The Effects of Non-Darcy Flow on the Behavior of Hydraulically Fractured Gas Wells (includes associated paper 6417 )

Abstract

A reservoir simulator modified to include non-Darcy flow and fractureclosure was used to demonstrate the effects of non-Darcy gas flow in ahydraulic fracture on well performance. Results illustrate the effects onthe gas-well productivity index and on the analysis of pressure builduptests. Introduction Laminar flow of fluid through porous media can bedescribed using Darcy's law:(1) This equation indicates that if the resistance (mu/k)remains constant, the pressure gradient (delta p/delta L) isproportional to the velocity of the fluid (v). However, when thevelocity is increased such that the flow is not laminar, thepressure drop will increase more than the proportional increase in velocity. Fancher et al. recognized this behavior and publisheda paper in 1933 that gave an analogy between the flow offluids through porous media and the flow of fluidsthrough pipe. Several authors, including Brownell andKatz and Tek, have since published methods forpredicting the laminar and turbulent regions of flow inporous media based on correlations similar to the Reynoldsnumber for flow in pipe. The generalized equation for flow through porousmedia may be represented by the following equationsuggested by Forchheimer. (2) If the constant (a) or velocity (i,) approaches zero. thenthe second term can be ignored and Eq. 2 is equal toDarcy's law (Eq. 1). Cornell and Katz reformulated Eq. 2 as follows: (3) In Eq. 3, the constant (a) was replaced by the product ofthe fluid density (rho) and the beta factor, which is acharacteristic of the porous medium. Several authors havepublished empirical correlations of the beta factor with theporosity and permeability of the porous media. Geertsma pointed out that the analogy betweenlaminar and turbulent flow of fluids in porous media to theflow of fluids in pipes could be misleading. Geertsmastated that turbulence does not actually occur in the smallpore systems of reservoir rock, and the cause of theincreased pressure gradients at high fluid velocities isinertial resistance. Consequently, Geertsma defined theparameter beta as the coefficient of inertial resistance. Geertsma's paper, therefore, has created a bit ofcontroversy concerning the terminology of the parameter betain the Forchheimer equation. In reality, the excess pressure gradients at high fluidvelocities can be caused by either turbulence or inertialresistance, or by a combination of the two, depending onthe particular pore configuration of the reservoir rockbeing considered. In this paper, the parameter beta isreferred to as the beta factor. Regardless of its name, the beta factoris a value used to calculate the correct pressure gradientsunder nondarcy flow conditions. Cooke investigated nondarcy flow in packed, hydraulically induced fractures. He noted that beta factors forfractures packed with multiple layers of sand had notbeen reported in the petroleum literature and suggested the following equation for calculating beta factors: (4) JPT P. 1169^

A Criterion for Non-Darcy Flow in Porous Media

“…Non-Darcy behavior has shown significant influence on well performance. Holditch and Morse (1976) numerically investigated the non-Darcy effect on effective fracture conductivity and gas well productivity. Their results show that at the near-wellbore region, non-Darcy flow could reduce the effective fracture conductivity by a factor of 20 or more, and gas production by 50%.…”

The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

“…In the field of reservoir engineering, fluid flow behavior near the well screen controls the efficiency of oil/gas production wells (e.g., Holditz and Morse 1976;Aulisa et al 2009), as well as the efficiency of injection/extraction wells in groundwater resources applications (e.g., Sen 1989;Mathias and Todman 2010;Wen et al 2011Wen et al , 2013Yeh and Chang 2013;Houben 2015;Mathias and Moutsopoulos 2016). Moreover, nonlinear flow at full-aquifer scale in a broad range of geological formations, such as gravel, karstic or fractured aquifers, is widely addressed in the literature (e.g., Moutsopoulos and Tsihrintzis 2005;Moutsopoulos 2007).…”

On the Analysis and Numerical Formulation of Miscible Fluid Flow in Porous Media Using Chebyshev Wavelets Collocation Method

“…In order to determine the appropriate conditions of operations as well as the machinery to use for the P. Amoako-Yirenkyi et al 1211 various operations and jobs, a number of parameters and the governing equations have to be predicted accurately. Several of the cases assumed that the flow follows a Darcy's law [6]- [8] which was the fundamental principle used to describe the flow of fluids in a reservoir; however, some researchers have extended their work to nonDarcy flow [2]- [4] [9]. The flow in porous media has been studied by several authors using methods like the Implicit Pressure Explicit Saturation (IMPES) method [10]- [13], fully implicit method [14] [15], the finite volume method [16], cell-centered finite difference method [17], discontinuous Galerkin Method [18], and sequential methods [15] [19] [20].…”