Mathematical Framework of the Well Productivity Index for Fast Forchheimer (Non-Darcy) Flows in Porous Media

Aulisa, Eugenio; Ibragimov, Akif; Valkó, Peter; Walton, Jay R.

doi:10.1142/s0218202509003772

Cited by 28 publications

(43 citation statements)

References 8 publications

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“…Given a constant production rate, the model takes into account the non-Darcy-flow effects inside the fracture, in the perforation tunnels, and in the reservoir for the flow that bypasses the fracture. This paper introduces an improvement in the calculation for non-Darcy flow inside the fracture that honors the velocity distribution inside the fracture (Aulisa et al 2009a(Aulisa et al , 2009b. The traditional approach using the largest velocity inside the fracture located near the intersection unnecessarily overestimates the non-Darcy pressure gradient inside the fracture.…”

Section: Model Descriptionsmentioning

confidence: 99%

Comprehensive Model for Flow Behavior of High-Performance-Fracture Completions

Zhang

Marongiu-Porcu

Ehlig-Economides

et al. 2010

SPE Production &Amp; Operations

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Experience shows that high-performance fractures (HPFs) may retain near-unit-flow efficiency (equivalent to zero skin in a vertical well) and rarely fail, even in highly deviated wells. This may be partly because overly simplistic models of the well flow behavior lead operators to maintain wells at lower production rates than could have been achieved for the same amount of injected proppant with a vertical-well-completion design. Rigorous models that account for widely accepted rock-mechanics fundamentals indicate that the fracture-to-well connection is compromised in deviated wells and lead to questions concerning whether the bulk of the flow to the well actually passes through the fracture.Distributed volumetric sources are used in this model to rigorously model a wide variety of possible fracture geometries such as an expanded wellbore because of halo effect, flow strictly through the fracture, and combined flow through a single fracture and to remaining flowing perforations not connected to the fracture. The model also includes turbulent-flow effects that may occur for radial-flow conditions in the fracture plane or in the reservoir opposite wellbore sections not connected to the fracture, along with high-velocity flow through the perforation tunnels. It also computes the effective flow area at the resulting face between the reservoir and the completion to check whether flow velocity exceeds conditions that would risk production of reservoir fines, and it estimates the screen-flow velocity on the basis of the number of flowing perforations.This comprehensive view of the HPF completion enables a thorough analysis of the risks of flowing the well at high rate. Field examples show that the new model depicts real field conditions in calculating the total skin, flow fractions, and the flux for HPF completions in high-rate gas and oil wells.Complete inflow-performance behavior for likely flow patterns for HPF wells in oil and gas reservoirs is provided.

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Section: Model Descriptionsmentioning

confidence: 99%

Comprehensive Model for Flow Behavior of High-Performance-Fracture Completions

Zhang

Marongiu-Porcu

Ehlig-Economides

et al. 2010

SPE Production &Amp; Operations

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“…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).…”

mentioning

confidence: 99%

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

et al. 2017

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The current study provides new experimental data on nonlinear flow behavior in various uniformly graded granular materials (20 samples) ranging from medium sands (d 50 > 0.39 mm) to gravel (d 50 = 6.3 mm). Generally, theoretical equations relate the Forchheimer parameters a and b to the porosity, as well as the characteristic pore length, which is assumed to be the median grain size (d 50 ) of the porous medium. However, numerical and experimental studies show that flow resistance in porous media is largely determined by the geometry of the pore structure. In this study, the effect of the grain size distribution was analyzed using subangular-subrounded sands and approximately equal compaction grades. We have used a reference dataset of 11 uniformly graded filter sands. Mixtures of filter sands were used to obtain a slightly more well-graded composite sand (increased C u values by a factor of 1.19 up to 2.32) with respect to its associated reference sand at equal median grain size (d 50 ) and porosity. For all composite sands, the observed flow resistance was higher than in the corresponding reference sand at equal d 50 , resulting in increased a coefficients by factors up to 1.68, as well as increased b coefficients by factors up to 1.44. A modified Ergun relationship with Ergun constants of 139.1 for A and 2.2 for B, as well as the use of d m − σ as characteristic pore length predicted the coefficients a and b accurately.

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“…Given a constant production rate, the model takes into account the non-Darcy flow effects inside the fracture, in the perforation tunnels, and in the reservoir for the flow that bypasses the fracture. This paper introduces an improvement in the calculation for non-Darcy flow inside the fracture that honors the velocity distribution inside the fracture (Aulisa et al 2009). The traditional approach using the largest velocity inside the fracture located near the intersection unnecessarily overestimates the non-Darcy pressure gradient inside the fracture.…”

Section: Model Descriptionsmentioning

confidence: 99%

“…Figure 4 compares the new model (Aulisa et al 2009) described in detail in Appendix C with the method currently favored in the literature based on the adjustment to the proppant pack permeability in the fracture first presented by Gidley (1990). Because the existing method overestimates the non-Darcy effects inside the fracture, it results in somewhat higher total skin and lower fracture flow fraction.…”

Section: Oil Well Sensitivity Studiesmentioning

confidence: 99%

“…Akif Ibragimov helped the authors of this paper to integrate a new approach accounting for non-Darcy flow with the already well developed DVS framework. This new approach (Aulisa et al 2009) developed a generalized nonlinear Darcy equation based on the two-terms Forchheimer Law, which can be simplified for homogeneous isotropic porous medium to be p p k…”

Section: Appendix a -Geometric Modelmentioning

confidence: 99%

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Comprehensive Model for Flow Behavior of High-Performance Fracture Completions

et al. 2009

View full text Add to dashboard Cite

Experience shows that high-performance fractures (HPFs) may retain near unit flow efficiency (equivalent to zero skin in a vertical well) and rarely fail, even in highly deviated wells. This may be partly because overly simplistic models of the well flow behavior lead operators to maintain wells at lower production rates than could have been achieved for the same amount of injected proppant with a vertical well completion design. Rigorous models that account for widely accepted rock mechanics fundamentals indicate that the fracture to well connection is compromised in deviated wells and lead to questions whether the bulk of the flow to the well actually passes through the fracture.Distributed volumetric sources are used in this model to rigorously model a wide variety of possible fracture geometries such as an expanded wellbore due to halo effect, flow strictly through the fracture, and combined flow to a single fracture and to remaining flowing perforations not connected to the fracture. The model also includes turbulent flow effects that may occur for radial flow conditions in the fracture plane or in the reservoir opposite wellbore sections not connected to the fracture as well as high velocity flow through the perforation tunnels. It also computes the effective flow area at the resulting face between the reservoir and the completion to check whether flow velocity exceeds conditions that would risk production of reservoir fines, and estimates the screen flow velocity based on the number of flowing perforations.This comprehensive view of the HPF completion enables a thorough analysis of the risks of flowing the well at high rate. Field examples show that the new model better depicts the real field conditions in calculating the total skin, flow fractions and the flux for HPF completions in high rate gas and oil wells.Complete inflow performance behavior for all likely flow patterns for HPF wells in oil and gas reservoirs is provided.

show abstract

Mathematical Framework of the Well Productivity Index for Fast Forchheimer (Non-Darcy) Flows in Porous Media

Cited by 28 publications

References 8 publications

Comprehensive Model for Flow Behavior of High-Performance-Fracture Completions

Comprehensive Model for Flow Behavior of High-Performance-Fracture Completions

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

Comprehensive Model for Flow Behavior of High-Performance Fracture Completions

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