A newly derived solution for capillary dominated flow is investigated by comparing it to experimental and numerical simulation data of spontaneous imbibition in water-wet rocks. The analytical solution allows for the estimation of relative permeability and capillary pressure data for rocks.
To validate the analytical solution, it is evaluated for published data for co-current and counter-current spontaneous imbibition on four water wet rock samples. The published experimental saturation data for these rocks is scaled by the square root of time, and the result is compared with the corresponding analytical solution. To further investigate the validity of the analytical solution, a 1-D numerical simulation model is created for the spontaneous imbibition experimental setup and run with identical conditions.
Experimental data for spontaneous imbibition, when scaled by the square root of time, converges approximately to a single curve. It is therefore evident that the analytical solution is valid for water-wet rocks. Saturation function curves that are obtained from the analytical solution are then used as inputs to 1-D numerical models of cores with properties and dimensions that are identical to the experiments. The saturation profiles obtained from numerical modelling results, when scaled by the square root of time, display good quantitative agreement with the analytical solution, with deviations between the two sets of results varying in the range of 1 – 6% for the four data sets.
The analytical solution is very promising in that it can be used as a basis to extract otherwise time consuming Special Core Analysis (SCAL) properties by carrying out relatively fast and simple spontaneous imbibition experiments. The procedure introduced can also be adopted as a complement to the existing SCAL experiments to verify results.