Integrated gasoline blending and order delivery operations: Part I. short‐term scheduling and global optimization for single and multi‐period operations

Gasoline is one of the most valuable products in an oil refinery and can account for as much as 60–70% of total profit. Optimal integrated scheduling of gasoline blending and order delivery operations can significantly increase profit by avoiding ship demurrage, improving customer satisfaction, minimizing quality give‐aways, reducing costly transitions and slop generation, exploiting low‐quality cuts, and reducing inventory costs. In this article, we first introduce a new unit‐specific event‐based continuous‐time formulation for the integrated treatment of recipes, blending, and scheduling of gasoline blending and order delivery operations. Many operational features are included such as nonidentical parallel blenders, constant blending rate, minimum blend length and amount, blender transition times, multipurpose product tanks, changeovers, and piecewise constant profiles for blend component qualities and feed rates. To address the nonconvexities arising from forcing constant blending rates during a run, we propose a hybrid global optimization approach incorporating a schedule adjustment procedure, iteratively via a mixed‐integer programming and nonlinear programming scheme, and a rigorous deterministic global optimization approach. The computational results demonstrate that our proposed formulation does improve the mixed‐integer linear programming relaxation of Li and Karimi, Ind. Eng. Chem. Res., 2011, 50, 9156–9174. All examples are solved to be 1%‐global optimality with modest computational effort. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2043–2070, 2016     

Continuous‐time modeling and global optimization approach for scheduling of crude oil operations

Scheduling of crude oil operations is a critical and complicated component of overall refinery operations, because crude oil costs account for about 80% of the refinery turnover. Moreover, blending with less expensive crudes can significantly increase profit margins. The mathematical modeling of blending different crudes in storage tanks results in many bilinear terms, which transforms the problem into a challenging, nonconvex, and mixed‐integer nonlinear programming (MINLP) optimization model. Two primary contributions have been made. First, the authors developed a novel unit‐specific event‐based continuous‐time MINLP formulation for this problem. Then they incorporated realistic operational features such as single buoy mooring (SBM), multiple jetties, multiparcel vessels, single‐parcel vessels, crude blending, brine settling, crude segregation, and multiple tanks feeding one crude distillation unit at one time and vice versa. In addition, 15 important volume‐based or weight‐based crude property indices are also considered. Second, they exploited recent advances in piecewise‐linear underestimation of bilinear terms within a branch‐and‐bound algorithm to globally optimize the MINLP problem. It is shown that the continuous‐time model results in substantially fewer bilinear terms. Several examples taken from the work of Li et al. are used to illustrate that (1) better solutions are obtained and (2) ε‐global optimality can be attained using the proposed branch‐and‐bound global optimization algorithm with piecewise‐linear underestimations of the bilinear terms. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Procurement planning in oil refining industries considering blending operations

This paper addresses procurement planning in oil refining, which has until now only had limited attention in the literature. We introduce a mixed integer nonlinear programming (MINLP) model and develop a novel two-stage solution approach, which aims at computational efficiency while addressing the problems due to discrepancies between a non-linear and a linearized formulation. The proposed model covers realistic settings by allowing the blending of crude oil in storage tanks, by modeling storage tanks and relevant processing units individually, and by handling more crude oil types and quality parameters than in previous literature. The developed approach is tested using historical data from Statoil A/S as well as through a comprehensive numerical analysis. The approach generates a feasible procurement plan within acceptable computation time, is able to quickly adjust an existing plan to take advantage of individual procurement opportunities, and can be used within a rolling time horizon scheme.     

Operational strategy and planning for raw natural gas refining complexes: Process modeling and global optimization

Optimal operational strategy and planning of a raw natural gas refining complex (RNGRC) is very challenging since it involves highly nonlinear processes, complex thermodynamics, blending, and utility systems. In this article, we first propose a superstructure integrating a utility system for the RNGRC, involving multiple gas feedstocks, and different product specifications. Then, we develop a large‐scale nonconvex mixed‐integer nonlinear programming (MINLP) optimization model. The model incorporates rigorous process models for input and output relations based on fundamentals of thermodynamics and unit operations and accurate models for utility systems. To reduce the noncovex items in the proposed MINLP model, equivalent reformulation techniques are introduced. Finally, the reformulated nonconvex MINLP model is solved to global optimality using state of the art deterministic global optimization approaches. The computational results demonstrate that a significant profit increase is achieved using the proposed approach compared to that from the real operation. © 2016 American Institute of Chemical Engineers AIChE J, 63: 652–668, 2017     

Fair profit allocation in supply chain optimization with transfer price and revenue sharing: MINLP model and algorithm for cellulosic biofuel supply chains

A mixed‐integer nonlinear programming (MINLP) formulation to simultaneously optimize operational decisions as well as profit allocation mechanisms in supply chain optimization, namely material transfer prices and revenue share policies among the supply chain participants is proposed. The case of cellulosic bioethanol supply chains is specifically considered and the game‐theory Nash bargaining solution approach is employed to achieve fair allocation of profit among the collection facilities, biorefineries, and distribution centers. The structural advantages of certain supply chain participants can be taken into account by specifying different values of the negotiation‐power indicators in the generalized Nash‐type objective function. A solution strategy based on a logarithm transformation and a branch‐and‐refine algorithm for efficient global optimization of the resulting nonconvex MINLP problem is proposed. To demonstrate the application of the proposed framework, an illustrative example and a state‐wide county‐level case study on the optimization of a potential cellulosic bioethanol supply chain in Illinois are presented. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3211–3229, 2014     

An MILP-MINLP decomposition method for the global optimization of a source based model of the multiperiod blending problem

The multiperiod blending problem involves binary variables and bilinear terms, yielding a nonconvex MINLP. In this work we present two major contributions for the global solution of the problem. The first one is an alternative formulation of the problem. This formulation makes use of redundant constraints that improve the MILP relaxation of the MINLP. The second contribution is an algorithm that decomposes the MINLP model into two levels. The first level, or master problem, is an MILP relaxation of the original MINLP. The second level, or subproblem, is a smaller MINLP in which some of the binary variables of the original problem are fixed. The results show that the new formulation can be solved faster than alternative models, and that the decomposition method can solve the problems faster than state of the art general purpose solvers.     

Short-term scheduling and recipe optimization of blending processes

The main objective of this paper is to develop an integrated approach to coordinate short-term scheduling of multi-product blending facilities with nonlinear recipe optimization. The proposed strategy is based on a hierarchical concept consisting of three business levels: Long-range planning, short-term scheduling and process control. Long-range planning is accomplished by solving a large-scale nonlinear recipe optimization problem (multi-blend problem). Resulting blending recipes and production volumes are provided as goals for the scheduling level. The scheduling problem is formulated as a mixed-integer linear program derived from a resource-task network representation. The scheduling model permits recipe changeovers in order to utilize an additional degree of freedom for optimization. By interpreting the solution of the scheduling problem, new constraints can be imposed on the previous multi-blend problem. Thus bottlenecks arising during scheduling are considered already on the topmost long-range planning level. Based on the outlined approach a commercial software system has been designed to optimize the operation of in-line blending and batch blending processes. The application of the strategy and software is demonstrated by a detailed case study.     

Optimal storage design for a multi-product plant: A non-convex MINLP formulation

We discuss a tank design problem for a multi product plant, in which the optimal cycle time and the optimal campaign size are unknown. A mixed-integer nonlinear programming (MINLP) formulation is presented, where non-convexities are due to the tank investment cost, storage cost, campaign setup cost and variable production rates. The objective of the optimization model is to minimize the sum of the production cost per ton per product produced. A continuous-time mathematical programming formulation is proposed and several extensions are discussed. The model is implemented in GAMS and computational results are reported for the two global MINLP solver BARON and LINDOGlobal as well as several nonlinear solvers available in GAMS.     

Short‐term scheduling of a large‐scale oil‐refinery operations: Incorporating logistics details

Refineries are increasingly concerned with improving the scheduling of their operations to achieve better economic performances by minimizing quality, quantity, and logistics give away. In this article, we present a comprehensive integrated optimization model based on continuous‐time formulation for the scheduling problem of production units and end‐product blending problem. The model incorporates quantity, quality, and logistics decisions related to real‐life refinery operations. These involve minimum run‐length requirements, fill‐draw‐delay, one‐flow out of blender, sequence‐dependent switchovers, maximum heel quantity, and downgrading of better quality product to lower quality. The logistics giveaways in our work are associated with obtaining a feasible solution while minimizing violations of sequence‐dependent switchovers and maximum heel quantity restrictions. A set of valid inequalities are proposed that improves the computational performance of the model significantly. The formulation is used to address realistic case studies where feasible solutions are obtained in reasonable computational time. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Scheduling of crude oil operations under demand uncertainty: A robust optimization framework coupled with global optimization

Scheduling of crude oil operations is an important component of overall refinery operations, because crude oil costs account for about 80% of the refinery turnover. The mathematical modeling of blending different crudes in storage tanks results in many bilinear terms, which transform the problem into a challenging, nonconvex, mixed‐integer nonlinear programming (MINLP) optimization model. In practice, uncertainties are unavoidable and include demand fluctuations, ship arrival delays, equipment malfunction, and tank unavailability. In the presence of these uncertainties, an optimal schedule generated using nominal parameter values may often be suboptimal or even become infeasible. In this article, the robust optimization framework proposed by Lin et al. and Janak et al. is extended to develop a deterministic robust counterpart optimization model for demand uncertainty. The recently proposed branch and bound global optimization algorithm with piecewise‐linear underestimation of bilinear terms by Li et al. is also extended to solve the nonconvex MINLP deterministic robust counterpart optimization model and generate robust schedules. Two examples are used to illustrate the capability of the proposed robust optimization approach, and the extended branch and bound global optimization algorithm for demand uncertainty. The computational results demonstrate that the obtained schedules are robust in the presence of demand uncertainty. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2373–2396, 2012     

Synthesis of Rice Processing Plants. II. MINLP Optimization

A systematic design approach was applied to develop the optimal process flowsheet for a rice processing plant. The optimization problem was formulated as a Mixed-Integer NonLinear Programme, MINLP, consisting of vectors of binary and continuous variables. A superstructure flowsheet comprising all serial structures of drying, cooling, and tempering units in the process was postulated. The set of optimum decision variables including the number of drying, cooling, and tempering units, temperature and relative humidity of drying air, drying time, cooling time, and tempering time were determine as the solution of the corresponding MINLP. Six objective functions were investigated as possible performance criteria: production time, number of the operating units, energy consumption, total operating cost, head rice yield, and the profit. The choice of objective function was found to have a significant effect on the optimal solution. Comparison with typical design and operating conditions, the MINLP results showed that a 22% reduction in energy consumption was possible along with a 2.4% increase in head rice yield. These savings, if applied to the world-wide rice industry, translate into more than $3 billion dollars/year increase in profit.     

Operational modeling of multistream heat exchangers with phase changes

Multistream heat exchangers (MSHE) enable the simultaneous exchange of heat among multiple streams, and are preferred in cryogenic processes such as air separation and LNG. Most MSHEs are complex; proprietary and involve phase changes of mixtures. Although modeling MSHE is crucial for process optimization, no such work exists to our knowledge. We present a novel approach for deriving an approximate operational (vs. design) model from historic data for an MSHE. Using a superstructure of simple 2‐stream exchangers, we propose a mixed‐integer nonlinear programming (MINLP) formulation to obtain a HE network that best represents the MSHE operation. We also develop an iterative algorithm to solve the large and nonconvex MINLP model in reasonable time, as existing commercial solvers fail to do so. Finally, we demonstrate the application of our work on an MSHE from an existing LNG plant, and successfully predict its performance over a variety of seasons and feed conditions. © 2008 American Institute of Chemical Engineers AIChE J, 2009     

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.     

Synthesis of Rice Processing Plants. II. MINLP Optimization

Abstract

A systematic design approach was applied to develop the optimal process flowsheet for a rice processing plant. The optimization problem was formulated as a Mixed-Integer NonLinear Programme, MINLP, consisting of vectors of binary and continuous variables. A superstructure flowsheet comprising all serial structures of drying, cooling, and tempering units in the process was postulated. The set of optimum decision variables including the number of drying, cooling, and tempering units, temperature and relative humidity of drying air, drying time, cooling time, and tempering time were determine as the solution of the corresponding MINLP. Six objective functions were investigated as possible performance criteria: production time, number of the operating units, energy consumption, total operating cost, head rice yield, and the profit. The choice of objective function was found to have a significant effect on the optimal solution. Comparison with typical design and operating conditions, the MINLP results showed that a 22% reduction in energy consumption was possible along with a 2.4% increase in head rice yield. These savings, if applied to the world-wide rice industry, translate into more than $3 billion dollars/year increase in profit.     

A Modular Mixed‐Integer Non‐Linear Programming Algorithm for Synthesis of Chemical Processes

A modular approach to the formulation and a solution of mixed‐integer non‐linear programming (MINLP) problems are presented, which reduce the size of MINLP and the computational expenses effectively. The method decomposes the synthesis task into three hierarchical levels—the superstructure, the structure, and the modules, with the layer of modules being the most critical to the problem solution. The strategy has been implemented in a simulation environment in which the variables of interest are defined as implicit functions of the optimization variables. The implicit relationships are handled using a data‐oriented process simulation technique (DOPS) that significantly simplify the simulation. The method has been effectively applied to two case studies, one from literature for the synthesis of hydrodesalkylation, and another from industrial process manufacturing methylene diphenylene diisocyanates.     

A formulation methodology for multicomponent distillation sequences based on stochastic optimization

Based on stochastic optimization strategy, a formulation methodology is proposed for synthesizing distillation column sequences, allowing more than one middle component as the distributing components between a pair of key components in the non-sharp split. In order to represent and manipulate the distillation configuration structures, a new coding procedure is proposed in the form of one-dimensional array. Theoretically, an array can represent any kind of split (non-sharp and sharp).With the application of a binary sort tree approach, a robust flow sheet encoding and decoding procedure is developed so that the problem formulation and solution becomes tractable. In this paper, the synthesis problem is formulated as a mixed-integer nonlinear programming (MINLP) problem and an improved simulated annealing approach is adopted to solve the optimization problem. Besides, a shortcut method is applied to the evaluation of all required design parameters as well as the total function.     

Integrated Scheduling and Dynamic Optimization of Sequential Batch Processes with Online Implementation

An efficient decomposition method to solve the integrated problem of scheduling and dynamic optimization for sequential batch processes is proposed. The integrated problem is formulated as a mixed‐integer dynamic optimization problem or a large‐scale mixed‐integer nonlinear programming (MINLP) problem by discretizing the dynamic models. To reduce the computational complexity, we first decompose all dynamic models from the integrated problem, which is then approximated by a scheduling problem based on the flexible recipe. The recipe candidates are expressed by Pareto frontiers, which are determined offline by using multiobjective dynamic optimization to minimize the processing cost and processing time. The operational recipe is then optimized simultaneously with the scheduling decisions online. Because the dynamic models are encapsulated by the Pareto frontiers, the online problem is a mixed‐integer programming problem which is much more computationally efficient than the original MINLP problem, and allows the online implementation to deal with uncertainties. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2379–2406, 2013     

Optimization of refinery hydrogen network based on chance constrained programming

Deterministic optimization approaches have been developed and used in the optimization of hydrogen network in refinery. However, uncertainties may have a large impact on the optimization of hydrogen network. Thus the consideration of uncertainties in optimization approaches is necessary for the optimization of hydrogen network. A novel chance constrained programming (CCP) approach for the optimization of hydrogen network in refinery under uncertainties is proposed. The stochastic properties of the uncertainties are explicitly considered in the problem formulation in which some input and state constraints are to be complied with predefined probability levels. The problem is then transformed to an equivalent deterministic mixed-integer nonlinear programming (MINLP) problem so that it can be solved by a MINLP solver. The solution of the optimization problem provides comprehensive information on the economic benefit under different confidence levels by satisfying process constraints. Based on this approach, an optimal and reliable decision can be made, and a suitable compensation between the profit and the probability of constraints violation can be achieved. The approach proposed in this paper makes better use of resources and can provide significant environmental and economic benefits. Finally, a case study from a refinery in China is presented to illustrate the applicability and efficiency of the developed approach.     

Improved continuous-time model for gasoline blend scheduling

This work introduces a reduced-size continuous-time model for scheduling of gasoline blends. Previously published model has been modified by (i) introducing new model features (penalty for deliveries in order to reduce sending material from different product tanks to the same order, product and blender-dependent minimum setup times, maximum delivery rate from component tanks, threshold volume for each blend), (ii) by reducing the number of integer variables, and (iii) by adding lower bounds on the blend and switching costs, which significantly improve convergence. Nonlinearities are introduced by ethyl RT-70 equations for octane blending. Medium-size linear problems (two blenders, more than 20 orders, 5 products) are solved to optimality within one or two minutes. Previously unsolved large scale blending problems (more than 35 orders, 5 product, 2 or 3 blenders) have also been solved to less than 0.5% optimality gap.     

A bilevel NLP sensitivity‐based decomposition for dynamic optimization with moving finite elements

Optimal control has guided numerous applications in chemical engineering, and exact determination of optimal profiles is essential for operation of separation and reactive processes, and operating strategies and recipe generation for batch processes. Here, a simultaneous collocation formulation based on moving finite elements is developed for the solution of a class of optimal control problems. Novel features of the algorithm include the direct location of breakpoints for control profiles and a termination criterion based on a constant Hamiltonian profile. The algorithm is stabilized and performance is significantly improved by decomposing the overall nonlinear programming (NLP) formulation into an inner problem, which solves a fixed element simultaneous collocation problem, and an outer problem, which adjusts the finite elements based on several error criteria. This bilevel formulation is aided by a NLP solver (the interior point optimizer) for both problems as well as an NLP sensitivity component, which provides derivative information from the inner problem to the outer problem. This approach is demonstrated on 11 dynamic optimization problems drawn from the optimal control and chemical engineering literature. © 2014 American Institute of Chemical Engineers AIChE J, 60: 966–979, 2014