Minimal surfaces in porous media: pore-scale imaging of multiphase flow in an altered-wettability Bentheimer sandstone

Qingyang Lin, Branko Bijeljic, Steffen Berg, Ronny Pini , Martin J Blunt , Sam Krevor

We observed features of pore scale fluid distributions during oil-brine displacement in a mixed-wet sandstone rock sample. High-resolution X-ray imaging was used in combination with differential pressure measurements to measure relative permeability and capillary pressure simultaneously during a steady-state waterflood experiment on a sample of Bentheimer sandstone 51.6 mm long and 6.1 mm in diameter. After prolonged contact with crude oil to alter the surface wettability, a refined oil and formation brine were injected through the sample at a fixed total flow rate but in a sequence of increasing brine fractional flows. When the pressure across the system stabilized, X-ray tomographic images were taken. The images were used to compute saturation, interfacial area, curvature and contact angle. From this information relative permeability and capillary pressure were determined as functions of saturation. We compare our results with a previously published experiment with strongly water-wet conditions. The oil relative permeability was lower than in the water-wet case, although a smaller residual oil saturation, of approximately 0.11, was obtained, since the oil remained connected in layers in the altered wettability rock. The capillary pressure was slightly negative and ten times smaller in magnitude than a similar water-wet rock, and approximately constant over a wide range of intermediate saturation. The oil-brine interfacial area was also largely constant in this saturation range. The measured static contact angles had an average of $80^{\circ}$ with a standard deviation of $17^{\circ}$.

We observed that the oil-brine interfaces were not flat, as may be expected for a very low mean curvature, but had two approximately equal, but opposite, curvatures in orthogonal directions. These interfaces were approximately minimal surfaces which allow efficient displacement and imply well-connected phases. Saddle-shaped menisci swept through the pore space at a constant capillary pressure and with an almost fixed area, removing most of the oil.