Assessment of the Influence of Water Saturation and Capillary Pressure Gradients on Size Formation of Two-Phase Filtration Zone in Compressed Low-Permeable Reservoir

The paper examines the influence of capillary pressure and water saturation ratio gradients on the size of the two-phase filtration zone during flooding of a low-permeable reservoir. Variations of water saturation ratio s in the zone of two-phase filtration are associated with the pressure variation of water injected into the reservoir; moreover the law of variation of water saturation ratio s(r, t) must correspond to the variation of injection pressure, i.e. it must be described by the same functions, as the functions of water pressure variation, but be subject to its own boundary conditions. The paper considers five options of s(r, t) dependency on time and coordinates. In order to estimate the influence of formation and fluid compressibility, the authors examine Rapoport – Lis model for incompressible media with a violated lower limit for Darcy’s law application and a time-dependent radius of oil displacement by water. When the lower limit for Darcy’s law application is violated, the radius of the displacement front depends on the value of capillary pressure gradient and the assignment of s function. It is shown that displacement front radii contain coefficients that carry information about physical properties of the reservoir and the displacement fluid. A comparison of two-phase filtration radii for incompressible and compressible reservoirs is performed. The influence of capillary pressure gradient and functional dependencies of water saturation ratio on oil displacement in low-permeable reservoirs is assessed. It is identified that capillary pressure gradient has practically no effect on the size of the two-phase filtration zone and the share of water in the arbitrary point of the formation, whereas the variation of water saturation ratio and reservoir compressibility exert a significant influence thereupon.

Lattice Boltzmann Modeling-based Design of a Membrane-free Liquid-liquid Microseparator

The benefits of continuous processing and the challenges related to the integration with efficient downstream units for end-to-end manufacturing have spurred the development of efficient miniaturized continuously-operated separators. Membrane-free microseparators with specifically positioned internal structures subjecting fluids to a capillary pressure gradient have been previously shown to enable efficient gas-liquid separation. Here we present initial studies on the model-based design of a liquid-liquid microseparator with pillars of various diameters between two plates. For the optimization of in silico separator performance, mesoscopic lattice-Boltzmann modeling was used. Simulation results at various conditions revealed the possibility to improve the separation of two liquids by changing the geometrical characteristics of the microseparator.

Bentonite Extrusion into Near-Borehole Fracture

In this paper, we discuss laboratory experiments of bentonite swelling and coupled finite element simulations to explicate bentonite extrusion. For the experiments, we developed a swell cell apparatus to understand the bentonite migration to the near-borehole fracture. We constructed the swell cell using acrylic, which comprised of a borehole and open fracture. Initially, the borehole of the swell cell was filled with bentonite and liquid. Then, the apparatus was sealed for observations. Due to the liquid saturation increase of bentonite, its swelling pressure increased. The developed pressure caused the extrusion of bentonite into the fracture, and the flow of bentonite from the borehole decreased with time. Moreover, for the effectiveness of bentonite-based plugging, there is a limiting condition, which represents the relation between the maximum bentonite migration length with the fracture aperture. Additionally, we also performed the bentonite free swelling test to assess the swelling potential to the fluid salinity, and we observed that with the increase of the salinity, the swelling potential decreased. In addition, we present a fully coupled two-phases fluids flow (e.g., liquid and gas) and deformation flow finite element (FE) model for the bentonite column elements and swell cell model. We also combined the Modified Cam Clay (MCC) model and the swelling model for the bentonite deformation flow model. Then, we also present the validation of the bentonite model. To model other sub-domains, we used the poro-elastic model. Additionally, we obtained the transition between the wetting phase (i.e., liquid) and non-wetting phase (i.e., gas) using the Brooks–Corey model. From the finite element results, we observed that due to the liquid intrusion into the bentonite, the developed capillary pressure gradient results in a change of the hydro-mechanical behavior of the bentonite. Initially, we observed that due to the high capillary pressure gradient, the liquid saturation and the swelling pressure increased, which also decreased with time due to a reduction in the capillary pressure gradient. Thereby, the swelling pressure-induced bentonite migration to the fracture also decreased over time, and after the equilibrium state (for a negligible pressure gradient), there was no significant transport of bentonite into the fracture.

Modeling of Spontaneous–Imbibition Experiments With Porous Disk—On the Validity of Exponential Prediction

Summary Imbibition experiments with porous disk can be used to derive accurate capillary pressure curves for porous media. An experimental setup is considered in which brine spontaneously imbibes cocurrently through a water-wet porous disk and into a mixed-wet core. Oil is produced from the core's top surface, which is exposed to oil. The capillary pressure is reduced in steps to determine points on the capillary pressure curve. A mathematical model is presented to interpret and design such experiments. The model was used to history match experimental data from Ahsan et al. (2012). An analytical model was then derived from a simplification of the general model, and validated by comparing the two by use of parameters from history matching. The main assumption of the analytical model is that the imbibition rate is sufficiently low, allowing fluids to redistribute inside the core, leading to a negligible capillary pressure gradient. This results in an exponential imbibition time profile with a time scale τ. Exponential matching has been applied earlier in the literature, but, for the first time, we derive this expression theoretically and provide an explicit formulation for the time scale. The numerical simulations show that, at low saturations, there can be a significant flow resistance in the core. A capillary-pressure gradient then forms, and the analytical solution overestimates the rate of recovery. At higher saturations, the fluids are more mobile, and imbibition rate is restricted by the disk. Under such conditions, the exponential solution is a good approximation. The demonstrated ability to predict the time scale in the late stage of the experiment is of significant benefit, because this part of the test is also the most time-consuming and most important to estimate. A method is presented to derive capillary pressure data point by point from measured imbibition data. It provides reliable data between the equilibrium points, and demonstrates consistent variations in flow resistance during the imbibition tests. Gravity had minor influence on the considered experimental data, but generally implies that equilibrium points have higher capillary pressure than the phase pressure difference defined by the boundary conditions.

The Role of Contact Line (Pinning) Forces on Bubble Blockage in Microchannels

This paper highlights the influence of contact line (pinning) forces on the mobility of dry bubbles in microchannels. Bubbles moving at velocities less than the dewetting velocity of liquid on the surface are essentially dry, meaning that there is no thin liquid film around the bubbles. For these “dry” bubbles, contact line forces and a possible capillary pressure gradient induced by pinning act on the bubbles and resist motion. Without sufficient driving force (e.g., external pressure), a dry bubble is brought to stagnation. For the first time, a bipartite theoretical model that estimates the required pressure difference across the length of stagnant bubbles with concave and convex back interfaces to overcome the contact line forces and stimulate motion is proposed. To validate our theory, the pressure required to move a single dry bubble in square microchannels exhibiting contact angle hysteresis has been measured. The working fluid was de-ionized water. The experiments have been conducted on coated glass channels with different surface hydrophilicities that resulted in concave and convex back interfaces for the bubbles. The experimental results were in agreement with the model's predictions for square channels. The predictions of the concave and convex back models were within 19% and 27% of the experimental measurements, respectively.

Hydromagnetic instability of a resistive hollow jet

The magnetohydrodynamic (MHD) stability criterion of a resistive hollow cylinder with respect to its capillary, pressure gradient, and electromagnetic forces is established. Numerous stability criteria are obtained as limiting cases from the present relation. The capillary force is destabilizing only for certain wavelengths to axisymmetric mode and stable to all other disturbances. There are three different cases for discussing the electromagnetic force (EMF) influence on the resistive hollow jet instability. As the fluid is with finite resistivity, the EMF does not have any influence on the capillary instability of a resistive hollow jet, however, the finite resistivity has a stabilizing tendency on the MHD hollow jet. As the fluid has infinite resistivity, the EMF is (de-)stabilizing according to restrictions. As the fluid is with zero resistivity, the EMF exerts an influence giving a sort of rigidity to the conducting fluid and that influence causes the bending and twisting of the lines of force in the fluid. Consequently, for a magnetic field of high intensity the capillary destabilization could be suppressed and stability arises.PACS No.: 47.17+e