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Applications of a novel integral transform to the convection-dispersion equations

Liang Xin (China University of Mining and Technology, State Key Laboratory for Geomechanics and Deep Underground Engineering, Xuzhou, China)
Liu Guannan (China University of Mining and Technology, School of Mechanics and Civil Engineering, Xuzhou, China)
Su Shanjie (China University of Mining and Technology, State Key Laboratory for Geomechanics and Deep Underground Engineering, Xuzhou, China)

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: integral transform, convection-dispersion equation, hydraulic fracturing