arXiv subjects

Behzad Ghanbarian

Publications and source records attributed to Behzad Ghanbarian.

25 records · Page 2Linked to original sources

arXiv2018

Application of effective medium theory to estimate gas permeability in tight-gas sandstones

Upscaling Klinkenberg-corrected gas permeability, k, in unconventional tight sandstones has numerous practical applications, particularly in gas exploration and production. In this study, we adapt the effective-medium approximation (EMA) model of Doyen - proposed first to estimate bulk electrical conductivity, σ_b, and permeability in sandstones from rock images - to scale up σ_b and k in tight-gas sandstones from pore to core. For this purpose, we calculate two characteristic pore sizes: an effective hydraulic and an effective electrical pore size from pore-throat size distributions - determined from mercury intrusion capillary pressure (MICP) curves - and pore-throat connectivity. The latter is estimated from critical volume fraction (or percolation threshold) for macroscopic flow. Electrical conductivity and permeability are then scaled up from the two characteristic pore sizes, tortuosity, and porosity by assuming two different pore geometries: cylindrical and slit-shaped. Comparison of results obtained for eighteen tight-gas sandstones indicates that the EMA estimates σ_b and k more accurately when pores are assumed to be cylindrical. We also estimate k from the pore-throat size distributions and the measured electrical conductivity using the EMA and critical path analysis (CPA), another upscaling technique borrowed from statistical physics. Theoretically, the former is valid in relatively heterogeneous porous media with narrow pore-throat size distribution, while the latter is valid in heterogeneous media with broad pore-throat size distribution. Results show that the EMA estimates k more accurately than CPA and arrives within a factor of two of the measurements on average.

physics.geo-ph↗

arXiv2018

A geometrical aperture-width relationship for rock fractures

The relationship between fracture aperture (maximum opening; dmax) and fracture width (w) has been the subject of debate over the past several decades. An empirical power law has been commonly applied to relate these two parameters. Its exponent (n) is generally determined by fitting the power-law function to experimental observations measured at various scales. Invoking concepts from fractal geometry we theoretically show, as a first- order approximation, that the fracture aperture should be a linear function of its width, meaning that n = 1. This finding is in agreement with the result of linear elastic fracture mechanics (LEFM) theory. We compare the model predictions with experimental observations available in the literature. This comparison generally supports a linear relationship between fracture aperture and fracture width, although there exists considerable scatter in the data. We also discuss the limitations of the proposed model, and its potential application to the prediction of flow and transport in fractures. Based on more than 170 experimental observations from the literature, we show that such a linear relationship, in combination with the cubic law, is able to scale flow rate with fracture aperture over ~14 orders of magnitude for variations in flow rate and ~5 orders of magnitude for variations in fracture width.

physics.geo-ph↗

arXiv2018

Theoretical bounds for the exponent in the empirical power-law advance-time curve for surface flow

A fundamental and widely applied concept used to study surface flow processes is the advance-time curve characterized by an empirical power law with an exponent r and a numerical prefactor p (i.e., x = p*t^r). In the literature, different values of r have been reported for various situations and types of surface irrigation. Invoking concepts from percolation theory, we related the exponent r to the backbone fractal dimension Db, whose value depends on two factors: dimensionality of the system (e.g., two or three dimensions) and percolation class (e.g., random or invasion percolation with/without trapping). We showed that the theoretical bounds of Db are in well agreement with experimental ranges of r reported in the literature for two furrow and border irrigation systems. We also used the value of Db from the optimal path class of percolation theory to estimate the advance-time curves of four furrows and seven irrigation cycles. Excellent agreement was obtained between the estimated and observed curves.

physics.flu-dyn↗

arXiv2017

Hysteretic behavior of electrical conductivity in packings of particles

We address the problem of predicting saturation-dependent electrical conductivity σ in packings of spheres during drainage and imbibition. The effective-medium approximation (EMA) and the universal power law of percolation for σ are used, respectively, at higher and low water saturations to predict the conductivity, with the crossover between the two occurring at some intermediate saturation Swx. The main input to the theory is a single parameter that we estimate using the capillary pressure data. The predictions are compared with experimental, as well as numerical data for three distinct types of packings. The results for drainage in all the packings indicate that the universal power law of percolation is valid over the entire range of Sw. For imbibition, however, the universal power law crosses over to the EMA at Swx = 0.5. We also find that the effect of the pore-size distribution on the σ-Sw relation is minimal during both drainage and imbibition.

physics.flu-dyn↗

arXiv2016

Scale-Dependent Pedotransfer Functions Reliability for Estimating Saturated Hydraulic Conductivity

Saturated hydraulic conductivity Ksat is a fundamental characteristic in modeling flow and contaminant transport in soils and sediments. Therefore, many models have been developed to estimate Ksat from easily measureable parameters, such as textural properties, bulk density, etc. However, Ksat is not only affected by textural and structural characteristics, but also by scale e.g., internal diameter and height. Using the UNSODA database and the contrast pattern aided regression (CPXR) method, we recently developed scale-dependent pedotransfer functions to estimate Ksat from textural data, bulk density, and sample dimensions. The main objectives of this study were evaluating the proposed pedotransfer functions using a larger database, and comparing them with seven other models. For this purpose, we selected more than nineteen thousands soil samples from all around the United States. Results showed that the scale-dependent pedotransfer functions estimated Ksat more accurately than seven other models frequently used in the literature.

cs.CE↗

arXiv2015

Measurement Scale Effect on Prediction of Soil Water Retention Curve and Saturated Hydraulic Conductivity

Soil water retention curve (SWRC) and saturated hydraulic conductivity (SHC) are key hydraulic properties for unsaturated zone hydrology and groundwater. In particular, SWRC provides useful information on entry pore-size distribution, and SHC is required for flow and transport modeling in the hydrologic cycle. Not only the SWRC and SHC measurements are time-consuming, but also scale dependent. This means as soil column volume increases, variability of the SWRC and SHC decreases. Although prediction of the SWRC and SHC from available parameters, such as textural data, organic matter, and bulk density have been under investigation for decades, up to now no research has focused on the effect of measurement scale on the soil hydraulic properties pedotransfer functions development. In the literature, several data mining approaches have been applied, such as multiple linear regression, artificial neural networks, group method of data handling. However, in this study we develop pedotransfer functions using a novel approach called contrast pattern aided regression (CPXR) and compare it with the multiple linear regression method. For this purpose, two databases including 210 and 213 soil samples are collected to develop and evaluate pedotransfer functions for the SWRC and SHC, respectively, from the UNSODA database. The 10-fold cross-validation method is applied to evaluate the accuracy and reliability of the proposed regression-based models. Our results show that including measurement scale parameters, such as sample internal diameter and length could substantially improve the accuracy of the SWRC and SHC pedotransfer functions developed using the CPXR method, while this is not the case when MLR is used. Moreover, the CPXR method yields remarkably more accurate soil water retention curve and saturated hydraulic conductivity predictions than the MLR approach.

cs.CE↗

arXiv2013

Solute transport predicts scaling of surface reaction rates in porous media: Applications to silicate weathering

We apply our theory of conservative solute transport, based on concepts from percolation theory, directly and without modification to reactive solute transport. This theory has previously been shown to predict the observed range of dispersivity values for conservative solute transport over ten orders of magnitude of length scale. We now show that the temporal dependence derived for the solute velocity accurately predicts the time-dependence for the weathering of silicate minerals over nine orders of magnitude of time scale, while its predicted length dependence agrees with data obtained for reaction rates over five orders of magnitude of length scale. In both cases, it is possible to unify lab and field results. Thus, net reaction rates appear to be limited by solute transport velocities. We suggest the possible relevance of our results to landscape evolution of the earth's terrestrial surface.

physics.flu-dyn↗