MW), reported in Table 1. Thus, ∑s =s ,l1 fs es+ represents the total power/mass flow rate entering layer l and N ∑s =s ,l1 fs es− is the total flow leaving layer l. Ns,l is the number of subsystems connected to layer l, so this constraint must be imposed for all the L layers of the superstructure (see Methodology section). The structure of the cost function is linearas shown in eqs 2 and 3so that the whole optimization problem belongs to the MILP category. Linear cost hypothesis keeps the problem
(2) (3)
where Cost1,s and Cost2,s are the fixed and variable operating cost. Similarly, Cinv1,s and Cinv2,s are the fixed and variable investment cost. S is the set of subsystems included in the superstructure. The problem includes integer variables ys ∈ {0,1} associated with the unit usewhich accounts for the existence of the unit s in the pathwayand the real fs ∈ ℜ 7040
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Industrial & Engineering Chemistry Research Table 1. Techno-Economic Parameters of Models Used in the Case Study.60,61 parameter
MeOH-a
MeOH-b
MeOH-c
MeOH-d
FICFB 570 −85 2007
FICFB 570 −59 2007
CFB 318 −18 2007
CFB 318 35 2007
investment [M€]
27
28
15
investment [M€]
365
363
156
gasification technology fuel output [kW/MW] net electricity [kW/MW] reference year
FT-EF_ind
(6)
and to interpolate the available points. C is the purchased cost, C0 is the cost of the equipment of size P0, and P is the required size of the equipment. Subsequently, a logarithmic linearization in a neighborhood of the design point is performed accordingly:40 ⎛P⎞ ln C = ln C0 + m ln⎜ ⎟ ⎝ P0 ⎠
FT-a
FT-b
FT-c
DME
SNG-a
SNG-b
EF 458 55 2007
CFB 303 155 2007
CFB 352 126 2007
FICFB 601 −4 2007
FICFB 561 −48 2007
FICFB 693 37 2006
CFB 750 26 2006
10
11
12
19
23
101
115
133
295
311
24 17 100 MW biomass 103 51
is applied to a linear problem; automated targeting is instead applied in the work of Ng et al.43 From the computational side, several researches focused on solving MILP problem,44 which is the most common typology of engineering problem.45 In Hooker et al.,46 a logic-cut approach to the process network selection is used while a disjunctive programming approach is proposed by Ponce-Ortega et al.47 The evaluation of different alternatives of conversion routes within the same process is considered in the works of Martin and Grossmann,26 Kokossis and Yang,48 and Dimian.49 In Danna et al.,50 three different algorithms are proposed to generate multiple solutions for the MILP problem, while Bao et al.51 suggested an original method to select various conversion processes for integrated biorefineries. In the latter, the integer-cuts method is used to generate a set of solutions using different objective functions (yield, payback period). This method was first suggested by Sahinidis et al.52 In Ng et al.,53,54 a two-stage optimization approach is developed to select the optimal pathways in an integrated biorefinery, evaluating the optimal chemical mixture first and then the best conversion pathway. The aim of the present work is to use the ICC method to systematically analyze different pathways in the superstructure. This requires an objective function to be defined, which is the comparison parameter in creating the rank of best pathways. A similar objective (i.e., to detect different pathways) was used by Wang et al.55 and Moncada et al.29 by applying a different technique. The Integer-Cuts constraints avoid the replication of already found solutions as it acts on the value of the integer variable associated with the unit use. Two formulations of the ICC are considered; the following eq 8 is suggested here and eq 9, which is taken from Fazlollahi et al.56 The first one is
simple and easy to be handled. If a good accuracy is desired, cost functions can be linearized only in a limited range. When nonlinear cost functions are available, they can be linearized in a more or less wide neighborhood depending on the shape of the cost function. A stepwise linearization can also be applied to increase the accuracy of the approximation. However, it is not considered here because of the high number of integer variables (one for each segment), which strongly increases the MILP complexity and computational time. In the case of scarce data about investment and size of the biomass fuelled plant, we suggest to take a typical cost function trend:39 ⎛ P ⎞m C = C 0⎜ ⎟ ⎝ P0 ⎠
FT-EF_dir
EF 637 −14 2007 20 MW biomass 15 7 400 MW biomass 136 88
(7)
Equation 6 is used to state the nonlinear function for which the linearization in eq 7 is made. In this way, a linear cost function is obtained and the problem is kept MILP. Cost2,s in eq 2 could be positive (as for the resource units, which represent a cost) or negative (as for service units, which generate an output revenue). Consequently, the objective function not only deals with the total production cost (including both operating and investment costs) but also takes into account the revenues generated by selling products. This is due to the fact that the platform is composed of multiproduct processes; to find the best one according to the economics, revenues must be considered. For instance, a plant with a poor biomass-to-fuel efficiency but with a valuable byproduct (electricity, for example) could be preferred to a highly efficient process which produces a higher amount of fuel but requires electricity. In conclusion, if the objective function is negative, there is a positive revenue from the plant. On the other hand, if the objective function is positive, the break even price of the input biomass can be calculated by evaluating the gap between market price and break even cost. Note that the performance characteristic of each unit is assumed to be constant to keep the size of the problem within manageable dimensions and therefore quickly solvable. Sorting Conversion Pathways. Once the superstructure is set, the following task is to find a methodology that generates an ordered set of pathways. Many approaches are available in the literature to select and compare different conversion pathways. In Tay et al.41 and Tan et al.,42 a fuzzy methodology
⎡ ∑Ns |y k − y k − j | ⎤ ∑ ⎢⎢ s = 1 s s ⎥⎥ ≥ k − 1 Ns ⎥ j=1 ⎢ k−1
(8)
where k is the index of the current pathway (solution), j ∈ {1,..,k − 1} is the index used to make the comparison with the previous k − 1 solutions, and yks ∈ {0,1} is the integer variable unit use of unit s in the k-th solution (where 1 means active, 0 inactive). The rationale of such a constraint is to compare the unit use of the current k-th solution with the corresponding unit use of all the previously found solutions: 1. The term |yks − yk−j s | compares the unit use of unit s at the current k-th solution with the unit use in the k − j solution. The result is either 0, if there is no change in the unit use, or 1 if the unit use changes. 2. The term ∑sN=s 1|yks − yk−j s | ∈ {0,1,.., Ns} gives an integer between 0 (which means that in the current solution the solver is analyzing an already found solution) and Ns (which means that all the unit use have changed status). 7041
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size) are variables of the optimization problem. A clear example of a fake solution is the combination of unit use ys = 1 and multiplication factor fs = 0, which represents a subsystem activated with zero size. This is a consequence of the use of ICC; it acts on the unit use, forcing the solver to look for new combinations. Nevertheless, the objective function consists in minimizing the total cost. Consequently, the result is the activation of a new unit in the superstructure so that a new combination having the smallest available size is obtained thus minimizing the objective function. The more units are included in the superstructure the slower the generation of results is because all the fake combinations must be analyzed before moving to a brand new feasible pathway. In order to avoid such problem, new constraints are added to limit the size of the problem and consequently accelerate the final result. Three additional constraints are analyzed. The first is aimed at increasing the minimum size of the units in the superstructure by stating f min,s > 0. Such constraint does not reduce the computational time but avoids the generation of fake solutions. The second constraint is the epsilon constraint.56 The rationale of the latter constraint is to force the objective function to increase at each step thus avoiding the replication of already found solutions: Fk(x) ≥ Fk−1(x) + ε, where Fk(x) is the objective function at the k−th run. The epsilon constraint is very effective as it reduces the computational time. However, its effectiveness is strongly related to the value of epsilon: high values cause the loss of interesting combinations (pathways). Sensitivity analysis on the value of epsilon proved that the εconstraint is not reliable as it is not possible to state the optimum value of ε a priori. The third constraint applied is a limit in the number of units allowed to work in parallel:
By dividing this term by the total number of units in the superstructure (Ns) results in a number less or equal to ∑
Ns
|y k − y k − j |
one s=1 Ns s ≤ 1. s 3. The application of the operator ceiling (a function that rounds up to the next integer) to the expression ⎡ ∑sN=s 1 |ysk − ysk −j | ⎤ ⎢⎢ ⎥⎥ ∈ {0, 1}, gives an integer which is 1, if Ns at least one unit use has changed status, or 0 if no changes occurred in the unit use of the k-th solution. 4. Finally, the constraint is obtained by summing up all changes occurred in the unit status in the past solutions. The sum must be grater or equal to the number of the past solutions minus 1. In fact, it is useless to confront the current solution with itself (so k − 1 comparisons are necessary). In conclusion, if eq 8 is verified, it means that the current solution is a new combination of units. The great advantage of this formula is that it is a unique constraint, which deals with all the previous solutions simultaneously. Besides this advantage, this formulation makes the problem MINLP because of the use of the ceiling function, which is nonlinear. In reality, in this paper, a different formulation56 is used instead of eq 8 to guarantee the MILP formulation: Ns
∑ s=1
(2ysk
Ns
− 1)ys ≤ (∑ ysk ) − 1
∀ k = 1, ..., nsol
s=1
(9)
Differently from the previous formulation, this constraint must be added at each run to prevent the replication of the past solutions; a new constraint is added at each iteration so that the number of constraint increases linearly at each run. The problem is then relaunched until all the solutions are retrieved, as it is presented in the flowchart of Figure 3. ICC Computational Issues. The application of ICC generates fake solutions. A fake solution is a pathway in which one or more units are activated but the size is too small (or at least zero). This is due to the fact that both the integer (the unit use) and the multiplication factor (which stands for the
Ns , t
∑ ys ≤ Nt s
∀t∈T (10)
where T is the set of available technologies, and Nt is the maximum number of processes of type t allowed to work in parallel. This constraint aims at reducing the size of the problem and consequently the computational time; it is effective in the case of multiple plant configurations of the same process. After running the model, a post-analysis of the result is necessary to clean and filter the results. In this postprocessing phase, fake solutions are discarded.
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CASE STUDY Can wood be a reliable renewable resource for Switzerland? What are the best processes that can be used to convert biomass into valuable products? These are the questions this case study tries to answer. In order to do so, first the Swiss wood potential is analyzed, second the models are organized in the Platform superstructure, and finally, the economic conditions are set. Two different input biomass sizes are evaluated: a pilot scale size (20 MW input biomass plant) and a big-sized facility (200 MW). Wood Model. In the wood model, the features of the input biomass are assumed according to Steubing et al.58 In the economic assessment of the cost of the wood, harvesting and transportation costs must be evaluated together with the market value of the biomass. The harvesting and transport models are taken from the work of Steubing et al.58 and Peduzzi et al.59 According to these hypothesis, in the worst case
Figure 3. Flowchart of the ICC algorithm.57 7042
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Industrial & Engineering Chemistry Research scenario, the supply cost for a 20 MW biomass plant is 0.045 USD/kWh and the transportation cost constitutes 12% of the total cost (0,0052 USD/kWh). In the case of a 200 MW biomass plant, the biomass cost is 0.047 USD/kWh, 17% of which is due to the transportation (0.0078 USD/kWh). Techno-Economic Process Models. As explained in the Superstructure Formulation section, the unit models used in the Platform are simple black boxes with fixed efficiency. Each unit (black box) is scaled linearly by the solver by multiplying both costs and streams for the multiplication factor of the unit. The scheme of the superstructure used in the model is presented in Figure 2. In the current case study, five main biomass conversion technologies are considered, each one with several plant configurations; the models of methanol synthesis (MeOH), dimethyl ethere (DME), and Fischer−Tropsch (FT) come from Tock et al.,60 while the SNG models are taken from Gassner61 and Gassner and Maréchal.62 Table 1 presents the features of each black box model: gasification technology, fuel output rate, and electricity production/consumption rate per MW of input biomass and investment cost according to size. Economic Boundary Conditions. Finally, the economic boundary conditions are assessed; market prices are assigned to the outputs (Table 2) in order to compare the biobased products with the fossil counterparts.
Table 3. Top-Ten Technologies According to the Objective Function Values for Two Different Sizes technologies
parameters
value
unit
ref
567.3 1.12 1.37 6 20 90 4 60,000 5 0.039 0.0052 0.0078 0.212 0.111 0.063 0.056 0.070
− USD/CHF USD/EUR % years % per shift USD/year % of Cgr USD/kWh USD/kWh USD/kWh USD/kWh USD/kWh USD/kWh USD/kWh USD/kWh
63 64 64
20 MW
200 MW
1 2 3 4 5 6 7 8 9 10
FT-a + Eout FT-b + Eout FT-EFdir + Eout SNG-a + Eout Ein + FT-EFind MeOH-d + Eout FT-EFind + MeOH-d FT-EFind + SNG-a FT-a + MeOH-b FT-EFind + SNG-b
FT-a + Eout FT-b + Eout SNG-a + Eout MeOH-d + Eout FT-EFdir + Eout FT-a + MeOH-b MeOH-b + SNG-a FT-b + MeOH-b MeOH-a + SNG-a Ein + FT-EFind
In Figure 4, the objective function (total cost expressed in dollars per second) is plotted together with the number of runs taken to retrieve that pathway. The evolution of the number of runs accounts for the speed of the proposed method to find a solution exploring the possible configurations; the steeper the graph is, the slower the solution seek is. This happens at the beginning of the superstructure exploration; the top-ranked pathways are detected within 40 runs (case 20 MW input biomass) and 70 runs (case 200 MW input biomass), subsequently the rest of the rank is found faster.
Table 2. Economic Parameters Used in the Case Study CEPCI index (2013) currency exchange rate currency exchange rate interest rate plant lifetime plant availability operators operators salary maintenance cost wood market price wood transp. cost (20 MW) wood transp. cost (200 MW) electricity price methanol price crude oil price natural gas price DME price
rank
61 65 66 59 59 67 68 69 70 71
Assessing prices for the products is a complex task because not all the products considered here are global commodities and therefore have a global price. For instance, methanol is a global commodities, while DME market is not well-defined, as the demand is low and localized. The SNG produced is fuel grade, and it can be pumped into the grid. The price of FT fuels was assumed equal to crude oil, as the model in analysis produces crude FT.
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RESULTS AND DISCUSSION The suggested method allows different pathways to be compared and ranked according to the total cost. In Table 3, the the top-ten conversion pathways to transform wooden biomass into biofuels are reported. The first positions are held by simple solutions, as the simplicity in the plant configuration prevails on the integration between different processes.
Figure 4. Results for the case study. 7043
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Industrial & Engineering Chemistry Research
constraints on the achievement of the results was not clear in advance due to the scarce literature about computational issues coming from the application of the ICC method. The set of constraints that has been developed in this study reduced the computational time up to 45−50%. The technology rank allows the best pathways and the gap between the renewable product and the fossil counterparts in the current Swiss economic market to be evaluated. The black box approach demonstrated to be useful to evaluate quickly a broad number of alternatives keeping good accuracy. The developed method applied to the OSMOSE Wood2CHem platform can pave the way for a broad variety of analysis related to biorefineries. In the next step, the black box model approach could be refined by adding the heat streams of each process and to perform an optimization which includes not only mass and energy balance but also energy integration. In the long term, the effect on the rank of different boundary conditions (market prices, wood availability, technology costs) could be evaluated to assess the best technologies that are worth developing. In this perspective, a tool capable to rank the possible processes will surely help government and decision makers not only to develop correct environmental policies but also to steer industrial production toward new promising products and markets. In conclusion, the ICC method applied in the current work leads to numerous future developments. The method can pave the way to a more complex and accurate analysis of biomass conversion pathways, being a great addition in pushing the development of biorefineries.
The objective function trend of Figure 4 shows the pathways having similar objective function values (i.e., points that lies in a flat part of the graph). In this case, other criteria can be applied to sort the best option; suboptimal solutions may be interesting to widen the choice from a single optimal point to a set of pathways. This is comparable to a Pareto-optimal solution30,31,55 but with a substantial difference: the obtained rank has a higher flexibility with respect to a Pareto-optimal result since it allows the decision maker to choose according to secondary objective. Such secondary objective can be stated in a subsequent moment and can be of any kind (e.g., available resources, both in term of technology or investments, market forecast, social impact), consequently the rank assumes the role of reference to support the decision maker in evaluating different options. The focal point is that the proposed method aims to perform a preanalysis of a broad variety of option in order to select the most promising ones to be further analyzed. In this perspective, the case study defines a rank of the best biomass-to-fuel technologies; FT turns out to be the best technology to convert biomass, then comes SNG and methanol, followed by a number of pathways obtained by coupling different processes. DME closes the chart. By coupling different technologies the goal is to investigate the performance of hybrid solutions that may be more efficient and/or less costly. Comparing the rank with the objective function trend of Figure 4, it is possible to evaluate the pathways which have slight difference in term of objective function. For instance, in the case of 20 MW biomass input, the solution numbers 3, 4, and 5 lie in a flat range of the graph. Consequently, those pathways can be considered as equivalent solutions and other aspects can be investigated to identify the best option. An economic evaluation of the case study can be done calculating the break even price of the wooden biomass, i.e., the cost of the wood which makes the profit zero. The wood break even price is 30% lower than the wood cost for small scale plants while, for big size plants, the gap between wood cost and wood break even cost decreases to 10%. Economy of scale affects the rank; some conversion routes are fostered as the input biomass increases (for instance, SNG-a gains a position in case of 200 MW input biomass). However, biomass supply becomes more and more expensive as the plant size grows. The low energy densitywhich affects the harvesting and transportationand the limited biomass availability are the great weaknesses of wooden feedstock biorefinery.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is part of the Wood2CHem project, a cooperation between the ETH Zurich and the EPF Lausanne fostered by Swiss National Research Programme “Resource Wood” (NRP 66)74 which aims to establish basic scientific knowledge and practical methods for increasing the availability of wood as a resource and expanding its use in Switzerland.
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CONCLUSIONS AND FURTHER DEVELOPMENTS The paper shows how the Integer-Cuts Constraint (ICC) method can be applied to systematically evaluate and rank conversion pathways for biorefineries. The proper ICC statement allows the replication of already-found trajectories, thus creating a rank of all the feasible pathways inside a superstructure. The application of Constraint Programming72,73 (1) keeps the problem simple and easy to be handled and (2) keeps the structure of the model flexible enough to be further expanded without boosting the computational time. The ICC method proved to be effective in achieving an ordered rank, but additional constraints turned out to be necessary to accelerate the solutions. The set of constraints which enable the result to be obtained in the fastest time was developed by means of a systematic test of different constraint statements. The testing phase was necessary because of the nonheuristic nature of the problem; the effect of different set of
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