Evaluation of numerical schemes for capturing shock waves in modeling proppant transport in fractures

查看全文 作　　者：Morteza [1]Roostaei;Alireza [1]Nouri;Vahidoddin [1]Fattahpour;Dave [1]Chan 机构地区：[1]Department of Civil and Environmental Engineering,University of Alberta,Edmonton,Canada 出　　处：《Petroleum Science》索引2017年第14卷第4期,共15页 基　　金：the research funding for this study provided by NSERC through CRDPJ 387606-09 摘　　要：In petroleum engineering, the transport phenomenon of proppants in a fracture caused by hydraulic fracturing is captured by hyperbolic partial differential equations(PDEs). The solution of this kind of PDEs may encounter smooth transitions, or there can be large gradients of the field variables. The numerical challenge posed in a shock situation is that high-order finite difference schemes lead to significant oscillations in the vicinity of shocks despite that such schemes result in higher accuracy in smooth regions. On the other hand, first-order methods provide monotonic solution convergences near the shocks,while giving poorer accuracy in the smooth regions.Accurate numerical simulation of such systems is a challenging task using conventional numerical methods. In this paper, we investigate several shock-capturing schemes.The competency of each scheme was tested against onedimensional benchmark problems as well as published numerical experiments. The numerical results have shown good performance of high-resolution finite volume methods in capturing shocks by resolving discontinuities while maintaining accuracy in the smooth regions. Thesemethods along with Godunov splitting are applied to model proppant transport in fractures. It is concluded that the proposed scheme produces non-oscillatory and accurate results in obtaining a solution for proppant transport problems. 关 键 词：PROPPANT TRANSPORT HYPERBOLIC partialdifferential equations Frac PACK Hydraulic FRACTURING