Sriniketh Srinivasan

Variant and invariant states for chemical reaction systems

Chemical reaction systems State decoupling Reaction variants Reaction invariants Reaction extents a b s t r a c t Models of chemical reaction systems can be quite complex as they typically include information regarding the reactions, the inlet and outlet flows, the transfer of species between phases and the transfer of heat. This paper builds on the concept of reaction variants/invariants and proposes a linear transformation that allows viewing a complex nonlinear chemical reaction system via decoupled dynamic variables, each one associated with a particular phenomenon such as a single chemical reaction, a specific mass transfer or heat transfer. Three aspects are discussed, namely, (i) the decoupling of reactions and transport phenomena in open non-isothermal both homogeneous and heterogeneous reactors, (ii) the decoupling of spatially distributed reaction systems such as tubular reactors, and (iii) the potential use of the decoupling transformation for the analysis of complex reaction systems, in particular in the absence of a kinetic

Variant and Invariant States for Reaction Systems

Models of chemical reactors can be quite complex as they include information regarding the reactions, the transfer of species between phases, the transfer of energy, and the inlet and outlet flows. Furthermore, the effects of the various phenomena are quite intertwined and thus difficult to quantify from measured data. This paper proposes a mathematical transformation of the balance equations that allows viewing a complex reaction system via decoupled dynamic variables, each one associated with a particular phenomenon such as a single chemical reaction, a specific mass transfer or heat transfer between the reactor and the jacket. Three aspects are investigated, namely, (i) the decoupling of mole balance equations, (ii) the decoupling of mole and heat balance equations, and (iii) the applicability of the decoupling transformation for model reduction, static state reconstruction and incremental kinetic identification.

Extent-based Kinetic Identification using Spectroscopic Measurements and Multivariate Calibration

Extent-based kinetic identification is a kinetic modeling technique that uses concentration measurements to compute extents and identify reaction kinetics by the integral method of parameter estimation. This article considers the case where spectroscopic data are used together with a calibration model to predict concentrations. The calibration set is assumed to be constructed from reacting data that include pairs of concentration and spectral data. Alternatively, one can use the concentration- and spectral contributions of the reactions and mass transfers, which are obtained by pretreatment in reaction- and mass-transfer-variant form. The extent-based kinetic identification using concentrations predicted from spectroscopic data is illustrated through the simulation of both a homogeneous and a gas-liquid reaction system.

Data Reconciliation in Reaction Systems using the Concept of Extents

Abstract of the conference paper Concentrations measured during the course of a chemical reaction are corrupted with noise, which reduces the quality of information. Since these measurements are used for identifying kinetic models, the noise impairs the ability to identify accurate models. The noise in concentration measurements can be reduced using data reconciliation, exploiting for example the material balances derived from stoichiometry as constraints. However, additional constraints can be obtained via the transformation of concentrations into extents and invariants, which leads to more efficient identification of kinetic models for multiple reaction systems. This paper uses the transformation to extents and invariants and formulates the data reconciliation problem accordingly. This formulation has the advantage that non-negativity and monotonicity constraints can be imposed on selected extents. A simulated example is used to demonstrate that reconciled measurements lead to the identification of more accurate kinetic models. Extended abstract Reliable kinetic models of chemical reaction systems should include information on all rate processes of significance in the system. Apart from chemical reactions, such models should also describe the mass exchanged with the environment via the inlet and outlet streams and the mass transferred between phases. Model identification and the estimation of rate parameters is carried out using measurements that are obtained during the course of the reaction [1]. Model identification often leads to the combinatorial complexity of identifying simultaneously all rate processes [1]. Alternatively, it can be carried out incrementally by transforming the concentrations to extents and identifying each extent separately [2]. Since measurements are inevitably corrupted by random measurement errors, the identification of kinetic models and estimation of rate parameters are affected by error propagation [3]. Data reconciliation is a technique that uses constraints to obtain more accurate estimates of variables by reducing the effect of measurement errors [4]. Data reconciliation can be formulated as an optimization problem constrained by the law of conservation of mass [5, 6] and positivity of reconciled concentrations. Consequently, model identification can be performed with reconciled concentrations. This paper presents a reformulation of the original reconciliation problem directly in terms of extents. This allows using additional constraints such as the monotonicity of extents. Such a reformulation improves the accuracy of the reconciled extents and hence of concentrations, and leads to better model discrimination and parameter estimation. The advantages derived from the use of reconciled extents are illustrated using a simulated example. References: [1] Bardow et al., Chem. Eng. Sci., 2004, 59, 2673 - 2684 [2] Bhatt et al., AIChE J., 2010, 56, 2873 - 2886 [3] Billeter et al., Chem. Intell. Lab. Syst., 2008, 93, 120 - 131 [4] S. Narasimhan and C. Jordache, Data Reconciliation and Gross Error Detection, Elsevier, 1999 [5] Reklaitis et al., Chem. Eng. Sci., 1975, 30, 243 - 247 [6] Srinivasan et al., IFAC Workshop on Thermodynamic Foundations of Mathematical Systems Theory, Lyon, 2013.

Shape constrained splines as transparent black-box models for bioprocess modeling

Identification of mathematical models is an important task for the design and optimization of biokinetic processes. The Monod rate law is often chosen by default, although this rate law is restrictive and cannot capture all biokinetic process dynamics, which ultimately reduces the predictive capability of the resulting models. This paper proposes an alternative rate-law structure consisting of a flexible black-box spline function that is forced to obey a predefined shape. This way, the difficult task of searching through potentially incomplete rate-law libraries can be circumvented. A simulated case study is used to illustrate the applicability of the method and its superiority to represent unconventional growth conditions, where neither Monod nor Tessier kinetics are appropriate.

Data reconciliation for chemical reaction systems using vessel extents and shape constraints

Abstract Concentrations measurements are typically corrupted by noise. Data reconciliation techniques improve the accuracy of measurements by using redundancies in the material and energy balances expressed as relationships between measurements. Since in the absence of kinetic models these relationships cannot integrate information regarding past measurements, they are expressed in the form of algebraic constraints. This paper shows that, even in the absence of a kinetic model, one can use shape constraints to relate measurements at different time instants, thereby improving the accuracy of reconciled estimates. The construction of shape constraints depends on the operating mode of the reactor. Moreover, it is shown that the representation of the reaction system in terms of vessel extents helps identify additional shape constraints. A procedure for deriving shape constraints from measurements is also described. Data reconciliation using both numbers of moles and extents is illustrated via a simulated case study.

Constrained multi-rate state estimator incorporating delayed measurements

Frequent and accurate concentration estimates are important for the on-line control and optimization of chemical reaction systems. Such estimates can be obtained using state estimation methods that fuse frequent (fast) delay-free on-line measurements with infrequent (slow) delayed laboratory measurements. In this paper, we demonstrate how several recent advances made in state estimation can be combined in an on-line recursive state estimation framework by imposing knowledge-based and measurement-based constraints on the state estimates of multi-rate concentration measurements with time-varying time delays. This framework is illustrated using a simulated example for a bacterial batch fermentation of recombinant l. lactis. It is shown that an extent-based formulation gives more accurate estimates than a conventional concentration-based formulation.

On the Use of Shape-Constrained Splines for Biokinetic Process Modelling

Identification of mathematical models is an important task for the design and the optimization of biokinetic processes. Monod or Tessier growth-rate models are often chosen by default, although these models are not able to represent the dynamics of all bacterial growth processes. This imperfect representation then affects the quality of the model prediction. This paper introduces an alternative approach, which is based on constraints such as monotonicity and concavity and the use of shape-constrained spline functions, to describe the substrate affinity with high parametric flexibility. This way, the difficult task of searching through potentially incomplete rate-model libraries can be circumvented. A simulated case study is used to illustrate the superiority of the proposed method to represent non-ideal growth conditions, where neither Monod nor Tessier kinetics offer a good approximation.

Identification of Biokinetic Models Using the Concept of Extents

The development of a wide array of process technologies to enable the shift from conventional biological wastewater treatment processes to resource recovery systems is matched by an increasing demand for predictive capabilities. Mathematical models are excellent tools to meet this demand. However, obtaining reliable and fit-for-purpose models remains a cumbersome task due to the inherent complexity of biological wastewater treatment processes. In this work, we present a first study in the context of environmental biotechnology that adopts and explores the use of extents as a way to simplify and streamline the dynamic process modeling task. In addition, the extent-based modeling strategy is enhanced by optimal accounting for nonlinear algebraic equilibria and nonlinear measurement equations. Finally, a thorough discussion of our results explains the benefits of extent-based modeling and its potential to turn environmental process modeling into a highly automated task.

On decoupling rate processes in chemical reaction systems – Methods and applications

Abstract Models of chemical reaction systems can be complex as they need to include information regarding the reactions and the mass and heat transfers. The commonly used state variables, namely, concentrations and temperatures, express the interplay between many phenomena. As a consequence, each state variable is affected by several rate processes. On the other hand, it is well known that it is possible to partition the state space into a reaction invariant subspace and its orthogonal complement using a linear transformation involving the reaction stoichiometry. This paper uses a more sophisticated linear transformation to partition the state space into various subspaces, each one linked to a single rate process such as a particular reaction, mass transfer or heat transfer. The implications of this partitioning are discussed with respect to several applications related to data reconciliation, state and rate estimation, modeling, identification, control and optimization of reaction systems.