Infoscience

Thesis

Extents of Reaction and Mass Transfer in the Analysis of Chemical Reaction Systems

Monitoring, control and optimization of chemical reaction systems often requires in-depth analysis of the underlying reaction mechanisms. This dissertation investigates appropriate tools that facilitate the analysis of homogeneous and gas-liquid reaction systems. The main contribution is a novel procedure for computing the extents of reaction and the extents of mass transfer for reaction systems with inlet and outlet streams. These concepts can help reduce the dimension of reaction models and are useful in the identification of reaction kinetics based on concentrations and spectral data. Extents of reaction, mass transfer and flow The concept of extents of reaction is well established for single-phase closed systems such as batch homogeneous reactors. However, it is difficult to compute the extent of reaction for open and heterogeneous reactors due to material exchange with the surroundings via inlet and outlet streams and between phases via mass transfer. For open homogeneous reaction systems involving S species, R independent reactions, p independent inlet streams and one outlet stream, this dissertation proposes a linear transformation of the number of moles vector (S states) into four distinct parts, namely, the extents of reaction, the extents of inlet, the extent of outlet and the invariants, using only the stoichiometry, the inlet composition and the initial conditions. The open gas-liquid reaction systems considered in this thesis involve Sg species, pg independent inlets and one outlet in the gas phase, Sl species, R independent reactions, pl independent inlets and one outlet in the liquid phase. In addition, there are pm mass-transfer fluxes between the two phases. For these systems, various extents are developed successively for the liquid and gas phases. Using only the stoichiometry, the inlet composition, the initial conditions, and knowledge of the species transferring between phases, a linear transformation of the numbers of moles (Sl states) in the liquid into five distinct parts is proposed, namely, the extents of reaction, the extents of mass transfer, the extents of liquid inlet, the extent of liquid outlet and the invariants. Similarly, a transformation of the numbers of moles (Sg states) in the gas phase into four distinct parts is proposed to generate the extents of mass transfer, the extents of gas inlet, the extent of gas outlet and the invariants. Minimal state representation and state reconstruction A state representation is minimal if (i) it can be transformed into variant states that evolve with time and invariants that are constant with time (representation condition), and (ii) the transformed model is minimal (minimality condition). Since the linear transformation transforms the numbers of moles into variant states (the extents) and invariant states, it satisfies the representation condition. For homogeneous reaction systems, the linearly transformed model is of the order (R + p + 1), while the order of the linearly transformed model for open gas-liquid reaction systems is (R + pl + pg + 2pm + 2). Using the concept of accessibility of nonlinear systems, the conditions under which the transformed models are minimal state representations are derived for both types of reaction systems. Since it is often not possible in practice to measure the concentrations of all the species, the unmeasured concentrations have to be reconstructed from available measurements. Using the measured flowrates and the proposed transformations, it is possible to reconstruct the unmeasured concentrations without knowledge of the reaction and mass-transfer rate expressions. Furthermore, it is shown that the minimal number of measured concentrations is R for homogeneous reactors and (R + pm) for gas-liquid reactors. Use of concentrations and spectral data The identification of reaction kinetics can be done incrementally or globally from experimental data. Using measured concentrations and spectral data with knowledge of pure-component spectra, incremental identification proceeds in two steps: (i) computation of the extents of reaction and mass transfer from measured data, and (ii) estimation of the parameters of the individual reaction and mass-transfer rates from the computed extents. In the first step, the linear transformation is applied to compute the extents of reaction, mass transfer and flow directly from measured concentrations without knowledge of the reaction and mass-transfer rate expressions. The transformation can be extended to measured spectral data, provided the pure-component spectra are known. An approach is developed for the case where concentrations are only available for a subset of the reacting species. In the second step, the unknown rates can be identified individually for each reaction or each mass transfer from the corresponding individual extent using the integral method. For the case of measured concentrations corrupted with zero-mean Gaussian noise, it is shown that the transformation gives unbiased estimates of the extents. For the case of spectral data with unknown pure-component spectra, the contributions of the reactions and mass transfers can be computed by removing the contributions of the inlet flows and the initial conditions. This leads to the reaction- and mass-transfer-variant (RMV) form of spectral data, from which the reaction and mass-transfer rate parameters can be estimated simultaneously. However, if the RMV-form is rank deficient, the rank must be augmented before applying factor-analytical methods. In such cases, it is shown that, for example, gas consumption data can be used for rank augmentation. The concepts and tools are illustrated using simulated data. Several special reactors such as batch, semi-batch and continuous stirred-tank reactors are considered.

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