State-of-Art Solution for Pressure Transient Analysis in Deviated Wells Penetrating Stratified Reservoirs With Crossflow

Abstract

The analysis of well test data for deviated wells penetrating layered reservoirs is usually a challenging problem due to the complexity of interlayer flow within reservoirs. These problems are as a result of insufficient data from unique layer flow into the wellbore. The aim of this work is to present a new analytical pressure-transient solution for deviated wells (0° ≤ θW  ≤ 12°) in layered reservoirs with cross-flow. The individual layer skin property was also investigated.  Green’s function for the layered system was obtained by Laplace transformation and double Fourier cosine transform. The wellbore was discretized into several segments and each segment was treated as a uniform flux source, a linear system was set up and the pressure drop solution was obtained in the Laplace space and transformed back to the real space. The nonlinear parameter estimation method was applied as a means to determine the layered skin. Applying the model to field data obtained from published works;  the pressure derivative curves indicated that the early-time behaviours of reservoirs are totally different even with little change in well inclination (except the bottom boundary is set as constant pressure), but late-time behaviours (radial flow) are very similar for all the cases. The results also showed that early time pressure drop in commingled reservoirs is much higher than that of cross-flow reservoirs, because the wellbore sees the boundary (interfaces between layers) earlier. Finally, the pressure responses of reservoirs are sensitive to the thickness of the layers.