Detailed kinetic models for the modeling of complex chemistries, including thermal cracking, catalytic reforming, catalytic cracking, and hydroprocessing, offer the compelling advantage chemical significance at the mechanistic level. They carry a considerable burden, however, in terms of species, reactions, and associated rate parameters. This, together with the batch and the plug flow reactor balances, requires solution of a large system of either stiff ordinary differential equations (ODE) or stiff differential algebraic equations (DAE), for both homogeneous and heterogeneous processes. It is often faster numerically to solve a stiff system of ODEs and, thus, it can be useful to convert a system of DAEs to ODEs for numerical solution schemes. For heterogeneous PFR systems, the reactor steady-state balances result in a set of DAEs, and it would therefore be desirable to construct the associated set of ODEs to minimize CPU demand. To this end, we propose that such a transformation can be achieved by making the "flowing surface species" approximation. This involves approximating the overall rate of reaction of surface species, which is identically equal to zero at reactor steady state, by a spatial derivative. We show that this approximation becomes better as the system of equations becomes stiffer, and, hence, is a reverse analogy of the kinetic steady-state approximation in the case of batch systems. To validate the proposition, we analyze various contrived and real examples of mechanistic kinetics for heterogeneous systems.