Column Case Study Research Articles

Model Predictive Control of an Industrial Distillation Column Based on a Hybrid Model: Adapting the Domain of Validity

In any model predictive control (MPC) implementation, the key factor is the quality of the employed system model in order to guarantee constraint satisfaction and to optimize the performance of the controlled system. However, it is difficult in practice to model all the phenomena of the true system which leads to plant-model mismatch. We propose to augment a simple first principles based model with a machine learning model to capture the plant dynamics which are not represented in the semi-rigorous model. The use of data-based models however can be problematic outside the region where the model was trained. In this work, we estimate the domain of validity of the data-based model using a one-class support vector machine (SVM) which is trained on a low-dimensional projection of the available training data. During the application of the controller, data of newly visited regions is collected and the domain of validity is adapted based on checking a performance criterion. The hybrid model incorporates a weighted contribution of the data-based model based on its predicted validity. We demonstrate the versatility and the benefits of the proposed adaptive MPC based on a hybrid model (AHMPC) approach via an industrial distillation column case study.

A port-stream based equation oriented modelling of complex distillation column: A dividing wall column case study

Dividing wall column (DWC) offers higher degree of freedom in comparison with the conventional column. Furthermore, the different sections configurations within the column are highly interacting with several recycle loops. Facing with such complex unit operation, describing its behaviour encourages the focal point on the resolution of ideal modelling approaches. Equation oriented (EO) modelling of DWC has been studied by several researchers involving complex algorithm and methodology. In this work, a new approach for modelling of DWC is presented. The modelling methodology involves variables connectivity based on ports and streams that is admissible to equation-oriented flow sheet. To verify the functionality of the proposed method, the modelled DWC is validated with two case studies depicted from experimental literature data to separate alcohol mixture and fatty acid fractionation. The model development was performed in MOSAIC, a web-based modelling tool and run in gPROMS. The model shows good convergence and has less than 10% error when compared to the above mentioned case studies. To furthermore extend the model capability, relative gain array (RGA) analysis was conducted for the fatty acid fractionation to determine the best control configuration in DWC. Result shows that L-S-V and L-S-B configurations are the best control configurations. Our analysis also shows that reflux flowrate, side flowrate and vapor boilup are best to control distillate product, side product and bottom product, respectively.

A post-stream based equation oriented modelling of complex distillation column: a dividing wall column case study

Dividing wall column (DWC) offers higher degree of freedom in comparison with the conventional column. Furthermore, the different sections configurations within the column are highly interacting with several recycle loops. Facing with such complex unit operation, describing its behaviour encourages the focal point on the resolution of ideal modelling approaches. Equation oriented (EO) modelling of DWC has been studied by several researchers involving complex algorithm and methodology. In this work, a new approach for modelling of DWC is presented. The modelling methodology involves variables connectivity based on ports and streams that is admissible to equation-oriented flow sheet. To verify the functionality of the proposed method, the modelled DWC is validated with two case studies depicted from experimental literature data to separate alcohol mixture and fatty acid fractionation. The model development was performed in MOSAIC, a web-based modelling tool and run in gPROMS. The model shows good convergence and has less than 10% error when compared to the abovementioned case studies. To furthermore extend the model capability, relative gain array (RGA) analysis was conducted for the fatty acid fractionation to determine the best control configuration in DWC. Result shows that L-S-V and L-S-B configurations are the best control configurations. Our analysis also shows that reflux flowrate, side flowrate and vapor boilup are best to control distillate product, side product and bottom product respectively.

A Parametric Study of Confinement Effects to the Interaction Diagram of P-M for High-Strength Concrete Columns

In reinforced concrete columns design, P-M interaction diagram is used as axial load control and column bending without taking into account the effect of lateral reinforcement bars. Design principles that ignore the effect of reinforcement bars will result in low value of actual axial capacity of column. This paper presents the effect of lateral reinforcement with a case study of square-sectional columns on high-strength concrete. The equation of unconfined concrete strength enhancement is based on Mander, Legeron, Imran, Antonius and Muguruma models. The reviewed parameters include compressive strength of concrete, reinforcement configuration, and spacings of confinement. The result of the analysis is a comparison of P-M diagram based on confinement models. It shows that confinement significantly influences axial capacity of column, yet it has a certain collapse point at point P = 0 in all models. This is caused by longitudinal reinforcement system. Configuration of reinforcement, spacing and confinement models greatly affects the collapse behavior of column, whether the collapse is classified as compressive collapse or tensile collapse based on the P-M diagram.

Controller Design and Sparse Measurement Selection in Self-optimizing control

Self-optimizing control focuses on minimizing loss for processes in the presence of disturbances by holding selected controlled variables at constant set-points. A measurement combination can be found, using the Null-space method, which further reduces the loss. Since self-optimizing control focuses on the steady-state operation, little attention has been put on the dynamic performance when selecting measurement combinations. In this work, an iterative LMI approach is combined with the sparsity promoting weighted l1-norm, to find a measurement subset together with PI controllers for the Null-space method. The measurement combination and the controllers are designed such that, the dynamic response is improved when the process is facing disturbances. The proposed method is illustrated on a Petlyuk column case study.

Operational loss modelling for process facilities using multivariate loss functions

This paper presents a methodology to develop multivariate loss functions to measure the operational loss of process facilities. The proposed methodology uses loss functions to provide a model for operational loss due to deviation of key process characteristics from their target values. Having estimated the marginal loss functions for each monitored process variable, copula functions are then used to link the univariate margins and develop the multivariate loss function. The maximum likelihood evaluation method is used to estimate the copula parameters. Akaike's information criterion (AIC) is then applied to rank the copula models and choose the best fitting copula. A simulation study is provided to demonstrate the efficiency of the copula estimation procedure. The flexibility of the proposed approach in using any form of the symmetrical and asymmetrical loss functions and the practical application of the methodology are illustrated using a separation column case study.

Probabilistic modeling of business interruption and reputational losses for process facilities

This article presents probabilistic models to estimate business losses due to abnormal situations in process facilities. The main elements of business loss are identified as business interruption loss and reputational loss. The business interruption insurance approach is used to model business interruption loss. The subelements of business interruption loss are modeled based on expert knowledge using Program Evaluation Review Technique, which are then integrated using the Monte Carlo simulation approach. The reputational loss is considered as Weibull distributed, and the parameters are estimated by applying a scenario‐based approach. Copula functions are then used to develop the distribution of the aggregate loss, considering the correlation between business interruption and reputational losses. The application of the loss models is demonstrated using a distillation column case study. The models presented here provide a mechanism to monitor process facility's business performance, with associated uncertainties, and to make swift operational and safety decisions. This will help to improve process facilities safety performance and optimal allocation of resources where they are needed the most. © 2015 American Institute of Chemical Engineers Process Saf Prog 34: 373–382, 2015

Engineering geometrically bi-linear columns to deliver fire resistance: Standard heating

This paper demonstrates the need for structural fire engineering in the design and specification of unusual structural arrangements. It is found that the required fire resistance of a structure cannot necessarily be achieved by considering only the fire resistance of individual elements of structure. A case study of columns that have a change of direction over their height (geometrically bi-linear columns) is used to illustrate how unusual arrangements may lead to early failure of key structural elements – even where design guidance is followed. These arrangements are parameterised to allow the relative importance of a number of key variables to be studied. A methodology is developed to estimate the required limiting temperature for the governing elements of the assembly in order to deliver the required performance.

Loss scenario analysis and loss aggregation for process facilities

This study presents an overall loss modelling methodology for process facilities. The methodology comprises loss scenario identification and aggregation of losses due to process deviations. The identification of loss scenarios and determination of the time periods at which a process experiences each scenario are described first. Then, the application of the copula functions and their integration with the Monte Carlo (MC) approach are proposed to address the existing challenge of loss aggregation for multiple-loss scenarios. The proposed loss aggregation provides a flexible and realistic approach to construct joint multivariate distribution of the losses by considering their interdependence. The sensitivity of the model to the choice of correlation parameters is investigated. The results serve as a reminder to risk analysts about the significance of choosing an appropriate loss aggregation model for risk analysis purposes. The application of the methodology is demonstrated using a distillation column case study.

On The Way To Autonomous Model Predictive Control: A distillation column simulation study

Model Predictive Control (MPC) is a powerful tool in the control of large scale chemical processes and has become the standard method for constrained multivariable control problems. Hence, the number of MPC applications is increasing steadily and it is being used in application domains other than petrochemical industries. A common observation by the industrial practitioners is that success of any MPC application requires not only encient initial deployment but also maintenance of initial effectiveness. To this end, we propose a novel high level automated support strategy for MPC systems. Such a strategy consists of components such as performance monitoring, performance diagnosis, least costly closed loop experiment design, re-identification and autotuning. This work presents the novel technological developments in each component and demonstrates them on a distillation column case study. We show that automated support strategy restores nominal performance after a performance drop is detected and takes the right course of action depending on its cause.

WORST CASE OF RELATIVE DISTURBANCE GAIN ARRAY FOR UNCERTAIN DISTILLATION SYSTEM

This article discusses the constrained nonlinear optimization formulation for calculating the worst case of lower and upper bounds of relative disturbance gain array (RDGA) for uncertain process models. The proposed approach seeks the minimum and maximum values of the relative disturbance gains subject to the constraints in which the process and disturbance gains are within their uncertainty ranges. RDGA ranges are useful for control structure determination and the related robustness, as they provide information regarding the sensitivity to gain uncertainties. The proposed method is demonstrated by ternary distillation column case study. Closed loop simulation results support the analysis based on the proposed method. It is shown that for a particular degree of uncertainties, the range of process gain determinant should not include zero to ensure the successfulness of the calculation. For the distillation system being studied, the maximum allowable α is 0.339 to avoid the singularity of matrix K.

Branch and bound method for regression-based controlled variable selection

Self-optimizing control is a promising method for selection of controlled variables (CVs) from available measurements. Recently, Ye, Cao, Li, and Song (2012) have proposed a globally optimal method for selection of self-optimizing CVs by converting the CV selection problem into a regression problem. In this approach, the necessary conditions of optimality (NCO) are approximated by linear combinations of available measurements over the entire operation region. In practice, it is desired that a subset of available measurements be combined as CVs to obtain a good trade-off between the economic performance and the complexity of control system. The subset selection problem, however, is combinatorial in nature, which makes the application of the globally optimal CV selection method to large-scale processes difficult. In this work, an efficient branch and bound (BAB) algorithm is developed to handle the computational complexity associated with the selection of globally optimal CVs. The proposed BAB algorithm identifies the best measurement subset such that the regression error in approximating NCO is minimized and is also applicable to the general regression problem. Numerical tests using randomly generated matrices and a binary distillation column case study demonstrate the computational efficiency of the proposed BAB algorithm.

An artificial immune system for adaptive fault detection, diagnosis and recovery

The human immune system provides rich metaphors for adaptive pattern recognition. Fault detection and diagnosis in chemical processes is commonly formulated as a pattern recognition problem. However, conventional methods for fault diagnosis often do not have a mechanism to adapt and learn as the process changes over time. In this paper, we propose an Artificial Immune System (AIS) framework that endows learning to statistical process monitoring techniques such as Principal component analysis. The proposed AIS framework also provides a direct means to incorporate recovery actions after a failure has been detected and diagnosed. We demonstrate the efficacy of the proposed framework using a simulated binary distillation column case study.

Quantitative methods for optimal regulatory layer selection

Controlled variables selection based on economic objectives using self optimizing concepts are developed. In this paper, we extend the self optimizing control ideas to find optimal controlled variables in the regulatory layer. The regulatory layer is designed to facilitate stable operation, to regulate and to keep the operation in the linear operating range and its performance is here quantified using the state drift criterion. Quantitative methods are proposed and evaluated on a distillation column case study with 41 stages that minimize state drift in composition states to obtain optimal regulatory layer with 1,2 and more closed loops.

Optimal Controlled Variable Selection with Structural Constraints Using MIQP Formulations

AbstractOptimal control structure selection is vital to operate the process plants optimally in the presence of disturbances. In this paper we review the controlled variable selection, c = Hy, where y includes all the measurements. The objective is to find the matrix H such that steady-state operation is optimized while controlled variables c's are kept constant using inputs, when there are disturbances. Several cases are studied such as the optimal individual measurements, the optimal combinations of fewer/all measurements and the optimal combinations with structural constraints. The proposed methods are evaluated on a distillation column case study with 41 trays.

Bidirectional Branch and Bound for Controlled Variable Selection Part III: Local Average Loss Minimization

The selection of controlled variables (CVs) from available measurements through exhaustive search is computationally forbidding for large-scale processes. We have recently proposed novel bidirectional branch and bound (B3) approaches for CV selection using the minimum singular value (MSV) rule and the local worst-case loss criterion in the framework of self-optimizing control. However, the MSV rule is approximate and worst-case scenario may not occur frequently in practice. Thus, CV selection by minimizing local average loss can be deemed as most reliable. In this work, the B3 approach is extended to CV selection based on local average loss metric. Lower bounds on local average loss and, fast pruning and branching algorithms are derived for the efficient B3 algorithm. Random matrices and binary distillation column case study are used to demonstrate the computational efficiency of the proposed method.

MIQP formulation for Controlled Variable Selection in Self Optimizing Control

In order to facilitate the optimal operation in the presence of process disturbances, the optimal selection of controlled variables plays a vital role. In this paper, we present a Mixed Integer Quadratic Programming methodology to select controlled variables c=Hy as the optimal combinations of fewer/all measurements of the process. The proposed method is evaluated on a toy test problem and on a binary distillation column case study with 41 trays.

Bidirectional branch and bound for controlled variable selection. Part II: Exact local method for self-optimizing control

The selection of controlled variables (CVs) from available measurements through enumeration of all possible alternatives is computationally forbidding for large-dimensional problems. In Part I of this work [Cao, Y., & Kariwala, V. (2008). Bidirectional branch and bound for controlled variable selection: Part I. Principles and minimum singular value criterion. Comput. Chem. Eng., 32 (10), 2306–2319], we proposed a bidirectional branch and bound (BAB) approach for subset selection problems and demonstrated its efficiency using the minimum singular value criterion. In this paper, the BAB approach is extended for CV selection using the exact local method for self-optimizing control. By redefining the loss expression, we show that the CV selection criterion for exact local method is bidirectionally monotonic. A number of novel determinant based criteria are proposed for fast pruning and branching purposes resulting in a computationally inexpensive BAB approach. We also establish a link between the problems of selecting a subset and combinations of measurements as CVs and present a partially bidirectional BAB method for selection of measurements, whose combinations can be used as CVs. Numerical tests using randomly generated matrices and binary distillation column case study demonstrate the computational efficiency of the proposed methods.

Bidirectional Branch and Bound Method for Selecting Controlled Variables

Controlled variable (CV) selection from available measurements through exhaustive search is computationally forbidding for large-scale problems. We have recently proposed novel bidirectional branch and bound (B 3 ) approaches for CV selection using the minimum singular value (MSV) rule and the local worst-case loss criterion in the framework of self-optimizing control. However, the MSV rule is approximate and worst-case scenario may not occur frequently in practice. In this work, the B 3 approach is extended to CV selection based on the recently developed local average loss metric, which represents the expected loss incurred over the long-term operation of the plant. Lower bounds on local average loss and fast pruning algorithms are derived for the efficient B 3 algorithm. Numerical tests and binary distillation column case study are used to demonstrate the computational efficiency of the proposed method.

Fuzzy risk matrix

A risk matrix is a mechanism to characterize and rank process risks that are typically identified through one or more multifunctional reviews (e.g., process hazard analysis, audits, or incident investigation). This paper describes a procedure for developing a fuzzy risk matrix that may be used for emerging fuzzy logic applications in different safety analyses (e.g., LOPA). The fuzzification of frequency and severity of the consequences of the incident scenario are described which are basic inputs for fuzzy risk matrix. Subsequently using different design of risk matrix, fuzzy rules are established enabling the development of fuzzy risk matrices. Three types of fuzzy risk matrix have been developed (low-cost, standard, and high-cost), and using a distillation column case study, the effect of the design on final defuzzified risk index is demonstrated.