  We propose a Kron-based model-order reduction method for mass-action kinetics
chemical reaction networks (CRN) with constant inflow and proportional outflow.
The reduced-order models preserve the CRN structure and we establish that the
resulting reduced-order models have the same DC-gain or zero-moment as that of
the full-order ones. Subsequently, we present the spectrum interlacing property
of the Kron-reduced open CRN and propose the use of Gramians-based approach for
single-species single-substrate chemical network to get the upper-bound of
approximation error and to use it in determining a good set of nodes to be
removed systematically. Finally, we evaluate the applicability and efficacy of
our results in two well-known biochemical kinetic models: the activated sludge
model (ASM) 1 and McKeithan's T-cell receptor model.
