Modelling and simulation of coal gases in a nano-porous medium: a biologically inspired stochastic simulation

  • Najeeb Alam KhanEmail author
  • Tooba Hameed
  • Oyoon Abdul Razzaq
Methodologies and Application


This paper aims to study the dynamics of the unsteady pressure flow of coal gases caused by the temperature conditions and compressibility in the presence of a nano-porous medium using soft computing technique. To immaculately understand the mechanism, a novelty in the partial differential equation is augmented by considering the fractional-order Caputo derivative, which produces theoretically significant and accurate approximation. Subsequently, the constructed model is experimentally simulated by means of artificial neural network (ANN) and a stochastic process based on a firefly algorithm (FFA). ANN has the ability to approximate and transform the differential equation into an error minimization problem, while FFA efficiently minimizes the error function and optimizes the unknown weights of the constructed network. Furthermore, two error measuring tools; mean absolute error and root mean square error, is also formulated to evaluate the performance index of the designed scheme. Accordingly, the designed scheme is systematically elaborated to assess the pressure sorption of coal gases such as nitrogen (N2) and carbon dioxide (CO2). The accuracy of the obtained approximation shows the competitiveness of the considered scheme. Notably, the deliberation provides substantial indications about the dynamical behaviour of coal gases, which can be implemented significantly on various dynamical problems.


Coal gases Unsteady gas equation Artificial neural network Firefly algorithm 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interests.

Ethical approval

This article does not contain any studies with animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Najeeb Alam Khan
    • 1
    Email author
  • Tooba Hameed
    • 1
  • Oyoon Abdul Razzaq
    • 2
  1. 1.Department of MathematicsUniversity of KarachiKarachiPakistan
  2. 2.Department of Humanities and Social SciencesBahria UniversityKarachiPakistan

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