An Investigation of Non-Darcy Flow Effects on Hydraulic Fractured Oil and Gas Well Performance

Abstract

The primary objective of hydraulic fracturing is to create a propped fracture with sufficient conductivity and length to optimize well performance. In permeable reservoirs, the design objective is to achieve a Dimensionless Fracture Capacity, CfD, of at least 2. In lower permeability applications, additional conductivity is required (CfD > 10) to allow effective fracture fluid cleanup and optimized well performance. In some tight formation gas applications, conventional cross-linked gel fracture stimulations are not creating the desired fracture dimensions. The potential reasons for the shorter than desired effective fracture lengths are numerous with the most likely being reservoir heterogeneity, excessive fracture height growth, and poor fracture fluid cleanup. In recent years, there has been much discussion regarding the causes for, or reasons that the dimensions of the hydraulic fracture are shorter than desired. These include: relative permeability effects, fracture fluid cleanup, multi-phase flow, and non-Darcy flow. The former causes and reasons have been investigated in some detail; however, little data has been published regarding the effects of non-Darcy flow on fracture conductivity and effective fracture length. Some in the industry have suggested that tight gas well performance is hindered significantly by non-Darcy flow effects. This view, though potentially correct, is supported by little actual data in the literature. Further, to mitigate this effect, tip screen-out fracturing techniques and larger fracture stimulation designs often utilizing much more expensive ceramic proppants have been recommended and executed even in very low permeability applications. These methods may not be effective in tight gas applications but they surely are more expensive, potentially eroding the economic benefits of fracturing these low deliverability applications. In addition, little actual well performance data has been presented to justify the importance of non-Darcy flow in fractures with much of the justification coming from the use of semi-analytical calculations and spreadsheets. This paper will document an investigation of non-Darcy flow to hydraulically fractured oil and gas well performance. The investigation will utilize both a three dimensional single-phase numeric finite difference simulator and actual well performance to investigate the importance of non-Darcy flow to hydraulically fractured oil and gas wells. This paper will demonstrate the following:The importance or lack of importance of non-Darcy flow on hydraulically fractured oil and gas well performance,Compare and contrast actual well performance of off-setting wells where sand and ceramics were utilized in East Texas, Trinidad, and North Sea applications,Develop treatment guidelines and fracture design objectives to limit/mitigate the effects of non-Darcy flow across a broad spectrum of fracturing applications. Introduction The industry has been aware of the potential for non-Darcy flow in propped fracture for many years - since the pioneering work by Cooke.1 Since that work, much additional technology has been added, and that history has been well covered and will not be reviewed here (except as appropriate below). The primary problem was that the importance of this behavior was, at best, difficult to prove or quantify. The "problem" was that fracturing was traditionally (at least in the 70's and 80's when this idea was broached) applied to low permeability formations. The traditional, "definitive" test for non-Darcy effects (multi-rate drawdown) was difficult to apply operationally to such wells, and, again, at best, difficult to interpret as normal fractured well transient flow tends to mask non-Darcy effects. More recently, several papers have dealt with new analysis approaches that may make analysis for these effects more definitive in the future, but that is outside the realm of this work. Because of this "problem", the bulk of the literature has dealt with theoretical (analytical and numerical and semi-numerical) studies and extensive laboratory testing. However, very few papers have examined well test data over a range of conditions to compare the magnitude of the non-Darcy effects with these predictions.

Applicability of the Forchheimer Equation for Non-Darcy Flow in Porous Media

“…The effect of non-Darcy flow as one of the most critical factors in reducing the productivity of hydraulically fractured high-rate wells has been documented extensively with examples of field cases (Barree and Conway 2004;Holditch and Morse 1976;Olson et al 2004;Smith et al 2004;Vincent et al 1999). The inertia resistance factor, or the so-called beta factor ␤, a parameter in the Forchheimer equation for quantifying the non-Darcy flow effect, is now routinely measured for proppant packs.…”

Coupled Geomechanics and Fluid Flow Model for Production Optimization in Naturally Fractured Shale Reservoirs

“…The effects of non-Darcy flow expressed as apparent or effective conductivity results in conductivities always less than the true or laminar Darcy flow conductivity. This can lead to a reduction of 10-35% in well performance for high rate oil wells (Smith et al, 2004). Apparent conductivity can be calculated using the definitions of dimensionless fracture conductivity (3.12) and the ratio of non-Darcy drag forces on the flow in the fracture to the Darcy drag forces as given in oil field units below:…”

“…is the fracture width (ft), ℎ ! is the fracture height (ft), and is the fluid viscosity (cp) (Smith et al, 2004). Then combining (3.12) and (3.16), the relationship for apparent conductivity can be defined as below (Smith et al, 2004):…”

A Modification to the Jones Inflow Model for Improving Completion Efficiency and Production Optimization by Turbulence Analysis

“…According to Smith et al (2004), the drawdown is about 60% of the actual drawdown when non-Darcy effects are neglected, implying that rate-dependent skin has decreased the well productivity by over 40%. This implies that, at high rates, well productivity is often affected by non-Darcy flow, which increases the pressure drop at a given rate, or decreases the flow rate at a given pressure drop.…”