A sound source's apparent distance provides information about spatial relations that can have primary salience relative to other dimensions, including azimuth and elevation in the scene of a story told in 3D. Having methods to create a sense of presence and to control this attribute in immersive content are therefore valuable capabilities in sound design, particularly in object-based audio. This paper examines the ability of the reverberant spatial audio object (RSAO) to cue apparent source distance, using acoustic parameters extracted from publicly-available spatial room impulse responses (RIRs) of real environments measured at a range of source-receiver distances. The RSAO's spatio-temporal reverb representation derived from the directional B-format RIRs encoded the timing, direction and timbre of early reflections, as well as the onset, colouration and decay times of the late reverberation, which were rendered over a 42.1 setup in an acoustically- treated listening room to provide a quasi-transparent pipeline for the reproduced room impression, from recording to listening. An objective analysis of re-synthesised RIRs and re-estimated parameters demonstrated the pipeline's transparency for most parameters. However spectral leakage of bandpass filters in the late tail encouraged reverb time convergence across bands. Formal listening tests evaluated the apparent source distance that participants perceived via a multi-stimulus rating method. Statistical analysis indicates participants perceived reproduced distance changes, with logarithmic distance resolution inside the rooms' critical distance. Beyond this, ratings tended to saturate. These effects were clearer in the large hall than in the classroom, and for the voice source than the percussion. The results suggest that the RSAO can provide appropriate cues for source distance perception with resolution comparable to natural sound fields. Further work will investigate how distance perception performs across reproduction setups and develop methods to extrapolate source distance by adapting the RSAO parameters.