Chi Wai Hui

An industrial application using mixed-integer programming technique: A multi-period utility system model

This paper addresses the application of Mixed Integer Programming (MIP) techniques for the optimization of site utility systems. Linear Programming (LP) and Non-Linear Programming (NLP) methods are often used in industry for optimizing the operating conditions of plant utility systems. These techniques are efficient and robust making them suitable for on-line optimization. However, on-line optimization of this type normally considers only current operating conditions and therefore minimum operating costs over a longer period cannot be guaranteed. In addition, LP and NLP methods cannot easily be used to make discrete decisions such as turning equipment on and off. These difficulties can be resolved by employing a multi-period mixed-integer utility plant model. Moreover, other important topics can be investigated with the models such as boiler and maintenance schedules, new equipment selection for utility system debottlenecking, fuel balance optimization and storage, electricity import or export profile optimization, inter-sites electricity backup, etc. In this paper, an industrial example is used to demonstrate MIP techniques for the optimization of plant utility systems.

Aqueous mercury adsorption by activated carbons

Due to serious public health threats resulting from mercury pollution and its rapid distribution in our food chain through the contamination of water bodies, stringent regulations have been enacted on mercury-laden wastewater discharge. Activated carbons have been widely used in the removal of mercuric ions from aqueous effluents. The surface and textural characteristics of activated carbons are the two decisive factors in their efficiency in mercury removal from wastewater. Herein, the structural properties and binding affinity of mercuric ions from effluents have been presented. Also, specific attention has been directed to the effect of sulfur-containing functional moieties on enhancing the mercury adsorption. It has been demonstrated that surface area, pore size, pore size distribution and surface functional groups should collectively be taken into consideration in designing the optimal mercury removal process. Moreover, the mercury adsorption mechanism has been addressed using equilibrium adsorption isotherm, thermodynamic and kinetic studies. Further recommendations have been proposed with the aim of increasing the mercury removal efficiency using carbon activation processes with lower energy input, while achieving similar or even higher efficiencies.

Film-pore diffusion modeling and contact time optimization for the adsorption of dyestuffs on pith

Abstract The sorption of four dyestuffs, namely, Acid Blue 25 (AB25), Acid Red 114 (AR114), Basic Blue 69 (BB69) and Basic Red 22 (BR22) onto bagasse pith has been studied using an agitated batch sorber system. The equilibrium isotherms were determined and kinetic runs were performed over a range of concentrations for each dye and masses of pith. A film-pore diffusion mass transfer model has been developed based on a single effective diffusion coefficient for each system. Error analysis of the experimental and theoretical data indicated relatively large errors at low initial dyestuff concentrations. In this paper, a contact time optimization methodology of a two-stage batch adsorber system taking minimum contact time as the objective function has been developed. The initial concentration of the second stage and adsorbent weight have been designated as variables. Contact time optimization of a two-stage batch adsorber system has been demonstrated at two different conditions/cases for the adsorption of dyes on pith. The optimization solutions show that there is a significant difference for minimum contact time at different process conditions.

Integrating CDU, FCC and product blending models into refinery planning

Abstract The accuracy of using linear models for crude distillation unit (CDU), fluidize-bed catalytic cracker (FCC) and product blending in refinery planning has been debated for decades. Inaccuracy caused by nonrigorous linear models may reduce the overall profitability or sacrifice product quality. On the other hand, using rigorous process models for refinery planning imposes unnecessary complications on the problem because these models lengthen the solution time and often hide critical issues and parameters for profit improvements. To overcome these problems, this paper presents a refinery planning model that utilizes simplified empirical nonlinear process models with considerations for crude characteristics, products’ yields and qualities, etc. The proposed model can be easily solved with much higher accuracy than a traditional linear model. This paper will present how the CDU, FCC and product blending models are formulated and applied to refinery planning. Several case studies are used to illustrate the features of the refinery-planning model proposed.

Film-pore diffusion modeling for the sorption of metal ions from aqueous effluents onto peat.

The sorption of three metal ions, namely, copper, nickel and lead onto sphagnum peat moss has been studied using an agitated batch sorber system. The equilibrium isotherms were determined and kinetic runs were performed over a range of concentrations for each metal ion. A film-pore diffusion mass transfer model has been developed based on a single effective diffusion coefficient for each system. Error analysis of the experimental and theoretical data indicated relatively large errors at low initial metal ion concentrations. Therefore the model was modified to introduce a surface coverage concentration dependent effective diffusivity to account for a contribution from surface diffusion.

A novel MILP formulation for short-term scheduling of multi-stage multi-product batch plants with sequence-dependent constraints

Abstract This paper presents a continuous-time mixed-integer linear programming (MILP) model for short-term scheduling of multi-stage multi-product batch plants. The model determines the optimal sequencing and the allocation of customer orders to non-identical processing units by minimizing the earliness and tardiness of order completion. This is a highly combinatorial problem, especially when sequence-dependent relations are considered such as the setup time between consecutive orders. A common approach to this scheduling problem relies on the application of tetra-index binary variables, i.e. (order, order, stage, unit) to represent all the combinations of order sequences and assignments to units in the various stages. This generates a huge number of binary variables and, as a consequence, much time is required for solutions. This paper proposes a novel formulation that replaces the tetra-index binary variables by one set of tri-index binary variables (order, order, stage) without losing the models generality. By the elimination of the unit index, the new formulation requires considerably fewer binary variables, thus significantly shortening the solution time.

Constant approach temperature model for HEN retrofit

This paper proposes a solution method based upon mathematical programming for Heat Exchanger Network (HEN) retrofit. This is a two-step approach. The first step uses a Constant Approach Temperature (CAT) model to optimize the structure of the final HEN. The CAT model simultaneously takes into account the cost of utilities, structural modifications and heat transfer areas by assuming the approach temperatures of all heat transfers inside the HEN to be a constant. The main advantage of this assumption is that area calculations are linearized, therefore, the model could be solved as a Mixed Integer Linear (MILP) problem. This shortens the solution time and removes the possibility of being trapped at local optimums. The CAT model does not guarantee feasible solutions; however, it determines a good network structure and drives the solution very close to the global optimum. Starting with this network structure, a Mixed Integer Nonlinear (MINLP) model is then used in the second step, which takes into account the actual approach temperatures, to finalize the design. Example problems from literature are used to demonstrate the effectiveness of the approach in terms of the solution quality and time.

Minimum cost heat recovery between separate plant regions

Abstract Process plants are often divided into logically identifiable regions, each having associated processing tasks. Heat recovery between these seperate regions of a plant or process is becoming more frequently addressed, both in the literature and in practice. Most procedures to date for such inter-region heat integration focus on minimizing energy costs. However, the methods only tentatively consider capital cost by aiming for a few number of interconnections between the process regions and by the assumed minimum temperature difference for heat exchange. So far, the energy-capital optimization for such situations has not been considered. This paper deals with the overall cost tradeoff between energy, heat exchange area and the number of interconnections for heat recovery between seperate regions of a plant or process. The purpose is to gain some understanding of the optimization and develop a procedure to obtain near-minimum cost designs for such systems.

A novel MILP formulation for short-term scheduling of multistage multi-product batch plants

Abstract This study presents a continuous-time mixed-integer linear programming model for short-term scheduling of multistage multi-product batch plants. The model determines the optimal sequencing and the allocation of customer orders to non-identical processing units by minimizing the earliness and tardiness of order completion. This is a highly combinatorial problem, especially when sequence-dependent relations considered to be are such as the setup time between consecutive orders. A common approach to this scheduling problem relies on the application of tetra-index binary variables, i.e. (order, order, stage unit) to represent all the combinations of order sequences and assignments to units in the various stages. This generates a huge number of binary variables and, as a consequence, much time is required for solutions. This study proposes a novel formulation that replaces the tetra-index binary variables by one set of tri-index binary variables (order, order, stage) without losing the models generality. By the elimination of the unit index, the new formulation requires considerably fewer binary variables, thus significantly shortening the solution time.

Short-term site-wide maintenance scheduling

Abstract Preventive maintenance is essential for every chemical production site to prevent failure and accidents, however, it upsets material and utility flows inside the site and also causes production loss. In order to minimize the loss, maintenance of each plant unit has to be carefully scheduled together with considerations on site-wide material and utility balances. This will involve both production and utility systems, and indeed is a very complicated problem. A scheduling strategy is then employed to handle the problem efficiently. It divides the scheduling into two steps, long-term and short-term. Long-term maintenance scheduling determines the combination of plant shutdown in a period of 2–5 years. Base upon the long-term schedule, a short-term maintenance scheduling optimizes the exact timing of plant shutdown, overhaul, inspection and startup within a maintenance period of 4–10 weeks. Short-term maintenance scheduling involves pre-set utility and material demand profiles during a plant shutdown, overhaul and startup making it a very challenging task. In this paper, a multi-period mixed integer linear programming (MILP) model, a site-model, is proposed as an aid to optimize short-term site-wide maintenance schedule. A special formulation is also developed to deal with the pre-set utility and material demand profiles in the site-model.