History effects on nonwetting fluid residuals during desaturation flow through disordered porous media

We investigate experimentally the sweeping of a nonwetting fluid by a wetting one in a quasi-two-dimensional porous medium consisting of random obstacles. We focus primarily on the resulting phase distributions and the residual nonwetting phase saturation as a function of the normalized wetting fluid flow rate-the capillary number Ca-at steady state. The wetting liquid is then flowing in the medium partially saturated by immobile nonwetting liquid blobs. The decrease of the nonwetting saturation is an irreversible process that depends strongly on flow history and more specifically on the highest value of Ca reached in the past. At lower Ca values, when capillary forces are dominant, the residual steady state saturation depends significantly on the initial phase configuration. However, at higher Ca, the saturation becomes independent of the history and thus follows a master curve that converges to an asymptotic residual value. Blob sizes range over four orders of magnitude in our experimental domain, following a probability distribution function P that scales with the blob size s as P(s) alpha s(-2) for blob sizes larger than the typical pore size. It also exhibits a maximum size cutoff s(max), that decreases as s(max) alpha Ca-1. To determine the flow properties, we have measured the pressure drop (B) versus the flow rate (Ca). In the ranges of low and high Ca values, the relationship between Ca and B is found to be linear, following Darcy's law (B alpha Ca). In the intermediate regime, the progressive mobilization of blobs leads to a nonlinear dependence B alpha Ca-0.65, due to an increase of the available flow paths.