General Correlation for the Effect of Non-Darcy Flow on Productivity of Fractured Wells

Abstract

The paper describes a systematic study of the effect of the turbulence on productivity (or injectivity) of fractured wells. It extends significantly beyond previous work, and shows its limitations. A new correlation has been developed, based on over 2,000 high-accuracy numerical solutions for vertically fractured well for a simple geometry. The base correlation was developed for fully penetrating fracture and it is applicable to liquid and high-pressure gas systems. The general correlation for fully penetrating fracture is a function of the two dimensionless parameters and two other parameters, which can be chosen as fracture conductivity and permeability. Additional results are provided for the effect of partial perforations on a fully penetrating fracture. As a limiting case, this scenario can represent also transversely fractured horizontal well. The final correlation therefore involves 5 variables. The results show that the conventional notion that turbulence is important only in high rate gas wells is often false. Turbulence effect on productivity or injectivity can be significant for liquid flow in high permeability formations, with limited perforations and especially in transversely fractured horizontal wells. Introduction Non-Darcy (turbulence) effects have been traditionally studied primarily for gas wells. The work of Guppy1,2 showed that the effect of turbulence can be expresses as an "apparent conductivity" and a solution was obtained which correlates the ratio of the apparent to true conductivity with dimensionless rate QD and dimensionless fracture conductivity CfD. More recently, turbulence has been shown to reduce productivity in high-rate oil wells. Smith et al.3 have shown that for typical "indirect" fracture completions in the Cook formation of the Gullfaks field, that turbulence can reduce well productivity index (PI) by up to 40%. Approximate analytical method, as well as numerical simulation, was used to obtain those results. Settari et al.4 have applied similar modeling techniques to the investigation of productivity of gas condensate wells. Their results also indicated reduction of PI of 30–40% due to turbulence, both in single phase, and multiphase flow conditions. Stark et al.5,6 conducted a numerical study of turbulence in gas wells. The study introduced the concept of a "neutral skin" whereby the negative skin due to fracturing would negate the positive skin from turbulence such that the well PI would be equal to that of an unfractured well without turbulence. The work showed that in many cases fracturing could not even restore the well to the neutral skin. These studies indicate that evaluating the effect of turbulence is important in many more situations than previously thought. Similar results would be expected in high-rate water injection wells, which have been converted from fractured producers. The paper describes a systematic study of the effect of the turbulence on productivity (or injectivity) of fractured wells. It extends significantly beyond the previous works, and shows the limitations of the Guppy correlation. The study was performed in two parts. In the first part, the correlations for a fully penetrating fracture were developed. In the second part, the effect of partial perforation was studied and added to the correlation. Additional work is ongoing to verify the applicability for parameters, which have not been varied in this work.

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

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

“…Settari et al (2000) demonstrated that examining the effect of turbulence is critical, as negative skin from fracturing can cancel-out the effect of positive skin due to turbulence. In a further work, Settari et al (2002) noted that turbulence effect on productivity or injectivity can be significant for liquid flow in high permeability formations (which also implies wells with high conductivity such as high rate wells) having limited perforations. Ajab and Yu-Shu (2011) in their research on modeling non-Darcy flow for pressure transient analysis on porous and fractured reservoirs (which are synonymous to reservoirs produced by high rate wells) illustrated that an increase in the production rate can result in significant increase in pressure drop at the wellbore resulting from non-Darcy flow effects especially for high production rates.…”

Constant-Pressure Analysis of Infinite-Conductivity Fractured Gas Wells Influenced by Non-Darcy Flow Effects

“…Recent publications 30,42 have proven that MHF treatments are not only used in low-permeability gas reservoirs to enhance the productivity, but they are also applied to highpermeability reservoirs. The ultimate goal of the treatment in this case is to reduce the non-Darcy flow effects around the wellbore.…”