A dual-porosity model for gas reservoir flow incorporating adsorption behaviour—Part II. Numerical algorithm and example applications |
| |
Authors: | Luke Daulton Connell Meng Lu |
| |
Institution: | (1) Unconventional Gas Reservoirs, CSIRO Petroleum, Ian Wark Laboratory, Bayview Avenue, Clayton, Melbourne, VIC, 3168, Australia |
| |
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. |
| |
Keywords: | Porous media Dual-porosity Adsorption Permeability Diffusion Integro-differential equation Finite difference method Quadrature scheme Sequestration of CO2 |
本文献已被 SpringerLink 等数据库收录! |
|