Abstract
Counter-current imbibition is an important recovery mechanism during waterflooding in fractured reservoirs. While this may be a rapid and efficient recovery process in strongly water-wet systems, the vast majority of reservoirs show some mixed-wet or oil-wet characteristics. If the reservoir is mixed-wet, it is possible for some water to imbibe spontaneously, but the ultimate recovery is lower and the imbibition rate may be several orders of magnitude slower than for strongly water-wet rock.
We use quasi-static pore-scale network modeling as a tool to study the behavior of mixed-wet rocks and to predict relative permeability and capillary pressure. The model uses a topologically disordered network that represents the pore space of Berea sandstone. We adjust the distribution of contact angles at the pore scale to match previously publised experimental co-current waterflood recoveries and wettability indices on Berea. We then input the relative permeabilities and capillary pressures into a conventional grid-based code and simulate counter-current imbibition in one dimension. We make predictions, with no matching parameters, of the recovery as a function of time and compare the results with the experimental measurements. We are able to reproduce the observed dramatic increase in imbibition time as the system changes from being water-wet to mixed-wet. In a mixed-wet system spontaneous imbibition, where the capillary pressure is positive, is limited to a narrow saturation range where the water saturation is small. At these low saturations the water is poorly connected through the network in wetting layers and the water relative permeability is extremely low, leading to recovery rates tens to thousands of times slower than for water-wet media.
We present a semi-empirical equation to correlate imbibition recovery in mixed-wet rocks with different wettability states and for a wide range of viscosity ratios. We show that the recovery rate is proportional to the water mobility at the end of imbibition.
