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Transport in Porous Media

, Volume 89, Issue 3, pp 505–532 | Cite as

Gas Condensate Flow Around Hydraulically Fractured Wells

  • H. Mahdiyar
  • M. JamiolahmadyEmail author
  • M. Sohrabi
Article

Abstract

Fracturing is one of the most common well-stimulation techniques especially for tight gas-condensate reservoirs. Considerable efforts have been devoted to this subject albeit mainly for single-phase or conventional gas oil systems. Gas condensate flow around hydraulically fractured wells (HFWs) is different from that in conventional gas oil systems. Previous studies (Danesh et al. in Gas Condensate Recovery Studies, 1994; Jamiolahmady in Transp Porous Media 41(1): 17–46, 2000) have shown that at low to moderate velocities, the relative permeability of these low interfacial tension systems increases as velocity increases and/or interfacial tension decreases. At very high velocity values, on the other hand, the inertial effect becomes dominant, reducing the relative permeability as velocity increases (Forchheimer in Hydraulik, Chap 15, Teubner, Leipzik, 1914). Description of HFWs in gas condensate reservoirs using the existing reservoir simulators requires the use of very fine grids to capture the abrupt changes in flow and rock parameters for these systems. This task is very cumbersome, time consuming and impractical. In this work, a two-dimensional mathematical simulator has been developed, based on finite-difference methods. The simulator accounts for phase change, condensate drop out, coupling and inertial effects. This single-well model has been used to investigate the impact of important geometrical and flow parameters on the performance of a HFW. Based on this investigation new formulae have been developed for fracture skin factor and effective wellbore radius. The developed formula for effective wellbore radius, which is applicable under both steady state and pseudo-steady state conditions, can be used in an equivalent open-hole system replicating flow around HFWs. The approach is similar to that followed for single phase systems albeit with a modified formula for the fracture conductivity term as developed here. Another important application of these formulae is in the optimization of fracture dimensions for a given fracture volume, in gas condensate reservoirs.

Keywords

Hydraulic fracturing Coupling and inertial effects Reynolds and capillary number effects Gas condensate Flow around wellbore 

Abbreviations

AAD%

Average absolute deviation (percentage)

EOS PR3

Peng Robinson (3 parameters) equation of state

OH

Open-hole

EOH

Equivalent open-hole

GTR

Gas to total (gas plus condensate) flow rate ratio

HFW

Hydraulically fractured well

IFT

Interfacial tension

PSS

Pseudo-steady state

SEE

Standard error of estimate

SS

Steady state

List of Symbols

A

A parameter showing the effect of fracture penetration ratio on effective wellbore radius at steady state conditions

B

A parameter, showing the effect of fracture penetration ratio on effective wellbore radius at pseudo-steady state conditions

C1

Methane

C4

Butane

C10

Decane

CfD

Dimensionless absolute fracture conductivity

CfD-eff

Dimensionless effective fracture conductivity

FND

Non-Darcy function

h

Formation thickness

k

Absolute matrix permeability

kf

Absolute fracture permeability

\({\overline{{ M}}_{\rm rf}}\)

Average relative mass mobility in the fracture

\({\overline{{M}}_{\rm rbf}}\)

Average relative base mobility in the fracture

\({\overline{{M}}_{\rm rm}}\)

Average relative mass mobility in the matrix

\({\dot {m}}\)

Mass flow rate

MRav

Ratio of average relative mass mobility

P

Pressure

PD

Dew point pressure

qw

Volumetric production rate at bottomhole conditions

r

Radius

\({r_{\rm w}^{\prime}}\)

Effective wellbore radius

Re

Reynolds number

\({S^{{\prime}}_{\rm f}}\)

Pseudo fracture skin factor

v

Velocity (scalar value)

\({\vec {\rm v}}\)

Velocity vector

xe

Half length of the square reservoir

xf

Half length of the fracture

wf

Fracture width

Greek Letters

δ

A parameter used in Eqs. 30 and 31

μ

viscosity

β

Single-phase inertial factor (scalar value)

ρ

Density

Ψ

Pseudo pressure

Subscripts

D

Dimensionless

e

Exterior

eq

Equivalent

eff

Effective

f

Fracture

m

Matrix

OH

Open-hole

w

Wellbore

T

Two-phase

Operators

Δ

Difference operator

\({\nabla.}\)

Divergence operator

\({\nabla}\)

Gradient operator

Differential operator

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Shiraz UniversityShirazIran
  2. 2.Heriot-Watt UniversityEdinburghUK

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