Investigating wettability-controlled fluid displacements in heterogeneous rock using fast laboratory based X-ray microtomography

<p>Multiphase fluid flow is a common process in geological systems and has important applications such as aquifer remediation and Carbon Capture and Storage (CSS). Understanding how pore-scale fluid displacements link to the macroscopic descriptions of multiphase flow forms an important gap in our current understanding of this process. At the mesoscale, between the pore and the continuum scale, the distribution of the fluids in the pore network develops into different patterns depending on e.g. flow regime, pore geometry and surface chemistry. Over the years, significant effort has been put into identifying the underlying pore-scale displacement mechanisms[e.g. 1] and classifying these displacement patterns in model porous media based on e.g. the capillary number, viscosity ratio and wettability[2]–[4]. However, subsurface rocks tend to be far more complex in terms of pore structure and wettability than the model materials on which these classifications are based. We hypothesize that pore-scale complexities might induce local variations in the viscous-capillary force balance which could translate in qualitatively new multiphase flow behavior.</p><p>To test this hypothesis, we use fast laboratory based X-ray microtomography to image n-decane-brine drainage and imbibition experiments performed on two medium-grained calcareous sandstone samples of the Luxembourg Sandstone Formation (lower Jurassic) at slow flow rates (Ca 10<sup>-9</sup>). One of these samples was treated using octadecyltrichlorosilane (OTS) to induce an mixed wettability distribution. The experiments were imaged continuously at 60s per 360° rotation using a laboratory based X-ray microtomography scanner optimized for fast image acquisition to generate a time series of images with a reconstructed voxel size of 8µm/vx. We quantify fluid displacements on a pore-by-pore basis to investigate the times scales associated with the fluid displacements. We identify a previously undescribed type of filling event that occurred during water-flooding under mixed-wet conditions, where certain large pores fill at a time scale that is four orders of magnitude slower than the Haines jumps that occur in neighboring pores. This displacement type is responsible for about 20% of the total displacement of the n-decane phase in our sample during water-flooding. The rate-limited behavior of these events can be explained by the fact that under mixed-wet conditions the persistent connectivity of the fluid phases allows the invasion of poorly connected, large pores through low-conductivity pore regions which locally control the flow rates.</p><p>[1]        R. Lenormand, C. Zarcone, en A. Sarr, ‘Mechanisms of the displacement of one fluid by another in a network of capillary ducts’, J. Fluid Mech., nr. 135, pp. 337–353, feb. 1983.<br>[2]        R. Lenormand, E. Touboul, en C. Zarcone, ‘Numerical models and experiments on immiscible displacements on immiscible displacements in porous media’, J. Fluid Mech., nr. 189, pp. 165–187, jun. 1988.<br>[3]        B. Zhao e.a., ‘Comprehensive comparison of pore-scale models for multiphase flow in porous media’, Proc. Natl. Acad. Sci., vol. 116, nr. 28, pp. 13799–13806, jul. 2019, doi: 10.1073/pnas.1901619116.<br>[4]        R. Holtzman, ‘Effects of Pore-Scale Disorder on Fluid Displacement in Partially-Wettable Porous Media’, Sci. Rep., vol. 6, nr. 1, p. 36221, dec. 2016, doi: 10.1038/srep36221.</p>

Some models for immiscible displacements in Hele-Shaw cells

We study the linear stability of the immiscible displacement of some fluids in 2D and 3D Hele-Shaw cell. We give a method for avoiding the singularities phenomenons which appears in previous papers. In the case of a non - Newtonian fluid displaced by air in a 3D Hele-Shaw cell, we give a growth constant σ of perturbations, which contains two new terms compared with the Saffman-Taylor formula. Our σ has a very high growth as a parameter appearing in the constitutive relations approaches a critical value.

Numerical simulations of immiscible displacement in the cavities via lattice Boltzmann method

In this paper, the immiscible displacements in the different cavities are studied by the pseudo-potential lattice Boltzmann (LB) model. We first validate the model with a two-dimensional (2D) layered flow, and find that the numerical results agree well with the corresponding analytical solutions. Then, we perform some numerical simulations to study the immiscible displacements in the cavities, and focus on the effects of the surface wettability, capillary number and density ratio on the displacement efficiency. The numerical results show that the displacement efficiency increases with the increase of the capillary number at first and then presents a decrease with the capillary number when it is large enough. The increase of the contact angle θ1 or decrease of the density ratio increases the displacement efficiency but decreases the critical capillary number. Finally, it is also found that both the size and geometry of cavity have a significant influence on the displacement efficiency.