Well testing analysis for horizontal well with consideration of threshold pressure gradient in tight gas reservoirs

A fundamental solution for homogeneous reservoir in infinite space is derived by using the point source function with the consideration of the threshold pressure gradient. The fundamental solution of the continuous point source function is then derived based on the Green function. Various boundary conditions of the reservoirs are considered for this case and the corresponding solutions are obtained through the mirror image reflection and the principle of superimposition. The line source solution is obtained by integration. Subsequently, the horizontal-well bottom hole pressure response function for a non-linear gas flow in the homogeneous gas reservoir is obtained, and the response curve of the dimensionless bottom hole pressure and the derivative for a horizontal well in the homogeneous gas reservoir are obtained. In the end, the sensitivities of the relevant parameters are analyzed. The well test model presented in this paper can be used as the basis of the horizontal well test analysis for tight gas reservoirs.