scholarly journals Statistical characterization of gas-patch distributions in partially saturated rocks

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. WA51-WA64 ◽  
Author(s):  
Julianna Toms-Stewart ◽  
Tobias M. Müller ◽  
Boris Gurevich ◽  
Lincoln Paterson
Keyword(s):  
Correlation Function ◽  
Autocorrelation Function ◽  
Correlation Length ◽  
Wave Attenuation ◽  
Length Scales ◽  
Gas Saturation ◽  
Partially Saturated ◽  
Statistical Measures ◽  
Fluid Saturation ◽  
Limestone Sample

Reservoir rocks are often saturated by two or more fluid phases forming complex patterns on all length scales. The objective of this work is to quantify the geometry of fluid phase distribution in partially saturated porous rocks using statistical methods and to model the associated acoustic signatures. Based on X-ray tomographic images at submillimeter resolution obtained during a gas-injection experiment, the spatial distribution of the gas phase in initially water-saturated limestone samples are constructed. Maps of the continuous variation of the percentage of gas saturation are computed and associated binary maps obtained through a global thresholding technique. The autocorrelation function is derived via the two-point probability function computed from the binary gas-distribution maps using Monte Carlo simulations.The autocorrelation function can be approximated well by a single Debye correlation function or a superposition of two such functions. The characteristic length scales and show sensitivity (and hence significance) with respect to the percentage of gas saturation. An almost linear decrease of the Debye correlation length occurs with increasing gas saturation. It is concluded that correlation function and correlation length provide useful statistical information to quantify fluid-saturation patterns and changes in these patterns at the mesoscale. These spatial statistical measures are linked to a model that predicts compressional wave attenuation and dispersion from local, wave-induced fluid flow in randomly heterogeneous poroelastic solids. In particular, for a limestone sample, with flow permeability of 5 darcies and an average gas saturation of [Formula: see text], significant [Formula: see text]-wave attenuation is predicted at ultrasonic frequencies.

Fluid distribution effect on sonic attenuation in partially saturated limestones

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 154-160 ◽  
Author(s):  
Thierry Cadoret ◽  
Gary Mavko ◽  
Bernard Zinszner
Keyword(s):  
Wave Attenuation ◽  
Water Saturation ◽  
High Water ◽  
Fluid Distribution ◽  
Computer Assisted ◽  
Fluid Content ◽  
Partially Saturated ◽  
Fluid Saturation ◽  
Distribution Effect ◽  
Saturation Method

Extensional and torsional wave‐attenuation measurements are obtained at a sonic frequency around 1 kHz on partially saturated limestones using large resonant bars, 1 m long. To study the influence of the fluid distribution, we use two different saturation methods: drying and depressurization. When water saturation (Sw) is higher than 70%, the extensional wave attenuation is found to depend on whether the resonant bar is jacketed. This can be interpreted as the Biot‐Gardner‐White effect. The experimental results obtained on jacketed samples show that, during a drying experiment, extensional wave attenuation is influenced strongly by the fluid content when Sw is between approximately 60% and 100%. This sensitivity to fluid saturation vanishes when saturation is obtained through depressurization. Using a computer‐assisted tomographic (CT) scan, we found that, during depressurization, the fluid distribution is homogeneous at the millimetric scale at all saturations. In contrast, during drying, heterogeneous saturation was observed at high water‐saturation levels. Thus, we interpret the dependence of the extensional wave attenuation upon the saturation method as principally caused by a fluid distribution effect. Torsional attenuation shows no sensitivity to fluid saturation for Sw between 5% and 100%.

scholarly journals Problems of Clustering of Radiogalaxies

2012 ◽  
Vol 8 (S290) ◽  
pp. 215-216
Author(s):  
Włodzimierz Godłowski ◽  
Agnieszka Pollo ◽  
Jacek Golbiak
Keyword(s):  
Correlation Function ◽  
Active Galactic Nuclei ◽  
Autocorrelation Function ◽  
Correlation Length ◽  
Power Law ◽  
Preliminary Analysis ◽  
Control Sample ◽  
Galactic Nuclei

AbstractWe present the preliminary analysis of clustering of a sample of 1157 radio-identified galaxies from Machalski & Condon (1999). We found that for separations 2–15 h−1 Mpc their redshift space autocorrelation function ξ(s) can be approximated by the power law with the correlation length ~3.75h−1 Mpc and slope γ ~ 1.8. The correlation length for radiogalaxies is found to be lower and the slope steeper than the corresponding parameters of the control sample of optically observed galaxies. Analysis the projected correlation function Ξ(r) displays possible differences in the clustering properties between active galactic nuclei (AGN) and starburst (SB) galaxies.

Attenuation methods for quantifying gas saturation in organic-rich shale and tight gas formations

Geophysics ◽  
2020 ◽  
pp. 1-44
Author(s):  
Qiaomu Qi ◽  
Li-Yun Fu ◽  
Jixin Deng ◽  
Junxing Cao
Keyword(s):  
Wave Attenuation ◽  
Rock Physics ◽  
Accurate Estimate ◽  
Neutron Density ◽  
Median Frequency ◽  
Tight Gas ◽  
S Wave ◽  
Gas Saturation ◽  
Fluid Saturation ◽  
Positive Linear Correlation

Quantitative interpretation of waveform attenuation for determining petrophysical properties remains one of the most challenging problems associated with rock physics. In this study, we extract $P$- and $S$-wave attenuations from monopole and dipole waveforms by median-frequency shift and multi-frequency inversion methods, respectively. Two effective methods are then proposed to compute gas saturation in organic-rich shale and tight gas formations from the full-waveform sonic attenuations. Crossplots of the $P$-to-$S$ wave attenuation ratio ( Qp-1/ Qs-1) and core gas saturation show a positive linear correlation. The Qp-1/ Qs-1 and neutron-density porosity difference exhibit an identical log trend across different formations. The coincidence of these two different hydrocarbon indicators implies that the Qp-1/ Qs-1 is most sensitive to pore-fluid saturation and less affected by variations in lithology. In the first method, the core-calibrated Qp-1/ Qs-1 yields an accurate estimate of gas saturation. The second method is suited for the absence of core saturation data, which employs the probability distribution of Qp-1/ Qs-1 for the evaluation of gas saturation. Compared to conventional resistivity methods, the proposed attenuation method, as a non-electric approach, provides more accurate gas saturation prediction for low-resistivity reservoir rocks. Finally, we analyze the characteristics of attenuation-saturation relations in low porosity rocks and discuss the possible attenuation mechanisms.

Low-frequency reflections from a thin layer with high attenuation caused by interlayer flow

Geophysics ◽  
2009 ◽  
Vol 74 (1) ◽  
pp. N15-N23 ◽  
Author(s):  
Beatriz Quintal ◽  
Stefan M. Schmalholz ◽  
Yuri Y. Podladchikov
Keyword(s):  
Reflection Coefficient ◽  
Wave Attenuation ◽  
Low Frequency ◽  
Incident Wavelength ◽  
High Attenuation ◽  
Partially Saturated ◽  
Fluid Saturation ◽  
Wide Range ◽  
Wave Induced ◽  
Approximate Equations

The 1D interlayer-flow (or White’s) model is based on Biot’s theory of poroelasticity and explains low-frequency seismic wave attenuation in partially saturated rocks by wave-induced fluid flow between two alternating poroelastic layers, each saturated with a different fluid. We have developed approximate equations for both the minimum possible value of the quality factor, [Formula: see text], and the corresponding fluid saturation for which [Formula: see text] is minimal. The simple approximate equations provide a better insight into the dependence of [Formula: see text] on basic petrophysical parameters and allow for a fast assessment of the minimal value of [Formula: see text]. The approximation is valid for a wide range of realistic petrophysical parameter values for sandstones partially saturated with gas and water, and shows that values of [Formula: see text] can be as small as two. We ap-plied the interlayer-flow model to study the reflection coefficient of a thin (i.e., between 6 and 11 times smaller than the incident wavelength) layer that is partially saturated with gas and water. The reflection coefficient of the layer, caused only by a contrast in attenuation between the layer and the nonattenuating background medium, can be larger than 10% for [Formula: see text] within the layer. The reflection coefficient was calculated with finite difference simulations of wave propagation in heterogeneous, poroelastic solids and in equivalent viscoelastic solids. The reflection coefficient of the layer is also estimated with an analytical solution using a complex velocity for the layer. The numerical and analytical results agree well. Our results indicate that reflection coefficients of gas reservoirs can be significantly increased and frequency dependent in the low-frequency range because of attenuation within the reservoir caused by wave-induced flow.

scholarly journals SARIMA Approach to Generating Synthetic Monthly Rainfall in the Sinú River Watershed in Colombia

Atmosphere ◽  
2020 ◽  
Vol 11 (6) ◽  
pp. 602
Author(s):  
Luisa Martínez-Acosta ◽  
Juan Pablo Medrano-Barboza ◽  
Álvaro López-Ramos ◽  
John Freddy Remolina López ◽  
Álvaro Alberto López-Lambraño
Keyword(s):  
Time Series ◽  
Water Resources ◽  
Autocorrelation Function ◽  
Information Criterion ◽  
Monthly Rainfall ◽  
Statistical Characteristics ◽  
Rainfall Time Series ◽  
River Watershed ◽  
Statistical Measures ◽  
Sarima Models

Seasonal Auto Regressive Integrative Moving Average models (SARIMA) were developed for monthly rainfall time series. Normality of the rainfall time series was achieved by using the Box Cox transformation. The best SARIMA models were selected based on their autocorrelation function (ACF), partial autocorrelation function (PACF), and the minimum values of the Akaike Information Criterion (AIC). The result of the Ljung–Box statistical test shows the randomness and homogeneity of each model residuals. The performance and validation of the SARIMA models were evaluated based on various statistical measures, among these, the Student’s t-test. It is possible to obtain synthetic records that preserve the statistical characteristics of the historical record through the SARIMA models. Finally, the results obtained can be applied to various hydrological and water resources management studies. This will certainly assist policy and decision-makers to establish strategies, priorities, and the proper use of water resources in the Sinú river watershed.

scholarly journals Effects of Irreducible Fluid Saturation and Gas Entry Pressure on Gas Production from Hydrate-Bearing Clayey Silt Sediments by Depressurization

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Xiaolong Ma ◽  
Youhong Sun ◽  
Wei Guo ◽  
Rui Jia ◽  
Bing Li
Keyword(s):  
Water Saturation ◽  
Gas Production ◽  
Production Volume ◽  
Water Production ◽  
Shenhu Area ◽  
Gas Saturation ◽  
Fluid Saturation ◽  
Entry Pressure ◽  
Clayey Silt ◽  
Irreducible Water Saturation

Gas hydrates in the Shenhu area are mainly hosted in clayey silt sediments, which have the relatively high irreducible fluid saturation and gas entry pressure. And then, they will have an impact on gas production from hydrate-bearing clayey silt sediments, which was evaluated by the numerical simulations of SH2 site in Shenhu area in this paper. The results showed that, with the increase in irreducible water saturation and irreducible gas saturation, the amount of water production and gas production was obviously reduced. When the irreducible water saturation increased from 0.10 to 0.50, the cumulative CH4 production volume decreased from 1668799 m3 to 1536262 m3, and the cumulative water production volume dropped from 620304 m3 to 564797 m3, respectively. When the irreducible gas saturation increased from 0.01 to 0.05, the cumulative CH4 production volume dropped from 1812522 m3 to 1622121 m3, and the cumulative water production volume dropped from 672088 m3 to 600617 m3, respectively. In addition, the capillary pressure increased obviously with the increase in gas entry pressure, but the effect on gas production was small and the effect on water production could be negligible. In conclusion, irreducible water and gas saturation had an important effect on the gas production from gas hydrate, whereas the effects of gas entry pressure could be ignored.

Impact of fluid saturation on the reflection coefficient of a poroelastic layer

Geophysics ◽  
2011 ◽  
Vol 76 (2) ◽  
pp. N1-N12 ◽  
Author(s):  
Beatriz Quintal ◽  
Stefan M. Schmalholz ◽  
Yuri Y. Podladchikov
Keyword(s):  
Fluid Flow ◽  
Reflection Coefficient ◽  
Analytical Solution ◽  
Quality Factor ◽  
Velocity Dispersion ◽  
Normal Incidence ◽  
Sand Layer ◽  
Partially Saturated ◽  
Fluid Saturation ◽  
Wave Induced

The impact of changes in saturation on the frequency-dependent reflection coefficient of a partially saturated layer was studied. Seismic attenuation and velocity dispersion in partially saturated (i.e., patchy saturated) poroelastic media were accounted for by using the analytical solution of the 1D White’s model for wave-induced fluid flow. White’s solution was applied in combination with an analytical solution for the normal-incidence reflection coefficient of an attenuating layer embedded in an elastic or attenuating background medium to investigate the effects of attenuation, velocity dispersion, and tuning on the reflection coefficient. Approximations for the frequency-dependent quality factor, its minimum value, and the frequency at which the minimum value of the quality factor occurs were derived. The approximations are valid for any two alternating sets of petrophysical parameters. An approximation for the normal-incidence reflection coefficient of an attenuating thin (compared to the wavelength) layer was also derived. This approximation gives insight into the influence of contrasts in acoustic impedance and/or attenuation on the reflectivity of a thin layer. Laboratory data for reflections from a water-saturated sand layer and from a dry sand layer were further fit with petrophysical parameters for unconsolidated sand partially saturated with water and air. The results showed that wave-induced fluid flow can explain low-frequency reflection anomalies, which are related to fluid saturation and can be observed in seismic field data. The results further indicate that reflection coefficients of partially saturated layers (e.g., hydrocarbon reservoirs) can vary significantly with frequency, especially at low seismic frequencies where partial saturation may often cause high attenuation.

Huge wave attenuation in partially saturated fractured reservoirs

2007 ◽  
Vol 2007 (1) ◽  
pp. 1-3
Author(s):  
Miroslav Brajanovski ◽  
Tobias Müller
Keyword(s):  
Wave Attenuation ◽  
Fractured Reservoirs ◽  
Partially Saturated

Numerical modeling and laboratory measurements of seismic attenuation in partially saturated rock

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. L13-L20 ◽  
Author(s):  
Maria Kuteynikova ◽  
Nicola Tisato ◽  
Ralf Jänicke ◽  
Beatriz Quintal
Keyword(s):  
Numerical Modeling ◽  
Seismic Attenuation ◽  
Laboratory Measurements ◽  
Berea Sandstone ◽  
Mesoscopic Scale ◽  
Partially Saturated ◽  
Saturated Rock ◽  
Fluid Saturation ◽  
The Matrix ◽  
Wave Induced

To better understand the effects of fluid saturation on seismic attenuation, we combined numerical modeling in poroelastic media and laboratory measurements of seismic attenuation in partially saturated Berea sandstone samples. Although in laboratory experiments many physical mechanisms for seismic attenuation take place simultaneously, with numerical modeling we separately studied the effect of a single physical mechanism: wave-induced fluid flow on the mesoscopic scale. Using the finite-element method, we solved Biot’s equations of consolidation by performing a quasistatic creep test on a 3D poroelastic model. This model represents a partially saturated rock sample. We obtained the stress-strain relation, from which we calculated frequency-dependent attenuation. In the laboratory, we measured attenuation in extensional mode for dry and partially water-saturated Berea sandstone samples in the frequency range from 0.1 to 100 Hz. All the measurements were performed at room pressure and temperature conditions. From numerical simulations, we found that attenuation varies significantly with fluid distribution within the model. In addition to binary distributions, we used spatially continuous distributions of fluid saturation for the numerical models. Such continuous saturation distribution was implemented using properties of an effective single-phase fluid. By taking into account the matrix anelasticity, we found that wave-induced fluid flow on the mesoscopic scale due to a continuous distribution of fluid saturation can reproduce seismic attenuation data measured in a partially saturated sample. The matrix anelasticity was the attenuation measured in the room-condition dry sample.

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