Effect of sample shape on counter-current spontaneous imbibition production vs time curves

Counter-current spontaneous imbibition experiments on porous media are usually carried out using cylindrical core samples. Sometimes the cores are sealed on some of the faces, and experiments then give production curves of significantly different duration and slightly different shape. Results can be correlated for rock properties (porosity and permeability) and fluid properties (viscosity and interfacial tension). A single overall scale factor is usually used to correlate for different core sizes and shapes. Although the real imbibition process is actually quite complicated, by making the approximations that there is (a) frontal displacement and (b) constant saturation behind the front, a simple analytical solution is possible. The analysis gives the production vs time function and a new core shape scale factor. These assumptions also allow the scale factors of Ma et al. [Ma, S., Morrow, N.R. & Zhang, X., 1997, J. Pet. Sci. Eng., 18, 165-178.] and Ruth et al. [Ruth, D., Mason, G. & Morrow, N.R., 2003, Proc. Soc. Core Analysts Symp., Pau, SCA2003-16, 1-12.] to be used to predict the shape of the production vs time curves. In order to challenge the predictions of the production vs time curves and the Ma, Ruth and new scale factors, counter-current spontaneous imbibition experiments were carried out with matched oil-saturated cores of different shape using brine to spontaneously displace the mineral oil. Amongst others, cylindrical cores with an axial hole were used with either the inner or outer cylindrical face open. These have radial geometry with imbibition into a contracting or expanding volume. Analysis of the experimental results with the new theory confirmed that the Ma and Ruth scale factors are good to excellent for most situations but that the new one is marginally better for extreme shape variations. The theory also predicts that all of the results should be linked by a universal properties factor (G). The variability of the G factor can be explained by some of the cores not having enough exposed surface and not enough rock depth. These factors seem to be of greater importance than the differences between the scale factors. For reproducible results it appears that a core should have an imbibition face area of at least 40 cm2 and a thickness (open face to no-flow boundary) of at least 1 cm.