  A new algorithm is presented for simulating volume-controlled invasion of a
non-wetting phase into voxel images. This method is complementary to the
traditional morphological image opening method which mimics pressure-based
invasion. A key advantage of the volume-based approach is that all saturations
between 0 and 1 can obtained rather than the irregularly and widely spaced
saturation steps obtained by pressure-based methods. Because of the incremental
increases in saturation, it becomes possible to correctly predict defending
phase trapping, which is not the case when pressure-based steps are applied.
The algorithm is validated against morphological image opening and obtains near
perfect agreement at equal saturations as expected from theory. It is also
demonstrated that a volume-controlled capillary pressure curve can be obtained
that displays the characteristic jumps in capillary pressure, and moreover, the
envelop of peak pressures yields the pressure-based capillary pressure obtained
by morphological opening, so in fact the results of the proposed algorithm are
a superset of the morphological approach. Finally, results are compared to
multiphase lattice Boltzmann and qualitatively similar results were achieved in
substantially less time. The lattice Boltzmann method is more flexible in terms
of variable contact angle and inclusion of viscous effects, but for
quasi-static volume-based injection of a non-wetting fluid, the proposed method
is viable alternative.
