Thokozani Majozi

Wastewater minimisation using central reusable water storage in batch plants

This paper presents a continuous-time mathematical formulation for freshwater and wastewater minimisation in multipurpose batch plants with and without a central reusable water storage facility. The minimisation of wastewater is achieved through the exploitation of recycle and reuse opportunities. A superstructure that entails all the possible recycle and reuse possibilities is used as the basis for the formulation. Initially, the formulation is based on a predefined schedule characterized by a priori specification of starting or finishing times. The formulation is then extended to embed wastewater minimisation within an established scheduling framework in which starting and finishing times become optimization variables. In both forms the formulation can readily be extended to multiple contaminant media, although this will be the subject of another publication. Fixing the outlet concentration and the contaminant mass load for each water using operation in the absence of central reusable water storage initially renders the formulation a nonconvex mixed integer nonlinear program (MINLP) which is linearized exactly to yield a convex mixed integer linear program (MILP). On the other hand, allowing the outlet concentration to vary within predefined bounds while fixing both the water requirement and contaminant mass load yields a MINLP formulation for which global optimality cannot be guaranteed in complex problems. The developed formulation is applied to a published literature example as well as case studies involving production scheduling.

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.

Novel continuous time MILP formulation for multipurpose batch plants. 2. Integrated planning and scheduling

While the part 1 focuses on the application of the proposed formulation to scheduling, this paper focuses mainly on the integration of planning and scheduling in multipurpose batch plants. In dealing with this problem, the method presented in part 2 exploits the mathematical structure of the overall plant model. It is discovered that the overall model exhibits a block angular structure that is decomposed by raw material allocation. If raw materials can be allocated optimally to individual plants, solving individual models for each plant can produce the same results as solving an overall model for the site. This discovery leads to a decomposition strategy that consists of two levels. In the first level, only planning decisions are made, and the objective function is the maximization of the overall profit. The results from solving the planning model give optimal raw material allocation to different plants. In the second level, the raw material targets from the first (planning) level are incorporated into the scheduling submodels for each plant, which are solved independently without compromising global optimality. The objective function for each scheduling submodel is the maximization of product throughput. The scheduling level uses the concept of the state sequence network presented in part 1. Solving scheduling submodels for individual plants rather than the overall site model leads to problems with much a smaller number of binary variables and, hence, shorter CPU times. If conflicts arise, i.e., the planning targets are too optimistic to be realized at the scheduling level, the planning model is revisited with more realistic targets. This eventually becomes an iterative procedure that terminates once the planning and scheduling solutions converge within a specified tolerance. In this way, the planning model acts as coordination for scheduling models for individual plants. An industrial case study with three chemical processes is presented to demonstrate the effectiveness of this approach.

Simultaneous targeting and design for cooling water systems with multiple cooling water supplies

This paper presents a technique for simultaneous targeting and design in cooling water systems comprising of at least two cooling towers and several cooling water using operations. The presented technique is based on a superstructure from which a mathematical formulation is derived using system specific variables and parameters. It is demonstrated that in a system like this, true optimality can only be realized by a holistic consideration of the entire cooling water system. Consideration of individual subsets of cooling towers with their dedicated cooling water operations yields suboptimal results. Four operational cases are considered and structural considerations of corresponding mathematical formulations presented. The first case results in a linear programming (LP) formulation, the second case yields a mixed integer linear programming (MILP) formulation whilst the other two cases yield mixed integer nonlinear programming (MINLP) formulations which cannot be exactly linearized. However, in all cases significant improvements in excess of 40% were realized in targeting, without compromising the heat duty of the cooling water using operations. The main objective of this investigation is to debottleneck the overall cooling water supply for the cooling water network.

Wastewater minimization in multipurpose batch plants with a regeneration unit: Multiple contaminants

Wastewater minimization can be achieved by employing water reuse opportunities. This paper presents a methodology to address the problem of wastewater minimization by extending the concept of water reuse to include a wastewater regenerator. The regenerator purifies wastewater to such a quality that it can be reused in other operations. This further increases water reuse opportunities in the plant, thereby significantly reducing freshwater demand and effluent generation. The mathematical model determines the optimum batch production schedule that achieves the minimum wastewater generation within the same framework. The model was applied to two case studies involving multiple contaminants and wastewater reductions of 19.2% and 26% were achieved.

Short-Term Scheduling

In this chapter, the concept of the state sequence network (SSN) representation, which is the cornerstone of the material entailed in this textbook, is presented. This representation is based on states only, eliminating the use of tasks and units. Using this new representation as a basis, a novel continuous time MILP formulation for short-term scheduling of multipurpose batch plants is developed (Majozi and Zhu, 2001, Ind. Eng. Chem. Res., 40(25): 5935–5949). The presented formulation can readily be extended to intermediate due date scenarios. Time points are used to denote the use or production of a particular state. This formulation leads to a small number of binary variables and much better results when compared to other continuous time formulations published in literature. The reduced number of binary variables is a result of considering states only, thereby eliminating binary variables corresponding to tasks and units. This method has been applied to literature examples and industrial problems which show significant improvement in reducing the number of binary variables, hence CPU times. The last section of this chapter introduces the concept of units aggregation in reducing the binary dimension of large-scale problems. This makes it possible for the method to solve large-scale industrial problems. In the forthcoming chapters of this textbook it will be demonstrated how this formulation is applied in the context of batch process integration with the ultimate aim of freshwater and energy optimization.

A combined fuzzy set theory and MILP approach in integration of planning and scheduling of batch plants—Personnel evaluation and allocation

This paper presents the application of fuzzy set theory (FST) within the context of integrated planning and scheduling. Fuzzy set theory provides a framework for modelling uncertain or ambiguous information, which is commonly encountered in industry. A typical example of an industrial situation wherein uncertainty cannot be avoided due to the type of data required is operator evaluation (grading). This usually requires information on experience, expertise, responsibility, age, etc., which tend to be more qualitative than quantitative, and involve high levels of imprecision. Consequently, traditional mathematical procedures fail to address this issue effectively. Since human intervention is crucial in the operation and performance of batch chemical plants, the issue of operator evaluation demands attention. It is generally accepted that operators with different skills will have different process understanding and response times, which will eventually impact on plant performance. Moreover, different plants will have different requirements in terms of the aforementioned evaluation criteria. Therefore, efficiency of any operator evaluation procedure is entirely dependent on the quality of operator allocation to different plants. Another aspect that should not be overlooked when dealing with operators, is remuneration, which is determined by the grade. Operators with high levels of skill (experience) and expertise (education) tend to command high salaries. Therefore, they should only be hired on mandatory rather than discretionary grounds. The presentation made in this paper demonstrates the application of FST in dealing with qualitative features of plant personnel as well as plant requirements in order to maximise plant performance, whilst accounting for the financial aspects. The FST output can then be incorporated in an MILP formulation to determine the optimal allocation of operators to different plants. The second part of this series presents the impact of personnel allocation on the overall integrated planning and scheduling framework.

Studies on pore blocking mechanism and technical feasibility of a hybrid PAC-MF process for reclamation of irrigation water from biotreated POME

ABSTRACT An integrated low-cost adsorption (with powdered activated carbon, PAC) and cross-flow membrane filtration (with microfiltration membranes of 0.1 and 0.2 μm pore sizes) process was employed for the treatment of biotreated palm oil mill effluent (POME) to produce irrigation water that is fully benchmarked with water-quality standards. The permeate quality was within the recommended standard for irrigation water, as the concentrations of all critical constituents were well below their recommended values. Sustainability of the process integration was further confirmed with the domination of cake filtration over other blocking mechanisms with higher R2 values at all trans-membrane pressures. Suitable extended usage of permeate was found for toilet/urinal flushing.

Synthesis and optimisation of an integrated water and membrane network framework with multiple electrodialysis regenerators

Abstract The shrinking supplies of freshwater globally, coupled with strict environmental regulations, have driven the manufacturing industry towards sustainable water management for the minimisation of freshwater intake and wastewater generation. By using process integration and its enabling tools, this work considers the synthesis of an optimal water network with multiple regeneration capabilities. Development of the proposed framework is achieved by embedding a subnetwork of detailed electrodialysis models within a water network. Based on a superstructure and fixed flowrate, the optimisation problem is formulated as an MINLP model and solved in GAMS/DICOPT. To demonstrate the applicability of the proposed mathematical model a literature case study on a pulp and paper plant is presented and the results indicate a potential of 12% savings in freshwater intake, 16% reduction in wastewater generated and a 14% saving in the total annualised cost for the entire network.

Heat integration of intermittently available continuous streams in multipurpose batch plants

Abstract 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.