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Sustainable batch process retrofit design under uncertainty—An integrated methodology
Accepted Manuscript Title: Sustainable batch process retrofit design under uncertainty − An Integrated Methodology Author: Tˆania Pinto-Varela Ana Barbosa-P´ovoa Ana Carvalho PII: DOI: Reference:
S0098-1354(16)30389-1 http://dx.doi.org/doi:10.1016/j.compchemeng.2016.11.040 CACE 5629
To appear in:
Computers and Chemical Engineering
Received date: Revised date: Accepted date:
3-6-2016 28-11-2016 30-11-2016
Please cite this article as: Pinto-Varela, Tˆania., Barbosa-P´ovoa, Ana., & Carvalho, Ana., Sustainable batch process retrofit design under uncertainty − An Integrated Methodology.Computers and Chemical Engineering http://dx.doi.org/10.1016/j.compchemeng.2016.11.040 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Sustainable batch process retrofit design under uncertainty – An Integrated Methodology Tânia Pinto-Varela*, Ana Barbosa-Póvoa, Ana Carvalho CEG-IST, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal *[email protected]
Highlights
Methodology for sustainable batch retrofit design under uncertainty Combined heuristic and optimization methodology Combination of design and optimization tools Application through a multipurpose batch plant case study
Abstract This work explores the problem of optimizing batch processes’ retrofit design pursuing an increase of production efficiency and efficacy while accounting for the associated processes’ sustainability, aspect that within the process industry is nowadays of increasing concern. Batch processes are often complex structures, where retrofitting is not always a straightforward procedure for the decision maker, requiring then supporting tools. Such tools are often characterized by having to deal with large scale optimization problems, where solutions are difficult to obtain. Moreover, the presence of uncertainty adds to the already complex problems an extra level of difficulty. Within this context, the present work proposes an integrated solution approach, uSB-Design, which aims to guide decision-makers in the definition of sustainable batch retrofit designs under uncertainty. The applicability of the proposed methodology is shown through a batch plant case study.
Keywords: Retrofit; Batch; SustainPro; Optimization; Uncertainty
1. Introduction The increasing importance of chemical plants’ retrofit design is constantly observed, due to the need of costs rationalization and minimization of environmental impacts. This ought to be considered while maintaining plants efficiency and efficacy. Guinand (2001) defined retrofit design as: “The redesign of an operating chemical process to find new configuration and operating parameters that will adapt the plant to changing conditions to maintain its optimal
performance.” The retrofit problem in general and in batch process plants in particular, are complex problems (Barbosa-Póvoa, 2007) that require decision supporting tools enhanced with models and solution approaches that would be able to deal with the associated problems complexity. Based on this challenge several authors have been developing heuristics, metaheuristics and optimization models attempting to systematize procedures that will help practitioners in their retrofit activities. However as identified by Barbosa-Póvoa (2007) and more recently in Moniz et al (2015) new methodologies are still required, which should explore the integration of such approaches (heuristics and optimization methods) in order to solve the complex problems in a real time context. The study of such integrated approaches has recently gained the interest of some authors. Chibeles et al. (2010) presented a meta-heuristic approach to improve computation results of the design and scheduling of multipurpose batch plants using Simulated Annealing and compared the results with exact methods. Later on in 2013, Moniz et at (2013) proposed a formulation based on the Resource Task Network for the optimal scheduling of multipurpose batch plants, where equipment redesign is considered simultaneously with scheduling decisions. The equipment redesign problem is defined by the implementation of modifications in the processing units so as to change their suitability to perform certain tasks. A solution approach to solve the resulted complex problem was devised. Seid and Majozi (2013) studied the design, synthesis, and scheduling of multipurpose batch plants. A based robust scheduling formulation was used as a platform for the integration of the design problem where the integrated approach explicitly considered the different locations of materials in the plant. Good computational times were obtained when compared with previous published formulations. In the same year Fumero et al. (2013) also addressed an integrated problem where a multi period MILP model for the design, planning and scheduling of multistage multiproduct batch plants was presented. Market fluctuations were considered in a multi period context where different production campaign in each period were operated. More recently, Patil et al. (2015), proposed a methodology that addresses simultaneously: design, scheduling, and control of multiproduct processes. This considers disturbances by the identification of their critical frequency, which is used to quantify the worstcase variability in the controlled variables via frequency response analysis. Demand uncertainty is addressed through scenarios where different probabilities of occurrence are considered. When analyzing the above works no focus on sustainability aspects has been identified. However, such concerns are nowadays a reality. The sustainable development has raised its importance after the definition presented by WCED (1987) in the Brundtland Report: “the development that meets the needs of the present without compromising the ability of future generations to meet their own needs”. Afterwards, Elkington (1998) translated the sustainable development into three pillars: economic, environmental and social. These two works appears as seminal when defining sustainability and have been used widely by different authors as main references in the area. Today, sustainability is a top priority of any company and batch processes industries are not an exception (Carvalho et al., 2009). Some methodologies considering sustainability in batch process design have been presented in the literature, however the number of publications in this area is still limited. In (2003), Pinto et al. proposed a mixed integer linear formulation for design of multipurpose batch facilities, considering heat integration and economic utilities savings. Halim et al. (2006) presented an intelligent system for batch processes waste minimization, based on heuristic rules (BATCHENVOPExpert). Simon et al. (2008) proposed a decision support framework for batch processes’ retrofit design based on a heuristic method. The framework identifies improvement opportunities in a batch plants through the analysis of the product market situation. Carvalho et. al. (2009) proposed a
methodology that screens the batch design alternatives using economic, environmental, and social aspects (e.g. safety indicators), in order to identify the batch process bottlenecks and propose new design alternatives. In the same year, Chen and Chang (2009) integrated task scheduling and heat recovery aspects into an unified framework for multi-purpose batch processes. A mixed-integer linear program (MILP) was developed, where the new formulation could be solved in a standalone mode or using an heat-integrated mode. In the heat-integrated mode, the processes was defined, while keeping the operation flexibility with slightly expanded model size. Nonyane and Majozi (2012), considered cyclic scheduling concepts applied to wastewater minimization and production schedule optimization in a multipurpose batch facility. The formulation is based on a continuous-time formulation. In 2013, Yue and You (2013) addressed a bi-objective approach of batch scheduling problems considering economic and environmental aspects. The profit rate was defined as economic objective, followed by the environmental objective defined per functional unit based on the life cycle assessment methodology. Each instance was formulated as a mixed-integer linear fractional program (MILFP), which is a special class of non-convex mixed-integer nonlinear programs. In order to globally optimize the MILFPs obtained, a tailored reformulation-linearization method and Dinkelbach’s algorithm was used, followed by a multi-ojective approach, ε-constraint. Adekola et al. (2013) and Seid and Majozi (2014) proposed methodologies to address water and energy minimization, while schedule optimization was pursued. Adekola et al. (2013) explored opportunities for direct water and indirect water reuse while Seid and Majozi (2014) explored the presence of multiple contaminants in a stream as well as temperature variation. Recently, Li et al. (2015) proposed a hybrid optimization approach for sustainable process planning and scheduling, using meta-heuristcs. The honey-bee mating and annealing processes are simulated to optimize multi-objectives including energy consumption, make span and the balanced machine utilization. Despite some work has been done on the design, plan and scheduling of batch processes while considering sustainability concerns, as summarized in Table 1, further work is still required.
From Table 1, it is possible to verify that it is still missing in the literature the association of uncertainty when dealing with the sustainable batch design. Additionally when considering the retrofit problem, which more often appears within existing plants, the identified need is still a reality. In this context, the present work presents a generic and systematic approach for the simultaneous design/retrofit and scheduling of multipurpose batch plants while considering sustainability aspects in an uncertain demand environment. Due to the complexity of the system under analysis, integrated approaches for the problem resolution are required. Thus an integrated methodology, the uSB-Design is developed in the present work. This consists on an iterative process that allows a continuous improvement of existing plants, based on a combination of heuristics and optimization steps that pursue performance improvement of the processes under study while accounting for mass and energy process alternatives and accounting for demand uncertainty. The remaining sections of the paper are organized as follows. Section 2 presents a detailed description of uSB-Design approach and in section 3 the uSB-Design is applied to a case-study and the obtained results are discussed. Finally, conclusions are drawn in section 4.
2. Uncertainty Sustainable Batch Retrofit (uSB-Design) A methodology for sustainable batch retrofit design under uncertainty is proposed, the uSBDesign. This methodology analysis a batch design plant operation and identifies tasks, units or operating conditions that represent processes bottlenecks, based on which retrofit design alternatives are proposed that will eliminate the bottlenecks and/or improve the process performance. A bottleneck is defined as any path, task, unit or operation that is limiting the efficiency of the process and therefore that should be reduced or eliminated. For instance, a batch process might present bottlenecks in terms of water and/or energy consumption, processing time and capacity, which should be improved through retrofit actions. uSB-Design analysis can also deal with batch processes uncertainty scenarios, allowing processes’ bottlenecks identification, that come up under different circumstances. This extensive analysis leads to a more robust decision in terms of bottleneck identification and therefore in terms of new retrofit solutions for batch design. The uSB-Design integrated methodology is presented in Figure 1. It uses two main decision tools: an exact model formulation (see annex) developed for the design and scheduling of multipurpose batch plants, OptimRHI, (Pinto-Varela et al., 2009) and an indicator heuristic based methodology developed by Carvalho et al. (2009) which is incorporated in the SustainPro software tool (Carvalho et al., 2013). It is important to mention that the uSB methodology only provides problem reduction if alternatives in terms of processes or resources usages exist (e.g. alternative process paths; alternative processing units; alternative products portfolios, amongst others)
The integrated methodology develops along four main steps. Each step is described in more detailed below:
Step 1: Data Collection In this step plants and processes’ data collection is performed involving the gathering of data associated with: recipes, mass and energy consumptions, operation times, costs, equipment volumes, purchase and sale prices for each material and tasks environmental impacts. This data is the input for the next methodology´s step. Note that this data can be collected from an industrial plant or can be obtained from simulation software or databases. Step 2: Scenarios analysis under uncertainty The second step involves the solution of the optimization model, OptimRHI, for the input data gathered in step 1. The OptimRHI is represented in Figure 2 and defines the: process synthesis for the multipurpose batch plants, equipment design, process scheduling, resources usage and production profile under demand uncertainty. OptimRHI is characterized by a set of constraints (see annex) that can be grouped into three main groups: excess resources balances, where balances to the different resources are performed being these equipment, materials, energy, or human resources; equipment design, where capacities and plant topology definitions are considered; and finally capacity and operational restrictions, accounting for equipment limits for processing, storage and transportation as well as operational conditions that have to be obeyed,
such as minimum batch amounts, or demand to be satisfied in time and quantity, amongst others. The problem solved can be summarized in: Given: The process/plant description (in RTN terms); resources availability, characteristics and costs; utilities requirements; time horizon of planning; mode of operation; demand over the time horizon (production range); cost data; probability density function. Determine: A defined economic indicator considering the batch process design/retrofit model under demand uncertainty. As mentioned by Barbosa-Póvoa (2007) the complexity of the design/retrofit problems can easily lead to high computational burden when the optimality is pursued. However as the results obtained at this step work as a starting point to evaluate the batch process this limitation can be easily overcome by considering a reasonable optimality gap (e.g. 5%). The solution results from this step are feed into the next step and through the use of SustainPro the process/plants bottlenecks are identified.
As aforementioned the OptimRHI considers the presence of demand uncertainty and is assumed to operate in a periodic mode:
Uncertain demand characterization The demand uncertainty is integrated in the OptimRHI, using a two-stage stochastic programming approach, where the decision variables are classified in first- and second-stage variables. The first-stage variables are associated with decisions that cannot be reviewed, or which are less prone to be modified, once the future outcomes are realized. In the OptimRHI such variables are considered as the design variables associated to the equipment selection. The second-stage variables characterize decisions that can be reviewed after the scenario occurrence, i.e. additional information is obtained on the realization of some random vector. In OptimRHI such variables are the scheduling variables related to the production, storage and transfer decisions. After the demand is known, these decisions can be reviewed.
Periodic mode The periodic operation mode considered in the OptimRHI explores the concept of cycle time, T, which is repeated over the production time horizon, as shown in Figure 3. The operations´ sequence for all products‘ production are characterized over one cycle that will be repeated. The problem formulation is run for a single cycle, allowing tasks to overlap successive cycles modelled as defined in equation (1) through the wrap-around operator from Shah et al. (1993). Such operation mode assumes that the plant´s operation is the same at the beginning and at the end of the cycle.
t ( t ) ( t T )
if t 1 if t 0
(1) The OptimRHI uses a time discretization, where the cycle time is divided into T intervals of equal duration. The start of the cycle is defined as time t=1, and the end as t=T+1. The latter overlaps with the starting point of the next cycle. A planning horizon (H) is assumed, which is divided into N equal cycles of duration (T). A cycle is divided into a number of elementary time steps of fixed duration (), as shown in Figure 3.
The output of this step is the topology of the process in study, the product’s recipe, resources usage, tasks scheduling, and energy and water consumption for each scenario. As mentioned this data will be used as input data for step 3.
Step 3: Sustainability Retrofit Analysis The results obtained in the previous step are here analyzed through a sustainable design/retrofit methodology proposed by Carvalho, et al. (2009). This methodology is available in a software tool called SustainPro (Carvalho et al., 2013), which screens generates and prioritizes batch process design alternatives. This methodology can be summarized into four steps, being each step characterized below: A) plant/process decomposition in closed, open and accumulation paths; B) indicators calculation; C) sensitivity analysis; D) new batch design alternatives proposal. Figure 4 represents the integration of SustainPro in the uSB-Design methodology. The imported data from step 2 (mass and energy balances, processing times, capacities and recipes for each scenario) added to some data collected in step 1 (prices and compounds’ properties), allows the SustainPro to identify the bottlenecks in terms of energy, time, capacity and value added for the demand uncertainty scenarios characterized as step A of SustainaPro. The bottlenecks´ identification, starts with a process decomposition into closed-, open- and accumulation paths for energy and mass, which can be characterized as, see figure 5:
Closed-paths represent all flow-paths which start and end in the same unit of the process (Carvalho, et al., 2008). Open-paths represent all compound flows that enter and leave the process (Carvalho, et al., 2008). Accumulation-paths are related to the build-up of mass and energy in the batch operations (Carvalho, et al., 2009)
Step B calculates the indicators´ quantification for each path, in order to define the paths bottlenecks and possible retrofit actions. These indicators assess several process problems such as material, energy, costs and time problems (e.g. MVA-Material Value Added; EWC-Energy Waste Cost; OTF-Time Factor). Table 2 summarizes the most relevant indicators.
Based on the indicators values the bottleneck paths are identified. This means that paths presenting the highest values of EWC, TF and EF define a process bottleneck in terms of energy/water from utilities consumption, processing time and energy potential for heat integration. Negative values of MVA indicate that products/by-products leaving the process are losing value through the process, reflecting a higher cost in the compounds’ acquisition or in their raw materials purchase, when compared to the value obtained for that compound, when leaving the system. After analyzing the indicators values a list with the indicators with high potential for improvement (based on the indicators worst values obtained) is determined that defines the paths bottlenecks. Afterwards, step C of SustainPro is conducted. From the set of indicators that have been selected, a first sensitivity analysis is performed in order to identify the ones that will represent higher improvements in terms of sustainability. This is done performing the ISAAlgorithm described in Carvalho, et al. (2008). A second sensitivity analysis follows, in order to determine the most critical task in the selected path. This means that within a path some tasks, equipment or flows might be the main reason to obtain these indicators’ values. Through the two sensitivity analysis levels, the tasks, equipment or flow responsible for the process bottleneck are identified and retrofit design actions should be undertaken so that bottleneck is reduced or eliminated. Finally, in step D, through a heuristic based analysis new process design alternatives are proposed to eliminate the identified bottlenecks, for instance compounds’ recycles, identification of tasks where heat integration should be conducted, elimination of paths with non-value added activities, among others (complementary information about the heuristics can be found in Carvalho et al, 2008). At this step, the SustainPro’s analysis is undertaken over the several uncertain scenarios. The scenario’s analysis allows the identification of the bottleneck tasks, which negatively affect the different scenarios. Those bottlenecks are classified as top priority on batch retrofit design under uncertainty to pursue sustainability (e.g. elimination of a task, change of equipment, elimination of paths, new separation processes, and recovery of compounds). The output of this step is then a list of recommendations that will further tested and optimized in step 4, through a new run of the optimization model.
Step 4: Sustainable Planning and Scheduling The recommendations from step 3 are considered in the new input data for of OptimRHI. This data characterizes a much simpler process/plant design as non-added value paths were eliminated based on the results obtained in step 3. The OptimRHI results define in a much efficient way a more sustainable solution where is obtained the process synthesis, scheduling, equipment design and all the resources profile, considering an economic indicator maximization. At this point the sustainability of the new batch design is assessed comparing the obtained results with the initial batch design. The sustainability assessment is performed through the application of a set of sustainability metrics (Azapagic, 2002) and the WAR algorithm (Young and Cabezas, 1999). The social component is evaluated through the safety index (Heikkilä, 1999).
3. Case Study
3.1 Case Study Description This case study is based on a published case by Kallrath (2002) where a benchmark problem based on real case studies o process industry has been characterized. In this work this case study has been here extended to account for energy production and consumption. The problem to be solved is a retrofit batch plant problem aiming to attain a maximum plant profit and a more sustainable process while accounting for the process synthesis, equipment design and scheduling under an uncertain in market demand. A more sustainable process is characterized by lower values of sustainability metrics, such as: a lower safety index (Heikkilä, 1999) and a lower impact in the WAR algorithm (Young and Cabezas, 1999), simultaneously higher economic metrics (Azapagic, 2002). Five products are to be produced (P1 to P5) through different synthesis processes departing from a single raw material where consumption of energy is present. The process synthesis and task durations for all products are shown in Figure 6. The Ti-Ri defines that Ti can be operated in equipment, Ri; RM, Ii and Pi defines raw-material, intermediate resource, and final product, respectively. A periodic mode strategy is assumed, with a production campaign time horizon of 52 weeks (6240 h) associated with a cycle time of one week (120 h). Market uncertainty demand is characterized within three scenarios: pessimist, expected and optimistic, with probabilities, 0.1, 0.5, 0.4, respectively, as shown in Table 3. The multipurpose characteristics of the equipment and task´s energy characterization are shown in Table 4. The unit´s capacity range from 0 to 300 [m.u./m2], except unit one and two with maximum capacity of 100 [m.u./m2]. The associated fixed and variable costs are 30/ 0.5 [103c.u.], respectively. The connectivity´s costs are 0.1/ 0.01 [103c.u.] for fixed/variable cost, respectively.
3.2 Case Study Results Step 1- Data Collection The first step is defined by collecting all the data for the methodology´s input. The process synthesis are characterized by several alternatives for each product´s production, as is present in Figure 6. The production range of each demand scenario for all the products is shown in Table 3, followed by the multipurpose characteristics of the equipment, in Table 4. The heat requirement specifications for each task is given in
Table 5, followed by the product´s final price, in Table 6.
Step 2- Scenarios analysis under uncertainty In the second step the OptimRHI runs for a 5% gap and the results are feed into SustainPro in step 3. The results in terms of energy requirements for each task over the uncertainty scenarios are shown in , followed by the production of each product over a cycle, Table 8.
Step 3- Sustainability Retrofit Analysis under Uncertainty Considering the three scenarios´ results obtained in the previous step, and the data presented in step 1, SustainPro is applied. It starts by decomposing the process topology into closed-, open- and accumulation-paths, which result in none closed paths, 41 open-paths and 9 accumulation-paths, obtained over all scenarios. Then the indicators for all the paths have been calculated. Through the two sensitivity analysis, these indicators have been screened and the paths and the tasks bottlenecks have been determined following the ISA-Algorithm procedure (Carvalho et al., 2008). MVA, EWC and TF indicators turned to be the bottlenecks of the system and they are presented in
Table 9 and Table 10. The paths corresponding to those indicators are characterized in Table 11.
From the indicators analysis it is possible to verify that:
-
-
Material Value Added (MVA) of open-path 3 has a negative value (see Table 10), which means that value has been lost in Task 1 (between the raw materials consumption and production of S1). MVA, for OP3 was negative in the three scenarios indicating that OP3 is a system important bottleneck in terms of value added. The highest values of Energy Waste Cost (EWC) define the highest energy consumption, representing energy bottlenecks. These were observed in the three scenarios for: OP1, OP2, OP3, OP4, OP5, OP8, OP9. However scenario two identified as energy bottlenecks paths also OP6 and OP12. For the new design alternatives, the bottlenecks identified over all scenarios should have priority in the retrofit design problem. Therefore, retrofit design efforts should focus on OP1, OP2, OP3, OP4, OP5, OP8, OP9. Through the operational sensitivity analysis, T8R5 in OP5 has been identified as a critical task, presenting the highest energy consumption over all the scenarios. For paths OP1, OP2, OP3, OP4 and OP8 the major energy problems are related to tasks T2R2 and T3R3. However, these tasks are a cornerstone of the process topology and they are difficult to improve in terms of energy reduction, as are tasks using reactors to produce intermediate materials, required for the production of all final products. By changing energy consumption in those tasks will change the reactional mechanism or the reaction conditions, representing an even higher retrofit design investment and therefore it should be avoided when other bottlenecks are present and with potential to be improved (heuristic rules presented in Carvalho, et al 2008). Finally, in path OP9, task T9R5 was identified as bottleneck of energy that should be reduced. Regarding processing time, it is possible to identify several tasks as bottlenecks of the process, identified by the same and high value of TF. The high value of TF reflects long processing times that should be reduced in order to increase the efficiency of the process. Based on the process topology of Figure 6, several paths are available to produce the same product (e.g. I9 could be processed in T13_R8 or T13_R9). The paths identified in this step as containing bottleneck tasks, should be screen before the following step, and not considered as an option for more sustainable scheduling and planning decisions. Or on the other hand, these tasks should be replaced by other non-limiting tasks in order to overcome the time limitation of the process.
Based on the previous analysis, SustainPro recommends the following retrofit design proposal, which will be considered in step 4:
Based on the MVA value S1 should be recycled to task 2.
Task T8_R5 is a bottleneck in terms of energy and time and therefore should not be considered in the new batch design. Alternatively, to T8_R5, task T8_R10 should be considered. T9_R5 was identified as a critical task in terms of time and energy. Its elimination will prevent product P3 production. Based on positive values of MVA indicator for P3, its values are the lowest, reflecting the low value added of product P3. Therefore, P3 should not be produced and tasks T9_R5, T14_R8 and T14_R9 should not be considered as a possible network for the new batch process topology. T11_R7 and T16_R9 are critical in terms of time and therefore they should not be included as an option in the new batch topology, which leaves the production of P4 to follow tasks T11_R6 and T16_R8.
Step 4- Sustainable Planning and Scheduling Based on the results of the previous step, a new iteration is performed by the OptimRHI. The paths identified as bottleneck in utilities consumption and time restrictions over the three demand uncertainty scenarios are deleted from the previous synthesis process characterization. The OptimRHI runs with the new data considering the worst sustainable scenario, but simultaneously avoiding service level impacts. This is activated by running the OptimHRI for the scenario with highest demand. As results of OptimHRI for the new process synthesis the retrofit and scheduling are obtained. These are shown in Figure 7 and Figure 8, respectively. A comparison analysis of sustainability and computational effort between step 2 and step 4 is done in Table 12, and Table 13, respectively.
From Table 12 it is possible to verify that the initial process has been improved in all aspects. The energy bottlenecks elimination provided an improvement of energy consumption of 6%, and when assessed in terms of consumption per unit value added an improvement of 21% is observed. The economic performance shows an improvement of 18% from the initial design to the new design proposal. Also in terms of net water consumed a 3% improvement is observed. Finally, environmental impact has decreased of 104%, resulting from the additional recycling of S1, the waste that has been avoided and the fact that safety index has decreased (3%), trigged by the decrease of energy consumption in the tasks. In conclusion, the identification of the bottlenecks and their elimination leads to more sustainable processes both in economic and environmental terms. If the decision-maker aims to further improve the process, through the identification of new bottlenecks, one more run of the methodology could be performed (Figure 1). In a second run of uSB-Design a new set of bottlenecks could be identified by SustainPro, and a new process synthesis proposed. The process will be concluded by the decision- maker when suitable sustainable solution is reached (e.g. budget limitations, achieved goals, etc).
Despite the proposed synthesis eliminated the production of P3, the global results have improved. The statistics´ comparison between the initial and the proposed synthesis improved in 15 % and 91% over the initial synthesis data, for profit and time, respectively.
4. Conclusions A methodology, called uSB-Design, has been proposed to attain sustainable batch design/retrofit designs. uSB-Design is a stepwise procedure that integrates heuristic methods and optimization models applied to the synthesis, design/retrofit and scheduling of batch process. More sustainable process synthesis are obtained with lower computational complexity when uncertainty is considered. The proposed methodology allows the identification of a set of bottlenecks through a heuristic procedure (SustainPro) triggering the decrease of combinatory level of the optimization problem without comprising the economics and environmental aspects of the processes in study. Summarizing, uSB-Design has the following benefits: 1) The time consumed in the batch retrofit design is reduced; 2) more sustainable solutions are proposed; 3) deals with uncertainty in the batch design/retrofit design; 4) guides decision-makers in the retrofit analysis. As future work the methodology should be further tested in other more complex cases and an interface can be established to link the different tools and to facilitate the data flow between them. The interface could also manage the iterative process derived from the methodology.
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Appendix 1. Nomenclature r - resource
k- task t –time m- Scenarios Sets: C= {r: set of all material resources} Cis={r: set of intermediate material with dedicated storage} Cr={r: set of material resources with dedicated storage} Cp / Cf = {r: set of final products /raw materials} D = {r: set of all equipment resources} Dfp/Drm={r D: set of dedicated storage vessels for final product/ raw-material} Dc/Dv={r D: set of all connections/ storage vessels} Dp={r D: set of process equipment resources} Dpd={r D: set of process equipment resources with discrete sizes} Sr={s S: set of discrete sizes of a given process equipment resources, r} M={m : set of all potential scenarios } TK = {k: set of all tasks operating in an equipment resource} TP={k: set of processing tasks in an equipment resource, r} TS={k: set of storage task for raw and product materials in dedicated vessel} TR= {k: set of all tasks requiring an equipment resource, r} TV ={k, r Dv: transfer task, k, for an intermediate storage vessel, r, which is a sink} TT ={k: set of all transfer tasks} Parameters: H - planning horizon T - cycle time CCF - capital charge factor v r /pr - price of resource (raw material / product)
k0 / k1 - fixed and variable cost coefficients
rmax - size factor Rr0 m - resource r available initially in scenario m min max / Rrm - resource minimum/maximum quantity at H in scenario m Rrm
kr/ kr - consumption or production of a renewable(-1,1)/non-renewable(-1,0) resource r, at the start/end of
max r - maximum resource available of r
m probability of scenario m k - duration of task k Vˆrs - set of discrete size s available for equipment r Variables:
Rrmt - excess of resource at t in scenario m
kmt - batch size of task k at time t in scenario m r - amount of resource r required Vr - capacity of resource r Nkmt - number of processing tasks k at instant t, in scenario m (t)- wrap-around time operator Etr=1 if processing resource r is installed; 0 otherwise Ecr=1 if transfer resource r is installed; 0 otherwise Zrs = defines which equipment, r, with discrete size, s, is selected Constraints: The renewable and non-renewable resource´s balance are defined by constraints (2) and (3), respectively. intermediate storage materials, To guarantee that the quantities of resource at the beginning and at the end of the cycle are the same for the intermediate materials, constraint (4) is used, followed by the products’ resource balance (5). The equipment resource existence and its allocation to the suitable task is guaranteed by constraint (6). The resource capacity constraints is guaranteed by constraints (7), (8), followed by constraint (9) and (10) for the equipment design characterization. The capacity and batch size are defined by constraints (11)-(15). The storage constraints are defined by constraints(16)-(20). The connectivity between equipment and its capacity are characterized by (21) and (22). Constraint (23) characterize the production requirements, followed by the objective function and its terms characterization, (24) and (25)- (28).
Rrmt = Rr m (t 1) + k 0 k r Nk m (t ) k
Rr mt = Rr0m|t 1,rC f + Rr m (t 1)|t 2 +
r Dp, m M, t =1...T
k
k
(2)
k r k m (t )
0
r C/{ Cp}, m M, t =1...T
(3)
Rr mt|t 1 = Rr mt|t T 1 r Cis, m M Rr mt = Rr m (t 1)|1t T 1 +
k
k
(4)
k r k m (t )|t T 1
0
r Cp, m M, t =1...T+1 t
N
t 't k 1 k Tr
k mt '
0 Rr mt r
r r Dp, m M, t =1...T r Dp, m M, t =1...T+1
(5) (6)
(7)
0 r max r
r Dp r Dp
Vrmin r Vr rVrmax
t
Vr
k mt
(8) (9)
k TS, r Dv, m M
(10)
k
N kmax
N jkmt 1
j 0
N kmax
jN
Nk mt
j 1
j k mt
0 Vrjkmt Vrmax N jkmt N kmax
V
Vr
rjkmt
j 0
N kmax
jV
min kr
rjkmt
j 1
kmt
max kr
k Tp, m M, t=1...T
(11)
k Tp, m M, t=1...T
(12)
k Tp, r Dp, j=1...Nkmax, m M, t=1...T
(13)
k Tp, r Dp, j=1...Nkmax, m M, t=1...T
(14)
N kmax
jV j 1
rjkmt
k Tp, r D, j=1...Nkmax, m M, t=1...T
(15)
(R
Rrmt ) Vr|rDrm
m M, t=1+T
(16)
R
Vr|rD fp
m M, t=1+T
(17)
r0 m
m rC f
m rC p
rmt
Vrmin Etr Vr Vrmax Etr
m M ,r Dv
(18)
r Dv, k TV, m M, t=1...T
(19)
r Dv, k TV, m M, t=1...T
(20)
t
kmt
M r Etr 0
k
kmt
rmaxVr
k
k TT, r Dc , m M
kmt krmaxVr
(21)
Vrmin Ecr Vr Vrmax Ecr
r Dc, m M
(22)
H max Rrm T
r Cp, t = 1+T
(23)
min Rrm Rrmt
H Max Profit PR OC RMC (CC CCF ) T
( CC
CC
0 r
r
rD p
Vr r CCr1 )
[ CC r
rD pd
0 r
sSr
Vrs r CCr1 ]
rD
( Ecr CC Vr CC ) ( Etr CC Vr CC ) 0 r
rDC
OC=
m
RMC =
t
1 r
m
( k0 Nkmt k1kmt )
r0 m
r
k TP, m M, t=1...T
(25)
(26)
Rrmt ) vr m
r Cf, m M, t=T
(27)
r
PR = Rrmt pr m m
1 r
k
( R m
rDv
0 r
(24)
r Cp, m M, t=1+T
(28)
Methodology
Computational Tool
1. Data Collection
Databases
2. Scenarios analysis under uncertainty
3. Sustainability Retrofit Analysis under Uncertainty 4. Deterministic Sustainable Planning and Scheduling
Yes
Other Improvements?
No Final Design
Figure 1: USB-Design Methodology flowdiagram.
Optimization model
SustainPro
Optimization model
Figure 2: Integration of OptimRHI in the USB-Design Methodology.
Cycle N-1
Cycle N
1
Cycle N+1
T T+1
Figure 3-Time discretization for a single cycle
Figure 4: Integration of Step 3 in the USB-Design Methodology
Figure 5: Path decomposition – SustainPro
RM
T1_R1/ 4h
S1
0.6
0.4
T2_R2/ 8h
I3
I2
T8_R10/ 10h
T8_R5/ 12h
I9
T13_R8/ 8h
T4_R4/ 8h
T5_R4/ 8h
T3_R3/ 4h
I5
I6
I4
T10_R6/ 8h
T13_R9 / 9h
T10_R7/ 10h
S1
T9_R5/ 12h
T6_R4/ 8h
T7_R4/ 8h
I10
I7
I8
0.5 I11
P1 T15_R8/ 8h
0.5 T14_R8/ 8h
T14_R9/ 12h
T11_R6/ 10h
T11_R7/ 12h
T12_R7/ 12h
T12_R8/ 12h
P2 P3
I12
T16_R8/ 12h
I13
T16_R9/ 12h
P4
T17_R8/ 12h
T17_R9/ 12h
P5
Figure 6. Products’ receipt (rectangles tasks: task name_equipment/processing time; circles: materials names)
RM
T1_R1/ 4h
0.31 S1
0.6
0.4
T2_R2/ 8h
I3
I2
T8_R10/ 10h
T4_R4/ 8h
T5_R4/ 8h
I9
I5
I6
T3_R3/ 4h 0.69
T10_R6/ 8h
T13_R8/ 8h
T6_R4/ 8h
T10_R7/ 10h
T7_R4/ 8h
I4
I8
I7
0.5 I11 P1 T15_R8/ 8h
T11_R6/ 10h
T12_R7/ 12h
T12_R8/ 12h
0.5 I13 I12
P2 T16_R8/ 12h
T17_R8/ 12h
T17_R9/ 12h
P5 P4
Figure 7 - Proposed synthesis´s process.
R1
T1 T1 T1
T1 T2
T2
R2 T3
R3
T2
T2
T2
T2
T3
T7
R4
T1 T1
T1
T3
T6
T5
T4
T7
T1 T2
T2
T3
T3
T8
R10 T16
R8
T17
T12
R6 0
8
T16
T13 T11
24
32
40
48
T15
T10 56
T15
72
T17
80
88
104
112
T2
T2
T3
T6
T16
120
T2
T5
T4
T7
T1 T2
T2
T3
T3 T7
T6
T4
T8
T11 96
T2
T3
T7
T13
T12
T10 64
T17
T1 T1
T1
T2
T2
T8
T12 16
T1
T3
T7
T6
T4
T1 T1 T1
T17
T12 8
T8 T16
T13 T11
T12 16
24
32
40
48
T15
T10 56
T15
Figure 8 – Final Scheduling for the new synthesis proposal.
72
T17
T13
T12
T10 64
T17
80
88
T11 96
104
112
120
Table 1 – Models features´ characterizations for batch process. Pinto et al. (2003) Halim et al. (2006) Simon et al. (2008) Carvalho et al. (2009) Chen and Chang (2009) Chibeles et al. (2010) Moniz et al. (2010) Nonyane and Majozi (2012) Seid am Mazoji (2013) Yue and You (2013) Fumero et al. (2013) Adekota et al. (2013) Seid and Mazoji (2014) Patil et al. (2015) Li et al. (2015)
Design
Scheduling
X
X
Planning
Multipurpose
Formulation
X
Exact approach Meta-heuristics
Uncertainty
Sustainability X X
X
Meta-heuristics
X
Heuristics
X
X
Heuristics
X
X
X
X
Meta-heuristics
X
X
X
Exact approach
X
X
Exact approach
X
X
Exact approach
X
X X
X
X
X
Exact approach X
Exact approach
X X
X
Exact approach
X
X
Exact approach
X
X X
X
Methodology Meta-heuristics
X X
Table 2: Summary of the most relevant indicators (Carvalho, et al., 2008 and Carvalho et al, 2009) Indicator
Description
Definition
(c) (c) c MVAop mop PPopc PRop
MVA
Material Value Added
(c ) mop
flowrate of the compound c in open-path op; PR c price; op purchase price U
EWC
(c) k
PE u Qu u 1
mk( c ) Au( c,k) T , p UK
m
uk 1
EWC
Energy Waste Cost
uk
PPopc
sale
Au ,uk T , p
First term is energy cost and second term is the allocation factor to each path. Where: k - open- or the closed-path; uunit index; uk - index of all compound path flows in u; U total number of units in the path; UK - total number of compound path flows in a sub-operation; PEu - price of the utility; Qu - energy consumption; A - allocation factor
TF j ,c
tj k y1 y 2 ( c ) J FAP tj MW ( c ) j 0 c
tj k 1 y Max 1 z J 2 1 (c ) RM FAP tj MW c j 0 c
First term is the allocation of time to production of a by-product and second term is the allocation time for a reactant TF
Time Factor
(c ) FAP -flowrate of accumulation-path AP for compound c; tj -time
of operation j; J - total number of operations in the process; MW(c) - molecular weight of compound c; k - reaction rate constant; υ stoichiometric coefficient of compound c. y1 - binary variable for the inert/solvent presence (y1 = 0 if a compound is a inert/solvent and y1 =1 otherwise), y2 - binary variable for the reactants/byproducts presence (y2 = 1 if a compound is a reactant and y2 = 0 if a compound is a by-product). z1 - fraction of raw materials mass that reacts to give our desired product. H f H f H f H f H f E j c EF j ,i FAP H R y x CO (1 x)1 CO 1 y x CO 1 CO (1 x) CO J ( co ) ( co ) ( co ) H (f co ) E j H (f co ) H f H f H f co co co co co j
EF
Energy Factor
First term is the allocation of energy to consumption of rawmaterial or product production and second term is the energy fraction consumed in a given path. (c ) FAP - flowrate of accumulation-path AP for compound c; Ej H f energy of operation j; H R -heat of the reaction; - heat
of formation; y1-binary variable if a compound is a solvent/inert (y1 = 1 if a compound is a inert/solvent and y1 =0 otherwise); y2-binary variable if a compound in an accumulation-path is a reactant or a product (y2 = 1 if a compound is a reactant and y2 = 0 if a compound is a by-
product); y3 - Binary variable to define if the reaction is exothermic or endothermic (y3 = 0 if the reaction is exothermic and y3 = 1 if the reaction is endothermic).
Table 3. Production range for the scenario-based demands (m.u.). Scenarios P1, P2,P3 P4 P5
Expected 0:3120 0:2080 0:4160
Optimistic 0: 4680 0: 3120 0: 6240
Pessimistic 0: 1560 0: 1040 0: 2080
Table 4. Units, processing time. Unit R1 R2 R3 R4 R5 R6 R7 R8 R9 R10
Tasks (processing time in h) T1 (4) T2 (8) T3 (4) T4 (8), T5 (8), T6 (8), T7 (8) T8 (12), T9 (12) T10 (8), T11 (10), T12 (12) T10 (10), T11 (12), T12 (12) T13 (8) ,T14 (8),T 15 (8), T16 (12), T17(12) T13 (12),T14 (12), T16 (12), T17 (12) T8 (10)
Table 5 – Energy requirements´ specification.
Calorific Constant. (J/Kg.Temp variation)
Tasks T1_R1 T2_R2 T3_R3 T4_R4 T5_R4 T6_R4 T7_R4 T8_R5 T9_R5 T10_R6 T11_R6 T12_R6 T10_R7 T11_R7 T12_R7 T13_R8 T15_R8 T14_R8 T16_R8 T17_R8 T13_R9 T14_R9 T16_R9 T17_R9 T8_R10
Endo Exo Endo Exo Exo Exo Exo Endo Endo Exo Exo Exo Exo Exo Exo Endo Endo Endo Endo Endo Endo Endo Endo Endo Endo
301,392 837,2 301,392 1255,8 627,9 418,6 209,3 502,32 602,784 418,6 711,62 627,9 418,6 711,62 627,9 502,32 301,392 200,928 361,6704 341,5776 502,32 301,392 200,928 361,6704 341,5776
Table 6 – Products price Product Price
m.u/kg
P1 P3 P2 P4 P5
70 50 40 100 120
Table 7 – Energy requirements for each task in (J/Kg) over a cycle, for the three scenarios.
T1_R1 T3_R3 T8_R5 T13_R9 T15_R8 T9_R5 T14_R8 T16_R9 T17_R8 T8_R10 T2_R2 T4_R4 T5_R4 T10_R7 T6_R4 T11_R7 T7_R4 T12_R7
Expected 8609,271 3931,174 1506,96 1506,96 753,475 1808,34 602,76 401,84 1366,28 1506,96 27300 1569,75 784,875 523,25 837,2 1423,24 837,2 2511,6
Optimist 12913,906 5896,761 2197,65 2197,65 1356,255 2712,51 904,14 602,76 2049,42 2197,65 40950 28255,5 1412,775 941,85 1255,8 2134,86 1255,8 3767,4
Pessimist 3960,265 1808,34 753,48 753,48 687,169 229,049 200,92 683,14 753,48 12558
418,6 711,62 418,6 1255,8
Table 8 – Final product produced over a cycle, for each scenario.
Products
Expected
Optimist
Pessimist
P1
60
87,5
30
P3
60
90
22,8
P2
50
90
-
P4
40
60
20
P5
80
120
40
Table 9 - Description of the most critical batch indicators - SustainPro analysis Operation
OTF (%)
T8_R5
0,05
T13_R9
0,05
T9_R5
0,05
T14_R9
0,05
T11_R7
0,05
T16_R8
0,05
T16_R9
0,05
T12_R7
0,05
T12_R8
0,05
T17_R8
0,05
T17_R9
0,05
Table 10 - Description of the most critical mass and energy indicators - SustainPro analysis Scenario 1
Scenario 2
Scenario 3
Path #
MVA (103$/yr)
Path #
EWC (103$/yr)
Path #
MVA (103$/yr)
Path #
EWC (103$/yr)
Path #
MVA (103$/yr)
Path #
EWC (103$/yr)
OP 3
-8933
OP 2
468600
OP 3
-13400
OP 2
702901
OP 3
-4109
OP 2
215556
OP 1
123062
OP 1
184593
OP 1
56608
OP 8
82138
OP 12
167564
OP 4
37809
OP 4
77140
OP 6
137023
OP 5
37809
OP 5
77140
OP 8
123207
OP 8
37783
OP 3
64835
OP 4
113288
OP 3
29824
OP 9
64072
OP 5
113288
OP 9
26272
OP 3
97253
OP 9
96109
Table 11 - Description of the most relevant path - SustainPro analysis Path #
Path Description
OP 1
Entering RM as raw material and reaction in T1_R1
OP 2
S1 produced in the reaction at T1_R1 and reaction in T2_R2
OP 3
S1 produced in the reaction at T3_R3 and leaving the process
OP 4
I2 produced in the reaction at T2_R2 and reaction in T8_R10
OP 5
I2 produced in the reaction at T2_R2 and reaction in T8_R5
OP 6
I2 produced in the reaction at T2_R2 and reaction in T4_R4
OP 8
I3 produced in the reaction at T2_R2 and reaction in T3_R3
OP 9
I4 produced in the reaction at T3_R3 and reaction in T9_R5
OP 12 I5 produced in the reaction at T4_R4 and reaction in T15_R8
Table 12 - Sustainability analysis comparison. Initial Synthesis
Proposed Synthesis
Improvement
Total Net Primary Energy Usage rate (J/y)
21994
20576
6%
Total Net Primary Energy Usage per unit value added (kJ/€)
0,017
0,013
21%
Net water consumed per unit value added (Kg/€)
0,027
0,026
3%
1323157
1560642
18%
11001
-435
104%
38
37
3%
Profit (€/year) WAR- Environmental Impact (Total PEI) Safety Index
Table 13 – Computational Statistics Single equations Single variables Discrete variables Optimal objective value Optimality margin (%) CPU time (s)
Initial Synthesis 181 312 119 062 27 074 1.323e6 5 3063
Proposed Synthesis 46 584 29 553 6 554 1.561e6 5 274
S0098-1354(16)30389-1 http://dx.doi.org/doi:10.1016/j.compchemeng.2016.11.040 CACE 5629
To appear in:
Computers and Chemical Engineering
Received date: Revised date: Accepted date:
3-6-2016 28-11-2016 30-11-2016
Please cite this article as: Pinto-Varela, Tˆania., Barbosa-P´ovoa, Ana., & Carvalho, Ana., Sustainable batch process retrofit design under uncertainty − An Integrated Methodology.Computers and Chemical Engineering http://dx.doi.org/10.1016/j.compchemeng.2016.11.040 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Sustainable batch process retrofit design under uncertainty – An Integrated Methodology Tânia Pinto-Varela*, Ana Barbosa-Póvoa, Ana Carvalho CEG-IST, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal *[email protected]
Highlights
Methodology for sustainable batch retrofit design under uncertainty Combined heuristic and optimization methodology Combination of design and optimization tools Application through a multipurpose batch plant case study
Abstract This work explores the problem of optimizing batch processes’ retrofit design pursuing an increase of production efficiency and efficacy while accounting for the associated processes’ sustainability, aspect that within the process industry is nowadays of increasing concern. Batch processes are often complex structures, where retrofitting is not always a straightforward procedure for the decision maker, requiring then supporting tools. Such tools are often characterized by having to deal with large scale optimization problems, where solutions are difficult to obtain. Moreover, the presence of uncertainty adds to the already complex problems an extra level of difficulty. Within this context, the present work proposes an integrated solution approach, uSB-Design, which aims to guide decision-makers in the definition of sustainable batch retrofit designs under uncertainty. The applicability of the proposed methodology is shown through a batch plant case study.
Keywords: Retrofit; Batch; SustainPro; Optimization; Uncertainty
1. Introduction The increasing importance of chemical plants’ retrofit design is constantly observed, due to the need of costs rationalization and minimization of environmental impacts. This ought to be considered while maintaining plants efficiency and efficacy. Guinand (2001) defined retrofit design as: “The redesign of an operating chemical process to find new configuration and operating parameters that will adapt the plant to changing conditions to maintain its optimal
performance.” The retrofit problem in general and in batch process plants in particular, are complex problems (Barbosa-Póvoa, 2007) that require decision supporting tools enhanced with models and solution approaches that would be able to deal with the associated problems complexity. Based on this challenge several authors have been developing heuristics, metaheuristics and optimization models attempting to systematize procedures that will help practitioners in their retrofit activities. However as identified by Barbosa-Póvoa (2007) and more recently in Moniz et al (2015) new methodologies are still required, which should explore the integration of such approaches (heuristics and optimization methods) in order to solve the complex problems in a real time context. The study of such integrated approaches has recently gained the interest of some authors. Chibeles et al. (2010) presented a meta-heuristic approach to improve computation results of the design and scheduling of multipurpose batch plants using Simulated Annealing and compared the results with exact methods. Later on in 2013, Moniz et at (2013) proposed a formulation based on the Resource Task Network for the optimal scheduling of multipurpose batch plants, where equipment redesign is considered simultaneously with scheduling decisions. The equipment redesign problem is defined by the implementation of modifications in the processing units so as to change their suitability to perform certain tasks. A solution approach to solve the resulted complex problem was devised. Seid and Majozi (2013) studied the design, synthesis, and scheduling of multipurpose batch plants. A based robust scheduling formulation was used as a platform for the integration of the design problem where the integrated approach explicitly considered the different locations of materials in the plant. Good computational times were obtained when compared with previous published formulations. In the same year Fumero et al. (2013) also addressed an integrated problem where a multi period MILP model for the design, planning and scheduling of multistage multiproduct batch plants was presented. Market fluctuations were considered in a multi period context where different production campaign in each period were operated. More recently, Patil et al. (2015), proposed a methodology that addresses simultaneously: design, scheduling, and control of multiproduct processes. This considers disturbances by the identification of their critical frequency, which is used to quantify the worstcase variability in the controlled variables via frequency response analysis. Demand uncertainty is addressed through scenarios where different probabilities of occurrence are considered. When analyzing the above works no focus on sustainability aspects has been identified. However, such concerns are nowadays a reality. The sustainable development has raised its importance after the definition presented by WCED (1987) in the Brundtland Report: “the development that meets the needs of the present without compromising the ability of future generations to meet their own needs”. Afterwards, Elkington (1998) translated the sustainable development into three pillars: economic, environmental and social. These two works appears as seminal when defining sustainability and have been used widely by different authors as main references in the area. Today, sustainability is a top priority of any company and batch processes industries are not an exception (Carvalho et al., 2009). Some methodologies considering sustainability in batch process design have been presented in the literature, however the number of publications in this area is still limited. In (2003), Pinto et al. proposed a mixed integer linear formulation for design of multipurpose batch facilities, considering heat integration and economic utilities savings. Halim et al. (2006) presented an intelligent system for batch processes waste minimization, based on heuristic rules (BATCHENVOPExpert). Simon et al. (2008) proposed a decision support framework for batch processes’ retrofit design based on a heuristic method. The framework identifies improvement opportunities in a batch plants through the analysis of the product market situation. Carvalho et. al. (2009) proposed a
methodology that screens the batch design alternatives using economic, environmental, and social aspects (e.g. safety indicators), in order to identify the batch process bottlenecks and propose new design alternatives. In the same year, Chen and Chang (2009) integrated task scheduling and heat recovery aspects into an unified framework for multi-purpose batch processes. A mixed-integer linear program (MILP) was developed, where the new formulation could be solved in a standalone mode or using an heat-integrated mode. In the heat-integrated mode, the processes was defined, while keeping the operation flexibility with slightly expanded model size. Nonyane and Majozi (2012), considered cyclic scheduling concepts applied to wastewater minimization and production schedule optimization in a multipurpose batch facility. The formulation is based on a continuous-time formulation. In 2013, Yue and You (2013) addressed a bi-objective approach of batch scheduling problems considering economic and environmental aspects. The profit rate was defined as economic objective, followed by the environmental objective defined per functional unit based on the life cycle assessment methodology. Each instance was formulated as a mixed-integer linear fractional program (MILFP), which is a special class of non-convex mixed-integer nonlinear programs. In order to globally optimize the MILFPs obtained, a tailored reformulation-linearization method and Dinkelbach’s algorithm was used, followed by a multi-ojective approach, ε-constraint. Adekola et al. (2013) and Seid and Majozi (2014) proposed methodologies to address water and energy minimization, while schedule optimization was pursued. Adekola et al. (2013) explored opportunities for direct water and indirect water reuse while Seid and Majozi (2014) explored the presence of multiple contaminants in a stream as well as temperature variation. Recently, Li et al. (2015) proposed a hybrid optimization approach for sustainable process planning and scheduling, using meta-heuristcs. The honey-bee mating and annealing processes are simulated to optimize multi-objectives including energy consumption, make span and the balanced machine utilization. Despite some work has been done on the design, plan and scheduling of batch processes while considering sustainability concerns, as summarized in Table 1, further work is still required.
From Table 1, it is possible to verify that it is still missing in the literature the association of uncertainty when dealing with the sustainable batch design. Additionally when considering the retrofit problem, which more often appears within existing plants, the identified need is still a reality. In this context, the present work presents a generic and systematic approach for the simultaneous design/retrofit and scheduling of multipurpose batch plants while considering sustainability aspects in an uncertain demand environment. Due to the complexity of the system under analysis, integrated approaches for the problem resolution are required. Thus an integrated methodology, the uSB-Design is developed in the present work. This consists on an iterative process that allows a continuous improvement of existing plants, based on a combination of heuristics and optimization steps that pursue performance improvement of the processes under study while accounting for mass and energy process alternatives and accounting for demand uncertainty. The remaining sections of the paper are organized as follows. Section 2 presents a detailed description of uSB-Design approach and in section 3 the uSB-Design is applied to a case-study and the obtained results are discussed. Finally, conclusions are drawn in section 4.
2. Uncertainty Sustainable Batch Retrofit (uSB-Design) A methodology for sustainable batch retrofit design under uncertainty is proposed, the uSBDesign. This methodology analysis a batch design plant operation and identifies tasks, units or operating conditions that represent processes bottlenecks, based on which retrofit design alternatives are proposed that will eliminate the bottlenecks and/or improve the process performance. A bottleneck is defined as any path, task, unit or operation that is limiting the efficiency of the process and therefore that should be reduced or eliminated. For instance, a batch process might present bottlenecks in terms of water and/or energy consumption, processing time and capacity, which should be improved through retrofit actions. uSB-Design analysis can also deal with batch processes uncertainty scenarios, allowing processes’ bottlenecks identification, that come up under different circumstances. This extensive analysis leads to a more robust decision in terms of bottleneck identification and therefore in terms of new retrofit solutions for batch design. The uSB-Design integrated methodology is presented in Figure 1. It uses two main decision tools: an exact model formulation (see annex) developed for the design and scheduling of multipurpose batch plants, OptimRHI, (Pinto-Varela et al., 2009) and an indicator heuristic based methodology developed by Carvalho et al. (2009) which is incorporated in the SustainPro software tool (Carvalho et al., 2013). It is important to mention that the uSB methodology only provides problem reduction if alternatives in terms of processes or resources usages exist (e.g. alternative process paths; alternative processing units; alternative products portfolios, amongst others)
The integrated methodology develops along four main steps. Each step is described in more detailed below:
Step 1: Data Collection In this step plants and processes’ data collection is performed involving the gathering of data associated with: recipes, mass and energy consumptions, operation times, costs, equipment volumes, purchase and sale prices for each material and tasks environmental impacts. This data is the input for the next methodology´s step. Note that this data can be collected from an industrial plant or can be obtained from simulation software or databases. Step 2: Scenarios analysis under uncertainty The second step involves the solution of the optimization model, OptimRHI, for the input data gathered in step 1. The OptimRHI is represented in Figure 2 and defines the: process synthesis for the multipurpose batch plants, equipment design, process scheduling, resources usage and production profile under demand uncertainty. OptimRHI is characterized by a set of constraints (see annex) that can be grouped into three main groups: excess resources balances, where balances to the different resources are performed being these equipment, materials, energy, or human resources; equipment design, where capacities and plant topology definitions are considered; and finally capacity and operational restrictions, accounting for equipment limits for processing, storage and transportation as well as operational conditions that have to be obeyed,
such as minimum batch amounts, or demand to be satisfied in time and quantity, amongst others. The problem solved can be summarized in: Given: The process/plant description (in RTN terms); resources availability, characteristics and costs; utilities requirements; time horizon of planning; mode of operation; demand over the time horizon (production range); cost data; probability density function. Determine: A defined economic indicator considering the batch process design/retrofit model under demand uncertainty. As mentioned by Barbosa-Póvoa (2007) the complexity of the design/retrofit problems can easily lead to high computational burden when the optimality is pursued. However as the results obtained at this step work as a starting point to evaluate the batch process this limitation can be easily overcome by considering a reasonable optimality gap (e.g. 5%). The solution results from this step are feed into the next step and through the use of SustainPro the process/plants bottlenecks are identified.
As aforementioned the OptimRHI considers the presence of demand uncertainty and is assumed to operate in a periodic mode:
Uncertain demand characterization The demand uncertainty is integrated in the OptimRHI, using a two-stage stochastic programming approach, where the decision variables are classified in first- and second-stage variables. The first-stage variables are associated with decisions that cannot be reviewed, or which are less prone to be modified, once the future outcomes are realized. In the OptimRHI such variables are considered as the design variables associated to the equipment selection. The second-stage variables characterize decisions that can be reviewed after the scenario occurrence, i.e. additional information is obtained on the realization of some random vector. In OptimRHI such variables are the scheduling variables related to the production, storage and transfer decisions. After the demand is known, these decisions can be reviewed.
Periodic mode The periodic operation mode considered in the OptimRHI explores the concept of cycle time, T, which is repeated over the production time horizon, as shown in Figure 3. The operations´ sequence for all products‘ production are characterized over one cycle that will be repeated. The problem formulation is run for a single cycle, allowing tasks to overlap successive cycles modelled as defined in equation (1) through the wrap-around operator from Shah et al. (1993). Such operation mode assumes that the plant´s operation is the same at the beginning and at the end of the cycle.
t ( t ) ( t T )
if t 1 if t 0
(1) The OptimRHI uses a time discretization, where the cycle time is divided into T intervals of equal duration. The start of the cycle is defined as time t=1, and the end as t=T+1. The latter overlaps with the starting point of the next cycle. A planning horizon (H) is assumed, which is divided into N equal cycles of duration (T). A cycle is divided into a number of elementary time steps of fixed duration (), as shown in Figure 3.
The output of this step is the topology of the process in study, the product’s recipe, resources usage, tasks scheduling, and energy and water consumption for each scenario. As mentioned this data will be used as input data for step 3.
Step 3: Sustainability Retrofit Analysis The results obtained in the previous step are here analyzed through a sustainable design/retrofit methodology proposed by Carvalho, et al. (2009). This methodology is available in a software tool called SustainPro (Carvalho et al., 2013), which screens generates and prioritizes batch process design alternatives. This methodology can be summarized into four steps, being each step characterized below: A) plant/process decomposition in closed, open and accumulation paths; B) indicators calculation; C) sensitivity analysis; D) new batch design alternatives proposal. Figure 4 represents the integration of SustainPro in the uSB-Design methodology. The imported data from step 2 (mass and energy balances, processing times, capacities and recipes for each scenario) added to some data collected in step 1 (prices and compounds’ properties), allows the SustainPro to identify the bottlenecks in terms of energy, time, capacity and value added for the demand uncertainty scenarios characterized as step A of SustainaPro. The bottlenecks´ identification, starts with a process decomposition into closed-, open- and accumulation paths for energy and mass, which can be characterized as, see figure 5:
Closed-paths represent all flow-paths which start and end in the same unit of the process (Carvalho, et al., 2008). Open-paths represent all compound flows that enter and leave the process (Carvalho, et al., 2008). Accumulation-paths are related to the build-up of mass and energy in the batch operations (Carvalho, et al., 2009)
Step B calculates the indicators´ quantification for each path, in order to define the paths bottlenecks and possible retrofit actions. These indicators assess several process problems such as material, energy, costs and time problems (e.g. MVA-Material Value Added; EWC-Energy Waste Cost; OTF-Time Factor). Table 2 summarizes the most relevant indicators.
Based on the indicators values the bottleneck paths are identified. This means that paths presenting the highest values of EWC, TF and EF define a process bottleneck in terms of energy/water from utilities consumption, processing time and energy potential for heat integration. Negative values of MVA indicate that products/by-products leaving the process are losing value through the process, reflecting a higher cost in the compounds’ acquisition or in their raw materials purchase, when compared to the value obtained for that compound, when leaving the system. After analyzing the indicators values a list with the indicators with high potential for improvement (based on the indicators worst values obtained) is determined that defines the paths bottlenecks. Afterwards, step C of SustainPro is conducted. From the set of indicators that have been selected, a first sensitivity analysis is performed in order to identify the ones that will represent higher improvements in terms of sustainability. This is done performing the ISAAlgorithm described in Carvalho, et al. (2008). A second sensitivity analysis follows, in order to determine the most critical task in the selected path. This means that within a path some tasks, equipment or flows might be the main reason to obtain these indicators’ values. Through the two sensitivity analysis levels, the tasks, equipment or flow responsible for the process bottleneck are identified and retrofit design actions should be undertaken so that bottleneck is reduced or eliminated. Finally, in step D, through a heuristic based analysis new process design alternatives are proposed to eliminate the identified bottlenecks, for instance compounds’ recycles, identification of tasks where heat integration should be conducted, elimination of paths with non-value added activities, among others (complementary information about the heuristics can be found in Carvalho et al, 2008). At this step, the SustainPro’s analysis is undertaken over the several uncertain scenarios. The scenario’s analysis allows the identification of the bottleneck tasks, which negatively affect the different scenarios. Those bottlenecks are classified as top priority on batch retrofit design under uncertainty to pursue sustainability (e.g. elimination of a task, change of equipment, elimination of paths, new separation processes, and recovery of compounds). The output of this step is then a list of recommendations that will further tested and optimized in step 4, through a new run of the optimization model.
Step 4: Sustainable Planning and Scheduling The recommendations from step 3 are considered in the new input data for of OptimRHI. This data characterizes a much simpler process/plant design as non-added value paths were eliminated based on the results obtained in step 3. The OptimRHI results define in a much efficient way a more sustainable solution where is obtained the process synthesis, scheduling, equipment design and all the resources profile, considering an economic indicator maximization. At this point the sustainability of the new batch design is assessed comparing the obtained results with the initial batch design. The sustainability assessment is performed through the application of a set of sustainability metrics (Azapagic, 2002) and the WAR algorithm (Young and Cabezas, 1999). The social component is evaluated through the safety index (Heikkilä, 1999).
3. Case Study
3.1 Case Study Description This case study is based on a published case by Kallrath (2002) where a benchmark problem based on real case studies o process industry has been characterized. In this work this case study has been here extended to account for energy production and consumption. The problem to be solved is a retrofit batch plant problem aiming to attain a maximum plant profit and a more sustainable process while accounting for the process synthesis, equipment design and scheduling under an uncertain in market demand. A more sustainable process is characterized by lower values of sustainability metrics, such as: a lower safety index (Heikkilä, 1999) and a lower impact in the WAR algorithm (Young and Cabezas, 1999), simultaneously higher economic metrics (Azapagic, 2002). Five products are to be produced (P1 to P5) through different synthesis processes departing from a single raw material where consumption of energy is present. The process synthesis and task durations for all products are shown in Figure 6. The Ti-Ri defines that Ti can be operated in equipment, Ri; RM, Ii and Pi defines raw-material, intermediate resource, and final product, respectively. A periodic mode strategy is assumed, with a production campaign time horizon of 52 weeks (6240 h) associated with a cycle time of one week (120 h). Market uncertainty demand is characterized within three scenarios: pessimist, expected and optimistic, with probabilities, 0.1, 0.5, 0.4, respectively, as shown in Table 3. The multipurpose characteristics of the equipment and task´s energy characterization are shown in Table 4. The unit´s capacity range from 0 to 300 [m.u./m2], except unit one and two with maximum capacity of 100 [m.u./m2]. The associated fixed and variable costs are 30/ 0.5 [103c.u.], respectively. The connectivity´s costs are 0.1/ 0.01 [103c.u.] for fixed/variable cost, respectively.
3.2 Case Study Results Step 1- Data Collection The first step is defined by collecting all the data for the methodology´s input. The process synthesis are characterized by several alternatives for each product´s production, as is present in Figure 6. The production range of each demand scenario for all the products is shown in Table 3, followed by the multipurpose characteristics of the equipment, in Table 4. The heat requirement specifications for each task is given in
Table 5, followed by the product´s final price, in Table 6.
Step 2- Scenarios analysis under uncertainty In the second step the OptimRHI runs for a 5% gap and the results are feed into SustainPro in step 3. The results in terms of energy requirements for each task over the uncertainty scenarios are shown in , followed by the production of each product over a cycle, Table 8.
Step 3- Sustainability Retrofit Analysis under Uncertainty Considering the three scenarios´ results obtained in the previous step, and the data presented in step 1, SustainPro is applied. It starts by decomposing the process topology into closed-, open- and accumulation-paths, which result in none closed paths, 41 open-paths and 9 accumulation-paths, obtained over all scenarios. Then the indicators for all the paths have been calculated. Through the two sensitivity analysis, these indicators have been screened and the paths and the tasks bottlenecks have been determined following the ISA-Algorithm procedure (Carvalho et al., 2008). MVA, EWC and TF indicators turned to be the bottlenecks of the system and they are presented in
Table 9 and Table 10. The paths corresponding to those indicators are characterized in Table 11.
From the indicators analysis it is possible to verify that:
-
-
Material Value Added (MVA) of open-path 3 has a negative value (see Table 10), which means that value has been lost in Task 1 (between the raw materials consumption and production of S1). MVA, for OP3 was negative in the three scenarios indicating that OP3 is a system important bottleneck in terms of value added. The highest values of Energy Waste Cost (EWC) define the highest energy consumption, representing energy bottlenecks. These were observed in the three scenarios for: OP1, OP2, OP3, OP4, OP5, OP8, OP9. However scenario two identified as energy bottlenecks paths also OP6 and OP12. For the new design alternatives, the bottlenecks identified over all scenarios should have priority in the retrofit design problem. Therefore, retrofit design efforts should focus on OP1, OP2, OP3, OP4, OP5, OP8, OP9. Through the operational sensitivity analysis, T8R5 in OP5 has been identified as a critical task, presenting the highest energy consumption over all the scenarios. For paths OP1, OP2, OP3, OP4 and OP8 the major energy problems are related to tasks T2R2 and T3R3. However, these tasks are a cornerstone of the process topology and they are difficult to improve in terms of energy reduction, as are tasks using reactors to produce intermediate materials, required for the production of all final products. By changing energy consumption in those tasks will change the reactional mechanism or the reaction conditions, representing an even higher retrofit design investment and therefore it should be avoided when other bottlenecks are present and with potential to be improved (heuristic rules presented in Carvalho, et al 2008). Finally, in path OP9, task T9R5 was identified as bottleneck of energy that should be reduced. Regarding processing time, it is possible to identify several tasks as bottlenecks of the process, identified by the same and high value of TF. The high value of TF reflects long processing times that should be reduced in order to increase the efficiency of the process. Based on the process topology of Figure 6, several paths are available to produce the same product (e.g. I9 could be processed in T13_R8 or T13_R9). The paths identified in this step as containing bottleneck tasks, should be screen before the following step, and not considered as an option for more sustainable scheduling and planning decisions. Or on the other hand, these tasks should be replaced by other non-limiting tasks in order to overcome the time limitation of the process.
Based on the previous analysis, SustainPro recommends the following retrofit design proposal, which will be considered in step 4:
Based on the MVA value S1 should be recycled to task 2.
Task T8_R5 is a bottleneck in terms of energy and time and therefore should not be considered in the new batch design. Alternatively, to T8_R5, task T8_R10 should be considered. T9_R5 was identified as a critical task in terms of time and energy. Its elimination will prevent product P3 production. Based on positive values of MVA indicator for P3, its values are the lowest, reflecting the low value added of product P3. Therefore, P3 should not be produced and tasks T9_R5, T14_R8 and T14_R9 should not be considered as a possible network for the new batch process topology. T11_R7 and T16_R9 are critical in terms of time and therefore they should not be included as an option in the new batch topology, which leaves the production of P4 to follow tasks T11_R6 and T16_R8.
Step 4- Sustainable Planning and Scheduling Based on the results of the previous step, a new iteration is performed by the OptimRHI. The paths identified as bottleneck in utilities consumption and time restrictions over the three demand uncertainty scenarios are deleted from the previous synthesis process characterization. The OptimRHI runs with the new data considering the worst sustainable scenario, but simultaneously avoiding service level impacts. This is activated by running the OptimHRI for the scenario with highest demand. As results of OptimHRI for the new process synthesis the retrofit and scheduling are obtained. These are shown in Figure 7 and Figure 8, respectively. A comparison analysis of sustainability and computational effort between step 2 and step 4 is done in Table 12, and Table 13, respectively.
From Table 12 it is possible to verify that the initial process has been improved in all aspects. The energy bottlenecks elimination provided an improvement of energy consumption of 6%, and when assessed in terms of consumption per unit value added an improvement of 21% is observed. The economic performance shows an improvement of 18% from the initial design to the new design proposal. Also in terms of net water consumed a 3% improvement is observed. Finally, environmental impact has decreased of 104%, resulting from the additional recycling of S1, the waste that has been avoided and the fact that safety index has decreased (3%), trigged by the decrease of energy consumption in the tasks. In conclusion, the identification of the bottlenecks and their elimination leads to more sustainable processes both in economic and environmental terms. If the decision-maker aims to further improve the process, through the identification of new bottlenecks, one more run of the methodology could be performed (Figure 1). In a second run of uSB-Design a new set of bottlenecks could be identified by SustainPro, and a new process synthesis proposed. The process will be concluded by the decision- maker when suitable sustainable solution is reached (e.g. budget limitations, achieved goals, etc).
Despite the proposed synthesis eliminated the production of P3, the global results have improved. The statistics´ comparison between the initial and the proposed synthesis improved in 15 % and 91% over the initial synthesis data, for profit and time, respectively.
4. Conclusions A methodology, called uSB-Design, has been proposed to attain sustainable batch design/retrofit designs. uSB-Design is a stepwise procedure that integrates heuristic methods and optimization models applied to the synthesis, design/retrofit and scheduling of batch process. More sustainable process synthesis are obtained with lower computational complexity when uncertainty is considered. The proposed methodology allows the identification of a set of bottlenecks through a heuristic procedure (SustainPro) triggering the decrease of combinatory level of the optimization problem without comprising the economics and environmental aspects of the processes in study. Summarizing, uSB-Design has the following benefits: 1) The time consumed in the batch retrofit design is reduced; 2) more sustainable solutions are proposed; 3) deals with uncertainty in the batch design/retrofit design; 4) guides decision-makers in the retrofit analysis. As future work the methodology should be further tested in other more complex cases and an interface can be established to link the different tools and to facilitate the data flow between them. The interface could also manage the iterative process derived from the methodology.
References Adekola, O., Stamp, J. D., Majozi, T., Garg, A., & Bandyopadhyay, S. (2013). Unified Approach for the Optimization of Energy and Water in Multipurpose Batch Plants Using a Flexible Scheduling Framework. Industrial & Engineering Chemistry Research, 52, 8488-8506. Carvalho, A., Matos, H. A., & Gani, R. (2009). Design of batch operations: Systematic methodology for generation and analysis of sustainable alternatives. Computers & Chemical Engineering, 33, 2075-2090. Carvalho, A., Matos, H. A., & Gani, R. (2013). SustainPro-A tool for systematic process analysis, generation and evaluation of sustainable design alternatives. Computers & Chemical Engineering, 50, 8-27. Chen, C.-L., & Chang, C.-Y. (2009). A resource-task network approach for optimal shortterm/periodic scheduling and heat integration in multipurpose batch plants. Applied Thermal Engineering, 29, 1195-1208. Kallrath, J., Planning and Scheduling in the Process Industry, OR Spectrum, 2002, 24 (3), 219250. Li, X. X., Li, W. D., Cai, X. T., & He, F. Z. (2015). A hybrid optimization approach for sustainable process planning and scheduling. Integrated Computer-Aided Engineering, 22, 311-326.
Moniz, S., Barbosa-Póvoa, A. P., & Pinho De Sousa, J. (2013). New general discrete-time scheduling model for multipurpose batch plants. Industrial and Engineering Chemistry Research, 52, 17206-17220. Nonyane, D. R., & Majozi, T. (2012). Long term scheduling technique for wastewater minimisation in multipurpose batch processes. Applied Mathematical Modelling, 36, 2142-2168. Patil, B. P., Maia, E., & Ricardez-Sandoval, L. A. (2015). Integration of scheduling, design, and control of multiproduct chemical processes under uncertainty. Aiche Journal, 61, 24562470. Pinto-Varela, T., Barbosa-Povoa, A., & Novais, A. Q. (2009). Design and Scheduling of Periodic Multipurpose Batch Plants under Uncertainty. Industrial & Engineering Chemistry Research, 48, 9655-9670. Pinto, T., Novais, A. Q., & Barbosa-Povoa, A. P. F. D. (2003). Optimal design of heat-integrated multipurpose batch facilities with economic savings in utilities: A mixed integer mathematical formulation. Annals of Operations Research, 120, 201-230. Seid, E. R., & Majozi, T. (2014). Optimization of energy and water use in multipurpose batch plants using an improved mathematical formulation. Chemical Engineering Science, 111, 335-349. Shah, N., C.C. Pantelides, R.W.H. Sargent. (1993). Optimal Periodic Scheduling of Multipurpose Batch Plant. Annals of Operations Research, 42, 193-228. Simon, L. L., Osterwalder, N., Fischer, U., & Hungerbuehler, K. (2008). Systematic retrofit method for chemical batch processes using indicators, heuristics, and process models. Industrial & Engineering Chemistry Research, 47, 66-80. Yue, D., & You, F. (2013). Sustainable scheduling of batch processes under economic and environmental criteria with MINLP models and algorithms. Computers & Chemical Engineering, 54, 44-59.
Appendix 1. Nomenclature r - resource
k- task t –time m- Scenarios Sets: C= {r: set of all material resources} Cis={r: set of intermediate material with dedicated storage} Cr={r: set of material resources with dedicated storage} Cp / Cf = {r: set of final products /raw materials} D = {r: set of all equipment resources} Dfp/Drm={r D: set of dedicated storage vessels for final product/ raw-material} Dc/Dv={r D: set of all connections/ storage vessels} Dp={r D: set of process equipment resources} Dpd={r D: set of process equipment resources with discrete sizes} Sr={s S: set of discrete sizes of a given process equipment resources, r} M={m : set of all potential scenarios } TK = {k: set of all tasks operating in an equipment resource} TP={k: set of processing tasks in an equipment resource, r} TS={k: set of storage task for raw and product materials in dedicated vessel} TR= {k: set of all tasks requiring an equipment resource, r} TV ={k, r Dv: transfer task, k, for an intermediate storage vessel, r, which is a sink} TT ={k: set of all transfer tasks} Parameters: H - planning horizon T - cycle time CCF - capital charge factor v r /pr - price of resource (raw material / product)
k0 / k1 - fixed and variable cost coefficients
rmax - size factor Rr0 m - resource r available initially in scenario m min max / Rrm - resource minimum/maximum quantity at H in scenario m Rrm
kr/ kr - consumption or production of a renewable(-1,1)/non-renewable(-1,0) resource r, at the start/end of
max r - maximum resource available of r
m probability of scenario m k - duration of task k Vˆrs - set of discrete size s available for equipment r Variables:
Rrmt - excess of resource at t in scenario m
kmt - batch size of task k at time t in scenario m r - amount of resource r required Vr - capacity of resource r Nkmt - number of processing tasks k at instant t, in scenario m (t)- wrap-around time operator Etr=1 if processing resource r is installed; 0 otherwise Ecr=1 if transfer resource r is installed; 0 otherwise Zrs = defines which equipment, r, with discrete size, s, is selected Constraints: The renewable and non-renewable resource´s balance are defined by constraints (2) and (3), respectively. intermediate storage materials, To guarantee that the quantities of resource at the beginning and at the end of the cycle are the same for the intermediate materials, constraint (4) is used, followed by the products’ resource balance (5). The equipment resource existence and its allocation to the suitable task is guaranteed by constraint (6). The resource capacity constraints is guaranteed by constraints (7), (8), followed by constraint (9) and (10) for the equipment design characterization. The capacity and batch size are defined by constraints (11)-(15). The storage constraints are defined by constraints(16)-(20). The connectivity between equipment and its capacity are characterized by (21) and (22). Constraint (23) characterize the production requirements, followed by the objective function and its terms characterization, (24) and (25)- (28).
Rrmt = Rr m (t 1) + k 0 k r Nk m (t ) k
Rr mt = Rr0m|t 1,rC f + Rr m (t 1)|t 2 +
r Dp, m M, t =1...T
k
k
(2)
k r k m (t )
0
r C/{ Cp}, m M, t =1...T
(3)
Rr mt|t 1 = Rr mt|t T 1 r Cis, m M Rr mt = Rr m (t 1)|1t T 1 +
k
k
(4)
k r k m (t )|t T 1
0
r Cp, m M, t =1...T+1 t
N
t 't k 1 k Tr
k mt '
0 Rr mt r
r r Dp, m M, t =1...T r Dp, m M, t =1...T+1
(5) (6)
(7)
0 r max r
r Dp r Dp
Vrmin r Vr rVrmax
t
Vr
k mt
(8) (9)
k TS, r Dv, m M
(10)
k
N kmax
N jkmt 1
j 0
N kmax
jN
Nk mt
j 1
j k mt
0 Vrjkmt Vrmax N jkmt N kmax
V
Vr
rjkmt
j 0
N kmax
jV
min kr
rjkmt
j 1
kmt
max kr
k Tp, m M, t=1...T
(11)
k Tp, m M, t=1...T
(12)
k Tp, r Dp, j=1...Nkmax, m M, t=1...T
(13)
k Tp, r Dp, j=1...Nkmax, m M, t=1...T
(14)
N kmax
jV j 1
rjkmt
k Tp, r D, j=1...Nkmax, m M, t=1...T
(15)
(R
Rrmt ) Vr|rDrm
m M, t=1+T
(16)
R
Vr|rD fp
m M, t=1+T
(17)
r0 m
m rC f
m rC p
rmt
Vrmin Etr Vr Vrmax Etr
m M ,r Dv
(18)
r Dv, k TV, m M, t=1...T
(19)
r Dv, k TV, m M, t=1...T
(20)
t
kmt
M r Etr 0
k
kmt
rmaxVr
k
k TT, r Dc , m M
kmt krmaxVr
(21)
Vrmin Ecr Vr Vrmax Ecr
r Dc, m M
(22)
H max Rrm T
r Cp, t = 1+T
(23)
min Rrm Rrmt
H Max Profit PR OC RMC (CC CCF ) T
( CC
CC
0 r
r
rD p
Vr r CCr1 )
[ CC r
rD pd
0 r
sSr
Vrs r CCr1 ]
rD
( Ecr CC Vr CC ) ( Etr CC Vr CC ) 0 r
rDC
OC=
m
RMC =
t
1 r
m
( k0 Nkmt k1kmt )
r0 m
r
k TP, m M, t=1...T
(25)
(26)
Rrmt ) vr m
r Cf, m M, t=T
(27)
r
PR = Rrmt pr m m
1 r
k
( R m
rDv
0 r
(24)
r Cp, m M, t=1+T
(28)
Methodology
Computational Tool
1. Data Collection
Databases
2. Scenarios analysis under uncertainty
3. Sustainability Retrofit Analysis under Uncertainty 4. Deterministic Sustainable Planning and Scheduling
Yes
Other Improvements?
No Final Design
Figure 1: USB-Design Methodology flowdiagram.
Optimization model
SustainPro
Optimization model
Figure 2: Integration of OptimRHI in the USB-Design Methodology.
Cycle N-1
Cycle N
1
Cycle N+1
T T+1
Figure 3-Time discretization for a single cycle
Figure 4: Integration of Step 3 in the USB-Design Methodology
Figure 5: Path decomposition – SustainPro
RM
T1_R1/ 4h
S1
0.6
0.4
T2_R2/ 8h
I3
I2
T8_R10/ 10h
T8_R5/ 12h
I9
T13_R8/ 8h
T4_R4/ 8h
T5_R4/ 8h
T3_R3/ 4h
I5
I6
I4
T10_R6/ 8h
T13_R9 / 9h
T10_R7/ 10h
S1
T9_R5/ 12h
T6_R4/ 8h
T7_R4/ 8h
I10
I7
I8
0.5 I11
P1 T15_R8/ 8h
0.5 T14_R8/ 8h
T14_R9/ 12h
T11_R6/ 10h
T11_R7/ 12h
T12_R7/ 12h
T12_R8/ 12h
P2 P3
I12
T16_R8/ 12h
I13
T16_R9/ 12h
P4
T17_R8/ 12h
T17_R9/ 12h
P5
Figure 6. Products’ receipt (rectangles tasks: task name_equipment/processing time; circles: materials names)
RM
T1_R1/ 4h
0.31 S1
0.6
0.4
T2_R2/ 8h
I3
I2
T8_R10/ 10h
T4_R4/ 8h
T5_R4/ 8h
I9
I5
I6
T3_R3/ 4h 0.69
T10_R6/ 8h
T13_R8/ 8h
T6_R4/ 8h
T10_R7/ 10h
T7_R4/ 8h
I4
I8
I7
0.5 I11 P1 T15_R8/ 8h
T11_R6/ 10h
T12_R7/ 12h
T12_R8/ 12h
0.5 I13 I12
P2 T16_R8/ 12h
T17_R8/ 12h
T17_R9/ 12h
P5 P4
Figure 7 - Proposed synthesis´s process.
R1
T1 T1 T1
T1 T2
T2
R2 T3
R3
T2
T2
T2
T2
T3
T7
R4
T1 T1
T1
T3
T6
T5
T4
T7
T1 T2
T2
T3
T3
T8
R10 T16
R8
T17
T12
R6 0
8
T16
T13 T11
24
32
40
48
T15
T10 56
T15
72
T17
80
88
104
112
T2
T2
T3
T6
T16
120
T2
T5
T4
T7
T1 T2
T2
T3
T3 T7
T6
T4
T8
T11 96
T2
T3
T7
T13
T12
T10 64
T17
T1 T1
T1
T2
T2
T8
T12 16
T1
T3
T7
T6
T4
T1 T1 T1
T17
T12 8
T8 T16
T13 T11
T12 16
24
32
40
48
T15
T10 56
T15
Figure 8 – Final Scheduling for the new synthesis proposal.
72
T17
T13
T12
T10 64
T17
80
88
T11 96
104
112
120
Table 1 – Models features´ characterizations for batch process. Pinto et al. (2003) Halim et al. (2006) Simon et al. (2008) Carvalho et al. (2009) Chen and Chang (2009) Chibeles et al. (2010) Moniz et al. (2010) Nonyane and Majozi (2012) Seid am Mazoji (2013) Yue and You (2013) Fumero et al. (2013) Adekota et al. (2013) Seid and Mazoji (2014) Patil et al. (2015) Li et al. (2015)
Design
Scheduling
X
X
Planning
Multipurpose
Formulation
X
Exact approach Meta-heuristics
Uncertainty
Sustainability X X
X
Meta-heuristics
X
Heuristics
X
X
Heuristics
X
X
X
X
Meta-heuristics
X
X
X
Exact approach
X
X
Exact approach
X
X
Exact approach
X
X X
X
X
X
Exact approach X
Exact approach
X X
X
Exact approach
X
X
Exact approach
X
X X
X
Methodology Meta-heuristics
X X
Table 2: Summary of the most relevant indicators (Carvalho, et al., 2008 and Carvalho et al, 2009) Indicator
Description
Definition
(c) (c) c MVAop mop PPopc PRop
MVA
Material Value Added
(c ) mop
flowrate of the compound c in open-path op; PR c price; op purchase price U
EWC
(c) k
PE u Qu u 1
mk( c ) Au( c,k) T , p UK
m
uk 1
EWC
Energy Waste Cost
uk
PPopc
sale
Au ,uk T , p
First term is energy cost and second term is the allocation factor to each path. Where: k - open- or the closed-path; uunit index; uk - index of all compound path flows in u; U total number of units in the path; UK - total number of compound path flows in a sub-operation; PEu - price of the utility; Qu - energy consumption; A - allocation factor
TF j ,c
tj k y1 y 2 ( c ) J FAP tj MW ( c ) j 0 c
tj k 1 y Max 1 z J 2 1 (c ) RM FAP tj MW c j 0 c
First term is the allocation of time to production of a by-product and second term is the allocation time for a reactant TF
Time Factor
(c ) FAP -flowrate of accumulation-path AP for compound c; tj -time
of operation j; J - total number of operations in the process; MW(c) - molecular weight of compound c; k - reaction rate constant; υ stoichiometric coefficient of compound c. y1 - binary variable for the inert/solvent presence (y1 = 0 if a compound is a inert/solvent and y1 =1 otherwise), y2 - binary variable for the reactants/byproducts presence (y2 = 1 if a compound is a reactant and y2 = 0 if a compound is a by-product). z1 - fraction of raw materials mass that reacts to give our desired product. H f H f H f H f H f E j c EF j ,i FAP H R y x CO (1 x)1 CO 1 y x CO 1 CO (1 x) CO J ( co ) ( co ) ( co ) H (f co ) E j H (f co ) H f H f H f co co co co co j
EF
Energy Factor
First term is the allocation of energy to consumption of rawmaterial or product production and second term is the energy fraction consumed in a given path. (c ) FAP - flowrate of accumulation-path AP for compound c; Ej H f energy of operation j; H R -heat of the reaction; - heat
of formation; y1-binary variable if a compound is a solvent/inert (y1 = 1 if a compound is a inert/solvent and y1 =0 otherwise); y2-binary variable if a compound in an accumulation-path is a reactant or a product (y2 = 1 if a compound is a reactant and y2 = 0 if a compound is a by-
product); y3 - Binary variable to define if the reaction is exothermic or endothermic (y3 = 0 if the reaction is exothermic and y3 = 1 if the reaction is endothermic).
Table 3. Production range for the scenario-based demands (m.u.). Scenarios P1, P2,P3 P4 P5
Expected 0:3120 0:2080 0:4160
Optimistic 0: 4680 0: 3120 0: 6240
Pessimistic 0: 1560 0: 1040 0: 2080
Table 4. Units, processing time. Unit R1 R2 R3 R4 R5 R6 R7 R8 R9 R10
Tasks (processing time in h) T1 (4) T2 (8) T3 (4) T4 (8), T5 (8), T6 (8), T7 (8) T8 (12), T9 (12) T10 (8), T11 (10), T12 (12) T10 (10), T11 (12), T12 (12) T13 (8) ,T14 (8),T 15 (8), T16 (12), T17(12) T13 (12),T14 (12), T16 (12), T17 (12) T8 (10)
Table 5 – Energy requirements´ specification.
Calorific Constant. (J/Kg.Temp variation)
Tasks T1_R1 T2_R2 T3_R3 T4_R4 T5_R4 T6_R4 T7_R4 T8_R5 T9_R5 T10_R6 T11_R6 T12_R6 T10_R7 T11_R7 T12_R7 T13_R8 T15_R8 T14_R8 T16_R8 T17_R8 T13_R9 T14_R9 T16_R9 T17_R9 T8_R10
Endo Exo Endo Exo Exo Exo Exo Endo Endo Exo Exo Exo Exo Exo Exo Endo Endo Endo Endo Endo Endo Endo Endo Endo Endo
301,392 837,2 301,392 1255,8 627,9 418,6 209,3 502,32 602,784 418,6 711,62 627,9 418,6 711,62 627,9 502,32 301,392 200,928 361,6704 341,5776 502,32 301,392 200,928 361,6704 341,5776
Table 6 – Products price Product Price
m.u/kg
P1 P3 P2 P4 P5
70 50 40 100 120
Table 7 – Energy requirements for each task in (J/Kg) over a cycle, for the three scenarios.
T1_R1 T3_R3 T8_R5 T13_R9 T15_R8 T9_R5 T14_R8 T16_R9 T17_R8 T8_R10 T2_R2 T4_R4 T5_R4 T10_R7 T6_R4 T11_R7 T7_R4 T12_R7
Expected 8609,271 3931,174 1506,96 1506,96 753,475 1808,34 602,76 401,84 1366,28 1506,96 27300 1569,75 784,875 523,25 837,2 1423,24 837,2 2511,6
Optimist 12913,906 5896,761 2197,65 2197,65 1356,255 2712,51 904,14 602,76 2049,42 2197,65 40950 28255,5 1412,775 941,85 1255,8 2134,86 1255,8 3767,4
Pessimist 3960,265 1808,34 753,48 753,48 687,169 229,049 200,92 683,14 753,48 12558
418,6 711,62 418,6 1255,8
Table 8 – Final product produced over a cycle, for each scenario.
Products
Expected
Optimist
Pessimist
P1
60
87,5
30
P3
60
90
22,8
P2
50
90
-
P4
40
60
20
P5
80
120
40
Table 9 - Description of the most critical batch indicators - SustainPro analysis Operation
OTF (%)
T8_R5
0,05
T13_R9
0,05
T9_R5
0,05
T14_R9
0,05
T11_R7
0,05
T16_R8
0,05
T16_R9
0,05
T12_R7
0,05
T12_R8
0,05
T17_R8
0,05
T17_R9
0,05
Table 10 - Description of the most critical mass and energy indicators - SustainPro analysis Scenario 1
Scenario 2
Scenario 3
Path #
MVA (103$/yr)
Path #
EWC (103$/yr)
Path #
MVA (103$/yr)
Path #
EWC (103$/yr)
Path #
MVA (103$/yr)
Path #
EWC (103$/yr)
OP 3
-8933
OP 2
468600
OP 3
-13400
OP 2
702901
OP 3
-4109
OP 2
215556
OP 1
123062
OP 1
184593
OP 1
56608
OP 8
82138
OP 12
167564
OP 4
37809
OP 4
77140
OP 6
137023
OP 5
37809
OP 5
77140
OP 8
123207
OP 8
37783
OP 3
64835
OP 4
113288
OP 3
29824
OP 9
64072
OP 5
113288
OP 9
26272
OP 3
97253
OP 9
96109
Table 11 - Description of the most relevant path - SustainPro analysis Path #
Path Description
OP 1
Entering RM as raw material and reaction in T1_R1
OP 2
S1 produced in the reaction at T1_R1 and reaction in T2_R2
OP 3
S1 produced in the reaction at T3_R3 and leaving the process
OP 4
I2 produced in the reaction at T2_R2 and reaction in T8_R10
OP 5
I2 produced in the reaction at T2_R2 and reaction in T8_R5
OP 6
I2 produced in the reaction at T2_R2 and reaction in T4_R4
OP 8
I3 produced in the reaction at T2_R2 and reaction in T3_R3
OP 9
I4 produced in the reaction at T3_R3 and reaction in T9_R5
OP 12 I5 produced in the reaction at T4_R4 and reaction in T15_R8
Table 12 - Sustainability analysis comparison. Initial Synthesis
Proposed Synthesis
Improvement
Total Net Primary Energy Usage rate (J/y)
21994
20576
6%
Total Net Primary Energy Usage per unit value added (kJ/€)
0,017
0,013
21%
Net water consumed per unit value added (Kg/€)
0,027
0,026
3%
1323157
1560642
18%
11001
-435
104%
38
37
3%
Profit (€/year) WAR- Environmental Impact (Total PEI) Safety Index
Table 13 – Computational Statistics Single equations Single variables Discrete variables Optimal objective value Optimality margin (%) CPU time (s)
Initial Synthesis 181 312 119 062 27 074 1.323e6 5 3063
Proposed Synthesis 46 584 29 553 6 554 1.561e6 5 274