The analysis of continuous-flow situations requires identification of a “system,” which is the region of particular interest, and its “surroundings,” which are represented by conditions imposed at the boundary of the “system.” General procedures for choosing boundary conditions at surfaces at which no phase boundary exists, i.e. “synthetic” boundaries, seem to be lacking. Drawing on the example of immiscible displacement of oil by water in a one-dimensional, semi-infinite porous medium, we compare four types of synthetic downstream boundary conditions—Dirichlet (first kind), Neumann (second kind), Robin (third kind), and what is in essence none—to find which is the most efficient when predictions are to be computed from the solution of the governing equation set. The Robin-type condition proves best: it gives the most accurate solution at fixed cost or, alternatively, requires the least work to achieve a given accuracy. To represent faithfully the physics of the situation, the Dirichlet and Neumann conditions must be imposed farther downstream of the region of interest than the Robin condition. In addition, we explore the behavior of a “pseudo-boundary condition,” which is in fact not a proper boundary condition at all, but discretization and truncation errors mask its redundant nature and allow it to perform well in cases where there is little upstream signalling. Although our findings are drawn from the displacement problem, they are more broadly applicable to analysis of transport phenomena.