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APPLICATIONS OF A NOVEL INTEGRAL TRANSFORM TO THE CONVECTION-DISPERSION EQUATIONS

ABSTRACT
In this paper, we extend the novel integral transform of some functions by the duality relationship between it and Laplace transform. Additionally, applying the novel integral transform, we solve a 1-D convection-dispersion equation describing the dispersion process of chemical additives in porous rocks during the hydraulic fracturing. The results indicate that the novel integral transform can provide a new idea to obtain more exact solutions of different convection-dispersion problems.
KEYWORDS
PAPER SUBMITTED: 2017-03-08
PAPER REVISED: 2017-04-28
PAPER ACCEPTED: 2017-05-13
PUBLISHED ONLINE: 2017-12-02
DOI REFERENCE: https://doi.org/10.2298/TSCI17S1233L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Supplement 1, PAGES [S233 - S240]
REFERENCES
  1. Ahfir, N. D., et al., Transport and Deposition of Suspended Particles in Saturated Porous Media: Hydrodynamic Effect, Hydrogeology Journal, 15 (2007), 4, pp. 659-668
  2. Bennacer, L., et al., Suspended Particles Transport and Deposition in Saturated Granular Porous Medium: Particle Size Effects, Transport in Porous Media, 100 (2013), 3, pp. 377-392
  3. Ahfir, N. D., et al., Influence of Internal Structure and Medium Length on Transport and Deposition of Suspended Particles: A Laboratory Study, Transport in Porous Media, 76 (2009), 2, pp. 289-307
  4. Wang, L., et al., Element Mobilization from Bakken Shales as a Function of Water Chemistry, Chemosphere, 149 (2016), Apr., pp. 286-293
  5. Li, Y., et al., The Status Quo Review and Suggested Policies for Shale Gas Development in China, Renewable & Sustainable Energy Reviews, 59 (2016), June, pp. 420-428
  6. Hou, P., et al., Experimental Investigation on the Failure and Acoustic Emission Characteristics of Shale, Sandstone and Coal under Gas Fracturing, Journal of Natural Gas Science and Engineering, 35 (2016), Sept., pp. 211-223
  7. Torres, L., et al., A Review on Risk Assessment Techniques for Hydraulic Fracturing Water and Produced Water Management Implemented in Onshore Unconventional Oil and Gas Production, Science of the Total Environment, 539 (2016), Jan., pp.478-493
  8. Kang, Y., et al., Comprehensive Evaluation of Formation Damage Induced by Working Fluid Loss in Fractured Tight Gas Reservoir, Journal of Natural Gas Science & Engineering, 18 (2014), 18, pp. 353-359
  9. Wang, H., et al., Particle Transport in a Porous Medium: Determination of Hydrodispersive Characteristics and Deposition Rates, Comptes Rendus de l Académie des Sciences-Series IIA-Earth and Planetary Science, 331 (2000), 2, pp. 97-104
  10. Yang, X. J., A New Integral Transform Method for Solving Steady Heat Transfer Problem, Thermal Science, 20 (2016), Suppl. 3, pp. S639-S642
  11. Yang, X. J., A New Integral Transform with an Application in Heat Transfer Problem, Thermal Science, 20 (2016), Suppl. 3, pp. S677-S681
  12. Liang, X, et al., Applications of a Novel Integral Transform to Partial Differential Equations, Journal of Nonlinear Science and Applications, 10 (2017), 2, pp. 528-534
  13. Yang, X. J., A New Integral Transform Operator for Solving the Heat-Diffusion Problem, Applied Mathematics Letters, 64 (2016), Feb., pp. 193-197
  14. Yang, X. J., et al., A New Technology for Solving Diffusion and Heat Equations, Thermal Science, 21 (2017), 1A, pp. 133-140
  15. Beerends, R. J., et al., Fourier and Laplace Transforms, Cambridge University Press, Oxford, UK, 2003
  16. Feynman, R. P., et al., Quantum Mechanics and Path Integrals, Dover Publications, Mineola, N. Y., USA, 2010
  17. Debnath, L., Bhatta, D., Integral Transforms and Their Applications, CRC Press, Boca Raton, Fla., USA, 2015
  18. Polyanin. A. D., Zaitsev, V. F., Exact Solutions for Ordinary Differential Equations, CRC Press, Boca Raton, Fla., USA, 1995

© 2017 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence