Abstract: Embarking from the mass conservation principle and the Darcy′s law, the flow equation of the elastic porous medium and the slightly compressible single phase fluid are deduced with the quadratic pressure gradient for constant compressibility and isothermal flow. Considering the well bore storage effects, the well test model has been established for the infinite reservoir with the onephase constant voluemetric sandface rate production. Through variable substitution and linearizing the flow equation, the Laplace space analytic solution and procuring the real space solution is obtained by use of the numerical inversion. In the end, the pressure and the pressure derivative bilogarithmic type curves are drawn up. From the physical seepaging mechanism, the analysis to the curve shape characteristics is carried on, then the influence result of the dimensionless quadratic pressure gradient coefficient alpha to the transfusion and the well test curve is obtained. Specially on low permeable reservoir and the heavy oil reservoir, the influence of the quadratic pressure gradient term should not be neglected, the result can be used in the study of the flow rule and the well test analysis of heavy oil reservoir.

Key words: quadratic pressure gradient, nonlinear flow, well test analysis, model, Laplace transformation