Transient Analysis of Contaminant Diffusion in the Wellbore of Shale Gas Horizontal Wells

  • Zhi-bin Liu
  • Xiao-xu DongEmail author
  • Chao Min


This study focuses on the transient analysis of diffusion of a contaminant ejected by an external source into a laminar flow of recovered water. The influence of density variation with contaminant concentration is approximated according to the Boussinesq approximation. On the basis of momentum conservation and mass conservation theory, recovered water flow and mass transfer partial differential equations (PDEs) describing contaminant diffusion are obtained. This problem under three kinds of boundary conditions is solved analytically using Laplace transform method. By comparing the actual measured concentration in horizontal well of X shale gas reservoir and the concentration obtained from the models, the type of boundary conditions of X shale gas reservoir is determined. After that, sensitivity analysis of the influence of each parameter on the concentration of contaminant is presented. The determination of boundary condition type can determine the fracture form, which provides the basis for the flow and diffusion of the fluid in the fracture. The model also can be quite useful for available necessary early warning methods for detecting or predicting contaminant concentration and hence help mitigate related environmental pollution by earlier instituting relevant decontamination measures.


Recovered water Contaminant concentration Contaminant diffusion Laplace transform 


Funding Information

This project is supported by the National Science Fund-Tianyuan Mathematical Fund (No. 11526173) and applied fundamental research (major frontier projects) of Sichuan Province (No. 16JC0314).


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of SciencesSouthwest Petroleum UniversityChengduChina

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