• Atul Kumar

      Articles written in Journal of Earth System Science

    • Analytical solutions of one-dimensional advection–diffusion equation with variable coefficients in a finite domain

      Atul Kumar Dilip Kumar Jaiswal Naveen Kumar

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      Analytical solutions are obtained for one-dimensional advection –diffusion equation with variable coefficients in a longitudinal finite initially solute free domain,for two dispersion problems.In the first one,temporally dependent solute dispersion along uniform flow in homogeneous domain is studied.In the second problem the velocity is considered spatially dependent due to the inhomogeneity of the domain and the dispersion is considered proportional to the square of the velocity. The velocity is linearly interpolated to represent small increase in it along the finite domain.This analytical solution is compared with the numerical solution in case the dispersion is proportional to the same linearly interpolated velocity.The input condition is considered continuous of uniform and of increasing nature both.The analytical solutions are obtained by using Laplace transformation technique.In that process new independent space and time variables have been introduced. The effects of the dependency of dispersion with time and the inhomogeneity of the domain on the solute transport are studied separately with the help of graphs.

    • One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium

      Sanjay K Yadav Atul Kumar Dilip K Jaiswal Naveen Kumar

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      The one-dimensional linear advection–diffusion equation is solved analytically by using the Laplace integral transform. The solute transport as well as the flow field is considered to be unsteady, both of independent patterns. The solute dispersion occurs through an inhomogeneous semi-infinite medium. Hence, velocity is considered to be an increasing function of the space variable, linearly interpolated in a finite domain in which solute dispersion behaviour is studied. Dispersion is considered to be proportional to the square of the spatial linear function. Thus, the coefficients of the advection–diffusion equation are functions of both the independent variables, but the expression for each coefficient is considered in degenerate form. These coefficients are reduced into constant coefficients with the help of a new space variable, introduced in our earlier works, and new time variables. The source of the solute is considered to be a stationary uniform point source of pulse type.

    • Petrographic controls on phosphorous distribution in coal seams of the Jharia basin, India

      Atul Kumar Varma Sumit Mishra Balram Tiwari Bodhisatwa Hazra Susheel Kumar Durga Charan Panigrahi Anwita Ojha

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      In recent years, the international coking coal market is experiencing an acute shortage of coal supply which has caused a fluctuation in its price. Degradation of coke, in the blast furnace, is largely controlled by its inherent mineral matter. Phosphorous occurs in all coals in minor or trace amounts and is an important parameter to coal users, particularly in steel industries. The mode of occurrence and distribution of phosphorous minerals in 17 coal samples of the Jharia coal basin were investigated through petrographic examinations, technological characterisation and phosphorous distribution. The results reveal that the dull bands are eight times more enriched in phosphorous than the bright bands. The macerals of the inertinite group and mineral matter positively correlate with the phosphorous content, whereas vitrinite macerals have an apathetic correlation. The impact of the thermal alterations is localised and diminishes away from the contact of the intrusion. In contrast, the faulting does not appear to have any effect on the phosphorous content.

    • Application of neural network modelling for classifying hydrocarbon bearing zone, water bearing zone and shale with estimation of petrophysical parameters in Cauvery basin, India

      ATUL KUMAR PANDEY RIMA CHATTERJEE BISWAJIT CHOUDHURY

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      This work has been developed to classify sand and shale from seven wells in the Cauvery basin using a multilayered feedforward neural network (MLFN) model. Seven wells distributed over $5100 \rm{km}^{2}$ of this basin have been utilized for analysis of conventional well logs and reservoir characterization. Hydrocarbon bearing sediments of Andimadam, Bhuvanagiri, Nannilam and Niravi formations of the Cauvery basin are evaluated in terms of shaliness, cementation factor, porosity, water saturation, and permeability. Pickett plot has been applied to investigate the cementation factor, formation water resistivity, permeability. The cementation factor ($m$) varies from 1.31 to 1.86 in these formations, whereas permeability varies from 0.01 to 400 md. Very good quality reservoir exists in the Bhuvanagiri formation with high permeability 300–400 md, whereas a good quality reservoir is occurring in Niravi, Nannilam and Andimadam formations with hydrocarbon saturation 60–70%.

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