Closed-form solution for determination of pore pressure field around horizontal wellbore

  • Affiliations:

    1 Le Quy Don Technical University, Hanoi, Viet Nam
    2 Hanoi University of Mining and Geology, Hanoi, Viet Nam

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  • Received: 24th-Mar-2022
  • Revised: 5th-July-2022
  • Accepted: 31st-July-2022
  • Online: 31st-Aug-2022
Pages: 91 - 101
Views: 3361
Downloads: 2217
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Wellbores are usually located in saturated geological layers. The determination of pore water pressure field around the wellbore is necessary during the design calculation and drilling stages. This paper presents analytical approach to determine the pore water pressure field around a horizontal wellbore at deep geological layer that exhibits heterogeneous, isotropic or transversely isotropic behavior. Thus, the wellbore is considered to be in an infinite medium. The pore water pressure at the well wall, equal to the drilling mud pressure, together with the pore water pressure at infinity is assumed to be constant. The closed-form solutions are based on the theory of fluid transport in porous medium and the conformal mapping technique of the complex variable method. The closed-form solutions are established with the condition of transient fluid flow for the case of isotropic medium and with the condition of steady state fluid flow for the case of transversely isotropic medium. The accuracy of the closed-form solutions is validated by numerical solutions based on the finite element method. The obtained solutions can be used as tools to determine quickly and accurately the pore pressure field around the horizontal wellbore, which serves to evaluate the stability of the well wall in preliminary design of the wellbore, as well as the amount of water inflow into it. Furthermore, the closed-form solutions are also considered as reference solutions to evaluate the accuracy and reliability of numerical models.

How to Cite
Tran, H.Nam, Nguyen, N.Thu Thi and Trieu, T.Hung 2022. Closed-form solution for determination of pore pressure field around horizontal wellbore (in Vietnamese). Journal of Mining and Earth Sciences. 63, 4 (Aug, 2022), 91-101. DOI:

El Tani M., (2003). Circular tunnel in a semi-infinite aquifer. Tunn Undergr Space Technol 18 (1). 49–55.

Fitts, C. R., (2006). Exact solution for two-dimensional flow to a well in an anisotropic domain. Ground Water 44(1). 99–101.

Jacob C. E., Lohman S. W., (1952). Nonsteady flow to a well of constant drawdown in an extensive aquifer. Trans AGU 33(4). 559–569.

Lekhnitskii S. G., (1963). Theory of elasticity of an anisotropic elastic body. San Francisco: Holden-Day, Inc.

Ming H., Wang M., Tan Z., Wang X., (2010). Analytical solutions for steady seepage into an underwater circular tunnel. Tunn Undergr Space Technol. 25(4). 391–396.

Nguyen T. P, (2019). Design of traffic tunnel. Construction Publisher. 384 pages.

Park K., Owatsiriwong A., Lee J., (2008). Analytical solution for steady-state groundwater inflow into a drained circular tunnel in a semi-infinite aquifer: a revisit. Tunn Undergr Space Technol. 23 (2). 206–209.

Perrochet, P., (2005). A simple solution to tunnel or well discharge under constant drawdown. Hydrogeol. J. 13. 886–888.

Tran T. M, (2020). Mechanics and calculation of structures for underground works (Volume 2). Construction Publisher. 372 pages.

Vu T. T. G, Do N. T, (2012). Analysis of the time of the erection of the tunnel shell structure according to Convergence-Confinement Method for Tunnel Design. Vietnam Road and Bridge journal, 5, pp. 25-30..

Wang H. F., (2000). Theory of linear poroelasticity with applications to geomechanics and hydrogeology. Princeton University Press, Princeton.