Exact Analytical Solution to Perched Aquifer Problem of Steady Seepage Devoured by a Low-Permeable Sublayer: Kirkham-Brock?s Legacy Revisited

Получено aналитическое решение для стационарного 2-мерного потенциального безнапорного фильтрационного потока из незакольматированного и не-экранированного земляного канала в высоко-проницаемый горизонт, с насыщенной зоной сужающейся к горизонтальной границе с нижележащим слабопроницаемым основанием

Size and Shape of Steady Seawater Intrusion, Sharp-Interface Wedge: the Polubarinova-Kochina Analytical Solution to the Dam Problem Revisited

Путем перемасштабирования геометрических размеров и величины гидравлической проводимости в классической задаче двумерного потенциального течения через прямоугольную земляную перемычку с пустым нижним бьефом показано, что это дает математически эквивалентную задачу о вторжения морской воды с резкой границей раздела пресных грунтовых и соленых морских вод. Горизонтальный водоносный горизонт разгружается в море через вертикальный отрезок пляжа. Форма границы раздела вод, вертикальные, горизонтальные размеры статического языка и его площадь поперечного сечения записаны в явном виде, используя исправленные формулы Полубариновой-Кочиной. Плотности двух жидкостей, коэффициент фильтрации и толщина пласта, а также бытовой гидравлический градиент служат в качестве входных параметров модели. С уменьшением градиента (например, связанного с откачками и водозабором из скважин) размеры клина быстро увеличиваются

Analytic Solutions for Infiltration-Evaporation Formed Fresh Groundwater Lenses Floating on Saline Water Table Under Desert Dunes: Kunin-Van Der Veer Legacy Revisited

Explicit expressions for the vector fields of specific discharge and scalar fields of stream functions and piezometric heads in a Darcian steady-state essentially two-dimensional (2-D) flow through a three-component composite representing a vertical or horizontal well with a gravel pack and annular skin are obtained and analysed. The refraction conditions along two concentric circles, which represent interfaces between three porous media of contrasting hydraulic conductivities, are exactly satisfied. Flow nets, isotachs, the locus of the stagnation point bounding the capture zone of the well, and functionals quantifying area-averaged hydraulic characteristics are found. The flow topology and drawdowns near the well illustrate that at small pumping rates a common concept of a purely radial 1-D flow can be superficially plausible but misleading.1-1

Evaporation Induced Capillary Siphoning Through Hydraulically Connected Porous Domains: the Vedernokov-Bouwer Model Revisited

Evaporation-driven wicking of soil water through porous domains with contrasting hydraulic properties is studied analytically by conformal mappings and compared to numerical solutions. Initially, the connected rectangular domains are fully saturated. The first rectangle, Gp, is comprised of a coarse-textured porous medium with large permeability and low capillary forces. Evaporation-induced capillary flow pulls water horizontally across the domains to the surface of fine-textured rectangular domain, Gz, through an interfacial hydraulic exchange region that shrinks with time. The flow field in Gz is 2-D and is analytically expressed by the Vedernikov-Bouwer model that assumes a constant hydraulic conductivity for pressure heads higher than the air-entry value. The rate of 1-D drop of the phreatic surface in Gp is proportional to the evaporation rate (decreasing with time) from the Gz surface. The complex potential domain Gw "shrinks" with time, and at any time instance, it is conformally mapped onto Gz via two auxiliary planes using the Schwarz-Christoffel and Mobius transformations. The resulting Cauchy problem for an integro-differential equation with respect to an affix of the conformal mapping is solved using numerical algebra routines. A similar capillary coupled flow problem was numerically simulated using HYDRUS2D considering 2-D flow in both Gp and Gz. New insights into process dynamics are gained from a solution of an auxiliary optimization for a vertical imbibition in a column brought in contact with a water table where particle size (linking capillarity and permeability) is used as a control variable and counter-gravity front propagation dynamics as criteria.1-2

Modelign of seepage through embankments of earth-filled recharge dams in Oman: steady and transient regimes

Аналитически исследована линейная фильтрация через ядро плотины и примыкающие к нему сильнопористые присыпки. Течение в ядре анализируется с помощью конформного отображения пентагона в области годографа скорости на треугольник в физической плоскости

Moisture and temperature in a proppant-enveloped silt block of a recharge dam reservoir: Laboratory experiment and 1-D mathematical modelling

Mosaic 3-D cascade of parallelepiped-shaped silt blocks, which sandwich sand- lled cracks, has been discovered in the eld and tested in lab experiments. Controlled wetting-drying of these blocks, collected from a dam reservoir, mimics field ponding-desiccation conditions of the topsoil layer subject to caustic solar radiation, high temperature and wind, typical in the Batinah region of Oman. In 1-D analytical modelling of a transient Richards’ equation for vertical evaporation, the method of small perturbations is applied, assuming that the relative permeability is Avery-anov’s 3.5-power function of the moisture content and capillary pressure is a given (measured) function. A linearized advective dispersion equation is solved with respect to the second term in the series expansion of the moisture content as a function of spatial coordinates and time. For a single block of a nite thickness we solve a boundary value problem with a no- ow condition at the bottom and a constant moisture content at the surface. Preliminary comparisons with theta-, TDR- probes measuring the moisture content and temperature at several in-block points are made. Results corroborate that a 3-D heterogeneity of soil physical properties, in particular, horizontal and vertical capillary barriers emerging on the interfaces between silt and sand generate eco-niches with stored soil water compartments favourable for lush vegetation in desert conditions. Desiccation significantly increases the temperature in the blocks and re-wetting of the blocks reduces the daily average and peak temperatures, the latter by almost 15°C. This is important for planning irrigation in smartly designed soil substrates and sustainability of wild plants in the region where the top soil peak temperature in the study area exceeds 70°C in Summer but smartly structured soils maintain lash vegetation. Thee layer of dry top-blocks acts as a thermal insulator for the subjacent layers of wet blocks that may host the root zone of woody species

Control of Topology of Water Fluxes in Arid Agriculture: Amalgamation of Subsurface Irrigation, Managed Aquifer Recharge and Engineered Soil Substrat

We present the results of field-, farm- observations and experiments, as well as mathematical modeling of optimal control of descending, ascending and lateral water fluxes (viz., evapotranspiration, infiltration, seepage from/to subsurface emitters/drains, losses/gains from/to a deeper confined aquifer commingled via a leaky layer with the irrigated one, and water uptake by roots)

Review: Horizontal, directionally drilled and radial collector wells

Horizontal wells play an often overlooked role in hydrogeology and aquifer remediation but can be an interesting option for many applications. This study reviews the constructional and hydraulic aspects that distinguish them from vertical wells. Flow patterns towards them are much more complicated than those for vertical wells, which makes their mathematical treatment more demanding. However, at some distance, the drawdown fields of both well types become practically identical, allowing simplified models to be used. Due to lower drawdowns, the yield of a horizontal well is usually higher than that of a vertical well, especially in thin aquifers of lower permeability, where they can replace several of the latter. The lower drawdown, which results in lower energy demand and slower ageing, and the centralized construction of horizontal wells can lead to lower operational costs, which can make them an economically feasible option

Profiling Ponded Soil Surface in Saturated Seepage Into Drain-Line Sink: Kalashnikov's Method of Lateral Leaching Revisited

Two boundary value problems are solved for potential steady-state 2-D Darcian seepage flows towards a line sink in a homogeneous isotropic soil from a ponded land surface, which is not flat but profiled with the aim of "uniformization" the velocity and travel time between this surface and a horizontal drain modelled by the sink. The complex potential domain is a half-strip, which is mapped onto a reference plane. Either the velocity magnitude or a vertical coordinate along the land surface are control variables. Either a complexified velocity or complex physical coordinate are reconstructed by solving mixed problems with the help of the Keldysh-Sedov formula via singular integrals, the kernel of which are the control functions. The flow nets, isotachs, and breakthrough curves are found by computer algebra routines. A designed soil hump above the drain ameliorates an unwanted "preferential flow" (shortcut) and improves leaching of salinized soil of a cropfield during a pre-cultivation season.1-1