caa a22 4500 463162978 CHVBK 20180406164753.0 cr unu---uuuuu 170326e20070901xx s 000 0 eng 10.1007/s11242-007-9140-5 doi (NATIONALLICENCE)springer-10.1007/s11242-007-9140-5 A dual-porosity model for gas reservoir flow incorporating adsorption behaviour—Part II. Numerical algorithm and example applications [Elektronische Daten] [Luke Connell, Meng Lu] In the present study, an algorithm is presented for the dual-porosity model formulated in Part I of this series. The resultant flow equation with the dual-porosity formulation is of an integro-(partial) differential equation involving differential terms for the Darcy flow in large fractures and integrals in time for diffusion within matrix blocks. The algorithm developed here to solve this equation involves a step-by-step finite difference procedure combined with a quadrature scheme. The quadrature scheme, used for the integral terms, is based on the trapezoidal method which is of second-order precision. This order of accuracy is consistent with the first- and second-order finite difference approximations used here to solve the differential terms in the derived flow equation. In an approach consistent with many petroleum reservoir and groundwater numerical flow models, the example formulation presented uses a first-order implicit algorithm. A two-dimensional example is also demonstrated, with the proposed model and numerical scheme being directly incorporated into the commercial gas reservoir simulator SIMED II that is based on a fully implicit finite difference approach. The solution procedure is applied to several problems to demonstrate its performance. Results from the derived dual-porosity formulation are also compared to the classic Warren-Root model. Whilst some of this work confirmed previous findings regarding Warren-Root inaccuracies at early times, it was also found that inaccuracy can re-enter the Warren-Root results whenever there are changes in boundary conditions leading to transient variation within the domain. Springer Science+Business Media B.V., 2007 Porous media nationallicence Dual-porosity nationallicence Adsorption nationallicence Permeability nationallicence Diffusion nationallicence Integro-differential equation nationallicence Finite difference method nationallicence Quadrature scheme nationallicence Sequestration of CO2 nationallicence Connell Luke Unconventional Gas Reservoirs, CSIRO Petroleum, Ian Wark Laboratory, Bayview Avenue, Clayton, 3168, Melbourne, VIC, Australia aut Lu Meng Unconventional Gas Reservoirs, CSIRO Petroleum, Ian Wark Laboratory, Bayview Avenue, Clayton, 3168, Melbourne, VIC, Australia aut Transport in Porous Media Kluwer Academic Publishers 69/2(2007-09-01), 139-158 0169-3913 69:2<139 2007 69 11242 https://doi.org/10.1007/s11242-007-9140-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-007-9140-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Connell Luke Unconventional Gas Reservoirs, CSIRO Petroleum, Ian Wark Laboratory, Bayview Avenue, Clayton, 3168, Melbourne, VIC, Australia aut NATIONALLICENCE 700 1- Lu Meng Unconventional Gas Reservoirs, CSIRO Petroleum, Ian Wark Laboratory, Bayview Avenue, Clayton, 3168, Melbourne, VIC, Australia aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 69/2(2007-09-01), 139-158 0169-3913 69:2<139 2007 69 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer