Fluid-solid substitution in rocks with disconnected and partially connected porosity

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. WB89-WB95 ◽  
Author(s):  
Vladimir Grechka
Keyword(s):  
Pore Space ◽  
Fluid Substitution ◽  
Analytic Proof ◽  
Numerical Tests ◽  
Aspect Ratios ◽  
Effective Elasticity ◽  
Self Similar ◽  
Gassmann Fluid Substitution

It is usually believed that Gassmann fluid substitution can be performed only for a fully interconnected portion of the pore space. While this is certainly true, the presence of disconnected porosity does not necessarily invalidate Gassmann’s predictions. This unconventional view is supported with an analytic proof of the equivalence of Gassmann theory and the noninteraction approximation for the effective elasticity of solids with isolated self-similar pores. Numerical tests for more realistic microgeometries, where pores have diverse shapes and the pore space is partially disconnected, demonstrate that errors in Gassmann-type infill substitution are typically small and unlikely to exceed a few percent as long as the aspect ratios of pores are greater than approximately 0.2. If the fracture-like pores are aligned or elasticities of the substituted infills are close, Gassmann theory remains accurate for isolated pores with smaller aspect ratios.

Modeling squirt dispersion and attenuation in fluid-saturated rocks using pressure dependency of dry ultrasonic velocities

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. WA157-WA168 ◽  
Author(s):  
Osni Bastos de Paula ◽  
Marina Pervukhina ◽  
Dina Makarynska ◽  
Boris Gurevich
Keyword(s):  
Aspect Ratio ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Pore Space ◽  
Geometrical Parameters ◽  
Laboratory Measurements ◽  
Significant Linear Trend ◽  
Aspect Ratios ◽  
Pressure Dependency ◽  
Dispersion And Attenuation

Modeling dispersion and attenuation of elastic waves in fluid-saturated rocks due to squirt flow requires the knowledge of a number of geometrical parameters of the pore space, in particular, the characteristic aspect ratio of the pores. These parameters are usually inferred by fitting measurements on saturated rocks to model predictions. To eliminate such fitting and thus make the model more predictive, we propose to recover the geometrical parameters of the pore space from the pressure dependency of elastic moduli on dry samples. Our analysis showed that the pressure dependency of elastic properties of rocks (and their deviation from Gassmann’s prediction) at ultrasonic frequencies is controlled by the squirt flow between equant, stiff, and so-called intermediate pores (with aspect ratios between [Formula: see text]). Such intermediate porosity is expected to close at confining pressures of between 200 and 2000 MPa, and thus cannot be directly obtained from ultrasonic experiments performed at pressures below 50 MPa. However, the presence of this intermediate porosity is inferred from the significant linear trend in the pressure dependency of elastic properties of the dry rock and the difference between the bulk modulus of the dry rock computed for spherical pores and the measured modulus at 50 MPa. Moreover, we can infer the magnitude of the intermediate porosity and its characteristic aspect ratio. Substituting these parameters into the squirt model, we have computed elastic moduli and velocities of the water-saturated rock and compared these predictions against laboratory measurements of these velocities. The agreement is good for a number of clean sandstones, but not unexpectedly worse for a broad range of shaley sandstones. Our predictions showed that dispersion and attenuation caused by the squirt flow between compliant and stiff pores may occur in the seismic frequency band. Confirmation of this prediction requires laboratory measurements of elastic properties at these frequencies.

scholarly journals The structure and characteristic scales of molecular clouds

2020 ◽  
Vol 642 ◽  
pp. A177
Author(s):  
Sami Dib ◽  
Sylvain Bontemps ◽  
Nicola Schneider ◽  
Davide Elia ◽  
Volker Ossenkopf-Okada ◽  
...  
Keyword(s):  
Molecular Clouds ◽  
Spatial Scales ◽  
Dynamical Evolution ◽  
Major Axis ◽  
Distribution Functions ◽  
Underlying Structure ◽  
Aspect Ratios ◽  
Self Similar ◽  
Characteristic Scales ◽  
Variance Spectrum

The structure of molecular clouds holds important clues regarding the physical processes that lead to their formation and subsequent dynamical evolution. While it is well established that turbulence imprints a self-similar structure onto the clouds, other processes, such as gravity and stellar feedback, can break their scale-free nature. The break of self-similarity can manifest itself in the existence of characteristic scales that stand out from the underlying structure generated by turbulent motions. In this work, we investigate the structure of the Cygnus-X North and Polaris Flare molecular clouds, which represent two extremes in terms of their star formation activity. We characterize the structure of the clouds using the delta-variance (Δ-variance) spectrum. In the Polaris Flare, the structure of the cloud is self-similar over more than one order of magnitude in spatial scales. In contrast, the Δ-variance spectrum of Cygnus-X North exhibits an excess and a plateau on physical scales of ≈0.5−1.2 pc. In order to explain the observations for Cygnus-X North, we use synthetic maps where we overlay populations of discrete structures on top of a fractal Brownian motion (fBm) image. The properties of these structures, such as their major axis sizes, aspect ratios, and column density contrasts with the fBm image, are randomly drawn from parameterized distribution functions. We are able to show that, under plausible assumptions, it is possible to reproduce a Δ-variance spectrum that resembles that of the Cygnus-X North region. We also use a “reverse engineering” approach in which we extract the compact structures in the Cygnus-X North cloud and reinject them onto an fBm map. Using this approach, the calculated Δ-variance spectrum deviates from the observations and is an indication that the range of characteristic scales (≈0.5−1.2 pc) observed in Cygnus-X North is not only due to the existence of compact sources, but is a signature of the whole population of structures that exist in the cloud, including more extended and elongated structures.

scholarly journals Toward a better understanding of low-frequency electrical relaxation — An enhanced pore space characterization

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. MR257-MR270
Author(s):  
Sabine Kruschwitz ◽  
Matthias Halisch ◽  
Raphael Dlugosch ◽  
Carsten Prinz
Keyword(s):  
Mercury Intrusion Porosimetry ◽  
Characteristic Length ◽  
Pore Space ◽  
Relaxation Times ◽  
Low Frequency ◽  
Size Difference ◽  
Chemical Compositions ◽  
Length Scales ◽  
Mercury Intrusion ◽  
Aspect Ratios

The relaxation phenomena observed in the electrical low-frequency range (approximately 1 MHz–10 kHz) of natural porous media such as sandstones are often assumed to be directly related to the dominant (modal) pore throat sizes measured, for instance, with mercury intrusion porosimetry. Attempts to establish a universally valid relationship between pore size and peak spectral induced polarization (SIP) relaxation time have failed, considering sandstones from very different origins and featuring great variations in textural and chemical compositions as well as in geometric pore space properties. In addition working with characteristic relaxation times determined in Cole-Cole or Debye decomposition fits to build the relationship have not been successful. In particular, samples with narrow pore throats are often characterized by long SIP relaxation times corresponding to long “characteristic length scales” in these media, assuming that the diffusion coefficients along the electrical double layer were constant. Based on these observations, three different types of SIP relaxation can be distinguished. We have developed a new way of assessing complex pore spaces of very different sandstones in a multimethodical approach to combine the benefits of mercury intrusion porosimetry, micro-computed tomography, and nuclear magnetic resonance. In this way, we achieve much deeper insight into the pore space due to the different resolutions and sensitivities of the applied methods to pore constrictions (throats) and wide pores (pore bodies). We experimentally quantify pore aspect ratios and volume distributions within the two pore regions. We clearly observe systematic differences between three SIP relaxation types identified previously, and we can attribute the SIP peak relaxation times to measured characteristic length scales within our materials. We highlight selected results for a total of nine sandstones. It seems that SIP relaxation behavior depends on the size difference of the narrow pore throats to the wide pore bodies, which increases from SIP type 1 to type 3.

Seismic pore space compressibility and Gassmann’s relation

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1743-1749 ◽  
Author(s):  
Gary Mavko ◽  
Tapan Mukerji
Keyword(s):  
Bulk Modulus ◽  
Pore Space ◽  
Pore Fluid ◽  
Fluid Substitution ◽  
Effective Moduli ◽  
Pore Compressibility ◽  
Robust Model ◽  
Gassmann’S Equation ◽  
Model Independent

The pore space compressibility of a rock provides a robust, model‐independent descriptor of porosity and pore fluid effects on effective moduli. The pore space compressibility is also the direct physical link between the dry and fluid‐saturated moduli, and is therefore the basis of Gassmann’s equation for fluid substitution. For a fixed porosity, an increase in pore space compressibility increases the sensitivity of the modulus to fluid substitution. Two simple techniques, based on pore compressibility, are presented for graphically applying Gassmann’s relation for fluid substitution. In the first method, the pore compressibility is simply reweighted with a factor that depends only on the ratio of fluid to mineral bulk modulus. In the second technique, the rock moduli are rescaled using the Reuss average, which again depends only on the fluid and mineral moduli.

scholarly journals Modelling the seismic responses of Amangihydrocarbon field using Gassmann fluid substitution

2014 ◽  
Vol 2 (2) ◽  
pp. 106-114
Author(s):  
Sonny Inichinbia ◽  
◽  
Peter O. Sule ◽  
Aminu L. Ahmed ◽  
Halidu Hamza
Keyword(s):  
Fluid Substitution ◽  
Seismic Responses ◽  
Gassmann Fluid Substitution

Elastic moduli of dry and water-saturated carbonates — Effect of depositional texture, porosity, and permeability

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. N65-N78 ◽  
Author(s):  
Ida L. Fabricius ◽  
Gregor T. Bächle ◽  
Gregor P. Eberli
Keyword(s):  
Frequency Ratio ◽  
Elastic Moduli ◽  
Reference Frequency ◽  
Fluid Substitution ◽  
Water Softening ◽  
Effect Of Water ◽  
Porosity And Permeability ◽  
Gassmann Fluid Substitution ◽  
Water Saturated ◽  
Frequency Ratios

Elastic moduli of water-saturated sedimentary rocks are in some cases different from moduli derived using Gassmann fluid substitution on data for rocks in the dry state. To address this discrepancy, we use a data set representing 115 carbonate samples from different depositional settings and a wide range of porosity and permeability. Depositional texture is reflected in the effect of water on elastic moduli and in the porosity-permeability relationship. Depositional texture is taken into account when porosity and permeability are combined in the effective specific surface of pores, which is related for a given pore fluid to the reference frequency as defined by Biot. For a given frequency of elastic waves, we obtain Biot’s frequency ratio between measured ultrasonic wave frequency and Biot reference frequency. For mostsamples with a frequency ratio above 10, elastic moduli in the water-saturated case are higher than predicted from elastic moduli in the dry case by Gassmann fluid substitution. This stiffening effect of water in some cases may be described by Biot’s high-frequency model, although in heterogeneous samples, a squirt mechanism is more probable. For data representing frequency ratios of 0.01 to 1, Gassmann fluid substitution works well. For samples with frequency ratios below 0.001, elastic moduli in the water-saturated case are lower than would be expected according to Gassmann’s equations or to Biot’s theory. This water-softening effect becomes stronger with decreasing frequency ratio. Water softening or stiffening of elastic moduli may be addressed by effective-medium modeling. In this study, we used the isoframe model to quantify water softening as a function of frequency ratio.

An Integrated Analysis of Petrophysics, Cross-Plots and Gassmann Fluid Substitution for Characterization of Fimkassar Area, Pakistan: A Case Study

2014 ◽  
Vol 40 (1) ◽  
pp. 181-193 ◽  
Author(s):  
Aamir Ali ◽  
Muhammad Kashif ◽  
Matloob Hussain ◽  
Jamil Siddique ◽  
Irfan Aslam ◽  
...  
Keyword(s):  
Integrated Analysis ◽  
Fluid Substitution ◽  
Gassmann Fluid Substitution
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