Analytical Exact Solution for Co-Current Spontaneous Imbibition in Porous Media Considering Early- and Late-Time Effects

Abstract

Spontaneous imbibition (SI) of the wetting phase through the porous medium to displace the nonwetting phase is determined by capillary diffusion and injection fluid advection. This system is described using a transport equation of involved mechanisms and a pressure equation. The Buckley−Leverett solution is a particular case when capillary pressure is negligible. There are also analytical solutions available for cases with capillary diffusion as the dominant involved mechanism. In this study, a new mathematical model is developed to consider how both effects are significant. The model proposes an exact valid solution for both early-time (until the saturation front reaches effluent) and late-time imbibition. The accuracy of the model has been validated by comparing the suggested analytical model with numerical and experimental data. One of the advantages of the developed model is that despite the previous models, the injection rate does not need to be proportional to the square root of time, and other functional forms can be applied. Furthermore, the suggested analytical scheme is valid for strongly water-wet (SWW), weakly water-wet (WWW), and mixed-wet (MW) rock surfaces.

Residual Co2 Trapping and Enhanced Oil Recovery in Carbonate Reservoirs: Three-Phase Flow Dynamics Examined Via Nmr

“…( 2)) which were initially mostly occupied by oil; note that connate water initially occupied the small pores but still some water may exist in the intermediate and/or large pores as well. However, P 4 amplitudes decreased with further CO 2 injection, implying that CO 2 displaced oil and/or water from large pores (a CO 2 saturation of 32% was measured at S CO2,i after injecting 10 pore volumes of CO 2 and S o decreased from 65% to 43%, Tables 2 and 4) -these fluid configurations are consistent with independent X-ray micro-tomography experiments reported in the literature [49] and mathematical modelling [61]. As CO 2 is not a hydrogen-containing fluid, it cannot be detected via NMR [40].…”

Exact Analytical Solutions of Countercurrent Imbibition with Both Capillary and Gravity Effects

“…When matrix blocks are delimited by water, displacement efficiency reduces dramatically due to the increased significance of countercurrent imbibition. This has been confirmed by numerous experimental and numerical studies. , A complete analytical description of SI requires differentiation between cocurrent and countercurrent SI as well as physical properties and reservoir characteristics . Countercurrent SI (COUCSI) is related to the cases where vertical or horizontal imbibition of wetting and nonwetting phases occurs from the same side.…”

“…Schematic illustration of continuity equations for saturation and ion concentration in a porous medium (eq ). A detailed explanation is given within the text (reproduced from ref . Copyright 2021 American Chemical Society).…”