NDLI: A dual-porosity model for gas reservoir flow incorporating adsorption behaviour—Part II. Numerical algorithm and example applications

Content Provider	Springer Nature Link
Author	Connell, Luke Daulton Lu, Meng
Copyright Year	2007
Abstract	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.
Starting Page	139
Ending Page	158
Page Count	20
File Format	PDF
ISSN	01693913
Journal	Transport in Porous Media
Volume Number	69
Issue Number	2
e-ISSN	15731634
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2007-06-13
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Porous media Dual-porosity Adsorption Permeability Diffusion Integro-differential equation Finite difference method Quadrature scheme Sequestration of CO$_{2}$ Mechanics, Fluids, Thermodynamics Hydrogeology Civil Engineering Industrial Chemistry/Chemical Engineering Geotechnical Engineering
Content Type	Text
Resource Type	Article
Subject	Catalysis

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