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Reports: DNI652054-DNI6: Fundamental Studies of the Morphology and Dynamics of the Phase Entrapment in Immiscible Two-Phase Flow through Porous Media

Nima Shokri, PhD, University of Manchester

We conducted a comprehensive series of imbibition experiments using Hele-Shaw cells packed with spherical and crushed glass beads saturated with two different types of oil to investigate the relationship between the capillary number (defined as the ratio of viscous to capillary forces) and residual saturation.  Two Hele-Shaw cells were used in the experiments with the dimension of 0.1 m in length and 0.1 m in width and thicknesses of 0.003 and 0.004 m. Spherical and crushed glass beads with sizes ranging from 0.5 to 1.0 mm were used as model porous media. Two types of oils were used in our experiments as the non-wetting fluids which were Soltrol 220 and PCE with the oil to water viscosity ratio of about 4.5 and 1, respectively. Dyed water as the displacing fluid was injected into the cells at different flow rates. A high resolution digital camera was used to capture the dynamics of oil and water distributions during the imbibition experiments. To quantify the phase distribution, the gray-scale images were segmented into black and white using customized codes developed in MATLAB. Using the measured images, we could investigate the Capillary Desaturation Curve (CDC) under different boundary conditions. The results ate presented in Figure 1. This figure consists of four sets of data namely: water displacing Soltrol 220 through the cell with the thickness of 3 and 4 mm packed with spherical glass bead; water displacing Soltrol 220 through the cell with the thickness of 4 mm packed with crushed beads; and finally water displacing PCE through the cell with the gap thickness of 3 mm packed with spherical glass beads. Our results confirm a non-monotonic relation between the residual saturation and capillary number of the displacing fluid.

Figure 1. Variation of the residual oil saturation Sr through spherical and crushed glass beads as a function of the capillary number. The errorbars indicate the standard deviation of the measured data (after Khosravian et al. (2014)). 

Figure 1 indicates that at low capillary numbers, the residual saturation may increase as the capillary number increases up to a certain threshold. Such behavior has been rarely reported in literature. We attribute the observed pattern to the local geometry of the packed beads. At low capillary numbers, the capillary forces control the invasion. However, due to homogenous pore size distribution and the quasi two-dimensionality of the medium, the water may imbibe homogeneously with a stable front which will reduce trapping significantly. With increase of flow rate under unfavorable viscosity ratio, viscous forces will induce flow through more permeable zone that would lead to trapped phase behind the invasion front. At higher capillary numbers the amount of trapped phase decreases with increase of capillary number due to the mobilization of the trapped oil. The curves shown in Figure 1 pose the possibility of presenting all data in a single curve if the parameters are defined properly. Thus we proposed the following equation relating the saturation to the capillary number expressed as (Khosravian et al., 2014):

where Smax denotes the maximum trapped phase saturation, Cacr denotes the critical capillary number where the maximum trapped phase saturation is obtained, Ca is the capillary number and ‘a’ is a fitting parameter. The capillary number measured in the laboratory is based on the macroscopic definition of capillary number. However, it has been shown that mobilization of a trapped phase occurs at the critical capillary number equal to 1 if defined based on micro-scale properties. Based on the micro-scale definition of capillary number, Eq. (1) can be rearranged as (Khosravian et al., 2014):

where Camicro=Ca/Cacr. Using Eq. (2), our experimental results have been scaled as shown in Figure 2 presenting the change of S/Smax versus Ca/Cacr under different conditions. Interestingly all data obtained in our experiments could be presented by almost a single curve described by Eq. (2).

Figure 2. Physically-based scaling of capillary desaturation curve. The legend indicates the same as in Figure 1 (after Khosravian et al. (2014)).

The experiments discussed above were conducted at macro-scale. We have started to look into the relation between the capillary number and the residual saturation at micro-scale using micro-models manufactured in Pacific Northwest National Laboratory, WA, USA. Figure 3 illustrates a typical example of the phase distributions through the micro-model saturated with oil displaced by air. The design of the micro-model’s flow network is based on Delaunay triangulation which provides a realistic representation of a natural porous medium. The main focus of the remaining part of this project in 2015 will be on checking the validity of the proposed Eqs. (1) and (2) at micro-scale using the micro-model and a sophisticated microscope capable of recording the dynamics of immiscible two-phase flow at pore-scale.

Figure 3. Displaced (light gray) and displacing fluid (dark gray) distribution in the micro-model with the dimension of 14 mm by 7 mm with the average channel size of 70 microns. The micro-model was initially saturated by oil (light gray). The displacing fluid (dark gray) was injected from the right side. White indicates the solid phase.

In addition to the above mentioned research, this funding was used to support the research of two PhD students resulted in the publication of one journal paper and a second one which is currently under review. This PRF-DNI grant helped the PI tremendously who was at the early stage of his career. He could initiate a new research line in his career which already resulted in some peer-reviewed papers published in high impact factor journals. Two PhD students, one undergraduate student and 2 post-doc researchers have been so far involved in this project illustrating the great impact of this funding on the development of the PI’s research group. This funding was also very instrumental in securing a few more research funding to support the PI’s research on topics related to the focus of this project.

Khosravian, H., Joekar-Niasar, V. and Shokri, N. (2014), Effects of flow history on oil entrapment in porous media: An experimental study. AIChE J.. doi: 10.1002/aic.14708.