  We present a systematic, quantitative assessment of the impact of pore size
disorder and its interplay with flow rates and wettability on immiscible
displacement of a viscous fluid. Pore-scale simulations and micromodel
experiments show that reducing disorder increases the displacement efficiency
and compactness, minimizing the fluid-fluid interfacial area, through (i)
trapping at low rates and (ii) viscous fingering at high rates. Increasing the
wetting angle suppresses both trapping and fingering, hence reducing the
sensitivity of the displacement to the underlying disorder. A modified
capillary number $\mathrm{Ca^*}$ that includes the impact of disorder $\lambda$
on viscous forces (through pore connectivity) is direct related to $\lambda$,
in par with previous works. Our findings bear important consequences on sweep
efficiency and fluid mixing and reactions, which are key in applications such
as microfluidics to carbon geosequestration, energy recovery, and soil aeration
and remediation.
