scholarly journals A quantitative interpretation of the saturation exponent in Archie’s equations

2021 ◽  
Vol 18 (2) ◽  
pp. 444-449
Author(s):  
Tong-Cheng Han ◽  
Han Yan ◽  
Li-Yun Fu
Keyword(s):  
Aspect Ratio ◽  
Pore Space ◽  
Fluid Distribution ◽  
Air Bubbles ◽  
Quantitative Interpretation ◽  
Porous Rocks ◽  
Homogeneous Fluid ◽  
Quantitative Understanding ◽  
Saturation Exponent ◽  
Wagner Theory

AbstractSaturation exponent is an important parameter in Archie’s equations; however, there has been no well-accepted physical interpretation for the saturation exponent. We have theoretically derived Archie’s equations from the Maxwell–Wagner theory on the assumption of homogeneous fluid distribution in the pore space of clay-free porous rocks. Further theoretical derivations showed that the saturation exponent is in essence the cementation exponent for the water–air mixture and is quantitatively and explicitly related to the aspect ratio of the air bubbles in the pores. The results have provided a theoretical backup for the empirically obtained Archie’s equations and have offered a more physical and quantitative understanding of the saturation exponent.

Squirt-flow seismic dispersion models: a comparison

2020 ◽  
Vol 222 (3) ◽  
pp. 2068-2082 ◽  
Author(s):  
Yongyang Sun ◽  
José M Carcione ◽  
Boris Gurevich
Keyword(s):  
Aspect Ratio ◽  
Pore Space ◽  
Crack Density ◽  
Fluid Pressure ◽  
Porous Rocks ◽  
Dispersion Models ◽  
Pore Characteristics ◽  
Low Frequencies ◽  
High Frequencies ◽  
Significant Difference

SUMMARY The anelastic properties of porous rocks depend on the pore characteristics, specifically, the pore aspect ratio and the pore fraction (related to the soft porosity). At high frequencies, there is no fluid pressure communication throughout the pore space and the rock becomes stiffer than at low frequencies, where the pore pressure is fully equilibrated. This causes a significant difference between the moduli at low and high frequencies, which is known as seismic dispersion and is commonly explained by the squirt-flow mechanism. In this paper, we consider and contrast three squirt-flow dispersion models: the modified Mavko–Jizba model, valid for a porous medium with arbitrary shapes of the pores and cracks, and two other models, based on idealized geometries of spheres and ellipsoids: the EIAS (equivalent inclusion-average stress) and CPEM (cracks and pores effective medium) models. We first perform analytical comparisons and then compute several numerical examples to demonstrate similarities and differences between the models. The analytical comparison shows that when the stiff pores are spherical and the crack density is small, the theoretical predictions of the three models are very close to each other. However, when the stiff pores are spheroids with an aspect ratio smaller than 1 (say, between 0.2 and 1), the predictions of inclusion based models are not valid at frequencies of ultrasonic measurements on rock samples. In contrast, the predictions of the modified Mavko–Jizba model are valid at ultrasonic frequencies of about 106 Hz, which is a typical frequency of laboratory measurements on core samples. We also introduce Zener-based bulk and shear dispersion indices, which are proportional to the difference between the high- and low-frequency stiffness moduli, and are a measure of the degree of anelasticity, closely related to the quality factors by view of the Kramers–Kronig relations. The results show that the three models yield similar moduli dispersion with very small differences when the crack density is relatively high. The indices versus crack density can be viewed as a template to obtain the crack properties from low- and high-frequency velocity measurements.

scholarly journals Use of Image Correlation to Measure Macroscopic Strains by Hygric Swelling in Sandstone Rocks

2021 ◽  
Vol 11 (6) ◽  
pp. 2495
Author(s):  
Belén Ferrer ◽  
María-Baralida Tomás ◽  
David Mas
Keyword(s):  
Cross Correlation ◽  
Pore Space ◽  
Digital Camera ◽  
Experimental Methods ◽  
Image Correlation ◽  
Rock Surface ◽  
Experimental Setup ◽  
Porous Rocks ◽  
Porous Sandstone ◽  
Variable Displacement

Some materials undergo hygric expansion when soaked. In porous rocks, this effect is enhanced by the pore space, because it allows water to reach every part of its volume and to hydrate most swelling parts. In the vicinity, this enlargement has negative structural consequences as adjacent elements support some compressions or displacements. In this work, we propose a normalized cross-correlation between rock surface texture images to determine the hygric expansion of such materials. We used small porous sandstone samples (11 × 11 × 30 mm3) to measure hygric swelling. The experimental setup comprised an industrial digital camera and a telecentric objective. We took one image every 5 min for 3 h to characterize the whole swelling process. An error analysis of both the mathematical and experimental methods was performed. The results showed that the proposed methodology provided, despite some limitations, reliable hygric swelling information by a non-contact methodology with an accuracy of 1 micron and permitted the deformation in both the vertical and horizontal directions to be explored, which is an advantage over traditional linear variable displacement transformers.

scholarly journals Clogging sensitivity of flow distributors designed for radially elongated hexagonal pillar array columns: a computational modelling

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Farideh Haghighi ◽  
Zahra Talebpour ◽  
Amir Sanati-Nezhad
Keyword(s):  
Pressure Drop ◽  
Aspect Ratio ◽  
Contact Zone ◽  
Separation Efficiency ◽  
Fluid Dynamic ◽  
Computational Modelling ◽  
Channel Width ◽  
Fluid Distribution ◽  
Design Parameters ◽  
Pillar Array

AbstractFlow distributor located at the beginning of the micromachined pillar array column (PAC) has significant roles in uniform distribution of flow through separation channels and thus separation efficiency. Chip manufacturing artifacts, contaminated solvents, and complex matrix of samples may contribute to clogging of the microfabricated channels, affect the distribution of the sample, and alter the performance of both natural and engineered systems. An even fluid distribution must be achieved cross-sectionally through careful design of flow distributors and minimizing the sensitivity to clogging in order to reach satisfactory separation efficiency. Given the difficulty to investigate experimentally a high number of clogging conditions and geometries, this work exploits a computational fluid dynamic model to investigate the effect of various design parameters on the performance of flow distributors in equally spreading the flow along the separation channels in the presence of different degrees of clogging. An array of radially elongated hexagonal pillars was selected for the separation channel (column). The design parameters include channel width, distributor width, aspect ratio of the pillars, and number of contact zone rows. The performance of known flow distributors, including bifurcating (BF), radially interconnected (RI), and recently introduced mixed-mode (MMI) in addition to two new distributors designed in this work (MMII and MMIII) were investigated in terms of mean elution time, volumetric variance, asymmetry factors, and pressure drop between the inlet and the monitor line for each design. The results show that except for pressure drop, the channel width and aspect ratio of the pillars has no significant influence on flow distribution pattern in non-clogged distributors. However, the behavior of flow distributors in response to clogging was found to be dependent on width of the channels. Also increasing the distributor width and number of contact zone rows after the first splitting stage showed no improvement in the ability to alleviate the clogging. MMI distributor with the channel width of 3 µm, aspect ratio of the pillars equal to 20, number of exits of 8, and number of contact zones of 3 exhibited the highest stability and minimum sensitivity to different degrees of clogging.

Subpixel determination of wormhole tip position in 4D tomography of dissolving limestone cores

2021 ◽  
Author(s):  
Rishabh Prakash Sharma ◽  
Max P. Cooper ◽  
Anthony J.C. Ladd ◽  
Piotr Szymczak
Keyword(s):  
Flow Field ◽  
Pore Space ◽  
Nonlinear Process ◽  
Linear Interpolation ◽  
Flow Fields ◽  
Porous Rocks ◽  
Dissolution Experiment ◽  
Novel Approach ◽  
Highly Nonlinear ◽  
Computed Microtomography

<p>Dissolution of porous rocks by reactive fluids is a highly nonlinear process resulting in a variety of dissolution patterns, the character of which depends on physical conditions such as flow rate and reactivity of the fluid. Long, finger-like dissolution channels, “wormholes”, are the main subject of interest in the literature, however, the underlying dynamics of their growth remains unclear. </p><p>While analyzing the tomography data on wormhole growth.  one open question is to define the exact position of the tip of the wormhole. Near the tip the wormhole gradually thins out and the proper resolution of its features is hindered by the finite spatial resolution of the tomographs. In particular, we often observe in the near-tip region several disconnected regions of porosity growth, which - as we hypothesized - are connected by the dissolution channels at subpixel scale. In this study, we show how these features can be better resolved by using numerically calculated flow fields in the reconstructed pore-space. </p><p>We used 70 micrometers, 16-bit grayscale X-ray computed microtomography (XCMT) time series scans of limestone cores, 14mm in diameter and 25mm in length. Scans were performed during the entire dissolution experiment with an interval of 8 minutes. These scans were further processed using a 3-phase segmentation proposed by Luquot et al.[1], in which grayscale voxels are converted to macro-porosity, micro-porosity and grain phases from their grayscale values. The macro-porous phase is assigned a porosity of 1, while the grain phase is assigned 0. Micro-porous regions are assigned an intermediate value determined by linear interpolation between pore and grain threshold using grayscale values. An OpenFOAM based, Darcy-Brinkman solver, porousFoam, is then used to calculate the flow field in this extracted porosity field. </p><p>Porosity contours reconstructed from the tomographs show some disconnected porosity growth near the tip region which later become part of the wormhole in subsequent scans. We have used a novel approach by including the micro-porosity phase in pore-space to calculate the flow-fields in the near-tip region. The calculated flow fields clearly show an extended region of focused flow in front of the wormhole tip, which is a manifestation of the presence of a wormhole at the subpixel scale. These results show that micro-porosity plays an important role in dissolution and 3-phase segmentation combined with the flow field calculations is able to capture the sub-resolved dissolution channels. </p><p> </p><p> [1] Luquot, L., Rodriguez, O., and Gouze, P.: Experimental characterization of porosity structure and transport property changes in limestone undergoing different dissolution regimes, Transport Porous Med., 101, 507–532, 2014</p>

Chemotaxis under flow disorder shapes microbial dispersion in porous media 

2021 ◽  
Author(s):  
Pietro de Anna ◽  
Amir A. Pahlavan ◽  
Yutaka Yawata ◽  
Roman Stocker ◽  
Ruben Juanes
Keyword(s):  
Porous Media ◽  
Dispersion Coefficient ◽  
Pore Space ◽  
Low Flow ◽  
Pore Scale ◽  
Porous Rocks ◽  
Chemical Gradients ◽  
Deep Earth ◽  
Bacterium Bacillus Subtilis ◽  
Bacterium Bacillus

<div> <div> <div> <p>Natural soils are host to a high density and diversity of microorganisms, and even deep-earth porous rocks provide a habitat for active microbial communities. In these environ- ments, microbial transport by disordered flows is relevant for a broad range of natural and engineered processes, from biochemical cycling to remineralization and bioremediation. Yet, how bacteria are transported and distributed in the sub- surface as a result of the disordered flow and the associ- ated chemical gradients characteristic of porous media has remained poorly understood, in part because studies have so far focused on steady, macroscale chemical gradients. Here, we use a microfluidic model system that captures flow disorder and chemical gradients at the pore scale to quantify the transport and dispersion of the soil-dwelling bacterium Bacillus subtilis in porous media. We observe that chemotaxis strongly modulates the persistence of bacteria in low-flow regions of the pore space, resulting in a 100% increase in their dispersion coefficient. This effect stems directly from the strong pore-scale gradients created by flow disorder and demonstrates that the microscale interplay between bacterial behaviour and pore-scale disorder can impact the macroscale dynamics of biota in the subsurface.</p> </div> </div> </div>

scholarly journals Effects of Foam Microbubbles on Electrical Resistivity and Capillary Pressure of Partially Saturated Porous Media

Molecules ◽  
2020 ◽  
Vol 25 (15) ◽  
pp. 3385 ◽  
Author(s):  
Abdulrauf R. Adebayo ◽  
Abubakar Isah ◽  
Mohamed Mahmoud ◽  
Dhafer Al-Shehri
Keyword(s):  
Porous Media ◽  
Electrical Resistivity ◽  
Capillary Pressure ◽  
Oil Recovery ◽  
Water Saturation ◽  
Porous Plate ◽  
Fluid Distribution ◽  
Cross Sectional ◽  
Injection Process ◽  
Saturation Exponent

Laboratory measurements of capillary pressure (Pc) and the electrical resistivity index (RI) of reservoir rocks are used to calibrate well logging tools and to determine reservoir fluid distribution. Significant studies on the methods and factors affecting these measurements in rocks containing oil, gas, and water are adequately reported in the literature. However, with the advent of chemical enhanced oil recovery (EOR) methods, surfactants are mixed with injection fluids to generate foam to enhance the gas injection process. Foam is a complex and non-Newtonian fluid whose behavior in porous media is different from conventional reservoir fluids. As a result, the effect of foam on Pc and the reliability of using known rock models such as the Archie equation to fit experimental resistivity data in rocks containing foam are yet to be ascertained. In this study, we investigated the effect of foam on the behavior of both Pc and RI curves in sandstone and carbonate rocks using both porous plate and two-pole resistivity methods at ambient temperature. Our results consistently showed that for a given water saturation (Sw), the RI of a rock increases in the presence of foam than without foam. We found that, below a critical Sw, the resistivity of a rock containing foam continues to rise rapidly. We argue, based on knowledge of foam behavior in porous media, that this critical Sw represents the regime where the foam texture begins to become finer, and it is dependent on the properties of the rock and the foam. Nonetheless, the Archie model fits the experimental data of the rocks but with resulting saturation exponents that are higher than conventional gas–water rock systems. The degree of variation in the saturation exponents between the two fluid systems also depends on the rock and fluid properties. A theory is presented to explain this phenomenon. We also found that foam affects the saturation exponent in a similar way as oil-wet rocks in the sense that they decrease the cross-sectional area of water available in the pores for current flow. Foam appears to have competing and opposite effects caused by the presence of clay, micropores, and conducting minerals, which tend to lower the saturation exponent at low Sw. Finally, the Pc curve is consistently lower in foam than without foam for the same Sw.

A dynamic elastic model for squirt-flow effect and its application on fluid-viscosity-associated velocity dispersion in reservoir sandstones

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. MR201-MR212
Author(s):  
Zhi-Qiang Yang ◽  
Tao He ◽  
Chang-Chun Zou
Keyword(s):  
Velocity Dispersion ◽  
Pore Space ◽  
Pore Fluid ◽  
Quantitative Prediction ◽  
Elastic Model ◽  
Fluid Viscosity ◽  
Porous Rocks ◽  
S Wave ◽  
Flow Effect ◽  
Reservoir Sandstones

Velocity dispersion is a common phenomenon for fluid-charged porous rocks and carries important information on the pore structure and fluid in reservoir rocks. Previous ultrasonic experiments had measured more significant non-Biot velocity dispersion on saturated reservoir sandstones with increasing pore-fluid viscosity. Although wave-induced local squirt-flow effect could in theory cause most of the non-Biot velocity dispersion, its quantitative prediction remains a challenge. Several popular models were tested to predict the measured velocities under undrained conditions, but they either underestimated the squirt-flow effect or failed to simultaneously satisfy P- and S-wave velocity dispersions (especially for higher viscosity fluids). Based on the classic double-porosity theory that pore space is comprised of mainly stiff/Biot’s porosity and minor compliant porosity, an effective “wet frame” was hypothesized to account for the squirt-flow effect, whose compliant pores are filled with a hypothesized fluid with dynamic modulus. A new dynamic elastic model was then introduced by extending Biot theory to include the squirt-flow effect, after replacing the dry-frame bulk/shear moduli with their wet-frame counterparts. In addition to yielding better velocity predictions for P- and S-wave measurements of different fluid viscosities, the new model is also more applicable because its two key tuning parameters (i.e., the effective aspect ratio and porosity of compliant pores) at in situ reservoir pressure could be constrained with laboratory velocity measurements associated with pore-fluid viscosities.

scholarly journals Multiple air-bubble enhanced oil rupture on nanostructured cellulose fabric for easy-oil cleaning fouled in a dry state

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Min-Sung Kim ◽  
Tae-Jun Ko ◽  
Seong Jin Kim ◽  
Young-A. Lee ◽  
Kyu Hwan Oh ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Solid Fraction ◽  
High Aspect Ratio ◽  
Air Bubbles ◽  
Oil Droplets ◽  
Water Contact ◽  
Air Bubble ◽  
Cellulose Fabric ◽  
Oily Water ◽  
Oil Fouling

Abstract Nanostructured cellulose fabric with an air-bubble-enhanced anti-oil fouling property is introduced for quick oil-cleaning by water even with the surface fouled by oil before water contact under a dry state. It is very challenging to recover the super-hydrophilicity because once the surface is oil-fouled, it is hard to be re-wetted by water. Anti-oil-fouling under a dry state was realized through two main features of the nanostructured, porous fabric: a low solid fraction with high-aspect-ratio nanostructures significantly increasing the retracting forces, and trapped multiscale air bubbles increasing the buoyancy and backpressure for an oil-layer rupture. The nanostructures were formed on cellulose-based rayon microfibers through selective etching with oxygen plasma, forming a nanoscale open-pore structure. Viscous crude oil fouled on a fabric under a dry state was cleaned by immersion into water owing to a higher water affinity of the rayon material and low solid fraction of the high-aspect-ratio nanostructures. Air bubbles trapped in dry porous fibers and nanostructures promote oil detachment from the fouled sites. The macroscale bubbles add buoyancy on top of the oil droplets, enhancing the oil receding at the oil-water-solid interface, whereas the relatively smaller microscale bubbles induce a backpressure underneath the oil droplets. The oil-proofing fabric was used for protecting underwater conductive sensors, allowing a robot fish to swim freely in oily water.

Oil content prediction of lacustrine organic-rich shale from wireline logs: A case study of intersalt reservoirs in the Qianjiang Sag, Jianghan Basin, China

2020 ◽  
Vol 8 (3) ◽  
pp. SL79-SL88
Author(s):  
Xin Nie ◽  
Jing Lu ◽  
Roufida Rana Djaroun ◽  
Peilin Wang ◽  
Jun Li ◽  
...  
Keyword(s):  
Experimental Data ◽  
Oil Content ◽  
Pore Space ◽  
Oil Reservoirs ◽  
Fluid Distribution ◽  
Shale Oil ◽  
Oil Saturation ◽  
Archie’S Law ◽  
The Core ◽  
Shale Oil Reservoirs

Shale oil is an unconventional oil resource with great potential. Oil saturation ([Formula: see text]) is an essential parameter for formation evaluation. However, due to the complexity of matrix mineral components and pore structure, Archie’s law cannot be used directly to calculate [Formula: see text] in shale oil reservoirs. We have developed a new saturation model for shale oil reservoirs. This model allows us to separate the organic from the inorganic pores, eliminate the background conductivity mainly caused by the borehole fluid or conductive minerals and determine the effective conductive porosity, which rules out nonconductive porosity, including isolated pores and the pore space affected by the fluid distribution. By analyzing the logging and core experimental data from the Qianjiang Sag, Jianghan Oilfield, we found that the T2 cutoff porosities of nuclear magnetic resonance logging are strongly related to the nonconductive porosities. After we determine the T2 cutoff value using the core experimental data, we can use it to obtain nonconductive porosity fraction in each depth point, which allows us to efficiently calculate [Formula: see text]. We calculate oil saturation values and use them to estimate the oil content. The results are coherent with the core experimental data, which indicates the efficiency of this model.

The Equations Archie Forgot: Anisotropy of the Rocks

2010 ◽  
Vol 13 (05) ◽  
pp. 823-836 ◽  
Author(s):  
Carlos F. Haro
Keyword(s):  
Ad Hoc ◽  
Water Saturation ◽  
Power Laws ◽  
Fluid Distribution ◽  
Data Sets ◽  
Solution Flow ◽  
Original Analysis ◽  
Particular Solution ◽  
Saturation Exponent ◽  
Complex Formations

Summary Archie's empirical equation is used extensively to estimate hydrocarbons in place. This power-laws combination has stood the test of time with few changes. However, it is still poorly understood and considered an ad hoc relation. Our original analysis will prove these laws rigorously, show how they must be amended, and introduce additional accompanying equations. This comprehensive model, which represents the electrical flow through the intricate conductive paths of the rock, is confirmed with Archie's and Hamada's core data sets. It corrects for Archie's inaccuracies. A thorough appreciation of the pore-scale physics behind the modified version of Archie's equation is presented. The principles can be applied in clean and complex formations (shaly sands, thin beds, and vuggy or fractured carbonates) to obtain enhanced values of water saturation. The theory sheds light on the role and quantification of anisotropy. Solving for the elaborate pore geometry, we use the Laplace differential equation (not Ohm's law), appropriate in the analysis of electrostatic fields in charge-free regions. Rock morphology dictates its boundary conditions (Jin 2007; Ghous 2005), characterized as corner angles. The corresponding particular solution (flow around a corner) and modeling tactic delineate the streamlines throughout the pores. The angles establish strong mathematical links among the exponents of Archie's equation, the geometry of the rock frame, and the spatial fluid distribution. This quantitative method is lacking in previous saturation models. The solution constitutes the basis to solve more-complicated rock layouts. It enables the calculation of equivalent resistivities (normalized resistances) to take advantage of well-established electrical relationships. The extra equations compute the variable exponents and coefficients of Archie's equation at every depth. They obtain the saturation exponent in clean rocks as a function of water saturation, crucial to the quality control of core electrical data and to the quantification of reservoirs under changing saturation (waterflooding). Therefore, improved calculations of original and remaining hydrocarbons are achieved.

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