A phase-field model of two-phase Hele-Shaw flow

2014 ◽  
Vol 758 ◽  
pp. 522-552 ◽  
Author(s):  
Luis Cueto-Felgueroso ◽  
Ruben Juanes

AbstractWe propose a continuum model of two-phase flow in a Hele-Shaw cell. The model describes the multiphase three-dimensional flow in the cell gap using gap-averaged quantities such as fluid saturation and Darcy flux. Viscous and capillary coupling between the fluids in the gap leads to a nonlinear fractional flow function. Capillarity and wetting phenomena are modelled within a phase-field framework, designing a heuristic free energy functional that induces phase segregation at equilibrium. We test the model through the simulation of bubbles and viscously unstable displacements (viscous fingering). We analyse the model’s rich behaviour as a function of capillary number, viscosity contrast and cell geometry. Including the effect of wetting films on the two-phase flow dynamics opens the door to exploring, with a simple two-dimensional model, the impact of wetting and flow rate on the performance of microfluidic devices and geological flows through fractures.

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Jinhui Liu ◽  
Yang Ju ◽  
Yingqi Zhang ◽  
Wenbo Gong

Abstract Accurate understanding and predicting the flow paths of immiscible two-phase flow in rocky porous structures are of critical importance for the evaluation of oil or gas recovery and prediction of rock slides caused by gas-liquid flow. A 2D phase field model was established for compressible air-water two-phase flow in heterogenous porous structures. The dynamic characteristics of air-water two-phase interface and preferential paths in porous structures were simulated. The factors affecting the path selection of two-phase flow in porous structures were analyzed. Transparent physical models of complex porous structures were prepared using 3D printing technology. Tracer dye was used to visually observe the flow characteristics and path selection in air-water two-phase displacement experiments. The experimental observations agree with the numerical results used to validate the accuracy of phase field model. The effects of channel thickness on the air-water two-phase flow behavior and paths in porous structures were also analyzed. The results indicate that thick channels can induce secondary air flow paths due to the increase in flow resistance; consequently, the flow distribution is different from that in narrow channels. This study provides a new reference for quantitatively analyzing multi-phase flow and predicting the preferential paths of immiscible fluids in porous structures.


2021 ◽  
Author(s):  
Pierre Aérens ◽  
Carlos Hassan Torres-Verdin ◽  
D. Nicolas Espinoza

Abstract An uncommon facet of Formation Evaluation is the assessment of flow-related in situ properties of rocks. Most of the models used to describe two-phase flow properties of porous rocks assume homogeneous and/or isotropic media, which is hardly the case with actual reservoir rocks, regardless of scale; carbonates and grain-laminated sandstones are but two common examples of this situation. The degree of spatial complexity of rocks and its effect on the mobility of hydrocarbons are of paramount importance for the description of multiphase fluid flow in most contemporary reservoirs. There is thus a need for experimental and numerical methods that integrate all salient details about fluid-fluid and rock-fluid interactions. Such hybrid, laboratory-simulation projects are necessary to develop realistic models of fractional flow, i.e., saturation-dependent capillary pressure and relative permeability. We document a new high-resolution visualization technique that provides experimental insight to quantify fluid saturation patterns in heterogeneous rocks and allows for the evaluation of effective two-phase flow properties. The experimental apparatus consists of an X-ray microfocus scanner and an automated syringe pump. Rather than using traditional cylindrical cores, thin rectangular rock samples are examined, their thickness being one order of magnitude smaller than the remaining two dimensions. During the experiment, the core is scanned quasi-continuously while the fluids are being injected, allowing for time-lapse visualization of the flood front. Numerical simulations are then conducted to match the experimental data and quantify effective saturation-dependent relative permeability and capillary pressure. Experimental results indicate that flow patterns and in situ saturations are highly dependent on the nature of the heterogeneity and bedding-plane orientation during both imbibition and drainage cycles. In homogeneous rocks, fluid displacement is piston-like, as predicted by the Buckley-Leverett theory of fractional flow. Assessment of capillary pressure and relative permeability is performed by examining the time-lapse water saturation profiles. In spatially complex rocks, high-resolution time-lapse images reveal preferential flow paths along high permeability sections and a lowered sweep efficiency. Our experimental procedure emphasizes that capillary pressure and transmissibility differences play an important role in fluid-saturation distribution and sweep efficiency at late times. The method is fast and reliable to assess mixing laws for fluid-transport properties of rocks in spatially complex formations.


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