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

• Published in: Water, air, and soil pollution air, and soil pollution, 2018-07, Vol.229 (7), p.1-15, Article 221
• Main Authors: Liu, Zhi-bin, Dong, Xiao-xu, Min, Chao
• Format: Article
• Language: English
• Subjects: Analysis; Approximation; Atmospheric Protection/Air Quality Control/Air Pollution; Boundary conditions; Boussinesq approximation; Climate Change/Climate Change Impacts; Conservation; Conservation of momentum; Contaminants; Decontamination; Differential equations; Diffusion; Dye dispersion; Earth and Environmental Science; Ejection; Environment; Environmental monitoring; Horizontal wells; Hydraulic flow; Hydrogeology; Laminar flow; Laplace transforms; Mass transfer; Mathematical models; Momentum; Parameter sensitivity; Partial differential equations; Reservoirs; Sedimentary rocks; Sensitivity analysis; Shale; Shale gas; Shale oils; Shales; Soil Science & Conservation; Transient analysis; Water conservation; Water flow; Water pollution; Water Quality/Water Pollution
• ISSN: 0049-6979; 1573-2932
• DOI: 10.1007/s11270-018-3870-6

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.