Rainfall induced groundwater mound in wedge-shaped promontories: The Strack–Chernyshov model revisited

© 2016 Elsevier LtdAn analytical solution to the Poisson equation governing Strack's discharge potential (squared thickness of a saturated zone in an unconfined aquifer) is obtained in a wedge-shaped domain with given head boundary conditions on the wedge sides (specified water level in an open water body around a porous promontory). The discharge vector components, maximum elevation of the water table in promontory vertical cross-sections, quantity of groundwater seeping through segments of the wedge sides, the volume of fresh groundwater in the mound are found. For acute angles, the solution to the problem is non-unique and specification of the behaviour at infinity is needed. A “basic” solution is distinguished, which minimizes the water table height above a horizontal bedrock. MODFLOW simulations are carried out in a finite triangular island and compare solutions with a constant-head, no-flow and “basic” boundary condition on one side of the triangle. Far from the tip of an infinite-size promontory one has to be cautious with truncation of the simulated flow domains and imposing corresponding boundary conditions. For a right and obtuse wedge angles, there are no positive solutions for the case of constant accretion on the water table. In a particular case of a confined rigid wedge-shaped aquifer and incompressible fluid, from an explicit solution to the Laplace equation for the hydraulic head with arbitrary time-space varying boundary conditions along the promontory rays, essentially 2-D transient Darcian flows within the wedge are computed. They illustrate that surface water waves on the promontory boundaries can generate strong Darcian waves inside the porous wedge. Evaporation from the water table and sea-water intruded interface (rather than a horizontal bed) are straightforward generalizations for the Poissonian Strack potential

Can heterogeneity of the near-wellbore rock cause extrema of the Darcian fluid inflow rate from the formation (the Polubarinova-Kochina problem revisited)?

Darcian steady 2-D flow to a point sink (vertical well) placed eccentrically with respect to two circles demarcating zones of contrasting permeability is studied by the methods of complex analysis and numerically by MODFLOW package. In the analytical approach, two conjugated Laplace equations for a characteristic flow function are solved by the method of images, i.e. the original sink is mirrored about two circles that generates an infinite system of fictitious sinks and source. The internal circle of the annulus models formation damage (gravel pack) near the well and the ring-shaped zone represents a pristine porous medium. On the external circle the head (pressure) is fixed and on the internal circle streamlines are refracted. The latter is equivalent to continuity of pressure and normal component of specific discharge that is satisfied by the choice of the intensity and loci of fictitious sinks. Flow net and dependence of the well discharge on eccentricity are obtained for different annulus radii and permeability ratios. A non-trivial minimum of the discharge is discovered for the case of the ring domain permeability higher than that of the internal circle. In the numerical solution, a finite difference code is implemented and compared with the analytical results for the two-conductivity zone. Numerical solution is also obtained for an aquifer with a three-conductivity zonation. The case of permeability exponentially varying with one Cartesian coordinate within a circular feeding contour is studied analytically by series expansions of a characteristic function obeying a modified Helmholtz equation with a point singularity located eccentrically inside the feeding contour. The coefficients of the modified Bessel function series are obtained by the Sommerfeld addition theorem. A trivial minimum of the flow rate into a small-radius well signifies the trade-off between permeability variation and short-cutting between the well and feeding contour. © 2010 Elsevier Ltd

Optimal Water Allocation from Subsurface Dams: A Risk-Based Optimization Approach

Subsurface dams, strongly advocated in the 1992 United Nations Agenda-21, have been widely studied to increase groundwater storage capacity. However, an optimal allocation of augmented water with the construction of the subsurface dams to compensate for the water shortage during dry periods has not so far been investigated. This study, therefore, presents a risk-based simulation–optimization framework to determine optimal water allocation with subsurface dams, which minimizes the risk of water shortage in different climatic conditions. The developed framework was evaluated in Al-Aswad falaj, an ancient water supply system in which a gently sloping underground channel was dug to convey water from an aquifer via the gravity force to the surface for irrigation of downstream agricultural zones. The groundwater dynamics were modeled using MODFLOW UnStructured-Grid. The data of boreholes were used to generate a three-dimensional stratigraphic model, which was used to define materials and elevations of five-layer grid cells. The validated groundwater model was employed to assess the effects of the subsurface dam on the discharge of the falaj. A Conditional Value-at-Risk optimization model was also developed to minimize the risk of water shortage for the augmented discharge on downstream agricultural zones. Results show that discharge of the falaj is significantly augmented with a long-term average increase of 46.51%. Moreover, it was found that the developed framework decreases the water shortage percentage in 5% of the worst cases from 87%, 75%, and 32% to 53%, 32%, and 0% under the current and augmented discharge in dry, normal, and wet periods, respectively

Seepage through earth dam with clay core and toe drain: the Casagrande–Numerov analytical legacy revisited

© 2019, © 2019 Indian Society for Hydraulics. Seepage through a zoned earth-filled dam with a vertical clay core, two permeable shoulders and toe drain are studied. Seepage through the core and the downstream shoulder are coupled. The flow rate and phreatic surface are found. The hodograph method is used, viz. a conformal mapping of a rectangle in the complex potential plane onto a circular triangle. Numerically, MODFLOW 2005 simulated seepage with the refraction of the streamlines at the interfaces between the core and both shoulders

Rainfall induced groundwater mound in wedge-shaped promontories: The Strack–Chernyshov model revisited

© 2016 Elsevier LtdAn analytical solution to the Poisson equation governing Strack's discharge potential (squared thickness of a saturated zone in an unconfined aquifer) is obtained in a wedge-shaped domain with given head boundary conditions on the wedge sides (specified water level in an open water body around a porous promontory). The discharge vector components, maximum elevation of the water table in promontory vertical cross-sections, quantity of groundwater seeping through segments of the wedge sides, the volume of fresh groundwater in the mound are found. For acute angles, the solution to the problem is non-unique and specification of the behaviour at infinity is needed. A “basic” solution is distinguished, which minimizes the water table height above a horizontal bedrock. MODFLOW simulations are carried out in a finite triangular island and compare solutions with a constant-head, no-flow and “basic” boundary condition on one side of the triangle. Far from the tip of an infinite-size promontory one has to be cautious with truncation of the simulated flow domains and imposing corresponding boundary conditions. For a right and obtuse wedge angles, there are no positive solutions for the case of constant accretion on the water table. In a particular case of a confined rigid wedge-shaped aquifer and incompressible fluid, from an explicit solution to the Laplace equation for the hydraulic head with arbitrary time-space varying boundary conditions along the promontory rays, essentially 2-D transient Darcian flows within the wedge are computed. They illustrate that surface water waves on the promontory boundaries can generate strong Darcian waves inside the porous wedge. Evaporation from the water table and sea-water intruded interface (rather than a horizontal bed) are straightforward generalizations for the Poissonian Strack potential

Rainfall induced groundwater mound in wedge-shaped promontories: The Strack–Chernyshov model revisited

© 2016 Elsevier LtdAn analytical solution to the Poisson equation governing Strack's discharge potential (squared thickness of a saturated zone in an unconfined aquifer) is obtained in a wedge-shaped domain with given head boundary conditions on the wedge sides (specified water level in an open water body around a porous promontory). The discharge vector components, maximum elevation of the water table in promontory vertical cross-sections, quantity of groundwater seeping through segments of the wedge sides, the volume of fresh groundwater in the mound are found. For acute angles, the solution to the problem is non-unique and specification of the behaviour at infinity is needed. A “basic” solution is distinguished, which minimizes the water table height above a horizontal bedrock. MODFLOW simulations are carried out in a finite triangular island and compare solutions with a constant-head, no-flow and “basic” boundary condition on one side of the triangle. Far from the tip of an infinite-size promontory one has to be cautious with truncation of the simulated flow domains and imposing corresponding boundary conditions. For a right and obtuse wedge angles, there are no positive solutions for the case of constant accretion on the water table. In a particular case of a confined rigid wedge-shaped aquifer and incompressible fluid, from an explicit solution to the Laplace equation for the hydraulic head with arbitrary time-space varying boundary conditions along the promontory rays, essentially 2-D transient Darcian flows within the wedge are computed. They illustrate that surface water waves on the promontory boundaries can generate strong Darcian waves inside the porous wedge. Evaporation from the water table and sea-water intruded interface (rather than a horizontal bed) are straightforward generalizations for the Poissonian Strack potential

Seepage through earth dam with clay core and toe drain: the Casagrande–Numerov analytical legacy revisited

© 2019, © 2019 Indian Society for Hydraulics. Seepage through a zoned earth-filled dam with a vertical clay core, two permeable shoulders and toe drain are studied. Seepage through the core and the downstream shoulder are coupled. The flow rate and phreatic surface are found. The hodograph method is used, viz. a conformal mapping of a rectangle in the complex potential plane onto a circular triangle. Numerically, MODFLOW 2005 simulated seepage with the refraction of the streamlines at the interfaces between the core and both shoulders

Rainfall induced groundwater mound in wedge-shaped promontories: The Strack–Chernyshov model revisited

© 2016 Elsevier LtdAn analytical solution to the Poisson equation governing Strack's discharge potential (squared thickness of a saturated zone in an unconfined aquifer) is obtained in a wedge-shaped domain with given head boundary conditions on the wedge sides (specified water level in an open water body around a porous promontory). The discharge vector components, maximum elevation of the water table in promontory vertical cross-sections, quantity of groundwater seeping through segments of the wedge sides, the volume of fresh groundwater in the mound are found. For acute angles, the solution to the problem is non-unique and specification of the behaviour at infinity is needed. A “basic” solution is distinguished, which minimizes the water table height above a horizontal bedrock. MODFLOW simulations are carried out in a finite triangular island and compare solutions with a constant-head, no-flow and “basic” boundary condition on one side of the triangle. Far from the tip of an infinite-size promontory one has to be cautious with truncation of the simulated flow domains and imposing corresponding boundary conditions. For a right and obtuse wedge angles, there are no positive solutions for the case of constant accretion on the water table. In a particular case of a confined rigid wedge-shaped aquifer and incompressible fluid, from an explicit solution to the Laplace equation for the hydraulic head with arbitrary time-space varying boundary conditions along the promontory rays, essentially 2-D transient Darcian flows within the wedge are computed. They illustrate that surface water waves on the promontory boundaries can generate strong Darcian waves inside the porous wedge. Evaporation from the water table and sea-water intruded interface (rather than a horizontal bed) are straightforward generalizations for the Poissonian Strack potential

How much floating light nonaqueous phase liquid can a phreatic surface sustain? Riesenkampf's scheme revisited

Steady, Darcian, one-phase, phreatic surface flow of groundwater into a horizontal well with a pancake lens of light nonaqueous phase liquid (LNAPL) accumulated in the water table trough is studied by the method of complex analysis. A sharp interface model assumes groundwater capped by two isobaric limbs (groundwater-vadose zone interfaces) of a free surface with an in-between cambered segment of an immiscible LNAPL-water interface, along which pressure is hydrostatically increasing with the depth of the LNAPL "channel." The complex potential polygon is mapped onto an auxiliary half plane where the complex physical coordinate of the flow domain is represented in terms of singular integrals as a solution of the Keldysh-Sedov problem. The shapes of semi-infinite "wings" of the water table contacting the vadose zone gas and of a finite length LNAPL-groundwater interface are found from parametric equations that involve the sink strength and location with respect to the pancake surface, the ordinate of the lowest trough point, and the volume of LNAPL accreted in the lens. Critical conditions, corresponding to the lens contour cusping toward the sink, are found. The Riesenkampf solution contains a free parameter, which is fixed by specifying either a point on the free surface or the volume of the trough-intercepted LNAPL. Copyright 2011 by the American Geophysical Union