Macroscopic mechanical properties of porous rock with one saturating fluid

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. MR223-MR239 ◽  
Author(s):  
Wubing Deng ◽  
Igor B. Morozov
Keyword(s):  
Mechanical Properties ◽  
Laboratory Experiments ◽  
Kinetic Equations ◽  
Low Frequency ◽  
Fluid Flows ◽  
Pore Fluid ◽  
P Wave ◽  
Rock Properties ◽  
Porous Rock ◽  
Arbitrary Boundary

Effective frequency-dependent moduli and [Formula: see text]-factors are broadly used for characterizing the behavior of earth media in laboratory and field seismic observations. However, such properties are wavemode- and experiment-dependent and are often incomplete and/or inaccurate for modeling realistic situations. For example, viscoelastic moduli for porous fluid-saturated rock are usually derived for primary waves, but they may not apply to cases in which secondary waves are important, such as reflections in finely layered poroelastic media or quasistatic pore-fluid flows in laboratory experiments. To obtain a model applicable to all cases, equations of mechanics should be used, and mechanical properties of the material must be identified. To reveal and measure such properties for fluid-saturated porous rock, we have developed a Biot-consistent model based on Lagrangian continuum mechanics. The model is “minimal,” purely macroscopic, and independent of the macrostructure or patterns of pore-fluid flows; thus, it could represent many existing wave-induced fluid-flow (WIFF) as well as non-WIFF models. Due to its mechanical definition, the model should be applicable to all rock-physics experiments (linear creep, pore flow, low-frequency, resonant, or ultrasonic), any waves in the field (primary, secondary, standing, surface, etc.) under arbitrary boundary conditions, and also finite-difference and finite-element numerical modeling. When based on this model, numerical simulations require no integral equations, fractional derivatives, memory variables, or additional kinetic equations. We further use the model to invert for detailed elastic and viscous properties of fluid-saturated Berea and Fontainebleau sandstones from recently published low-frequency laboratory experiments. All rock properties inferred in the model are time- and frequency-independent, comparable to other physical observations, and the model closely predicts the data. The model can be approximately pore-fluid independent, which allows performing rigorous fluid substitution with viscous pore fluids. As an illustration, P-wave velocity dispersion and attenuation in water-, oil-, and gas-saturated sandstone are simulated.

Inversion for Biot-consistent material properties in subresonant oscillation experiments with fluid-saturated porous rock

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. MR67-MR79 ◽  
Author(s):  
Igor B. Morozov ◽  
Wubing Deng
Keyword(s):  
Traveling Wave ◽  
Seismic Waves ◽  
Rock Specimen ◽  
Low Frequency ◽  
P Wave ◽  
Axial Deformation ◽  
Porous Rock ◽  
Frequency Dependent ◽  
Shear Moduli ◽  
Young’S Moduli

To quantitatively interpret the results of a subresonant laboratory or numerical experiment with wet porous rock, it is insufficient to merely state the measured frequency-dependent viscoelastic moduli and [Formula: see text]-factors. The measured properties are apparent, i.e., dependent on the experimental setup such as the length of the sample and boundary conditions for pore flows. To reveal the true properties of the material, all experimental factors need to be accurately modeled and corrected for. Here, such correction is performed by developing an effective Biot’s model for the material and using it to predict driven oscillations of a cylindrical rock specimen. The model explicitly describes elastic and inertial effects, Biot’s flows, and viscous internal friction within the solid frame and pore fluid, and it approximates squirt and other wave-induced flow effects. The model predicts the dynamic permeability of the specimen, fast (traveling) and slow (diffusive) P- and axial-deformation waves, and it allows accurate modeling of any other ultrasonic or seismic-frequency experiments with the same rock. To illustrate the approach, attenuation and dispersion data from two laboratory and numerical experiments with sandstones are inverted for effective, frequency-dependent moduli of drained sandstone. Several observations from this inversion may be useful for interpreting experiments with porous rock. First, Young’s moduli measured in a short rock cylinder differ from those in a traveling wave within an infinite rod. In particular, for the modeled 8 cm long rock specimen, modulus dispersion and attenuation ([Formula: see text]) are approximately 10 times greater than for a traveling wave. Second, P-wave moduli cannot be derived from the measured Young’s and shear moduli by using conventional (visco)elastic relations. Third, because of wavelengths comparable with the size of the specimen, slow waves contribute to its quasistatic and low-frequency behaviors. Similar observations should also apply to seismic waves traveling through approximately 10 cm layering in the field.

Simultaneous inversion of prestack seismic data for rock properties using simulated annealing

Geophysics ◽  
2002 ◽  
Vol 67 (6) ◽  
pp. 1877-1885 ◽  
Author(s):  
Xin‐Quan Ma
Keyword(s):  
Simulated Annealing ◽  
Seismic Data ◽  
Low Frequency ◽  
Optimization Procedure ◽  
P Wave ◽  
Rock Properties ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Simultaneous Inversion ◽  
Reflection Seismic

A new prestack inversion algorithm has been developed to simultaneously estimate acoustic and shear impedances from P‐wave reflection seismic data. The algorithm uses a global optimization procedure in the form of simulated annealing. The goal of optimization is to find a global minimum of the objective function, which includes the misfit between synthetic and observed prestack seismic data. During the iterative inversion process, the acoustic and shear impedance models are randomly perturbed, and the synthetic seismic data are calculated and compared with the observed seismic data. To increase stability, constraints have been built into the inversion algorithm, using the low‐frequency impedance and background Vs/Vp models. The inversion method has been successfully applied to synthetic and field data examples to produce acoustic and shear impedances comparable to log data of similar bandwidth. The estimated acoustic and shear impedances can be combined to derive other elastic parameters, which may be used for identifying of lithology and fluid content of reservoirs.

Bounds on low‐frequency seismic velocities in partially saturated rocks

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 918-924 ◽  
Author(s):  
Gary Mavko ◽  
Tapan Mukerji
Keyword(s):  
Low Frequency ◽  
Pore Fluid ◽  
Rock Properties ◽  
Upper And Lower Bounds ◽  
Small Scale ◽  
Seismic Velocities ◽  
Fluid Properties ◽  
Seismic Frequencies ◽  
The Individual ◽  
Wave Induced

The most common technique for estimating seismic velocities in rocks with mixed pore fluid saturations is to use Gassmann’s relations with an effective fluid whose density and compressibility are averages of the individual pore fluid properties. This approach is applicable only if the gas, oil, and brine phases are mixed uniformly at a very small scale, so the different wave‐induced increments of pore pressure in each phase have time to diffuse and equilibrate during a seismic period. In contrast, saturations that are heterogeneous over scales larger than the characteristic diffusion length, i.e., patchy saturation, will always lead to higher seismic velocities than if the same fluids are mixed uniformly at a fine scale. Critical saturation scales separating uniform from patchy behavior are typically of the order 0.1–1 cm for laboratory measurements and tens of centimeters for field seismic frequencies. For low seismic frequencies, velocities corresponding to patchy and homogeneous saturations represent approximate upper and lower bounds for given saturations and dry rock properties. For well‐consolidated rocks, both bounds can be estimated easily using Gassmann’s relations with Voigt and Reuss average effective fluids, respectively.

scholarly journals Experimental Investigation of the Relationship between the P-Wave Velocity and the Mechanical Properties of Damaged Sandstone

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Qi-Le Ding ◽  
Shuai-Bing Song
Keyword(s):  
Mechanical Properties ◽  
High Temperature ◽  
Young’S Modulus ◽  
Wave Velocity ◽  
Young's Modulus ◽  
P Wave ◽  
Rock Properties ◽  
High Temperature Treatment ◽  
P Wave Velocity ◽  
The Relationship

To obtain an improved and more accurate understanding of the relationship between the P-wave velocity and the mechanical properties of damaged sandstone, uniaxial compression tests were performed on sandstone subjected to different high-temperature treatments or freeze-thaw (F-T) cycles. After high-temperature treatment, the tests showed a generally positive relationship between the P-wave velocity and mechanical characteristics, although there were many exceptions. The mechanical properties showed significant differences for a given P-wave velocity. Based on the mechanical tests after the F-T cycles, the mechanical properties and P-wave velocities exhibited different trends. The UCS and Young’s modulus values slightly decreased after 30, 40, and 50 cycles, whereas both an increase and a decrease occurred in the P-wave velocity. The UCS, Young’s modulus, and P-wave velocity represent different macrobehaviors of rock properties. A statistical relationship exists between the P-wave velocity and mechanical properties, such as the UCS and Young’s modulus, but no mechanical relationship exists. Further attention should be given to using the P-wave velocity to estimate and predict the mechanical properties of rock.

scholarly journals On The Low-Frequency Elastic Response of Pierre Shale During Temperature Cycles

2021 ◽  
Author(s):  
Stian Rørheim ◽  
Andreas Bauer ◽  
Rune M Holt
Keyword(s):  
Wave Velocity ◽  
Low Frequency ◽  
P Wave ◽  
Rock Properties ◽  
Fluid Viscosity ◽  
S Wave ◽  
Temperature Cycles ◽  
Wave Velocities ◽  
Young’S Moduli ◽  
P Wave Velocity

Summary The impact of temperature on elastic rock properties is less-studied and thus less-understood than that of pressure and stress. Thermal effects on dispersion are experimentally observed herein from seismic to ultrasonic frequencies: Young’s moduli and Poisson’s ratios plus P- and S-wave velocities are determined by forced-oscillation (FO) from 1 to 144 Hz and by pulse-transmission (PT) at 500 kHz. Despite being the dominant sedimentary rock type, shales receive less experimental attention than sandstones and carbonates. To our knowledge, no other FO studies on shale at above ambient temperatures exist. Temperature fluctuations are enforced by two temperature cycles from 20 via 40 to 60○C and vice versa. Measured rock properties are initially irreversible but become reversible with increasing number of heating and cooling segments. Rock property-sensitivity to temperature is likewise reduced. It is revealed that dispersion shifts towards higher frequencies with increasing temperature (reversible if decreased), Young’s moduli and P-wave velocity moduli and P-wave velocity maxima occur at 40○C for frequencies below 56 Hz, and S-wave velocities remain unchanged with temperature (if the first heating segment is neglected) at seismic frequencies. In comparison, ultrasonic P- and S-wave velocities are found to decrease with increasing temperatures. Behavioural differences between seismic and ultrasonic properties are attributed to decreasing fluid viscosity with temperature. We hypothesize that our ultrasonic recordings coincide with the transition-phase separating the low- and high-frequency regimes while our seismic recordings are within the low-frequency regime.

scholarly journals Exact expression for the effective acoustics of patchy-saturated rocks

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. N87-N96 ◽  
Author(s):  
Bouko Vogelaar ◽  
David Smeulders ◽  
Jerry Harris
Keyword(s):  
Oil And Gas ◽  
Low Frequency ◽  
Exact Expression ◽  
P Wave ◽  
Rock Properties ◽  
Partially Saturated ◽  
P Wave Velocity ◽  
Seismic Frequencies ◽  
Exact Analytic Expression ◽  
Conventional Models

Seismic effects of a partially gas-saturated subsurface have been known for many years. For example, patches of nonuniform saturation occur at the gas-oil and gas-water contacts in hydrocarbon reservoirs. Open-pore boundary conditions are applied to the quasi-static Biot equations of poroelasticity to derive an exact analytic expression of the effective bulk modulus for partially saturated media with spherical gas patches larger than the typical pore size. The pore fluid and the rock properties can have different values in the central sphere and in the surrounding region. An analytic solution prevents loss of accuracy from ill-conditioned equations as encountered in the numerical solution for certain input. For a sandstone saturated with gas and water, we found that the P-wave velocity and attenuation in conventional models differ as much as 15% from the exact solution at seismic frequencies. This makes the use of present exact theory necessary to describe patchy saturation, although (more realistic) complex patch shapes and distributions were not considered. We found that, despite earlier corrections, the White conventional model does not yield the correct low-frequency asymptote for the attenuation.

Integration of Multi-geophysical Approaches to Identify Potential Pathways of Heavy Metals Contamination - A Case Study in Zeida, Morocco

2020 ◽  
Vol 25 (3) ◽  
pp. 415-423
Author(s):  
Ahmed Lachhab ◽  
El Mehdi Benyassine ◽  
Mohamed Rouai ◽  
Abdelilah Dekayir ◽  
Jean C. Parisot ◽  
...  
Keyword(s):  
Heavy Metals ◽  
Seismic Velocity ◽  
Seismic Refraction ◽  
Geophysical Methods ◽  
Low Frequency ◽  
Electrical Current ◽  
P Wave ◽  
Low Resistivity ◽  
Refraction Tomography ◽  
Geophysical Surveys

The tailings of Zeida's abandoned mine are found near the city of Midelt, in the middle of the high Moulouya watershed between the Middle and the High Atlas of Morocco. The tailings occupy an area of about 100 ha and are stored either in large mining pit lakes with clay-marl substratum or directly on a heavily fractured granite bedrock. The high contents of lead and arsenic in these tailings have transformed them into sources of pollution that disperse by wind, runoff, and seepage to the aquifer through faults and fractures. In this work, the main goal is to identify the pathways of contaminated water with heavy metals and arsenic to the local aquifers, water ponds, and Moulouya River. For this reason, geophysical surveys including electrical resistivity tomography (ERT), seismic refraction tomography (SRT) and very low-frequency electromagnetic (VLF-EM) methods were carried out over the tailings, and directly on the substratum outside the tailings. The result obtained from combining these methods has shown that pollutants were funneled through fractures, faults, and subsurface paleochannels and contaminated the hydrological system connecting groundwater, ponds, and the river. The ERT profiles have successfully shown the location of fractures, some of which extend throughout the upper formation to depths reaching the granite. The ERT was not successful in identifying fractures directly beneath the tailings due to their low resistivity which inhibits electrical current from propagating deeper. The seismic refraction surveys have provided valuable details on the local geology, and clearly identified the thickness of the tailings and explicitly marked the boundary between the Triassic formation and the granite. It also aided in the identification of paleochannels. The tailings materials were easily identified by both their low resistivity and low P-wave velocity values. Also, both resistivity and seismic velocity values rapidly increased beneath the tailings due to the compaction of the material and lack of moisture and have proven to be effective in identifying the upper limit of the granite. Faults were found to lie along the bottom of paleochannels, which suggest that the locations of these channels were caused by these same faults. The VLF-EM surveys have shown tilt angle anomalies over fractured areas which were also evinced by low resistivity area in ERT profiles. Finally, this study showed that the three geophysical methods were complementary and in good agreement in revealing the pathways of contamination from the tailings to the local aquifer, nearby ponds and Moulouya River.

scholarly journals Damage Evolution of Granodiorite after Heating and Cooling Treatments

Minerals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 779
Author(s):  
Mohamed Gomah ◽  
Guichen Li ◽  
Salah Bader ◽  
Mohamed Elkarmoty ◽  
Mohamed Ismael
Keyword(s):  
Mechanical Properties ◽  
Tensile Strength ◽  
Failure Mode ◽  
Physical And Mechanical Properties ◽  
P Wave ◽  
Physical Parameters ◽  
Slow Cooling ◽  
Heating And Cooling ◽  
Natural Rock ◽  
The Impact

The awareness of the impact of high temperatures on rock properties is essential to the design of deep geotechnical applications. The purpose of this research is to assess the influence of heating and cooling treatments on the physical and mechanical properties of Egyptian granodiorite as a degrading factor. The samples were heated to various temperatures (200, 400, 600, and 800 °C) and then cooled at different rates, either slowly cooled in the oven and air or quickly cooled in water. The porosity, water absorption, P-wave velocity, tensile strength, failure mode, and associated microstructural alterations due to thermal effect have been studied. The study revealed that the granodiorite has a slight drop in tensile strength, up to 400 °C, for slow cooling routes and that most of the physical attributes are comparable to natural rock. Despite this, granodiorite thermal deterioration is substantially higher for quick cooling than for slow cooling. Between 400:600 °C is ‘the transitional stage’, where the physical and mechanical characteristics degraded exponentially for all cooling pathways. Independent of the cooling method, the granodiorite showed a ductile failure mode associated with reduced peak tensile strengths. Additionally, the microstructure altered from predominantly intergranular cracking to more trans-granular cracking at 600 °C. The integrity of the granodiorite structure was compromised at 800 °C, the physical parameters deteriorated, and the rock tensile strength was negligible. In this research, the temperatures of 400, 600, and 800 °C were remarked to be typical of three divergent phases of granodiorite mechanical and physical properties evolution. Furthermore, 400 °C could be considered as the threshold limit for Egyptian granodiorite physical and mechanical properties for typical thermal underground applications.

Development of Low Carbon High Strength H-Beam Steel

2010 ◽  
Vol 168-170 ◽  
pp. 969-972
Author(s):  
Jian Qing Qian ◽  
Ji Ping Chen ◽  
Bao Qiao Wu ◽  
Jie Ca Wu
Keyword(s):  
Mechanical Properties ◽  
Laboratory Experiments ◽  
Theoretical Study ◽  
High Strength ◽  
Rolling Process ◽  
Low Carbon ◽  
Study Product ◽  
H Beam ◽  
Nitrogen Alloy

The application of vanadium-nitrogen alloy to develop a certain low carbon high strength H-beam steel was determined through the combination of theoretical study, product requirements and existing practical conditions. The specific rolling process was further defined through laboratory experiments. The developed low carbon high strength H-beam steel was trial produced and its properties were also analyzed. The results showed that the newly developed low carbon high strength H-beam steel had excellent mechanical properties and good weldability.

P- and S-wave attenuation logs from monopole sonic data

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 755-765 ◽  
Author(s):  
Xinhua Sun ◽  
Xiaoming Tang ◽  
C. H. (Arthur) Cheng ◽  
L. Neil Frazer
Keyword(s):  
Wave Attenuation ◽  
Fluid Velocity ◽  
P Wave ◽  
Reservoir Rock ◽  
Rock Properties ◽  
S Wave ◽  
Intrinsic Attenuation ◽  
Modified Method ◽  
Receiver Array ◽  
Attenuation Profiles

In this paper, a modification of an existing method for estimating relative P-wave attenuation is proposed. By generating synthetic waveforms without attenuation, the variation of geometrical spreading related to changes in formation properties with depth can be accounted for. With the modified method, reliable P- and S-wave attenuation logs can be extracted from monopole array acoustic waveform log data. Synthetic tests show that the P- and S-wave attenuation values estimated from synthetic waveforms agree well with their respective model values. In‐situ P- and S-wave attenuation profiles provide valuable information about reservoir rock properties. Field data processing results show that this method gives robust estimates of intrinsic attenuation. The attenuation profiles calculated independently from each waveform of an eight‐receiver array are consistent with one another. In fast formations where S-wave velocity exceeds the borehole fluid velocity, both P-wave attenuation ([Formula: see text]) and S-wave attenuation ([Formula: see text]) profiles can be obtained. P- and S-wave attenuation profiles and their comparisons are presented for three reservoirs. Their correlations with formation lithology, permeability, and fractures are also presented.

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