Non-Darcy flow is an important factor affecting productivity of gas and high production rate oil wells and the analysis of pressure-transient well tests in porous media. The motivation for this study to investigate, validate and extend the Barree-Conway model (BCM) for pressure-transient analysis of wells involving hydraulic fractures and naturally fractured reservoirs. Numerical models based on finite control-volume method were developed according to not only the Forchheimer equation and, for the first time in the literature, but also the Barree-Conway model specifically for pressure-transient analysis of single-phase fluid flow in porous and fractured reservoirs. The developed numerical models are capable of simulating all near wellbore effects coupled with the non-Darcy flow behavior in porous and fractured reservoirs.
This study shows that the BCM can be applied, similar to the Forchheimer model, to analyzing and interpreting pressure-transient responses of non-Darcy flow in porous and fractured reservoirs. The BCM predicts similar pressure-transient responses of non-Darcy flow as predicted by the Forchheimer model. The parameter of characteristic length among the BCM model parameters is more sensitive than the minimum permeability. The minimum permeability is only sensitive at low values of characteristic length or at extremely high flow rates. Numerical simulation results indicate that the value of characteristic length must be low for significant effect of non-Darcy flow and it is related to small effective radius. The non-Darcy flow parameters of the BCM may not be all estimated from single-rate tests in single-porosity reservoirs using conventional analysis approaches. However, they can be estimated by a fitting process based on non-linear optimization algorithm incorporated into the numerical model. Type curves generated by the BCM are provided to demonstrate a methodology for analyzing the effect of non-Darcy flow on pressure-transient tests in porous and fractured reservoirs. As application examples, numerical models of non-Darcy flow are used to model and interpret actual field pressure-transient data from high production rate oil wells in Kuwait.