Fernando V. Lima

OPERABILITY OF MULTIVARIABLE NON-SQUARE SYSTEMS

Abstract Non-square process control systems, with fewer inputs than the controlled outputs, are quite common in chemical processes. In these systems, it is impossible to control all measured variables at specific set points and many of the outputs are controlled within an interval. The objective of this paper is to introduce a multivariable Operability methodology for such non-square systems to be used in the design of nonsquare constrained controllers. In order to motivate the new concepts, we examine some simple non-square systems obtained from the control system of a Steam Methane Reformer process.

MODEL PREDICTIVE CONTROL AND DYNAMIC OPERABILITY STUDIES IN A STIRRED TANK: RAPID TEMPERATURE CYCLING FOR CRYSTALLIZATION

A stirred-tank reactor was built with the objective of rapid and accurate temperature control in the reaction vessel. A first-principles heat transfer model was developed for the jacketed batch system, with the jacket inlet temperature used to control the vessel temperature. A model predictive controller was implemented to follow a rapidly changing temperature profile that cycled between steep heating and cooling motifs, and it was tested experimentally at progressively shorter temperature cycles. For a water-solvent-water-jacket system, a cycle consisting of increasing and decreasing the temperature by 15°C over a period of 20 min was achieved in practice. The performance of the MPC controller was explained by calculating the dynamic operability characteristics of the process.

Analysis of the constraint characteristics of a Sheet Forming Control Problem using interval operability concepts

An Interval Operability-based approach [1, 2] is applied to calculate operable output constraints for the Sheet Forming Control Problem (SFCP) from DuPont. The SFCP attempts to control the sheet thickness at 15 different points, which represent 15 output variables, using 9 manipulated variables in the presence of 3 disturbances. Thus, this problem represents a computationally complex, high-dimensional non-square system with more outputs than inputs. The SFCP is addressed here under two study cases: 1) a non-square, where all the 15 outputs are controlled independently of each other; 2) a square, where 6 outputs are combined in pairs, or zone variables, and controlled within their corresponding zone. Results show that significant reduction of the constrained region of process operation can be achieved for different output targets specified. Specifically, the hyper-volume ratio of the initial to the designed constrained regions range between 103–105. The calculated constraints are validated by running DMCplusTM (Aspen Tech) simulations for the extreme values of the disturbances. These constraints are intended for use online in model-based controllers (e.g., Model Predictive Control) to calculate the tightness with which each of the outputs can be controlled.

ON THE OPERABILITY OF HIGH-ORDER MULTIVARIABLE NON-SQUARE SYSTEMS

Abstract Non-square process control systems, with fewer inputs than the controlled outputs, are quite common in industrial chemical processes. In these systems, it is impossible to control all the outputs at specific set-points and thus, many of them are controlled within intervals. The objective of this paper is to extend the non-square Operability methodology proposed by Lima and Georgakis (2006) to high-order systems to be used in the design of non-square constrained controllers. This is achieved by analyzing the general problem with n outputs, m inputs and 1 disturbance. The developed methodology is applied to non-square systems obtained from industrial problems.

Modeling and Design Optimization of Multifunctional Membrane Reactors for Direct Methane Aromatization

Due to the recent increase of natural gas production in the U.S., utilizing natural gas for higher-value chemicals has become imperative. Direct methane aromatization (DMA) is a promising process used to convert methane to benzene, but it is limited by low conversion of methane and rapid catalyst deactivation by coking. Past work has shown that membrane separation of the hydrogen produced in the DMA reactions can dramatically increase the methane conversion by shifting the equilibrium toward the products, but it also increases coke production. Oxygen introduction into the system has been shown to inhibit this coke production while not inhibiting the benzene production. This paper introduces a novel mathematical model and design to employ both methods in a multifunctional membrane reactor to push the DMA process into further viability. Multifunctional membrane reactors, in this case, are reactors where two different separations occur using two differently selective membranes, on which no systems studies have been found. The proposed multifunctional membrane design incorporates a hydrogen-selective membrane on the outer wall of the reaction zone, and an inner tube filled with airflow surrounded by an oxygen-selective membrane in the middle of the reactor. The design is shown to increase conversion via hydrogen removal by around 100%, and decrease coke production via oxygen addition by 10% when compared to a tubular reactor without any membranes. Optimization studies are performed to determine the best reactor design based on methane conversion, along with coke and benzene production. The obtained optimal design considers a small reactor (length = 25 cm, diameter of reaction tube = 0.7 cm) to subvert coke production and consumption of the product benzene as well as a high permeance (0.01 mol/s·m2·atm1/4) through the hydrogen-permeable membrane. This modeling and design approach sets the stage for guiding further development of multifunctional membrane reactor models and designs for natural gas utilization and other chemical reaction systems.

Dynamic Operability for the Calculation of Transient Output Constraints for Non-Square Linear Model Predictive Controllers

Abstract Abstract This paper introduces a dynamic operability-based approach for the determination of feasible output constraints during transient operation. This approach is based on previously published steady-state operability developments and the concept of output funnels. In this study, high-dimensional non-square systems with more outputs than inputs are of particular interest. Such systems are challenging because it is impossible to control all the outputs at specific set-points when there are fewer degrees of freedom available than the controlled variables. Thus, interval, instead of set-point, control is needed for at least some of the output variables. In order to motivate the new concepts, two non-square case studies are addressed, one illustrative and one industrial - obtained from the control system of a Steam Methane Reformer process. The calculated constraints are validated by running DMCplus™ (AspenTech) closed-loop simulations for the extreme values of the disturbances. These constraints are intended for use online in model-based controllers (e.g., Model Predictive Controllers) to ensure that each of the outputs will remain inside a feasibility envelope during transient operation.