Rock-physics-based estimation of critical-clay-volume fraction and its effect on seismic velocity and petrophysical properties

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. D175-D185 ◽  
Author(s):  
Hamid Adesokan ◽  
Yuefeng Sun
Keyword(s):  
Aspect Ratio ◽  
Seismic Velocity ◽  
Volume Fraction ◽  
Rock Physics ◽  
Clay Content ◽  
Elastic Behavior ◽  
Data Set ◽  
Abrupt Decrease ◽  
Shaly Sand ◽  
Clastic Reservoirs

Knowledge of the clay content in clastic reservoirs is important for predicting reservoir quality and properties. We used a microgeometrical model for shaly sand and sandy shale to define the critical-clay-volume fraction and explain the dependence of the bulk modulus on clay content. We found that the concept of the pore-aspect ratio relating to the critical-clay-volume fraction was important to interpret the elastic behavior of shaly sandstone. An abrupt decrease in pore-aspect ratio from about 0.23 to about 0.04 was observed where the clay-volume fraction was greater than the critical value of 32% for the studied data set. At the critical-clay-volume fraction of 32%, an increase in pore compressibility also occurred from about 0.6 to about [Formula: see text]. Results revealed that the microgeometrical model compared to other models can better explain the existence of highly scattered compressional velocity-porosity crossplots when the clay content is close to the critical amount. We discovered that the model can be applied in well-logging interpretations of shaly formations for determining shale cut-off and mapping of reservoir pore shape from velocity measurements.

Pore pressure estimation in reservoir rocks from seismic reflection data

Geophysics ◽  
2003 ◽  
Vol 68 (5) ◽  
pp. 1569-1579 ◽  
Author(s):  
José M. Carcione ◽  
Hans B. Helle ◽  
Nam H. Pham ◽  
Tommy Toverud
Keyword(s):  
Pore Pressure ◽  
Seismic Velocity ◽  
Rock Physics ◽  
Clay Content ◽  
Structural Features ◽  
P Wave ◽  
Velocity Versus ◽  
Seismic Reflection Data ◽  
The North ◽  
Fluid Saturation

A method is used to obtain pore pressure in shaly sandstones based upon an acoustic model for seismic velocity versus clay content and effective pressure. Calibration of the model requires log data—porosity, clay content, and sonic velocities—to obtain the dry‐rock moduli and the effective stress coefficients as a function of depth and pore pressure. The seismic P‐wave velocity, derived from reflection tomography, is fitted to the theoretical velocity by using pore pressure as the fitting parameter. This approach, based on a rock‐physics model, is an improvement over existing pore‐pressure prediction methods, which mainly rely on empirical relations between velocity and pressure. The method is applied to the Tune field in the Viking Graben sedimentary basin of the North Sea. We have obtained a high‐resolution velocity map that reveals the sensitivity to pore pressure and fluid saturation in the Tarbert reservoir. The velocity map of the Tarbert reservoir and the inverted pressure distribution agree with the structural features of the Tarbert Formation and its known pressure compartments.

Empirical relationships among seismic velocity, effective pressure, porosity, and clay content in sandstone

Geophysics ◽  
1989 ◽  
Vol 54 (1) ◽  
pp. 82-89 ◽  
Author(s):  
D. Eberhart‐Phillips ◽  
D-H. Han ◽  
M. D. Zoback
Keyword(s):  
Seismic Velocity ◽  
Clay Content ◽  
Large Data ◽  
Shear Velocity ◽  
Linear Increase ◽  
Effective Pressure ◽  
Data Set ◽  
Best Fitting ◽  
Water Saturated ◽  
Compressional Velocity

We use a multivariate analysis to investigate the influence of effective pressure [Formula: see text], porosity ϕ, and clay content C on the compressional velocity [Formula: see text] and shear velocity [Formula: see text] of sandstones. Laboratory measurements on water‐saturated samples of 64 different sandstones provide a large data set that was analyzed statistically. For each sample, relationships between effective pressure and [Formula: see text] and [Formula: see text] have been determined. All samples were well fit by relationships that have an exponential increase in velocity at low [Formula: see text], tapering to a linear increase with [Formula: see text] for [Formula: see text] greater than 0.2 kbar. There are differences in the pressure dependences of velocity for different rocks, particularly at very low pressures; however, the differences cannot be attributed to ϕ or C. For the combined set of measurements from all samples, the best fitting formulations are [Formula: see text] and [Formula: see text]. While this is admittedly a very simplified parameterization, it is remarkable how well the velocity of the rocks considered here can be predicted based on only the three parameters, ϕ, C, and [Formula: see text]. The model accounts for 95 percent of the variance and has rms error of 0.1 km/s. An increased value of [Formula: see text] can indicate a decrease in [Formula: see text], a decrease in porosity, or an increase in clay content or some combination thereof.

scholarly journals Digital rock physics in four dimensions: simulating cementation and its effect on seismic velocity

2020 ◽  
Vol 222 (3) ◽  
pp. 1606-1619 ◽  
Author(s):  
J Singh ◽  
P A Cilli ◽  
A Hosa ◽  
I G Main
Keyword(s):  
Aspect Ratio ◽  
Bulk Modulus ◽  
Seismic Velocity ◽  
Rock Physics ◽  
Staggered Grid ◽  
Carbonate Sediments ◽  
Structural Anisotropy ◽  
Measured Velocity ◽  
Geological Processes ◽  
Strong Control

SUMMARY Porosity exerts a strong control on the mechanical and hydraulic properties of rocks, but can often only be imaged indirectly from the surface using geophysical measurements, such as seismic velocity. Understanding and quantifying the relationship between seismic velocity and porosity is therefore a fundamental goal of many rock physics models. Simulating the geological processes that control porosity to generate digital rocks, and numerically modelling wave propagation to estimate their elastic properties, allows for flexible and rapid calibration of velocity–porosity trends. Here, the initial deposition of two digital carbonate sediments are simulated: grainstone (near spherical grains) and coquina (anisotropic shell fragments). The gradual precipitation of cement is then simulated, resulting in a suite of 3-D volumes of varying porosity with otherwise constant and known mineral and grain phases. These models are then used as input to a 3-D acoustic staggered-grid finite difference simulation of wavefield propagation, from which we estimate bulk seismic velocity and calculate the estimated bulk modulus. The resulting bulk modulus varies systematically with respect to porosity within the physical limits imposed by the Hashin–Shtrikman bounds. The samples exhibit anisotropy in the measured velocity consistent with structural anisotropy due to the settling of elongate grains under gravity. We use the resulting bulk velocity–porosity trends to test competing rock physics models, including one that accounts for varying effective pore-aspect ratio with porosity. The results validate the hypothesis that there is a power-law relationship between effective pore aspect ratio and porosity. This relationship is consistent with similar results obtained from a suite of natural carbonate grainstones examined in the laboratory. The results show the optimal rock physics model to be relatively insensitive to the degree of anisotropy in the fabric of the starting material, and may now be used with more confidence to link observed changes in effective pore aspect ratio to changes in porosity due to a range of geological processes, for example fracturing, dissolution and compaction, where other process-based models are available.

scholarly journals Jet Impingement Heat Transfer of Confined Single and Double Jets with Non-Newtonian Power Law Nanofluid under the Inclined Magnetic Field Effects for a Partly Curved Heated Wall

2021 ◽  
Vol 13 (9) ◽  
pp. 5086
Author(s):  
Fatih Selimefendigil ◽  
Hakan F. Oztop ◽  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Particle Size ◽  
Aspect Ratio ◽  
Power Law ◽  
Volume Fraction ◽  
Inclined Magnetic Field ◽  
Magnetic Field Effects ◽  
Power Law Nanofluid ◽  
Power Law Index

Single and double impinging jets heat transfer of non-Newtonian power law nanofluid on a partly curved surface under the inclined magnetic field effects is analyzed with finite element method. The numerical work is performed for various values of Reynolds number (Re, between 100 and 300), Hartmann number (Ha, between 0 and 10), magnetic field inclination (γ, between 0 and 90), curved wall aspect ratio (AR, between 01. and 1.2), power law index (n, between 0.8 and 1.2), nanoparticle volume fraction (ϕ, between 0 and 0.04) and particle size in nm (dp, between 20 and 80). The amount of rise in average Nusselt (Nu) number with Re number depends upon the power law index while the discrepancy between the Newtonian fluid case becomes higher with higher values of power law indices. As compared to case with n = 1, discrepancy in the average Nu number are obtained as −38% and 71.5% for cases with n = 0.8 and n = 1.2. The magnetic field strength and inclination can be used to control the size and number or vortices. As magnetic field is imposed at the higher strength, the average Nu reduces by about 26.6% and 7.5% for single and double jets with n greater than 1 while it increases by about 4.78% and 12.58% with n less than 1. The inclination of magnetic field also plays an important role on the amount of enhancement in the average Nu number for different n values. The aspect ratio of the curved wall affects the flow field slightly while the average Nu variation becomes 5%. Average Nu number increases with higher solid particle volume fraction and with smaller particle size. At the highest particle size, it is increased by about 14%. There is 7% variation in the average Nu number when cases with lowest and highest particle size are compared. Finally, convective heat transfer performance modeling with four inputs and one output is successfully obtained by using Adaptive Neuro-Fuzzy Interface System (ANFIS) which provides fast and accurate prediction results.

scholarly journals Elastic wave velocity and electrical conductivity in a brine-saturated rock and microstructure of pores

2019 ◽  
Vol 71 (1) ◽  
Author(s):  
Tohru Watanabe ◽  
Miho Makimura ◽  
Yohei Kaiwa ◽  
Guillaume Desbois ◽  
Kenta Yoshida ◽  
...  
Keyword(s):  
Electrical Conductivity ◽  
Elastic Wave ◽  
Wave Velocity ◽  
High Pressures ◽  
Seismic Velocity ◽  
Volume Fraction ◽  
Elastic Wave Velocity ◽  
Fluid Volume ◽  
Sem Observation ◽  
Wide Aperture

AbstractElastic wave velocity and electrical conductivity in a brine-saturated granitic rock were measured under confining pressures of up to 150 MPa and microstructure of pores was examined with SEM on ion-milled surfaces to understand the pores that govern electrical conduction at high pressures. The closure of cracks under pressure causes the increase in velocity and decrease in conductivity. Conductivity decreases steeply below 10 MPa and then gradually at higher pressures. Though cracks are mostly closed at the confining pressure of 150 MPa, brine must be still interconnected to show observed conductivity. SEM observation shows that some cracks have remarkable variation in aperture. The aperture varies from ~ 100 nm to ~ 3 μm along a crack. FIB–SEM observation suggests that wide aperture parts are interconnected in a crack. Both wide and narrow aperture parts work parallel as conduction paths at low pressures. At high pressures, narrow aperture parts are closed but wide aperture parts are still open to maintain conduction paths. The closure of narrow aperture parts leads to a steep decrease in conductivity, since narrow aperture parts dominate cracks. There should be cracks in various sizes in the crust: from grain boundaries to large faults. A crack must have a variation in aperture, and wide aperture parts must govern the conduction paths at depths. A simple tube model was employed to estimate the fluid volume fraction. The fluid volume fraction of 10−4–10−3 is estimated for the conductivity of 10−2 S/m. Conduction paths composed of wide aperture parts are consistent with observed moderate fluctuations (< 10%) in seismic velocity in the crust.

scholarly journals Modelling the Molecular Permeation through Mixed-Matrix Membranes Incorporating Tubular Fillers

Membranes ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 58
Author(s):  
Ali Zamani ◽  
F. Handan Tezel ◽  
Jules Thibault
Keyword(s):  
Aspect Ratio ◽  
Relative Permeability ◽  
Polymer Matrix ◽  
Volume Fraction ◽  
Mixed Matrix Membranes ◽  
Analytical Prediction ◽  
Mixed Matrix ◽  
Permeability Ratio ◽  
Filler Volume Fraction ◽  
Matrix Membranes

Membrane-based processes are considered a promising separation method for many chemical and environmental applications such as pervaporation and gas separation. Numerous polymeric membranes have been used for these processes due to their good transport properties, ease of fabrication, and relatively low fabrication cost per unit membrane area. However, these types of membranes are suffering from the trade-off between permeability and selectivity. Mixed-matrix membranes, comprising a filler phase embedded into a polymer matrix, have emerged in an attempt to partly overcome some of the limitations of conventional polymer and inorganic membranes. Among them, membranes incorporating tubular fillers are new nanomaterials having the potential to transcend Robeson’s upper bound. Aligning nanotubes in the host polymer matrix in the permeation direction could lead to a significant improvement in membrane permeability. However, although much effort has been devoted to experimentally evaluating nanotube mixed-matrix membranes, their modelling is mostly based on early theories for mass transport in composite membranes. In this study, the effective permeability of mixed-matrix membranes with tubular fillers was estimated from the steady-state concentration profile within the membrane, calculated by solving the Fick diffusion equation numerically. Using this approach, the effects of various structural parameters, including the tubular filler volume fraction, orientation, length-to-diameter aspect ratio, and permeability ratio were assessed. Enhanced relative permeability was obtained with vertically aligned nanotubes. The relative permeability increased with the filler-polymer permeability ratio, filler volume fraction, and the length-to-diameter aspect ratio. For water-butanol separation, mixed-matrix membranes using polydimethylsiloxane with nanotubes did not lead to performance enhancement in terms of permeability and selectivity. The results were then compared with analytical prediction models such as the Maxwell, Hamilton-Crosser and Kang-Jones-Nair (KJN) models. Overall, this work presents a useful tool for understanding and designing mixed-matrix membranes with tubular fillers.

scholarly journals A Micro-mechanical Investigation of Empirical Models for the Effective Properties of Aligned Short-Fibre Composites

1995 ◽  
Vol 4 (1) ◽  
pp. 096369359500400
Author(s):  
T.D. Papathanasiou
Keyword(s):  
Aspect Ratio ◽  
Volume Fraction ◽  
Tensile Modulus ◽  
Fibre Volume ◽  
Short Fibre ◽  
Computational Results ◽  
Volume Fractions ◽  
Fibre Composites ◽  
Effective Tensile Modulus ◽  
Fibre Aspect Ratio

The predictions of the Halpin equation concerning the effect of fibre volume fraction and fibre aspect ratio on the effective tensile modulus of uniaxially aligned short-fibre composites are compared with computational experiments on three-dimensional, multiparticle composite samples. The method of boundary elements is used to model the mechanical behaviour of composite specimens consisting of up to 40 discrete aligned fibres randomly dispersed in an elastic matrix. Statistical averages of computational results relating the effective tensile modulus to the aspect ratio and volume fraction of the fibres are found to agree very well with the predictions of the Halpin equation for fibre aspect ratio up to 10 and fibre volume fractions up to 20%. Computational results seem to indicate that the predictions of the Halpin equation fall bellow those of micro-mechanical models at higher volume fractions.

Uncertainty Quantification in Predicting Behaviour of Rubber-Like Materials in Uni-Axial Loading

2020 ◽  
Author(s):  
Aref Ghaderi ◽  
Vahid Morovati ◽  
Pouyan Nasiri ◽  
Roozbeh Dargazany
Keyword(s):  
Uncertainty Quantification ◽  
Mechanical Response ◽  
Pure Shear ◽  
Constitutive Models ◽  
Material Behavior ◽  
Elastic Behavior ◽  
Deterministic Models ◽  
Data Set ◽  
Material Parameters ◽  
Axial Extension

Abstract Material parameters related to deterministic models can have different values due to variation of experiments outcome. From a mathematical point of view, probabilistic modeling can improve this problem. It means that material parameters of constitutive models can be characterized as random variables with a probability distribution. To this end, we propose a constitutive models of rubber-like materials based on uncertainty quantification (UQ) approach. UQ reduces uncertainties in both computational and real-world applications. Constitutive models in elastomers play a crucial role in both science and industry due to their unique hyper-elastic behavior under different loading conditions (uni-axial extension, biaxial, or pure shear). Here our goal is to model the uncertainty in constitutive models of elastomers, and accordingly, identify sensitive parameters that we highly contribute to model uncertainty and error. Modern UQ models can be implemented to use the physics of the problem compared to black-box machine learning approaches that uses data only. In this research, we propagate uncertainty through the model, characterize sensitivity of material behavior to show the importance of each parameter for uncertainty reduction. To this end, we utilized Bayesian rules to develop a model considering uncertainty in the mechanical response of elastomers. As an important assumption, we believe that our measurements are around the model prediction, but it is contaminated by Gaussian noise. We can make the noise by maximizing the posterior. The uni-axial extension experimental data set is used to calibrate the model and propagate uncertainty in this research.

Porosity estimation based on rock skeleton general formula and comprehensive pore structure parameter – An application to a tight-sand reservoir

2021 ◽  
pp. 1-59
Author(s):  
Kai Lin ◽  
Xilei He ◽  
Bo Zhang ◽  
Xiaotao Wen ◽  
Zhenhua He ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Pore Structure ◽  
Seismic Data ◽  
Rock Physics ◽  
Structure Parameters ◽  
Pore Structure Parameter ◽  
Elastic Parameters ◽  
Physics Model ◽  
Rock Physics Model ◽  
Porosity Estimation

Most of current 3D reservoir’s porosity estimation methods are based on analyzing the elastic parameters inverted from seismic data. It is well-known that elastic parameters vary with pore structure parameters such as pore aspect ratio, consolidate coefficient, critical porosity, etc. Thus, we may obtain inaccurate 3D porosity estimation if the chosen rock physics model fails properly address the effects of pore structure parameters on the elastic parameters. However, most of current rock physics models only consider one pore structure parameter such as pore aspect ratio or consolidation coefficient. To consider the effect of multiple pore structure parameters on the elastic parameters, we propose a comprehensive pore structure (CPS) parameter set that is generalized from the current popular rock physics models. The new CPS set is based on the first order approximation of current rock physics models that consider the effect of pore aspect ratio on elastic parameters. The new CPS set can accurately simulate the behavior of current rock physics models that consider the effect of pore structure parameters on elastic parameters. To demonstrate the effectiveness of proposed parameters in porosity estimation, we use a theoretical model to demonstrate that the proposed CPS parameter set properly addresses the effect of pore aspect ratio on elastic parameters such as velocity and porosity. Then, we obtain a 3D porosity estimation for a tight sand reservoir by applying it seismic data. We also predict the porosity of the tight sand reservoir by using neural network algorithm and a rock physics model that is commonly used in porosity estimation. The comparison demonstrates that predicted porosity has higher correlation with the porosity logs at the blind well locations.

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