Design of multipurpose production facilities: A RTN decomposition-based algorithm

A general mathematical formulation for the design of multipurpose facilities has recently been presented by Barbosa-Póvoa and Pantelides (1997). The model proposed permits a detailed consideration of the design problem taking account of trade-offs between capital costs, revenues and operational flexibility. The optimal solution involves the selection of the required processing and storage equipment items and the required levels of provision of other production resources such as utilities, manpower, cleaning and transportation equipment.In order to guarantee solution optimality, the above design formulation has to consider a large number of equipment items, out of which it will select the ones that will actually be incorporated in the plant. This may result in large mixed-integer linear programming (MILP) problems that are expensive to solve.This paper presents a decomposition approach for the solution of large batch process design problems. The approach involves the iterative solution of a master problem (representing a relaxation of the original design problem) and a design sub-problem (in which several of the design decisions are already fixed).An example illustrating the effectiveness of the proposed decomposition approach is presented.     

OPTIMAL DESIGN OF MULTISITE BATCH-STORAGE NETWORK UNDER SCENARIO-BASED DEMAND UNCERTAINTY

An effective methodology is reported for the optimal design of multisite batch production/transportation and storage networks under uncertain demand forecasting. We assume that any given storage unit can store one material type that can be purchased from suppliers, internally produced, internally consumed, transported to or from other plant sites, and/or sold to customers. We further assume that a storage unit is connected to all processing and transportation stages that consume/produce or move the material to which that storage unit is dedicated. Each processing stage transforms a set of feedstock materials or intermediates into a set of products with constant conversion factors. A batch transportation process can transfer one material or multiple materials at once between plant sites. The objective for optimization is to minimize the probability averaged total cost, which consists of the raw material procurement cost, the cost of setting up processes, inventory holding costs of the storage units, and the capital costs of processes and storage units. A novel production and inventory analysis formulation, the PSW (periodic square wave) model, provides useful expressions for the upper/lower bounds and average level of the storage inventory. The expressions for the Kuhn-Tucker conditions of the optimization problem can be reduced to two sub-problems. The first yields analytical solutions for determining lot sizes, and the second is a separable concave minimization network flow sub-problem whose solution yields the average material flow rates through the networks for the given demand forecast scenario. The result of this study will contribute to the optimal design and operation of large-scale supply chain systems.     

Optimal design of batch‐storage network considering ownership

This article develops a model of multi‐national supply chain activities, which incorporates currency storage units to manage currency flows associated with activities such as raw material procurement, processing, inventory control, transportation, and finished product sales. The core contribution of this model is that it facilitates the quantitative investigation of the influence of macroscopic economic factors such as ownership on supply chain operational decisions. The supply chain system is modeled as a batch‐storage network with recycle streams. The supply chain optimization problem is posed with the objective of minimizing the opportunity costs of annualized capital investments and currency/material inventories, while taking into account the benefit to stockholders in the numeraire currency. The major constraints on the optimization are that the material and currency storage units must not be depleted. A production and inventory analysis formulation (the periodic square wave model) provides useful expressions for the upper and lower bounds and for the average levels of the currency and material inventory holdings. The expressions for the Kuhn‐Tucker conditions of the optimization problem are reduced to a subproblem that allows development of analytical lot‐sizing equations. The lot sizes of procurement, production, transportation, and financial transactions can be determined in closed form once the average flow rates are known. The key result we obtain is that optimal value of the economic order quantity changes substantially with variation in ownership, thus showing quantitatively that ownership structure does impact plant operation. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2418–2425, 2018     

OPTIMAL DESIGN AND OPERATION OF BATCH PROCESSES

The economical design of continuous chemical processes to produce commodity products has reached an advanced state of development. Modern computer tools are used routinely to simulate and optimize these processes. This is not the case, however, for the manufacture of speciality products which must be made in batch operations. The continuing shift towards the production of higher value-added specialty products by the CPI has stimulated efforts aimed at developing good computer assisted design strategies for batch processes.

This paper discusses the formulation of the problem for the optimal design and operation of batch processes. The batch problem differs from the continuous one in a number of important ways. First, batch plants do not operate at steady state. There are important trade-offs between the processing time and the severity (intensity) of processing in single units. Cycle time and performance trade-offs also exist among the various units in the process. Second, batch plants produce multiple products in many cases. There is often a competition for shared resources (labor, utilities, and equipment) among the various products. This paper presents a hierarchical solution approach for the design and optimization of a batch process. The approach is demonstrated by solving an example problem which illustrates the fundamental economic trade-offs.     

Optimal production sequence and processing schedules of multiproduct batch processes for heat integration and minimum equipment costs

The production sequence and the processing schedules of multiproduct batch processes can be changed for maximum heat recovery and minimum equipment costs between batch streams. However, the modified production sequence and processing schedule may increase the production cycle time, which causes the bigger equipment sizes required in batch processes. In this study, the required equipment sizes, the production sequence and the processing times of the multiproduct batch processes are mathematically formulated for maximum heat integration and low equipment costs in a mixed integer nonlinear programming. The optimal solution of this formulation was obtained by GAMS/DICOPT programming solver. Examples are presented to show the capabilities of the model.     

Optimal design of integrated agricultural water networks

This paper presents a mathematical programming model for the optimal design of water networks in the agriculture. The proposed model is based on a new superstructure that includes all configurations in terms of use, reuse and regeneration of water in a field constituted by a number of croplands. The model also includes the allocation of pipelines, pumps and storage tanks in different irrigation periods. The objective function consists in maximizing the annual profit that is formed by the economic incomes owing to the crop sell minus the costs for fresh water, fertilizer, storage tanks, treatment units, piping and pumping. The proposed multi-period optimization problem is formulated as a mixed integer non-linear programming formulation, which was applied to a case study to demonstrate the economic, environmental and social benefits that can be obtained.     

An integrated mathematical programming approach for the design and optimisation of offshore fields

The paper presents a systematic methodology for the optimal design and operational management of offshore oil fields. It is comprised of two stages. At the design stage, the optimal production capacity of a main field is determined with an adjacent satellite field and a well drilling schedule. The problem is formulated as a mixed-integer linear programming formulation. Continuous variables represent individual well, jacket and topsides costs. Binary variables are used to select individual wells within a defined field grid. The mathematical formulation is concise and efficient. An MINLP model is proposed for the operational management optimisation of the offshore oilfields. In the latter model, non-linear equations are extensively used to model the pressure drops in pipes and wells for multiphase flow. Non-linear cost equations have been derived for the production costs of each well accounting for the length, the production rate and their maintenance. Operational decisions determine the oil flowrates, the operation/shut-in for each well and the pressures for each point in the piping network.     

Optimization models for shale gas water management

There are four key aspects for water use in hydraulic fracturing, including source water acquisition, wastewater production, reuse and recycle, and subsequent transportation, storage, and disposal. Water use life cycle is optimized for wellpads through a discrete‐time two‐stage stochastic mixed‐integer linear programming model under uncertain availability of water. The objective is to minimize expected transportation, treatment, storage, and disposal cost while accounting for the revenue from gas production. Assuming freshwater sources, river withdrawal data, location of wellpads, and treatment facilities are given, the goal is to determine an optimal fracturing schedule in coordination with water transportation, and its treatment and reuse. The proposed models consider a long‐time horizon and multiple scenarios from historical data. Two examples representative of the Marcellus Shale play are presented to illustrate the effectiveness of the formulation, and to identify optimization opportunities that can improve both the environmental impact and economical use of water. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3490–3501, 2014     

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.     

Flexible retrofit design of multiproduct batch plants

We treat the addition of new equipment to an existing multiproduct batch plant for which new production targets and selling profits have been specified. This optimal retrofit design problem has been considered by Vaselenak et al. (Ind. Engng Chem. Res. 26, 718–728, 1987). Their constraint that new units must be used in the same manner for all products places a restriction on the design which could readily be overcome in practice. We present a mixed-integer nonlinear programming (MINLP) formulation which eliminates this constraint. A series of examples is presented which demonstrate greater profitability for plants designed with our formulation. The examples also bring to fight a further unwanted constraint in the Vaselenak, Grossmann and Westerberg formulation. In their formulation they limit batch size to the smallest unit at a stage, even when that unit is not needed. It is noted that, at the expense of some additional mathematical complexity, our formulation could be enhanced to allow reconnexion of existing units and alternate use of multiple additional units.     

Worst‐case design of subsea production facilities using semi‐infinite programming

The problem of designing novel process systems for deployment in extreme and hostile environments is addressed. Specifically, the process system of interest is a subsea production facility for ultra deepwater oil and gas production. The costs associated with operational failures in deepwater environments are prohibitively high and, therefore, warrant the application of worst‐case design strategies. That is, prior to the construction and deployment of a process, a certificate of robust feasibility is obtained for the proposed design. The concept of worst‐case design is addressed by formulating the design feasibility problem as a semi‐infinite optimization problem with implicit functions embedded. A basic model of a subsea production facility is presented for a case study of rigorous performance and safety verification. Relying on recent advances in global optimization of implicit functions and semi‐infinite programming, the design feasibility problem is solved, demonstrating that this approach is effective in addressing the problem of worst‐case design of novel process systems. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2513–2524, 2014     

Power scheduling and real-time optimization of industrial cogeneration plants

Scheduling of power and real-time optimization for three industrial cogeneration plants at one of Dow's Louisiana site is presented in this paper. A first principle mathematical model that includes mass and energy balances for gas turbines, heat recovery units, steam turbines, pressure relief valves and steam headers is used to formulate an optimization problem to recommend the best strategy to trade power. The model has detailed operational information that includes equipment status and control curves for different operating scenarios. The model can also accurately predict the effect of ambient temperature, thereby resulting in an optimal day-ahead schedule. Adjustment of power schedule is done in the real-time market 30 min prior to the hour and implementation of the dispatched power schedule is done using a model predictive controller.     

Optimal response under partial plant shutdown with discontinuous dynamic models

This work describes mathematical formulations for modeling aspects of partial shutdowns in multiunit plants. The specific type of partial shutdown considered is one that permits the decoupling of affected units from the rest of the plant, thus enabling continued plant operation, albeit in a more limited fashion. Parsimonious and computationally efficient mixed-integer formulations are presented for specific discontinuous phenomena that arise in partial shutdown modeling, such as shutdown thresholds, induced shutdowns, discontinuous costs, and minimum shutdown durations. It is demonstrated that induced shutdowns (secondary shutdowns triggered by the original shutdown) can be correctly penalized in the objective by capturing the shutdown's true discontinuous economic cost. The computed optimal solution is implemented in closed-loop by employing a multitiered model predictive shutdown controller, in which a discrete-time mixed-integer dynamic optimization (MIDO) problem is embedded. Both objectives of maximizing economics and minimizing restoration (shutdown recovery) time are considered.     

甲醇模块化生产中分时储热系统的优化设计

以“数量放大”为特征的模块化化工生产为克服原料供给和产品市场需求波动的生产流程优化操作提供新途径。为了提高生产系统的能量利用效率,需对生产系统中随时间变化的流股预热、冷却和反应热分时段进行储存和调度。针对可再生能源驱动的甲醇模块化生产系统,本文提出了分时储热策略,通过储罐设置及流股匹配、储罐储热温区确定和储罐容量配置及调度三步对甲醇模块化生产中分时储热系统进行优化设计,获得了分时储热系统的最优配置和优化调度方案。研究表明：在甲醇模块化生产系统中,分时储热系统可将前阶段的热量储存供后续阶段调用,以实现系统能量的最大化利用,而储热的适量废弃可降低储热系统的投资费用。本文所提出的储热系统优化方法可为波动生产过程中分时储热系统的优化设计提供分析工具。     

Simultaneous process synthesis and control design under uncertainty: A worst‐case performance approach

A new methodology that includes process synthesis and control structure decisions for the optimal process and control design of dynamic systems under uncertainty is presented. The method integrates dynamic flexibility and dynamic feasibility in a single optimization formulation, thus, reducing the costs to assess the optimal design. A robust stability test is also included in the proposed method to ensure that the optimal design is stable in the presence of magnitude‐bounded perturbations. Since disturbances are treated as stochastic time‐discrete unmeasured inputs, the optimal process synthesis and control design specified by this method remains feasible and stable in the presence of the most critical realizations in the disturbances. The proposed methodology has been applied to simultaneously design and control a system of CSTRs and a ternary distillation column. A study on the computational costs associated with this method is presented and compared to that required by a dynamic optimization‐based scheme. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2497–2514, 2013     

Integrated control and process design during optimal polymer grade transition operations

In this work we address the simultaneous process control and design problem of polymerization reactors during dynamic grade transition operation. The problem is cast as a Mixed-Integer Dynamic Optimization (MIDO) formulation and, by using the full discretization approach for solving dynamic optimization problems [Kameswaran, S., & Biegler, L. T. (2006). Simultaneous dynamic optimization strategies: Recent advances and challenges. Computers & Chemical Engineering, 30 (10–12), 1560–1575], is transformed into a Mixed-Integer Nonlinear Program (MINLP). The resulting MINLP is solved using a full space nonconvex optimization formulation [Flores-Tlacuahuac, A., & Biegler, L. T. (2007). Simultaneous Mixed-Integer Dynamic Optimization for integrated design and control. Computers & Chemical Engineering, 31, 588–600]. The control and design formulation has been applied to two polymerization reactors featuring highly nonlinear behavior. In both cases, the proposed MIDO formulation was capable of finding optimal solutions. This amounts to finding optimal steady states, reactor designs, as well as open-loop and closed-loop dynamic optimal trajectories, control structures and controller parameters by specifying either the polymer molecular weight distribution or monomer conversion. Because CPU solution time tends to increase with system complexity, some strategies for lowering CPU time are discussed.     

DESIGN OF BATCH GRAPE DRYERS

The mathematical model describing the batch operation of industrial dryers with trucks and trays is presented and analysed for the case of grape dehydrators. The optimum flowsheet configuration and operation conditions for the specific mode of operation and type of dryer employed, are sought and verified by appropriate formulation of design and optimization strategies. The optimization objective is the total annual cost of the plant, subject to constraints imposed by the operation of the dryer, thermodynamics, and construction reasoning. The decision variables were the number of trucks and the drying air stream conditions involving temperature and humidity. The MINLP nature of the design problem required mathematical programming techniques for its solution. The optimization was carried out for a wide range of production capacities, and the optimal points were evaluated in each case. A characteristic design study was presented in order to demonstrate the effectiveness of the proposed approach.     

An MILP Model for Optimal Scheduling of the Lubricant Production Plant

In this article we are developing a model that can be used for determining the optimal production schedule in a lubricant production plant. The model includes all the main stages in the lubricant production process, contains both continuous and binary variables, and results in the formulation of a mixed integer linear programming (MILP) problem that is solved using standard optimization techniques. The model can be easily adapted to any lube production facility, thus providing a valuable tool to refineries in their effort to automate the production scheduling process. The proposed tool can save valuable time and resources by eliminating the time-consuming search for a feasible production plan that production engineers go through in order to meet production demands.     

An efficient MILP continuous-time formulation for short-term scheduling of multiproduct continuous facilities

This paper presents a new MILP mathematical formulation for the scheduling of resource-constrained multiproduct plants involving continuous processes. In such facilities, a sequence of continuous processing steps is usually carried out to produce a significant number of final products and required intermediates. In order to reduce equipment idle time due to unbalanced stage capacities, storage tanks are available for temporary inventory of intermediates. The problem goal is to maximize the plant economic output while satisfying specified minimum product requirements. The proposed approach relies on a continuous time domain representation that accounts for sequence-dependent changeover times and storage limitations without considering additional tasks. The MILP formulation was applied to a real-world manufacturing facility producing seven intermediates and fifteen final products. Compared with previous scheduling methodologies, the proposed approach yields a much simpler problem representation with a significant saving in 0–1 variables and sequencing constraints. Moreover, it provides a more realistic and profitable production schedule at lower computational cost.