Modeling the characteristics of Bingham porous-flow mechanics for a horizontal well in a heavy oil reservoir

In order to investigate hydrodynamic characteristics of Bingham porous-flow mechanics in a heavy oil reservoir, this paper originally proposes a physical model of Bingham fluid flow for a horizontal well in a heavy oil reservoir. A corresponding mathematical model is established and solved. A series of typical pressure and pressure derivative curves are drawn by the use of the semi-analytical solution of the mathematical model. Hydrodynamic flow characteristics of Bingham fluid are thoroughly analyzed. Through the recognition of flow regimes from the typical curves, it is found that the flow process of Bingham fluid mainly includes the early radial flow regime, linear flow regime and late pseudo-radial flow regime. The curves controlled by different boundary conditions are especially studied, and it is found that the late curve shape, especially the shape of pressure derivative curve, differs completely for the various property of boundary. The curve sensitivity to different model parameters, such as dimensionless threshold pressure gradient and horizontal wellbore length, is deeply discussed. The findings are as follow: except the pure wellbore storage regime, the threshold pressure gradient influences the hydrodynamic flow behavior in all the regimes; the curve of Bingham fluid governed by the threshold pressure gradient upward deviates from that of Newtonian fluid; and the deviation of the curves increases with the increase of the threshold pressure gradient and the elapsed time. The research results of this paper sufficiently demonstrate the essential property of non-Newtonian porous-flow mechanics.