Multipurpose Batch Plants Research Articles

Novel Multiple Time-grid Continuous-time Mathematical Formulation for Short-term Scheduling of Multipurpose Batch Plants.

In this work, we have developed two novel unit-specific event-based mixed-integer linear programing models for scheduling multipurpose batch plants. The concept of indirect and direct material transfer is introduced to rigorously sequence and align tasks in different units. A batch after production is allowed to be partially transferred to storage and downstream processing units or held in processing units over multiple event points. The computational results demonstrate that the proposed models require a smaller number of event points in many cases to achieve optimality than existing unit-specific event-based models. It is interesting to find that no task is required to span over multiple event points to reach optimality for all addressed examples. The best variant developed is superior to existing unit-specific event-based models with the same or better objective values by a maximum improvement of 67%. The computational effort is significantly reduced by at least 1 order of magnitude in some cases.

Novel hybrid discrete differential evolution algorithm for the multi-stage multi-purpose batch plant scheduling problem

The multi-stage multi-product batch plant scheduling problem is an important part of batch chemical industry scheduling problems. Different from the multi-purpose batch scheduling problem, this problem can be characterized by multiple stages with non-identical parallel units, and multiple batches of customer orders. Numerous methodologies for this problem have been investigated to addressing scheduling cases of different production systems in the past two decades. This paper focus on the large-scale batch plant scheduling problem by minimizing the make-span in the scheduling horizon. And a novel hybrid discrete differential evolutionary algorithm is proposed to handle this problem. First, a novel two-line encoding scheme is constructed based on discrete and continuous variables. The sequence of orders is represented by a time-based representation method. Second, two novel mutation methods are proposed within the framework of encoding method. Two methods provide multiple search directions which helps improve the exploration ability and diversity of the population. At last, two local permutation methods are applied to improve the local optimal for the algorithm. The proposed work is tested through several real industrial instances with different sizes and characteristics by comparing with mixed integer linear programming method and meta-heuristic algorithms. The improvement of proposed work is also analyzed by the instances. The results report the efficiency and effectiveness of the novel proposed evolutionary algorithm in solving large scale multi-stage multi-product batch plant scheduling problem.

Improved Multipopulation Discrete Differential Evolution Algorithm for the Scheduling of Multipurpose Batch Plants

The multipurpose batch plant scheduling problem (MSP) has been widely studied in the fields of theoretical research and practical industrial application environments in-depth for decades as it belo...

Optimum Water Network Design for Multipurpose Batch Plants with a Detailed Electrodialysis Regeneration Model

Stringent environmental regulations and economic expansion in the recent decades has justified the need for sustainable water usage in the process industry. This work presents a mathematical formul...

A comprehensive framework for synthesis and design of heat-integrated batch plants: Consideration of intermittently-available streams

Significant opportunities for energy savings in batch plants exist through Heat Integration of intermittently-available material transfer streams between processing and storage units. Such opportunities may, however, be limited by the structure of the process flowsheet and the scheduling in place. This work presents results obtained when the design, scheduling and Heat Integration of multipurpose batch plants are carried out simultaneously. A rigorous stream-task-oriented scheduling formulation is presented, which enables explicit description of the movements of the intermittently-available streams. This thorough treatment of streams opens up more degrees of freedom than realised in previous stream Heat Integration formulations. On such a basis, design and Heat Integration constraints are added, to result in a mixed integer nonlinear programming formulation. The optimisation objective is to maximise annual net profit, which is a trade-off between production throughput, capital costs, and operational costs arising from hot and cold utility consumption. When applied to a literature example, results show higher annual net profit and reduction in utility costs by as much as 15%, compared to when each of the design, scheduling and Heat Integration steps are carried out in sequence.

Heat integration and cyclic scheduling of multipurpose batch plants using three index unit-specific event based model

Process scheduling with a long time horizon always leads to large problem size, which is challenging to solve for global optimal solutions. The problem complexity further increases with the inclusion of additional tasks such as heat integration, water integration, material transfers and shared storage. Cyclic scheduling can be a potential option to handle the long time horizon scheduling problems. In this work, a novel unified three index unit-specific event-based mathematical formulation is presented for cyclic scheduling of multipurpose batch plants. The unified framework reduces to a simple case in the absence of cyclic scheduling. The task extending to the next cycle is integrated with the short term scheduling constraints using the active task concept. Further, the framework is also extended for simultaneous cyclic scheduling and heat integration of multipurpose batch plants. The computational performance of the unified framework is evaluated with benchmark examples taken from the literature.

Continuous‐time scheduling formulation for multipurpose batch plants

AbstractShort‐term scheduling of batch processes is a complex combinatorial problem with remarkable impact on the total revenue of chemical plants. It consists of the optimal allocation of limited resources to tasks over time in order to manufacture final products following given batch recipes. This article addresses the short‐term scheduling of multipurpose batch plants, using a mixed integer linear programming formulation based on the state‐task network representation. It employs both single‐grid and multi‐grid continuous‐time representations, derived from generalized disjunctive programming. In comparison to other multigrid scheduling models in the literature, the proposed multi‐grid model uses no big‐M constraints and leads to more compact mathematical models with strong linear relaxations, which often results in shorter computational times. The single‐grid counterpart of the formulation is not as favorable, as it leads to weaker linear relaxations than the multi‐grid approach and is not capable of handling changeover time constraints.

On the application of a metaheuristic suite with parallel implementations for the scheduling of multipurpose batch plants

In a recent publication by Woolway and Majozi (2018), a novel framework for the application of metaheuristics to the scheduling of multipurpose batch plants was proposed. The initial framework was only developed for continuous-time approaches. This work extends this framework to the discrete-time approach. Additionally, a suite of metaheuristics is applied to two well-known literature examples in both of these frameworks with serial and parallel implementations. Results show these metaheuristics capable of achieving global solutions in the discrete-time approaches and close-to-optimal solutions in continuous-time approaches. These solutions can be found in reduced computational times of up to six orders of magnitude when compared to modern mathematical programming approaches.

A novel metaheuristic framework for the scheduling of multipurpose batch plants

A genetic algorithm (GA) is proposed along with a general framework for the scheduling of a typical multipurpose/product batch plant. The majority of literature regarding these problems make use of mathematical programming methods. Modelling problems in this manner leads to numerous binary variables relating to material balance and sequence of batches along long time horizons, thus resulting in large computational time. The proposed GA does not suffer the same scalability issues of mathematical programming approaches. The GA makes use of a coupled chromosome system with specific crossover and mutation functions utilised with the purpose of profit maximisation. Results show that optimal or close-to-optimal solutions can be achieved with a reduction of up to 98.53% computational time in certain cases.

Gate-to-Gate Energy Consumption in Chemical Batch Plants: Statistical Models Based on Reaction Synthesis Type

Energy consumption in the chemical industry is an important operating cost and environmental impact factor and reducing it is also explicitly mentioned as one of the key principles of green chemistry. Energy consumption has thus been included in diverse process design and evaluation tools as a key metric. However, measurements of energy consumption at the process equipment level are scarce, especially in fine chemical production typically performed in multiproduct and multipurpose batch plants. In this work, we present a shortcut approach based on statistical models, such as probability density functions (PDF) and classification trees, for estimating steam consumption which typically represents the highest energy utility consumption in batch plants. The output of these models is in the form of intervals derived from PDF interquartile ranges and as classes derived from the classification trees, respectively. The validation results (i.e., goodness of fit, cross validation, and case studies) show that the mo...

Introducing the Concept of Roving Pumps in the Synthesis of Multipurpose Batch Plants

Presented in this manuscript is a novel technique for the exploitation of a unique feature of multipurpose batch plants, so called roving pumps. The discretized nature of batch processes allows for the allocation of pumps to different units and tasks depending on pump availability over the time horizon of interest. A MILP formulation is proposed to determine the optimal number and allocation of pumps within the batch plant while simultaneously synthesizing the plant and optimizing the production schedule with variable material transfer times. It is shown by way of an example that it is possible to decrease the number of pumps required for operation from seven to two pumps, while another example demonstrates a decrease in the number of pumps required from eleven to three. It is, therefore, possible to reduce capital and maintenance costs by implementing the formulation while still achieving or improving on existing throughputs.

Mixed-integer programming models for simultaneous batching and scheduling in multipurpose batch plants

We propose two novel discrete-time mixed-integer programming models for simultaneous batching and scheduling in multipurpose batch plants with storage constraints. The proposed models adopt two different modeling approaches. The first is based on explicit labeling of batches, while the second is based on identifying possible batch size intervals for each order and the corresponding unit routings. We also present extensions that allow us to consider limited shared utilities (with both fixed and time-varying availability and cost), storage with capacity limits and stage-dependent batch sizes. Finally, we study how instance characteristics (e.g. expected number of batches per order, uniformity in unit capacities) impact the effectiveness of the proposed models. We show that by carefully selecting the model allows us to effectively solve large-scale instances.

Discrete-time mixed-integer programming models for short-term scheduling in multipurpose environments

We present new discrete-time mixed-integer linear programming formulations for short-term scheduling in multi-purpose batch plants, the most general sequential production environment. We first discuss how multi-purpose batch plants can be expressed using State-Task Network and Resource-Task Network representations through batch-based definition of states (resources) and tasks. We then develop two models based on each representation that account for limited intermediate storage, and discuss extensions such as limited shared resources and time-varying resource availability/cost. Finally, we present several case studies to illustrate the applicability and performance of the proposed models.

Heat integration of multipurpose batch plants through multiple heat storage vessels

Energy minimisation in batch plants has garnered popularity over the past few decades, leading to direct and indirect heat integration techniques being formulated for multipurpose batch plants through the utilisation of mathematical formulations and insight-based methods Some mathematical formulations utilise predetermined scheduling frameworks which may result in suboptimal results, whilst other formulations only use one heat storage vessel which may cause limitations in the plant. The work presented in this manuscript is aimed at minimising energy consumption in multipurpose batch plants by exploring both direct and indirect heat integration through multiple heat storage vessels. It investigates the optimal number of heat storage vessels as well as design parameters, i.e. size and initial temperature of vessels. The cost of the heat storage vessels is considered within the model. The model is applied to two case studies resulting in significant increase in profits.

Long-term heat integration in multipurpose batch plants using heat storage

Most scheduling methods are limited to the short-term scheduling case and solution of problems over long time horizons may prove challenging or impossible with these methods. Including additional considerations such as Heat Integration further complicates the problem. A model for the simultaneous optimisation of the schedule and energy usage in heat integrated multipurpose batch plants operated over long time horizons has been presented. The method uses a cyclic scheduling solution procedure. The proposed model includes indirect Heat Integration via heat storage, rather than just direct Heat Integration. This has not been considered in long-term Heat Integration models in current literature. Both the heat storage size and initial heat storage temperature are also optimised. The solution obtained over 24 h using the proposed cyclic scheduling model with direct Heat Integration for a multipurpose example was compared to the result obtained from the direct solution and an error of less than 6% was achieved.

A multitasking continuous time formulation for short-term scheduling of operations in multipurpose plants

Short-term scheduling in multipurpose batch plants has received significant attention in the past two decades. Both discrete-time and continuous time formulations have been proposed to model the problem; however, multipurpose plants that have machines with the ability to process multiple tasks at the same time, i.e. multitasking, have been overlooked by the available continuous time formulations in the literature. This paper presents a novel MILP formulation that is capable of accommodating the multitasking feature in the machines of a facility. The performance of the presented formulation is studied in comparison with a single-tasking formulation. The results show that, while the multitasking formulation is not more costly in terms of solution time, it is capable of producing significantly better solutions. The presented formulation takes into account several other operational constraints of multipurpose facilities and can be readily applied to facilities that have machines capable of multitasking, including plants in the analytical services sector.

Simultaneous Optimization of Short-Term Scheduling and Heat Integration Schemes for Multipurpose Batch Plants

Simultaneous Optimization of Short-Term Scheduling and Heat Integration Schemes for Multipurpose Batch Plants

Simultaneous optimization of scheduling, equipment dimensions and operating conditions of sequential multi-purpose batch plants

Abstract The design of multi-purpose batch plants is a challenging task, because the number of degrees of freedom for optimization is high. Important optimization variables are the scheduling, operating conditions and the sizes of the equipment items. Since all factors interact, a simultaneous consideration would be beneficial in order to reduce capital and operating costs. In this article, this complex task is tackled for a new case study of a sequential plant for protein production. The case study contains comprehensive models of the unit operations to evaluate equipment dimensions, mass balances and operating times. Variable changeover times and semicontinuous unit operations are considered. For optimization, a MINLP model is used that consists of smaller NLP and MILP submodels in order to simplify modeling. Simulation runs for different product demands are performed and it is shown that good solutions can be found in an adequate time.

An improved model for Heat Integration of intermittent process streams in multipurpose batch plants

This paper presents a mathematical technique for simultaneous Heat Integration (HI) and process scheduling in multipurpose batch plants. Taking advantage of the intermittent continuous behaviour of process streams during transfer between processing units, as determined by the production recipe, the presented formulation aims to maximise the coincidence of availability of hot and cold stream pairs with feasible temperature driving forces for heat recovery, whilst taking into consideration process scheduling constraints. Distinct from similar contributions in the published literature, time is treated as one of the key optimisation variables instead of a predefined parameter, in which case the production schedule is allowed to change. HI during stream transfer has the added benefit of shortened processing time, which invariably improves the throughput, as more batches are likely to be processed within a given time horizon, compared to conventional heating and cooling in situ. Application of the proposed model to a case study shows improvements of up to 50% in utility cost savings and more than two-thirds in product revenue. In addition, further analysis reveals that the use of only three additional heat exchangers can achieve a more than 80% improvement in profit.

Heat integration of intermittently available continuous streams in multipurpose batch plants

Presented in this paper is a mathematical technique for simultaneous heat integration and process scheduling in multipurpose batch plants. Taking advantage of the intermittent continuous behavior of process streams during transfer from one processing unit to another, as determined by the recipe, the presented formulation aims to maximize the coincidence of availability of hot and cold stream pairs with feasible temperature driving forces, while taking into consideration process scheduling constraints. Contrary to similar contributions in published literature, time is treated as one of the key optimization variables instead of a parameter fixed a priori. Heat integration during stream transfer has the added benefit of shortened processing time, which invariably improves throughput, as more batches are likely to be processed within a given time horizon, compared to conventional heating and cooling in situ. Application of the proposed model to a case study shows improvements of more than 30% in energy savings and up to 15% in product output.