Fluid saturating the rocks (usually shales) and immovable under pressure gradient in practical time scales.
Opposite to free fluid.
Connate fluid occupy the closed pore volume and may also occupy the open pore volume (and still be immovable due to capillary effects).
See also
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Petrophysics (PP) / Volumetric Rock Model