Unforced invasion of wettability-altering aqueous surfactant solutions into an initially oil-filled oil-wet capillary tube has been observed to take place very slowly, and because this system is an analogue for certain methods of improved oil recovery from naturally fractured oil-wet reservoirs, it is important to identify the rate-controlling processes. We used a model for the process published by Tiberg et al. ( Tiberg , F. , Zhmud , B. , Hallstensson , K. and Von Bahr , M. Phys. Chem. Chem. Phys. 2000 , 2 , 5189 - 5196 ) and modified it for forced imbibitions. We show that when applied pressure differences are not too large invasion rates are controlled at large times by the value of the bulk diffusion coefficient for surfactant in the aqueous phase and at early times by the resistance to transfer of surfactant from the oil-water meniscus onto the walls of the capillary. For realistic values of the bulk diffusion coefficient, invasion rates are indeed slow, as observed. The model also predicts that the oil-water-solid contact angle during unforced displacement is close to pi/2, and so, the displacement occurs in a state of near-neutral wettability with the rate of invasion controlled by the rate of surfactant diffusion rather than a balance between capillary forces and viscous resistance. Under forced conditions, the meniscus moves faster, but the same kinds of dynamical balances between the various processes as were found in the spontaneous case operate. Once the capillary threshold pressure for entry into the initial oil-wet tube is exceeded, the effect of pressure on velocity becomes more significant, there is not sufficient time for the surfactant molecules to transfer in great quantity from the meniscus to the solid surface, and wettability alteration is then no longer important.
A previous paper (Hammond, P.; Unsal, E. Langmuir 2009, 25, 12591-12603) reported a simplified model for the flow of a surfactant solution into an oil-wet capillary. Results were computed by neglecting the spreading of surfactant molecules ahead of the moving oil/water meniscus onto the hydrophobic surface. We now present a more thorough version of the theory where such spreading is considered. Both spontaneous and forced imbibitions are studied. As the differential pressure across the capillary increases, a slow increase in the meniscus velocity is observed until the capillary threshold pressure is reached. At this point, the pattern changes and the velocity increases dramatically. The surfactant concentration did not have a significant effect on the speed under differential pressures greater than the capillary threshold. For lower pressures, there is a critical surfactant concentration below which the interface was not able to advance into the capillary even under positive differential pressure.
curves need to be interpreted to calculate pore sizes using the Young and Laplace equation Pore size distributions of porous media are of interest to soil scientists, geologists, and engineers with a variety of backgrounds. If known,pore size distributions can be used to determine fluid retention and permeability relationships. In this study, we propose a methodology to predict pore size distributions from air permeability measurements where P c (Pa) is the capillary pressure, (N m Ϫ1 ) is the combined with a numerical model representing a porous medium.liquid surface tension, ␣ is the liquid-material contactThe model is an extension of the capillary model, which was modified angle, and r (m) is the pore radius. This method is elaboso that the capillaries are composed of sections with different diamerate and time-consuming. In fact, it is not uncommonters. An optimization scheme that makes use of the measured air permefor this test to last 3 to 4 wk.ability values was developed to predict the best possible pore sizeIn the impregnation method, molten paraffin or epdistribution and pore arrangement. A genetic algorithm, a popular oxy is applied to the undisturbed soil sample, which is evolutionary computational methodology, was chosen for the optimiplaced in a sampling tin with both ends open. Once zation process. During our numerical study, we observed that it is not only the pore size distribution that is important, but also how the impregnated, the sample is cooled to room temperature, pores are distributed, in other words, the pore geometry.the core is then sawed and sections are photographed. The calculations are based on two-dimensional slices, thus limiting the representativeness. In the Hg injection
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