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Applied Mathematics and Mechanics

, Volume 23, Issue 6, pp 627–633 | Cite as

Dynamic production prediction and parameter identification for gas well with vertical fracture

  • Guo Da-li
  • Liu Ci-qun
  • Zhao Jin-zhou
Article

Abstract

In order to devoid the hard work and factitious error in selecting charts while analyzing and interpreting hydraulic fracturing fracture parameters, on the basis of the non-Darcy flow factor, this paper put out the non-Darcy flow mathematical model of real gas in the formation and fracture, established the production history automatic matching model to identify fracture parameters, and offered the numerical solutions of those models, which took the variation of fracture conductivity in production process. These results offered a precise and reliable method to understand formation, analyze and evaluate the fracturing treatment quality of gas well.

Key words

gas well fracturing non-Darcy flow in porous media fracture conductivity parameter identification automatic matching 

CLC number

TE357.1 

Nomenclature

B

volume coefficient of formation fluid, dimensionless

Cft

comprehensive compressing coefficient of fluid in fracture, (MPa)−1

Cp

weight of single layer proppant per unit fracture area, kg/m2

Ct

comprehensive compressing coefficient of formation fluid, (MPa)−1

dBHN

Brown’s rigidity of formation rock, kg/mm2

h

height of payzone, m

K

formation permeability, μm2

Kf

fracture permeability, μm2

(KfWf)D

non-dimensional conductivity, dimensionless

L

number of layer of packed proppant, number

Lf

half fracture length, m

N

number of tested production data, number

P

formation pressure, MPa

Pc

fracture closure pressure, MPa

PF

formation fracturing pressure, MPa

Pf

fracture pressure, MPa

Pi

initial formation pressure, MPa

Pwf

wellbore bottom pressure, MPa

Qiobs

No.i practically tested production, m3/d

Wf

fracture width, m

xe,ye

distance from wellborn to non-permeable boundary, m

Z

compressing factor of natural gas, dimensionless

δ

non-Darcy flow factor, dimensionless

μ

fluid viscosity, mPa·s

ϕ

formation porosity, dimensionless

ϕf

fracture (proppant) porosity, dimensionless

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References

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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Guo Da-li
    • 1
  • Liu Ci-qun
    • 2
  • Zhao Jin-zhou
    • 3
  1. 1.Department of Computer ScienceSouthwest Petroleum InstituteNanchongP R China
  2. 2.Institute of Porous Flow and Fluid MechanicsChinese Academy of SciencesLangfangP R China
  3. 3.Department of Post GraduateSouthwest Petroleum InstituteNanchongP R China

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