  One of the long-term goals of exoplanet science is the atmospheric
characterization of dozens of small exoplanets in order to understand their
diversity and search for habitable worlds and potential biosignatures.
Achieving this goal requires a space mission of sufficient scale. We seek to
quantify the exoplanet detection performance of a space-based mid-infrared
nulling interferometer that measures the thermal emission of exoplanets. For
this, we have developed an instrument simulator that considers all major
astrophysical noise sources and coupled it with Monte Carlo simulations of a
synthetic exoplanet population around main-sequence stars within 20 pc. This
allows us to quantify the number (and types) of exoplanets that our mission
concept could detect over a certain time period. Two different scenarios to
distribute the observing time among the stellar targets are discussed and
different apertures sizes and wavelength ranges are considered. Within a
2.5-year initial search phase, an interferometer consisting of four 2 m
apertures with a total instrument throughput of 5% covering a wavelength range
between 4 and 18.5 $\mu$m could detect up to ~550 exoplanets with radii between
0.5 and 6 R$_\oplus$ with an integrated SNR$\ge$7. At least ~160 of the
detected exoplanets have radii $\le$1.5 R$_\oplus$. Depending on the observing
scenario, ~25-45 rocky exoplanets (objects with radii between 0.5 and 1.5
$_{\oplus}$) orbiting within the empirical habitable zone (eHZ) of their host
stars are among the detections. With an aperture size of 3.5 m, the total
number of detections can increase to up to ~770, including ~60-80 rocky, eHZ
planets. With 1 m aperture size, the maximum detection yield is ~315
exoplanets, including $\le$20 rocky, eHZ planets. In terms of predicted
detection yield, such a mission can compete with large single-aperture
reflected light missions. (abridged)
