Applied Mathematics and Mechanics

, Volume 22, Issue 4, pp 385–393 | Cite as

3-D Fracture propagation simulation and production prediction in coalbed

  • Guo Da-li
  • Ji Lu-jun
  • Zhao Jin-zhou
  • Liu Ci-qun


In accordance with the fracturing and producing mechanism in coalbed methane well, and combining the knowledge of fluid mechanics, linear elastic fracture mechanics, thermal transfer, computing mathematics and software engineering, the three-dimensional hydraulic fracture propagating and dynamical production predicting models for coalbed methane well is put forward. The fracture propagation model takes the variation of rock mechanical properties and in-situ stress distribution into consideration. The dynamic performance prediction model takes the gas production mechanism into consideration. With these models, a three-dimensional hydraulic fracturing optimum design software for coalbed methane well is developed, and its practicality and reliability have been proved by example computation.

Key words

coalbed fracturing three-dimensional fracture propagation production predicting desorption diffusion 

CLC number



A(x, t)

Cross-section area of fracture at timet and sitex, m2


Coalbed gas and water volume factor, dimensionless


Langmuir factor, (MPa)−1


Coalbed gas, rock and water compressibility coefficient, (MPa)−1


Sand ratio, dimensionless

Ci(x, t)

Total fracturing fluid leak-off coefficient, m/s0.5


Proppant diameter, m


Elastic modulus of coalbed, upper burden and lower burden formation, MPa

H, Hp

Formation depth, thickness, m;h(x, t),h 1(x, t),h u(x, t) — Total fracture height, upper and lower fracture height, m

\(\bar h\)

Average fracture height, m


Coalbed absolute permeability, μm2


Rock toughness of coalbed, upper and lower barrier, MPa·m0.5


Relative permeability of water and gas, dimensionless


Fracturing fluid consistency index, MPa·sn


Fracture half-length, m


Fracturing fluid flow behavior index, dimensionless

p(x, t), pf(x, t)

Pressure inside fracture, fracturing fluid pressure, MPa


Coalbed pressure, original coalbed pressure, gas pressure, water pressure, MPa

Q, q(x, t)

Injection rate, flow rate in fracture, m3/s


Minimum horizontal principal stress in coalbed, upper and lower barrier, MPa


Gas and water saturation


Injection time, s


Temperature in coalbed, °C


Desorption gas volume, diffusion gas volume and maximum gas volume, m3/t


Injection total volume, m3

w(x, z, t), w(x, 0, t)

Fracture width and center fracture width, m

\(\bar w\)

Average fracture width, m


Rectangular coalbed reservoir length and width, m


Poisson's ratio of pay zone, upper barrier and lower barrier, dimensionless


Viscosity of coalbed gas and water, MPa·s


Fracturing fluid efficiency, dimensionless


Desorption time, s


Fracturing fluid contact time with formation atx, s


Coalbed porosity, dimensionless


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Palmer I D, Metealfe R S, Yee D, et al.Coalbed Methane Formation Evaluation and Production Technology [M]. QIN Yong, ZENG Yong Eds. Xuzhou: China Mining University Press, 1996. (Chinese version)Google Scholar
  2. [2]
    ZHAO Jin-zhou, GUO Da-li, HU Yong-quan. Hrydraulic fracturing technique for low permeability coalbed methane gas reservoirs[A]. SPE 38095, 1997.Google Scholar
  3. [3]
    Van Eekelen. Hydraulic fracture geometry: fracture containment in layered formation [J].Soc Pet Eng J 1982,22(6):341–349.Google Scholar
  4. [4]
    Advani S H. Finite element model simulations associated with hydraulic fracturing [A]. SPE/DOC 8941, 1980.Google Scholar
  5. [5]
    Settari A, Cleary M P. Three-dimensional simulation of hydraulic fracturing [J].J Pet Tech, 1984,36(7):1170–1190.Google Scholar
  6. [6]
    Settari A, Cleary M P. Development and testing of a pseudo-three-dimensional model of hydraulic fracture geometry (P3DH)[A]. SPE 10505, 1982.Google Scholar
  7. [7]
    Palmer I D, Carrol H B. Numerical solution for height and elonged hydraulic fracturing [A]. SPE 11627, 1983.Google Scholar
  8. [8]
    Palmer I D, Craig H R. Modeling of asymetric vertical growth in elongated hydraulic fracture and application to first MWX stimulation [A]. SPE 12879, 1984.Google Scholar
  9. [9]
    ZHANG Ping, ZHAO Jin-zhou, GUO Da-li, et al. 3-D numerical simulation of hydraulic fracturing [J].Oil Drilling & Production Technology, 1997,19(3):53–59. (in Chinese)Google Scholar
  10. [10]
    ZHAO Jing-zhou, GUO Jian-chun. Performance prediction for hydraulically fractured well [J].Oil Drilling & Production Technology, 1995,17(6):55–61. (in Chinese)Google Scholar
  11. [11]
    ZHAO Jing-zhou, REN Shu-quan. Numerical model for fracture geometry considering temperature effects [J].Acta Petrolei Sinica, 1987,8(1):71–82. (in Chinese)Google Scholar
  12. [12]
    ZHAO Jin-zhou, HU Yong-quan, GUO Da-li. Moving and distribution of proppant-laden slurry in the fracture [A]. In:The 27th Annual Meeting of the Fine Particle Society [C]. 1996.Google Scholar
  13. [13]
    GUO Da-li, CHEN Wen-bin, ZHAO Jin-zhou. New method for analyzing post-treatment pressure decline [J].Oil Drilling & Production Technology, 1997,19(4):70–73. (in Chinese)Google Scholar
  14. [14]
    ZHANG Ping, GUO Da-li, CHEN Wen-bin, et al. Analysis and interpretation technique for post-treatment pressure test data [J].Natural Gas Industry, 1997,17(5):55–57. (in Chinese)Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Guo Da-li
    • 1
  • Ji Lu-jun
    • 2
  • Zhao Jin-zhou
    • 3
  • Liu Ci-qun
    • 4
  1. 1.Department of Computer ScienceSouthwest Petroleum InstituteNanchongP R China
  2. 2.Department of Petroleum EngineeringSouthwest Petroleum InstituteNanchongP R China
  3. 3.Department of Post GraduateSouthwest Petroleum InstituteNanchongP R China
  4. 4.Institute of Porous Flow and Fluid MechanicsChinese Academy of ScienceLangfangP R China

Personalised recommendations