Articles written in Journal of Earth System Science

    • Longitudinal dispersion with time-dependent source concentration in semi-infinite aquifer

      Mritunjay Kumar Singh Nav Kumar Mahato Premlata Singh

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      An analytical solution is obtained to predict the contaminant concentration along unsteady ground-water flow in semi-in finite aquifer. Initially,the aquifer is not supposed to be solute free ,i.e.,aquifer is not clean.A time-dependent source concentration is considered at the origin of the aquifer and at the other end of the aquifer, it is supposed to be zero. The time-dependent forms of unsteady velocities are considered in which one such form ,i.e., sinusoidal form represents the seasonal pattern in a year in tropical regions. The Laplace Transformation Technique (LTT)is used to get an analytical solution and a graphical representation is made through MATLAB.

    • Groundwater contamination in mega cities with finite sources


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      Groundwater contamination due to multiple sources occurring in mega cities was modelled. One constant source contamination was considered at the source boundary, whereas other sources may join in between at various locations at different times. Initially, the aquifer was contamination-free in mega cities and was subsequently contaminated by means of different sources in due course of time. One-dimensional ADE (Advection Dispersion Equation) for modelling groundwater contamination was used and solved analytically in the semi-infinite aquifer domain for a finite number of point sources. A numerical solution wasalso obtained for two sources to compare analytical solutions. Results were examined for different velocity profiles to show the maximum contaminant concentration level with distance. This may be helpful to model the maximum possible number of point sources of contamination (i.e., it represents approximately what happens in the field situation). Some remedial measures may be taken to overcome these kinds of contamination problems in mega cities by treating the sources so that recharge of the aquifer is not affected.

    • Influence of fluid viscosity and flow transition over non-linear filtration through porous media


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      The present study investigates two important though relatively unexplored aspects of non-linear filtration through porous media. The first aspect is the influence of viscosity variation over the coefficients of the governing equations used for modelling non-linear filtration through porous media. Velocity and hydraulic gradient data obtained for a wide range of fluid viscosities (8.03E-07 to 3.72E-05 N/m$^2$) were studied. An increase in fluid viscosity resulted in an increased pressure loss through packing which can be quantified using the coefficients of the governing equations. Coefficients of Forchheimer equation represent linearly increasing trend with the kinematic viscosity. On the other hand, coefficient of Wilkins equation represents similar values for different Cuid viscosities and remained unaffected by the variation in packing properties. Obtained data were utilized to understand the nature of flow transition in porous media. Behaviour of polynomial and Power-law coefficient with variation in flow velocity were also examined. Critical Reynolds number corresponding to the deviation of flow from Darcy regime varies with the porous packing and was observed to be in the range of 0–100. Coefficients of polynomial (Forchheimer) model were observed to be independent of the range of flow velocity, whereas the Power law coefficients are extremely sensitive to the data.


      $\bullet$ Increased fluid viscosity results in greater pressure drop for a given velocity through any porous packing.

      $\bullet$ Forchheimer coefficients represent linearly proportional variation trend with fluid viscosity.

      $\bullet$ Wilkins coefficient ${\alpha}$ which accounts for the viscosity variation has a constant value.

      $\bullet$ Limiting values of Reynolds number indicating flow transition in porous media are packing specific.

      $\bullet$ Power law coefficients are sensitive to the flow velocity range, but the binomial coefficients are not.

    • Advances in analytical solutions for time-dependent solute transport model


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      This study adopts generalized dispersion theory in one-dimensional advection–dispersion equation (ADE), where time-dependent dispersion and velocity are considered. The generalized dispersion theory allows mechanical dispersion to be directly proportional to seepage velocity with power n, where n is any real number. Homotopy analysis method (HAM) that uses a simple algorithm is adopted to handle the non-linearity that occurred in the ADE under the generalized dispersion. A point source is introduced to the entry boundary and a line source is introduced to the entire model domain. Three time-dependent point sources in the form of (i) exponentially decreasing function, (ii) linear function and (iii) sinusoidal function, at the entry boundary are considered. Two-line sources are considered in the form of (i) linear space-dependent function and (ii) nonlinear space-time-dependent function. Using the HAM, semi-analytical solutions for any power n are derived and semi-analytical solutions for n = 1 and n = 1.5 are discussed in particular. Comparison with the analytical solution is discussed and found good agreement for 6th order of solution obtained by HAM.


      $\bullet$ Generalized dispersion theory in 1-D ADE

      $\bullet$ Generalized semi-analytical solution using HAM

      $\bullet$ Compared with analytical solution

      $\bullet$ Good agreement for 6th order of semi-analytical solution

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