Hydraulic conductivity in surface active soils

Soil Research ◽  
1976 ◽  
Vol 14 (2) ◽  
pp. 121 ◽  
Author(s):  
P Basak ◽  
MR Madhav

Kozeny's equation based on a capillary tube model with constant viscosity does not give satisfactory results for fine-grained soils. When surface forces dominate over gravity forces, the pore water behaves abnormally and the physical properties of this pore water are found to be quite different from free water. Flow through saturated fine-grained soils is known to be affected by the properties and thickness of loosely and strongly bound water, whose viscosity is observed to be higher because of the modified water structure induced by clay-water interaction. An analytical solution based on a capillary tube model taking into account the changed viscosity of bound water and variation of viscosity within the bound water in relation to its thickness is attempted. The derived equation appears to be general in nature and is applicable for both surface active and inactive soils. It is shown that Kozeny's equation turns out to be the particular case of the derived equation when the thickness of the bound water is zero or when the variation of viscosity is not taken into account.

2015 ◽  
Vol 23 (02) ◽  
pp. 1550011 ◽  
Author(s):  
R. O. Nunes ◽  
R. N. Faria ◽  
N. Bouzidi ◽  
L. Machado ◽  
R. N. N. Koury

This paper presents a mathematical model for a capillary tube using CO 2 as fluid in steady flow transcritical cycle. The capillary tube is divided into N volumes controls and the model is based on applying the equations of conservation of energy, mass and momentum in the fluid in each of these volumes controls. The model calculates the mass flow of the CO 2 in the capillary tube as a function of CO 2 pressures at the inlet and outlet of the capillary and the temperature of CO 2 at the input of this device. The capillary tube is considered to be adiabatic, and the limit of operation due to blocked flow condition is also considered in the model. The validation of the model was performed with experimental data and the results showed that the model is capable of predicting the mass flow in the capillary tube with errors less than 10%. The model was also used to determine the minimum diameter of the capillary tube for various conditions of CO 2 transcritical cycle.


2019 ◽  
Vol 58 (45) ◽  
pp. 20806-20814 ◽  
Author(s):  
Ying Li ◽  
Haitao Li ◽  
Shengnan Chen ◽  
Qirui Ma ◽  
Chang Liu

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Fuyong Wang ◽  
Peiqing Lian ◽  
Liang Jiao ◽  
Zhichao Liu ◽  
Jiuyu Zhao ◽  
...  

This paper investigated fractal characteristics of microscale and nanoscale pore structures in carbonates using High-Pressure Mercury Intrusion (HPMI). Firstly, four different fractal models, i.e., 2D capillary tube model, 3D capillary tube model, geometry model, and thermodynamic model, were used to calculate fractal dimensions of carbonate core samples from HPMI curves. Afterwards, the relationships between the calculated fractal dimensions and carbonate petrophysical properties were analysed. Finally, fractal permeability model was used to predict carbonate permeability and then compared with Winland permeability model. The research results demonstrate that the calculated fractal dimensions strongly depend on the fractal models used. Compared with the other three fractal models, 3D capillary tube model can effectively reflect the fractal characteristics of carbonate microscale and nanoscale pores. Fractal dimensions of microscale pores positively correlate with fractal dimensions of the entire carbonate pores, yet negatively correlate with fractal dimensions of nanoscale pores. Although nanoscale pores widely develop in carbonates, microscale pores have greater impact on the fractal characteristics of the entire pores. Fractal permeability model is applicable in predicting carbonate permeability, and compared with the Winland permeability model, its calculation errors are acceptable.


2007 ◽  
Vol 44 (12) ◽  
pp. 1446-1461 ◽  
Author(s):  
Greg Siemens ◽  
James A. Blatz ◽  
Douglas Ruth

Swelling mechanisms occurring on the pore scale or at the molecular level of high plasticity, unsaturated soils often control macroscopic behaviour. In this paper, a new capillary tube model is proposed. The model is used to represent laboratory-scale infiltration tests on a bentonite-rich soil. The goal is to develop a greater understanding of bulk behaviour by closely examining microscopic behaviour. A decrease in hydraulic conductivity with increasing water content has been observed in laboratory studies on flow through shrink–swell materials. The proposed mechanism causing a decrease in conductivity is a change in pore-size distribution. The unique feature of the new capillary-tube model is that, as water flows down the tube, the tube’s cross-sectional area contracts to restrict flow, thus representing the change in pore-size distribution observed in the physical tests. Flow data from the capillary tube are used to model the laboratory results, and new insight is gained into bulk flow behaviour. Finally, a comparison with a three-dimensional network model for bentonite-coated sand mixtures is presented.


1971 ◽  
Vol 11 (03) ◽  
pp. 236-242 ◽  
Author(s):  
Kinji Magara

Abstract Abnormal fluid pressures in shale-sandstone sequences commonly occur in the relatively deeper parts of the sequences. The causes of these parts of the sequences. The causes of these anomalous pressures may be explained by the shale permeability and the fluid-expulsion mechanisms permeability and the fluid-expulsion mechanisms related to compaction. The volume of fluids that should be expelled from shales in unit time for the compaction equilibrium (or the hydrostatic pressure) condition to be maintained would increase with increases both in the rate of sedimentation and in the total thickness of the sequence. The minimum permeability necessary for maintenance of the hydrostatic pressure condition would, therefore, increase with increases in the sedimentation rate and the total thickness. When the actual permeability in the subsurface is less than this estimated minimum permeability /or the equilibrium condition, some fluids will remain in the shale, in such a case, the compaction equilibrium condition cannot be attained and abnormal pressures will result. Results obtained from an analysis of data on the Gull Coast area tend to support this theory. Introduction If the pore water in a shale or mudstone can escape easily, the rate of compaction is rapid and a hydrostatic pressure condition prevails. However, if the escape of pore water is hindered by low permeability, the rate of compaction is slow and the permeability, the rate of compaction is slow and the pore water must support a part of the weight of pore water must support a part of the weight of overburden. In other words, an abnormal pressure occurs. According to Thomeer and Bottema, favorable conditions for abnormal pressures below shale columns may be found in younger sedimentary basins where thick shales were relatively rapidly deposited over considerable areas-time thus being too short for hydrostatic equilibrium condition to be reached. With respect to the common occurrence of abnormal pressure in more deeply buried shale successions, pressure in more deeply buried shale successions, Rubey and Hubbert advanced the following explanation: "When the rate of sedimentation is somewhat greater, pore water may still escape rapidly enough to maintain an essentially hydrostatic pressure in the relatively porous mudstone at shallow pressure in the relatively porous mudstone at shallow and intermediate depths but not in the more compacted and therefore less permeable rock at greater depths." In a significant recent contribution, Powers advanced a new interpretation of the origin of abnormal fluid pressure in the deep subsurface, based on the application of current knowledge of clay colloid chemistry and mineralogy. According to Powers, alteration of montmorillonite to illite begins Powers, alteration of montmorillonite to illite begins at a depth of about 6,000 ft and continues at an increasing rate to a depth, usually about 9,000 to 10,000 ft, where there is no montmorillonite left. The alteration offers a mechanism for desorbing the last few layers of bound water in clay and transferring it as free water to interparticle locations. The last few layers of bound water have a considerably greater density than free water, and water increases its volume as it is desorbed from between unit layers. As the water expands, A increases the pore fluid pressure to abnormally high levels. (See also Burst.) pressure to abnormally high levels. (See also Burst.) In this paper, we discuss qualitatively and quantitatively an alternative explanation of abnormal fluid pressure in the relatively deeper part of sedimentary sequence. This alternative explanation is based on shale permeability and fluid-expulsion mechanisms related to compaction. EXPULSION OF FLUIDS FROM SHALES DURING SUBSIDENCE Suppose a clay or shale sequence in which the clay or shale has reached a compaction equilibrium and within which the fluid pressure is hydrostatic (Stage A of Fig. 1). Additional sediments are added above this sequence in the marine condition and the sequence subsides F in time interval t. If the entire slide makes a new equilibrium condition of compaction after the subsidence of, such porosity distribution as shown by Stage B in Fig. 1 would be established. An exponential function between shale porosity -and depth would be established at Stages porosity -and depth would be established at Stages A and B (compaction equilibrium conditions). SPEJ P. 236


Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
C. J. A. Sinn ◽  
J. Klaver ◽  
R. Fink ◽  
M. Jiang ◽  
J. Schmatz ◽  
...  

Organic-rich shale samples from a lacustrine sedimentary sequence of the Newark Basin (New Jersey, USA) are investigated by combining Broad Ion Beam polishing with Scanning Electron Microscopy (BIB-SEM). We model permeability from this 2D data and compare our results with measured petrophysical properties. Three samples with total organic carbon (TOC) contents ranging from 0.7% to 2.9% and permeabilities ranging from 4 to 160 nD are selected. Pore space is imaged at high resolution (at 20,000x magnification) and segmented from representative BIB-SEM maps. Modeled permeabilities, derived using the capillary tube model (CTM) on segmented pores, range from 2.3 nD to 310 nD and are relatively close to measured intrinsic permeabilities. SEM-visible porosities range from 0.1% to 1.8% increasing with TOC, in agreement with our measurements. The CTM predicts permeability correctly within one order of magnitude. The results of this work demonstrate the potential of 2D BIB-SEM for calculating transport properties of heterogeneous shales.


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