Theoretical Analysis of Bottom Water Invasion at Oil Wells Due to Transverse Dispersion

Abstract

Abstract Inaccurate modeling of fluid flow near-wellbores is commonly recognized as shortcoming of numerical reservoir simulators. After water breaks through, the well's inflow involves two or three fluids flowing at velocity exponentially increasing with reducing distance to the well. Understanding of the oil/water inflow to wells and possible improvement of its simulation is the objective of this study. Current commercial simulators disregard the effect of dispersion due to high flow velocity. They only consider effects of viscous and gravity forces, capillary pressure and sometimes Non-Darcy flow effects. We postulate that a process of transverse immiscible dispersion should be considered in evaluating the oil/water transition zone around a well and the production water cut. Transverse dispersion is a process of mixing two fluids in the direction perpendicular to the segregated flow of two phases. In the process, one phase enters the stream of another phase and contributes to the flow characters and the saturation distribution change. Away from the well where the flow velocity is low, the effect is small and overshadowed by the capillary pressure effect. It, however, may significantly increase as the two-phase flow is approaching well since the transverse dispersion coefficient is a function of velocity. Thus, at the well, transition zone size and distribution might be significantly affected by transverse dispersion resulting in water production larger than results of current simulators. In this paper, an analytical model of transverse dispersion in porous media is derived and used to study various factors influencing the dispersion. The results show that radial distance and mechanical dispersion coefficient are essential to transverse dispersion. It also shows that transverse dispersion controls transition zone growth at the bottom of well's completion where vertical gradient of horizontal velocity is the largest – up to 0.25 ft/s-ft.