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