Infiltration under Ponded Conditions

Ponded infiltration processes occur in agricultural lands irrigated by flooding of their soil surface or under insufficient drainage conditions. The existing equations describing the phenomenon of vertical infiltration under ponded conditions have not considered the actual contribution of the pressure head gradient to the flow. In this study, simple equations are proposed to describe the horizontal and vertical infiltration under various ponding heads incorporating the actual contribution of the pressure head gradient to the flow. Six soils with known hydraulic properties, covering a wide range of soil textures, were used. Horizontal and vertical infiltration data are obtained by numerical simulation for all soils studied using the Hydrus-1D code. To validate the accuracy of the proposed equations, the solutions of horizontal and vertical infiltrations provided by the proposed equations were compared with numerically simulated ones provided by the Hydrus 1-D. The analysis of the results showed a very good agreement in all soils studied. The proposed vertical infiltration equation was also compared to a simple and accurate equation which does not incorporate the actual contribution of the pressure head gradient to the flow and differences between them were observed in all soils studied.

Barrier effect of underground structures on aquifers

Impervious structures below the water table modify the natural groundwater flow in aquifers. They act as barriers, causing heads to rise upgradient and to fall downgradient. We define the barrier effect as the increase in head loss across the barrier with respect to the natural conditions prior to construction. We distinguish between regional (the minimum head loss observed at long distances) and local (the maximum head loss observed close to the structure) barrier effects. We use numerical and analytical methods to derive semi-empirical equations to quantify the two barrier effects for semi-permeable, partially penetrating (or fully penetrating but finite in length), and barriers with a by-pass in confined aquifers. The resulting equations depend on the barrier geometry and on the natural head gradient in the aquifer and they are easy to apply. We test their validity at two construction sites, obtaining excellent agreement between the computed and observed barrier effects.

Analytical expressions for macrodispersion in three-dimensional Sub-Gaussian hydraulic conductivity fields

<p>Subsurface flow and transport settings are typically characterized by spatial variability of the underlying hydro-geological attributes (e.g., permeability and porosity) and a high degree of uncertainty associated with data and model parameter estimates. In this context, we rely on a stochastic approach and analyse conservative solute transport taking place within three-dimensional, sub-Gaussian domains with isotropic, exponential correlation structure of the associated log-conductivity fields. The flow is uniform in the mean and driven by an imposed average head gradient. We present an analytical solution based on a small perturbation approach that allows assessing the temporal evolution of longitudinal and transverse macrodispersion. Similar to what is observed for Gaussian log-conductivity domains, these are seen to attain a (<em>Fickian</em>) asymptotic regime after the solute plume has travelled a sufficient number of conductivity correlation scales. We also derive closed-form analytical expressions for other statistical moments of interest (e.g., seepage velocity and particle displacement covariance) and benchmark these solutions against numerical Monte Carlo simulations for various degrees of domain heterogeneity. This enables us to assess the extent at which a small perturbation approximation can embed the key features of macrodispersion within three-dimensional sub-Gaussian conductivity fields of increasing heterogeneity levels. Our results suggest that, similar to what already observed for Gaussian fields, the analytical formulation fully captures the trend of longitudinal macrodispersion for values of log-conductivity variance smaller than the unity, the goodness of the results becoming worse as the variance increases. Our formulation also captures directional displacement and seepage velocity covariances, even though the degree of agreement with their numerical Monte Carlo counterparts rapidly deteriorates with increasing conductivity variance. Particularly refined numerical grids are required to capture the nugget effect exhibited by the analytical longitudinal velocity covariance, thus posing a challenge to assess the system behaviour at short distances.</p>

Feasibility of Diffusion Weighting with a Local Inside-Out Nonlinear Gradient Coil for Prostate MRI

Purpose: Prostate cancer remains the 2nd leading cancer killer of men, yet it is also a disease with a high rate of overtreatment. Diffusion weighted imaging (DWI) has shown promise as a reliable, grade-sensitive imaging method, but it is limited by low image quality. Currently, DWI image quality is directly related to low gradient ampli-tudes, since weak gradients must be compensated with long echo times. Methods: We propose a new type of MRl accessory, an "inside-out" and nonlinear gradient, whose sole purpose is to deliver diffusion encoding to a region of interest. Performance was simulated in OPERA and the resulting fields were used to simulate DWI with two compartment and kurtosis models. Experiments with a nonlinear head gradient prove the accuracy of DWI and ADC maps diffusion encoded with nonlinear gradients. Results: Simulations validated thermal and mechanical safety while showing a 5 to 10-fold increase in gradient strength over prostate. With these strengths, lesion CNR in ADC maps approximately doubled for a range of anatomical positions. Proof-of-principle experiments show that spatially varying b-values can be corrected for accurate DWI and ADC. Conclusions: Dedicated nonlinear diffusion encoding hardware could improve prostate DWI.

Feasibility of Diffusion Weighting with a Local Inside-Out Nonlinear Gradient Coil for Prostate MRI

Purpose: Prostate cancer remains the 2nd leading cancer killer of men, yet it is also a disease with a high rate of overtreatment. Diffusion weighted imaging (DWI) has shown promise as a reliable, grade-sensitive imaging method, but it is limited by low image quality. Currently, DWI image quality is directly related to low gradient ampli-tudes, since weak gradients must be compensated with long echo times. Methods: We propose a new type of MRl accessory, an "inside-out" and nonlinear gradient, whose sole purpose is to deliver diffusion encoding to a region of interest. Performance was simulated in OPERA and the resulting fields were used to simulate DWI with two compartment and kurtosis models. Experiments with a nonlinear head gradient prove the accuracy of DWI and ADC maps diffusion encoded with nonlinear gradients. Results: Simulations validated thermal and mechanical safety while showing a 5 to 10-fold increase in gradient strength over prostate. With these strengths, lesion CNR in ADC maps approximately doubled for a range of anatomical positions. Proof-of-principle experiments show that spatially varying b-values can be corrected for accurate DWI and ADC. Conclusions: Dedicated nonlinear diffusion encoding hardware could improve prostate DWI.

A new approach for studying vertical infiltration

The exact contribution of the pressure head gradient term during the vertical infiltration process, occurring in homogeneous porous media under zero ponding head, is determined analytically to advance the knowledge related to the infiltration phenomenon. This contribution is smaller than that of the horizontal infiltration by a factor at which is a measurable function of the infiltration time t, characteristic of each porous body. By adding to this contribution that of gravity, a new two-term analytical equation is formulated which exactly reproduces an available vertical cumulative curve and satisfies the physics governing infiltration process. The properties of at allow the derivation of an equation accurate for small and moderate t and of another one accurate for all t, including large values. By applying new methodologies, the values of the sorptivity and hydraulic conductivity are determined analytically from an available cumulative infiltration curve. Philip’s two-term equation, which does not satisfy the physical requirements at the upper extreme of t, and three other equations that do satisfy it, are examined in the light of the findings of the present work. The proposed equations are able to describe the vertical infiltration process and may be used to provide the hydraulic properties.