Multipurpose Batch Research Articles

Optimal Event Point Determination for Short-Term Scheduling of Multipurpose Batch Plants via Unit-Specific Event-Based Continuous-Time Approaches

In the past two decades, three types of continuous-time models have been developed for the short-term scheduling of multipurpose batch plants: sequence-based, slot-based, and event-based models. Both slot- and event-based models require an iterative procedure proposed by Ierapetritou and Floudas (Ind. Eng. Chem. Res. 1998, 37, 4341) to determine the number of event points or slots, which results in increased computational time and no optimal number of event points or slots in some cases. In this work, we first enhance the recently proposed three-index unit-specific event-based model developed by Shaik and Floudas (Ind. Eng. Chem. Res. 2009, 48, 2947) and extend it to handle different wait policies. Then, we develop a general framework to obtain the optimal number of event points where an iterative procedure is employed to obtain the maximum number of event points and determine the critical intermediate states. The approach proposed by Janak and Floudas (Comput. Chem. Eng. 2008, 32, 913) is used to obtain ...

A binary coding genetic algorithm for multi-purpose process scheduling: A case study

This paper presents a novel genetic algorithm (GA) for the scheduling of a typical multi-purpose batch plant with a network structure. Multi-purpose process scheduling is more difficult to deal with compared to single-stage or multi-stage process scheduling. A large amount of literature on this problem has been published and nearly all of the authors used mathematical programming (MP) methods for solution. In the MP methods, a huge number of binary variables, as well as numerous constraints to consider mass balance and sequencing of batches in space/time dimensions, are needed for the large-size problem, which leads to very long computational time. In the proposed GA, only a small part of the binary variables are selected to code into binary chromosomes, which is realized through the identification of crucial products/tasks/units. Due to the logical heuristics utilized to decode a chromosome into a schedule, only the feasible solution space is searched. Our genetic algorithm has first been devised with particular crossover for makespan minimization and then adjusted for production maximization.

Cleaner manufacture of multipurpose batch chemical and biochemical plants. Scheduling and optimal choice of production recipes

This study presents an approach for cleaner management of multipurpose batch chemical or biochemical plants. Given that manufacture of most of the products could be carried out in multiple ways depending on chosen production recipes, the scheduling framework is extended by involving the choice of appropriate production recipes. Using as optimization criteria the Global or Local Environmental Impact Assessments defined in Minimum Environmental Impact Methodology, the mathematical formulation that results in multi-objective optimization problems is presented for a special class of schedules. The approach is implemented on an example from dairy industry. Production of two types of curds by selection from two available recipes for each one of them is considered. The problem is translated to a single objective. Two most reliable solutions are obtained, which differ in chosen production recipes, milkfat content and units involved for tasks implementation. Comments on the impacts on the load of Biochemical Oxygen Demand at the end of each production cycle due to simultaneous curds manufacturing and contributions of individual dairy wastes in Global Biochemical Oxygen Demand are also provided.

Safer management of process changes in chemical reactors

Nowadays many chemical industries are SMEs where multi-purpose batch or semi-batch reactors are commonly used. Vent sizing for realistic runaway scenario is not an easy task for such enterprises since they have usually few resources and use multi-purpose reactors with fast process turnovers. As a consequence these batch and semi-batch reactors are usually equipped with emergency relief systems sized once forever when the reactor is designed. This can lead to a large underestimation of the vent area in case of runaway reactions occurring when processes different from the ones considered for originally sizing the vent are carried out. The approach proposed in this work aims to identify the maximum reactor load leading to safe conditions even in case of runaway phenomena to be handled with the emergency relief system already installed (or even with a smaller vent area). This approach allows avoiding the change of the emergency relief system with a larger vent area (as required every time a new more hazardous process has to be carried out on existing reactors) at the price of lower plant productivity.

A novel approach to scheduling multipurpose batch plants using unit‐slots

AbstractSeveral models for scheduling multipurpose batch plants exist in the literature. The models using unit‐specific event points have shown better solution efficiency on various literature examples. This article presents a novel approach to scheduling multipurpose batch plants, which uses unit‐slots instead of process‐slots to manage shared resources such as material storage. We develop two slightly different models that are even more compact and simpler than that of Sundaramoorthy and Karimi, Chem Eng Sci. 2005;60:2679–2702. Although we focus on material as a shared resource, our multi‐grid approach rationalizes, generalizes, and improves the current multi‐grid approaches for scheduling with shared resources. Our models allow nonsimultaneous transfers of materials into and out of a batch. We show by an example that this flexibility can give better schedules than those from existing models in some cases. Furthermore, our approach uses fewer slots (event‐points) on some examples than even those required by the most recent unit‐specific event‐based model. Numerical evaluation using literature examples shows significant gains in solution efficiency from the use of unit‐slots except where the number of unit‐slots required for the optimal solution equals that of process slots. We also highlight the importance of constraint sequencing in GAMS implementation for evaluating mixed‐integer linear programming based scheduling models fairly. © 2009 American Institute of Chemical Engineers AIChE J, 2010

Improving benders decomposition using maximum feasible subsystem (MFS) cut generation strategy

A new multi-generation of cuts algorithm is presented in this paper to improve the efficiency of Benders decomposition approach for the cases that optimality cuts are difficult to be achieved within the iterations of the algorithm. This strategy is referred to as maximum feasible subsystem (MFS) cut generation strategy. In this approach in each iteration of the Benders algorithm an additional cut is generated that has the property to restrict the value of the objective function of the Benders master problem. To illustrate the efficiency of the proposed strategy, it is applied to a scheduling problem of multipurpose multiproduct batch plant. Two different partitioning alternatives are tested in order to show the importance of the way that a problem is decomposed upon the efficiency of the Benders algorithm. The application of the proposed acceleration procedure results in substantial reduction of CPU solution time and the total number of iterations in both decomposition alternatives.

Introducing a new operational policy: The PIS operational policy

A novel operational policy, the Process Intermediate Storage operational policy, is introduced and used to synthesize, schedule and design multipurpose batch plants. The model is based on the State Sequence Network and non-uniform discretization of the time horizon of interest model developed by Majozi and Zhu [Majozi, T., Zhu, X. (2001). A novel continuous-time MILP formulation for multipurpose batch plants. 1. Short-term scheduling. Industrial and Engineering Chemistry Research, 40(23), 5935–5949]. Two cases are studied to determine the effectiveness of this operational policy. In the first case, which excludes any dedicated storage, the use of this operational policy results in 50% improvement in throughput. The second case is used to determine the minimum amount of intermediate storage while maintaining the throughput achieved with infinite intermediate storage. This results in 20% reduction in the amount of dedicated intermediate storage. The models developed for both cases are MILP models. An MINLP design model is then developed to exploit the attributes of the PIS operational policy.

Design and Scheduling of Periodic Multipurpose Batch Plants under Uncertainty

This work deals with the design of multipurpose batch plants under uncertainty. The model proposed by Pinto et al. [Comput. Chem. Eng. 2005, 29 (6), 1293−1303] for the detailed design of batch plants is extended to address the problem of uncertainty associated with production demand. Equipment choices, as well as plant topology and associated schedule, are defined simultaneously under an uncertain demand environment. Uncertainty is treated through a two-stage stochastic model leading to a mixed-integer linear programming (MILP) formulation, where profit is maximized and the expected value of perfect information (EVPI) is determined; the latter is estimated as the difference between the values of profit obtained for the wait-and-see and the here-and-now models. A scenario is set up where demand is represented by a discrete probability function and a cyclic operation considered, together with mixed storage policies and sharing of resources. Some illustrative examples are solved to show the model applicability and the EVPI are determined and analyzed.

Operational Planning of Large-Scale Industrial Batch Plants under Demand Due Date and Amount Uncertainty. I. Robust Optimization Framework

The operational planning of a large-scale industrial batch plant typically occurs over a time horizon of several months with the goal of providing daily production targets and raw material requirements for the plant in question. Due to the length of the time horizon, demand uncertainty should be taken into account in order to ensure that the operational planning model provides reliable production targets and/or raw material requirements. A robust novel operational planning model has been developed in order to address the objective of providing a reliable daily production profile which is immune to various forms of demand uncertainty. The ability of the proposed planning model to address the aforementioned objectives of an operational planning model has been validated through an industrial case study of a large-scale, multiproduct, and multipurpose batch plant having the capability of producing hundreds of different products over a time horizon of three months.

A mathematical optimisation approach for wastewater minimisation in multipurpose batch plants: Multiple contaminants

This paper presents a methodology for wastewater minimisation in multipurpose batch plants characterised by multiple contaminant streams. Firstly a situation in which central reusable water storage does not exist is considered. In this case, water from one operation is directly reused in another operation as long as the source and sink operations, respectively, end and begin simultaneously. Secondly, the case with central reusable water storage is considered. In this case water from a source operation can temporarily be stored in dedicated storage before use by the sink process. The methodology is based on an existing scheduling framework which then makes it possible to generate the required schedule to realise the absolute minimum wastewater generation for a problem. The methodology involves a two-step solution procedure. In the first step the resulting MINLP problem is linearised and solved to provide a starting point for the exact MINLP problem.

Usage of inherent storage for minimisation of wastewater in multipurpose batch plants

Wastewater minimisation in batch plants is gaining importance due to intensifying environmental legislation and the gradual reduction in the number of freshwater sources. Intrinsic in the minimisation of wastewater in batch plants is the reuse of wastewater through intermediate storage vessels. However, the intermediate storage vessels take up unnecessary space which is undesirable in processes which are generally undertaken in limited spaces. Furthermore, in any batch process there are processing units that are not used extensively in the time horizon. In other words, these units remain idle for the major part of the time horizon, amounting to wasted return on capital investment. The idle processing units can be used as storage vessels, since any processing unit is, in essence, a storage vessel. In doing this one can reduce the size of the central storage and increase the utilisation of capital intensive processing units. The methodology presented in this paper deals with the minimisation of single contaminant wastewater by exploiting the inherent storage possibilities in idle processing units. The methodology is applied to two cases. In the first case the objective is to minimise the amount of effluent and the size of the central storage vessel through the usage of inherent storage, as commonly encountered in grassroot design. In the second case the objective is to determine the minimum wastewater target through the usage of both inherent storage and fixed central storage, as encountered in retrofit design.

A novel network-based continuous-time representation for process scheduling: Part I. Main concepts and mathematical formulation

A novel network-based framework for the short-term scheduling of multi-purpose batch processes is presented. The novelty of the proposed approach lies in five key concepts. First, it is based on a new continuous-time representation that does not require tasks to start (end) exactly at a time point; thus reducing the number of time points needed to represent a solution. Second, processing units are modeled as being in different activity states to allow storage of input/output materials. Third, time variables for “idle” and “storage” periods of a unit are introduced to enable the matching between tasks and time points without big-M constraints. Fourth, material transfer variables are introduced to explicitly account for unit connectivity. Fifth, inventory variables for storage in processing units are incorporated to model non-simultaneous and partial material transfers. The proposed representation leads to MILP formulations which address limitations of existing scheduling methods.

Minimization of energy use in multipurpose batch plants using heat storage: an aspect of cleaner production

A mathematical technique for optimization of energy use through the exploitation of heat storage in heat integrated multipurpose batch plants is presented in this document. Storage of heat is effected through the use of a heat transfer fluid. The resultant mathematical formulation exhibits a mixed integer linear programming (MILP) structure, which yields a globally optimal solution for a predefined storage size. The concept of heat integration in batch plants with the objective of minimising energy use is indeed an aspect of cleaner production that has received very limited attention in published literature. This is largely because batch plants are perceived to be less energy-intensive compared to their continuous production counterparts which is untrue for some batch operations, like dairy and brewing processes; hence the need for dedicated techniques. Application of the proposed method to an agrochemical facility has shown savings of more than 75% in external utility steam consumption.

Practical infeasibility of cross-transfer in batch plants with complex recipes: S-graph vs MILP methods

Multipurpose batch processes entail various operational policies that have been widely investigated in published literature. In this paper, no-intermediate-storage (NIS), zero-wait (ZW) and common-intermediate-storage (CIS) operational policies are of particular interest. In all these policies, no dedicated storage facility is available between two consecutive units. Unlike the other operational policies, these particular policies bear some subtle practical infeasibility that has gone unnoticed in literature. In essence, this infeasibility has been reported as optimal, thus assumed to be feasible, by various authors using mathematical programming techniques. It pertains to a unit transferring product to one or more units whilst simultaneously receiving feed from another, which is practically infeasible and as such need not be considered as a possible solution. This feature is particularly conspicuous in batch processes with complex recipes wherein production paths can be in opposite directions. This paper presents the unique feature of the S-graph framework to isolate cross-transfer during optimization, whereas the available mathematical programming methods inherently fail neither to detect nor to eliminate this infeasibility. A few examples taken from published literature are presented for demonstration purposes.

Bottom-up Modeling of the Steam Consumption in Multipurpose Chemical Batch Plants Focusing on Identification of the Optimization Potential

A detailed approach for modeling the steam consumption in a multipurpose chemical batch plant was developed, tested, and used for analysis of the energy-efficiency. The main advantage of the approach presented in this paper compared to available modeling approaches is the ability to describe the transient steam consumption. Thus, the new approach can be used for the dynamic optimization of batch operations with respect to the energy efficiency. The bottom-up method was implemented by modeling particular unit operations (UOs) in a case study plant, and validation was accomplished with direct measurements on both UO and building level. The principle of the bottom-up model is a detailed energy balance of each particular UO for which process parameter measurements are necessary as input data. These were extracted from the measurements archive of the case study plant for a period of two months. Process data from almost 1000 sensors installed in ca. 100 UOs were acquired, transformed into a time-series with common time basis, and used as an input data for the model. Special attention was paid to model the losses of the UOs because in earlier studies it was found that these are significant. Loss models were developed in the form of empirical parametric equations considering the losses due to radiation and the internal losses in the heating/cooling system due to inefficient operation. The parameters of the loss models were fitted, based on the developed methodology, to steam measurements of 4 UOs and consequently integrated into the overall bottom-up model for modeling other UOs as well. The energy usage efficiency of the UOs was inferred and the optimization spots were identified. The results in the case study plant have indicated that the energy savings potential for particular UOs with low steam-usage efficiency can be easily identified and serve as a good hint for the overall plant energy auditing and steam consumption optimization.

Design of Multipurpose Batch Plants: A Comparative Analysis between the STN, m-STN, and RTN Representations and Formulations

This paper presents and discusses different unified frameworks that can be used for design of multipurpose batch plants. The first framework is based on the state−task network (STN) process representation proposed by Kondili, Pantelides, and Sargent (1993, 1998) for the scheduling of batch plants. The second is the maximal state−task network (m-STN) where design and operational characteristics are represented simultaneously (Barbosa-Póvoa and Machietto, 1994). Finally, the third framework uses the resource−task network (RTN), proposed by Pantelides (1994) for the scheduling problem. The application of these three representations to the design problem is explored and generalized formulations are developed, which are described and characterized. A set of examples is solved and results are compared and discussed, with an emphasis on the adequacy and effectiveness of these representations to the modeling and solution of the design of multipurpose batch plants.

A resource-task network approach for optimal short-term/periodic scheduling and heat integration in multipurpose batch plants

This article aims to integrate the task scheduling and heat recovery problems into an unified framework for multi-purpose batch processes. The batch scheduling formulation is extended from the continuous Resource-Task Network (RTN) formulation which was originally proposed by Castro et al. [P.M. Castro, A.P. Barbosa-Póvoa, H.A. Matos, Optimal periodic scheduling of batch plants using RTN-based discrete and continuous-time formulations: a case study approach, Ind. Eng. Chem. Res. 42 (2003) 3346–3360; P.M. Castro, A.P. Barbosa-Póvoa, H.A. Matos, A.Q. Novais, Simple continuous-time formulation for short-term scheduling of batch and continuous processes, Ind. Eng. Chem. Res. 43 (2004) 105–118]. Besides the integrated heat recovery and short-term batch scheduling, a full set of heat-integrated periodic scheduling for batch processes, which is more useful in industrial environments, is also presented. The heat-integrated batch scheduling problem can be formulated as a mixed-integer linear program (MILP), where the new formulation can also be solved in standalone or heat-integrated modes by user’s preferences. In the heat-integrated mode, the processes can be precisely defined while keeping the operation flexibility with slightly expanded model size. Two literature examples are demonstrated to show the efficiency and flexibility of the model.

Integrated Operational Planning and Medium-Term Scheduling for Large-Scale Industrial Batch Plants

The operational planning and the medium-term scheduling of a multipurpose and multiproduct batch chemical plant are inter-related activities that involve the allocation of plant resources. Because of their disparate time scales, however, the effective integration of planning and scheduling has proven to be a formidable task. The lack of an integrative framework for planning and scheduling will invariably cause the planning model to provide unrealistic production targets to the scheduling level, leading to the misallocation of plant resources. In response to this issue, a novel framework for the integration of planning and scheduling for a multipurpose and multiproduct batch plant is presented. The framework entails integrating a novel planning with production disaggregation model with a medium-term scheduling model through a forward-rolling horizon approach.

A novel precedence-based and heuristic approach for short-term scheduling of multipurpose batch plants

Many continuous-time formulations have been proposed during the last decades for short-term scheduling of multipurpose batch plants. Although these models establish advantages over discrete-time representations, they are still inefficient in solving moderate-size problems, such as maximization of profit in long horizon, and minimization of makespan. Unlike existing literature, this paper presents a new precedence-based mixed integer linear programming (MILP) formulation for short-term scheduling of multipurpose batch plants. In the new model, multipurpose batch plants are described with a modified state-task network (STN) approach, and binary variables express the assignments and sequences of batch processing and storing. To eliminate the drawback of precedence-based formulations which commonly include large numbers of batches, an iterative procedure is developed to determine the appropriate number of batch that leads to global optimal solution. Moreover, four heuristic rules are proposed to selectively prefix some binary variables to 0 or 1, thereby reducing the overall number of binary variables significantly. To evaluate model performance, our model and the best models reported in the literature (S&K model and I&F model) are utilized to solve several benchmark examples. The result comparison shows that our model is more effective to find better solution for complex problems when using heuristic rules. Note that our approach not only can handle unlimited intermediate storage efficiently as well as the I&F model, but also can solve scheduling problems in limited intermediate storage more quickly than the S&K model.

Flexible mass transfer model for water minimization in batch plants

This paper presents the least constrained mass transfer mathematical formulation for freshwater minimization in multipurpose batch chemical processes with central reusable water storage. The mathematical formulation is an extension of the model developed by Majozi [T. Majozi, Wastewater minimization using central reusable water storage in batch processes, Computers and Chemical Engineering Journal 29 (7) (2005) 1631–1646]. In the latter model four scenarios were considered with various limitations or constraints. In the scenario presented in this paper only the mass load is fixed, whilst both the quantity of water used in a particular operation and outlet concentration are allowed to vary. In essence, fixing the mass load is more representative of the practical case. A solution procedure for the resultant nonconvex mixed integer nonlinear programming (MINLP) model is also presented. The solution procedure first involves reformulating the MINLP into a relaxed linear model (MILP). The MILP is first solved, the solution of which forms a feasible starting solution for the MINLP. Presented are two illustrative examples.