A. R. Kacimov

Modeling Groundwater Flow and Seawater Intrusion in the Coastal Aquifer of Wadi Ham, UAE

Groundwater pumping from Kalbha and Fujairah coastal aquifer of the United Arab Emirates (UAE) has increased significantly during the last two decades to meet the agriculture water demands. Due to the lack of natural replenishment from rainfall and the excessive pumping, groundwater levels have declined significantly causing an intrusion of seawater in the coastal aquifer of Wadi Ham. As a result, many pumping wells in the coastal zone have been terminated and a number of farms have been abandoned. In this paper, MODFLOW was used to simulate the groundwater flow and assess the seawater intrusion in the coastal aquifer of Wadi Ham. The model was calibrated against a five-year dataset of historical groundwater levels and validated against another eleven-year dataset. The effects of pumping on groundwater levels and seawater intrusion were investigated. Results showed that reducing the pumping from Khalbha well field will help to reduce the seawater intrusion into the southeastern part of the aquifer. Under the current groundwater pumping rates, the seawater will continue to migrate inland.

Analytical solution for a sharp interface problem in sea water intrusion into a coastal aquifer

Steady two–dimensional groundwater flow in an aquifer of constant thickness discharging into an inclined sea bottom is studied by the methods of complex analysis. The shape of an abrupt interface between moving fresh water and stagnant saline water appearing at the bottom corner of the aquifer is determined in an explicit analytical form depending on the values of the incident flow, hydraulic conductivity of the aquifer, its thickness, slope angle and densities of the two waters. The hodograph domain in this problem is an infinite curvilinear triangle. Its conformal mapping on an auxiliary half–plane and the mappings of the physical domain and a priori unknown complex potential domain are obtained by the method of PolubarinovaKochina based on the analytic theory of ordinary differential equations. The solution shows that, at small values of the incident flow, sea water intrudes deeply landward into the aquifer. Comparisons with special cases of a horizontal bottom and vertical beach are presented.

Explicit calculation of the friction factor in pipeline flow of Bingham plastic fluids: a neural network approach

Abstract An artificial neural network (ANN) approach was used in this paper to develop an explicit procedure for calculating the friction factor, f, under both laminar and turbulent flow conditions of Bingham plastic fluids in closed conduits and pipe networks. The procedure aims at reducing the computational efforts as well as eliminating the need for conducting complex and time-consuming iterative solutions of the governing implicit equations for calculating the friction factor, f. The ANN approach involved the establishment of an explicit relationship among the Reynolds number, Re, Hedstrom number, He, and the friction factor, f, under both laminar and turbulent flow conditions. Although, an analytical solution of the governing equation under the laminar flow regime was also feasible (such an equation is also provided in this paper), the ANN model is applicable under both laminar and turbulent flow conditions where the analytical approach will have major limitations (especially when considering the implicit equation that govern the turbulent flow regime).

Problems of seepage to empty ditch and drain

Analytical solutions for the maximum area of the cross section of a drain ditch and a mole drain are obtained. In the case of seepage to a ditch from an underflooded soil surface, the extreme curve is represented by a semicircle, with a constant value of flow velocity along the curve. Seepage to a system of empty horizontal drains is studied for one of three possible patterns of water tables. At low values of infiltration to a phreatic surface, the drain of a maximum area is nearly circular.

Analytical determination of seeping soil slopes of a constant exit gradient

Soil slopes satisfying the condition of a constant exit gradient (constant Darcian velocity) and the seepage face (isobaricity) condition are found by complex analysis. For an empty drainage trench, soil is infinitely deep and the flow domain is bounded by two branches of a phreatic surface and the trench contour. The problem is solved by conformal mapping of the Zhukovskii domain (half-plane) onto the hodograph domain (lune). The ultimately stable seepage face and the inflow rate are determined as functions of a specified exit gradient. With decreasing of the gradient the trench flattens. If the gradient is 1, the depth-width aspect ratio of the trench reaches 0.21. Similar conformal mapping of a lune in the hodograph plane on a half-strip in the complex potential plane is used to solve the problem of a phreatic surface flow from a soil channel, whose equipotential contour satisfies the condition of constant entrance gradient. For a dam slope, the flow domain is underlain by an impermeable bottom and the hodograph is a circular triangle with a unit-gradient circle as the slope image. The Polubarinova-Kochina method of analytical differential equations is modified to reconstruct the complex coordinate and the complex potential as a function of an auxiliary variable. The resulting slope of unit exit gradient has a depth-width ratio of 1.22.

Analytical solutions of seepage theory problems. Inverse method, variational theorems, optimization and estimates (a review)

The results of analytical studies of the problems arising in connection with the prediction of ground water flow in civil engineering, hydrogeology and irrigation engineering are reviewed.Numerical techniques have become of ever greater significance in solving practical problems of seepage theory since the introduction of powerful computers in the sixties. However, even so analytical methods have proved to be necessary not only to develop and test the numerical algorithms but also to gain a deeper understanding of the underlying physics, as well as for the parametric analysis of complex flow patterns and the optimization and estimation of the properties of seepage fields, including in situations characterized by a high degree of uncertainty with respect to the porous medium parameters, the mechanisms of interaction between the fluid and the matrix, the boundary conditions and even the flow domain boundary itself.The review covers studies of ground water dynamics directly related to the problems of flow in domains with incompletely specified boundaries related to the authors interests. Mathematically, these problems reduce to boundary value problems for partial differential equations of elliptic type in domains with unknown boundaries found using specified boundary conditions. These are either deduced from the physical model of the process (the depression surface being an example) or determined by structural considerations (such as the underground shape of a dam or embankment).

Green-Ampt one-dimensional infiltration from a ponded surface into a heterogeneous soil.

Saturated hydraulic conductivity and wetting front pressure head (as soil properties) on an abrupt Green-Ampt front are assumed to increase and decrease with depth of a porous heterogeneous soil subject to a constant ponding or infiltration-evaporation depleted ponding on the surface. The corresponding Cauchy problem for a nonlinear ordinary differential equation describing the wetting front propagation in the soil profile is solved by computer algebra routines. Sensitivity of the cumulative infiltration to variation of hydraulic conductivity and capillarity is studied. A concave-convex infiltration graph is obtained for some values of parameters of the assumed exponential growth/decay of conductivity/capillarity. Texture of soil samples collected from a pedon is used for calculation of conductivity from a pedotransfer function. Synthesis of heterogeneity resulting in a specified front dynamics is discussed.

Optimal shape of a variable condenser

The shape of a condenser of maximal cross‐sectional area at a given capacity is derived in an analytical explicit form. Optimization is performed in the class of practically arbitrary curves by solution of the Dirichlet boundary‐value problem for a complex coordinate and expansions of the Cauchy integral kernels in Chebyshev polynomials. The criterion (area) becomes a quadratic form of the Fourier coefficients and both the necessary and sufficient extremum conditions are rigorously satisfied such that a global and unique extremum is achieved. The resulting curve coincides with the Polubarinova‐Kochina contour of a concrete dam of constant hydraulic gradient, which in its own term coincides with the Taylor‐Saffman bubble. In the limit of high capacitance, the Polubarinova‐Kochina contour tends to the SaffmanTaylor finger, which in its own turn coincides with the Morse‐Feshbach condenser contour of constant field intensity. Thus the contour found is of a minimal breakdown danger in the dielectric between charged surfaces (non‐isoperimetric optimum) and of maximal confined area (isoperimetric extremum).

Steady, two-dimensional flow of ground water to a trench

The problem under consideration is a steady ground water inflow to a single trench which drains a water-bearing layer of infinite extent. The equipotential corresponding to the trench outline is determined from the solution for extremum problems. The isoperimetric constraints selected for solution of these problems include cross-sectional area, seepage flow rate and size of a region with a guaranteed head loss. The equations for the required extremals and variable functions are written explicitly in terms of the solution for the Dirichlet problem.

Three-dimensional groundwater flow to a lake: an explicit analytical solution.

Steady, Darcian groundwater flow near a hemispherical lake contacting a confined homogeneous aquifer of semi-infinite depth is studied analytically by the method of separation of variables. The lake bottom is modeled either as an equipotential (the Dirichlet boundary) or as a surface with a thin sediment skin (the Robin boundary). The lake disturbs an incident uniform flow such that three regimes (gaining, losing and flow-through) are possible depending on the ambient velocity, aquifer conductivity, lake diameter, the bottom head, sediment thickness and conductivity in case of silted beds. Explicit expressions for the specific discharge and stream function are derived. Inflow and outflow rates are calculated. Implications for other equipotential surfaces placed in ambient fields are discussed.