Development of accurate well models for numerical reservoir simulation

Abstract

The Peaceman well model has been an industrial standard in numerical reservoir simula-tion. With the help of defined equivalent radius, the bottom-hole inflow or outflow flux is calculated as being proportional to the difference between the bottom-hole pressure and the well-grid block pressure. We show in this paper that, although the bottom-hole flux is calculated accurately in the Peaceman well model, some significant errors of pressure arise near the well for a large value of the length-to-width ratio of the mesh. We propose two alternative methods, the source term compensation method and the pattern competition method, both of which are based on an analytic solution induced by the source term for the homogeneous case. In the source term compensation method, the auxiliary pressure, which strictly satisfies the Laplace equation, is defined and solved instead of the original pressure variable only satisfying 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 an specific value of the transmissibility of the two adjacent grid blocks. The smallest transmissibility will outcompete, and be used for solving the discrete pressure equations. Numerical results show that not only the bottom-hole flux but also the pressure fields can be calculated accurately using both of proposed methods.