Extent based reconstruction of the inlet composition matrix in process systems with feed variability and unknown reaction dynamics

Extent-based representation is a powerful tool for reaction systems since it decouples the reaction related dynamics and inlet flow dynamics. However it assumes that the inlet flow composition is exactly known. In this paper, we present the design of an estimation procedure to partially reconstruct the approximate inlet composition matrix based on the extent representation of the process. This is especially necessary when process systems have recycles streams or the inlet composition matrix contains traces of other species. The estimation is done by transforming the measured moles to the extent basis based on a nominal but incorrect inlet composition. The use of this incorrect composition will reveal the difference between the true process and the nominal model. The error between these two can be exploited to be cast a constrained linear optimization problem to estimate the uncertainty in the inlet composition. The correction of the inlet composition matrix will be crucial in obtaining an appropriate extent-based representation that can be used for control, and state and parameter estimation approaches. The use of extents is motivated because it allows to represent the system with a set of decoupled dynamics, avoiding the necessity of the reaction dynamics in the estimation procedure. The techniques developed in this paper are ultimately tested in a simple case study of a CSTR with a recycle stream from a flash evaporator.