At a given crystal size, an important control on porosity is the amount of calcite, which is believed to be recrystallized lime mud.
Different productive zones in the same field may have different dolomite textures, [12] suggesting that original sediment texture and chemistry were the main factors determining the distribution of crystal sizes. From measurements of specific surface area, the equivalent grain diameter is computed to range from 1. As indicated in Fig. The addition of pore space produces modest gains in permeability low slopes for the two data sets in Fig.
Mortensen et al. Lucia [1] found a size effect in limestones and dolostones, as evidenced by dolostone data shown in Fig. To obtain petrophysically viable groupings, Lucia grouped all dolomitized grainstones with mud-dominated samples having large dolomite crystals and grouped dolomitized packstones with mud-dominated samples having medium-sized dolomite crystals key in Fig.
He suggests that the plot can be used to estimate permeability of a nonvuggy carbonate rock if the porosity and particle size are known. He points out that the effect of vugs is to increase porosity but not alter permeability much. In Fig. It appears that the fundamental controls observed in the sandstones are also present in these selected carbonates, if care is exercised in categorizing the carbonates in terms of grain or crystal size. Such linear trends are often seen in samples from an individual rock unit or formation.
These trends have the general form of. However it masks the dependence of log k on pore throat size and thereby obscures the physics of flow in porous media, as is shown in Single phase permeability models based on grain size.
Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read. Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro. Single phase permeability. Permeability determination. Lithology and rock type determination. Help with editing Content of PetroWiki is intended for personal use only and to supplement, not replace, engineering judgment. Carbonate Reservoir Characterization. Berlin: Springer. American Association of Petroleum Geologists Bull.
How Permeable Are Clays and Shales? Water Resources Research 30 2 : Empirical Prediction of Porosity and Permeability in Sandstones. Geologie en Mijnbouw 42 4 : J Pet Technol 36 12 : The strain of the fracture surface along the tangential direction should be neglected based on the model shown in Figure 9. By simplifying Eq. Under the action of stress, the fracture width will be changed, which can result in the change of permeability coefficient.
According to Eqs. Figure 10 presents the calculation model of the displacement of single-fracture heterogeneous rock under triaxial stress condition. A and B represent bedrocks with different lithological properties existed on two sides of the fracture surface.
Let the length of bedrocks and fracture be , , and. According to the established calculation model, overall displacement of the single-fracture heterogeneous rock along x direction can be determined by where denotes the total strain increments of single-fracture rock along the direction of x , respectively.
The total displacements of the rock masses on both two sides of the fracture can be calculated as where and denote the strain increments of rock mass A and rock mass B along the direction of x , respectively. Thus, fracture displacement can be calculated as. Under tridirection compression, confining pressure and pore water pressure all cause compression deformation in rock blocks.
Therefore, by taking into account the lithology of the single-fracture heterogeneous rock, hydraulic pressure and net confining pressure in the fracture, the strain increment of the single-fracture rock and the rock masses on two sides of the fracture along the direction of x can be calculated as where denotes the increment of hydraulic pressure in the fracture.
By substituting Eq. The last item in Eq. It can be concluded that the hydraulic pressure in the fracture can compress the rock masses on both two sides of the fracture surface, thereby leading to increasing fracture width. For single-fracture homogeneous rock and heterogeneous rock mass, the permeability coefficient can be calculated by Eq.
For single-fracture homogenous rock, let , , and. Then, the above three calculation coefficients can be simplified to. In the present tests, forces on the single-fracture rocks were simplified, during which only confining pressure and hydraulic pressure in the fracture were applied while no axial pressure was applied.
In addition, only the effect of normal stress on the fracture surface of the rock was taken into account while the effect of shearing stress was not considered. Therefore, Figure 11 displays force condition on the rock specimen and the fracture surface, in which denotes the net confining pressure i.
At the beginning of test, and. Accordingly, original displacement of the fracture in the single-fracture rock, i. As the hydraulic pressure increased with a constant, overall displacement of the fracture can be written as where is the constant value that can be reached after the hydraulic pressure increases. The absolute value of Eq. During the tests, the hydraulic pressure in the fracture was applied and remained unchanged until it reached a certain value; next, the confining pressure was changed.
At that moment, , and the initial fracture width is. Therefore, the validation formula of the permeability coefficient of single-fracture heterogeneous rock can be described as where. For single-fracture homogenous rock i. As stated above, only the effect of normal stress on the fracture was taken into account while the effect of shearing stress was neglected. According to the theoretical calculation formulas, Eq.
Table 2 lists parameter results of the fractured rocks. Figure 12 compares the calculated permeability coefficients of different single-fracture fractured rock specimens and the measured values. The theoretical calculated results fit well with the test data. Specifically, these two sets of values were within a same order of magnitude and exhibited almost identical variation tendencies with the net confining pressure.
Therefore, the derived theoretical calculation formula of permeability coefficient of the fractured rock was verified to be accurate and applicable. The application condition of Eq. When the hydraulic pressure in the fracture and the confining pressure change simultaneously, the permeability coefficient of the fractured rock should be calculated according to Eq.
Because of the restriction in experimental condition, accuracy and applicability of Eq. In this paper, we analyzed the seepage characteristics of weakly cemented sandstone with different granularity based on experimental and theoretical methods.
A theoretical calculation formula of permeability coefficient of single-fracture heterogeneous rock i. The theoretical results and experimental results were then compared.
The main conclusions are drawn as follows: 1 As hydraulic pressure in the fracture increases, hydraulic fracturing effect is triggered, thereby generating slight normal deformation of the rock masses on both two sides of the fracture surface and decreasing the contact area in the fracture.
Accordingly, both fracture width and permeability coefficient increase. As the applied normal stress exceed to a certain value, hydraulic pressure in the fracture is relatively smaller compared with normal stress and only residue fracture can be observed i. Therefore, under a high normal stress, hydraulic pressure in the fracture imposes slight effect on the permeability coefficient of the fractured rock 2 The permeability coefficients of different types of fractured rocks all drop with the increasing normal stress but exhibit different magnitudes.
Under identical hydraulic pressure and confining pressure, the permeability coefficient of single-fracture coarse sandstone is greatest, followed by that of single-fracture heterogeneous rock, and the permeability coefficient of single-fracture fine sandstone is lowest 4 All the parameters in the calculation model can be experimentally measured, which are independent of empirical and semiempirical settings.
Moreover, theoretical calculation results of permeability coefficient fit well with the test data, which confirmed the variation tendencies of permeability coefficient and stress on the fracture surface. The data used to support the findings of this study are available from the corresponding author upon request.
This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article of the Year Award: Outstanding research contributions of , as selected by our Chief Editors. Read the winning articles. Journal overview. Special Issues. Academic Editor: Mohammad Sarmadivaleh.
Received 20 Jul Accepted 29 Oct Published 15 Jan Abstract Fractured rocks are a type of complex media that widely exist in various projects including energy, hydraulic, and underground space engineering, whose permeability properties are a hotspot in current rock mechanics domain. Introduction Seepage in fractured rocks can significantly affect construction stability in underground engineering [ 1 — 3 ], foundation engineering [ 4 , 5 ], and rock-soil bodies on side slopes [ 6 — 8 ].
Test Materials and Method 2. Test Materials and Instrument Artificial cutting cracks are essentially different from the cracks in rock mass under natural loading in terms of openness, roughness, and coincidence of fracture surfaces. Figure 1. Figure 2. Figure 3. Treatment method of specimens for unidirectional fissure seepage.
Figure 4. Figure 5. Table 1. Mechanical parameters of coarse sandstone and fine sandstone. Figure 6. Figure 7. Relationship between permeability coefficient and osmotic pressure. Figure 8. Relationship between permeability coefficient and normal stress.
Figure 9. Equivalent continuum model of heterogeneous rock mass with single fissure. Figure Displacement calculation model of heterogeneous rock mass with single fissure under three-direction stress condition.
Table 2. Calculation of various parameters and permeability coefficient of fractured rock mass. Comparison of calculated values and experimental values of permeability coefficient. References D. Or, M. Tuller, and R. Bian, M. Xiao, and J. Li, Y. Chen, Q. Jiang, R. Hu, and C. Xiang, L. Wang, S. Wu, H. Yuan, and Z. The aquifer system consists of layered rocks that are deeply buried where they dip into large structural basins. It is a classic confined, or artesian, system and contains three aquifers fig.
In descending order, these are the St. Peter-Prairie du Chien-Jordan aquifer sandstone with some dolomite , the Ironton-Galesville aquifer sandstone , and the Mount Simon aquifer sandstone. The aquifers are named from the principal geologic formations that comprise them. Confining units of poorly permeable sandstone and dolomite separate the aquifers.
Low-permeability shale and dolomite compose the Maquoketa confining unit that overlies the uppermost aquifer and is considered to be part of the aquifer system. Wells that penetrate the Cambrian-Ordovician aquifer system commonly are open to all three aquifers, which are collectively called the sandstone aquifer in many reports.
The rocks of the aquifer system are exposed in large areas of northern Wisconsin and eastern Minnesota, adjacent to the Wisconsin Dome, a topographic high on crystalline Precambrian rocks. From this high area, the rocks slope southward into the Forest City Basin in southwestern Iowa and northwestern Missouri, southeastward into the Illinois Basin in southern Illinois, and eastward toward the Michigan Basin, a circular low area centered on the Lower Peninsula of Michigan.
The configuration of the top of the Mount Simon sandstone that forms the Mount Simon aquifer is shown in figure The map shows that this aquifer, which represents the lower part of the Cambrian-Ordovician aquifer system, is buried to depths of 2, to 3, feet below sea level in these structural basins. The configuration of the tops of the overlying Ironton-Galesville and St. The deeply buried parts of the aquifer system contain saline water.
Regionally, water in the Cambrian-Ordovician aquifer system moves from topographically high recharge areas, where the aquifers crop out or are buried to shallow depths, eastward and southeastward toward the Michigan and Illinois Basins. A map of the potentiometric surface of the St. Peter-Prairie du Chien-Jordan aquifer fig. The map also shows that water moves subregionally toward major streams, such as the Mississippi and the Wisconsin Rivers, and toward major withdrawal centers, such as those at Chicago, Illinois, and Green Bay and Milwaukee, Wisconsin.
In and near aquifer outcrop areas, water moves along short flow paths toward small streams. Movement of water in the underlying Ironton-Galesville and Mount Simon aquifers is similar to that in the St.
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