Given a system of reactions with known reaction kinetics and a known feed, it is of interest to find all the possible outlet conditions (the attainable region) for an arbitrary system of steady-flow reactors with any total volume. A geometric approach was used to derive a set of necessary conditions as well as a limited, but powerful, sufficiency condition for the attainable region. These results extend those previously obtained for isothermal, constant-density systems in concentration space to include adiabatic and variable-density systems in composition-volume space. It is also shown how the method can be used to find the attainable region for systems with constraints. In a previous paper (Glasser et al., 1987) (called GCH), the problem of finding the best steady-flow (one that will not support sustained oscillations) system of chemical reactors, given a set of reactions with its associated kinetics, was investigated. The system was constrained to be isothermal with no density changes on reaction or mixing, and the region examined was confined to the concentration space. The problem was solved by the use of geometric techniques to find the attainable region, that is, the region in the stoichiometric subspace that can be reached by any possible reactor system. Horn (1964) showed that if one could find the attainable region for a system then, provided the objective function was a simple function of only the basis variables, the problem of the optimization was relatively straightforward. There has been much previous work in the field of optimization of such systems. The method to minimize the total residence time for a single reaction occurring in a reactor system comprised of CSTR’s and plug flow and recycle reactors in series is, for instance, well-known. The minimum residence time is found by minimizing the area, representing the residence time of the reactors, on a reciprocal of the rate versus conversion graph. This usually involves a graphical search in order to determine the best