MRITUNJAY KUMAR SINGH
Articles written in Journal of Earth System Science
Volume 117 Issue 6 December 2008 pp 945-949
Longitudinal dispersion with time-dependent source concentration in semi-infinite aquifer
Mritunjay Kumar Singh Nav Kumar Mahato Premlata Singh
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.
Volume 129 All articles Published: 1 January 2020 Article ID 0001 Research Article
Groundwater contamination in mega cities with finite sources
AYAN CHATTERJEE MRITUNJAY KUMAR SINGH VIJAY P SINGH
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.
Volume 130 All articles Published: 1 October 2021 Article ID 0201 Research article
Influence of fluid viscosity and flow transition over non-linear filtration through porous media
ASHES BANERJEE SRINIVAS PASUPULETI MRITUNJAY KUMAR SINGH DANDU JAGAN MOHAN
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.
$\bf{Highlights}$
$\bullet$ 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.
Volume 131 All articles Published: 30 May 2022 Article ID 0131 Research article
Advances in analytical solutions for time-dependent solute transport model
ROHIT KUMAR AYAN CHATTERJEE MRITUNJAY KUMAR SINGH FRANK T-C TSAI
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
$\bf{Highlights}$
$\bullet$ 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
Volume 131, 2022
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