scholarly journals Capillary Desaturation Curve for Residual Nonwetting Phase in Natural Fractures

SPE Journal ◽  
2018 ◽  
Vol 23 (03) ◽  
pp. 788-802 ◽  
Author(s):  
B. I. AlQuaimi ◽  
W. R. Rossen
Keyword(s):  
Capillary Number ◽  
Rock Fracture ◽  
Force Balance ◽  
Flow In Porous Media ◽  
Correlation Lengths ◽  
Hydraulic Aperture ◽  
Capillary Desaturation ◽  
Single Rock Fracture ◽  
Definition Of ◽  
Aperture Distribution

Summary The displacement of a nonwetting phase by a wetting phase is characterized by the capillary number. Different forms of capillary number have been used in the literature for flow in porous media. A capillary number for a single rock fracture has been defined in the literature, using the mean aperture to characterize the trapping and mobilization in a fracture. We propose a new capillary-number definition for fractures that incorporates geometrical characterization of the fracture, dependent on the force balance on a trapped ganglion. The new definition is validated with laboratory experiments using five distinctive model fractures. The model fractures are made of glass plates, with a wide variety of hydraulic apertures, degrees of roughness, and correlation lengths of the roughness. The fracture surfaces were characterized in detail and statistically analyzed. The aperture distribution of each model fracture was represented as a 2D network of pore bodies connected by throats. The hydraulic aperture of each model fracture was measured experimentally. Capillary desaturation curves (CDCs) were generated experimentally using water/air in forced imbibition. The transparent nature of the system permits us to determine the residual air saturation as a function of pressure gradient from the captured images. The residual nonwetting saturation/capillary-number relationship obtained from different fractures varying in aperture and roughness can be represented approximately by a single curve in terms of the new definition of the capillary number. They do not fit a single trend using the conventional definition of the capillary number.

scholarly journals Numerical Modeling of Fluid Flow in Single Rock Fracture during Shear with Special Algorism for Contact Areas

2008 ◽  
Vol 124 (2) ◽  
pp. 129-136 ◽  
Author(s):  
Yujing JIANG ◽  
Tomofumi KOYAMA ◽  
Bo LI ◽  
Yusuke TASAKU ◽  
Ryousuke SAHO ◽  
...  
Keyword(s):  
Numerical Modeling ◽  
Fluid Flow ◽  
Rock Fracture ◽  
Contact Areas ◽  
Single Rock Fracture

Investigation of grouting diffusion in a single rock fracture considering the influences of obstructions

2021 ◽  
Author(s):  
Wenqi Ding ◽  
Dong Zhou ◽  
Xiaoqing Chen ◽  
Chao Duan ◽  
Qingzhao Zhang
Keyword(s):  
Diffusion Process ◽  
Rock Fracture ◽  
Temporal Distribution ◽  
The Finite Element Method ◽  
Single Plate ◽  
Plate Fracture ◽  
Test Platform ◽  
Grouting Reinforcement ◽  
Spatio Temporal ◽  
Single Rock Fracture

Grouting reinforcement was used to improve rock strength and avoid seepage in rock engineering. A self-developed visualised test platform was developed and the influences of different fracture openness on grouting diffusion modes were revealed; the Bingham rheological model was imported to simulate the grouting diffusion process in a single plate fracture, the spatio-temporal distribution of the velocity field under different obstructions was determined using the finite element method. The results indicate that: 1) The grout diffuses faster with the increase of fracture openness, while a stagnation effect of the grouting diffusion velocity behind the obstruction occurs. 2) Due to obstructions, the grouting diffusion process can be divided into four stages: circular diffusion, flat diffusion, vortex diffusion, and butterfly diffusion. 3) The grouting diffusion area is divided into a fully-reinforced zone and a semi-reinforced zone, and the area of the latter increases with the fracture openness, while being little affected by the size of any obstruction. 4) Furthermore, some new grouting diffusion laws were revealed considering the asymmetrical arrangement of obstructions. The results presented in this work will be helpful for describing and predicting the grouting process in fracture networks.

Mechanics of left ventricular relaxation, early diastolic lengthening, and suction investigated in a mathematical model

2011 ◽  
Vol 300 (5) ◽  
pp. H1678-H1687 ◽  
Author(s):  
Espen W. Remme ◽  
Anders Opdahl ◽  
Otto A. Smiseth
Keyword(s):  
Mathematical Model ◽  
Relaxation Rate ◽  
Left Ventricular ◽  
Force Balance ◽  
Passive Stiffness ◽  
Ventricular Relaxation ◽  
Active Fiber ◽  
Restoring Forces ◽  
Definition Of ◽  
Early Filling

We investigated the determinants of ventricular early diastolic lengthening and mechanics of suction using a mathematical model of the left ventricle (LV). The model was based on a force balance between the force represented by LV pressure (LVP) and active and passive myocardial forces. The predicted lengthening velocity ( e′) from the model agreed well with measurements from 10 dogs during 5 different interventions ( R = 0.69, P < 0.001). The model showed that e′ was increased when relaxation rate and systolic shortening increased, when passive stiffness was decreased, and when the rate of fall of LVP during early filling was decreased relative to the rate of fall of active stress. We first defined suction as the work the myocardium performed to pull blood into the ventricle. This occurred when contractile active forces decayed below and became weaker than restoring forces, producing a negative LVP. An alternative definition of suction is filling during falling pressure, commonly believed to be caused by release of restoring forces. However, the model showed that this phenomenon also occurred when there had been no systolic compression below unstressed length and therefore in the absence of restoring forces. In conclusion, relaxation rate, LVP, systolic shortening, and passive stiffness were all independent determinants of e′. The model generated a suction effect seen as lengthening occurring during falling pressure. However, this was not equivalent with the myocardium performing pulling work on the blood, which was performed only when restoring forces were higher than remaining active fiber force, corresponding to a negative transmural pressure.

Numerical Simulation of Solute Transport Instantaneously Injected in a Single Rock Fracture System: Inclusion of a Nonlinear Sorption Term

1994 ◽  
Vol 353 ◽  
Author(s):  
Yoko Fujikawa ◽  
M. Fukui
Keyword(s):  
Numerical Simulation ◽  
Solute Transport ◽  
Nonlinear Term ◽  
Transport Model ◽  
Rock Fracture ◽  
Porous Matrix ◽  
Nonlinear Sorption ◽  
The Laplace Transform ◽  
Single Rock Fracture ◽  
System Inclusion

AbstractThe effect of nonlinear Freundlich sorption isotherm on the transport of sorptive solute in a system of fracture and porous matrix was investigated through numerical simulation. To solve a set of partial differential equations of solute transport with nonlinear term, use of the Laplace transform Galerkin (LTG) technique was investigated. It was shown that the LTG method could be applied successfully to solve quasi-linearized transport equation. Sensitivity analysis showed that nonlinear sorption in porous matrix with order less than 1 increased the skewness of the breakthrough curve. The fitting of experimental effluent data using a transport model with nonlinear isotherms was also conducted.

Quantitative evaluation of fracture geometry influence on nonlinear flow in a single rock fracture

2020 ◽  
Vol 589 ◽  
pp. 125162
Author(s):  
Guan Rong ◽  
Jie Tan ◽  
Hongbin Zhan ◽  
Renhui He ◽  
Ziyang Zhang
Keyword(s):  
Quantitative Evaluation ◽  
Rock Fracture ◽  
Nonlinear Flow ◽  
Fracture Geometry ◽  
Single Rock Fracture

Research Advance in Fluid Flow through a Single Rock Fracture

2012 ◽  
Vol 204-208 ◽  
pp. 628-634
Author(s):  
Bao Hua Guo ◽  
Cai Xia Tian
Keyword(s):  
Fluid Flow ◽  
Fractured Rock ◽  
Rock Fracture ◽  
Research Work ◽  
Engineering Practice ◽  
Flow Through ◽  
Research Advance ◽  
Single Rock Fracture ◽  
Fractured Rock Masses ◽  
Channeling Flow

Flow properties through a single rock fracture are the foundation of researching fluid flow in fractured rock masses. Many researchers at home and abroad are engaging in this subject for the urgent need of engineering practice. This article mainly introduces concepts of roughness, aperture, tortuosity, channeling flow, and influencing factors of stress, temperature, anisotropic, inlet head, scale effect, solution etc. Finally, some research work should be done in future are given.

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