Helen Durand

Process operational safety using model predictive control based on a process Safeness Index

Abstract It has been repeatedly suggested that the common cause-and-effect approach to evaluating process safety has deficiencies that could be addressed by a systems engineering perspective. A systems approach should consider safety as a system-wide property and thus would be required to integrate all aspects of the process involved with monitoring or manipulating the process dynamics, including the control, alarm, and emergency shut-down systems while operating them independently for redundancy. In this work, we propose initial steps in the first systems safety approach that coordinates the control and safety systems through a common metric (a Safeness Index) and develop a controller formulation that incorporates this index. Specifically, this work presents an economic model predictive control (EMPC) scheme that utilizes a Safeness Index function as a hard constraint to define a safe region of operation termed the safety zone. Under the proposed EMPC design, the closed-loop state of a nonlinear process is guaranteed to enter the safety zone in finite time in the presence of uncertainty while maximizing a stage cost that reflects the economics of the process. Closed-loop stability is established for a nonlinear process under the proposed implementation strategy.

Economic model predictive control designs for input rate-of-change constraint handling and guaranteed economic performance

Abstract Economic model predictive control (EMPC) has been a popular topic in the recent chemical process control literature due to its potential to improve process profit by operating a system in a time-varying manner. However, time-varying operation may cause excessive wear of the process components such as valves and pumps. To address this issue, input magnitude constraints and input rate-of-change constraints can be added to the EMPC optimization problem to prevent possible frequent and extreme changes in the requested inputs. Specifically, we develop input rate-of-change constraints that can be incorporated in Lyapunov-based EMPC (LEMPC) that ensure controller feasibility and closed-loop stability. Furthermore, we develop a terminal equality constraint for LEMPC that can ensure that the performance of LEMPC is at least as good as that of a Lyapunov-based controller in finite-time and in infinite-time. Chemical process examples demonstrate the incorporation of input rate-of-change constraints and terminal state constraints in EMPC.

Elucidation of the role of constraints in economic model predictive control

Abstract Economic model predictive control (EMPC) is a predictive feedback control methodology that unifies economic optimization and control. EMPC uses a stage cost that reflects the process/system economics. In general, the stage cost used is not a quadratic stage cost like that typically used in standard tracking model predictive control. In this paper, a brief overview of EMPC methods is provided. In particular, the role of constraints imposed in the optimization problem of EMPC for feasibility, closed-loop stability, and closed-loop performance is explained. Three main types of constraints are considered including terminal equality constraints, terminal region constraints, and constraints designed via Lyapunov-based techniques. The paper closes with a well-known chemical engineering example (a non-isothermal CSTR with a second-order reaction) to illustrate the effectiveness of time-varying operation to improve closed-loop economic performance compared to steady-state operation and to demonstrate the impact of economically motivated constraints on optimal operation.

Temperature balancing in steam methane reforming furnace via an integrated CFD/data-based optimization approach

Abstract In this work, we introduce a furnace-balancing scheme that generates an optimal furnace-side feed distribution that has the potential to improve the thermal efficiency of a reformer. The furnace-balancing scheme is composed of four major components: data generation, model identification, a model-based furnace-balancing optimizer and a termination checker. Initially, a computational fluid dynamics (CFD) model of an industrial-scale reformer, developed in our previous work, is used for the data generation as the model has been confirmed to simulate the typical transport and chemical reaction phenomena observed during reformer operation, and the CFD simulation data is in good agreement with various sources in literature. Then, we propose a model identification process in which the algorithm is formulated based on the least squares regression method, basic knowledge of radiative heat transfer and the existing furnace-side flow pattern. Subsequently, we propose a model-based furnace-balancing optimizer that is formulated as an optimization problem within which the valve position distribution is the decision variable, and minimizing the sum of the weighted squared deviations of the outer reforming tube wall temperatures from a set-point value for all reforming tubes with a penalty term on the deviation of the valve positions from their fully open positions is the objective function. CFD simulation results provide evidence that the optimized furnace-side feed distribution created by the furnace-balancing scheme can reduce the severity of nonuniformity in the spatial distribution of furnace-side temperature in the combustion chamber even when the reformer is under the influence of common valve-related disturbances.

Process operational safety via model predictive control: Recent results and future research directions

Abstract The concept of maintaining or enhancing chemical process safety encompasses a broad set of considerations which stem from management/company culture, operator procedures, and engineering designs, and are meant to prevent incidents at chemical plants. The features of a plant design that take action to prevent incidents on a moment-by-moment basis are the control system and the safety system (i.e., the alarm system, safety instrumented system, and safety relief system). Though the control and safety systems have a common goal in this regard, coordination between them has been minimal. One impediment to such an integrated control-safety system design is that the traditional industrial approach to safety focuses on root causes of incidents and on keeping individual measured variables within recommended ranges, rather than seeking to understand incidents from a more fundamental perspective as the result of the dynamic process state evolving to a value at which consequences to humans and the environment occur. This work reviews the state of the art in control system designs that incorporate explicit safety considerations in the sense that they have constraints designed to prevent the process state from taking values at which incidents can occur and in the sense that they are coordinated with the safety system. The intent of this tutorial is to unify recent developments in this area and to encourage further research by showcasing that the topic, though critical for safe operation of chemical processes particularly as we move to more tightly integrated and economics-focused operating strategies, is in its infancy and that many open questions remain.

Stiction compensation via model predictive control

In this work, we develop a model predictive control (MPC) strategy incorporating stiction dynamics, input rate of change constraints, and actuation magnitude constraints as a stiction compensation methodology. Stiction is a nonlinear friction phenomenon that causes poor performance of control loops in the process industries. In this work, we develop an MPC formulation including detailed valve dynamics for a sticky valve and additional constraints on the input rate of change and actuation magnitude to reduce control loop performance degradation and to prevent the MPC from requesting physically unrealistic control actions from the valve due to stiction. Using a chemical process example with an economic model predictive controller (EMPC), we demonstrate the selection of appropriate constraints for the proposed method and show that the incorporation of the stiction dynamics and actuation magnitude constraints in the EMPC improves its selection of control actions so that the valves are able to reach the set-points requested by the EMPC and to meet operating constraints.

Safe economic model predictive control of nonlinear systems

Abstract This work focuses on the design of a new class of economic model predictive control (EMPC) systems for nonlinear systems that address simultaneously the tasks of economic optimality, safety and closed-loop stability. This is accomplished by incorporating in the EMPC an economics-based cost function and Control Lyapunov-Barrier Function (CLBF)-based constraints that ensure that the closed-loop state does not enter unsafe sets and remains within a well-characterized set in the system state-space. The new class of CLBF-EMPC systems is demonstrated using a nonlinear chemical process example.

Distributed economic model predictive control with Safeness-Index based constraints for nonlinear systems

Abstract In this work, sequential and iterative distributed economic model predictive control (DEMPC) architectures are developed with constraints based on a metric (termed the Safeness Index) that is indicative of the safeness of operating a process at a given state in state-space. The DEMPC’s may have lower computation times than a centralized economic model predictive control (EMPC) design with Safeness Index-based constraints, without significantly limiting closed-loop economic performance, which enhances their practicality and ability to improve process operational safety. Sufficient conditions are derived under which the implementation strategies for the DEMPC’s guarantee closed-loop stability.

CFD Modeling of a Pilot-Scale Steam Methane Reforming Furnace

Hydrogen is a required key material for petroleum refineries that convert crude oil into a variety of products with higher economic value, e.g., gasoline. In chemical process plants and petroleum refineries, hydrogen is produced primarily by the steam methane reforming (SMR) process synthesizing hydrogen and carbon oxides from methane and superheated steam in the presence of a nickel-based catalyst network in a steam methane reformer. Traditionally, the optimized and profitable operating conditions of a steam methane reformer are analyzed and determined by on-site parametric study at industrial-scale plants or pilot-scale units, which is an experimental approach, and therefore, it must be conducted by changing process parameters in small increments over a long time period in order to prevent significant production and capital loss. Motivated by the above considerations, the present work focuses on developing a computational fluid dynamics (CFD) model of a pilot-scale steam methane reformer comprised of four industrial-scale reforming reactors, three industrial-scale burners and three flue gas tunnels. The pilot-scale reformer CFD model is developed by analyzing well-established physical phenomena, i.e., the transport of momentum, material and energy, and chemical reactions, i.e., combustion and the SMR process, that take place inside the steam methane reformer. Specifically, the \(P-1\) radiation model, standard \(k-\epsilon \) turbulence model, compressible ideal gas equation of state and finite rate/eddy dissipation (FR/ED) turbulence-chemistry interaction model are adopted to simulate the macroscopic and microscopic events in the reformer. The conditions for the tube-side feed, burner feed and combustion chamber refractory walls are consistent with typical reformer plant data Latham (2008) so that the simulation results generated by the pilot-scale reformer can be validated by the plant data. The simulation results are shown to be in agreement with publicly available plant data reported in the literature and also with the simulation data generated by a well-developed single reforming tube CFD model. Subsequently, the proposed pilot-scale reformer CFD model is employed for a parametric study of the mass flow rate of the burner feed, i.e., a \(20\,\%\) increase from its nominal value. The corresponding simulation results demonstrate the advantages offered by this CFD model for parametric study by showing that with the increased burner feed, the outer reforming tube wall temperature exceeds the maximum allowable temperature; these results were developed quickly with the aid of a CFD model, compared to the timescale on which parametric studies are performed on-site and without the potential for rupture of the reforming tubes during the study.

Integrating production scheduling and process operation via economic model predictive control

Managing production schedules and tracking time-varying demand of certain products while optimizing process economics are subjects of central importance in industrial applications. Production schedule following is generally required for a small subset of the total process state vector. Motivated by this, the present work proposes an approach that targets achieving the desired production schedule while maximizing economics using economic model predictive control (EMPC), which is a feedback control approach that optimizes plant economics in a receding horizon fashion. Conditions for closed-loop stability are derived for a general class of nonlinear systems. The proposed EMPC scheme was applied to a chemical process example where the product concentration was requested to follow a certain production schedule. Simulation results demonstrate that the proposed EMPC was able to maintain closed-loop stability, achieve the desired production schedule, and maximize plant economics.