Continuous Stirred Tank Reactor Case Research Articles

Closed‐loop dynamic real‐time optimization with stabilizing model predictive control

AbstractDynamic real‐time optimization (DRTO) is a supervisory strategy at the upper level of the industrial process automation architecture that computes economically optimal set‐point trajectories that are in turn passed on to the lower‐level model predictive control (MPC) for tracking. The economically optimal solution, in several process industries, could lead to operating the plant at or around an unstable steady state. The present article accounts for this by developing a closed‐loop DRTO (CL‐DRTO) formulation that enables handling unstable operating points via an underlying MPC with stability constraints. To this end, a stabilizing MPC that handles trajectory tracking for unstable systems is embedded within the upper‐level DRTO. The resulting CL‐DRTO problem is reformulated by applying a simultaneous solution approach. The economic benefits realized by the proposed strategy are illustrated through applications to both linearized and nonlinear dynamic models for single‐input single‐output and multi‐input multi‐output continuous stirred tank reactor case studies.

Sensitivity-assisted Robust Nonlinear Model Predictive Control with Scenario Generation

We propose a sensitivity-assisted multistage Nonlinear Model Predictive Control strategy, called samNMPC, to address multistage stochastic programs for robust NMPC. Our approach divides the scenario sets in the stochastic programming formulation into critical and noncritical sets. Critical scenarios are selected by scenario generation based on worst-case constraint determination, while stage costs for noncritical scenarios are determined by sensitivity-based approximations. The resulting multi-stage NMPC problem leads to a first order accurate control profile that satisfies all constraints under uncertainty. Moreover, computational costs of this formulation scale independently of the number of disturbance variables, and only linearly with the robust horizon and number of constraints. Our proposed approach is illustrated on a CSTR (continuous stirred tank reactor) case study with two uncertain parameters. Compared to competing approaches, samNMPC delivers robust performance of multi-stage NMPC with significantly less computational cost.

Bond graph modeling for fault diagnosis: the continuous stirred tank reactor case study

Supervision of chemical and biochemical processes is difficult due to various factors, for example the evolution of nonlinear state variables, uncertainties in parameters and disturbances, and system operating conditions. The complexities arise out of the energetic couplings in the model. In this work, the bond graph representation, as a unified and multidisciplinary tool, is used for dynamic modeling and diagnosis for process engineering, incorporating the chemical kinetics of an equilibrated reaction, heat and mass transport phenomena. A pseudo bond graph model technique is applied to a pilot reactor fitted with a mono-fluid heating/cooling system. A modeling structure has been implemented through process sub-units and validated through experimental observations. This technique is proposed to indicate physico-chemical failures, for example matter leakage, caloric isolation, or the occurrence of a secondary reaction or temperature runaway when a very exothermic reaction occurs. It provides the computational algorithms to eliminate unknown variables from coupled thermochemical models and thus generate analytical redundancy relations (ARRs) in terms of measurements and parameters for online diagnosis.

A model of protocell based on the introduction of a semi-permeable membrane in a stochastic model of catalytic reaction networks

In this work we introduce some preliminary analyses on the role of a semi-permeable membrane in the dynamics of a stochastic model of catalytic reaction sets (CRSs) of molecules. The results of the simulations performed on ensembles of randomly generated reaction schemes highlight remarkable differences between this very simple protocell description model and the classical case of the continuous stirred-tank reactor (CSTR). In particular, in the CSTR case, distinct simulations with the same reaction scheme reach the same dynamical equilibrium, whereas, in the protocell case, simulations with identical reaction schemes can reach very different dynamical states, despite starting from the same initial conditions.

From Brayton-Moser formulation to Port Hamiltonian representation: the CSTR case study

AbstractThis paper shows that any thermodynamic potential fulfilling some thermodynamic stability criterion (e.g. the chemical affinity or the ectropy) can be used as a potential function for the dissipative (pseudo) Port Hamiltonian formulation of the non isothermal Continuous Stirred Tank Reactor (CSTR) model. Besides Brayton-Moser formulation is used to obtain some dissipative Port Hamiltonian representation.

Thermodynamics and chemical systems stability: The CSTR case study revisited

This paper is dedicated to the stability analysis of the Continuous Stirred Tank Reactor (CSTR) model by considering thermodynamics based arguments. Different Lyapunov function candidates related to the thermodynamics, more specifically based on the entropy, the entropy production and the internal energy, are considered. These provide new insight and physical interpretation in the stability/instability of the equilibrium points of the CSTR. This includes in particular extension of the results of Georgakis [C. Georgakis, On the use of extensive variables in process dynamics and control, Chemical Engineering Science 41(6) (1986) 1471–1484] for less restrictive conditions on the system dynamics and thermodynamics, and invariants sets for the stable equilibrium points of the CSTR by considering an internal energy based Lyapunov function.

A Systematic Framework for the Development and Analysis of Signed Digraphs for Chemical Processes. 2. Control Loops and Flowsheet Analysis

The objectives of this part of the two part paper are (i) development of signed digraph (SDG) models for control loops and (ii) discussion of a framework for application of graph-based approaches at a flowsheet level. Further, two case studies are used to explain the methods developed in part 11 (Ind. Eng. Chem. Res. 2003, 42, in press) and this paper. The first case study (continuous stirred tank reactor case study) explains the basic concepts of the generate and test method for SDG analysis, generation of redundant equations using algebraic manipulation, and analysis of systems with a single control loop. Case study 2 (flash vaporizer case study) deals with different methods of generating redundant equations and the analysis of systems with multiple interacting control loops.