Non-Darcy Porous-Media Flow According to the Barree and Conway Model: Laboratory and Numerical-Modeling Studies

Abstract

Summary This paper presents the results of our new experimental studies conducted for high flow rates through proppant packs, which show that the Barree and Conway (2004) flow model is capable of overcoming limitations of the Forchheimer non-Darcy equation at very high flow rates. To quantify the non-Darcy flow behavior using the Barree and Conway model, a numerical model is developed to simulate non-Darcy flow. In addition, an analytical solution is presented for steady-state linear non-Darcy flow and is used to verify the numerical-simulation results. The numerical model incorporates the Barree and Conway model into a general-purpose reservoir simulator for modeling multidimensional, single-phase non-Darcy flow in porous and fractured media and supplements the laboratory findings. The numerical model is then used to perform sensitivity analysis of the Barree and Conway flow model's parameters and to investigate transient behavior of non-Darcy flow at an injection well.

Effects of Non-Darcy Flow and Penetrating Ratio on Performance of Horizontal Wells with Multiple Fractures

“…By replacing the inertial factor in the Forchheimer's model with two new parameters, i.e., minimum permeability plateau and characteristic length, the Barree-Conway model is claimed to be capable of describing non-Darcy flow behaviour from low to high flow rates (Barree and Conway, 2004;Lai et al, 2012). According to the Barree-Conway model (2004), the flow equation in the fracture subsystem is expressed as follows,…”

“…It is assumed that fracture conductivity (C fD ) and fracture diffusivity (C η ) are to be 10 and 10 5 , respectively (Cinco-Ley et al, 1978). Table 2 presents the basic parameters used in the experiments by Lai et al (2012). The flow rate ranges from 707.2 Sm 3 /d to 283168.2 Sm 3 /d, covering the most possible field production rates.…”

“…Then, Barree and Conway (2004) proposed a new model by replacing the inertial factor in the Forchheimer's model with two new parameters, i.e., minimum permeability plateau and characteristic length. According to the experimental measurements, Lai et al (2012) claimed that the Barree-Conway model is capable of describing non-Darcy flow in a wider velocity range than the traditional Forchheimer's model. Either the Forchherimer's model or the Barree-Conway model can be used to examine the effects on the transient pressure behaviour, leading to a strong non-linear partial differential equation which is difficult to be solved analytically.…”

“…Either the Forchherimer's model or the Barree-Conway model can be used to examine the effects on the transient pressure behaviour, leading to a strong non-linear partial differential equation which is difficult to be solved analytically. Although numerical simulation is the primary choice by discretizing both space and time (Holditch and Morse, 1976;Belhaj et al, 2003;Lai et al, 2012), the semi-analytical method (Guppy et al, 1982a;Zeng and Zhao, 2010) has also seen its extensive applications where only fracture is divided into number of segments and the solution in each segment can be obtained analytically. In general, steady-state non-Darcy flow is assumed to occur in the fracture, whereas unsteady-state Darcy flow is assumed in the matrix.…”

Non-Darcy Displacement in Linear Composite and Radial Flow Porous Media

“…Recent studies [ Baree andConway, 2004 and2007;Lai et al 2009] indicated that Forchheimer equation could not accurately predict fluid flow behavior at very high velocity in porous media and presented an alternative equation for both singlephase and multiphase flows.…”