A risk-based methodology for the optimal placement of hazardous gas detectors

Hazardous gas detection systems play an important role in preventing catastrophic gas-related accidents in process industries. Even though effective detection technology currently exists for hazardous gas releases and a majority of process installations have a large number of sensitive detectors in place, the actual operating performance of gas detection systems still does not meet the expected requirements. In this paper, a risk-based methodology is proposed to optimize the placement of hazardous gas detectors. The methodology includes three main steps, namely, the establishment of representative leak scenarios, computational fluid dynamics (CFD)-based gas dispersion modeling, and the establishment of an optimized solution. Based on the combination of gas leak probability and joint distribution probability of wind velocity and wind direction, a quantitative filtering approach is presented to select representative leak scenarios from all potential scenarios. The commercial code ANSYS-FLUENT is used to estimate the consequence of hazardous gas dispersions under various leak and environmental conditions. A stochastic mixed-integer linear programming formulation with the objective of minimizing the total leak risk across all representative leak scenarios is proposed, and the greedy dropping heuristic algorithm (GDHA) is used to solve the optimization model. Finally, a practical application of the methodology is performed to validate its effectiveness for the optimal design of a gas detector system in a high-sulfur natural gas purification plant in Chongqing, China. The results show that an appropriate number of gas detectors with optimal cost-effectiveness can be obtained, and the total leak risk across all potential scenarios can be substantially reduced. This methodology provides an effective approach to guide the optimal placement of point-type gas detection systems involved with either single or mixed gas releases.     

失效情景下气体探测器多目标布置优化

目前有关气体探测器布置优化研究较少考虑探测器的失效情景,本文以某柴油加氢装置的硫化氢气体探测器布置优化为例,提出一种失效情景下气体探测器多目标布置优化方法。首先对待检测区域的潜在泄漏源进行辨识,构建泄漏场景集并进行场景缩减,通过计算流体力学方法预测泄漏实时浓度场。其次,以时效性和鲁棒性作为评价指标,以考虑泄漏场景概率和探测器失效概率的检测时间最小化、探测器网络鲁棒性最大化作为优化目标函数,并结合逻辑约束条件建立数学模型。在此基础上,采用基于模拟退火的多目标粒子群算法对模型进行求解,得到Pareto非劣解集,采用理想点逼近法（TOPSIS）对Pareto解集进行排序得到最优方案,最后决策者可根据不同需求确定最终布置方案。     

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 placement of gas detectors: A P‐median formulation considering dynamic nonuniform unavailabilities

A stochastic programming formulation (SPqt), based on the P‐median problem, is proposed for determining the optimal placement of detectors in mitigation systems while considering nonuniform dynamic detector unavailabilities. Unlike previously proposed formulations, SPqt explicitly considers backup detection levels. This allows the modeller to determine the maximum degree of the nonlinear products to be used based on the trade‐off between computational complexity and solution accuracy. We analyze this trade‐off on formulation SPqt results by using 4 real data sets for the gas detector placement problem while using unavailability values obtained from real industry gas detector data. For this data, our results show that two detection levels are sufficient to find objective values within 1% of the optimal solution. Using two detection levels reduces the nonlinear formulation to a quadratic formulation. Three solution strategies are proposed for this quadratic formulation and then compared from the computational efficiency perspective. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2728–2739, 2016     

Optimal operation of cryogenic air separation systems with demand uncertainty and contractual obligations

Cryogenic air separation is an efficient technology for supplying large quantities of nitrogen, argon, and oxygen to chemical, petroleum and manufacturing customers. However, numerous uncertainties make effective operation of these complex processes difficult. This work addresses the problem of determining an optimal operating strategy to maximize the total profit of a cryogenic air separation process while considering demand uncertainty and contractual obligations. A rigorous process model is included as constraints in a nonlinear programming formulation. Uncertain demands are assumed to be normally distributed with known mean and standard deviation, and expected profit in the objective function is evaluated using the standard loss function. A probabilistic fill-rate expression, also based on the loss function, is used to model the contractual obligations by providing a lower bound on the expected product sales. In the single period case with one customer satisfaction constraint, the nonlinear programming formulation can be solved efficiently using the general purpose nonlinear optimization package, Ipopt. This formulation is then extended to include multiple time periods, the potential for product storage, and customer satisfaction constraints on multiple products. To solve the large-scale nonlinear programming formulation that considers a seven-day operating horizon, a tailored parallel nonlinear programming algorithm is used. This approach makes use of a Schur complement decomposition strategy to exploit the block structure of the problem and allow efficient solution in parallel. Using these tools, we solve for a set of optimal operating strategies over the complete space of different fill rates. This produces planning figures that identify key trade-offs between profitability and contractual obligations.     

基于不可用性及表决机制的探测器优化布置

在化工工业中,危险气体探测系统的表决机制以及失效问题对于探测器的网络布设至关重要。本文通过引入表决系统需求失效概率以及对探测系统表决逻辑进行分析,提出了一种基于不可用性及表决机制的探测器优化布置方法。首先对探测系统表决逻辑进行分析获得各逻辑回路参与表决的探测时间及需求失效概率,以所有泄漏扩散场景各级探测器的总探测时间最小化为目标函数,结合探测器数量和位置约束构建数学优化模型。其次以各候选探测器监测点为基因,基于遗传算法编写优化模型求解程序。最后利用泄漏扩散场景模拟数据作为输入值,求解得到不同探测器数量条件下的布置方案。通过对各布置方案的场景探测结果进行分析,验证了该方法在不同需求条件下的实用性。     

Optimizing inventory policies in process networks under uncertainty

We address the inventory planning problem in process networks under uncertainty through stochastic programming models. Inventory planning requires the formulation of multiperiod models to represent the time-varying conditions of industrial process, but multistage stochastic programming formulations are often too large to solve. We propose a policy-based approximation of the multistage stochastic model that avoids anticipativity by enforcing the same decision rule for all scenarios. The proposed formulation includes the logic that models inventory policies, and it is used to find the parameters that offer the best expected performance. We propose policies for inventory planning in process networks with arrangements of inventories in parallel and in series. We compare the inventory planning strategies obtained from the policy-based formulation and the analogous two-stage approximation of the multistage stochastic program. Sequential implementation of the planning strategies in receding horizon simulations shows the advantages of the policy-based model, despite the increase in computational complexity.     

Robust optimization and stochastic programming approaches for medium-term production scheduling of a large-scale steelmaking continuous casting process under demand uncertainty

Scheduling of steelmaking-continuous casting (SCC) processes is of major importance in iron and steel operations since it is often a bottleneck in iron and steel production. In practice, uncertainties are unavoidable and include demand fluctuations, processing time uncertainty, and equipment malfunction. In the presence of these uncertainties, an optimal schedule generated using nominal parameter values may often be suboptimal or even become infeasible. In this paper, we introduce robust optimization and stochastic programming approaches for addressing demand uncertainty in steelmaking continuous casting operations. In the robust optimization framework, a deterministic robust counterpart optimization model is introduced to guarantee that the production schedule remains feasible for the varying demands. Also, a two-stage scenario based stochastic programming framework is investigated for the scheduling of steelmaking and continuous operations under demand uncertainty. To make the resulting stochastic programming problem computationally tractable, a scenario reduction method has been applied to reduce the number of scenarios to a small set of representative realizations. Results from both the robust optimization and stochastic programming methods demonstrate robustness under demand uncertainty and that the robust optimization-based solution is of comparable quality to the two-stage stochastic programming based solution.     

Design under uncertainty of hydrocarbon biorefinery supply chains: Multiobjective stochastic programming models,decomposition algorithm,and a Comparison between CVaR and downside risk

A bicriterion, multiperiod, stochastic mixed‐integer linear programming model to address the optimal design of hydrocarbon biorefinery supply chains under supply and demand uncertainties is presented. The model accounts for multiple conversion technologies, feedstock seasonality and fluctuation, geographical diversity, biomass degradation, demand variation, government incentives, and risk management. The objective is simultaneous minimization of the expected annualized cost and the financial risk. The latter criterion is measured by conditional value‐at‐risk and downside risk. The model simultaneously determines the optimal network design, technology selection, capital investment, production planning, and logistics management decisions. Multicut L‐shaped method is implemented to circumvent the computational burden of solving large scale problems. The proposed modeling framework and algorithm are illustrated through four case studies of hydrocarbon biorefinery supply chain for the State of Illinois. Comparisons between the deterministic and stochastic solutions, the different risk metrics, and two decomposition methods are discussed. The computational results show the effectiveness of the proposed strategy for optimal design of hydrocarbon biorefinery supply chain under the presence of uncertainties. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Optimal PID controller tuning using stochastic programming techniques

We argue that stochastic programming provides a powerful framework to tune and analyze the performance limits of controllers. In particular, stochastic programming formulations can be used to identify controller settings that remain robust across diverse scenarios (disturbances, set‐points, and modeling errors) observed in real‐time operations. We also discuss how to use historical data and sampling techniques to construct operational scenarios and inference analysis techniques to provide statistical guarantees on limiting controller performance. Under the proposed framework, it is also possible to use risk metrics to handle extreme (rare) events and stochastic dominance concepts to conduct systematic benchmarking studies. We provide numerical studies to illustrate the concepts and to demonstrate that modern modeling and local/global optimization tools can tackle large‐scale applications. The proposed work also opens the door to data‐based controller tuning strategies that can be implemented in real‐time operations. © 2017 American Institute of Chemical Engineers AIChE J, 64: 2997–3010, 2018     

A stochastic programming approach for the Bayesian experimental design of nonlinear systems

Several approaches for the Bayesian design of experiments have been proposed in the literature (e.g., D-optimal, E-optimal, A-optimal designs). Most of these approaches assume that the available prior knowledge is represented by a normal probability distribution. In addition, most nonlinear design approaches involve assuming normality of the posterior distribution and approximate its variance using the expected Fisher information matrix. In order to be able to relax these assumptions, we address and generalize the problem by using a stochastic programming formulation. Specifically, the optimal Bayesian experimental design is mathematically posed as a three-stage stochastic program, which is then discretized using a scenario based approach. Given the prior probability distribution, a Smolyak rule (sparse-grids) is used for the selection of scenarios. Two retrospective case studies related to population pharmacokinetics are presented. The benefits and limitations of the proposed approach are demonstrated by comparing the numerical results to those obtained by implementing a more exhaustive experimentation and the D-optimal design.     

A flexible design framework for process systems under demand-side management

Demand response (DR) has been an appealing strategy for both residential and commercial/industrial customers of electricity due to the increasing penetration of renewable energy resources into the power grid and the deregulation of the energy markets. For industrial DR participants, the management of energy consumption along with the satisfaction of production expectations is generally referred to as demand-side management. Recent research in this area has focused mostly on process scheduling and capacity planning, especially for energy-intensive processes. This article presents a new direction through an optimization-based process design paradigm that allows for the potential reconfiguration of the process flow sheet in real time. Based on a case study of pump network design, a network superstructure is first defined, followed by a two-stage stochastic optimization model. The method of progressive hedging is used to solve the resulting mixed-integer stochastic programming problem. The results demonstrate that, under various scenarios, the reconfigurable design offers significant benefits compared to a fixed network structure in terms of total design cost and expected operating cost.     

Deciphering and handling uncertainty in shale gas supply chain design and optimization: Novel modeling framework and computationally efficient solution algorithm

The optimal design and operations of shale gas supply chains under uncertainty of estimated ultimate recovery (EUR) is addressed. A two‐stage stochastic mixed‐integer linear fractional programming (SMILFP) model is developed to optimize the levelized cost of energy generated from shale gas. In this model, both design and planning decisions are considered with respect to shale well drilling, shale gas production, processing, multiple end‐uses, and transportation. To reduce the model size and number of scenarios, we apply a sample average approximation method to generate scenarios based on the real‐world EUR data. In addition, a novel solution algorithm integrating the parametric approach and the L‐shaped method is proposed for solving the resulting SMILFP problem within a reasonable computational time. The proposed model and algorithm are illustrated through a case study based on the Marcellus shale play, and a deterministic model is considered for comparison. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3739–3755, 2015     

考虑原油性质波动的炼厂氢气网络集成优化

针对原油性质的不确定性,提出了一种基于质量传递机理的随机规划建模框架,以实现炼厂氢气网络在经济效益和抗扰能力上的同步优化。该框架耦合了常减压蒸馏、加氢精制以及闪蒸分离等过程单元,从微观上解析原油性质波动对网络运行的影响;采用了代理模型技术增设脱硫模块,并利用了二阶段随机规划方法改造管网,从宏观上优化氢气网络以满足生产要求。为验证所提方法的有效性和适用性,对某一现有的炼厂氢网络进行了改造设计研究。结果表明,集成过程单元的多场景优化策略能够有效提升网络的经济性能,并且能使其灵活应对因原油性质波动引起的操作场景的改变。     

一种新型搅拌桨多相混合性能研究

提出了一种新构型的搅拌桨一错位桨,并以空气-水-石英砂三相体系为研究对象,与传统的径流桨(Rushton桨)和轴流桨(斜叶桨)在功率消耗、混合时间、气体循环方面进行了比较.结果表明,错位桨相对于传统Rushton桨,功率消耗降低.适应气速范围广,轴向混合能力明显提升;在同等条件下与斜叶浆相比,气体分散能力强,混合时间少.这种新型桨能克服径向流叶轮在轴向混合方面能力的缺陷,有较好的潜在工业应用价值.     

基于带补偿随机规划的蒸汽动力系统优化设计

在蒸汽动力系统优化设计中,考虑不确定因素的优化策略能避免基于确定性设计策略的保守设计,并能针对不确定因素的实现提出相应的调度调节策略.本研究分析了蒸汽动力系统设计包含的不确定因素的特性及其对蒸汽动力系统优化目标和约束条件的影响.不确定因素的表达分成两类:基于时间变化表达和基于发生概率表达.对基于时间变化表达的因素,转化为多周期问题进行处理;对外部工艺过程变化引起的汽电需求不确定波动等基于发生概率表达的因素,应用随机规划策略,补偿不确定参数的实现可能引起的约束背离.基于本研究建立的多周期带补偿的二阶段随机规划MILP模型,求解蒸汽动力系统结构,同时优化调度调节策略,用调节决策和惩罚不足应对汽电需求等不确定因素的实现,实现系统安全稳定运行和经济效益最优.     

Shale gas pad development planning under price uncertainty

In this article, we study shale gas pad development under natural gas price uncertainty. We optimize the sequence of operations, gas curtailment, and storage on a single pad to maximize the net present value. The optimization problem is formulated as an mixed-integer linear programming model, which is similar to the one proposed by Ondeck et al. We investigate how natural gas price uncertainty affects the operation strategy in the pad development. Both two-stage and multistage stochastic programming are used as the mathematical framework to hedge against uncertainty. Our case study shows that there is value of using stochastic programming when the price variance is high. However, when the variance of the price is low, solving the stochastic programming problems does not create additional value compared with solving the deterministic problem.     

Capacity expansion planning through augmented Lagrangian optimization and scenario decomposition

Stochastic programming is a typical method for addressing the uncertainties in capacity expansion planning problem. However, the corresponding deterministic equivalent model is often intractable with considerable number of uncertainty scenarios especially for stochastic integer programming (SIP) based formulations. In this article, a hybrid solution framework consisting of augmented Lagrangian optimization and scenario decomposition algorithm is proposed to solve the SIP problem. The method divides the solution procedure into two phases, where traditional linearization based decomposition strategy and global optimization technique are applied to solve the relaxation problem successively. Using the proposed solution framework, a feasible solution of the original problem can be obtained after the first solution phase whereas the optimal solution is obtained after the second solution phase. The effectiveness of the proposed strategy is verified through a numerical example of two stage stochastic integer program and the capacity expansion planning examples. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

基于条件场景的不确定性石化供应链优化方法

针对产品需求及其价格存在不确定性的石化供应链计划层最优化问题,本文建立了一种基于条件场景的石化供应链最优化方法。用多个离散场景近似随机变量概率的连续分布,根据随机变量的概率分布特征,对场景发生的概率进行参数估计,进而建立了基于场景的两阶段混合整数线性规划(MILP)模型。利用基于场景的优化结果随离散网格数增加而逐渐趋近连续的随机优化结果这一规律,给出了获得最佳离散网格数的方法,实现了计算时间成本与计算精度之间的平衡。在此基础上引入条件概率方法,利用两个随机变量间的相关性,建立了以产品价格及其需求量为不确定性的石化供应链优化方法。结果表明,与传统未考虑随机变量间相关性的一般场景划分方法相比,本文基于条件场景的随机优化方法可以更快地获得最佳场景数目,进而有效降低了计算量。     

A stochastic programming approach for clinical trial planning in new drug development

The paper presents a multi-stage stochastic programming formulation for the planning of clinical trials in the pharmaceutical research and development (R&D) pipeline. Scenarios are used to account for the endogenous uncertainty in clinical trial outcomes. Given a portfolio of potential drugs and limited resources, the model determines the trials to be performed in each planning period and scenario. To reduce the size of the formulation we employ a reduced set of scenarios without compromising the quality of uncertainty representation. Furthermore, we present a number of ideas that allow us to reduce the number of non-anticipativity constraints necessary to model indistinguishable scenarios. The proposed approach is the first stochastic programming formulation to address this problem.