Coupled flow–geomechanics simulation is expensive, and it needs to be known whether it changes the forecast. For single-phase flow to a single well the answer has been known since the 1980s: an exponential dependence of permeability on effective stress reduces the problem to one dimensionless group. Whether this extends to two-phase displacement in heterogeneous rock has not been examined. This is tested on a field-scale quarter five-spot, in which a stress-dependent permeability is imposed through a uniaxial-strain poroelastic closure and swept over one homogeneous and four heterogeneous log-normal fields, in 104 simulations. At issue is not the constitutive law, assumed alike by simulation and scaling, but whether the geometric cancellation behind the single-well result is preserved under heterogeneity and a second mobile phase. It is shown to be preserved. The ratio of coupled to uncoupled injector-to-producer pressure difference is collapsed onto a closed-form curve with a median error below one per cent, even though the uncoupled difference itself is shifted by a factor of four across the heterogeneity levels tested; the collapse is insensitive to grid resolution, the pressure solver, and whether permeability is tied to effective stress directly or through porosity. The displacement measures are barely affected: although permeability is varied by an order of magnitude and injection pressure is reduced by up to three quarters, breakthrough time and recovery factor shift by less than one per cent. Under a prescribed rate, the pressure field is rescaled by the coupling without the flow being redirected, and the same dimensionless group is shown to govern a well held at fixed pressure, where the coupling appears as a gain in injectivity rather than as a drop in pressure. Inverting the scaling yields a screening rule that costs nothing to apply and determines whether a coupled simulation is required.