A Laplace-transform boundary element model for pumping tests in irregularly shaped double-porosity aquifers
•A novel BEM model in irregularly shaped double-porosity aquifers are developed.•The effect of a mixed boundary condition on drawdown is not negligible.•The effect of double-porosity parameters on drawdown are obvious.•The effect of boundary shape and location on drawdown are not still negligible. I...
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| Vydané v: | Journal of hydrology (Amsterdam) Ročník 567; s. 712 - 720 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier B.V
01.12.2018
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| ISSN: | 0022-1694, 1879-2707 |
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| Abstract | •A novel BEM model in irregularly shaped double-porosity aquifers are developed.•The effect of a mixed boundary condition on drawdown is not negligible.•The effect of double-porosity parameters on drawdown are obvious.•The effect of boundary shape and location on drawdown are not still negligible.
In this paper, a novel Laplace-transform boundary element model for pumping tests in irregularly shaped double-porosity aquifers is presented. The aquifer could be associated with various boundary conditions, such as the general Robin boundary conditions or even the mixed boundary conditions with no-flow boundary on one side and constant head boundary on the other side. The derived solution has analytical characteristics since it is obtained through the Green’s function method within the domain. Unlike traditional numerical methods, the proposed solution using the Laplace-transform boundary element method does not require discretization in spatial and temporal dimensions. In this study, boundary integral equation using Green's second theorem and the fundamental solution of Green function for dual-porosity models are given. A boundary element matrix in Laplace space is established, which allow us to consider irregularly shaped boundary. The drawdown and flux on the boundary can be obtained through solving the boundary element matrix by Gauss's elimination method. The final solution for wellbore drawdown is evaluated using numerical Laplace inversion algorithm of Stehfest (1970). Many previous solutions for transient flow in finite single-porosity aquifers with no-flow outer boundary condition are shown to be special cases of the present solution. Furthermore, the solution with a mixed outer boundary condition is used to investigate the effect of important parameters of aquifers on wellbore drawdown, including fracture storage coefficient, inter-porosity flow coefficient from matrix to fissures, boundary shape, boundary location, and interference of multiple wells. |
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| AbstractList | In this paper, a novel Laplace-transform boundary element model for pumping tests in irregularly shaped double-porosity aquifers is presented. The aquifer could be associated with various boundary conditions, such as the general Robin boundary conditions or even the mixed boundary conditions with no-flow boundary on one side and constant head boundary on the other side. The derived solution has analytical characteristics since it is obtained through the Green’s function method within the domain. Unlike traditional numerical methods, the proposed solution using the Laplace-transform boundary element method does not require discretization in spatial and temporal dimensions. In this study, boundary integral equation using Green's second theorem and the fundamental solution of Green function for dual-porosity models are given. A boundary element matrix in Laplace space is established, which allow us to consider irregularly shaped boundary. The drawdown and flux on the boundary can be obtained through solving the boundary element matrix by Gauss's elimination method. The final solution for wellbore drawdown is evaluated using numerical Laplace inversion algorithm of Stehfest (1970). Many previous solutions for transient flow in finite single-porosity aquifers with no-flow outer boundary condition are shown to be special cases of the present solution. Furthermore, the solution with a mixed outer boundary condition is used to investigate the effect of important parameters of aquifers on wellbore drawdown, including fracture storage coefficient, inter-porosity flow coefficient from matrix to fissures, boundary shape, boundary location, and interference of multiple wells. •A novel BEM model in irregularly shaped double-porosity aquifers are developed.•The effect of a mixed boundary condition on drawdown is not negligible.•The effect of double-porosity parameters on drawdown are obvious.•The effect of boundary shape and location on drawdown are not still negligible. In this paper, a novel Laplace-transform boundary element model for pumping tests in irregularly shaped double-porosity aquifers is presented. The aquifer could be associated with various boundary conditions, such as the general Robin boundary conditions or even the mixed boundary conditions with no-flow boundary on one side and constant head boundary on the other side. The derived solution has analytical characteristics since it is obtained through the Green’s function method within the domain. Unlike traditional numerical methods, the proposed solution using the Laplace-transform boundary element method does not require discretization in spatial and temporal dimensions. In this study, boundary integral equation using Green's second theorem and the fundamental solution of Green function for dual-porosity models are given. A boundary element matrix in Laplace space is established, which allow us to consider irregularly shaped boundary. The drawdown and flux on the boundary can be obtained through solving the boundary element matrix by Gauss's elimination method. The final solution for wellbore drawdown is evaluated using numerical Laplace inversion algorithm of Stehfest (1970). Many previous solutions for transient flow in finite single-porosity aquifers with no-flow outer boundary condition are shown to be special cases of the present solution. Furthermore, the solution with a mixed outer boundary condition is used to investigate the effect of important parameters of aquifers on wellbore drawdown, including fracture storage coefficient, inter-porosity flow coefficient from matrix to fissures, boundary shape, boundary location, and interference of multiple wells. |
| Author | Xue, Liang Wang, Lei |
| Author_xml | – sequence: 1 givenname: Lei surname: Wang fullname: Wang, Lei organization: ERE & BIC-ESAT, College of Engineering, Peking University, Beijing 100871, China – sequence: 2 givenname: Liang surname: Xue fullname: Xue, Liang email: xueliang@pku.edu.cn organization: State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China |
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| Cites_doi | 10.2118/9293-MS 10.1016/j.cageo.2004.06.003 10.2118/426-PA 10.1007/s11242-012-0121-y 10.1029/WR010i002p00303 10.1029/WR015i004p00861 10.1016/S0022-1694(01)00453-X 10.1029/2001WR000401 10.5194/hess-16-441-2012 10.1016/j.jhydrol.2016.07.028 10.2118/22716-MS 10.1029/WR020i007p00831 10.1002/2017WR022217 10.1111/j.1745-6584.1995.tb00293.x 10.1016/j.jconhyd.2009.04.010 10.2118/3818-PA 10.2118/08-05-63 10.1111/j.1745-6584.1994.tb00921.x 10.1007/s11242-012-0041-x 10.1007/s11075-012-9625-3 10.1016/j.advwatres.2007.09.001 10.1061/(ASCE)0733-9429(2002)128:2(175) 10.1029/96WR01464 10.1002/2014WR016502 10.1145/361953.361969 10.1016/S0309-1708(03)00046-0 10.1029/2008WR007479 10.1029/WR008i004p01031 10.1002/2016WR019443 10.2118/2156-A 10.1016/0022-1694(77)90005-1 |
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| Snippet | •A novel BEM model in irregularly shaped double-porosity aquifers are developed.•The effect of a mixed boundary condition on drawdown is not negligible.•The... In this paper, a novel Laplace-transform boundary element model for pumping tests in irregularly shaped double-porosity aquifers is presented. The aquifer... |
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| SubjectTerms | algorithms aquifers Boundary element Double-porosity medium drawdown equations Green’s function Irregularly shaped boundary transient flow Wellbore drawdown wells |
| Title | A Laplace-transform boundary element model for pumping tests in irregularly shaped double-porosity aquifers |
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