Development of accurate well models for numerical reservoir simulation

Peaceman well model is widely used in numerical reservoir simulation. With the help of the defined equivalent radius, the bottom-hole inflow or outflow flux can be calculated and is proportional to the difference of the bottom-hole pressure and the well grid pressure. It is shown in this article, though the bottom-hole flux is calculated accurately in Peaceman well model, there are some significant errors of pressure near the well for the large value of the length-to-width ratio of the mesh. Two alternative methods, the source term compensation method and the pattern competition method, which are both based on the analytic solution induced by the source term, are proposed for homogeneous medium. In the source term compensation method, auxiliary pressure, which satisfies the Laplace equation strictly, is defined and solved instead of the original pressure variable, which actually satisfies the Poisson equation. In the pattern competition method, different flow patterns including the linear flow pattern and radial flow pattern are considered. Each flow pattern corresponds to a transmissibility of the adjacent two grids and all the transmissibilities are calculated respectively. The smallest transmissibility will outcompete, and be used for solving the discrete pressure equations. Numerical results show that for the two proposed methods, not only the bottom-hole flux but also the pressure fields can be calculated accurately.