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

Abstract 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 vari...

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Autores principales:	Morteza Roostaei, Alireza Nouri, Vahidoddin Fattahpour, Dave Chan
Formato:	article
Lenguaje:	EN
Publicado:	KeAi Communications Co., Ltd. 2017
Materias:	Proppant transport Hyperbolic partial differential equations Frac pack Hydraulic fracturing Science Q Petrology QE420-499
Acceso en línea:	https://doaj.org/article/4f4500e1d49f4a01a152ed4247092445
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spelling	oai:doaj.org-article:4f4500e1d49f4a01a152ed42470924452021-12-02T06:08:53ZEvaluation of numerical schemes for capturing shock waves in modeling proppant transport in fractures10.1007/s12182-017-0194-x1672-51071995-8226https://doaj.org/article/4f4500e1d49f4a01a152ed42470924452017-11-01T00:00:00Zhttp://link.springer.com/article/10.1007/s12182-017-0194-xhttps://doaj.org/toc/1672-5107https://doaj.org/toc/1995-8226Abstract 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 one-dimensional 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. These methods 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.Morteza RoostaeiAlireza NouriVahidoddin FattahpourDave ChanKeAi Communications Co., Ltd.articleProppant transportHyperbolic partial differential equationsFrac packHydraulic fracturingScienceQPetrologyQE420-499ENPetroleum Science, Vol 14, Iss 4, Pp 731-745 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Proppant transport Hyperbolic partial differential equations Frac pack Hydraulic fracturing Science Q Petrology QE420-499
spellingShingle	Proppant transport Hyperbolic partial differential equations Frac pack Hydraulic fracturing Science Q Petrology QE420-499 Morteza Roostaei Alireza Nouri Vahidoddin Fattahpour Dave Chan Evaluation of numerical schemes for capturing shock waves in modeling proppant transport in fractures
description	Abstract 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 one-dimensional 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. These methods 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.
format	article
author	Morteza Roostaei Alireza Nouri Vahidoddin Fattahpour Dave Chan
author_facet	Morteza Roostaei Alireza Nouri Vahidoddin Fattahpour Dave Chan
author_sort	Morteza Roostaei
title	Evaluation of numerical schemes for capturing shock waves in modeling proppant transport in fractures
title_short	Evaluation of numerical schemes for capturing shock waves in modeling proppant transport in fractures
title_full	Evaluation of numerical schemes for capturing shock waves in modeling proppant transport in fractures
title_fullStr	Evaluation of numerical schemes for capturing shock waves in modeling proppant transport in fractures
title_full_unstemmed	Evaluation of numerical schemes for capturing shock waves in modeling proppant transport in fractures
title_sort	evaluation of numerical schemes for capturing shock waves in modeling proppant transport in fractures
publisher	KeAi Communications Co., Ltd.
publishDate	2017
url	https://doaj.org/article/4f4500e1d49f4a01a152ed4247092445
work_keys_str_mv	AT mortezaroostaei evaluationofnumericalschemesforcapturingshockwavesinmodelingproppanttransportinfractures AT alirezanouri evaluationofnumericalschemesforcapturingshockwavesinmodelingproppanttransportinfractures AT vahidoddinfattahpour evaluationofnumericalschemesforcapturingshockwavesinmodelingproppanttransportinfractures AT davechan evaluationofnumericalschemesforcapturingshockwavesinmodelingproppanttransportinfractures
_version_	1718400050129797120

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

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