An Innovative Finite Tube Method for Coupling of Mine Ventilation Network and Gob Flow Field: Methodology and Application in Risk Analysis


Explosions and fires originated from longwall gob due to the formation of methane-air mixture have been a severe threat to coal miner’s lives. Many numerical studies on coal mine fire and explosion hazards have focused on the airflow in roadways and mine gobs. However, most of these studies isolate the gob from its surrounding roadways, and the network analysis and the CFD method are applied independently to model the two classes of airflows. This approach greatly limits the ability of simulating mine ventilation flow, especially unable to consider the effects of gob boundary conditions on air exchange between the gob and the surrounding airways. An innovative finite tube method (FTM) is developed to couple the one-dimensional mine ventilation network (MVN) and the 2D/3D gob flow field (GFF). In FTM, GFF is discretized into a finite number of flow tubes each of which is formed by any two adjacent stream lines. These tubes, representing the gob’s field flow, connect the MVN into a new coupling network. To solve the coupling model between MVN and GFF, an iterative solution technique is developed in which the MVN analysis is used to evaluate the boundary pressures for GFF simulation and in turn the FTM feeds the GFF results back to the coupling network. Based on the FTM approach, a model for gas migration in gob has been established for delineating the hazard zones of explosive methane concentration and spontaneous combustion. A computer program is developed to implement the FTM simulation. An illustrative example with five flow tubes representing the GFF is created to verify the stability and convergence of the FTM solution process. A simulation example also indicates that the accuracy of FTM is improved by 12% compared with previous method. Results of an application case show that the program is capable of quantitatively evaluating the gob’s risk zones prone for spontaneous combustion and gas explosion as well as performing risk analysis for various ventilation scenarios.

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  1. 1.

    Brune JF (2013) Methane-air explosion hazard within coal mine gobs. Trans Soc Min Metall Explor 334:376–390

    Google Scholar 

  2. 2.

    Wang CJ, Yang SQ, Li XW (2018) Simulation of the hazard arising from the coupling of gas explosions and spontaneously combustible coal due to the gas drainage of a gob. Process Saf Environ Prot 118:296–306

    Article  Google Scholar 

  3. 3.

    Dudzińska A, Cygankiewicz J (2015) Analysis of adsorption tests of gases emitted in the coal self-heating process. Fuel Process Technol 137:109–116

    Article  Google Scholar 

  4. 4.

    Su HT, Zhou FB, Song XL (2017) Risk analysis of spontaneous coal combustion in steeply inclined longwall gobs using a scaled-down experimental set-up. Process Saf Environ Prot, 111, 1–12, 1

  5. 5.

    Yuan L, Smith AC (2008) Numerical study on effects of coal properties on spontaneous heating in longwall gob areas. Fuel 87(15):3409–3419

    Article  Google Scholar 

  6. 6.

    Krawczyk J, Janus J (2014) Modeling of the propagation of methane from the longwall goaf, performed by means of a two-dimensional description. Arch Min Sci 59(4):851–868

    Google Scholar 

  7. 7.

    Xia T, Zhou F, Wang X, Zhang Y, Li Y, Kang J, Liu J (2016) Controlling factors of symbiotic disaster between coal gas and spontaneous combustion in longwall mining gobs. Fuel 182:886–896

    Article  Google Scholar 

  8. 8.

    Shao H, Jiang S, Wang L (2011) Bulking factor of the strata overlying the gob and a three-dimensional numerical simulation of the air leakage flow field. Min Sci Technol 21:261–266

    Google Scholar 

  9. 9.

    Brunner DJ (1985) Ventilation models for longwall gob leakage simulation. In: 2nd US mine ventilation symposium. Reno, NV, pp 655–662

    Google Scholar 

  10. 10.

    Wedding WC (2014) Multi-scale modeling of the mine ventilation system and flow through the gob. University of Kentucky, USA, PhD. Dissertations

    Google Scholar 

  11. 11.

    Wu FL, Chang XT, Dan Z (2018) A mine ventilation program integrated with gob flow field simulation. In: Chang X (ed) Proceedings of the 11th international mine ventilation congress. Springer, Singapore, pp 888–898

    Google Scholar 

  12. 12.

    Zienkiewicz OC, Taylor RL, Nithiarasu P (2014) The finite element method for fluid dynamics. Butterworth-Heinemann, Waltham, pp 15–53

    Google Scholar 

  13. 13.

    Bear J (1972) Dynamics of fluids in porous media. America Elsevier Publishing Company Inc., New York, pp 182–183

  14. 14.

    Li Z, Liu Y, Wu Q (2008) Improved iterative algorithm for nonlinear seepage in flow field of caving goaf. Journal of Chongqing University 31(2):186–190 (In Chinese)

  15. 15.

    Hartman HL, Mutmansky JM, Ramani RV et al (1997) Mine ventilation and air conditioning. Wiley, New York, pp 265–275

    Google Scholar 

  16. 16.

    Acuna EI, Lowndes IS (2014) A review of primary mine ventilation system optimization. Interfaces 44(2):163–175

    Article  Google Scholar 

  17. 17.

    Wu FL, Gao JN, Chang XT et al (2016) Symmetry property of Jacobian matrix of mine ventilation network and its parallel calculation model. J China Coal Soc 41(6):1454–1459 (In Chinese)

    Google Scholar 

  18. 18.

    Schenk O, Gärtner K (2004) Solving unsymmetric sparse systems of linear equations with PARDISO. Journal of Future Generation Computer Systems 20:475–487

    Article  Google Scholar 

  19. 19.

    Heinrich JC, Huyakorn PS, Zienkiewicz OC, Mitchell AR (1977) An upwind finite element scheme for two-dimensional convective transport equation. Int J Numer Methods Eng 11(1):131–143

    Article  Google Scholar 

  20. 20.

    Yang Y, Li Z, Hou S (2014) The shortest period of coal spontaneous combustion on the basis of oxidative heat release intensity. Int J Min Sci Technol 24(1):99–103

    Article  Google Scholar 

Download references


This work is supported by the National Natural Science Foundation of China [grant numbers 51974232, 51574193] and Fundamental Research Funds of Shaanxi Province, China [grant number 2017JM5039].

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Correspondence to Fengliang Wu.

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Wu, F., Luo, Y. An Innovative Finite Tube Method for Coupling of Mine Ventilation Network and Gob Flow Field: Methodology and Application in Risk Analysis. Mining, Metallurgy & Exploration 37, 1517–1530 (2020).

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  • Network flow
  • Field flow
  • Mine ventilation network
  • Coal mine gob
  • Risk zones