Approximate Finite Difference Modeling of the Performance of Horizontal Wells in Heterogeneous Reservoirs

Abstract

Abstract A simplified representation of reservoir heterogeneity is applied to the finite difference modeling of horizontal wells operating under two phase flow conditions. The heterogeneity model, referred to as the s-k* approach, was developed and applied in earlier studies for single phase flow scenarios. The model represents heterogeneous permeability fields in terms of a constant background permeability k* and a variable skin s, which captures the effects of near-well heterogeneity. This simplified permeability representation is applied to the modeling of multiple realizations of heterogeneous permeability fields characterized by three different sets of permeability statistics. Comparisons to simulation results using the detailed permeability field and to results using a homogeneous permeability field are presented. The s-k* permeability representation is shown to provide an accurate means of representing reservoir heterogeneity in models of horizontal well performance. Integrated quantities, such as well productivity index, are captured with better accuracy than are more local quantities such as water cut. The s-k* models are more accurate than the homogeneous models in all cases considered. The use of the new modeling approach for the coarse scale modeling of horizontal well performance is also demonstrated.