The analysis of continuous-flow problems requires specifying a "system," which is a region of particular interest, and its "surroundings," which are represented by conditions imposed at the boundary of the system. General procedures for assigning boundary conditions at "synthetic" boundaries, i.e. surfaces at which no physical boundary exists, seem to be lacking. Using the context of continuous-flow reactors with finite entrance and exit sections, we demonstrate the importance of choosing synthetic boundary conditions that describe accurately the interactions of a system and its surroundings. Specifically, we show that the steady-state solution of Danckwerts (1953, Chem. Engng Sci. 2, 1-13) is unfit to predict reactant concentrations in well-mixed reactors with entrance sections that are as long as or shorter than the reactor itself. In the case of unsteady states, we propose and apply two extremes of flow behavior, namely insranr mixing and instant removal, which delimit the concentration gradient that may be imposed at a synthetic boundary. Whereas our findings bear directly on analyses of reactor performance and on the evaluation of axial dispersion coefficients from tracer response experiments, they are more broadly relevant because of the partial analogies among mass, heat and momentum transport.