Luis Guarracino

Seismoacoustic signatures of fracture connectivity

Wave-induced fluid flow (WIFF) between fractures and the embedding matrix as well as within connected fractures tends to produce significant seismic attenuation and velocity dispersion. While WIFF between fractures and matrix is well understood, the corresponding effects related to fracture connectivity and the characteristics of the energy dissipation due to flow within fractures are largely unexplored. In this work, we use oscillatory relaxation simulations based on the quasi-static poroelastic equations to study these phenomena. We first consider synthetic rock samples containing connected and unconnected fractures and compute the corresponding attenuation and phase velocity. We also determine the relative fluid displacement and pressure fields in order to gain insight into the physical processes involved in the two manifestations of WIFF in fractured media. To quantify the contributions of the two WIFF mechanisms to the total seismic attenuation, we compute the spatial distribution of the local energy dissipation. Finally, we perform an exhaustive sensitivity analysis to study the role played by different characteristics of fracture networks on the seismic signatures. We show that in the presence of connected fractures both P wave attenuation and phase velocity are sensitive to some key characteristics of the probed medium, notably to the lengths, permeabilities, and intersection angles of the fractures as well as to the overall degree of connectivity of the fracture network. This, in turn, indicates that a deeper understanding of these two manifestations of WIFF in fractured media may eventually allow for the extraction of some of these properties from seismic data.

Seismic wave attenuation and dispersion due to wave-induced fluid flow in rocks with strong permeability fluctuations

Oscillatory fluid movements in heterogeneous porous rocks induced by seismic waves cause dissipation of wave field energy. The resulting seismic signature depends not only on the rock compressibility distribution, but also on a statistically averaged permeability. This so-called equivalent seismic permeability does not, however, coincide with the respective equivalent flow permeability. While this issue has been analyzed for one-dimensional (1D) media, the corresponding two-dimensional (2D) and three-dimensional (3D) cases remain unexplored. In this work, this topic is analyzed for 2D random medium realizations having strong permeability fluctuations. With this objective, oscillatory compressibility simulations based on the quasi-static poroelasticity equations are performed. Numerical analysis shows that strong permeability fluctuations diminish the magnitude of attenuation and velocity dispersion due to fluid flow, while the frequency range where these effects are significant gets broader. By comparing the acoustic responses obtained using different permeability averages, it is also shown that at very low frequencies the equivalent seismic permeability is similar to the equivalent flow permeability, while for very high frequencies this parameter approaches the arithmetic average of the permeability field. These seemingly generic findings have potentially important implications with regard to the estimation of equivalent flow permeability from seismic data.

A Simple Hysteretic Constitutive Model for Unsaturated Flow

In this paper, we present a constitutive model to describe unsaturated flow that considers the hysteresis phenomena. This constitutive model provides simple mathematical expressions for both saturation and hydraulic conductivity curves, and a relationship between permeability and porosity. The model is based on the assumption that the porous media can be represented by a bundle of capillary tubes with throats or “ink bottles” and a fractal pore size distribution. Under these hypotheses, hysteretic curves are obtained for saturation and relative hydraulic conductivity in terms of pressure head. However, a non-hysteretic relationship is obtained when relative hydraulic conductivity is expressed as a function of saturation. The proposed relationship between permeability and porosity is similar to the well-known Kozeny–Carman equation but depends on the fractal dimension. The performance of the constitutive model is tested against different sets of experimental data and previous models. In all of the cases, the proposed expressions fit fairly well the experimental data and predicts values of permeability and hydraulic conductivity better than others models.

Modeling Forced Imbibition Processes and the Associated Seismic Attenuation in Heterogeneous Porous Rocks

Quantifying seismic attenuation during laboratory imbibition experiments can provide useful information towards the use of seismic waves for monitoring injection and extraction of fluids in the Earths crust. However, a deeper understanding of the physical causes producing the observed attenuation is needed for this purpose. In this work, we analyze seismic attenuation due to mesoscopic wave-induced fluid flow (WIFF) produced by realistic fluid distributions representative of imbibition experiments. To do so, we first perform two-phase flow simulations in a heterogeneous rock sample to emulate a forced imbibition experiment. We then select a sub-sample of the considered rock containing the resulting time-dependent saturation fields, and apply a numerical upscaling procedure to compute the associated seismic attenuation. By exploring both saturation distributions and seismic attenuation we observe that two manifestations of WIFF arise during imbibition experiments: the first one is produced by the compressibility contrast associated with the saturation front, whereas the second one is due to the presence of patches containing very high amounts of water that are located behind the saturation front. We demonstrate that while the former process is expected to play a significant role in the case of high injection rates, which are associated with viscous-dominated imbibition processes, the latter becomes predominant during capillary-dominated processes, that is, for relatively low injection rates. We conclude that this kind of joint numerical analysis constitutes a useful tool for improving our understanding of the physical mechanisms producing seismic attenuation during laboratory imbibition experiments.

Groundwater response to tidal fluctuations in wedge-shaped confined aquifers

Most of the analytical solutions to describe tide-induced head fluctuations assume that the coastal aquifer has a constant thickness. These solutions have been applied in many practical problems ignoring possible changes in aquifer thickness, which may lead to wrong estimates of the hydraulic parameters. In this study, a new analytical solution to describe tide-induced head fluctuations in a wedge-shaped coastal aquifer is presented. The proposed model assumes that the aquifer thickness decreases with the distance from the coastline. A closed-form analytical solution is obtained by solving a boundary-value problem with both a separation of variables method and a change of variables method. The analytical solution indicates that wedging significantly enhances the amplitude of the induced heads in the aquifer. However, the effect on time lag is almost negligible, particularly near the coast. The slope factor, which quantifies the degree of heterogeneity of the aquifer, is obtained and analyzed for a number of hypothetical scenarios. The slope factor provides a simple criterion to detect a possible wedging of the coastal aquifer.RésuméLa plupart des solutions analytiques destinées à décrire les variations de charge hydraulique induites par la marée supposent que l’aquifère côtier a une épaisseur constante. Ces solutions ont été appliquées à de nombreux problèmes pratiques en ignorant les possibles variations de l’épaisseur de l’aquifère, qui peuvent conduire à des estimations erronées des paramètres hydrodynamiques. Dans cette étude, une nouvelle solution analytique est présentée pour décrire les variations de charge hydraulique induites par la marée dans un aquifère côtier en forme de biseau. Le modèle proposé suppose que l’épaisseur de l’aquifère décroît avec la distance depuis le littoral. Une solution analytique de forme fermée est obtenue en résolvant un problème de valeur à la limite avec à la fois une méthode de séparation des variables et une méthode de changement de variables. La solution analytique indique que le biseau augmente significativement l’amplitude des charges hydrauliques induites dans l’aquifère. Cependant, l’effet sur le déphasage temporel est presque négligeable, particulièrement près du littoral. Le facteur de pente, qui quantifie le degré d’hétérogénéité de l’aquifère, est obtenu et analysé pour de nombreux scénarios hypothétiques. Le facteur de pente fournit un critère simple pour détecter un possible biseau de l’aquifère côtier.ResumenLa mayoría de las soluciones analíticas para describir las fluctuaciones de la carga hidráulica inducidas por mareas asume que el acuífero costero posee un espesor constante. Estas soluciones han sido utilizadas en numerosos problemas prácticos, ignorando posibles cambios en el espesor del acuífero que pueden conducir a estimaciones erróneas de los parámetros hidráulicos. En este estudio, se presenta una nueva solución analítica para describir las fluctuaciones de la carga hidráulica inducidas por mareas en un acuífero costero acuñado. El modelo propuesto asume que el espesor del acuífero decrece con la distancia a la línea de costa. Una solución analítica cerrada se obtiene resolviendo un problema de contorno con los métodos de separación y de cambio de variables. La solución analítica muestra que el acuñamiento aumenta significativamente la amplitud de las carga hidráulicas inducidas en el acuífero. Sin embargo, el efecto sobre el desfasaje temporal es casi despreciable, particularmente cerca de la costa. El factor de pendiente, que cuantifica el grado de heterogeneidad del acuífero, se calcula y analiza para varios escenarios hipotéticos. Este factor provee un criterio simple para detectar un posible acuñamiento del acuífero costero.摘要大多数描述潮汐引起的水头波动的解析方法假定沿海含水层具有恒定的厚度。这些解决方法应用于许多实际问题中,忽略了含水层厚度的可能变化,可能导致错误的水力参数估算结果。在本研究中,介绍了一种新的描述楔形沿海含水层潮汐引起的水头波动的解析方法。提出的模型假定含水层厚度随着离开海岸线的距离而降低。通过采用变量分离法和变量变化法解决边界值问题获取了封闭式的解析方法。解析方法表明,楔入大大增强了含水层诱发水头的幅度。然而,时间滞后的影响几乎可以忽略,特别是在海岸附近。针对若干假设方案获取和分析了量化含水层非均质性程度的坡度因子。坡度因子提供了一个探测沿海含水层可能的楔入简单的标准。ResumoA maioria das soluções analíticas para descrever flutuações de carga induzidas por marés assumem que os aquíferos costeiros têm uma espessura constante. Essas soluções têm sido aplicadas em muitos problemas práticos, ignorando possíveis mudanças na espessura do aquífero, o que pode levar a estimativas errôneas dos parâmetros hidráulicos. Nesse estudo, uma nova solução analítica para descrever flutuações de carga induzidas por marés em um aquífero costeiro em forma de cunha é apresentada. O modelo proposto assume que a espessura do aquífero diminui com a distância da linha costeira. Uma solução analítica de forma fechada é obtida pela resolução de um problema de valores de contorno com ambos os métodos de separação de variáveis e mudança de variáveis. A solução analítica indica que o encunhamento aumenta significativamente a amplitude das cargas induzidas no aquífero. Entretanto, o efeito na defasagem do tempo é quase negligenciável, particularmente próximo à costa. O fator de inclinação, que quantifica o grau de heterogeneidade do aquífero, é obtido e analizado por vários cenários hipotéticos. O fator de inclinação fornece um critério simples para detectar um possível encunhamento do aquífero costeiro.

An Analytical Solution of Tide-Induced Head Fluctuations in an Inhomogeneous Coastal Aquifer

A new analytical solution for tide-induced head fluctuations in a confined aquifer with hydraulic conductivity that increases quadratically with the distance to the coastline is presented. To derive the analytical solution the following assumptions are made: the aquifer ends at the coastline and extends landward infinitely, the water flow is horizontal and obeys Darcy’s law, the specific storativity is constant, and the sea tide is described by a sinusoidal function. The proposed analytical solution has a relatively simple mathematical expression and it is used to estimate the hydraulic conductivity from experimental data. In general terms, it can be concluded that the quadratic heterogeneity produces dampened amplitudes near the coastline and a faster transmission of the tidal effect into the aquifer.

Seasonal Variability of Land Water Storage in South America Using GRACE Data

The objective of the present study is to analyze seasonal variability of land water storage in South America from GRACE data. High precision estimate of temporal variations in the Earth’s gravity are obtained using monthly Release-04 (RL04) gravity field coefficients provided by the Center for Space Research (CSR) of the University of Texas at Austin. Water mass anomalies, as equivalent height of water, are calculated based on the direct relationship between gravity and mass. To remove the effects of the noise observed in the equivalent-water thickness solutions at high harmonic degrees, an optimized smoothing technique is applied. Finally, temporal distributions of land water storage are compared to monthly mean precipitation data extracted from in-situ rain gauge records in order to identify, correlate and understand patterns of water movement at continental scale in South America.

Numerical modeling of actual evapotranspiration of a coffee crop

The evapotranspiration estimation has great importance to crop productivity and agricultural water management. In this study, evapotranspiration is analyzed in a coffee (Coffea arabica L.) crop located in Piracicaba, state of Sao Paulo (Brazil) using a numerical method based on the simulation of both water flow and crop activity in the unsaturated zone of the soil. Actual evapotranspiration is estimated from potential evapotranspiration using water stress functions, meteorological data, soil hydraulic parameters, crop coefficients and leaf area index values. Crop transpiration and soil evaporation are individually quantified improving the analysis of the evapotranspiration process. The numerical procedure can predict periods of crop water stress and becomes an attractive tool to analyze the effect of non-standard conditions on coffee crops and to design efficient irrigation schedules. Simulated evapotranspiration values are in good agreement with experimental values determined in the study site.

A Physically Based Analytical Model to Describe Effective Excess Charge for Streaming Potential Generation in Water Saturated Porous Media

Among the different contributions generating self-potential, the streaming potential is of particular interest in hydrogeology for its sensitivity to water flow. Estimating water flux in porous media using streaming potential data relies on our capacity to understand, model, and upscale the electrokinetic coupling at the mineral-solution interface. Different approaches have been proposed to predict streaming potential generation in porous media. One of these approaches is the flux averaging which is based on determining the excess charge which is effectively dragged in the medium by water flow. In this study, we develop a physically based analytical model to predict the effective excess charge in saturated porous media using a flux-averaging approach in a bundle of capillary tubes with a fractal pore size distribution. The proposed model allows the determination of the effective excess charge as a function of pore water ionic concentration and hydrogeological parameters like porosity, permeability, and tortuosity. The new model has been successfully tested against different set of experimental data from the literature. One of the main findings of this study is the mechanistic explanation to the empirical dependence between the effective excess charge and the permeability that has been found by several researchers. The proposed model also highlights the link to other lithological properties, and it is able to reproduce the evolution of effective excess charge with electrolyte concentrations.

An analytical effective excess charge density model to predict the streaming potential generated by unsaturated flow

The self-potential (SP) method is a passive geophysical method that relies on the measurement of naturally occurring electrical field. One of the contributions to the SP signal is the streaming potential, which is of particular interest in hydrogeophysics as it is directly related to both the water flow and porous medium properties. The streaming current is generated by the relative displacement of an excess of electrical charges located in the electrical double layer surrounding the minerals of the porous media. In this study, we develop a physically based analytical model to estimate the effective excess charge density dragged by the water flow under partially saturated conditions. The proposed model is based on the assumption that the porous media can be represented by a bundle of tortuous capillary tubes with a fractal pore size distribution. The excess charge that is effectively dragged by the water flow is estimated using a flux averaging approach. Under these hypotheses, this new model describes the effective excess charge density as a function of saturation and relative permeability while also depending on the chemical and interface properties, and on petrophysical parameters of the media. The expression of the model has an analytical single closed-form which is consistent with a previous model developed from a different approach. The performance of the proposed model is then tested against previous models and different sets of laboratory and field data from the literature. The predictions of the proposed model fits fairly well the experimental data and shows improvements to estimate the magnitude of the effective excess charge density over the previous models. A relationship between the effective excess charge density and permeability can also be derived from the proposed model, representing a generalization to unsaturated conditions of a widely used empirical relationship. This new model proposes a simple and efficient way to model the streaming current generation for partially saturated porous media.