Transient Behavior and Analysis of Non-Darcy Flow in Porous and Fractured Reservoirs According to the Barree and Conway Model

Abstract

Abstract This study introduces the usage of the Barree and Conway flow model in well testing pressure-transient applications for a single-phase non-Darcy flow in porous and fractured reservoirs. The non-Darcy flow behavior is handled using a three-dimensional, general purpose reservoir simulator. This numerical model incorporates non-Darcy flow effect according to the Barree and Conway flow model and the developed numerical model is capable of simulating all near wellbore effects, such as the wellbore storage and skin effects, coupled with the non-Darcy flow behavior. In addition, a steady-state non-Darcy radial flow solution is derived analytically according to the Barree and Conway model. The numerical simulation results are verified with the analytical solution. The numerical model is used to model and interpret the radial flow pressure-transient responses for both pressure buildup and drawdown well tests in porous and fractured reservoirs. In simulating pressure drawdown tests with the non-Darcy flow effects according to Barree and Conway model and assuming no skin and wellbore storage effects, the permeability, estimated using the standard straight-line analysis, is an apparent permeability and not the Darcy's constant permeability. The estimated permeability ranges from the minimum permeability and to less than the Darcy's permeability. Thus in pressure drawdown tests the standard straight-line analysis techniques underestimate the Darcy's permeability when non-Darcy flow behavior exists. A pressure buildup test, following non-Darcy flow drawdown tests, may be good for determining Darcy's permeability values using standard straight-line analysis when non-Darcy flow effect is insignificant. The Barree and Conway non-Darcy flow model parameters may not be directly estimated from the pressure-transient well tests with a simple graphic approach. However, they can be estimated by a matching process, based on non-linear optimization algorithm incorporated into the developed numerical model. The type curves generated by the numerical model are provided to demonstrate a methodology for modeling single phase transient non-Darcy flow behavior in porous and fractured rocks. The developed numerical model in this study is used to interpret and match actual pressure drawdown and buildup well tests from wells of high production rates in Kuwait.