Impact of Effective Normal Stress on Capillary Pressure in a Single Natural Fracture

Abstract Multiphase fluid flow through rock fractures occurs in many reservoir applications such as geological CO2 storage, Enhanced Geothermal Systems (EGS), nuclear waste disposal, and oil and gas production. However, constitutional relations of capillary pressure versus fluid saturation, particularly considering the change of fracture aperture distributions under various stress conditions, are poorly understood. In this study, we use fracture geometries of naturally-fractured granodiorite cores as input for numerical simulations of two-phase brine displacement by super critical CO2 under various effective normal stress conditions. The aperture fields are first mapped via photogrammetry, and the effective normal stresses are applied by means of a Fast Fourier Transform (FFT)-based convolution numerical method. Throughout the simulations, the capillary pressure is evaluated from the local aperture. Two approaches to obtain the capillary pressure are used for comparison: either directly using the Young-Laplace equation, or the van Genuchten equation fitted from capillary pressure-saturation relations generated using the pore-occupancy model. Analyses of the resulting CO2 injection patterns and the breakthrough times enable investigation of the relationships between the effective normal stress, flow channelling and aperturebased capillary pressures. The obtained results assist the evaluation of two-phase flow through fractures in the context of various subsurface applications.

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Flow-through Drying during CO2 Injection into Brine-filled Natural Fractures: A Tale of Effective Normal Stress

International Journal of Greenhouse Gas Control ◽

10.1016/j.ijggc.2021.103378 ◽

2021 ◽

Vol 109 ◽

pp. 103378

Author(s):

Marina Grimm Lima ◽

Hoda Javanmard ◽

Daniel Vogler ◽

Martin O. Saar ◽

Xiang-Zhao Kong

Keyword(s):

Normal Stress ◽

Co2 Injection ◽

Natural Fractures ◽

Effective Normal Stress ◽

Flow Through

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Experimental Investigation of Two-Phase Flow Properties of Heterogeneous Rocks for Advanced Formation Evaluation

10.2118/206334-ms ◽

2021 ◽

Author(s):

Pierre Aérens ◽

Carlos Hassan Torres-Verdin ◽

D. Nicolas Espinoza

Keyword(s):

Capillary Pressure ◽

Relative Permeability ◽

Two Phase Flow ◽

Time Lapse ◽

Phase Flow ◽

Flow Properties ◽

Fractional Flow ◽

Two Phase ◽

Fluid Saturation ◽

Heterogeneous Rocks

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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Modeling multiphase flow with a hybrid model based on the Pore-network and the lattice Boltzmann method

E3S Web of Conferences ◽

10.1051/e3sconf/202019502009 ◽

2020 ◽

Vol 195 ◽

pp. 02009

Author(s):

Eduard Puig Montellà ◽

Chao Yuan ◽

Bruno Chareyre ◽

Antonio Gens

Keyword(s):

Lattice Boltzmann Method ◽

Capillary Pressure ◽

Hybrid Model ◽

Lattice Boltzmann ◽

Computation Time ◽

Pore Network ◽

Two Phase ◽

Excellent Description ◽

Flow Through ◽

Boltzmann Method

Lattice Boltzmann method (LBM) simulations provide an excellent description of two-phase flow through porous media. However, such simulations require a significant computation time. In order to optimize the computation resources, we propose a hybrid model that combines the efficiency of the pore-network approach and the accuracy of the lattice Boltzmann method at the pore scale. The hybrid model is based on the decomposition of the granular assembly into small subsets, in which LBM simulations are performed to determine the main hydrostatic properties (entry capillary pressure, capillary pressure - liquid content relationship and liquid morphology for each pore throat). A primary drainage of a random packing of spheres is presented and contrasted to the results of the same problem fully resolved by the LBM. Liquid morphology and invasion paths are correctly reproduced by the hybrid method.

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Dynamic capillary pressure effects in two-phase flow through heterogeneous porous media

Computational Methods in Water Resources: Volume 1 - Developments in Water Science ◽

10.1016/s0167-5648(04)80087-x ◽

2004 ◽

pp. 631-644 ◽

Cited By ~ 6

Author(s):

Sabine Manthey ◽

S. Majid^Hassanizadeh ◽

Oubbol Oung ◽

Rainer Helmig

Keyword(s):

Porous Media ◽

Capillary Pressure ◽

Two Phase Flow ◽

Heterogeneous Porous Media ◽

Pressure Effects ◽

Phase Flow ◽

Two Phase ◽

Dynamic Capillary Pressure ◽

Flow Through

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Conversion of a Micro-CT Scanned Rock Fracture Into a Useful Model

Volume 1: Symposia, Parts A, B and C ◽

10.1115/fedsm2009-78118 ◽

2009 ◽

Author(s):

Dustin Crandall ◽

Grant Bromhal ◽

Duane H. Smith

Keyword(s):

Rock Fracture ◽

Fluid Motion ◽

Natural Fracture ◽

Fracture Aperture ◽

Micro Ct ◽

Parallel Plates ◽

Micro Computed Tomography ◽

Data Set ◽

Physical Geometry ◽

Flow Through

Within geologic reservoirs the flow of fluids through fractures is often orders of magnitude greater than through the surrounding, low-permeability rock. Because of the number and size of fractures in geological fields, reservoir-scale discrete-fracture simulators often model fluid motion through fractures as flow through narrow, parallel plates. In reality fractures within rock are narrow openings between two rough rock surfaces. In order to model the geometry of an actual fracture in rock, a ∼9 cm by 2.5 cm fracture within Berea sandstone was created and the aperture distribution was obtained with micro-Computed Tomography (CT) scans by Karpyn et al. [1]. The original scans had a volume-pixel (voxel) resolution of 27 by 27 by 32 microns. This data was up-scaled to voxels with 120 microns to a side to facilitate data transfer and for practicality of use. Using three separate reconstruction techniques, six different fracture meshes were created from this up-scaled data set, each with slightly different final geometries. Flow through each of these fracture meshes was evaluated using the finite-volume simulator FLUENT. While certain features of the fracture meshes, such as the shape of the fracture aperture distributions and overall volume of the void, remained similar between the different geometric reconstructions, the flow in different models was observed to vary dramatically. Rough fracture walls induced more tortuous flow paths and a higher resistance to flow. Natural fractures do vary in-situ, due to sidewall dissolution and mineral precipitation, smoothing and coarsening fracture walls respectively. Thus for our study the range of fracture properties was actually beneficial, allowing us to describe the flow through a range of fracture types. A compromise between capturing the geometric details within a domain of interest and a tractable computational mesh must always be addressed when flow through a physical geometry is modeled. The fine level of detail that is currently available from micro-CT scanning equipment can compound this problem. This study evaluates several methods of obtaining rational CFD meshes from a complex physical geometry, and discusses the benefits and disadvantages of the different procedures as they pertain to flow through a natural fracture in rock.

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ANALYTICAL SOLUTIONS FOR WATER–GAS FLOW THROUGH 3D ROCK FRACTURE NETWORKS SUBJECTED TO TRIAXIAL STRESSES

Fractals ◽

10.1142/s0218348x18500536 ◽

2018 ◽

Vol 26 (03) ◽

pp. 1850053 ◽

Cited By ~ 9

Author(s):

RICHENG LIU ◽

BO LI ◽

HONGWEN JING ◽

WEI WEI

Keyword(s):

Normal Stress ◽

Analytical Solutions ◽

Gas Flow ◽

Fractal Dimensions ◽

Fracture Aperture ◽

Gas Phases ◽

Triaxial Stresses ◽

Flow Through ◽

Aperture Distribution ◽

Water Gas

This study presented the analytical solutions for water–gas flow through three-dimensional (3D) fracture networks subjected to triaxial stresses. The relationship between fractal dimension for fracture aperture distribution subjected to triaxial stresses and that subjected to no stresses is established, and the analytical solutions for fractal dimensions for aperture distribution and the equivalent permeability of both fluid and gas phases were derived. The results show that the calculated relative permeability of water phase-saturation curves agree well with those reported in the literature, which indicates that the proposed solutions are validate. With the increment of normal stresses applied on the fracture surface, both the maximum aperture and minimum aperture decrease; however, their ratio increases first and then decreases. The fractal dimensions for fracture aperture distribution of water and gas phases with respect to saturation are axisymmetric along saturation [Formula: see text]. With the increase in saturation, the fractal dimension for fracture aperture distribution of water phase increases significantly when the saturation is less than 0.1, and then gently when the saturation is continuously increased by up to 1.0. The normal stress increased by two orders of magnitude for a larger normal stress (i.e. increased from [Formula: see text][Formula: see text]MPa to 10[Formula: see text]MPa) corresponds to smaller variations in equivalent permeability of both water and gas phases for a smaller normal stress (i.e. increased from [Formula: see text][Formula: see text]MPa to [Formula: see text][Formula: see text]MPa).

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